If the relationships below are given in the form (input, output) which pairing always describes a function?

Answer:

We conclude that the mean waiting time is less than 10 minutes.

Step-by-step explanation:

We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.

Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.3 minutes with a standard deviation of 1.5 minutes.

Let [tex]\mu[/tex] = mean waiting time.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 10 minutes      {means that the mean waiting time is more than or equal to 10 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 minutes      {means that the mean waiting time is less than 10 minutes}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

                     T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean waiting time = 7.3 minutes

             s = sample standard deviation = 1.5 minutes

             n = sample of occasions = 18

So, test statistics  =  [tex]\frac{7.3-10}{\frac{1.5}{\sqrt{18}}}[/tex]  ~ [tex]t_1_7[/tex]

                              =  -7.637

The value of t test statistics is -7.637.

Now, the P-value of the test statistics is given by the following formula;

               P-value = P( [tex]t_1_7[/tex] < -7.637) = Less than 0.05%

Since, our P-values of test statistics is less than the level of significance as 0.05% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the mean waiting time is less than 10 minutes.

Answer:

Jade's statement is incorrect because "8 divided by ½" does not mean the same thing as "½ of 8".

Explanation:

No, I don't agree with Jade's statement.

When we say "8 divided by ½", it means we are dividing 8 into two equal parts, each representing one-half. Mathematically, [tex]\(8 \div \frac{1}{2}\)[/tex] means we are dividing 8 by [tex]\(\frac{1}{2}\)[/tex] , which is equivalent to multiplying 8 by the reciprocal of [tex]\(\frac{1}{2}\)[/tex], which is 2. So:

[tex]\[ 8 \div \frac{1}{2} = 8 \times 2 = 16 \][/tex]

On the other hand, "½ of 8" means finding half of 8, which is indeed 4. However, this is not the same as "8 divided by ½".

Answer:

(a) The standard error of the mean in this experiment is $0.052.

(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.

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 means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=40\\\mu=\$3.82\\\sigma=\$0.33[/tex]

As n = 40 > 30, the distribution of sample mean is [tex]\bar X\sim N(3.82,\ 0.052^{2})[/tex].

(a)

The standard error is the standard deviation of the sampling distribution of sample mean.

Compute the standard deviation of the sampling distribution of sample mean as follows:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

    [tex]=\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052[/tex]

Thus, the standard error of the mean in this experiment is $0.052.

(b)

Compute the probability that the sample mean is between $3.78 and $3.86 as follows:

[tex]P(3.78<\bar X<3.86)=P(\frac{3.78-3.82}{0.052}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.86-3.82}{0.052})[/tex]

                               [tex]=P(-0.77<Z<0.77)\\=0.77935-0.22065\\=0.5587[/tex]

Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c)

If the difference between the sample mean and the population mean is less than $0.01 then:

[tex]\bar X-\mu_{\bar x}<0.01\\\\\bar X-3.82<0.01\\\\\bar X<\$3.83[/tex]

Compute the value of [tex]P(\bar X<3.83)[/tex] as follows:

[tex]P(\bar X<3.83)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.83-3.82}{0.052})[/tex]

                    [tex]=P(Z<0.19)\\=0.57535\\\approx 0.5754[/tex]

Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d)

Compute the probability that the sample mean is greater than $3.92 as follows:

[tex]P(\bar X>3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{3.92-3.82}{0.052})[/tex]

                    [tex]=P(Z<1.92)\\=0.97257\\\approx 0.9726[/tex]

Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.

The standard error is 0.0522. The probability of the sample mean lying in a certain range and the difference from the population mean being less than a certain value can be determined using Z-scores and a Z-table. The likelihood of the sample mean being more than a certain value can also be determined in the same way.

An economist is using the average price of a gallon of milk to measure inflation. The average price ($3.82) and the population standard deviation ($0.33) is known. Here are answers to your questions:

a. Standard Error of the mean: The Standard error (SE) is calculated by dividing the standard deviation by the square root of the sample size. So SE = Standard Deviation / √n = 0.33 / √40 = 0.0522 per gallon.

b. Probability of the sample mean between $3.78 and $3.86: This is a Z-score question. Z = (X- µ)/SE. So, first find the Z-scores for $3.78 and $3.86, and then find the probability corresponding to these Z-scores from the Z-table. This probability is the chance that the sample mean is between $3.78 and $3.86.

c. Probability of the difference: Similarly, find the Z-score for the difference of $0.01 and look up the probability in the Z-table. This gives the likelihood of the sample mean being less than $0.01 away from the population mean.

d. Likelihood the sample mean is greater than $3.92: Use the same method to work out the Z-score for $3.92. The Z-table gives you the probability of the sample mean being less than $3.92, so subtract that from 1 to get the probability of it being more than $3.92.

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A complimentary angle has to add up two angles to equal 90 degrees.

We have one angle which is 43.5 degrees, so all we have to do is subtract 43.5 degrees from 90 degrees to find the missing angle.

90 degrees minus 43.5 degrees is 46.5 degrees.

That means the missing angle is 46.5 degrees.

It should be noted that the complementary angles is 46.5°.

From the information given, measure of an angle is 43.5 degree. It should be noted that the sum of the angles in complementary angles equal 90°.

Therefore, the value of the remaining angle will be:

= 90 - 43.5°

= 46.5°

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Answer:

Step-by-step explanation:

CORRECT ANSWER IS : $641.51

Use the compound interest formula and substitute the given values: A=$500(1+0.0254)4(10). Simplify using the order of operations: A=$500(1.00625)40=$500(1.283026821)≈ $641.51.

After ten years, Matthew will have $641.51 in the account, rounded to the closest penny.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. [tex]A = P(1 + r/n)^{nt[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

We can use the formula for compound interest to calculate how much money Matthew will have in the account after 10 years:

[tex]A = P(1 + r/n)^{nt[/tex]

Where:

A = final amount

P = principal (initial amount invested) = $500

r = annual interest rate (as a decimal) = 0.025

n = number of times interest is compounded per year = 4 (quarterly)

t = time in years = 10

Plugging in the values, we get:

[tex]A = 500(1 + 0.025/4)^(4*10)\\A = 500(1.00625)^{40}\\A = 500(1.305011)[/tex]

A = $641.51

Therefore, Matthew will have $641.51 in the account after 10 years, rounded to the nearest cent.

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Answer:

HERE IS YOUR ANSWER

Step-by-step explanation:

4

Answer:

A) 120 cm^3

Step-by-step explanation:

area of triangle = 1/2 x 5 x 12 = 30

volume = 1/3 x 30 x 12 = 120

Answer:

A

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Plug in 3 for x, and the equation is 6 + 3, which is equal to 9.

Answer:

6 + x = 9

Step-by-step explanation:

If x equals 3

6 plus x (when x equals 3)

Thus, 6 plus 3

= 9

9 will be your answer

Answer:

  see below

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between triangle sides and trig functions. For the angle of interest, the diagram shows values for the Opposite side (12) and the Adjacent side (16.5). The mnemonic tells you that these are related to the Tangent of the angle:

  Tan = Opposite/Adjacent

  tan(θ) = (12/16.5)

Answer:

11.2

Step-by-step explanation:

20 percent of 14 is 2.8 14 minus 2.8 is 11.2

The equation of the line that has a slope of 5/2 and passes through the point (4, -9) is y = 5/2x -19.

The equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope and b is the y-intercept. We're given that this line has a slope of 5/2 and it passes through the point (4, -9).

Plugging the known values into the equation, we get: -9 = (5/2) * 4 + b. By solving for b, we find the y-intercept of the line.

-9 = 10 + b --> b = -9 - 10 = -19

So the equation of the line in slope-intercept form is y= 5/2x - 19

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Answer:

0 is an inflection point

1/4 is a local maximum.

Step-by-step explanation:

To begin with you find the first derivative of the function and get that

[tex]h'(x) = 3x^2 - 12x^3[/tex]

to find the critical points you equal the first derivative to 0  and get that

[tex]3x^2 - 12x^3 = 0, x = 0,1/4[/tex]

To find if they are maximums or local minimums you use the second derivative.

[tex]h''(x) = 6x-36x^2[/tex]

since [tex]h''(0) = 0[/tex] is neither an inflection point, and since [tex]h''(1/4) = -3/4 <0[/tex] then 1/4 is a maximum.

Answer:

34.86% probability that it will be huge​ success

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Receiving a favorable review.

Event B: Being a huge success.

Information on previous textbooks published show that 20 % are huge​ successes

This means that [tex]P(B) = 0.2[/tex]

99 % of the huge successes received favorable​ reviews

This means that [tex]P(A|B) = 0.99[/tex]

Probability of receiving a favorable review:

20% are huge​ successes. Of those, 99% receive favorable reviews.

30% are modest​ successes. Of those, 70% receive favorable reviews.

30% break​ even. Of those, 40% receive favorable reviews.

20% are losers. Of those, 20% receive favorable reviews.

Then

[tex]P(A) = 0.2*0.99 + 0.3*0.7 + 0.3*0.4 + 0.2*0.2 = 0.568[/tex]

Finally

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.2*0.99}{0.568} = 0.3486[/tex]

34.86% probability that it will be huge​ success

Answer:

2 people

Step-by-step explanation:

Total number of people (n) = 50

Borderlands II (B) = 20

Fortnite (F) = 33

Minecraft (M) = 19

Borderlands and Fortnite (B&F) = 15

Borderlands and Minecraft (B&M)= 10

All games (B&M&F) = 5

The number of people that claimed more than one game as their favorite (X) is given by:

[tex]X=M+B+F-n\\X=19+20+33-50\\X=22\ people[/tex]

Those people can be divided in B&F only, B&M only, M&F only and B&M&F:

[tex]X=(B\&M-B\&M\&F)+(B\&F-B\&M\&F)+(M\&F-B\&M\&F)+B\&M\&F\\X=B\&M+B\&F+M\&F-2*B\&M\&F\\22=10+15+M\&F-2*5\\M\&F=7\ people[/tex]

7 people claimed that Minecraft and Fortnite were their favorites however, 5 of those people claimed all of the games as their favorite. Therefore, only 2 people declared Minecraft and Fortnite (exclusively) as their favorites.

Answer:

2

Step-by-step explanation:

Answer:

(2). 26 (4). 547 (6). 3,132 (8). 46.1 (10). 10.6

Step-by-step explanation:

Answer:

1 2/4

Step-by-step explanation: 2/4 * 3 = 1 2/4

Answer:40 hr and  35 hr

Step-by-step explanation:

Given

Harris family sprinkler output rate is [tex]20\ L/\text{per hour}[/tex]

and Baker family sprinkler output rate is [tex]35\ L/\text{per hour}[/tex]

Total output of two is [tex]2025\ L[/tex]

Suppose Harris family sprinkler used for [tex]t_1[/tex] time and Baker family for [tex]t_2 [/tex]time then

[tex]20\times t_1+35\times t_2=2025\quad \ldots(i)[/tex]

and [tex]t_1+t_2=75[/tex]

[tex]t_1=75-t_2[/tex]

Substitute the value in [tex](i)[/tex]

[tex]\Rightarrow 20\times (75-t_2)+35t_2=2025[/tex]

[tex]\Rightarrow 1500-20t_2+35t_2=2025[/tex]

[tex]\Rightarrow 15t_2=525[/tex]

[tex]\Rightarrow t_2=\frac{525}{15}[/tex]

[tex]\Rightarrow t_2=35\ hr[/tex]

[tex]\therefore \ t_1=75-35=40\ hr[/tex]

Therefore Harris family use [tex]40\ hr[/tex] of sprinkler and Baker family use [tex]35\ hr[/tex] of sprinkler

Answer:

[tex] (0.79-0.72) -1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.0376[/tex]

[tex] (0.79-0.72) +1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.1024[/tex]

And the 95% confidence interval for the difference of the two proportions is given by:

[tex] 0.0376 \leq p_1 -p_2 \leq 0.1024[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] X_1 = 948[/tex] number of people that they read at least one book in the last 3 months in 2011

[tex]n_1 = 1200[/tex] the sample size selected for 2011

[tex] X_2 = 1080[/tex] number of people that they read at least one book in the last 3 months in 2015

[tex]n_2 = 1500[/tex] the sample size selected for 2015

The estimated proportions people that they read at least one book in the last 3 months for each year are given by:

[tex]\hat p_1 = \frac{948}{1200}= 0.79[/tex]

[tex]\hat p_2 = \frac{1080}{1500}= 0.72[/tex]

And the confidence interval for the true difference of proportions is given by:

[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]

The confidence level is 95% so then the significance is 0.05 or 5% and [tex]\alpha/2 =0.025[/tex] and the critical value for this case using the normal standard distribution is:

[tex]z_{\alpha/2}=\pm 1.96[/tex]

And replacing into the confidence interval formula we got:

[tex] (0.79-0.72) -1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.0376[/tex]

[tex] (0.79-0.72) +1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.1024[/tex]

And the 95% confidence interval for the difference of the two proportions is given by:

[tex] 0.0376 \leq p_1 -p_2 \leq 0.1024[/tex]

Answer:

( 11 b 2 + 7 ) ( 11 b 2 − 7 )

Step-by-step explanation:

Answer:

121b⁴ − 49 = (11b² + 7) • (11b² - 7)

Step-by-step explanation:

The difference of two squares.

Step 1: reformat equation

11²b² - 49

Step 2: Factoring: 121b⁴- 49

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

A² - B²

Factorization is : (11b² + 7) • (11b² - 7)

Answer:

(See explanation for further details)

Step-by-step explanation:

An approach is handling the trigonometric equation so that number of trigonometric functions can be reduce to one, in order to determine the periodicity of complete expression and therefore, to determine the complete set of solutions.

Answer:

4(x-3)(x+6)

Step-by-step explanation:

Factor out the 4

4(x2 + 3x - 18)

what 2 numbers add to 3 and multiply to - 18?

-3 and 6

therefore 4x2 + 12x − 72 = 4(x-3)(x+6)

Answer:

(4x² + 24x)- (12x + 72)

4x( x+ 6)- 12(x + 6)

ans = (4x - 12)(x + 6)

Answer:

slope = -3

Step-by-step explanation:

1) Rearrange eqn into slope intercept form

slope intercept form: y = mx + b

where...

m = the slope

b = the y-intercept (where the line crosses the y axis)

3x + y = 12

y = -3x+12

2) Know parallel rule. A line that runs parallel has the same slope but a different y-intercept

So the slope is: -3

Answer:

The median number of miles that Sam drove during those months is 1044 miles

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

For a set of n values

First we order the values in an increasing way.

If n is odd, the median is the value at the position (n+1)/2

If n is even, the median is the average of the values at the positions n/2 and (n/2) + 1

In this problem:

6 values

Ordered in an increasing way:

880, 997, 1002, 1086, 1534, 1637

6 is an even value.

6/2 = 3. The third element is 1002

6/2 + 1 = 4. The fourth element is 1086.

Average: (1002 + 1086)/2 = 1044

The median number of miles that Sam drove during those months is 1044 miles

Answer:

a) D. The group of all of the babies whose recorded weights were examined

b) A. The weights of the babies at birth

c) i) Ux' = u = 3370;

s.d = 43.95

ii) Ux' = u = 3370

s.d = 35.109

Step-by-step explanation:

Given:

Mean, u = 3370

Standard deviation = 582

a) Population in statistics involves every member of the group in study.

Here, the correct population is the group of all of the babies whose recorded weights were examined.

b) In statistics, variable involves data collected.

The correct variable is the weights of the babies at birth

c)

i) at X' = 175

Sample mean:

Ux' = u = 3370

Standard deviation:

[tex] \sigma x' = \frac{\sigma}{\sqrt{n}} = \frac{582}{\sqrt{175}} = 43.995 [/tex]

ii) at X' = 175

Sample mean:

Ux' = u = 3370

Stanard deviation:

[tex] \sigma x' = \frac{\sigma}{\sqrt{n}} = \frac{582}{\sqrt{350}} = 35.109 [/tex]

a. The population includes all babies whose recorded weights were examined, and the variable is the birth weights of the babies.

b. For sample sizes of 175, the mean birth weight remains 3370 grams, with a standard deviation of approximately 43.96 grams.

c.  For sample sizes of 350, the mean birth weight remains 3370 grams, with a standard deviation of approximately 31.15 grams.

Let's address each part of the question step-by-step to ensure clarity and accuracy.

Part (a): Identifying Population and Variable

To identify the correct population:

To identify the correct variable:

Hence, the correct answers are:

Part (b): Calculating Mean ([tex]\mu_\bar{x}[/tex]) and Standard Deviation ([tex]\sigma_\bar{x}[/tex]) for Sample Size 175

For samples of size 175, we need to find the mean and standard deviation of all possible sample means:

Part (c): Calculating Mean ([tex]\mu_\bar{x}[/tex]) and Standard Deviation ([tex]\sigma_\bar{x}[/tex]) for Sample Size 350

For samples of size 350, we perform similar calculations:

In summary, we have identified the population and variable, and calculated the mean and standard deviation for different sample sizes of 175 and 350.

Answer:

y= 7.5

Step-by-step explanation:

25y = 15y +75

-15y -15y

10y = 75

÷10 ÷10

y = 7.5

Answer:

figure it out

Step-by-step explanation:

Answer: b

Step-by-step explanation: ik

Answer:

is there a pic i need more info...

Step-by-step explanation:

the answer is b I'm sure

Answer:

a) The function that represents the amount of water as a function of time is

f(x) = 30,000 - 400x

b) The amount of water left in the sink after half an hour of starting to empty it

= 18,000 litres

c) The time it will take to empty the sink completely = 75 minutes.

Step-by-step explanation:

English Translation

A sink is emptied with a pump that extracts water at the rate of 400 liters per minute. when turning on the pump in the sink there were 30000 liters of water.

a) The time (in minutes) from when the pump is turned on is called x. find the function that represents the amount of water left in the sink as a function of time

b) Determine the amount of water left in the sink after half an hour of starting to empty it.

c) Determine the time it will take to empty the sink completely?

a) Speed is a quantity that is described as the rate of change of another quantity with time.

So, the speed of emptying the sink is given as

Speed = (Amount of water emptied) ÷ (Time taken to empty that amount of water).

The Speed of emptying the sink is given as 400 litres/min

Time taken to empty the sink = x

Let the amount of water left in the sink, a function of the time taken to empty the sink, be f(x)

Amount of water emptied = 30,000 - f(x)

400 = [30000 - f(x)] ÷ x

30000 - f(x) = 400x

f(x) = 30,000 - 400x

b) Determine the amount of water left in the sink after half an hour of starting to empty it.

f(x) = 30000 - 400x

x = 30 mins

f(x) = 30000 - 400(30) = 18,000 litres

c) Determine the time it will take to empty the sink completely?

f(x) = 30000 - 400x

when the sink is completely empty, the amount of water left in the sink is 0 litres, that is, f(x) = 0 litres

0 = 30000 - 400x

400x = 30000

x = (30000/400) = 75 minutes.

Hope this Helps!!!