Answer:
The probability that a randomly selected student didn’t take economics but did take statistics is 13%.
Step-by-step explanation:
Let the event that a student offers Economics be E.
The event that a student does NOT offer Economics is E'.
Let the event that a student offers Statistics be S.
The event that a student does NOT offer Statistics be S'.
P(E) = 13.5% = 0.135
P(S) = 24.7% = 0.247
P(E n S) = 11.7% = 0.117
Find the probability that a randomly selected student didn’t take economics but did take statistics
This probability = P(E' n S)
Since E and E' are mutually exclusive events,
P(S) = P(E' n S) + P(E n S)
P(E' n S) = P(S) - P(E n S)
P(E' n S) = 0.247 - 0.117 = 0.13 = 13%
Hope this Helps!!!
A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
For each of the sequences below, find a formula that generates the sequence. (a) 4, 10, 16, 22, 28, 34, 40, . . . (b) 5, 15, 45, 135, 405, . . . (c) 10, 20, 10, 20, 10, 20, 10
Answer:
[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]
Step-by-step explanation:
[tex]6(1)-2=4[/tex]
[tex]6(2)-2=10[/tex]
[tex]5 \times 3^{(3)-1}=45[/tex]
[tex]5 \times 3^{(4)-1}=135[/tex]
[tex]5(-1^{(5)}+3)=10[/tex]
[tex]5(-1^{(6)}+3)=20[/tex]
a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)
b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹
c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is an = 10 + 10 * ((n + 1) % 2)
(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.
To learn more about sequence click on,
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SIMPLIFY THE EXPRESSION -4 X 4 X 4 X 4 X4 X 4 X 4 X4
Answer:
-4 · [tex]4^{7}[/tex]
Step-by-step explanation:
Which statement could be an interpretation of the graph’s x-intercept or y-intercept?
On a coordinate plane, a line goes through points (0, 800) and (400, 0).
Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
[tex] y=mx +b[/tex]
Where
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Answer:
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
Where
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 25.325.3 milligrams and standard deviation of 2.72.7 milligrams for a sample of n equals 9n=9 cigarettes. Construct a 9090% confidence interval for the mean nicotine content of this brand of cigarette.
Answer:
The 90% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
M = T*s = 1.8595*2.7 = 5
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 25.3 - 5 = 20.3 milligrams
The upper end of the interval is the sample mean added to M. So it is 25.3 + 5 = 30.3 milligrams.
The 90% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.
Please help! Correct answer only, please! The following information matrices show how many of each vehicle type sold and the bonus amount each salesperson receives for selling that type of vehicle for the car dealership for the week. Which salesperson sold the most vehicle for the week described?A. Scott B. Each sold the same number of vehicles C. Kelly D. Mark
Answer: b) Each sold the same number of vehicles
Step-by-step explanation:
This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.
Kelly: 8 + 2 + 6 = 16
Scott: 7 + 8 + 1 = 16
Mark: 10 + 4 + 2 = 16
The total number of vehicles sold by each person is the same
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Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
A cylinder with a base diameter of x units has a volume of
cubic units
Which statements about the cylinder
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is ax? square units.
The area of the cylinder's base is nx square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Corrected Question
A cylinder with a base diameter of x units has a volume of [tex]\pi x^3[/tex] cubic units
Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units. The radius of the cylinder is 2x units. The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.Answer:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]
Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]
Volume =Base Area X Height
[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]
Therefore:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
The perimeter of the shape is 28 cm. Find the value of radius.
Answer:
r = 4.2805cm
Step-by-step explanation:
ok first the shape its made of two slant height and and an arc of degree 70°
The total perimeter = 28cm
The formula for the total perimeter= 2l + 2πl(70/360)
Where l is the radius of the shape.
But l = 2r
So
= 2l + 1.2217l
= 3.2217l
28 = 3.2217l
l = 28/3.2217
l = 8.691
Recall that l = 2r
8.691= 2r
r = 8.691/2
r = 4.2805cm
Suppose a simple random sample of size n= 11 is obtained from a population with u = 62 and a = 14.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
(b) Assuming the normal model can be used, determine P(x < 65.8).
(c) Assuming the normal model can be used, determine P(x 2 64.2).
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) What must be true regarding the distribution of the population?
O A. Since the sample size is large enough, the population distribution does not
need to be normal.
B. The population must be normally distributed and the sample size must be large.
OC. The population must be normally distributed.
OD. There are no requirements on the shape of the distribution of the population.
Answer:
a) C. The population must be normally distributed.
b) P(x < 65.8) = 0.8159
c) P(x > 64.2) = 0.3015
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
n < 30, so the distribution of the population must be normal.
The correct answer is:
C. The population must be normally distributed.
(b) Assuming the normal model can be used, determine P(x < 65.8).
This is the pvalue of Z when X = 65.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65.8 - 62}{4.22}[/tex]
[tex]Z = 0.9[/tex]
[tex]Z = 0.9[/tex] has a pvalue of 0.8159.
So
P(x < 65.8) = 0.8159
(c) Assuming the normal model can be used, determine P(x > 64.2).
This is 1 subtracted by the pvalue of Z when X = 64.2. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.2 - 62}{4.22}[/tex]
[tex]Z = 0.52[/tex]
[tex]Z = 0.52[/tex] has a pvalue of 0.6985.
1 - 0.6985 = 0.3015
So
P(x > 64.2) = 0.3015
Please help! Will give Brainliest!
Steps 1-4 in attachment (#4 below)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x-1| -3Step-by-step explanation:
1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...
g(x) = 2|x|
__
2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.
g(x) = -2|x|
__
3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.
g(x) = -2|x| -3
__
4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...
g(x) = -2|x -1| -3
On a number line, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with number a. For example b= 11/4 when a= -11/4
A) b=-a
B) -b=-a
C) b-a=0
D) b(-a)=0
Answer:
B and A
Step-by-step explanation:
So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is AnswerWhat is the area of triangle ABC?
3 square units
0 7 square units
11 square units
15 square units
[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
The height of water in a bathtub ,h, is a function of time ,t, let p represent this function height is measured in inches and time in minutes
The complete question is;
The height of water in a bathtub,h, is a function of time,t. Let P represent this function. Height is measured in inches and time in minutes.
Match each statement in function notation with a description.
A: P(0) = 0
B: P(4) = 10
C: P(10) = 4
D: P(20) = 0
1:After 20 minutes, the bathtub is empty.
2:The bathtub starts out with no water.
3:After 10 minutes, the height of the water is 4 inches.
4:The height of the water is 10 inches after 4 minutes.
Answer:
-option D is the correct answer for sentence 1.
-option A is the correct answer for sentence 2.
-option C is the correct answer for sentence 3.
-option B is the correct answer for sentence 4
Step-by-step explanation:
The height of water in a bathtub h is a function of time t.
-If t = 20 minutes, then height of water represented by P is empty so, P(20) = 0. Thus, option D is the correct option for sentence 1.
-The bath tub starts out with no water. Thus, P(0) = 0. So option A is the correct option for sentence 2.
-After 10 minutes, the height of the water is 4 inches. Thus, P(10) = 4. So, option C is the correct option for sentence 3.
- The height of the water is 10 inches after 4 minutes. Thus, P(4) = 10. So option B is the correct answer for sentence 4
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) 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 = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. What is the probability that the next customer will request mid-grade gas and fill the tank
Answer:
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Step-by-step explanation:
In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:
probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks
probability that the next customer will request mid-grade gas and fill the tank= 30%*60%
probability that the next customer will request mid-grade gas and fill the tank= 0.1800
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
According to a recent census, 16% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which has a random sample of 437 county residents, and found that 44 of those surveyed are of Hispanic origin.Randomization condition:Choose the correct statement.Select one:a. The 437 county residents were a voluntary response sample of all county residents.b. The 437 county residents is a systematic response sample of all county residents.c. The 437 county residents were a random sample of all county residents.
Answer:
Option C is correct.
The 437 county residents were a random sample of all county residents.
a) If p is the proportion of Hispanics in the county,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.35
b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.
c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
Test statistic = -4.09
p-value = 0.000043
d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.
Step-by-step explanation:
According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.
a) 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, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).
Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).
The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).
Mathematically,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.16
b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.
Hence, the model of this test is two-tailled, one-proportion test.
And the major conditions for an hypothesis test is that
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.
- The sample must be a normal distribution sample or approximate a normal distribution.
The conditions to check this is that
np ≥ 10
and
np(1-p) ≥ 10
p = sample proportion = (44/437) = 0.101
np = 437×0.101 = 44 ≥ 10
np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10
The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.
c) So, we compute the t-test statistic
z = (x - μ)/σₓ
x = sample proportion = 0.101
μ = p₀ = The proportion we are comparing against = 0.16
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 437
σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144
z = (0.101 - 0.16) ÷ 0.0144
z = -4.093 = -4.09
checking the tables for the p-value of this z-statistic
Degree of freedom = df = n - 1 = 437 - 1 = 436
Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)
The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).
p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043
The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
d) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.000043
0.000043 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.
Hope this Helps!!!
Results of 99% confidence intervals are consistent with results of two-sided tests with which significance level? Explain the connection. A 99% confidence interval is consistent with a two-sided test with significance level alphaequals nothing because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.
Answer:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
Step-by-step explanation:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.
Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
Yes
Step-by-step explanation:
1 book = $4
2 books = 2*$4
3 books = 3*$4
4 books = 4*$4
5 books = 5*$4
This can be shown as: y=4x
y=ax+b is linear function, Irena is right
Wyoming fisheries contend that the mean number of cutthroat trout caught during a full day of fly-fishing on the Snake, Buffalo, and other rivers and streams in the Jackson Hole area is 4.0. To make their yearly update, the fishery personal asked a sample of fly-fishermen to keep a count of the number caught during the day. The numbers were: 4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6. At the 0.05 significance level, can we conclude that the mean number caught is greater than 4.0?
Answer:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Step-by-step explanation:
We have the following data given:
4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6
The sample mean and deviation from these data are:
[tex]\bar X=4.5[/tex] represent the sample mean
[tex]s=2.680[/tex] represent the sample deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =4[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to verify if the true mean is equal to 4, the system of hypothesis would be:
Null hypothesis:[tex]\mu =4[/tex]
Alternative hypothesis:[tex]\mu \neq 4[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the the info we got:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
you secure a mortgage to buy a house with a loan of $140,000 at 8.5% for 20 years. answer the following questions about that loan for the first two months of payments: a) what is the monthly payment? b)how much of the monthly payment goes toward interest when you submit your first payment? c)what is your balance after the first payment? d) how much of the monthly payment goes toward interest when you submit your second payment? e) what is your balance after the second payment?
Answer:
monthly payment $1214.951st month's interest $991.67balance after 1st payment $139,776.722nd month's interest $990.09balance after 2nd payment $139,551.86Step-by-step explanation:
The monthly interest rate is ...
[tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]
a) The monthly payment is given by the amortization formula:
A = Pr/(1 -(1+r)^-n)
where r is the monthly interest rate on a loan of amount P for n months.
A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95
The monthly payment is $1214.95.
__
b) The amount to interest is the product of the remaining principal and the monthly interest rate.
first month's interest = $140,000·0.0070833 = $991.67
__
c) The balance after the first payment is ...
new balance = $140,000 +991.67 -1214.95 = $139,776.72
__
d) The amount to interest for the second payment is computed the same way:
second month's interest = $139,776.72·0.00708333 = $990.09
__
e) The balance after the second payment is computed the same way:
new balance = $139,776.72 +990.09 -1214.95 = $139,551.86
Which of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph
A man driving a car leaves a point A drives up to 32.5 km in a direction of 070. A cyclist leaves the same point in a direction 130 travelling. After some few hours both drivers are 80 km apart. Use this information to answer 3 questions. (1). What is the distance covered by the cyclist at this time in 2 d.p. (2). Find the bearing of Cyclist from the Car. correct to 1 d.p. (3). Find the shortest distance between the car and the line of path of the cyclist, in 2 d.p.
Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
Learn more about the right angle triangle property here;
https://brainly.com/question/22790996
work out the value of 7^2+4^3 divided by 2^5
113/32
Step-by-step explanation:
7 squared is 49, 4 cubed is 64, 2 to the 5th power is 32.
49 plus 64 is 113 divided by 32
3.53125
Step-by-step explanation:
7^2+4^3/2^5
= 49+64/32
= 113/32
= 3.53125
Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
A researcher studying the effect of price promotions on consumers' expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Students in a marketing course are randomly assigned to view one or the other price history on a computer. Some students see a steady price, while others see regular promotions that temporarily cut the price. Then the students are asked what price they would expect to pay for the detergent.
Is this study an experiment? Why?A. Yes. Each subject is randomly assigned to a treatment.B. No. Each subject is randomly assigned to a treatment. C. Yes. Each subject is not randomly assigned to a treatment.D. No. Each subject is not randomly assigned to a treatment.
Answer:
A. Yes. Each subject is randomly assigned to a treatment
Step-by-step explanation:
In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.
In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.
What’s the correct answer for this question?
Answer
A. 18(3/4)π
Explanation
In the attached file