Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 The test statistic to test the null hypothesis equals _____. a. 4.17 b. 28.8 c. 1.8 d. .432

Final answer:

To find the total distance Cannor travels, multiply his hourly distance of 62 1/4 miles by the total travel time of 4 hours, resulting in 249 miles.

Explanation:

The question asks about calculating the total distance traveled by Cannor on Saturday. Since Cannor drives 62 1/4 miles each hour and travels for 4 hours, we can find the total distance by multiplying the number of miles driven in an hour by the number of hours traveled.

To calculate this, convert 62 1/4 to an improper fraction which is 249/4 and multiply it by 4 (the number of hours):

Total Distance = (249/4 miles/hour) × 4 hours

When we do the multiplication, the hours unit cancels out and we get:

Total Distance = 249 miles

This calculation shows how far Cannor will travel altogether if he maintains his speed for the entire duration of his trip.

Answer:

x^2 - 64

Step-by-step explanation:

A difference of squares is a special product in the form (a^2 - b^2)..their factored form is (a - b)(a + b)..

Thus here a = x and b = 8, thus if x + 8 is a factor, then x - 8 is also a factor..

(x + 8)(x - 8) <-- expand this out using difference of squares rules..

= (x)^2 - (8)^2 

= x^2 - 64 <-- answer...

You could also expand that using FOIL (FOIL - first, outer, inner, last)..

(x + 8)(x - 8) 

= (x)(x) + (x)(-8) + (8)(x) + (8)(-8) 

= x^2 - 8x + 8x - 64 <-- the -8x and 8x cancels out..leaving you with..

= x^2 - 64

The difference of squares that has a factor of x+8 is x² - 64.

An algebraic identity is an equality that holds for any values of its variables.

For example, the identity ( x + y )² = x² + 2xy + y²

(x+y)² = x² + 2xy + y²

(x+y)²=x²+2xy+y² holds for all values of x and y.

As, Difference of two squares

x² - y² = (x - y)(x + 8)

So, for difference of squares that has (x -8) as one of the factor.

The other factor is (x + 8)

So, we can write

(x - 8)(x + 8) = x² - 8²

                    =  x² - 64.

Learn more about Algebraic Identity here:

https://brainly.com/question/28853516

#SPJ6

Answer:

x=test value before , y = test value after

The system of hypothesis for this case are:

Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]

Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]

If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:

Null hypothesis: [tex]\mu_d = 0[/tex]

Alternative hypothesis: [tex]\mu_d \neq 0[/tex]

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation  

x=test value before , y = test value after

The system of hypothesis for this case are:

Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]

Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]

If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:

Null hypothesis: [tex]\mu_d = 0[/tex]

Alternative hypothesis: [tex]\mu_d \neq 0[/tex]

Answer:

line graph

Step-by-step explanation:

Answer:

The area of a sector of a circle = 19.2325

Step-by-step explanation:

Explanation:-

Given θ be the measure of angle and radius of circle

The area of a sector of a circle (see diagram)

                                        [tex]A = \frac{theta}{360} \pi r^{2}[/tex]

Given the radius of circle 'r' = 7cm and given angle θ = 45°

The area of a sector of a circle

                                      [tex]A = \frac{45}{360} \pi( 7)^{2}[/tex]

  Use pi =3.14

                                      [tex]A = \frac{45X 3.14( 7)^{2}}{360}[/tex]

                                      A = 19.2325

Final answer:-

The area of a sector of a circle = 19.2325

Answer:

its 9 to 12 is greater than 4 to 6.

Step-by-step explanation:

As per the given question, the correct option is the ratio 9 to 12 is greater than 4 to 6.

In comparing the ratios 9 to 12 and 4 to 6, we first need to simplify both ratios. The ratio 9 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 3. This gives us a simplified ratio of 3 to 4.

Similarly, the ratio 4 to 6 can be simplified by dividing both numbers by their greatest common divisor, which is 2, giving us a simplified ratio of 2 to 3.

If we convert both ratios to decimals by dividing the first number by the second in each pair, we'll find that 9/12 = 0.75 and 4/6 = 0.67, which shows that the first ratio is greater. Therefore, we find that the correct statement is the ratio 9 to 12 is greater than 4 to 6.

https://brainly.com/question/33628538

#SPJ3

Answer:

The second number is 40

Step-by-Step:

There is a pattern in the ratio table: you need to multiply the first number by 4, and the answer is the second number. So if the first number is 10, you will need to multiply that by 4 to get the second number. So the second number is 40

Answer:

1323

Step-by-step explanation:

Answer:

The vertex of the function is at (2,3).

Step-by-step explanation:

I graphed the equation on the graph below.

If this answer is correct, please make me Brainliest!

The vertex of the graph of the function [tex]f(x)=2(x-2)^2+3[/tex] is at (2, 3). This is obtained by comparing the given function of the graph with the vertex form function of a parabola.

Given that the function of the graph is [tex]f(x)=2(x-2)^2+3[/tex].

We have the vertex form as [tex]y=a(x-h)^2+k[/tex]

So, the graph shows a parabola for the given equation.

On comparing the given equation with the vertex form,

f(x)=y, a=2, h=2, and k=3.

Then, (h, k)=(2, 3)

It is shown in the graph below.

Therefore, the vertex of the graph is at the point (2, 3).

Learn more about the vertex of a graph here:

https://brainly.com/question/1480401

#SPJ2

Answer:

Step-by-step explanation:

4 % of 600 over 8 months is 16

600-16=584

Answer:

2 containers should be used

As the system improves, neither more or fewer containers be required

Step-by-step explanation:

According to the given data we have the following:

D=83 pieces per hour.

T=80 minutes=1.33 hour

X=0.18

C=53

In order to calculate how many containers should be used we would have to use the following formula:

Number of containers=DT(1+X)

                                         C

Number of containers=(83)(1.33)(1+0.18)

                                                 53

Number of containers=2.45=2

2 containers should be used.

As the system improves, neither more or fewer containers be required

Answer:

a) Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Eᶜ) = (1/2) = 0.5

P(Upper E Superscript c) = (1/2) equals 0.5

Step-by-step explanation:

The set that represents the universal set with all the sample spaces is set S and is given by

Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

S = {7,8,9,10,11,12,13,14,15,16,17,18}

Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet

Event E = {7,8,9,10,11,12}

a) Find Eᶜ

Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E

Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Upper E Superscript c) = P(Eᶜ)

= n(Eᶜ) ÷ n(S)

Each outcome is equally likely, hence,

n(Eᶜ) = number of outcomes in the event Eᶜ = 6

n(S) = number of outcomes in the set S = 12

P(Eᶜ) = (6/12) = (1/2) = 0.5

Hope this Helps!!!

Answer:

232 total votes

Step-by-step explanation:

change 80% to a decimal.... .8 and then multiply that by 290

Answer:

232

Step-by-step explanation:

80% of 290 is 232

290-232 is 58

20% of 290 is 58

Answer:

196

Step-by-step explanation:

7 x 13 = 91 + 105

Answer:

6 seconds

Step-by-step explanation:

The ball will hit the ground when its height is 0, so you can plug this into the equation to find your answer.

-16t^2+96t=0

Factoring out -16t, you get:

-16t(t-6), meaning that the solutions are 0 and 6 seconds. Since 0 is the starting point, the answer is 6 seconds. Hope this helps!

Answer:

  $4,508.64

Step-by-step explanation:

The compound interest formula can answer this for you.

  A = P(1 +r/n)^(nt)

where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).

Putting the given values into the formula, doing the arithmetic tells us ...

  A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64

There will be $4,508.64 in the account at the end of 6 years.

Answer:

f(-2) = 0

Step-by-step explanation:

If x + 2 is a factor, then f(x) = 0 when x + 2 = 0.

x + 2 = 0

x = -2

f(-2) = 0

For the polynomial, f(0) = 2 and f(-2) = 0.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given x+2 is a factor,

And values of x from the options are x = 0, -2 and 2.

We will put the values of x to the factor,

f(0) = 0 +2 = 2

f(-2) = -2 +2 = 0

f(2) = 4

Therefore from the result only two options satisfy the factor and those are f(0) = 2 and f(-2) = 0.

To learn more about the Polynomials;

brainly.com/question/11536910

#SPJ2

Answer:

Step-by-step explanation:

84/128=.65625

.65625x100=65.625=66%

Final answer:

To calculate the percentage of adult tickets sold for the school play, subtract the student tickets from the total tickets sold to find the number of adult tickets (44), and then divide by the total number of tickets and multiply by 100 to get the percentage, which is approximately 34%.

Explanation:

The question asks us to find what percent of the total tickets sold at a school play were adult tickets. Alton High School sold a total of 128 tickets, of which 84 were student tickets. To calculate the number of adult tickets, we subtract the number of student tickets from the total number of tickets: 128 - 84 = 44 adult tickets.

Next, we calculate the percent of adult tickets out of the total tickets sold by using the formula:

Percent = (Number of adult tickets / Total number of tickets)  imes 100

Plugging in our numbers, we get:

Percent = (44 / 128)  imes 100

Percent = 0.34375  imes 100

Percent ≈ 34%

Rounded to the nearest percent, we find that approximately 34% of the tickets sold were for adults.

Answer:

p^7

Step-by-step explanation:

p^5⋅p^2  =   p ^(5+2) =  p^7

Answer:

Take the square root of each side

D (x+b/2a)  =±sqrt( (b^2-4ac)/ 4a^2)

Step-by-step explanation:

We have

(x+b/2a) ^2 = (b^2-4ac)/ 4a^2

We need to take the square root of each side to continue to isolate x

(x+b/2a)  =±sqrt( (b^2-4ac)/ 4a^2)

Answer:

Option 3

Step-by-step explanation:

[x + b/2a]² = (b² - 4ac)/4a²

Taking square root both sides, you get this:

x + b/2a = +/- sqrt(b² - 4ac)/2a

Remember we're trying to make x the subject,

So does get rid of the square by applying square root both sides

Answer:

The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%

Step-by-step explanation:

Average time to find a new job for someone over 55 years = μ = 22 weeks

Standard deviation = σ = 2 weeks

We have to find the probability that if 8 workers are selected at random what will be the probability that it will take them more than 20 weeks to find a job. So, this means that the sample size is n = 8.

Since, the distribution is normal and we have the value of population standard deviation, we will use the z-distribution to find the desired probability. For this, first we need to convert the value (20 weeks) to its equivalent z-score. The formula to calculate the z-score is:

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

x = 20, converted to z-score will be:

[tex]z=\frac{20-22}{\frac{2}{\sqrt{8}}}=-2.83[/tex]

Thus, probability of time being greater than 20 weeks is equivalent to probability of z score being greater than - 2.83.

i.e.

P( X > 20 ) = P( z > -2.83 )

Using the z-table we can find this probability:

P( z > -2.83 ) = 1 - P( z < -2.83)

= 1 - 0.0023

= 0.9977

Since, P( X > 20 ) = P( z > -2.83 ), we can conclude that:

The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%

The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 99.77%.

To solve this problem, we need to use the concepts of the sampling distribution of the sample mean and the properties of the normal distribution. Here are the steps to find the probability that the average time for eight workers over the age of 55 to find a job is more than 20 weeks:

Step 1: Understand the given data

- Mean time[tex](\(\mu\))[/tex] = 22 weeks

- Standard deviation [tex](\(\sigma\))[/tex] = 2 weeks

- Sample size [tex](\(n\))[/tex]  = 8 workers

The sample mean [tex]\(\bar{X}\)[/tex] for a sample of size (n) from a normal distribution with mean [tex]\(\mu\)[/tex] and standard deviation [tex]\(\sigma\)[/tex] is itself normally distributed with:

- Mean:[tex]\(\mu_{\bar{X}} = \mu\)[/tex]

- Standard deviation: [tex]\(\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}\)[/tex]

Calculate the standard deviation of the sample mean:

[tex]\[\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{8}} = \frac{2}{2.828} \approx 0.707\][/tex]

We want to find the probability that the sample mean [tex]\(\bar{X}\)[/tex] is greater than 20 weeks. First, we convert this to a Z-score:

[tex]\[Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}}\][/tex]

Calculate the Z-score for [tex]\(\bar{X} = 20\)[/tex]  weeks:

[tex]\[Z = \frac{20 - 22}{0.707} = \frac{-2}{0.707} \approx -2.83\][/tex]

Using standard normal distribution tables or a Z-score calculator, we find the probability that (Z) is less than -2.83.

The cumulative probability for (Z = -2.83) is approximately 0.0023. This represents the probability that the sample mean is less than 20 weeks. However, we want the probability that the sample mean is more than 20 weeks:

[tex]\[P(\bar{X} > 20) = 1 - P(\bar{X} \leq 20) = 1 - 0.0023 = 0.9977\][/tex]

The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 0.9977, or 99.77%.

Therefore, we can conclude that there is a very high probability (99.77%) that the average time for these eight workers to find a job is more than 20 weeks.

Answer:

x=3

Step-by-step explanation:

24-9

15/5

3

x=3

Answer:

x = 3

Step-by-step explanation:

3 * 5 + 9 =24

We have been given that the population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000.

We are asked to find the time it will take the fish population to reach 1,000,000.

We will use exponential growth formula to solve our given problem.

An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Growth rate in decimal form,

x = Time

[tex]2.2\%=\frac{2.2}{100}=0.022[/tex]

[tex]y=350,000\cdot (1+0.022)^x[/tex]

To find the time for the fish population to reach 1,000,000, we will substitute [tex]x=1,000,000[/tex] in our equation as:

[tex]1,000,000=350,000\cdot (1+0.022)^x[/tex]

[tex]1,000,000=350,000\cdot (1.022)^x[/tex]

[tex]\frac{1,000,000}{350,000}=\frac{350,000\cdot (1.022)^x}{350,000}[/tex]

[tex]2.8571428571428571=(1.022)^x[/tex]

Now we will take natural log on both sides:

[tex]\text{ln}(2.8571428571428571)=\text{ln}((1.022)^x)[/tex]

[tex]\text{ln}(2.8571428571428571)=x\cdot \text{ln}(1.022)[/tex]

[tex]x=\frac{\text{ln}(2.8571428571428571)}{\text{ln}(1.022)}[/tex]

[tex]x=\frac{1.0498221244986776733}{0.0217614917815127}[/tex]

[tex]x=48.2421947[/tex]

Upon rounding to nearest tenth, we will get:

[tex]x\approx 48.2[/tex]

Therefore, it will take approximately 48.2 years for the fish population to reach 1,000,000.

Answer:

47.7

Step-by-step explanation:

right answer

Answer:

2664

Step-by-step explanation:

(2285gallons - 1619gallons) =

666 gallons * 4quarts(in a gallon) =

2664 Quarts

Answer:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).

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:

1291 tenth graders, 1098 read above the eighth grade level.

1291 - 1098 = 193 read at or below this level.

We want the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.

So [tex]n = 1291, \pi = \frac{193}{1291} = 0.149[/tex]

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}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.13[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.168[/tex]

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).

Answer:

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 190

Standard deviation = 14

Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?

148 = 190 - 3*14

So 148 is 3 standard deviations below the mean.

232 = 190 + 3*14

So 232 is 3 standard deviations above the mean

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

Answer:

7

Step-by-step explanation:

63 ÷ 9 = 7

Answer:

3/20

Step-by-step explanation:

because there is only 3 purple socks out of 20 socks total

Answer:

The volume of the cube would be 125in³

Step-by-step explanation:

The volume of a cube is s³ (side). 5 x 5 x 5 = 125.