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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:

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:

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:

m\angle ABC=124^o

Step-by-step explanation:

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:

( 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:

20%

Step-by-step explanation:

(54/45) - 1 = 0.2 or 20%

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: x^2+8x+15

Step-by-step explanation:

(x+5)(x+3)

x^2+3x+5x+15

x^2+8x+15

To expand the polynomial (x + 5)(x + 3), multiply each term from the first binomial by each term from the second binomial and combine like terms.

To expand the polynomial (x + 5)(x + 3), we need to use the distributive property. We multiply each term from the first binomial by each term from the second binomial. So, we have:

Combining like terms, we get x^2 + 3x + 5x + 15. Simplifying further, we have the expanded polynomial:

x^2 + 8x + 15.

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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:

[tex]\hat p = \frac{0.244+0.326}{2}=0.285[/tex]

[tex] ME = \frac{0.326-0.244}{2}=0.041[/tex]

[tex] 0.285 \pm 0.041[/tex]

Step-by-step explanation:

For this case we have a confidence interval given as a percent:

[tex] 24.4\% \leq p \leq 32.6\%[/tex]

If we express this in terms of fraction we have this:

[tex] 0.244 \leq p \leq 0.326 [/tex]

We know that the confidence interval for the true proportion is given by:

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And thats equivalent to:

[tex]\hat p \pm ME[/tex]

We can estimate the estimated proportion like this:

[tex]\hat p = \frac{0.244+0.326}{2}=0.285[/tex]

And the margin of error can be estimaed using the fact that the confidence interval is symmetrical

[tex] ME = \frac{0.326-0.244}{2}=0.041[/tex]

And then the confidence interval in the form desired is:

[tex] 0.285 \pm 0.041[/tex]

Answer:

11.2

Step-by-step explanation:

20 percent of 14 is 2.8 14 minus 2.8 is 11.2

Answer:

is there a pic i need more info...

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:

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: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:

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!!!

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:

y= 7.5

Step-by-step explanation:

25y = 15y +75

-15y -15y

10y = 75

÷10 ÷10

y = 7.5

Answer:

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

Step-by-step explanation:

the answer is b I'm sure

Answer:

A. False

B. False

C. False

D. True

Step-by-step explanation:

A. False

Remember that E[aX+b] = aE[X] + b, therefore the equality would be true only if E[X] = 1.

B. False

Remember that [tex]V[aX+b] = a^2 V[X][/tex].

C. False

In other words they are telling you in words that [tex]V[X+b] = V[X]+b[/tex], that is false because [tex]V[X+b] = V[X][/tex]

D. True

That is a property of the expected value E[X+b] = E[X]+b

Option D is correct in stating that adding a constant to each value of a random variable shifts the expected value of that variable by that same constant. Adding a constant does not alter the variance.

The correct answer among the given options is D. This statement says that if a constant c is added to each possible value of a discrete random variable X, then the expected value of X will be shifted by that same constant amount. This is in accordance with the properties of expected value, where the expected value of (X + c) is E(X) + c. On the other hand, adding a constant does not affect the variance of a random variable. Variance measures the dispersion of a variable's possible values from its expected value, and adding a constant shifts every possible value, including the expected value, by the same amount, leaving dispersion unchanged.

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Answer:

The treatment should be stated by the four companies,since it more interested in the quality among each of the companies to be compared.

Step-by-step explanation:

From the example given, Since an electronic company wants to differentiate  their cell phones quality to the cell phones from their three main competitors.

If ANOVA is used to determine the average number of defects, then the treatment  should be defined for the four companies because it is more interested in comparing the quality among the different companies.

In ANOVA analysis for the given question, the treatments would be defined as the cell phones from the electronics company itself and three of its competitors. ANOVA evaluates if there is any significant difference in the average number of defects amongst these four groups.

In the situation described, an electronics company testing the quality of their cell phones against three competitors, the treatments in the context of ANOVA (Analysis of Variance) would be the four different companies' cell phones. Specifically, a one-way ANOVA is being used here since there is only one factor or variable (the company) affecting the outcome variable (the number of defects).

Each sample of phones (10 from each company) represents a level within the treatment. Therefore, the treatments here are the cell phones from the electronics company, and Cell Phone Company 1, Cell Phone Company 2, and Cell Phone Company 3.

This comparison is made by analyzing the variance within each group's data and between the groups. The essential goal of ANOVA is to test if there is any significant difference between these means. In this case, it is used to ascertain whether the mean number of defects is significantly different across the four companies.

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Answer:

1 9/10 or 1.9

Answer:

1.9

Step-by-step explanation:

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: b

Step-by-step explanation: ik

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:

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:

(a) The total number of ways to select 4 officers from from 25 students is 12,650.

(b) The total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

Step-by-step explanation:

(a)

It is provided that there are a total of n = 25 students.

Officers need to be elected for four positions:

President, Vice-President, Secretary, and Treasurer.

k = 4

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]

Compute the number of ways to select 4 students from from 25 as follows:

[tex]{25\choose 4}=\frac{25!}{4!(25-4)!}[/tex]

      [tex]=\frac{25!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22\times 21!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22}{4\times 3\times 2\times 1}\\\\=12650[/tex]

Thus, the total number of ways to select 4 officers from from 25 students is 12,650.

(b)

It is provided that of the 25 students, there are 13 girls and 12 boys in the class.

For the post of President and Treasurer only girls are selected.

For the post of Vice-President and Secretary only boys are selected.

Compute the number of ways to select 2 girls for the post of President and Treasurer as follows:

[tex]{13\choose 2}=\frac{13!}{2!(13-2)!}[/tex]

      [tex]=\frac{13!}{2!\times 11!}\\\\=\frac{13\times 12\times 11!}{2!\times 11!}\\\\=\frac{13\times 12}{ 2\times 1}\\\\=78[/tex]

Compute the number of ways to select 2 boys for the post of Vice-President and Secretary as follows:

[tex]{12\choose 2}=\frac{12!}{2!(12-2)!}[/tex]

      [tex]=\frac{12!}{2!\times 10!}\\\\=\frac{12\times 11\times 10!}{2!\times 10!}\\\\=\frac{12\times 11}{ 2\times 1}\\\\=66[/tex]

The number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is:

[tex]{13\choose 2}\times {12\choose 2}=78\times 66=5148[/tex]

Thus, the total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.