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]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

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

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!!!

She will receive a lot more money because she is already retired from work already and will win as bit more money

Answer:

156 minutes

Step-by-step explanation:

So we need to create an equation to represent how Frank's phone company bills him

So the phone company charges an $8 monthly fee, so this value remains constant and will be our "y-intercept"

They then charge $0.06 for every minute he talks, this will be our "slope"

Combining everything into an equation, we have: y = 0.06x + 8

Now since we were given Franks phone bill total and want to figure out how many minutes he used, we just need to solve the equation for x and plug in our known y value

Frank used up a total of 156 minutes

Answer:

Step-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

Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.

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

Answer:

answer B [tex]\boxed{ \ 569 \ }\\[/tex]

Step-by-step explanation:

f(8)=-2*8+5=-11

g(8)=9*8*8+4=580

f(8)+g(8)= -11+580=569

Answer:

a) The velocity at which the water leaves the gun = 37.66 m/s

b) The volume rate of flow = (1.183 × 10⁻⁴) m³/s

c) The water hits the ground 18.64 m from the point where the water gun was shot.

Step-by-step explanation:

a) Using Bernoulli's equation, an equation that is based on the conservation of energy.

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

The two levels we are considering is just inside the water reservoir and just outside it.

ρgh is an extension of potential energy and since the two levels are at the same height,

ρgh₁ = ρgh₂

Bernoulli's equation becomes

P₁ + ½ρv₁² = P₂ + ½ρv₂²

P₁ = Pressure inside the water reservoir = 8 atm = 8 × 101325 = 810,600 Pa

ρ = density of water = 1000 kg/m³

v₁ = velocity iof f water in the reservoir = 0 m/s

P₂ = Pressure outside the water reservoir = atmospheric pressure = 1 atm = 1 × 101325 = 101,325 Pa

v₂ = velocity outside the reservoir = ?

810,600 + 0 = 101,325 + 0.5×1000×v₂²

500v₂² = 810,600 - 101,325 = 709,275

v₂² = (709,275/500) = 1,418.55

v₂ = √(1418.55) = 37.66 m/s

b) Volumetric flowrate is given as

Q = Av

A = Cross sectional Area of the channel of flow = πr² = π×(0.001)² = 0.0000031416 m²

v = velocity = 37.66 m/s

Q = 0.0000031416 × 37.66 = 0.0001183123 m³/s = (1.183 × 10⁻⁴) m³/s

c) If the height of gun above the ground is 1.2 m. Where does the water hit the ground?

The range of trajectory motion is given as

R = vT

v = horizontal component of the velocity = 37.66 m/s

T = time of flight = ?

But time of flight is given as

T = √(2H/g) (Since the initial vertical component of the velocity = 0 m/s

H = 1.2 m

g = acceleration due to gravity = 9.8 m/s²

T = √(2×1.2/9.8) = 0.495 s

Range = vT = 37.66 × 0.495 = 18.64 m

Hope this Helps!!!

Answer:

A

Step-by-step explanation:

Calculate the products in the multiple choice and see if any equal the product in the problem.

Hence as the products calculated in choice A equal that in the problem;the answer is A

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

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.

Answer:

2880

Step-by-step explanation:

Consider the 5 boys to be 1 group.  The boys and 3 girls can be arranged in 4! ways.

Within the group, the boys can be arranged 5! ways.

The total number of permutations is therefore:

4! × 5! = 2880

Answer:

5.94% of customers carries a balance of GH¢100 or lower.

82.64% of customers carries a balance of GH¢500 or lower.

0% of current account customers carries average daily balances exactly equal to GH¢500.

76.7% of customers maintains account balance between GH¢100 and GH¢500

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 350, \sigma = 160[/tex]

What percentage of customers carries a balance of GH¢100 or lower?

This is the pvalue of Z when X = 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 350}{160}[/tex]

[tex]Z = -1.56[/tex]

[tex]Z = -1.56[/tex] has a pvalue of 0.0594

5.94% of customers carries a balance of GH¢100 or lower.

What percentage of customers carries a balance of GH¢500 or lower?

This is the pvalue of Z when X = 500.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 350}{160}[/tex]

[tex]Z = 0.94[/tex]

[tex]Z = 0.94[/tex] has a pvalue of 0.8264

82.64% of customers carries a balance of GH¢500 or lower.

What percentage of current account customers carries average daily balances exactly equal to GH¢500?

In the normal distribution, the probability of finding a value exactly equal to X is 0. So

0% of current account customers carries average daily balances exactly equal to GH¢500.

What percentage of customers maintains account balance between GH¢100 and GH¢500?

This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 100.

From b), when X = 500, Z = 0.94 has a pvalue of 0.8264

From a), when X = 100, Z = -1.56 has a pvalue of 0.0594

0.8264 - 0.0594 = 0.767

76.7% of customers maintains account balance between GH¢100 and GH¢500

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

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

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

Answer

A. 18(3/4)π

Explanation

In the attached file

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

Answer:

Option (3)

Step-by-step explanation:

A stone has been thrown off towards the ground from a height [tex]h_{0}[/tex] = 18 feet

Initial speed of the stone 'u' = 4.5 feet per second

Since height 'h' of a projectile at any moment 't' will be represented by the function,

h(t) = ut - [tex]\frac{1}{2}(g)(t)^2[/tex] + [tex]h_{0}[/tex]

h(t) = 4.5t - [tex]\frac{1}{2}(32)t^2[/tex]+ 18 [ g = 32 feet per second square]

h(t) = 4.5t - 16t² + 18

h(t) =-16t² + 4.5t + 18

Therefore, Option (3) will be the answer.

Solution,

Radius=2 m

Area =pi r^2

= 3.142*(2)^2

=12.568 m^2

hope it helps

Good luck on your assignment

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.

Answer:

option 2

Step-by-step explanation:

4^2=16/8=2.  4^2=16/16=1.  2-1=1

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.

Answer:

-4 · [tex]4^{7}[/tex]

Step-by-step explanation:

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

Answer: The volume of the​ sculpture is 141.84 cubic-feet

Step-by-step explanation: Please see the attachments below

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

Answer:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

Step-by-step explanation:

For this case we have this equation given:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2