The 95% confidence interval for the number of hours students at the college study weekly, given a sample size of 49, mean of 12.2 hours, and standard deviation of 1.6, is from 11.62 hours to 12.78 hours.
Explanation:In statistics, the 95% confidence interval for the mean number of hours students study in a week can be calculated using the collected data and the t-distribution. Given that the sample size is 49 (n=49), the sample mean(x) is 12.2 hours, and the standard deviation(s) is 1.6 hours, we need to apply the formula for the confidence interval which is x ± t∗(s/√n). The t-value for 95% confidence with 48 degrees of freedom (49-1) can be found using the t-distribution Inverse Calculator applet, which is about 2.01 (it varies slightly depending on the calculator used).
Now, plug in the given values into the formula: 12.2 ± 2.01 * (1.6 / √49), it simplifies to 12.2 ± 0.58. So, the 95% confidence interval for the number of hours students in the college study each week is from 11.62 hours to 12.78 hours.
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Which of the following is the correct interpretation of the p-value? A. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners. B. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is a difference in the mean number of partners. C. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the sample mean number of partners. D. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is a difference in the sample mean number of partners.
Answer:
The correct option is (A).
Step-by-step explanation:
The p-value is well defined as the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
From the provided options we can guess that the hypothesis was defined as follows:
H₀: There is no difference in the mean number of partners, i.e. μ₁ - μ₂ = 0.
Hₐ: There is difference in the mean number of partners, i.e. μ₁ - μ₂ ≠ 0.
The test is two tailed mean difference test.
A z-test or a t-test can be used to conclude the result.
In this case the p-value can be defined as the probability of obtaining a test statistic value equal to or more extreme that the results obtained from the sample, when the difference between the mean number of partners is 0.
Thus, the correct interpretation of the p-value is provided by statement (A).
The p-value represents the likelihood of obtaining a test statistic as extreme as our observed data, assuming the null hypothesis is true. The null hypothesis usually posits there's no difference or effect. A small p-value would suggest rejecting the null hypothesis in favor of the alternative hypothesis, indicating a significant effect or difference.
Explanation:The correct interpretation of the p-value is: The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners.
In other words, the p-value measures how likely you are to get the observed data if the null hypothesis is true. The null hypothesis typically represents a theory that there is no effect or no difference between the groups you're comparing. Hence, if there's no difference in the mean number of partners (which is our null hypothesis here), then the p-value tells how likely we are to observe a test statistic as extreme as our sample result.
For example, if the p-value is very small, it might be less than our significance level (commonly 0.05 or 5%). In such a case, we have evidence to reject our null hypothesis in favor of the alternative hypothesis. The alternative hypothesis generally represents a theory that there is an effect or a difference between the groups. So, in this case, a small p-value would indicate a statistically significant difference in the mean number of partners.
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The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is (1 point)
Answer:
Domain: { -3,1,6}
Step-by-step explanation:
The domain is the input values
Domain: { 6,1,-3,-3}
We usually put them in numerical order and we do not list the same value twice
Domain: { -3,1,6}
Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.
Which could be a possible length of side DE?
2 in.
3 in.
7 in.
16 in.
Answer:
7
Step-by-step explanation:
THe Triangle Inequality Theorem states that the sum of the two least sides of a triangle must be greater than the third side. In this case, 2 and 6 are less than 10, 3 and 6 are less than 10, 6 and 10 are greater than 16, so the only number left is 7. The sum of seven and six is greater than ten so seven would be the correct answer.
Question:
Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.
Which could be a possible length of side DE?
2 in.
3 in.
7 in.
Answer:
C.) 7 in.
Step-by-step explanation:
To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c. Remember the formula for finding the perimeter of a triangle. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm. Thus, the perimeter of an equilateral triangle is 3 times the length of each side. Area of a two-dimensional shape is the space occupied by the shape.
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You are in an airplane 5.7 miles above the ground. What is the measure of BD⌢
the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)
The measure of the portion of Earth that can be seen from an airplane 5.7 miles above the ground is approximately 0.163 degrees, when rounded to the nearest tenth. This is found using the formula for the angle subtended by an arc, and then converting from radians to degrees.
Explanation:To solve this problem, we can use the properties of a circle, since the Earth is approximately spherical in shape. The formula to calculate the angle subtended by an arc (BD⌢) on the Earth's surface is as follows: θ = 2 * arcsin((distance_to_object)/(2 * radius_of_earth)).
So inserting the given values:
The distance to the airplane is 5.7 miles above groundThe Earth's radius is roughly 4000 milesWe get: θ = 2 * arcsin((5.7)/(2 * 4000)). This will give you an answer in radians, to convert this to degrees multiply by 180/π. In this case, the answer is approximately 0.163 degrees, rounded to the nearest tenth.
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For the same signal emitted by a radio antenna,
Observer A measures its intensity to be 16 times the
intensity measured by Observer B. The distance of
Observer A from the radio antenna is what fraction
of the distance of Observer B from the radio
antenna?
Answer: The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Step-by-step explanation:
We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:
Intensity(r) = A/r^2
Observer A measures 16 the intensity of observer B.
if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:
Ia = 16Ib
A/(ra)^2 = 16*A/(rb)^2
1/(ra)^2 = 16/(rb)^2
rb^2 = 16*ra^2
and we know that 16 = 4*4 = 4^2
rb^2 = (4*ra)^2
then rb = 4*ra
this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.
The fraction is ra = rb/4
The distance of
Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is 4 times the distance of Observer B.
Explanation:Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. Let's denote the distance of Observer A from the radio antenna as dA and the distance of Observer B as dB.
We can use the inverse square law to relate the intensity to the distance: Intensity is inversely proportional to the square of the distance.
So, we have:
IntensityA/IntensityB = (dA/dB)^2 = 16
Solving for dA/dB, we find:
dA/dB = sqrt(16) = 4
Therefore, the distance of Observer A from the radio antenna is 4 times the distance of Observer B.
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Suppose seven pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why?Since there are 7 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be . It follows that if a minimum of Incorrect: Your answer is incorrect. boots are chosen, at least two must be from the same pair.
Answer:
We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.
Step-by-step explanation:
From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.
Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;
Number of single boots = 7 x 2 = 14
Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.
Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.
To ensure getting a matched pair from a pile of 7 pairs of boots, you would need to pick eight individual boots. This is based on the counting principle in mathematics where in the worst-case scenario, each boot you pick could be from a different pair.
Explanation:The question is about probability and counting principles in mathematics, specifically about how to identify a matched pair of boots from a pile of similar looking pairs. In the pile, there are seven pairs of boots, which means there are 14 individual boots from seven different pairs.
Now, if you randomly pick one boot, it could be from any pair. If you pick a second boot, it could also be from any pair, including the same pair as the first one. But to be sure that you get a matched pair, you will have to pick up eight boots. This is because, in the worst-case scenario, you might pick seven different boots each from a different pair. Once you pick the eighth boot, it is guaranteed to match one of the earlier seven because there are only seven pairs.
The minimum number of individual boots that you must pick to be sure of getting a matched pair is eight.
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A researcher is studying the monthly gross incomes of drivers for a ride sharing company. (Gross incomes represent the amount paid to drivers before accounting for the costs associated with driving.) The researcher obtains a list of all the drivers in San Francisco and randomly selects 200 of them to contact. The list of incomes in the sample has an average of $800 per month, with an SD of $1000. (a) Does the histogram of the sample incomes follow the normal curve? Explain why or why not.
Answer:
The histogram of the sample incomes will follow the normal curve.
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 mean will be approximately normally distributed.
In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.
He selects a sample of n = 200 drivers and ask them their monthly salary.
As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.
Thus, the histogram of the sample incomes will follow the normal curve.
Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.8 months and a standard deviation of 6.5 months.
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Answer:
a) The company should expect to replace 11.51% of its batteries.
b) 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
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 = 43.8, \sigma = 6.5[/tex]
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 43.8}{6.5}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151.
The company should expect to replace 11.51% of its batteries.
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 43.8}{6.5}[/tex]
[tex]X - 43.8 = -1.28*6.5[/tex]
[tex]X = 35.48[/tex]
To the nearest month, 35 months.
Final answer:
To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36.
Explanation:
In this question, we are given information about the average life of a Quick Start car battery, which follows a normal distribution with a mean of 43.8 months and a standard deviation of 6.5 months.
(a) To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36. We can use the z-score formula to standardize the value of 36 and then use a standard normal distribution table to find the corresponding area. The percentage of batteries that will be expected to be replaced is the same as the percentage of batteries that fall within the range of 0 to 36 months.
Subtract the mean from 36: 36 - 43.8 = -7.8Divide the result by the standard deviation: -7.8 / 6.5 = -1.2Using the z-score -1.2, find the corresponding area under the standard normal distribution curve using a standard normal distribution table or a calculator with standard normal distribution capabilities.For the graffiti cat sweater on page 9, Dodd knit
12 stitches to make 2 inches in width. The sweater is
9 inches wide from the left edge to the beginning of the
black smile. How many stitches wide is that?
Answer: 54 stitches
Step-by-step explanation:
12/2=6
6 stitches= 1 inch
X stitches=9 inches
X=54 stitches
A college entrance exam company determined that a score of 2323 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 150150 students who completed this core set of courses results in a mean math score of 23.423.4 on the college entrance exam with a standard deviation of 3.23.2. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 2323 on the math portion of the exam? Complete parts a) through d) below.
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]
c) Test statistic t=1.53
P-value=0.064
d) The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that students who complete the core curriculum are ready for college-level mathematics. That is that the true score for the group is not significantly higher than 23.
Step-by-step explanation:
The question is incomplete:
a) State the appropriate null and alternative hypotheses.
c) Use the P-value approach at the 0.05 level of significance to test the hypotheses in part (a). ldentify the test statistic. (Round to two decimal places as needed.) Identfy the P-value. P-value (Round to three decimal places as needed.)
d) Write a conclusion based on the results. Choose the correct answer below. ? the null hypothesis and claim that there ? sufficient evidence to conclude that the population mean is ? than 20.
This is a hypothesis test for the population mean.
The claim is that students who complete the core curriculum are ready for college-level mathematics.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=150.
The sample mean is M=23.4.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.2}{\sqrt{150}}=0.261[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{23.4-23}{0.261}=\dfrac{0.4}{0.261}=1.531[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=150-1=149[/tex]
This test is a right-tailed test, with 149 degrees of freedom and t=1.531, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>1.531)=0.064[/tex]
As the P-value (0.064) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that students who complete the core curriculum are ready for college-level mathematics.
graph the two lines y=2x + 5 and y= x -1 what is the the x-value of the point where they intersect
Answer:
x=-6
Step-by-step explanation:
y=2x + 5
y= x -1
Plug in the equation for y
x-1=2x+5
Combine like terms
-1=x+5
-6=x
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Sequence: 10, 21, 32, 43, 54, ... Find the 75th term.
Answer:
186
Step-by-step explanation:
definition: a_n = a_1 + f × (n-1)
Common difference is 11
The sum of all numbers up through the 17th: 1666
Answer: 824
Step-by-step explanation:
This is problem on progression.
Considering the series/ sequence,
10, 21, 32, 43, 54, ........
To find the 75th term, we first of all find which of the sequence is it, is it, Arithmetic or Geometric sequence .
Now fro this, it is an AP sequence because, when the first term us subtracted from the second term and the common difference added to the second term it produces the third term and so on, . Haven't gotten this, we now apply the formula for finding the number if terms in an AP.
Tn = a + (n - 1 )d, where n = number of terms we are computing for = 75, a = first term = 10, and d = 21 - 10 = 11.
Now substitute for those values in the formula above
T75 = 10 + ( 75 - 1 )11
= 10 + 74 × 11
= 10 + 814
= 824.
Is 5/8 mile larger or less than 1 mile
Answer:
5/8 mile is less than 1 mile
Step-by-step explanation:
in this question, one could assume a mile is 8/8
5/8<8/8
-)) In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 5.4 millimeters and c = 8.3 millimeters, what is a? If necessary, round to
the nearest tenth
Answer:
a = 6.3mm
Step-by-step explanation:
Use Pythagoras theorem here
[tex]a^{2} + b^{2} = c^{2}[/tex]
Rearrange for a by subtracting [tex]b^{2}[/tex] from both sides of the equation
[tex]a^{2} + b^{2} -b^{2} = c^{2} -b^{2}[/tex]
Simplify
[tex]a^{2} = c^{2} -b^{2}[/tex]
Substitute in our numbers and solve for a
[tex]a^{2}[/tex] = [tex]8.3^{2} - 5.4^{2}[/tex]
[tex]a^{2}[/tex] = 68.89 - 29.16
[tex]a^{2}[/tex] = 39.73
a = [tex]\sqrt{39.73}[/tex]
a = 6.3mm
Final answer:
To find the length of leg a when b = 5.4 mm and c = 8.3 mm in a right triangle, we use the Pythagorean theorem a^2 + b^2 = c^2. We solve for a, yielding a ≈ 6.3 mm (rounded to the nearest tenth).
Explanation:
The student is asking how to find the length of leg a in a right triangle where the lengths of leg b and the hypotenuse c are given. Since b = 5.4 millimeters and c = 8.3 millimeters, we can use the Pythagorean theorem to find leg a.
First, we'll apply the theorem: a2 + b2 = c2. To solve for a, we rearrange it: a2 = c2 - b2.
Substitute the given values:
a2 = c2 - b2
= 8.32 - 5.42
= 68.89 - 29.16
= 39.73
Now, we take the square root of both sides to find a:
a =
√39.73
≈ 6.3 millimeters (rounded to the nearest tenth)
Therefore, the length of leg a is approximately 6.3 millimeters.
Dean mixed together different kind of nuts as a snack. There were 9 nuts in the bowl, 7 of
which were hazelnuts.
If Dean randomly chose to eat 6 of the nuts, what is the probability that all of them are
hazelnuts?
Write your answer as a decimal rounded to four decimal places.
Answer:
0.0833
Step-by-step explanation:
There are 7C6 = 7 ways to choose 6 hazelnuts from the 7 present.
There are 9C6 = 84 ways to choose 6 nuts from the 9 present.
The probability of choosing 6 hazelnuts from the 9 present is ...
7/84 = 1/12 = 0.0833...(repeating)
The probability of interest is 0.0833.
____
Comment on the notation
The notation nCk means n!/(k!(n-k)!). It is the number of ways k items can be chosen from n items without regard to order. It can be pronounced "n choose k."
Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20. The population standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21
Answer:
95.44% probability that a sample of 100 steady smokers spend between $19 and $21
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 20, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]
What is the probability that a sample of 100 steady smokers spend between $19 and $21
This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So
X = 21
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{21 - 20}{0.5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 19
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19 - 20}{0.5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that a sample of 100 steady smokers spend between $19 and $21
To find the probability that a sample of 100 steady smokers spend between $19 and $21, calculate the Z-score and use a standard normal distribution table or calculator. The probability is approximately 0.3413.
Explanation:To find the probability that a sample of 100 steady smokers spend between $19 and $21, we can use the Z-score formula. The Z-score is calculated as the difference between the sample mean and the desired value (in this case, $20), divided by the population standard deviation, multiplied by the square root of the sample size.
Z = (x - μ) / (σ / √n)
Plugging in the values we have:
Z = (21 - 20) / (5 / √100) = 1
We can then use a standard normal distribution table or a calculator to find the probability associated with a Z-score of 1. The probability of obtaining a Z-score of 1 or less is approximately 0.8413. Since we want the probability between $19 and $21, we subtract the probability of getting a Z-score of less than 1 from the probability of getting a Z-score of less than or equal to 0. This gives us:
Probability = 0.8413 - 0.5000 = 0.3413
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
ere'o - 10
and is the least intense sound a human ear can hear. What is the approximate loudness of a
dinner conversation with a sound intensity of 10-7?
O -58 Db
O -50 Db
O 9 Db
O 50 Db
Answer:
[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans
[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation
And replacing this into the formula we got:
[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]
So then the best answer for this case would be:
O 50 Db
Step-by-step explanation:
For this case we can use the following equation for decibels:
[tex] dB = 10 log_{10} (\frac{I}{I_o})[/tex]
Where:
[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans
[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation
And replacing this into the formula we got:
[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]
So then the best answer for this case would be:
O 50 Db
The approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db
Logarithm functionsGiven the general expression for calculating the loudness, L, measured in decibels (Db), of sound intensity, I as:
L = 10log(I0/I)
Given the following parameters
I0 = 10^-12 Wb/m²
I = 10^-7 Wb/m²
Substitute
L = 10log(10^-12/10^-7)
L = 10log(10^-5)
L = -5(10)log10
L = -50Db
Hence the approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db
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Which is the unit rate if 4 tuna cans are sold for $6
Answer:
$1.50 per can
Step-by-step explanation:
6/4 = 1.5
to check your answer, do 1.50*4, and you get $6
hope this helps :)
Answer:
The unit rate is $1.50 per can.
Step-by-step explanation:
Price: $6
Number of Cans Purchased at This Price: 4
$6/4 cans=$1.50 per can
Which expression shows 20% of 60! Please give the right answer tryna pass
Answer:
1/5 - 60 or b
Step-by-step explanation:
The expression that shows 20% of 60 is 1/5 * 60
How to determine the correct expression?The expression is given as:
20% of 60
Express of as *
20% * 60
Express the percentage as fraction
20/100 * 60
Simplify the fraction
1/5 * 60
Hence, the expression that shows 20% of 60 is 1/5 * 60
Read more about product expressions at
https://brainly.com/question/4344214
Wendy had 20 apples. If 1/4 of them were red, how many apples were red?
Answer:
5
Step-by-step explanation:
split 20 into 4 and find out how much is one portion the four
Plz mark brainliest
what is the derivative of 66lnx +135
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 66 \ln x + 135[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[66 \ln x] + \frac{d}{dx}[135][/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 66\frac{d}{dx}[\ln x] + \frac{d}{dx}[135][/tex]Logarithmic Differentiation: [tex]\displaystyle y' = \frac{66}{x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Problem 3: Sampling methods
Willy wants to find what percent of students at his school drink the milk after
they finish their cereal. He is considering the following sampling methods:
QUESTION
He selects every tenth person who enters the school. What type of sampling
is this?
Choose 1 answer:
Willy is using a systematic sampling method by selecting every tenth person entering the school to understand milk consumption habits after cereal.
Explanation:When Willy selects every tenth person who enters the school to determine what percent of students drink the milk after they finish their cereal, he is using a systematic sampling method. This type of sampling involves selecting subjects at regular intervals from an ordered list.
It's a form of probability sampling where the first unit is selected randomly and the subsequent units are selected using a fixed periodic interval.
In the context of the situation provided, this method could potentially provide a more representative sample compared to methods like convenience sampling, but there could be inherent biases if there are underlying patterns in the student arrivals at school that correlate with milk drinking habits after cereal.
What is the height of the following triangle if the area is 60 square meters? Do not round your answer.
Answer:
The height of the triangle, h, is 8 m
Step-by-step explanation:
The formula for the area of a triangle of base b and height h is A = (1/2)(b)(h).
Here b = 15 m and A = 60 m^2. We want the measure of the height, h.
First we solve the area equation (above) for h: 2A = bh, or h = 2A/b,
and then substitute the given values for b and A:
2(60 m^2)
h = ------------------ = 8 m
15 m
The height of the triangle, h, is 8 m
Answer:
Answer is 8 because I did the quiz on my online school.
Hope it helps
Pls help me Idk what to do
Answer:
6
Step-by-step explanation:
The line in the middle of the box is the median
If "f" varies directly with "m," and f=-19 when m=14, what is "f" when m=2?if
Answer:-19/7
Step-by-step explanation:
f varies directly as m
f=k x m
When f=-19,m=14
-19=k x 14
k=-19/14
Relationship is f=-19m/14
When m is 2
f=(-19x2) ➗ 14
f=-38 ➗ 14
f=-19/7
What is the range of the data represented in the dot plot below?
Answer:
3
Step-by-step explanation:
Range is the difference between
The large exhibit at the aquarium has a viewing window that is 22 feet long 58.25 feet high and 13 inches thick estimate its volume in cubic feet remember remember 12 inches equal 1 foot
Answer:
Step-by-step explanation: convert feet to inches then multiply all 3 numbers. 264 x 699x13 = 2398968. Then decide that by 12 the amount of inches in a foot and get 199,914 ft^3
Suppose Julio is a veterinarian who is doing research into the weight of domestic cats in his city. He collects information on 174 cats and finds the mean weight for cats in his sample is 10.75 lb with a standard deviation of 4.30 lb. What is the estimate of the standard error of the mean (SE)
Answer:
The standard error of the mean (SE) is of 0.326lb.
Step-by-step explanation:
The standard error of the mean is given by the following formula:
[tex]SE = \frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
In this problem, we have that:
[tex]s = 4.3, n = 174[/tex]
Then
[tex]SE = \frac{s}{\sqrt{n}} = \frac{4.3}{\sqrt{174}} = 0.326[/tex]
The standard error of the mean (SE) is of 0.326lb.
I need help asap !!! please !!!
Answer:
2^-84
Step-by-step explanation:
First simplify inside the parentheses
2^-10 / 4^2
Rewriting 4 as 2^2
2^-10 / 4^2^2
We know that a^b^c = a^(b*c)
2^-10 / 2^(2*2) = 2^-10 / 2^4
We know that a^b / a^c = a^(b-c)
2^-10 / 2^4 = 2^(-10-4) = 2^-14
Replace the term in side the parentheses with 2^-14
2^-14 ^7
We know that a^b^c = a^(b*c)
2^(-14*7)
2^-84
If 3/4 of a number minus 1/2 of the number is 4. What is the number?
Answer:
16
Step-by-step explanation:
Number = x
(3/4 of x) - (1/2 of x) = 4
3x/4 - x/2 = 4
3x - 2x / 4 = 4
x/4 = 4
x = 16