A company conducted a survey to see wether its new toothpaste was more popular with children or adults. Of the children surveyed 28% use the toothpaste. Compare this what is the percent of adults who use toothpaste.

[tex]\bf \begin{cases} R(x)=58x-0.4x^2\\ C(x)=2x+14 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ P(x)\implies \stackrel{revenue}{R(x)}-\stackrel{costs}{C(x)}\implies (58x-0.4x^2)-(2x+14) \\\\\\ (58x-0.4x^2)-2x-14\implies 58x-0.4x^2-2x-14 \\\\\\ 56x-0.4x^2-14\implies \boxed{-0.4x^2+56x-14} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf R(80)\implies 58(80)-0.4(80)^2\implies R(80)=4640-2560\implies \boxed{R(80)=2080} \\\\[-0.35em] ~\dotfill\\\\ C(80)=2(80)+14\implies C(80)=160+14\implies \boxed{C(80)=174} \\\\[-0.35em] ~\dotfill\\\\ P(80)=-0.4(80)^2+56(80)-14 \\\\\\ P(80)=-2560+4480-14\implies \boxed{P(80)=1906}[/tex]

The profit function P(x) is 56x - 0.4x² - 14. When we plug x=80 into the equations, we find that R(80) = 3680, C(80) = 174, and P(80) = 3506.

To solve the student's question, firstly we use the provided data. The profit function P(x) can be expressed as the difference between the revenue function R(x) and the cost function C(x).

To find P(x), we subtract the equation for C(x) from the equation for R(x). So, P(x) = R(x) - C(x) = (58x - 0.4x²) - (2x + 14) = 56x - 0.4x² - 14.

To answer the second part of the question, we substitute x=80 into the equations for R, C, and P.
Therefore R(80) = 58×80 - 0.4×80² = 3680, C(80) = 2×80 + 14 = 174, and P(80) = 56×80 - 0.4×80² - 14 = 3506.

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Answer:

4.68

Step-by-step explanation:

Remember to line up the decimal point. Subtract as ordinarily.

8.31

-3.43

--------

4.68

4.68 is your answer

~

Answer: it will take 1.25 hours

Step-by-step explanation:

It

It will take the teacher 1.25 hours to print 6,000 pages.

To calculate how long it will take to print 6,000 pages with a copy machine that can print 80 sheets per minute, we need to divide the total number of pages by the rate of printing per minute to find out the time in minutes, and then convert that time into hours if necessary.

Step 1: Divide the total number of pages by the printing speed to find the time in minutes.

Total pages: 6,000

Printing speed: 80 pages/minute

Time calculation: 6,000 pages divided by 80 pages/minute = 75 minutes

Step 2: Convert minutes into hours by dividing by 60 since there are 60 minutes in an hour.

Conversion to hours: 75 minutes divided by 60 minutes/hour = 1.25 hours

Therefore, it will take the teacher 1.25 hours to print 6,000 pages.

Answer:

7/5

Step-by-step explanation:

reciprocal means flip the equation

The answer is 7/5.

Hope this helps!

Answer:

2.5

Step-by-step explanation:

lower quartile.

3, 4, 5, 5, 6, 6, 7, 7, 8

median = 6

lower quartile 1/4th position

(4+5)/2 = 4.5

Upper quartile 3/4th position

(7+7)/2 = 7

Interquartile range = upper quartile - lower quartile

                                = 7 - 4.5

                                 = 2.5

Answer:

Interquartile range = Q3 - Q1 = 7 - 4.5 = 2.5

Step-by-step explanation:

Before we calculate interquartile range, you should understand that:

Interquartile range is the range between Q3 and Q1 of a dataset i.e Q3 - Q1

Where,

Q1 is the middle value in the first half of the data set and

Q3 is the middle value in the second half of the data set.

So to calculate the interquartile range we find the Q3 and Q1

5, 6, 7, 3, 4, 5, 6, 8, 7

So in the data set to find Q1 and Q3, we rearrange the dataset and divide it into First half and second half.

3, 4, 5, 5, 6, 6, 7, 7, 8

First half = 3, 4, 5, 5

Second half = 6, 7, 7, 8

So

Q1 = (4+5)/2 = 4.5

Q3 = (7+7)/2 = 7

Interquartile range = Q3 - Q1 = 7 - 4.5 = 2.5

Answer:

The resulting cross section is a square an the area is [tex]A=16\ in^{2}[/tex]

Step-by-step explanation:

we know that

All the faces of the cube are square with side lengths measuring 4 inches

If the cube was sliced parallel to the base

then

the cross section is a square with side lengths measuring 4 inches

so

The area of a square is

[tex]A=b^{2}[/tex]

we have

[tex]b=4\ in[/tex]

substitute

[tex]A=4^{2}[/tex]

[tex]A=16\ in^{2}[/tex]

Answer:5

Step-by-step explanation:

6:30 is the ration

6/30 reduced is 1/5

1:5

so its 5

Max walks 0.2 laps per minute around the track. This conclusion was reached by dividing the total number of laps (6) by the total number of minutes (30).

The Mathematics problem posed is one concerning rates. It is given that Max walks 6 laps in 30 minutes. We need to find out how many laps would Max be able to walk in 1 minute.

To do this, we divide the total number of laps walked by the total number of minutes. In this case, we would divide 6 laps by 30 minutes.

6 laps ÷ 30 minutes = 0.2 laps per minute

Therefore, Max walks 0.2 laps around the track in 1 minute.

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Answer:

A

Step-by-step explanation:

3x² + 6 - 2x + 5x - 4x² + 9

Combine like terms:

3x² - 4x² - 2x + 5x + 6 + 9

-x² + 3x + 15

Final answer:

To simplify the polynomial, combine like terms by adding or subtracting coefficients of terms with the same variable and exponent. The terms simplify to -x^2 + 3x + 15, matching option A.

Explanation:

The subject of the student's question involves simplifying a polynomial. To simplify the given polynomial 3x2 + 6 - 2x + 5x - 4x2 + 9, we need to combine like terms. This process involves adding or subtracting the coefficients of terms with the same variable and exponent. Let's go through the steps:

Combine the terms with x2: 3x2 - 4x2 = -1x2

Combine the terms with x: -2x + 5x = 3x

Add the constant terms: 6 + 9 = 15

Putting it all together, the simplified form of the polynomial is -x2 + 3x + 15, which matches option A.

Remember, when simplifying polynomials, always look for like terms that can be combined and ensure the final expression is written in standard form, with terms ordered from highest to lowest degree.

Foil is an acronym that stands for:

First

Outside

Inside

Last

First:

(w + x )(w + x ) = [tex]w^{2}[/tex]

Outside:

(w + x )(w + x ) = wx

Inside:

(w + x )(w + x ) = wx

Last:

(w + x )(w + x ) = [tex]x^{2}[/tex]

so...

[tex]w^{2}[/tex] + wx + wx + [tex]x^{2}[/tex]

[tex]w^{2} +x^{2} + 2xw[/tex]

Hope this helped!

Answer: [tex]x^2+2wx+w^2[/tex]

Step-by-step explanation:

Given the expression [tex](w + x )(w + x )[/tex] , which indicates the multiplication of two binomials, you can simplify it with FOIL:

Multiply:

The first terms (w by w).

The outside terms  (w by x).

The inside terms together (x by w).

The last terms together (x by x).

Then, you get:

[tex](w + x )(w + x )=(w)(w)+(w)(x)+(x)(w)+(x)(x)=w^2+wx+wx+x^2[/tex]

Adding like terms, you get:

[tex]x^2+2wx+w^2[/tex]

Answer:

Step-by-step explanation:

-3x²-(4x²-x)

=-3x²-4x²+x

=-7x²+x

Answer:

[tex]-7x^2+x[/tex]

Step-by-step explanation:

(4x2-x) from -3x2 is

Subtract [tex]4x^2-x from -3x^2[/tex]

[tex]-3x^2 - (4x^2-x)[/tex]

Remove the parenthesis by multiplying negative sign inside the parenthesis

[tex]-3x^2 - 4x^2+x[/tex]

Now combine like terms, add -3 and -4 and it becomes -7

[tex]-7x^2+x[/tex]

The system of equations that can be used to determine the price of the hamburger and the soft drink is 4H + 5S = $27 (H = hamburger cost, S = soft drink cost) and 3H + 3S = $18.

The question you're asking involves setting up a system of equations to solve for the cost of a hamburger and a soft drink based on the given information. Since two different meals with different quantities of hamburgers and soft drinks have specific costs, we can make the following two equations where H represents the cost of a hamburger and S represents the cost of a soft drink: 4H + 5S = $27 and 3H + 3S = $18. This system of equations can be solved using various methods like substitution or elimination to determine the individual costs of a hamburger and a soft drink.

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Answer:

3456

Step-by-step explanation:

the given equation is: [tex](3^{2} 8) (4^{2} 3)[/tex]

= (9 × 8) (16 × 3)

= (72) (48)

= 3456

Answer:

y = 3x² - 6x - 72

Step-by-step explanation:

Since the roots are x = - 4 and x = 6 then the factors are

(x + 4) and (x - 6) and the quadratic function is

y = a(x + 4)(x - 6) ← a is a multiplier, in this case 3, so

y = 3(x + 4)(x - 6) ← expand factors and distribute by 3

y = 3(x² - 2x - 24)

y = 3x² - 6x - 72

3x²-6x-72. The quadratic equation whose  roots are -4 and 6 with a leading coefficient of 3 is 3x²-6x-72.

The solutions of a quadratic equation are x = -4 and x = 6 with a leading coefficient of 3. The solutions are two real numbers which means that (x + 4) and (x - 6) are the factors of our unknown quadratic equation and the leading coefficient is 3.

[tex]3(x+4)(x-6)=0[/tex]

Expand (x+4)(x-6):

[tex]3(x^{2} -2x-24)=0\\3x^{2} -6x-72=0[/tex] which is our quadratic equation.

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 9 and d = - 2, hence

[tex]a_{n}[/tex] = 9 -2(n - 1) = 9 - 2n + 2 = - 2n + 11

[tex]a_{n}[/tex] = - 2n + 11 ← n th term formula

Given that the volume of a rectangular prism is length x width x height, this problem can be solved by setting up the equation 2w * w * 8 = 400, where w is the width and 2w is the length. Solving this equation, we find that the width is 5 feet and the length is 10 feet.

In mathematics, the volume of a rectangular prism is given by the formula length x width x height. We are given that the volume of the storage container is 400 cubic feet, its height is 8 feet, and the length is twice the width. Let us denote the width as w, then the length is 2w.

From the given volume formula, we have:

Length x Width x Height = Volume

Substituting the values, we get:

2w * w * 8 = 400

Solving this equation, we find:

w^2 = 25

Taking the square root of both sides, we get:

w = 5

Substituting w=5 into 2w, we find the length:

Length = 2*5 = 10

So the width of the container is 5 feet and the length is 10 feet.

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Answer:

b

Step-by-step explanation:

7x+4+x=20

8x+4=20

8x+4-4=20-4

8x=16

Divide by 8 for 8x and 16

8x/8=16/8

x=2

Check answer by using substitution method

7(2)+4+2=20

14+6=20

20=20

Answer is x=2

Answer:

x=2

Step-by-step explanation:

7x+4+x=20

Combine like terms

8x +4 = 20

Subtract 4 from each side

8x+4-4 =20-4

8x = 16

Divide each side by 8

8x/8 = 16/8

x = 2

Answer:

Step-by-step explanation:

x-intercept: the intersection point of the graph with the x axis.

Therefore, the x-intercepts are x = 1 and x = 5 (look at the picture).

Answer:

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

therefore

|3| = 3 and |-3| = -(-3) = 3

Answer:

Graph 1 is the correct representation of absolute value of -3.            

Step-by-step explanation:

Absolute value of a number is the measure of positive distance on a number line from zero to that number.

It is denoted by:

[tex]\mid c \mid = c, \text{if c} > 0\\ ~~~~~ = -c, \text{if c} < 0[/tex]

So, the absolute value of -3 =

[tex]\mid -3 \mid = 3[/tex]

The correct representation of the absolute value option 1.

As the graph in option 1 represents the positive distance between zero and -3.

Answer:

B is the correct answer.

Step-by-step explanation:

Apex

Answer:

Quotient: [tex]2x^2-2x+2[/tex]

B is correct

Step-by-step explanation:

Given: The format of synthetic division.

We take first number at bottom row and multiply with -3, write the result below second number (4) and then simplify (4-6=-2)

Repeat the process at end.

At last we get 0 (Remainder)

Last number of last row shows remainder and rest are coefficient of quotient.

Synthetic Division: Please find attachment.

-3 | 2       4          -4         6 |

             -6           6        -6

     2      -2           2         0

last row : 2   -2    2  

Initially we had 4 terms ( three degree polynomial)

Quotient must have two degree polynomial.

Quotient: [tex]2x^2-2x+2[/tex]

Answer:

30 mph

Step-by-step explanation:

The average speed = Total distance / Total Time

Distance at 45 m/hr.

t = 20 minutes = 20/60 = 1/3 hour.

r = rate = 45 miles / hour

d = r * t

d = 45 * 1/3 = 15 miles.

Average Speed going home.

t =  30 minutes

t = 30 min / 60 min // hour = 1/2 hours

r = 15 miles / 1/2 = 15 * 2 =  30 miles / hr.

Answer:

the radius of sphere X is 2 times larger than the radius of sphere T

Step-by-step explanation:

Given

Surface area of sphere, T =452.16

Surface area of sphere, X= 1808.64

how many times larger is the radius of sphere X than the radius of sphere T?

Finding radius of both spheres:

Surface area of sphere is given as

A=4πr^2

Now putting value of Ta=452.16 in above formula

452.16=4πrt^2

rt^2=452.16/4π

rt^2=35.98

Taking square root on both sides

rt=5.99

Now putting value of Xa=1808.64 in above formula

1808.64=4πrx^2

rx^2=1808.64/4π

rx^2=143.92

Taking square root on both sides

rx=11.99

Comparing radius of sphere X and the radius of sphere T

rx/rt=11.99/5.99

      = 2.00

rx=2(rt)

Hence the radius of sphere X is 2 times larger than the radius of sphere T!

The answer is:

The radius of the  sphere X is 2 times larger than the radius of the sphere T

To solve the problem, we need to find the radius of both spheres using the following formula:

[tex]Area=\pi *radius^{2}\\\\radius=\sqrt{ \frac{Area}{\pi }}[/tex]

Where,

Area, is the area of the circle.

r, is the radius of the circle.

So,

We are given:

[tex]T_{area}=452.16units^{2}\\X_{area}=1808.64units^{2}[/tex]

Now, calculating we have:

For the sphere X,

[tex]X_{radius}=\sqrt{ \frac{X_{area}}{\pi }}=\sqrt{\frac{1808.64units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{1808.64units^{2} }{\pi }}=\sqrt{575.71units^{2} }=23.99units[/tex]

For the sphere T,

[tex]T_{radius}=\sqrt{ \frac{T_{area}}{\pi }}=\sqrt{\frac{452.16units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{452.16units^{2} }{\pi }}=\sqrt{143.93units^{2} }=11.99units[/tex]

Then, dividing the radius of the X sphere by the  T sphere to know the ratio (between their radius), we have:

[tex]ratio=\frac{23.99units}{11.99units}=2[/tex]

Hence, we have the radius of the sphere X is 2 times larger than the radius of the sphere T.

Have a nice day!

Which question ? Are you looking for?

4. Point A=-1.5 Point B =-.2. Point c= 1.2

5.8x 4=32. 32+21=53

Answer:

The sum of the angles that do not measure 22 degrees is equal to 316°

Step-by-step explanation:

The question in English is

A rhombus has a 22-degree angle. How much is the sum of its angles that do not measure 22 degrees worth?

we know that

The opposite internal angles of a rhombus are equal and the adjacent internal angles are supplementary

so

Let

x -----> the measure of an adjacent angle to 22 degrees in the rhombus

x+22°=180°

x=180°-22°=158°

therefore

The sum of the angles that do not measure 22 degrees is equal to

158°+158°=316°

Answer:

Option D is correct.

Step-by-step explanation:

Previous Balance Method uses the "previous" balance, that is, the balance from the month before.

Here, it is given that the  opening balance of one of her 30-day billing cycles was $2990. This means this was previous month amount or previous balance.

So, Annette will be charged the interest on $2990.

Hence, option D is correct.

Answer:

D.

Step-by-step explanation:

Answer:

The answer is D.35.5 got it right on plato

Step-by-step explanation:

The expected value of the random variable y found from its given probability distribution is given by: Option D: 35.5

Supposing that the considered random variable is discrete, we get:

[tex]\text{Mean} = E(X) = \sum_{\forall x_i} f(x_i)x_i[/tex]

where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values

and [tex]f(x_i)[/tex] is the probability of [tex]X = x_i[/tex]

The probability distribution of Y is given as:

Y = y   f(y) = P(Y = y)

10            0.10

20           0.25

30           0.05

40           0.30

50           0.20

60           0.10

Thus, the expectation (also called expected value) of y is calculated as:

[tex]E(Y) = \sum_{\forall y_i} f(y_i)y_i \\\\E(Y) = 10 \times 0.1 + 20\times 0.25 + 30 \times 0.05 + 40 \times 0.3 + 50 \times 0.2 + 60 \times 0.1\\\\E(Y) = 1 + 5 + 1.5 + 12 + 10 + 6 = 35.5[/tex]

Thus, the expected value of the random variable y found from its given probability distribution is given by: Option D: 35.5

Learn more about expectation of a random variable here:

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Answer:

35

Step-by-step explanation:

The geometric mean of n numbers is the n-th root of their product.

The geometric mean of these two numbers is ...

√(245·5) = √1225 = 35

Answer:

35

Step-by-step explanation:

Take the product of the two numbers, then get the square root of the product.

[tex]245*5=1225\\\sqrt{1225} = 35[/tex]

Final answer:

The function f(x) = 4(2)^(-x) - 3 approaches -3 as x approaches infinity and decreases without bound as x approaches negative infinity, with a horizontal asymptote at y = -3.

Explanation:

The end behavior of a function describes what happens to the function's values as x approaches infinity or negative infinity. For the function f(x) = 4(2)^(-x) - 3, as x approaches infinity, the term 2^(-x) approaches zero, because any non-zero base raised to the power of negative infinity is zero. Thus, the function approaches -3. Conversely, as x approaches negative infinity, the term 2^(-x) grows exponentially, and the function's values decrease without bound, heading towards negative infinity. However, since f(x) involves a negative exponential function, the graph ultimately will approach the horizontal asymptote y = -3.

Well I wanna do you want us to pick you guys up tomorrow at night to

Hello!

I want to help you but where is the image or answer choices? Thanks for asking— I’ll help if a I have the answer options or a photo because the question can’t be answered as there would be an infinite possible choices. It’d be great help! Thanks!

Have a great day!

~ Destiny ^_^

Answer:

24

Step-by-step explanation:

If its the figure shown, the answer is 24.