Using an Algebraic Expression to Represent a Problem
CAR
WASH
Fundraiser !!!
Raising money
The science club sponsors a car
wash every year to raise money for
the state robotics competition.
This year, the club raised $20 more
than twice what it raised last year.
Answer these questions to write an algebraic expression for the car wash problem.
Check Your Understanding- Question 1 of 3
Attempt 1 of 2
What missing piece of information would help you write an algebraic expression to
represent the amount of money raised this year?
A. The number of cars that were washed
B. The number of club members going to the robotics competition
C. The price of each car wash
D. How much the science club raised during last year's car wash

Answer:

1/16

Step-by-step explanation:

F(-4) = 2^-4

= 1/(2^4) = 1/16

Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.

Option C is the correct answer.

Given that;

[tex]\frac{4+\sqrt{5} }{\sqrt{5} -2}[/tex]

To rationalize the denominator, we multiply the expression by [tex]\frac{\sqrt{5} +2 }{\sqrt{5} +2}[/tex]

Hence

[tex]\frac{4+\sqrt{5} }{\sqrt{5}-2 } *\frac{\sqrt{5} +2 }{\sqrt{5} +2}\\\\\\\frac{(4+\sqrt{5}) }{(\sqrt{5}-2) } \frac{(\sqrt{5} +2) }{(\sqrt{5} +2)}\\\\\\\frac{(4+\sqrt{5})(\sqrt{5}+2) }{\sqrt{5}^2+\sqrt{5}*2-2\sqrt{5} -4 } \\\\\\\frac{(4+\sqrt{5} )(\sqrt{5}+2 )}{1}\\ \\(4+\sqrt{5} )(\sqrt{5}+2 )\\\\4\sqrt{5}+4*2+\sqrt{5}\sqrt{5}+\sqrt{5}*2\\ \\ 4\sqrt{5}+8+5+2\sqrt{5}\\ \\ 6\sqrt{5}+13[/tex]

Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.

Option C is the correct answer.

Learn more about how to Rationalize denominator here:https://brainly.com/question/27485639

#SPJ1

What I gather from the question is that [tex]X[/tex] has second moment [tex]E(X^2)=81[/tex] and variance [tex]V(X) = 58[/tex], and you're asked to find the expectation and variance of the random variable [tex]Y=2X+10[/tex].

From the given second moment and variance, we find the expectation of [tex]X[/tex] :

[tex]V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}[/tex]

Expectation is linear, so

[tex]E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}[/tex]

Using the same variance identity, we have

[tex]V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2[/tex]

and

[tex]E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}[/tex]

so that

[tex]V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}[/tex]

Alternatively, we can use the identity

[tex]V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232[/tex]

Answer:

The missing number is 11

Step-by-step explanation:

Step-by-step explanation:

x is the number

8x + 4 = 92 (8 times the number plus 4 is 92).

8x = 88

x = 11

the number is 11.

In order to determine the coordinates of the circumcenter of triangle DEF with the given vertices, let its circumcenter be P(x, y). Hence, PD = PE = PF.

By squaring all sides of triangle DEF, we have:

PD² = PE² = PF²

From PD² = PE², we have:

(x - 6)² + (y - 0)² = (x - 0)² + (y - 6)²

x² - 12x + 36 + y² = x² + y² - 12y + 36

-12x + 12y = 0    ..........equation 1.

From PE² = PF², we have:

(x - 0)² + (y - 6)² = (x - (-6))² + (y - 0)²

x² + y² - 12y + 36 = (x + 6)² + y²

x² + y² - 12y + 36 = x² + 12x + 36 + y²

-12x - 12y = 0     ..........equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

x = 0 and y = 0.

Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (0, 0).

From PD² = PE², we have:

(x - 0)² + (y - 0)² = (x - 6)² + (y - 0)²

x² + y² = x² - 12y + 36 + y²

12y = 36    

y = 3.

From PE² = PF², we have:

(x - 6)² + (y - 0)² = (x - 0)² + (y - 4)²

x² - 12x + 36 + y² = x² + y² - 8y + 16

-12x - 8y = -20    

-12x - 8(3) = -20

-12x - 24 = -20

12x = -4

x = -1/3.

Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (-1/3, 3).

Read more on circumcenter here: https://brainly.com/question/28027775

#SPJ1

Answer:

vertical shift is 3 units down

horizontal shift is 2 units left

Step-by-step explanation:

y=srx+2-3

vertical shift is 3 units down

horizontal shift is 2 units left

Answer:

Use sine rule.

Explanation:

[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]

If opposite side of an angle and hypotenuse is given.

Use sine rule: sin(θ) = opposite/hypotenuse

For example:

Given that opposite of the angle is 10 cm and hypotenuse is 20 cm.

To find the angle:

sin(θ) = 10/20

θ = sin⁻¹(10/20)

θ = sin⁻¹(1/2)

θ =  30°

Several ways

You can use sin directly

As

Then you can find Ø from it

Otherwise

You may find adjacent using Pythagorean theorem

Then you can use cos

You may use tan even

Answer:

3

Step-by-step explanation:

using the power we multiply the exponents (27^1/2)^2/3 to get 27^1/3=3

The number of problems Shelly has to complete is 25 problems

x = 10 + 2/7x

x - 2/7x = 10

(7x-2x)/7 = 10

5/7x = 10

x = 10 ÷ 5/7

= 10 × 7/5

= 70/5

x = 35 problems

So,

Number of problems to complete = Total problems - completed problem

= 35 - 10

= 25 problems

Learn more about fraction:

https://brainly.com/question/11562149

#SPJ1

Answer:

90.000 m³

Step-by-step explanation:

V = L × W × H

V = 6 × 5 × 3.000

V = 30 × 3.000

V = 90.000 m³

Hello !

[tex]6 \times 5 \times 3 = 90 {m}^{3} [/tex]

The amount of air is 90m³.

Have a nice day ;)

Answer: 89.7

Step-by-step explanation:

The mean of a data set is the average of all the information given. Therefore, the total combined score is the number of students multiplied by the mean

The total score of the first 44 students: 96.6*44 = 4250.4

The total score of the later 13 students: 66.3*13 = 861.9

(4250.4 + 861.9)/(44 + 13) = 89.7

Hope this helped

The missing algebra property justification for the equation solution is; Multiplicative Inverse

We are given the equation;

2x - 7 = 15

Step 1; Add 7 to both sides to get; 2x - 7 + 7 = 15 + 7

2x = 22

Reason; Addition property of equality

Step 2; Multiply both sides by 1/2(one half) to get;

(1/2) * 2x = (1/2) * 22

x = 11

Reason; Multiplicative Inverse

Read more about Algebraic Properties at; https://brainly.com/question/723406

#SPJ1

The probability that the sample proportion is less than 0.80 is mathematically given as P(z<-0.52)

Generally, the equation for probability is  mathematically given as

p=82/100

Therefore

p=0.82

q=1-p

q=1-0.82

q=0.18

[tex]SE=\sqrt{\frac{p(1-p)}{n}}\\\\SE=\sqrt{\frac{0.8(1-0.8)}{100}}\\\\SE=0.03841[/tex]

b)

[tex]P(p < 0.80)=p(\frac{p-0.82}{0.0384} < \frac{0.8-0.82}{0.0384})\\\\P(z < -0.52)[/tex]

Read more about probability

https://brainly.com/question/11234923

#SPJ1

Answer:

35

Step-by-step explanation:

This shape has 6 sides.

Sum of interior angles of a 6 sided shape is 720.

117 + 4x - 5 + 4x - 3 + 118

+ 3x + 6 + 3x - 3 = 720

4x + 4x + 3x + 3x

+ 117 + 118 + 6 - 5 - 3 - 3 = 720

14x + 241 - 11 = 720

14x + 230 = 720

14x = 720 - 230

14x = 490

x = 490/14

x = 35

The mistaken assumption is that the customer thinks the shoes are back to their original price.

The assumption is wrong because the price of the shoe is now lower than $150.

The cost of the shoe now is $126.

In order to retain the price of $150, the percentage decrease should have been 28.6%.

Price of the shoe after it was increased : 1.4 x 150 = 210

Price of the shoe after it was decreases: (1 - 0.4) x 210

0.6 x 210 = $126

The percentage the price should be decreased for the price to be back to $150 = (150 / 210) - 1 = 28.9%

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

Answer:

1800 m

Step-by-step explanation:

1 km = 1000 m

1.8 km = 1.8 × 1 km = 1.8 × 1000 m = 1800 m

The total cost for the increment is $13,000.

There are 5 employee's in Sasha's department. The total amount of increment is $5000. (5 x $1000).

The lowest salary is 32,000. If it is increased to $40,000. The total cost of the increment is $8000 (40,000 - 32,000)

Total cost of the increment = $8000 + $5000 = $13,000

To learn more about addition, please check: https://brainly.com/question/19628082

#SPJ1

The amount in lee's mutual fund account after 8 years will be $7600

Given: Principal amount (P) = $5000,

Time (t) = 10 years,

Rate of interest (r) = 6.5% per year

To find: lee's mutual fund account after only 8 years

We know that Simple interest (SI) is given by:

[tex]S.I = \frac{PTR}{100}[/tex].......(1)

So, by using equation (1) money (P') in a mutual fund account after 8 years will be

[tex]P'=P+\frac{PTR}{100}[/tex]

[tex]=5000+\frac{5000*6.5*8}{100}[/tex]

[tex]= 5000+50*6.5*8[/tex]

= 5000+2600

= 7600

Hence, the amount in lee's mutual fund account after 8 years will be $7600

Learn more about Simple Interest here https://brainly.com/question/25793394

#SPJ4

The inequality of the given graph in Slope Intercept Form is;

y ≥ 3x - 2

From the attached graph, we see that the boundary line passes through the points (0,-2) and (1,1), and as such the equation of the boundary line is gotten from the general formula;

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

Thus, we have;

(y + 2)/(x - 0) = (1 + 2)/(1 - 0)

(y + 2)/x = 3

y + 2 = 3x

y = 3x - 2

Now, the boundary line is a solid line and the shaded area lies above the boundary line, therefore the sign of inequality must be ≥.

The inequality of the given graph in Slope Intercept Form is;

y ≥ 3x - 2

Read more about Inequality in slope intercept form at; https://brainly.com/question/23884378

#SPJ1

Answer: 1/9

Step-by-step explanation:

-(8/24)^2 / -(8/24)^0

cancel the negatives and simplify 8/24 to 1/3

(1/3)^2 / (1/3)^0

(1/3)^0 = 1

so,

(1/3)^2 = 1/9

Final answer:

The answer is 10.65.

Step-by-step explanation:

Step 1

Substitute a=1,5 into expression

7.1a, a=1.5

7.1 x 1.5

Step 2

Multiply the numbers

7.1 x 1.5 = 10.65

Answer:

10.65

Step-by-step explanation:

Plug a into the expression

[tex]7.1\times1.5=10.65[/tex]

Hope I helped you in some way!

Answer:

A

Step-by-step explanation:

The graph is composed of two different rays.

Also, when x = -2, there is an open hole.

This leaves A as the answer.

Answer:

[tex]f^{-1}(x)=x^2+1[/tex]

Step-by-step explanation:

The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y

Original Equation:

[tex]f(x)=\sqrt{x-1}\\[/tex]

write f(x) as y (since that's what it represents)

[tex]y=\sqrt{x-1}[/tex]

Swap x and y

[tex]x=\sqrt{y-1}[/tex]

Square both sides

[tex]x^2=y-1[/tex]

Add 1 to both sides

[tex]x^2+1=y[/tex]

So this gives you the equation:

[tex]f^{-1}(x)=x^2+1[/tex]

Answer:

  x + 10

Step-by-step explanation:

You want to know how much money Joyce has if she won a bet with George in which they both started with the same money, both bet 5 cents, and George ended up with x cents.

We assume that both Joyce and George put 5 cents in the pool. After doing that, each had x cents. If Joyce won the 10-cent pool, she now has ...

  x + 10 cents

__

Additional comment

If they both bet against a house, or in a situation where a third party was involved, the amount Joyce ends with depends on the odds of the game, or the percentage collected by the house.

Given that the game is not specified, we have made up the rules.

<95141404393>

A function assigns the values. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The complete options of the question are mentioned in the below image.

The cost  cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. Therefore, the graph of the equation can be drawn as shown below.

Hence, the correct option is D.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

The area of a 2D form is the amount of space within its perimeter. The length of the rectangle is 29 inches and the width of the rectangle is 12 inches.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Let the width of the sheet be represented by x and the length be represented by y.

Area = x × y

348 = xy

x = 348/y

Perimeter = 2(x+y)

82 = 2(x+y)

41 = x + y

41 = (348/y) + y

0 = y² - 41y + 348

y = 29, 12

Therefore, the length of the rectangle is 29 inches and the width of the rectangle is 12 inches.

Learn more about the Area:

https://brainly.com/question/1631786

#SPJ1

The expression for the angle m∠RST from the given bisctor is; 6x - 18

From the given image in the attachment we are given that;

SQ bisects ∠TSR

m ∠RSQ = 3x - 9

Now, since  SQ is a bisector of ∠TSR, we can say that

m∠RST = 2 * m∠RSQ

Thus angle RST is expressed as;

m∠RST = 2(3x - 9)

m∠RST = 6x - 18

Read more about Angle expression at; https://brainly.com/question/16953095

#SPJ1

The difference between the rate of change of B and the rate of change of A is 15.

First, we need to get the two rates of change.

We have two linear functions.

A: y = 35*x

For function A the rate of change is the slope, wich is 35.

Function B is graphed.

Remember that if a line passes through two points (x₁, y₁) and (x₂,y₂) then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In the graph, we can see that line B passes through (0, 0) and (1, 50), then the slope is:

[tex]a = \frac{50 - 0}{1 - 0} = 50[/tex]

Then the rate of change of B is 50.

The difference between the rates of change is:

diff = 50 - 35 = 15

If you want to learn more about rates of change:

https://brainly.com/question/8728504

#SPJ1

Increase in Consumer Credit Card Debt is a debt Crisis , Option A is the correct answer.

What is Consumer Credit Card Debt ?

It is the debt which has been accumulated due to the consumers buying products and services out of the credit card and not paying them back in the period of 90 days.

In USA , the credit card balance is $841 billion in the first quarter of 2022 , which is $15 billion less form the last year but at a significant peak.

This extent of the consumer debt is a debt crisis.

The debt on the bank increases as the debt on the consumer increases , causing in bank recession and a recession brings harm to the economy , It is a crisis situation and need to be handled before it affects the market.

Therefore increase in Consumer Credit Card Debt is a debt Crisis , Option A is the correct answer.

To know more about consumer credit card debt

https://brainly.com/question/17286021

#SPJ1