Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round your answer to four decimal places. Enter your answers as a comma-separated list.)

f(x)= 5[tex]\sqrt{x}[/tex], [4,9]

Answer: There are 52 cards in a standard deck and half of them, 26 in all, are red.

Suppose that you are drawing 4 cards without replacement from a thoroughly shuffled deck. You have 26 cards choose 4 over 52 choose 4.

∴  P(pulling 4 cards from deck) =  (264)(524)

Answer:

X=-27

Step-by-step explanation:

X/-9 = 3

(-9) * X/-9  =(-9) * 3

X=(-9) * 3

X=-27

Answer:

x=-27

Step-by-step explanation:

x/-9=3

Multiply each side by -9

x=-27

That's it!

a) 25 % of customers receive the service for​ half-price.

b) The guaranteed time​ limit should be of 16 minutes.

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.

When the distribution is normal, we use the z-score formula.

The p-value is the probability that the value of the measure is smaller than X, which is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

we have that mean of 15 minutes and a standard deviation of 4 minutes.

​(a) Longer than 20 minutes is 1 subtracted by the p value of Z when X = 20. So

[tex]Z = \dfrac{{x} - \mu}{\sigma}[/tex]

Z = (20 - 15)/4

Z = 5/4

Z = 1.25

1.25 has a pvalue of 0.25

1 - 1.25= 0.25

25 % of customers receive the service for​ half-price.

(b)  The time limit should be the 100 - 7 = 93th percentile, which is X when Z has a pvalue of 0.93.  So X when Z = 0.25.

[tex]Z = \dfrac{{x} - \mu}{\sigma}[/tex]

0.25= (x- 15)/4

x = 16

The guaranteed time​ limit should be of 16 minutes.

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Step-by-step explanation:

sqrt(7) is larger than 2 (2² = 4) but smaller than 3 (as 3² is 9).

sqrt(220) is larger than 14 (14² = 196) but smaller than 15 (15² = 225).

so, the integers between them are

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

these are 12 integer values.

The value of k is 4.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Volume= 16

Width = 4

So, we can write the relation as

Volume= k (width)

k = Volume/ width

k= 16/4

k = 4

Hence, the value of k is 4.

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In  linear equation, option A,B,C are equal expect D .

What in mathematics is a linear equation?

The given equation is  3x -4y =21.

A.  (11, 3)

3(11) - 4(3) = 21

21 = 21 > equal

B.  (7, 0)

3(7) - 4(0) = 21

21 = 21 > equal

C.  (−1, −6)

3(-1) - 4(-6) = 21

21 = 21 > Equal

D.  (−3, 3)

3x – 4y = 21

3(-3) - 4(3) = 21

-21 = 21 > not equal

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On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.

Average:

Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

On average, Jaya drinks of a 6-ounce glass of water in 13 hours.

Here we need to find the number of glasses of water does she drink in one hour.

Let x be the number of glasses of water does she drink in one hour.

We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.

So, in order to find the average we have to divide the number of glasses by the time taken.

So, it can be written as,

=> 6/13

=> 0.46

Therefore, for one hour Jaya drinks 0.46 ounces of water.

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Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912

Step-by-step explanation:

[tex](2x-7)^9[/tex]

In this problem we use the following formula:

                              [tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]

a=2x         b=-7        n=9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

..........................................................

The 6th term of (2x-7)^9 is k=5

Hence,

[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]

- 33889212x⁴ is the coefficient of the 6th term in  binomial theorem .

What is binomial theorem?

( 2x - 7 )⁹

compare with formula

a = 2x    b = - 7  n = 9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

...................................................

The 6th term of (2x-7)^9 is k=5

hence

⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵  = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵

                            = 9!/4! * 5! 2⁴x⁴( -7)⁵

                              = 126(16) ( - 16807 )(x)⁴

                              =  - 33889212x⁴

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The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)

From the question, the equation is given as

-3x+16+5x+8

To start with, we need to rewrite the expression

So, we have the following representation

-3x + 16 + 5x + 8

The above expression is not an equation

Instead, it is an expression

This is so because there is no equality symbol i.e. = in the expression

So, we collect the like terms

-3x  + 5x + 8 + 16

Solving further, we need to evaluate the like terms

So, we have the following equation

-3x  + 5x + 24

Evaluate the like terms again

So, the equation becomes

2x + 24

The above expression cannot be further simplified, however, it can still be factored

Factor out 2 from the expression

This gives

2(x + 12)

Hence, the solution is 2(x + 12)

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Answer: 5n - 4

Step-by-step explanation:    

n is the number, 5 times the number is 5n.  4 less means subtract 4.  So the correct expression is 5n - 4

The different ways to make groups of 4 based on the napkins given is 6 ways.

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Thus can be illustrated by nCr

Combination formula

nCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

In this case, Elijah has red and yellow napkins. He must set out napkins for 4 people. This will be:

= n! / ((n – r)! r!)

= 4! / (4 - 2)! 2!

= 4! / 2!2!

= 4 × 3/2

= 6

Therefore, there are 6 ways.

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20   foot² is  the area of the wall.

What does a math area mean?

Length of concrete wall = [tex]2\frac{1}{2}[/tex] foot

Breadth of concrete wall = 8 foot

Since, area means product of dimensions so we use the formula mentioned below:

Area of the concrete wall = length× breadth

                                          = [tex]2\frac{1}{2}[/tex]  * 8

                                           = 5/2  * 8

                                            =  5 * 4 = 20 foot²

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The coordinates of G(4, 4) , H (0, 2),  J(8, 0)

In order to construct the three sets of relationships between the coordinates of each triangle's three sides' ends and the shared midpoint, we must first set up the three sets of relationships.

G(x(G), y(G))

K(2, 3) (2, 3)

M(6, 2) (6, 2)

H(x(H) and y(H))L (4, 1)

J(x(J), y(J))

K(2, 3) at the midway of side GH

According to the x-component:

x(H) = x(G - x(H))/2

x(G)-[x(H)-x(G)] = 2*x(H)

x(H) + x(G) = 4

x(H) = 4 - x(G) (G)

According to the y-component:

y(H) plus [y(G) - y(H)]/2 = 3.

2*y(H) plus [y(G-y(H)] = 6

y(H) + y(G) = 6

y(H) = 6 - y(G) (G)

Midpoint L(4) and side JH(1):

According to the x-component:

(x(H) + [x(J) - x(H)]/2) equals four.

2*x(H) plus [x(J)-x(H)] = 8

x(H) + x(J) = 8

x(H) = 8 - x(J) (J)

According to the y-component:

y(H) = y(J - y(H)]/2 + y(J) = 1

y(J) - y(H) = 2*y(H)

y(H) + y(J) = 2

y(H) = 2

Side GJ with M(6, 2) as the midpoint:

For the x - component, the formula is: x(J) = [x(G) - x(J)]/2 = 6 2*x(J) = [x(G)- x(J)] = 12 x(J) = 12 - x (G)

y(J) + [y(G) - y(J)]/2 = 2 2*y(J) + [y(G)- y(J)] for the y-component. = 4 y(J) = 4 - y + y(G) = 4 y(J) (G)

The x and y coordinates may now be easily separated, and we can use algebra to isolate each one and determine its location.

x(H) = 4 - x(G), 8 - x(J), and 12 - x(J) (G)

Because x(H) = x (H)

4 - x(G) = 8 - x(J) (J)

8 - x(J) - 8 - x(G) - 4 = -x(J) x(J) x(J) = 4 + x (G)

Using 1.c above and this relationship now x(J) = x(J), so:

-2 * x(G) = -8 x(G) =, 4 12 - x(G) = 4 + x(G) 12 - x(G) - x(G) - 12 = 4 + x(G) - x(G) - 12

Given that x(J) = 4 + x(G) above, x(J) = 4 + 4 = 8 and x(H) = 4 - x(G) = 4 - 4 = 0 respectively.

Let's now perform the identical procedure using the y-coordinates.

y(H) = 6 - y(G), y(H) = 2 - y(J), y(J) = 4 - y(G),

and since y(H) = y(H), 6 - y(G) = 2 - y(J), -y(G) = 2 - y(J) - 6 = -y(J) - 4 y(G) = y(J) + 4 Now that y(J) = 4 - y,

we may substitute (G).

y(H) = y(G) - 2 and y(H) + 4 - y(G) = 2

and y(H) + 4 - y(G) = 2 - 4 and y(G)

Since y(H) = 6 - y(G)

according to 1. above, y(H) = y(G) - 2 + 6 - y(G) 2 * y(H) = 4 y(H) = 2 y(H) = 2 - y(J) 2 = 2 - y(J) y(J) = 4 - y(G) 0 = 4 - y(G) y(G)

H(x(H), y(H)), G(x(G), y(G)), and J(x(J), y(J)) are the results.

To determine the coordinates of the angles or triangle's tips, we used the midpoints of each side.

The coordinates are: H (0, 2) G(4, 4) J(8, 0)

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Answer:

3/20

Step-by-step explanation:

3/5 : 4

3/5 x 1/4

3/20

After solving the formed equation from the question, the result will be equal to 4.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

The given statement of the question in the equation form will be,

5x + 12 = 32

5x = 20

x = 4

Therefore, the value of x will be equal to 4.

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Your complete question must be like this:

The product of a number and 5 is increased by 12 the result is 32 to find the number​.

The values of y and x are -7 and 2 respectively, completing the ordered pairs: (6,-7) and (2,1).

Given the equation in the question;

To find the y-value that completes the ordered pair ( 6,y ), replace all occurrence of x with 6 in the equation and solve for y.

y = −2x + 5

y = −2( 6 ) + 5

Multiply -2 and 6

y = -12 + 5

y = -7

Hence, the output value is -7, this forms an ordered pair of (6,-7).

To find the x-value that completes the ordered pair ( x,1 ), replace all occurrence of y with 1 in the equation and solve for x.

y = −2x + 5

1 = −2x + 5

Add 2x to both sides

1 + 2x = −2x + 2x + 5

1 + 2x = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, the input value is 2, this forms an ordered pair of (2,1).

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The total amount accumulated after 2 years is $3704. 0

The formula for calculating compound interest is expressed as;

A = P ( 1 + r/ n) ^nt

Where;

Now, let's substitute the values into the formula, we have;

A = $3500 ( 1 + 0. 03 / 0. 25) ^(0.25× 2)

Find the exponent

A = $3500 ( 1 + 0. 03 / 0. 25) ^0.5

A =  $3500( 1+ 0. 12)^0. 5

Expand the bracket

A = $3500 (1. 12)^0. 5

A = $3500(1. 05)

multiply the values

A = $3704. 0

Hence, the value is $3704. 0

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Answer:

9 m

Step-by-step explanation:

given,

area of floor of play pen = 5 m²

we know, area of a square = (side)² sq units

now according to the question,

5 = (side)²

⇒√(side)² = √5 [taking square root on both sides]

⇒ side = √5 m

now, we know,

perimeter of a square = 4 × side = 4 × √5 = 8.94 m (app.) ≈ 9 m

Answer:

Scientific notation: 5.2516 x [tex]10^{7}[/tex]

Standard notation 52,516,000

Step-by-step explanation:

Are you asking for the answer to be in scientific notation?

5.2516 x [tex]10^{7}[/tex] or 52,516,000

(1.8066 x [tex]10^{7}[/tex]) + (3.445 x [tex]10^{7}[/tex])

(1.8066 + 3.445) x [tex]10^{7}[/tex]

5.2516 x [tex]10^{7}[/tex]

The percent of Americans that had central heterochromia is A. 0061%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States

was 327,750,000 people.

The percent of Americans that had central heterochromia will be:

= Those with the disease / Total population × 100

= 200,000 / 327,750,000 × 100

= 0.0061%

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The equation that can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days is A. y = 50x + 150

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Abigail already knows 150 words from the vocabulary list and each day, she learns 50 additional words from the vocabulary list.

Let x be the number of days.

y = vocabulary list

The equation will be:

y = 150 + 50x

Therefore, the correct option is A.

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A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

 ? ---------------->280 bunnies

x=280/2.5

x=112 months

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Answer:

A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

What is meant by population?

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

? ---------------->280 bunnies

x=280/2.5

x=112 months

Answer:

9

Step-by-step explanation:

I hope this helps!

a) The test statistic is: t = -7.44.

b) The p-value is: < 0.0001.

c) The conclusion is that the null hypothesis is rejected.

d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.

From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:

The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.

Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.

The pop-ups with the information of the test are given by the image at the end of the answer.

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Using the greatest common factor, the number of light bulbs in each box is 24.

The greatest common factor (GCF) is the number that can divide two or more numbers without a remainder.

The GCF is a divisor that divides dividends evenly, leaving only quotients without remainders.

For instance, the greatest common factor of 120, 168, and even 288 is 24.

Using this GCF implies that 24 can divide 120, 168, and 288 without leaving any remainders.

                                            Company A      Company B        Total

Total orders for light bulbs         120                     168             288

Greatest common factor of          24                      24               24

Number of boxes delivered           5                        7                12

Thus, with the greatest common factor as 24 light bulbs in each box, Company A will be supplied 5 boxes, while Company B will be supplied with 7 boxes.

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