The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.

Write a function, C(x), to model the water used by the car wash on a shorter day.

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

Answer:

[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Step-by-step explanation:

The total number of ways in which 5 specimens can be selected from the  dish at random is given as C(40, 5).

Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).

3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).

Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Answer:

They are similar because corresponding sides are not proportional

Answer:

−5 < x < 10

Step-by-step explanation:

−6 < x − 1 < 9

Add 1 to all sides

−6+1 < x − 1+1 < 9+1

−5 < x < 10

Answer:

B

Step-by-step explanation:

Add one to everything

-5 < x < 10

Best of Luck!

Answer:

First, we can write:

x = 2 . ¯ 3

Next, we can multiply each side by  10 giving:

10 x = 23 . ¯ 3

Then we can subtract each side of the first equation from each side of the second equation giving:

10 x − x = 23 .¯ 3 − 2 . ¯ 3

We can now solve for  x  as follows:

10 x − 1 x = ( 23 + 0 . ¯ 3 ) − ( 2 + 0 . ¯ 3 )  ( 10 − 1 ) x = 23 + 0 . ¯ 3 − 2 − 0 . ¯ 3  

9 x = ( 23 -2 ) + ( 0 . ¯ 3 − 0 . ¯ 3 )  

9 x = 21 + 0

9 x = 21

9 x /9 = 21 /9

9 x /9 = 3 × 7 /3 × 3

x = 3 × 7 /3 × 3

x = 7 /3

Hope this helps!

Plz mark brainliest! ☜(ﾟヮﾟ☜)

Answer:

A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.

Step-by-step explanation:

Answer:

C.) A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.

Step-by-step explanation:

Answer:

u should put this also in English then type it in so it will translate

frustum of a cone is: = pi * l(R + r)

(l) = slant height of the frustum.

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

from 2929.645714 - 506.1257143

= 2423.52

= 2423.5cm

Answer:

30 cm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 6 and h = 10 , thus

A = [tex]\frac{1}{2}[/tex] × 6 × 10 = 3 × 10 = 30 cm²

and 7² = 7 × 7 = 49

Answer:

1)        30 cm²

2) Seven squared equals seven times 7

Step-by-step explanation:

Base = 6 cm

Height = 10 cm

Area of triangle = [tex]\frac{1}{2}[/tex]*base * height

                          = [tex]\frac{1}{2} * 6 * 10[/tex]

                         = 3 * 10

                          = 30 cm²

2) 7² = 7 * 7

Answer:

y =  4  or y = 6

Step-by-step explanation:

2log4y - log4 (5y - 12) = 1/2

​2log_4(y) - log_4(5y-12) = log_4(2)           apply law of logarithms

log_4(y^2) + log_4(1/(5y-12)) = log_4(/2)    apply law of logarithms

log_4(y^2/(5y-12)) = log_4(2)                     remove logarithm

y^2/(5y-12) = 2                                            cross multiply

y^2 = 10y-24                                                  rearrange and factor

y^2 - 10y + 24 = 0

(y-4)(y-6) = 0

y= 4 or y=6

a)

X + Y = 5

2X - Y = 9      

X + 2X + Y - Y = 5 + 9

3X = 14

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:

X+ Y = 5

14/3 + Y = 5

Y = 5 - 14/3

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

b)

3X - Y = 10

X + Y = 18        

3X + X - Y + Y = 10 + 18

4X = 28

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:

X + Y = 18

7 + Y = 18

Y = 18 - 7

Answer:

x = 1/8

Step-by-step explanation:

[tex]\log _2\left(x\right)=-3\\\\\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\\\\\log _2\left(x\right)=-3\quad \Rightarrow \quad \:x=2^{-3}\\\\Simplify\\\\x=\frac{1}{8}[/tex]

Answer:

y = 1/3x + 4/7

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Formula: y = mx + b

Step 1: Find slope m

m = (1 - 2)/(-3 - 4)

m = -1/-7

m = 1/7

y = 1/7x + b

Step 2: Find y-intercept b

1 = 1/7(3) + b

1 = 3/7 + b

b = 4/7

Step 3: Write linear equation

y = 1/3x + 4/7

Answer:

each shirt costs $17.50.

Step-by-step explanation:

we have the equation 4(12.50) + 4(2x) = 190

because each friend (4 total friends) get one hat and two shirts.

we simplify the equation to 50 + 8x = 190

subtract 50 from both sides

8x = 140

divide both sides by 8

x = 17.5

therefore, each shirt costs $17.50.

Answer:

After 6 years = 87120 people.

Before 6 years = 5808 people.

Step-by-step explanation:

To calculate how many populations that are added in every 10% in 3 years:

72600 × 10/100 = 7260

After 6 years = 72600 + 7260 × 2 = 87120 people.

Before 6 years = 72600 - 7260 × 2 = 5808 people.

Answer:

a) irrational

b) irrational

c) rational

d) rational

e) irrational

Note:

rational numbers are numbers that can be expressed in fractions.

irrational numbers are numbers that cannot be expressed in fractions i.e. they are never-ending-non-repeating decimals. examples √2, pi etc.

Answer:

We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Step-by-step explanation:

We are given that a researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Let [tex]\mu[/tex] = mean weight of cereal in its 18-ounce boxes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 18       {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 18      {mean that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces}

Also, it is given that the P-value is 0.01 and the level of significance is 0.05.

The decision rule based on the P-value is given by;

Here, clearly our P-value is less than the level of significance as 0.01 < 0.05, so we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.

Therefore, we conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.

Answer:

30-100/1000*120

Step-by-step explanation:

Source: Khan Academy

Answer:

30 - 100/1000 x 120

Step-by-step explanation:

Answer:

x = 58

Step-by-step explanation:

The secant- tangent angle 51° is half the difference of the measures of the intercepted arcs, that is

[tex]\frac{1}{2}[/tex] (160 - x) = 51 ( multiply both sides by 2 )

160 - x = 102 ( subtract 102 from both sides )

58 - x = 0 , thus

x = 58

Answer: The shop must order 695 boxes

Step-by-step explanation:

To find how many boxes that holds 100,080 candles, first divide the amount of candles that is needed to the measured amount of candles that is in a box.

144 candles= 1 box

100,080= ? Box(es)

So:

100,080 ÷ 144= 695 boxes

I hope this helps! I'm sorry if it's wrong.

Answer:

Add a zero to the remainder and a decimal point in the quotient. Then we can continue to divide decimals. We divide 64 by 5 and obtain 12 as a quotient and 4 as a remainder. Since the remainder is not zero, we can continue to get a decimal answer by adding a decimal point in the quotient and a zero to the remainder

Step-by-step explanation:

Answer:

Given the information above, the area of the square is 361 cm²

Step-by-step explanation:

A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.

The perimeter of the square is 76. So, let's divide 76 by 4.

76 ÷ 4 = 19

So, the lengths of each sides in the square is 19cm.

In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.

19 × 19 = 361

So, the area of the square is 361 cm²

Answer:

361 cm^2

Step-by-step explanation:

The area of a square can be found by squaring the side length.

[tex]A=s^2[/tex]

A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.

[tex]s=\frac{p}{4}[/tex]

The perimeter is 76 centimeters.

[tex]s=\frac{76 cm}{4}[/tex]

Divide 76 by 4.

[tex]s=19 cm[/tex]

The side length is 19 centimeters.

Now we know the side length and can plug it into the area formula.

[tex]A=s^2\\s=19cm[/tex]

[tex]A= (19 cm)^2[/tex]

Evaluate the exponent.

(19cm)^2= 19 cm* 19cm=361 cm^2

[tex]A= 361 cm^2[/tex]

The area of the square is 361 square centimeters.

Answer:Yes, because all integers have decimals. No, because integers do not have decimals. No, because integers cannot be negative. Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern.

Step-by-step explanation:

Answer:

  y = (x -1)² -3

Step-by-step explanation:

A quadratic with a vertex at (h, k) will have an equation of the form ...

 y = a(x -h)² +k

You have (h, k) = (1, -3), and a vertical scale factor* of 1. So, the equation of the graphed curve is ...

  y = (x -1)² -3

_____

* One way to determine the value of "a" in the form shown is to look at the vertical difference between the vertex and the points 1 unit right or left of the vertex. Here, those points are 1 unit above the vertex, so the vertical scale factor "a" is 1.

The dilation rule (x,y) --> (1.5x, 1.5y) says to multiply each coordinate by the scale factor 1.5

Point A in blue is located at (5,5). After dilation, it will move to A ' (7.5, 7.5)

Point B is located at (0,2) and it moves to B ' (0,3)

Point C is located at (1,-1) and it moves to C ' (1.5, -1.5)

This all matches with what is shown below, so the answer is choice B

Answer:

6

Step-by-step explanation:

To calculate x+10, we first need to find x. To do this, we can use the first equation.

We are given the equation:

[tex]x^2-8x=48[/tex]

To solve for x, turn one side of the equation into 0 and solve. Therefore:

[tex]x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12[/tex]

So, the possible values for x are -4 and 12.

However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.

So:

[tex]x+10\\(-4)+10\\=6[/tex]

Answer:

40 degrees.

Step-by-step explanation:

Rotations are a rigid transformation and therefore preserve size and angles.

Answer:

(13)^2 (13)^-14 (13)^5

=2197

Answer:

13^3

Step-by-step explanation:

-4+2+5=3

is it . that or something else ??

Answer:

cot α = 1/tan α = 1/2.4 = 0.42

Step-by-step explanation:

cot α=0.42

sin α = 0.92

we know that  cot α = 1/tan α

thus,

cot α = 1/tan α = 1/2.4 = 0.42

we know that

sin(x)=tan(x)1+tan2(x)√

[tex]\ sin(\alpha )=tan(\alpha )/\sqrt{ 1+tan^2(\alpha )} \\sin(\alpha )= 2.4/\sqrt{1+2.4^2} = 2.4/\sqrt{1+5.76}\\sin(\alpha )= 2.4/\sqrt{6.76} = 2.4/2.6 = 12/13 = 0.92[/tex]

sin α = 0.92