Answer:
[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]
[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]
And the best option would be:
c. 1450 +/- 12
Step-by-step explanation:
Information provided
[tex]\bar X=1450[/tex] represent the sample mean for the SAT scores
[tex]\mu[/tex] population mean (variable of interest)
[tex]s^2 = 900[/tex] represent the sample variance given
n=25 represent the sample size
Solution
The confidence interval for the true mean is given by :
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The sample deviation would be [tex]s=\sqrt{900}= 30[/tex]
The degrees of freedom are given by:
[tex]df=n-1=2-25=24[/tex]
The Confidence is 0.954 or 95.4%, the value of [tex]\alpha=0.046[/tex] and [tex]\alpha/2 =0.023[/tex], assuming that we can use the normal distribution in order to find the quantile the critical value would be [tex]z_{\alpha/2} \approx 2.0[/tex]
The confidence interval would be
[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]
[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]
And the best option would be:
c. 1450 +/- 12
Write a verbal expression for 3m-8n/13
Step-by-step explanation:
Three m minus eight n divided by thirteen
Which best describes the numbers satisfying the inequality x <7?
all numbers greater than 7
all numbers less than 7
all numbers greater than and including 7
all numbers less than and including
FU
O
RRET
Sa
Answer:
(B) all numbers less than 7
Step-by-step explanation:
Given the inequality:
x<7
It means that:
x cannot be equal to 7x cannot be greater than 7Therefore, x<7 consists of all numbers less than 7.
Answer:
B
Step-by-step explanation:
A schools enrollment in 2012 was 1234 now it is 1456 what does the expression look like that would help me find the percent change
Answer:
.18 % increase
Step-by-step explanation:
First you would find what the difference is between the school enrollment
you would do 1456 - 1234 = 222
Then you would divide 1234/1456 = 84.75% to see the total percentage
The increase however has a percentage of .18%
To check your work you would do .18 x 1234 = 222.12 ( round to the nearest whole number so it would just be 222) then add 1234+ 222 = 1456!
Answer:
A) (1,456-1,234) ÷ 1,456
What is the area of a regular pentagon with an apothem of 8 centimeters
Answer:
The of the pentagon is A=232.48cm²
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes, a pentagon
Now given the apothem the area can be expressed as
A=a²n tan (180/n)
where
a = the length of the apothem (in radius)
n = the number of sides= 5 for pentagon
tan is the tangent function calculated in degrees
Substituting our given data we can solve for the area A
A= 8²*5 tan (180/5)
A= 64*5 tan 36
A= 320tan 36
A= 320*0.7265
A=232.48cm²
A small tie shop finds that at a sales level of x ties per day its marginal profit is MP (x )dollars per tie, where MP (x )equals 1.85 plus 0.12 x minus 0.0024 x squared. Also, the shop will lose $65 per day at a sales level of x equals 0. Find the profit from operating the shop at a sales level of x ties per day.
Question:
A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per tie, where
MP(x) =1.85 + 0.12x - 0.0024x². Also, the shop will lose $65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.
Answer:
P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65
Step-by-step explanation:
MP(x) = 1.85 + 0.12(x) - 0.0024(x^2)
At sales level, x=0, loss = $65
P(0) = - $65
Integrating MP(x) with respect to x
P(x) = ∫MP(x) dx = ∫ 1.85 + 0.12(x) - 0.0024(x^2)
P(x) = 1.85x + 0.06x^2 - 0.0008x^3 + C
Therefore :
P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65
Correct question:
A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per tie, where
MP(x) =1.85 + 0.12x - 0.0024x². Also, the shop will lose $65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.
Answer:
P(x) =1.85x +0.06x² - 0.0008x³ - 65
Step-by-step explanation:
Given the marginal profit function:
MP(x) =1.85 +0.12x - 0.0024x², P(0)= -65
We are to find P(x).
P(x) = ∫MP(x) dx
P(x) = ∫(1.85 + 0.12x - 0.0024x²) dx
= ∫1.85 dx+∫0.12x dx+∫(-0.0024x²)dx + C
= 1.85x + 0.06x² - 0.0008x³ + C
Initial condition at P(0) = - 65
where x(0), P(x) = -65
we have:
-65 = 1.85(0)+0.06(0)² - 0.0008x(0)³ + C
-65 = 0 + 0 - 0 + C
-65 = C
C = -65
P(x) =1.85x + 0.06x² - 0.0008x³ - 65
Find the 12th term of the geometric sequence 1,−2,4
Answer:-2048
Step-by-step explanation:
First term(a)=1
Common ratio(r)=-2/1 or 4/-2
Common ratio(r)=-2
nth term=a x r^(n-1)
12th term=1 x (-2)^(12-1)
12th term=1 x (-2)^11
12th term=(-2)^11
12th term=-2048
The 12th term of the geometric sequence 1, −2, 4, .... is equal to -2048.
How to calculate the nth term of a geometric sequence?In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where:
[tex]a_n[/tex] is the nth term of any geometric sequence.r represents the common ratio.[tex]a_1[/tex] represents the first term of any geometric sequence.In this context, the common ratio would be determined as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -2/1
Common ratio, r = -2
Now, we can determine the 12th term in the sequence defined by this explicit rule;
[tex]a_n=a_1(r)^{n-1}\\\\a_{12}=1(-2)^{12-1}\\\\a_{12}=(-2)^{-11}\\\\a_{12}=-2048[/tex]
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Which measure of central tendency is MOST EASILY affected by outliers? A) mean Eliminate B) median C) mode D) IQR
Answer: A. Mean.
Explanation:
Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average is the most popular measure of central tendency.
The mean is strongly influenced by outliers because it is the average of the scores and it is not resistant.
Answer:
A) mean
Step-by-step explanation:
Mean is a measure of central tendency, it is the sum of all data divided by the number of data. Because the mean take into consideration each of the data in its calculations, it is generally affected by outliers (extremely high or low values)
Please help! ASAP :)
Answer:
3.14 miles but that doesn't sound right
Step-by-step explanation:
Assuming you have to find area of the circle its
A = πr² Radius is half of diameter so half of 2 = 1
A = 3.14 x 1²
A = 3.14 x 1
A = 3.14
If you have to find area than its 3.14 it just sounds odd
Sorry if its wrong
Prove that if A2 = O, then 0 is the only eigenvalue of A. STEP 1: We need to show that if there exists a nonzero vector x and a real number λ such that Ax = λx, then if A2 = O, λ must be . STEP 2: Because A2 = A · A, we can write A2x as A(Ax). STEP 3: Use the fact that Ax = λx and the properties of matrix multiplication to rewrite A2x in terms of λ and x. A2x = x STEP 4: Because A2 is a zero matrix, we can conclude that λ must be .
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Solve the system of equations:
y=2x-3
y=x2-3
Answer: x = 0 or x = 2
Step-by-step explanation:
To solve this, we must note that the two equations speaks of a single function of y. So
y = 2x - 3 = x² - 3
So from.here we can equate the two together and solve for x.
x² - 3 = 2x - 3, biw convert to a quadratic expression
x² - 2x - 3 + 3 = 0
x² - 2x = 0
Now factorize
x( x - 2 ) = 0, so solving for x
x = 0 or x = 2. .I believed getting the 2 won't be a problem
When x - 2 = 0
Then x = 2.
Consider two populations for which μ1 = 35, σ1 = 3, μ2 = 20, and σ2 = 4. Suppose that two independent random samples of sizes n1 = 47 and n2 = 54 are selected. Describe the approximate sampling distribution of x1 − x2 (center, spread, and shape). What is the shape of the distribution? The distribution would be non-normal. The distribution is approximately normal. The shape cannot be determined. What is the mean of the distribution? What is the standard deviation of the distribution?
Answer:
The distribution is approximately normal.
The mean and standard deviation are 15 and 0.98 respectively.
Step-by-step explanation:
The population of the random variables X₁ and X₂ are distributed as follows:
[tex]X_{1}\sim (\mu_{1}=35, \sigma_{1}^{2}=3^{2})\\\\X_{2}\sim (\mu_{2}=20, \sigma_{2}^{2}=4^{2})[/tex]
Two independent random samples of sizes,
[tex]n_{1}=47\\\\n_{2}=54[/tex]
are selected form the two populations.
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 mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Both the sample selected from the two populations are quite large, i.e. [tex]n_{1}=47>30\\\\n_{2}=54>30[/tex]
So, according to the central limit theorem the sampling distribution of sample means [tex]\bar X_{1}\ \text{and}\ \bar X_{2}[/tex] can be approximated by the Normal distribution.
Then, the distribution of [tex]\bar X_{1}[/tex] is:
[tex]\bar X_{1}\sim N(35,\ 0.44)[/tex]
And the distribution of [tex]\bar X_{2}[/tex] is:
[tex]\bar X_{2}\sim N(20,\ 0.54)[/tex]
If two random variables are normally distributed then their linear function is also normally distributed.
So, the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is Normal and the shape of the distribution is bell-shaped.
The mean of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:
[tex]E(\bar X_{1}\ -\ \bar X_{2})=E(\bar X_{1})-E(\bar X_{2})\\=35-20\\=15[/tex]
The standard deviation of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:
[tex]SD(\bar X_{1}-\bar X_{2})=SD(\bar X_{1})+SD(\bar X_{2})\\=0.44+0.54\\=0.98[/tex]
*X₁ and X₂ are independent.
Thus, the mean and standard deviation are 15 and 0.98 respectively.
A store stocked 150 bundles of Charmin Extra Soft and Fluffy toilet tissue for a weekend sale. Last weekend, 72 bundles of the Charmin Extra Soft and Fluffy toilet tissue were sold. What percent of the
bundles of stocked Charmin Extra Soft and Fluffy toilet paper were sold that weekend?
Answer:
48% was sold
Step-by-step explanation:
Let the percent sold be x
x/100 * 150 = 72
(This equation basically means...what percentage of 150 bundles will give us 72 bundles remaining? and that's the answer we need)
Simplifying...
150x/100 = 72
3x/2 = 72
3x = 144
x = 48%
A substance abuse researcher wants to know whether reaction time is decreased by frequent alcohol use. He randomly selects 164 alcoholics and finds that their mean reaction time (in ms) to a stimulus equals 283. Reaction times to the stimulus in the general population are distributed normally with a mean equal to 281 and a standard deviation equal to 28. Is there sufficient evidence at the 0.01 significance level to conclude that reaction time is decreased by frequent alcohol use
Answer:
We conclude that the reaction time is increased or remains same by frequent alcohol use.
Step-by-step explanation:
We are given that a substance abuse researcher wants to know whether reaction time is decreased by frequent alcohol use. He randomly selects 164 alcoholics and finds that their mean reaction time (in ms) to a stimulus equals 283.
Reaction times to the stimulus in the general population are distributed normally with a mean equal to 281 and a standard deviation equal to 28.
Let [tex]\mu[/tex] = mean reaction time after alcohol use.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 281 {means that the reaction time is increased or remains same by frequent alcohol use}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 281 {means that the reaction time is decreased by frequent alcohol use}
The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean reaction time (in ms) = 283
[tex]\sigma[/tex] = population standard deviation = 28
n = sample of alcoholics = 164
So, test statistics = [tex]\frac{283-281}{\frac{28}{\sqrt{164}}}[/tex]
= 0.915
The value of z test statistics is 0.915.
Now, at 0.01 significance level the z table gives critical value of -2.3263 for left-tailed test. Since our test statistics is more than the critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the reaction time is increased or remains same by frequent alcohol use.
The customers at a bank complained about long lines and the time they had to spend waiting for service. It is known that the customers at this bank had to wait 7 minutes, on average, before being served. The management made some changes to reduce the waiting time for its customers. A sample of 57 customers taken after these changes were made produced a mean waiting time of 6.5 minutes with a standard deviation of 2.1 minutes. Using this sample mean, the bank manager displayed a huge banner inside the bank mentioning that the mean waiting time for customers has been reduced by new changes. Do you think the bank manager’s claim is justifiable? Use a 10% significance level to answer this question. Use both approaches.
Answer:
[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]
Critical value
The degreed of freedom are given by:
[tex]df=n-1=57-1=56[/tex]
We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:
[tex] t_{\alpha}= -1.297[/tex]
And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes
P value
The p value for this case would be given by:
[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]
Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=6.5[/tex] represent the sample mean for tje waiting times
[tex]s=2.1[/tex] represent the sample standard deviation
[tex]n=57[/tex] sample size
[tex]\mu_o =7[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean for this case is less than 7 minutes, the system of hypothesis for this case sre:
Null hypothesis:[tex]\mu \geq 7[/tex]
Alternative hypothesis:[tex]\mu < 7[/tex]
Since we don;t know the population deviation the statistic for the t test is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
If we replace the info given we got:
[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]
Critical value
The degreed of freedom are given by:
[tex]df=n-1=57-1=56[/tex]
We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:
[tex] t_{\alpha}= -1.297[/tex]
And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes
P value
The p value for this case would be given by:
[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]
Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes
Following are the solution to the given question:
Given:
size [tex](n) = 58[/tex]
mean [tex]\mu = 7.4 \ minutes[/tex]
standard deviation [tex]\sigma = 2.3 \ minutes[/tex]
null and alternative hypotheses:
[tex]H_0 : \mu = 8 \ minutes\\\\H_a : \mu < 8 \ minutes\\\\[/tex]
Calculating the test statistic:
So, the observed value
Calculating the degrees of freedom:
[tex]\to 58 - 1 = 57[/tex]
Calculating the range of p-value:
Therefore the t is the critical value at the significance level that is 0.05 with of freedom is,
Therefore,
[tex]\to test \ statistic = -1.987 < -1.672[/tex] rejecting the null hypothesis.
Therefore, the conclusion of the manager's claim is "True".
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Four pencils are held together with a band.
Each of the pencils diameter 10mm.
Find the length of the band in this position
Give your answer in terms of π.
To find the length of the band holding four pencils together, calculate the circumference of each pencil using the formula C = 2πr, where C is the circumference and r is the radius. Multiply the circumference of each pencil by 4 to find the total length of the band.
Explanation:To find the length of the band holding four pencils together, you need to calculate the circumference of the pencils. The diameter of each pencil is given as 10 mm, so the radius is half of the diameter, which is 5 mm. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius. Therefore, the circumference of each pencil is 2π(5 mm) = 10π mm. Since there are four pencils, the total length of the band is 10π mm x 4 = 40π mm. This is your answer in terms of π.
What are the coordinates of the image of point A after the segment has been dilated by a scale factor of One-fourth with a center of dilation at the origin? On a coordinate plane, point B is at (negative 2, 4) and point A is at (4, negative 8). (–2, 1) (1, –2) (Negative one-half, 1) (1, negative one-half)
Answer:
The answer is B
Step-by-step explanation:
Just did the assignment on Egn.
Which of the following statements is false? a. When the alternative hypothesis is two-tailed, any hypothesis test is said to be a two-tailed test. b. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution. c. When the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution. d. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution. e. None of these.
Answer:
Step-by-step explanation:
For a two tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis.
The curve is symmetrical and the rejection regions would be in the left and right tails
In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.
Therefore, the following statements are false
B. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution.
D. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution.
Final answer:
Statement d is false because it combines parts of two separate true statements, which could be misleading. A two-tailed test is indicated by a not equals symbol in the alternative hypothesis, and the rejection region is split between the two tails of the test statistic's sampling distribution.
Explanation:
The false statement is d. While it's true that when the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution, statement d is false because it repeats the earlier part of the statement and combines it with a correct statement from option c, which can be misleading. The correct information is provided in separate statements b and c.
The alternative hypothesis indicates the type of test to be conducted. If the alternative hypothesis has a not equals symbol (≠), it indicates a two-tailed test. In a two-tailed test, the rejection region is split between the two tails of the test statistic's sampling distribution. In terms of p-value, it represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A small p-value (< 0.05) typically indicates strong evidence against the null hypothesis, leading to its rejection.
An office manager just got back from vacation, so she has a pile of 424 letters to read. Then, the mail carrier comes and delivers 41 more letters for her. How many letters does the office manager have now?
465
383
455
373
Answer:
465
Step-by-step explanation:
424+41=465
Which set of ordered pairs could be generated by an exponential function?
(1, 1), (2.2), (3, 3), (4-4)
• (1, 1), (2.4), (0.5) (470)
Answer:
(1, 1), (2.4), (0.5) (470)
Step-by-step explanation:
Honestly, I only know it's this one because the first one is a linear function. If you think about it on a graph, all of the points on the first one can connect with a straight line.
Dr. Vegapunk thinks that watching anime (Japanese animated shows) decreases social skills in college students. To test this, Dr. Vegapunk randomly selected 30 brooklyn college students and assigned them to watch an episode of anime everyday for a week. After the week, each of the students answered a questionnaire about their social skills. The results showed that the sample had a mean social skills score of 7.3 and a standard deviation of 2.4. A previous study showed that the overall population of brooklyn college students had a mean social skills score of 6.2, but the standard deviation was not reported. Dr. Vegapunk decides to use an alpha level of 0.05. e) what is the obtained statistic
Answer:
The test statistic = 2.51
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, Dr. Vegapunk wants to test the claim that watching anime decreases social skills in college students.
So, the null hypothesis would be that there isn't significant evidence to conclude that watching anime decreases social skills in college students. That is, watching anime does not decrease social skills in college students.
And the alternative hypothesis is that there is significant evidence to conclude that watching anime decreases social skills in college students.
If the previous known mean social skills of college students is 6.2 and the new population mean social skills of college students who watch anime is μ,
Mathematically,
The null hypothesis is represented as
H₀: μ ≥ 6.2
The alternative hypothesis is given as
Hₐ: μ < 6.2
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic
t = (x - μ)/σₓ
x = sample mean = 7.3
μ₀ = Standard to be compared against = 6.2
σₓ = standard error of sample mean = [σ/√n]
where n = Sample size = 30
σ = Sample standard deviation = 2.4
σₓ = (2.4/√30) = 0.4382
t = (7.3 - 6.2) ÷ 0.4382
t = 2.51
Hope this Helps!!!
find lim x →0 f(2+h)-f(2)/h if f(x)=x^3
Answer:
The value of the limit is 12.
Step-by-step explanation:
Small typing mistake, the limit is of h tending to 0.
We have that:
[tex]f(x) = x^{3}[/tex]
Then
[tex]f(2+h) = (2+h)^{3} = 8 + 12h + 6h^{2} + h^{3}[/tex]
[tex]f(2) = 2^{3} = 8[/tex]
Calling the limit L
[tex]L = \frac{f(2+h) - f(2)}{h}[/tex]
[tex]L = \frac{8 + 12h + 6h^{2} + h^{3} - 8}{h}[/tex]
[tex]L = \frac{h^{3} + 6h^{2} + 12h}{h}[/tex]
h is the common term in the numerator, then
[tex]L = \frac{h(h^{2} + 6h + 12)}{h}[/tex]
Simplifying by h
[tex]L = h^{2} + 6h + 12[/tex]
Since h tends to 0.
[tex]L = 0^{2} + 6*0 + 12[/tex]
[tex]L = 12[/tex]
So the answer is 12.
Using the definition of a derivative, the expression lim h→0 [f(2+h)-f(2)]/h for f(x)=x^3 simplifies to 12, which is the derivative of the function at x=2.
Explanation:The limit you are trying to find is representative of the definition of a derivative at a point. In this case, the function is f(x) = x^3 and we're trying to find the derivative at x = 2. This is the definition of the derivative at a point:
lim h→0 [f(x+h) - f(x)] / h
Now, we plug in the equation for f(x):
lim h→0 [(2+h)^3 - 2^3] / h = lim h→0 [8+12h+6h^2+h^3 - 8] / h
Simplify that to get:
lim h→0 h [12+6h+h^2] / h
Then, by cancelling the h's, you have:
lim h→0 [12+6h+h^2]
As h→0, 6h and h^2 become 0, so finally, you obtain 12 as the derivative of f at x=2.
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HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check all that apply.
Answer:
A, B, D
Step-by-step explanation:
The linear parent function is a straight line with equation x=y, which means that it has a slope of 1 and goes through the origin. However, it does not go through quadrants 2 and 4, only 1 and 3. Hope this helps!
Christina saves her coins in a cube-shaped coin bank. Her coin bank is 7 inches wide and 7 inches tall. What is the volume of Christina's coin bank?
The volume of Christina's cube-shaped coin bank is calculated by cubing the length of one of its sides, which is 7 inches. The volume is therefore 7 × 7 × 7, or 343 cubic inches.
Explanation:The volume of Christina's cube-shaped coin bank can be calculated using the formula for the volume of a cube, which is Volume = side × side × side. As all sides of a cube are equal and the coin bank is 7 inches wide and 7 inches tall, we can calculate the volume by multiplying 7 inches by 7 inches by 7 inches.
Calculation:
Volume = 7 in. × 7 in. × 7 in. = 343 cubic inches
Hence, the volume of Christina's coin bank is 343 cubic inches.
Final answer:
The volume of Christina's cube-shaped coin bank is calculated using the cube volume formula and is found to be 343 cubic inches.
Explanation:
To calculate the volume of Christina's coin bank, we use the formula for the volume of a cube, which is Volume = side³, where 'side' is the length of one side of the cube. Since the coin bank is 7 inches wide and 7 inches tall, each side is 7 inches. Thus, the volume of the coin bank is:
Volume = 7 in. × 7 in. × 7 in. = 343 in.³
Therefore, Christina's coin bank has a volume of 343 cubic inches.
A local hotel wants to estimate the average age of its guests that are from out-of-state. Preliminary estimates are that standard deviation of population of guests from out-of-state is 30. How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence? a. 12 b. 11 c. 139 d. 138
Answer:
c. 139
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.
How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence?
We need a sample size of n.
n is found when [tex]M = 5, \sigma = 30[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 1.96*\frac{30}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 1.96*30[/tex]
Simplifying by 5
[tex]\sqrt{n} = 1.96*6[/tex]
[tex](\sqrt{n})^{2} = (1.96*6)^{2}[/tex]
[tex]n = 138.30[/tex]
We round up,
So the correct answer is:
c. 139
Answer:
[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]
And if we round up to the nearest integer we got n =139, and the best answer for this case is:
c. 139
Step-by-step explanation:
For this case we have this previous info:
[tex]\sigma = 30[/tex] represent the previous estimation for the population deviation
[tex]Confidence =0.95[/tex] represent the confidence level
The margin of error for the true mean is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
The desired margin of error is ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for a 95% of confidence interval given now can be founded using the normal distribution. For this case the critical value would be given by [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]
And if we round up to the nearest integer we got n =139, and the best answer for this case is:
c. 139
Navibulgar is a bulgarian shipping company. the department that handles fragile shipping rolls prints and other documents into cylinders and then pack the cylinders into special containers that are triangular solids so that the cylinders would not roll around in the trailers. the surface area of a triangular prism container that would be needed to enclose a rolled document with a diameter of 10cm and a length of 85 cm? Round your answer to the nearest square centimeter. Assume the triangle face is an equilateral triangle
Answer:
Was the answer possibly C) 4,671 sq.cm. ?
Explanation:
Since the expert didn't get it right from what I'm seeing.
The surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.
To calculate the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm, we follow these steps:
1. Determine the dimensions of the equilateral triangle base:
- The diameter of the cylinder (10 cm) is equal to the side length of the equilateral triangle base.
2. Calculate the height of the equilateral triangle:
- The height \( h \) of an equilateral triangle with side length \( a \) is given by:
[tex]\[ h = \frac{\sqrt{3}}{2} a \] For \( a = 10 \) cm: \[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.66 \text{ cm} \][/tex]
3. Calculate the area of the equilateral triangle base:
- The area \( A \) of an equilateral triangle with side length \( a \) is given by:
[tex]\[ A = \frac{\sqrt{3}}{4} a^2 \] - For \( a = 10 \) cm: \[ A = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.30 \text{ cm}^2 \][/tex]
4. Calculate the lateral surface area of the prism:
- The lateral surface area is given by the perimeter of the triangular base times the length of the prism.
- The perimeter \( P \) of an equilateral triangle with side length \( a \) is:
[tex]\[ P = 3a \] For \( a = 10 \) cm: \[ P = 3 \times 10 = 30 \text{ cm} \][/tex]
- The length of the prism is 85 cm.
- The lateral surface area \( L \) is:
[tex]\[ L = P \times \text{length} = 30 \times 85 = 2550 \text{ cm}^2 \][/tex]
5. Calculate the total surface area of the prism:
- The total surface area \( S \) includes the lateral surface area and the area of the two triangular bases.
- Total surface area \( S \) is given by:
[tex]\[ S = L + 2 \times A \] - Substitute the values: \[ S = 2550 + 2 \times 43.30 = 2550 + 86.60 = 2636.60 \text{ cm}^2 \][/tex]
6. Round the total surface area to the nearest square centimeter:
[tex]\( S \approx 2637 \text{ cm}^2 \)[/tex]
So, the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.
The use of social networks has grown dramatically all over the world. In a recent sample of 24 American social network users and each was asked for the amount of time spent (in hours) social networking each day. The mean time spent was 3.19 hours with a standard deviation of 0.2903 hours. Find a 99% confidence interval for the true mean amount of time Americans spend social networking each day
Answer:
The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).
Step-by-step explanation:
The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=24\\\bar x=3.19\ \text{hours}\\s=0.2903\ \text{hours}[/tex]
Confidence level = 99%.
Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (24-1)}=t_{0.005, 23}=2.807[/tex]
*Use a t-table.
Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
[tex]=3.19\pm 2.807\times \frac{0.2903}{\sqrt{24}}\\\\=3.19\pm 0.1663\\\\=(3.0237, 3.3563)\\\\\approx (3.02, 3.36)[/tex]
Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).
How do you calculate the average mark?
Answer:
68.44%
Step-by-step explanation:
You compute the average the way you compute any average: add up the numbers and divide by their number.
Multiplication is a useful way to shorten the effort of repeated addition.
(64% × 3 + 58% × 7 + 88% × 3 +33% + 100% × 2)/(3 +7 +3 + 1 + 2)
= 1095%/16 = 68.4375%
≈ 68.44% . . . the average mark for the class
Katrina is asked to simplify the expression Negative 3 a minus 4 b minus 2 (5 a minus 7 b).
She writes: Negative 3 a minus 4 b minus 2 (5 a minus 7 b) = negative 3 a minus 4 b minus 10 a + 14 b
Answer:
-13a+10b
Step-by-step explanation:
A woman who is 5.75ft tall stands next to a lamp post that is 12ft tall. If its' shadow is 30ft long, how long is the shadow of the woman?
Answer:
The length of shadow of the woman is 14.375 ft.
Step-by-step explanation:
Here we are given that
Height of the woman = 5.75 ft
Height of the lamp post = 12 ft
Shadow of the lamp post = 30 ft
Let the angle of elevation of the light source be θ
By definition, in a right triangle, with respect to angle θ, we have;
tan(θ) = Opposite÷Adjacent
Therefore, tan(θ) = (Height of the lamp post)÷(Shadow of the lamp post)
and tan(θ) = 12 ft ÷ 30 ft = 0.4
θ = Actan(0.4) = tan⁻¹(0.4) = 21.8°
Since, angle of elevation of the light = Angle of depression of the light (alternate angles) = 21.8° we have
tan(θ) = (Height of the woman) ÷ (Length of shadow of the woman)
∴ Length of shadow of the woman = (Height of the woman) ÷ tan(θ)
Length of shadow of the woman = 5.75 ft ÷ tan(21.8) = 5.75 ft ÷ 0.4
Length of shadow of the woman = 5.75 ft ÷ 0.4 = 14.375 ft.
Evaluate the function. Find f(5). f(x)=4x-1
Answer:
19
Step-by-step explanation:
plug in 5 for x so f(5)=4(5)-1 = 20-1 = 19
The solution of expression f (x) = 4x - 1at x = 5 would be 19.
Given that the expression is,
f (x) = 4x - 1
Used the concept of substitution method to solve the expression.
Now, substitute x = 5 in the expression,
f (x) = 4x - 1
f (5) = 4(5) - 1
f (5) = 20 - 1
f (5) = 19
Therefore, the value of the expression is f (5) = 19.
To learn more about the mathematical expression visit:
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