Zoe keeps track of the miles per gallon her car gets per week. She has accumulated the following data:

(1, 24), (2, 24.38), (3, 24.76), (4, 25.14)

What is the common difference or ratio?

Answer:

The proportion of sampled students that complete their degree is 0.74.

The lower bound for the 95% confidence interval is 0.659 and the upper bound is 0.819.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 115, \pi = \frac{85}{115} = 0.739[/tex]

Rounded to two decimal places, the proportion of sampled students that complete their degree is 0.74.

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.739 - 1.96\sqrt{\frac{0.739*0.261}{115}} = 0.659[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.739 + 1.96\sqrt{\frac{0.739*0.261}{115}} = 0.819[/tex]

The lower bound for the 95% confidence interval is 0.659 and the upper bound is 0.819.

Answer:

b=-4a-52 or -b=4a+52

Step-by-step explanation:

because you can subtract 4a to the other side or you can subtract 52 to the other side then subtract b to get the second equation.

hope this helps :)

The independent variable is the variable you change.

The dependent variable is the variable you measure that depends on the independent variable.

Since b is the independent variable, you need to isolate/get the variable "a" by itself in the equation:  [this is because "b" is the variable you change, and "a" is the variable you measure that results/depends on "b"]

4a + b = -52       Subtract b on both sides

4a + b - b = -52 - b

4a = -52 - b        Divide 4 on both sides to get "a" by itself

[tex]\frac{4a}{4} =\frac{-52-b}{4}[/tex]

[tex]a=-13-\frac{b}{4}[/tex]

4 divided by 1/2 as a fraction is equal to 8/1 or simply 8.

To divide a number by a fraction, you can multiply the number by the reciprocal of the fraction.

In this case, we have 4 divided by 1/2. The reciprocal of 1/2 is 2/1 (or simply 2).

So, we can rewrite the expression as:

4 * (2/1)

Multiplying these numbers, we get:

8/1

Therefore, 4 divided by 1/2 as a fraction is equal to 8/1 or simply 8.

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Answer:the answer is B

Step-by-step explanation:

Answer:

B  0 (0.3] U (9,18); only (9,18] contains viable times for machine 1

Step-by-step explanation:

The graph is 0<x<3 or 9<x<18

Answer:

See attached files

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Perimeter= 4× 3.5 in

=14 in

Answer:

14 in

Step-by-step explanation:

[tex]3 \frac{1}{2} = \frac{7}{2} in[/tex]

Perimeter of a square = 4 × sides

[tex] = 4 \times \frac{7}{2} = 14 \: \: in[/tex]

Answer:

a) The probability that exactly three of them fail the test is 2.61%.

b) The probability that fewer than three of them fail the test is 97.02%.

c) The probability that more than two of them fail the test is 2.98%.

d) It would not be unusual for none of them to fail the test

Step-by-step explanation:

For each automobile, there are only two possible outcomes. Either it fails the test, or it does not. The probability of an automobile faiiling the test is independent of other automobiles. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

8% fail the emissions test.

This means that [tex]p = 0.08[/tex]

Nine automobiles.

This means that [tex]n = 9[/tex]

a. Find the probability that exactly three of them fail the test.

This is [tex]P(X = 3)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{9,3}.(0.08)^{3}.(0.92)^{6} = 0.0261[/tex]

The probability that exactly three of them fail the test is 2.61%.

b. Find the probability that fewer than three of them fail the test.

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722[/tex]

[tex]P(X = 1) = C_{9,1}.(0.08)^{1}.(0.92)^{8} = 0.3695[/tex]

[tex]P(X = 2) = C_{9,2}.(0.08)^{2}.(0.92)^{7} = 0.1285[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4722 + 0.3695 + 0.1285 = 0.9702[/tex]

The probability that fewer than three of them fail the test is 97.02%.

c. Find the probability that more than two of them fail the test.

Either fewer than three(two or less) fail, or more than two do. The sum of the probabilities of these events is 100%. So

97.02 + p = 100

p = 2.98

The probability that more than two of them fail the test is 2.98%.

d. Would it be unusual for none of them to fail the test?

More than 2.5 standard deviations from the mean is unusual.

[tex]E(X) = np = 9*0.08 = 0.72[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{9*0.08*0.72} = 0.81[/tex]

0 > 0.72 - 2*0.81

So

It would not be unusual for none of them to fail the test

To find the probabilities, we use the binomial probability formula. For each part of the question, we plug in the appropriate values and calculate the probabilities. To determine if it would be unusual for none of them to fail, we calculate the probability of exactly zero failures.

To find the probabilities in this question, we can use the binomial probability formula: P(x) = (nCx) * p^x * (1-p)^(n-x), where n is the number of trials (automobiles selected), x is the number of successes (fail the test), and p is the probability of success (8% or 0.08).

a. For exactly three failures, we use x = 3 and n = 9 in the formula. P(3) = (9C3) * 0.08^3 * (1-0.08)^(9-3).

b. For fewer than three failures, we find the probabilities of 0, 1, and 2 failures and sum them up: P(<3) = P(0) + P(1) + P(2).

c. For more than two failures, we find the probabilities of 3, 4, 5, 6, 7, 8, and 9 failures and sum them up: P(>2) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9).

d. To determine if it would be unusual for none of them to fail, we calculate P(0) using x = 0 and n = 9 in the formula. If P(0) is very low, it would be considered unusual.

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Answer:

5/9

Step-by-step explanation:

Answer:

D(1)=300

D(n)=d(n-1)× 1/5

Step-by-step explanation:

The 1st term is 300 and the common ratio is 1/5. You have to multiply times 1/5 to get to the next number.

Answer:

300

1/5

Step-by-step explanation:

Answer:

6x∧4 + 14x³ - 12x²

Step-by-step explanation:

2x²(3x² + 7x - 6)

6x∧4 + 14x³ - 12x²

Tell me if I am wrong.

Can I get brainliest

Answer: 12 Centimeter

Step-by-step explanation:

3 by 4 multiplied by 2

3cm x 4cm x 2

= 12cm x 2

= 24cm

Answer:

[tex]x = 8\\y=-7[/tex]

Step-by-step explanation:

[tex]-3y-4x=-11\\3y-5x=-61[/tex]

In order to eliminate one of the variables you can add both equations.

[tex]-9x=-72\\x=\frac{-72}{-9} \\x=8[/tex]

Replace in one of the main equations to find y

[tex]3y-5x=-61\\3y-5(8)=-61\\3y-40=-61\\3y=-61+40\\3y=-21\\y=\frac{-21}{3} \\y=-7[/tex]

Replace in one of the main equations to prove that your answers are correct.

[tex]-3y-4x=-11\\-3(-7)-4(8)=-11\\21-32=-11\\-11=-11[/tex]

Answer:

232.727

Step-by-step explanation:

Answer:

232.727272727

Step-by-step explanation:

just calculate it

Answer:

C. 324 square inches

Step-by-step explanation:

The area of the post is 240, and the sign is 84 including the triangle. 240 + 84, is 324

Answer:

1/16

Step-by-step explanation:

The spinner has 8 equal parts.

The probability of spinning a 5 is: 1/8 (because there is only one 5 to choose and 8 total parts that could be landed on).

The probability of spinning an even number is: 4/8 = 1/2 (because there are 4 even numbers, 2 4 6 8, and there are 8 total parts that could be landed on).

Now, we need to multiply these two probabilities together:

(1/8) * (1/2) = 1/16

Hope this helps!

Answer:

1/16

Step-by-step explanation:

Spinner has 8 sections:

1,2,...8

P(5) = 1/8

P(even) = 4/8 = 1/2

1/8 × 1/2

1/16

Answer:

  x + 3y = 3

Step-by-step explanation:

The standard form equation ...

  ax +by = c

has slope -a/b. Here, we want -a/b = -1/3, and we want a > 0. We can choose ...

  a = 1, b = 3

and we can find the constant c using the given point.

 x +3y = 12 +3(-3) = 3

The desired standard-form equation is ...

  x + 3y = 3

Answer:

Correct option is (d).

Step-by-step explanation:

A hypothesis test for single mean can be used to determine the significance of the claimed value of the population mean μ.

Now there are two test for mean:

A z-test is used when it is provided that the population is normally distributed, the sample is large and the population standard deviation value is provided.

A t-test is used when it is assumed that the population is normally distributed, the sample is large enough and the population standard deviation is not known.

So, in case there is no information about the population standard deviation (σ) but the sample standard deviation is either given or can be calculated from the provided data set, then the hypothesis test for single mean can be performed using the t-test.

Hence, the choice between a z-test and a t-test for a population mean depends primarily on whether the given standard deviation is from the population or the sample.

Thus, the correct option is (d).

Answer:

Line C

Step-by-step explanation:

I picked this answer because the slope of the line is 4, which is -12/-3.

If this answer is correct, please make me Brainliest!

The required situation could be modeled with the equation 40 ÷ 8 = 5 as "There are eight in each of the 40 groups. Which groupings are there, exactly?"

In mathematics, divides left-hand operands into right-hand operands in the division operation.

The equation is given in the question

40 ÷ 8 = 5

An equation of this kind may be used to model any situations in which 40 items are divided into 8 or 5 divisions. There are a few possibilities:

"There are eight in each of the 40 groups. Which groupings are there, exactly?"

"There are a total of 40, separated into 8 categories. In how many groups are there?"

Thus, the above situations could be modeled with the equation 40 ÷ 8 = 5.

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Answer:

it depends

Step-by-step explanation:

If you divide the fraction by a number greater than 1 then you will have a smaller fraction. If you divide the fraction by a number equal to 1 then you will have the same fraction. If you divide the fraction by a positive number smaller than 1 then you will have a greater fraction.

Answer:

Linearly independent

Step-by-step explanation:

let a,b,c be element of F. for all x element of F.

1) if a, b and c are zero then they are independent

2) if not all a,b,c are zero then it is independent.

Now lets write it as a linear combination

 i.e  8a +b Sinx +c Cosx = 0

equating the coefficients we have

: 8a =0 hence a = 0

: b Sinx = 0

b = 0

: c Cos x = 0

c is not 0

Hence it is Linearly independent

Final answer:

Linearly test the set {f(x) = 8, g(x) = sin(x), h(x) = cos(x)} for independence. If dependent, express one function as a combination of others.

Explanation:

To test for linear independence in the set ℱ = {f(x) = 8, g(x) = sin(x), h(x) = cos(x)}, we can see if the determinant of the matrix formed by the functions is zero. If it is, the set is linearly dependent. If the set is linearly dependent, we can write one function as a linear combination of the others, for example, h(x) = √(g(x)^2 + f(x)^2).

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 100g

For the alternative hypothesis,

µ < 100g

Due to the <, It means that it is left tailed test.

Since the number of samples is large, the population standard deviation is given, the z test would be used. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 100g

x = 99 g

σ = 1g

n = 30

z = (99 - 100)/(1/√30) = - 5.48

Looking at the normal distribution table, the probability corresponding to the z score is less than 0.00001

P value < 0.00001

The p-value is approximately 0, which means there is strong evidence to support the consumer advocacy group's suspicion that the company is under-filling the cans of caviar.

Step 1

To determine whether the consumer advocacy group's suspicion is statistically significant, we perform a hypothesis test. We can use a one-sample z-test since we know the population standard deviation.

The null hypothesis [tex](\(H_0\))[/tex] and the alternative hypothesis [tex](\(H_a\))[/tex] are:

- [tex]\(H_0: \mu = 100\)[/tex] (the mean weight is 100 grams)

- [tex]\(H_a: \mu < 100\)[/tex] (the mean weight is less than 100 grams)

Given:

- Population mean [tex](\(\mu\))[/tex] = 100 grams

- Sample mean [tex](\(\bar{x}\))[/tex] = 99 grams

- Population standard deviation [tex](\(\sigma\))[/tex] = 1 gram

- Sample size [tex](\(n\))[/tex] = 30

Step 2

First, calculate the standard error of the mean (SEM):

[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{1}{\sqrt{30}} \approx 0.1826 \][/tex]

Next, calculate the z-score:

[tex]\[ z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{99 - 100}{0.1826} \approx -5.48 \][/tex]

Now, we find the p-value corresponding to this z-score. Using the standard normal distribution table or a calculator, we find the probability that z is less than -5.48.

The p-value for z = -5.48 is extremely small. For practical purposes, it is close to 0.

Therefore, the p-value is:

[tex]\[ \text{P-value} \approx 0 \][/tex]

Since the p-value is significantly less than the common significance levels (e.g., 0.05, 0.01), we reject the null hypothesis.

Answer:

120 feet in total

Step-by-step explanation:

Hi there! I'm glad I was able to help you out!

We are given that one racetrack is 40 yards long in length.

We also know that there are three feet in one yard alone. In order to get the answer to this math problem, all we have to do is multiply 40 by 3, where the 40 represents the amount of yards and the 3 represents the amount of feet IN a single yard.

40 × 3 = 120

Therefore, there are 120 feet in total, in terms of the racetrack's length.

I hope I was able to help you understand this a little bit more! :)

There are 120 feet in total, in terms of the racetrack's length.

Here, we have,

a racetrack is 40 yards long.

we know that,

1 yard = 3 feet

We are given that one racetrack is 40 yards long in length.

We also know that there are three feet in one yard alone.

In order to get the answer to this math problem, all we have to do is multiply 40 by 3,

where the 40 represents the amount of yards

and the 3 represents the amount of feet IN a single yard.

40 × 3 = 120

Therefore, there are 120 feet in total, in terms of the racetrack's length.

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Answer:

Divide both by 3

Step-by-step explanation:

I figured it out that you divide it by three because the divisible rule for 3 is that you add up all the digitd in the number and if it’s divisible by three than it is a multiple of 3. In this case for the numerator I added 4+4+5+5 = 18 which is divisible by three so the numerator is divisible. Now for the denominator you add 1+9+2+3+0+2+4= 21 which is also divisible by three. So you can divide both by 3.

Answer:

[tex]z=\frac{0.35 -0.42}{\sqrt{\frac{0.42(1-0.42)}{250}}}=-2.24[/tex]  

Step-by-step explanation:

Data given and notation  

n=250 represent the random sample taken

[tex]\hat p=0.35[/tex] estimated proportion of readers owned a particular make of car

[tex]p_o=0.42[/tex] is the value that we want to test

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that that the percentage is actually different from the reported percentage.:  

Null hypothesis:[tex]p=0.42[/tex]  

Alternative hypothesis:[tex]p \neq 0.42[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.35 -0.42}{\sqrt{\frac{0.42(1-0.42)}{250}}}=-2.24[/tex]  

Answer:

a) For this case we select a sample size of n =9. And the distribution for the sample mean is given by:

[tex]\bar X \sim N (\mu , \sqrt{\frac{\sigma}{\sqrt{n}}}) [/tex]

With the following parameters:

[tex]\mu_{\bar X}= 96[/tex]

[tex]\sigma_{\bar X} = \frac{23.3}{\sqrt{9}} =7.767[/tex]

b) [tex] P(95< \bar X < 100)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for the limit we got:

[tex] z = \frac{95-96}{\frac{23.3}{\sqrt{9}}}= -0.129[/tex]

[tex] z = \frac{100-96}{\frac{23.3}{\sqrt{9}}}= 0.515[/tex]

[tex] P( -0.129 < Z< 0.515) = P(Z<0.515) -P(Z<-0.129) = 0.697-0.449= 0.248[/tex]

The sketch is on the figure attached

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(96,23.3)[/tex]  

Where [tex]\mu=96[/tex] and [tex]\sigma=23.3[/tex]

Part a

For this case we select a sample size of n =9. And the distribution for the sample mean is given by:

[tex]\bar X \sim N (\mu , \sqrt{\frac{\sigma}{\sqrt{n}}}) [/tex]

With the following parameters:

[tex]\mu_{\bar X}= 96[/tex]

[tex]\sigma_{\bar X} = \frac{23.3}{\sqrt{9}} =7.767[/tex]

Part b

For this case we want this probability:

[tex] P(95< \bar X < 100)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for the limit we got:

[tex] z = \frac{95-96}{\frac{23.3}{\sqrt{9}}}= -0.129[/tex]

[tex] z = \frac{100-96}{\frac{23.3}{\sqrt{9}}}= 0.515[/tex]

[tex] P( -0.129 < Z< 0.515) = P(Z<0.515) -P(Z<-0.129) = 0.697-0.449= 0.248[/tex]

The sketch is on the figure attached

Using the z-distribution, it is found that the researcher should select to measure 8 days.

The margin of error of a z-confidence interval is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The first step is finding the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.

In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.

For this problem, the variance is of 30º, hence [tex]\sigma = \sqrt{30}[/tex].

The number of days is n for which M = 4, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = 1.96\frac{\sqrt{30}}{\sqrt{n}}[/tex]

[tex]4\sqrt{n} = 1.96\sqrt{30}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{30}}{4}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{30}}{4}\right)^2[/tex]

[tex]n = 7.2[/tex]

Rounding up, the researcher should select to measure 8 days.

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To estimate the true mean water temperature within 4° with 95% confidence and a variance of 30°, the researcher should measure the temperature on approximately 8 days.

To determine the sample size needed to estimate the true mean water temperature in a lake within a margin of error of 4° with 95% confidence, we can use the formula for sample size in estimating a population mean with a known variance:

n = (Z^2 * σ^2) / E^2

where:

n is the required sample size,

Z is the Z-score corresponding to the desired confidence level (for 95% confidence, Z is approximately 1.96),

σ^2 is the variance of the water temperature (σ^2 = 30),

E is the margin of error (E = 4).

Substituting the values, we get:

n = ((1.96)^2 * 30) / (4^2)

n ≈ (3.8416 * 30) / 16

n ≈ 115.248 / 16

n ≈ 7.203

Rounding up to the nearest whole number, the researcher should select approximately 8 days to measure the water temperature to estimate the true mean within 4° with 95% confidence.

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Answer:

y=2x+2

Step-by-step explanation:

To find the y intercept of the equation you add 4 beacuse the point is 2 under the y intecrept and 2*2 is 4 so -2+4=2 so the y value of the y intercept is 2 so

y=2x+2

Answer:

y=2x+2

Step-by-step explanation:

Since we have a point and a slope, we can use the point slope formula:

y-y1=m(x-x1)

where m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point

We know the slope is 2, the y coordinate is -2, and the x coordinate is also -2, so we can substitute them in

y-y1=m(x-x1)

y- -2 =2(x - -2)

y+2=2(x+2)

Now we need to solve for/ isolate y

Distribute the 2

y+2=2*x+2*2

y+2=2x+4

Subtract 2 from both sides

y=2x+2