Answer:
(a) The standard error of the mean in this experiment is $0.052.
(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.
(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.
(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample mean is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=40\\\mu=\$3.82\\\sigma=\$0.33[/tex]
As n = 40 > 30, the distribution of sample mean is [tex]\bar X\sim N(3.82,\ 0.052^{2})[/tex].
(a)
The standard error is the standard deviation of the sampling distribution of sample mean.
Compute the standard deviation of the sampling distribution of sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052[/tex]
Thus, the standard error of the mean in this experiment is $0.052.
(b)
Compute the probability that the sample mean is between $3.78 and $3.86 as follows:
[tex]P(3.78<\bar X<3.86)=P(\frac{3.78-3.82}{0.052}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.86-3.82}{0.052})[/tex]
[tex]=P(-0.77<Z<0.77)\\=0.77935-0.22065\\=0.5587[/tex]
Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.
(c)
If the difference between the sample mean and the population mean is less than $0.01 then:
[tex]\bar X-\mu_{\bar x}<0.01\\\\\bar X-3.82<0.01\\\\\bar X<\$3.83[/tex]
Compute the value of [tex]P(\bar X<3.83)[/tex] as follows:
[tex]P(\bar X<3.83)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.83-3.82}{0.052})[/tex]
[tex]=P(Z<0.19)\\=0.57535\\\approx 0.5754[/tex]
Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.
(d)
Compute the probability that the sample mean is greater than $3.92 as follows:
[tex]P(\bar X>3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{3.92-3.82}{0.052})[/tex]
[tex]=P(Z<1.92)\\=0.97257\\\approx 0.9726[/tex]
Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.
The standard error is 0.0522. The probability of the sample mean lying in a certain range and the difference from the population mean being less than a certain value can be determined using Z-scores and a Z-table. The likelihood of the sample mean being more than a certain value can also be determined in the same way.
Explanation:An economist is using the average price of a gallon of milk to measure inflation. The average price ($3.82) and the population standard deviation ($0.33) is known. Here are answers to your questions:
a. Standard Error of the mean: The Standard error (SE) is calculated by dividing the standard deviation by the square root of the sample size. So SE = Standard Deviation / √n = 0.33 / √40 = 0.0522 per gallon.
b. Probability of the sample mean between $3.78 and $3.86: This is a Z-score question. Z = (X- µ)/SE. So, first find the Z-scores for $3.78 and $3.86, and then find the probability corresponding to these Z-scores from the Z-table. This probability is the chance that the sample mean is between $3.78 and $3.86.
c. Probability of the difference: Similarly, find the Z-score for the difference of $0.01 and look up the probability in the Z-table. This gives the likelihood of the sample mean being less than $0.01 away from the population mean.
d. Likelihood the sample mean is greater than $3.92: Use the same method to work out the Z-score for $3.92. The Z-table gives you the probability of the sample mean being less than $3.92, so subtract that from 1 to get the probability of it being more than $3.92.
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A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 21. Which of the following is a correct interpretation of the interval 10.6 < μ < 29.1? Check all that are correct.
A. With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
B. With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
C. The mean width of all widgets is between 10.6 and 29.1, 95% of the time.
D. We know this is true because the mean of our sample is between 10.6 and 29.1.
E. There is a 95% chance that the mean of the population is between 10.6 and 29.1.
F. There is a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean. A 95% confidence interval does not mean 95% probability. It is used to express how confident we are that the true population parameter lies within the confidence interval.
With a lower limit of 10.6 and an upper limit of 29.1, and confidence interval of 95%, the correct option is
With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
Final answer:
The 95% confidence interval represents the range within which the true mean of all widgets is likely to fall, not the individual sample mean.
Explanation:
A 95% confidence interval for widget width of 10.6 < μ < 29.1 means:
With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
There is not a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.
Therefore, the correct interpretations are A and F.
During a recent election, a clerk was responsible for the placement of candidates names on election ballots for a particular voting precinct. Party A candidates were selected for the first position in 30 of 40 ballots. Because the clerk was supposed to use a method of random selection, Party B claimed that instead of using randomness, the clerk used a method favoring Party A. Use a 0.05 significance level to test the claim that the method favored Party A. [Note: Favored means a proportion greater than 50%.]
Answer:
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
z = 3.16
P value = P(Z>3.16) = 0.0008
Decision: we reject the null hypothesis and accept the alternative hypothesis. That is, the clerk used a method favoring Party A.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n = 40 represent the number of samples taken
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 40
po = Null hypothesized value = 0.50
p^ = Observed proportion = 30/40 = 0.75
Substituting the values we have
z = (0.75-0.50)/√(0.50(1-0.50)/40)
z = 3.16227766
z = 3.16
To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.
P value = P(Z>3.16) = 0.0008
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.
The Normal model N(65, 2.5) describes the distribution of heights of college women (inches). Which of the following questions asks for a probability and which asks for a measurement (and is thus an inverse Normal question)? a. nbsp What is the probability that a random college woman has a height of 68 inches or more? b. nbsp To be in the Tall Club, a woman must have a height such that only 2% of women are taller. What is this height?
Answer:
a) 11.51% probability that a random college woman has a height of 68 inches or more
b) This height is 70.135 inches.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
The normal distribution has two parameters, which are the mean and the standard deviation.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 65, \sigma = 2.5[/tex]
a. What is the probability that a random college woman has a height of 68 inches or more?
This is 1 subtracted by the pvalue of Z when X = 68. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68 - 65}{2.5}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
1 - 0.8849 = 0.1151
11.51% probability that a random college woman has a height of 68 inches or more
b. To be in the Tall Club, a woman must have a height such that only 2% of women are taller. What is this height?
This weight is the 100-2 = 98th percentile, which is the value of X when Z has a pvalue of 0.98. So X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 65}{2.5}[/tex]
[tex]X - 65 = 2.054*2.5[/tex]
[tex]X = 70.135[/tex]
This height is 70.135 inches.
Find the value of X to the nearest tenth.
Choices are: 3, 6, 9, 12
Answer:
Here, we have BC // ST, by applying Thales theorem:
UB/US = UC/UT
=>UB = UC x US/UT =6 x 12/(6 + 18) = 3
=> x = US - UB = 12 - 3 = 9
=> Option C is correct.
Hope this helps!
:)
The City of Decatur finds that salaries for residents working in the technology sector follow an approximately normal distribution with a mean of $42,800 and a standard deviation of $8,365.
To the nearest hundredth, what Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000?
Answer:
- 1. 15
Step-by-step explanation:
Z score is used in statistic to calculate deviation of an observed value from mean value of sample of observation.
Mathematically it is given by
[tex]z = observed \ value - mean\ value/ standard\ deviation[/tex]
using the above formula and substituting the value of of
mean = $42,800
standard deviation = $8,365
observed value =$30,000
Z = (8,365 - 42,800) / $30,000
= - 34,435/ 30,000 = - 1. 14783
= - 1. 15 ( to the nearest hundredth)
- 1. 15 Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000
The 99.7% confidence interval for the mean length of frog jumps is (12.64 cm, 14.44 cm). Which of the following statements is a correct interpretation of 99.7% confidence? 99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm. There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm. There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm. If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
Answer:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
Step-by-step explanation:
For this case we need to remember that the confidence interval for the true mean is given by this formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
And for this case the 99.7 % confidence interval for the true mean is (12.64cm , 14.44cm) we analyze one by one the possible options in order to select one:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
False always the confidence interval contain the mean since is the middle value.
Final answer:
The correct interpretation of a 99.7% confidence interval for mean length of frog jumps is that if we repeat the sampling many times, 99.7% of the constructed confidence intervals would contain the true population mean. This emphasizes the methodology's reliability over repeated sampling rather than assuring specifics of individual outcomes.
Explanation:
The correct interpretation of a 99.7% confidence interval, like the one provided for the mean length of frog jumps (12.64 cm, 14.44 cm), is that if we were to repeat this sampling process many times, 99.7% of the confidence intervals we construct would contain the true population mean. The other statements provided misinterpret the concept of confidence intervals by implying a probability about individual measurements or the certainty of the mean falling within a specific interval, which is not accurate.
Confidence intervals are about the process of estimation rather than specifics about single outcomes. They provide a range in which we are certain to a specified level (in this case, 99.7%) that the true population mean lies, assuming the sampling and calculations are correct. The correct interpretation underscores the reliability of the methodology over repeated sampling rather than guaranteeing specifics of individual outcomes or the exact location of the population mean.
Six pyramids are shown inside of a cube. The height of the cube is h units.
Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid?
The height of each pyramid is One-halfh units.
The height of each pyramid is One-thirdh units.
The height of each pyramid is One-sixthh units.
The height of each pyramid is h units.
Answer:
its the 1st answer on edg
Step-by-step explanation:
I just took it
The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables
The volume of the cube = h unit * h unit * h unit = h³ unit³
Volume of each pyramid = (1/6) * h³ = (1/3) * base² * height
(1/6) * h³ = (1/3) * base² * height
(1/3) * h² * (1/2)h = (1/3) * base² * height
The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube.
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SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below. 380 520 480 510 560 630 670 490 500 550 400 350 440 490 620 660 700 730 740 560 Test if the standard deviation of the reading and writing section SAT score of the students in this school is higher than 100. What is the value of the test statistic (round off to the nearest integer)
Answer:
The value of test statistics is 25.
Step-by-step explanation:
We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;
380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560
Let [tex]\sigma[/tex] = population standard of the reading and writing section SAT score of the students in this school
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \leq[/tex] 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}
The test statistics that would be used here is One-sample Chi-square test statistics;
T.S. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2} __n_-_1[/tex]
where, [tex]s^{2}[/tex] = sample variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 13135.8
n = sample of 11th-grade students = 20
So, the test statistics = [tex]\frac{(20-1)\times 13135.8^{2} }{100^{2} }[/tex]
= 24.96 ≈ 25
Hence, the value of test statistics is 25.
On a coordinate plane, a graph has number of hours on the x-axis and number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
The graph represents the number of haircuts, y, a hair stylist can give over time, x. Use the graph to find the constant of proportionality and write an equation.
The constant of proportionality is .
The equation that represents the number of haircuts the stylist can give in an hour is .
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
On a coordinate plane, a graph has a number of hours on the x-axis and a number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
We know that the equation of the line passing through the two-point is given as
[tex]\rm (y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Then we have
[tex]\rm y-1 = \dfrac{2-1}{4-2} \times (x-2)\\\\y = \dfrac{1}{2}\ x - 1+1 \\\\y = \dfrac{1}{2}\ x[/tex]
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
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Answer:
first one is 1/2 second one is y = 1/2 x
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It is said that happy and healthy workers are efficient and productive. A company that manufactures exercising machines wanted to know the percentage of large companies that provide on-site health club facilities. A sample of 240 such companies showed that 96 of them provide such facilities. Construct a 97% confidence interval for the percentage of all such companies that provide such facilities on-site. What is the margin of error for this estimate
Answer:
The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
The absolute value of the subtraction of one of the bounds by the estimate [tex]\pi[/tex]
For this problem, we have that:
[tex]n = 240, \pi = \frac{96}{240} = 0.4[/tex]
97% confidence level
So [tex]\alpha = 0.03[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.03}{2} = 0.985[/tex], so [tex]Z = 2.17[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.3314[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.4686[/tex]
0.4686 - 0.4 = 0.0686
The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.
Final answer:
To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, the proportion p is calculated from the sample data and then substituted into the formula. The margin of error is also calculated using the formula.
Explanation:
To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, we can use the formula:
CI = p ± z*(√(p(1-p)/n))
Where:
p is the proportion of companies in the sample that provide on-site health club facilitiesz is the z-value corresponding to the desired confidence level (in this case, 97%)n is the sample sizeFirst, we calculate the proportion p = 96/240 = 0.4
Next, we find the z-value using a standard normal distribution table. For a 97% confidence level, the z-value is approximately 1.88
Finally, substituting the values into the formula:
CI = 0.4 ± 1.88*(√((0.4*(1-0.4))/240))
Calculating the margin of error:
ME = z*(√(p(1-p)/n))
ME = 1.88*(√((0.4*(1-0.4))/240))
ME ≈ 0.036
Therefore, the 97% confidence interval for the percentage of all such companies that provide on-site health club facilities is approximately 0.364 to 0.436. The margin of error for this estimate is approximately ±0.036.
is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is direct or inverse write a function to model it.
x 2 5 20 40
y 40 20 5 2
Answer:
Neither
Step-by-step explanation:
In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.
For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.
x 2 5 20 40
y 40 20 5 2
Here,
[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]
So, this is neither a direct variation nor an indirect variation.
Question 4
State the value of the discriminant of 3x2 + 8x = 2.
a) 100
b) 40
c) 88
d) 3
Answer:
40
Step-by-step explanation:
3x^2 + 8x = 2
3x^2 + 8x - 2 = 0
D = b^2+4ac
D = 8^2+4(3)(-2)
D = 64+(-24)
D = 64-24
D = 40
Terry ran 1/10 of the distance from school to home. He walked 3/10 more of the distance and then skipped 2/10 more the distance. What fraction of the distance
home does Terry still have to go?
Answer: 4/10, simplified to 2/5
Step-by-step explanation:
1/10 plus 3/10 plus 2/10 is 6/10
10/10 minus 6/10 is 4/10
4/10 simplified (divide the numerator and the denominator by 2) is 2/5
Final answer:
Terry has covered 3/5 of the distance to home by running, walking, and skipping. Therefore, he still has 2/5 of the distance left to cover.
Explanation:
The question asks how much distance Terry still has to cover to reach home, given the fractions of the journey he has completed by running, walking, and skipping.
Terry ran 1/10 of the distance, walked 3/10 more, and skipped 2/10 more of the distance. To find the total distance covered, we add these fractions together:
1/10 (running) + 3/10 (walking) + 2/10 (skipping) = 6/10 or 3/5 of the distance.To find the distance Terry still has to go, we subtract the fraction of the distance he has covered from the whole distance (1 or 5/5):
5/5 - 3/5 = 2/5Therefore, Terry still has to cover 2/5 of the distance to reach home.
La diagonal de un marco de fotos rectangular mide 2 cm más que el lado mayor. Si el perímetro mide 46 cm, ¿cuánto miden los lados del marco?
Answer:
The length of rectangular photo frame is 15 cm and the breadth is 8 cm.
Step-by-step explanation:
The question is:
The diagonal of a rectangular photo frame is 2 cm more than the longest side. If the perimeter is 46 cm, how long are the sides of the frame?
Solution:
Let the length of the rectangular photo frame be denoted by x and breadth by y.
It is provided that the diagonal is 2 cm more than the length.
That is:
d = x + 2
The perimeter is 46 cm.
That is:
46 = 2 (x + y)
⇒ x + y = 23
⇒ x = 23 - y
The triangle form by the length, breadth and the diagonal of the rectangle is a right angled triangle, with the diagonal as the hypotenuse, length as perpendicular and breadth as the base.
So, according to the Pythagoras theorem,
d² = x² + y²
(x + 2)² = x² + y²
x² + 4x + 4 = y²
4x + 4 = y²
4 (23 - y) + 4 = y²
92 - 4y + 4 = y²
y² + 4y - 96= 0
Factorize the expression by splitting the middle term as follows:
y² + 4y - 96= 0
y² + 12y - 8y - 96= 0
y (y + 12) - 8 (y + 12) = 0
(y + 12)(y - 8) = 0
Either y = -12 or y = 8.
Since y represents the breadth of a rectangle, it cannot be negative.
Thus, the breadth of rectangular photo frame is 8 cm.
Compute the length as follows:
x = 23 - y
= 23 - 8
= 15
Thus, the length of rectangular photo frame is 15 cm.
what’s the answer this question?
Answer:
(x-1)(x-42) or (x-1) x (x-42) <-----(they're basically the same thing)
Step-by-step explanation:
1. x^2-43x+42 2. x^2-x-42x+42 3. x(x-1)-42x+42 4. x(x-1)-42(x-1) 5. (x-1)(x-42)
6. answer is (x-1)(x-42)
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Graph the line your equations using the slope of the line and y-intercept taken from the slope intercept form of the equation. Find the intersection of the two graphs. Check that your solution is correct. Watch your place and minus slopes! In y=mx+b, m Is the slope of the line and b is the y-intercept.
Answer: (-2,3)
Step-by-step explanation:
What is the difference between the circumference and area of a circle?
Answer
The circumference of a circle is the length of its side, the area is the amount of space within it.
Step-by-step explanation:
The circumference of a circle represents the distance around the circle's boundary, while the area represents the surface area enclosed by the circle.
The difference between the circumference and area of a circle lies in their respective measurements and what they represent.
Circumference: The circumference of a circle is the measurement of the distance around the outer boundary of the circle. It is essentially the perimeter of the circle. The circumference is calculated using the formula:
Circumference = 2πr or πd
Where r represents the radius of the circle and d represents the diameter. It is a linear measurement and is typically expressed in units such as centimeters, inches, or meters.
Area: The area of a circle is the measurement of the region enclosed by the circle's boundary. It represents the total surface area within the circle. The area of a circle is calculated using the formula:
Area = πr²
Where r represents the radius of the circle. The area is a two-dimensional measurement and is typically expressed in square units such as square centimeters, square inches, or square meters.
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A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 95% confidence interval with an error of no more than 0.06. A consultant has informed them that a previous study found the mean to be 7.3 energy drinks per week and found the standard deviation to be 1.3. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answer:
The minimum sample size required to create the specified confidence interval is 1804.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Minimum sample size for a margin of error of 0.06:
This sample size is n.
n is found when [tex]M = 0.06, \sigma = 1.3[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.06 = 1.96*\frac{1.3}{\sqrt{n}}[/tex]
[tex]0.06\sqrt{n} = 1.96*1.3[/tex]
[tex]\sqrt{n} = \frac{1.96*1.3}{0.06}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*1.3}{0.06})^{2}[/tex]
[tex]n = 1803.41[/tex]
Rounding up to the next integer
The minimum sample size required to create the specified confidence interval is 1804.
Suppose you roll a standard number cube and spin a spinner with four equal-sized sections labeled 1, 2, 3, 4. What is the probability you will roll a prime number and spin a prime number
Answer:
25% probability you will roll a prime number and spin a prime number
Step-by-step explanation:
If we have two events, A and B, and they are independent, we have that:
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
In this question:
Event A: Rolling a prime number.
Event B: Spinning a prime number.
Both the cube and the spinner have four values, ranging from one to four.
2 and 3 are prime values, that is, 2 of those values. Then
[tex]P(A) = P(B) = \frac{2}{4} = \frac{1}{2}[/tex]
What is the probability you will roll a prime number and spin a prime number
The cube and the spinner are independent of each other. So
[tex]P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25[/tex]
25% probability you will roll a prime number and spin a prime number
Answer:
= 1/4
Step-by-step explanation:
In a cube , we have numbers labeled 1 - 6
the prime numbers we have is 2 , 3 and 5
The probability of selecting a prime number is
[tex]=\frac{3}{6} \\\\=\frac{1}{2}[/tex]
Now this means the probability of rolling a prime number here is 1/2
Now we calculate the probability of spinning a prime number
Prime numbers here are just 2 and 3
The probability of spinning a prime number is thus 2/4 = 1/2
Thus, the probability of rolling a prime number and spinning a prime number also becomes; 1/2 * 1/2
= 1/4
Manuel painted 0.75 of a rectangular banner green. After the paint dried, he painted 0.6 of the green area orange. What part of the banner is painted orange?
Answer:
0.45 part of the banner is painted orange.
Step-by-step explanation:
Given that the area for green = 0.75
The area of orange on green is = 0.6
So the area of orange is = 0.75*0.6 = 0.45
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To find the part of the banner that is painted orange, we multiply the green area by 0.6 and divide by the total area of the banner.
Explanation:To find the part of the banner that is painted orange, we need to calculate the orange area compared to the total area of the banner.
First, we calculate the green area by multiplying the total area of the banner by 0.75.Then, we find the orange area by multiplying the green area by 0.6.Finally, we divide the orange area by the total area of the banner to get the part that is painted orange.Let's say the total area of the banner is 100 square units. Using the steps above:
The green area is 100 * 0.75 = 75 square units.The orange area is 75 * 0.6 = 45 square units.The part of the banner that is painted orange is 45 / 100 = 0.45, which is 45%.Learn more about Calculating the part of a rectangular area that is painted orange here:https://brainly.com/question/30659007
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The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.
Step 2 of 2 : Suppose a sample of 1390 suspected criminals is drawn. Of these people, 514 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 1390
x = 514
p = 514/1390 = 0.37
q = 1 - 0.37 = 0.63
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.01 = 0.99
The z score corresponding to the area on the z table is 2.33. Thus, confidence level of 98% is 2.33
Therefore, the 98% confidence interval is
0.37 ± 2.33√(0.37)(0.63)/1390
Confidence interval = 0.37 ± 0.0302
Find the coordinates for the vertex of the graph of the function y = 2x' + 2x - 4.
Answer:
(-1/2,-9/2)
Step-by-step explanation:
that is the coordinates for the vertex of the function y=2xsqaured+2x-4
what is (2x - 4) - (6x + 6)
Answer:
Step-by-step explanation: (2x-4)-(6x+6)
= 2x -4 - 6x - 6 [ opening brackets]
= 2x-6x -4-6 [ bringing the same variables and numbers together]
= -4x-10
=2(2x-5)
Answer:
-4x-10
The 6x + 6 becomes negative due to the negative sign before the parenthesis. You then subtract 6x and 6 from 2x and -4 to get -4x-10
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
Answer:
- The number of t-shirts he needs to print to obtain maximum profit = 2.79 (in thousand), that is, 2790 t-shirts.
- The maximum profit for this number of shirts is then = 12.208761 (in thousand dollars) = $12209
Step-by-step explanation:
Complete Question
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
The profit function is given as
p(x) = -x³ + 4x² + x
The maximum profit will be obtained by investigating the maximum value of the profit function
At the maximum value of the function,
(dp/dx) = 0 and (d²p/dx²) < 0
p(x) = -x³ + 4x² + x
(dp/dx) = -3x² + 8x + 1
at maximum point
(dp/dx) = -3x² + 8x + 1 = 0
Solving the quadratic equation
x = -0.12 or 2.79
(d²p/dx²) = -6x + 8
at x = -0.12
(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0 (not a maximum point)
At x = 2.79
(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0 (this corresponds to a maximum point!)
So, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousand).
So, the maximum profits that corresponds to this number of t-shirts is obtained from the profit function.
p(x) = -x³ + 4x² + x
p(x) = -(2.79)³ + 4(2.79²) + 2.79
p(x) = -21.717639 + 31.1364 + 2.79
p(x) = 12.208761 (in thousand dollars) = $12209 to the mearest whole number.
Hope this Helps!!!
Keegan should print around 2,000 shirts to maximize his profits, resulting in approximately $12,000 in earnings
To find the number of t-shirts Keegan should print to maximize his profits, we need to find the critical points of the profit function p(x) = -x^3 + 4x^2 + x.
Taking the derivative, we get p'(x) = -3x^2 + 8x + 1. Setting this equal to zero and solving for x gives:
0 = -3x^2 + 8x + 1
Using the quadratic formula, we find two potential values for x: x ≈ 2.37 and x ≈ -0.12. Since x must be a positive value representing the number of shirts, we discard the negative root.
Next, we need to determine whether this value of x corresponds to a maximum or minimum. We can do this by examining the second derivative, p''(x) = -6x + 8. Since p''(2.37) > 0, we conclude that x ≈ 2.37 corresponds to a local minimum.
However, since we're dealing with a cubic function, we need to consider behavior as x approaches infinity. As x gets very large, the -x^3 term dominates, making the function tend toward negative infinity. This means there is no global maximum, but rather a local maximum.
To find the approximate number of shirts Keegan should print, we take the nearest whole number, which is 2. The maximum profit can be found by plugging this value back into the profit function:
p(2) ≈ -2^3 + 4(2)^2 + 2 ≈ 12 (in thousands).
So, Keegan should print around 2,000 shirts to maximize his profits, which will be approximately $12,000 (rounded to the nearest whole dollar).
Complete question:
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
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I’m on a roll ᕕ( ᐛ )ᕗ
Answer:
Yessirrr you are!!!
Step-by-step explanation:
please help with this one
Answer:
2
Step-by-step explanation:
y-intercept is where x = 0, and that point is (0,2), so it's 2
What is the sum of the
measures of the exterior
angles on a polygon with
20 sides?
Answer:
360 degree
Step-by-step explanation:
The sum of all the exterior angles is 360 for any polygon.
This can be proved for polygon with 20 sides also.
We know that sum of all the angles of polygon is given by formula = (2*n -4) *90
where n is the no. of sides of polygon
for 20 sides polygon sum of sum of all the angles = (2*20 -4) * 90
= (40-4)*90 = 36*90 = 3240 degree
measure of each angle of polygon = sum of total angles of polygon/ no of sides of polygon = 3240/20 = 162
We also know that sum of interior and exterior angle of triangle is 180 degree, as interior and exterior angle lies on straight line and they are supplementary
so
162 + value of exterior angle = 180
=> value of exterior angle = 180 - 162 = 18
Value of one exterior angle is 18 degree
in 20 sided polygon there are 20 exterior angle
therefore, value of 20 exterior angle is 18*20 degree which is 360 degree.
__________________________________________________________
As a general point one can memorize than sum of all the exterior angle for a polygon with any number of side is 360.
A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 female students and measure their heights. The mean of the sample is 65.3 inches. The standard deviation is 5.2 inches. Use the T-distribution Inverse Calculator applet to answer the following question. What is the 90% confidence interval for the mean height of all female students in their school? Group of answer choices (56.5, 74.1) (63.6, 67.0) (63.8, 66.8) (63.9, 66.7)
Answer: = ( 63.9, 66.7)
Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 65.3
Standard deviation r = 5.2
Number of samples n = 36
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
65.3 +/-1.645(5.2/√36)
65.3 +/-1.645(0.86667)
65.3+/- 1.4257
65.3+/- 1.4
= ( 63.9, 66.7)
Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)
Assume that when adults with smartphones are randomly selected, 42% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 24 of them use their smartphones in meetings or classes.
Answer:
0.00205%
Step-by-step explanation:
Use binomial probability:
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
n = 30, r = 24, p = 0.42, and q = 0.58.
P = ₃₀C₂₄ (0.42)²⁴ (0.58)³⁰⁻²⁴
P ≈ 0.00205%
the price increase of a set of golf clubs is from $250 to $750. What is the percent increase?
Answer:
Positive increase of 200%
Step-by-step explanation:
Answer:
Step-by-step explanation:
percentage increase =increase /original *100
=750-250/250×100
=500/250×100
=200%
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