A store clerk sold 25 Mathematics books and 10 English books for a total of $855. If she had sold 10 Mathematics books and 40 English books, she would have got $135 more. form a pair of linear equations and calculate the price of each book.

Answer:

The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".

Step-by-step explanation:

Given:

[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]

let

[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]

and

[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]

[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]

So,

[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]

         [tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]

OR

[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]

Derivate:  

[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]

Answer:

3.2 hours

Step-by-step explanation:

12 workers * 4 hours = 48 worker hours

15 workers  * x hours = 48 worker hours

48 /15 =3.2 hours

Answer:

3 hours and 12 minutes.

Step-by-step explanation:

12 Workers complete a job in 4 hours

1 worker complete a job 12 × 4 = 48

15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵

= 3 hours + 1/5 × 60  minutes = 3 hours 12 minutes.

Answer:

The parent cubic function has been vertically stretched by a factor of 4.

Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]

Answer: Option B

OAmalOHopeO

Answer:

[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]

updated response , given that you confirmed the question....

if the percent is the variable a% then ....

[tex]x*(\frac{a+100}{100}) = 2000[/tex]

[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]

I think that there is missing information here ....

you can make any number work here the result of the number being increased by the percent has to be 2000...

so if if the number is 1000 then the percent would be 100%

if you make the number  1500 then the percent would be 33 1/3 %

Step-by-step explanation:

The number is [tex]\frac{2000}{(1+\frac{a}{100})}[/tex]

Let us assume that the number be x.

When the number x is increased by  a% the new number will be,

[tex]x(1+\frac{a}{100})[/tex]

Now, this number is decreased by 80%. So, the new number will be,

[tex]x(1+\frac{a}{100})*(1-\frac{80}{100} )\\=x(1+\frac{a}{100})*(1-0.8 )\\=x(1+\frac{a}{100})*0.20[/tex]

By the given condition,

When x increased by a% and decreased by 80% it becomes 400

Therefore, we can write

[tex]x(1+\frac{a}{100})*0.20=400[/tex]

[tex]x(1+\frac{a}{100})=\frac{400}{0.20}[/tex]

[tex]x(1+\frac{a}{100})=2000[/tex]

[tex]x=\frac{2000}{(1+\frac{a}{100})}[/tex]

So, the number will be [tex]\frac{2000}{(1+\frac{a}{100})}[/tex].

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Answer:

The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{3.7}{\sqrt{582}} = 0.3[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 24.1 - 0.3 = 23.8

The upper end of the interval is the sample mean added to M. So it is 24.1 + 0.3 = 24.4.

The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).

Hello!

Out equation is: [tex]A=P(1+\frac{r}{n} )^t^n[/tex]

A= 6000

P=5000

N=1

T=5

R= What we are trying to find

This means we will have [tex]6000=5000(1+r)^5[/tex]

Divide both sides by 5000:

[tex]\frac{6000}{5000} = (1+r)^5[/tex]

Move the power to the other side by rooting both sides:

[tex]\frac{6000}{5000} ^1^/^5 = 1+r[/tex]

Subtract 1 from both sides:

[tex]\frac{6000}{5000} ^1^/^5 -1 = r[/tex]

Now we just need to calculate: R = 0.03713728...

I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.

I hope this helps! :)

Answer:

C

Step-by-step explanation:

C is the only function that have a consistent decrease while A is a trigonometric function, B is a non linear function, D is an exponential function

Answer:

1.083

Step-by-step explanation:

Exact form: 13/12

Decimal form: 1.083 (put a line above the 3)

Mixed number form: 1 1/12

Answer in picture

….

Set up equations for each gym.

multiply daily cost by number of days(x) and add the fee:

Muscle max: 2x + 30

Capital: 4x + 10

Now set them

Equal to each other and solve for x:

2x + 30 = 4x + 10

Subtract 2x from both sides :

30 = 2x + 10

Subtract 10 from both sides :

20 = 2x

Divide both sides by 2:

X = 10

It will take 10 days

Answer:

Average of the draws equals 420

Standard Error = 11.88

Step-by-step explanation:

Given

[tex]\mu = 420[/tex]

[tex]\sigma = 84[/tex]

[tex]n =50[/tex]

Solving (a): The average of the draws

This implies that we calculate the sample mean

This is calculated as:

[tex]\bar x = \mu[/tex]  --- Sample Mean = Population Mean

So, we have:

[tex]\bar x = 420[/tex]

Solving (b): The standard error

This is calculated as:

[tex]SE=\frac{\sigma}{\sqrt n}[/tex]

So, we have:

[tex]SE=\frac{84}{\sqrt {50}}[/tex]

Using the calculator, we have:

[tex]SE=11.88[/tex]

I REALLY HOPE THIS HELPS! I’m sorry if this was wrong but I really believe it’s true.

Answer:

The value of P is $6.75.

Step-by-step explanation:

In the diagram to the left, we see 6 apples, and are labeled that the price is $4.50.

If the prices are proportional, that may mean that each apple has the same price. To find the price of apples in the diagram to the right, divide the total price by 6:

4.50/6 = 0.75

So the price per apple is 0.75.

As seen on the diagram, P represents the total price of 9 apples.

Multiply the price per apple by 9:

0.75 x 9 = 6.75

So the value of P is $6.75

Answer:

Step-by-step explanation:

Triangular cross-section.

Answer:

it is a triangle cross-section

hope this answer helps you

Plz make me a brainlist

Answer:Mark Brainliest please

Answer is 4.86 which is rounded to 5

Step-by-step explanation:

Cos 40 degree = VW/7

0.694 =VW/7

0.694 * 7 =VW

4.858 =VW

VW=4.86 is the answer

Answer:

[tex]3\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

The answer is "[tex]H_0:\mu \geq 50.1\ \ and \ \ H_0: \mu \geq 50.1[/tex]"

Step-by-step explanation:

An initial random selection of mail-order physicians representing firm A worked an average of 50.1 hours per week. My goal is to reject the Null Hypothesis since it is employed to make no difference. In this case,[tex]H_0 =\mu \geq50.1[/tex]

Medical insurance changes are attributed to reducing the average workweek. New medical coverage is claimed to be have reduced your average workday after the government change. [tex]H_1: \mu <50.1[/tex]

Answer:

31.9617 rounded to 32

Step-by-step explanation:

set up is sin24=13/x

Answer:

The answer is −3y^2−y.

Steps:

Distribute the Negative Sign:

=−2y2+−1(y2+y)

=−2y2+−1y2+−1y

=−2y2+−y2+−y

Combine Like Terms:

=−2y2+−y2+−y

=(−2y2+−y2)+(−y)

=−3y2+−y

Answer:

-3y^2 - y

Step-by-step explanation:

-2y^2 - (y^2 + y)

Find the opposite of y^2 + y, so distribute the negative sign to the values inside the parentheses to get:

−2y^2 −y^2 − y

Then combine like terms to get:

-3y^2 - y

the slope-intercept form of the given equation is y = x/3 + 8.

The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.

The slope-intercept form of a line is Y = m*X +C.

Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.

3x-9y = -72

9y = 3x + 72

y = 1/3 * x + 8

Therefore y = x/3 + 8 is the slope-intercept form of the given equation.  where its slope is 1/3.

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(-1;2;-3)

а, b, c

~~~~~~

Answer:

30% of 30 has the least value out of all answer choices.

Step-by-step explanation:

Solve for the values of the given percentages of each number:

30% of 50:

Divide 50 by 100 to get 1%

50/100 = 0.5

Multiply 1% (0.5) by 50:

0.5 x 50 = 15

So 30% of 50 = 15

50 % of 30:

50% of a number means half of it since 50% is half of 100% so:

30/2 = 15

So 50% of 30 = 15

30% of 30:

Divide 30 by 100 to get 1%:

30/100 = 0.3

Multiply 1% (0.3) by 30:

0.3 x 30 = 9

So 30% of 30 = 9

50% of 50

50% of a number means half of it since 50% is half of 100% so:

50/2 = 25

So 50% of 50 = 25

Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:

25, 15, 15, 9

9 is the most least, it is the value equal to the answer choice “30% of 30”

HOPE THIS HELPED!

Answer:

0.72 litres

Step-by-step explanation:

Litres of syrup = 0.32 litres

Litres of water = 12 times the amount of syrup = 12 * 0.32 = 3.84 litres

Litres of orange squash = litres of syrup + litres of water

Litres of orange squash = (0.32 + 3.84) = 4.16 litres

Amount of orange squash litres split = 1.28 litres

Amount of orange squash left = (4.16 - 1.28) = 2.88 litres

Splitting the amount of squash left equally into 4 :

2.88 litres / 4 = 0.72 litres

9514 1404 393

Answer:

  17.  25 mile per gallon

  18. Eduardo did should have divided by -4.

Step-by-step explanation:

17. The least mileage will be had when the most gas is used to go a given distance. For the given distance, the most gas that could have been used (without adding any) is 18 gallons. Then the least mileage is ...

  (450 mi)/(18 gal) = 25 mi/gal

__

18. The appropriate method for solving this inequality is ...

  -4x/(-4) < 120/(-4) . . . . divide both sides by -4 (and reverse the > symbol)

  x < -30

The step Eduardo took of adding 4 will give ...

  -4x +4 > 124 . . . . . puts him one step farther away from a solution

Eduardo chose an operation to perform that did not get him closer to a solution.

Answer:

The student is completely incorrect because there is no solution to this inequality.

Answer:

D on edge

Step-by-step explanation:

Answer:

0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.

Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

11 students means that [tex]N = 11[/tex]

4 are Sarah, Jamal, Kate, and Mai, so [tex]k = 4[/tex]

4 are chosen, which means that [tex]n = 4[/tex]

What is the probability that Sarah, Jamal, Kate, and Mai are chosen in any order?

This is P(X = 4). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,11,4,4) = \frac{C_{4,4}*C_{7,0}}{C_{11,4}} = 0.003[/tex]

0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.

Answer:

a. P = 30

b. Y = 40

Step-by-step explanation:

Given the following data;

P = 1.2

Y = 100

First of all, we would have to determine the constant of proportionality;

P = k/Y (inverse proportion or relationship)

1.2 = k/100

k = 1.2 * 100

k = 120

a. To find the value of p when y = 4;

P = k/Y

P = 120/4

P = 30

b. To find the value of y when p = 3;​

P = k/Y

Y = k/P

Y = 120/3

Y = 40

Answer:

Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

its B

Option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

The expressions are [tex]4x-x+5 , 8-3x-3[/tex]

If the expressions are equivalent then,

⇒ [tex]4x-x+5 = 8-3x-3[/tex]

⇒ [tex]3x+5=-3x+5[/tex]

In both the sides the x has different values.

So, Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

Hence we can conclude that option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.

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x=3

Step-by-step explanation:

x+2=5

x=5-2

x=3