Tim’ mom filled the ga tank in her SUV and pent $72. 00 for 22. 5 gallon of unleaded gaoline. What i the contant of proportionality that relate the cot in dollar, y, to the number gallon of unleaded gaoline, x?

Answer:

P(x) = $31x - $840

Step-by-step explanation:

Let x be the number of bicycles.  The total cost for purchasing and repairing the bikes is $47x, plus a one-time purchase of $840 for a workshop and tools.  Total cost, C is therefore:

  C(x) = $47x + $840

We learn Aidan sells the bikes for $75 each.  Total revenue, R, is:

  R(x) = $75x

Profit, P, would be the difference of revenue, R, and costs, C:

  P(x) = R(x) - C(x) or $75x -($47x + $840)

    P(x) = $75x -$47x - $840

    P(x) = $31x - $840

P(x) represents the total profit for x bicycles.

See the attached graph.  Note the key features of the graph are the breakeven (27 bikes) and the initial investment (-$840).  We can find the breakeven point by looking for the value of x when the profits are $0.  A more accurate determination can be found by solving the equation we developed for the case in which P(x) = $0:

P(x) = $31x - $840

0 = $31x - $840    for P(x) = 0 (breakeven)

$31x = $840

x = 27.1 units.  We need to round to 27 units since 0.1 of a bicycle makes no sense in this context.

The solution of the mathematical statement is 102.5

From the question, we have the following mathematical statement that can be used in our computation:

"What is -5/2 times -41"

This means that

-5/2 times -41

Express as numbers

So, we have

-5/2 * -41

Divide 5 by 2

So, we have

-2.5 * -41

Evaluate the product

102.5

Hence, the result is 102.5

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The vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.

A parabola's vertex is the location where the curve turns steepest. If a parabolic function has the shape of a 'U', it has a minimum value; otherwise, it has a maximum value. The parabola's axis of symmetry intersects with the parabola at its vertex.

For any parabola Ax² + Bx + C, the x-coordinate of the vertex is given by -B/(2A).

So, according to our question

A = -1
B = 12
C = -4

So, z = - 12/2(-1)

z = - 12/- 2

z = 6

Plug the value in the equation

y = - (6)² + 12(6) -4

y = -36 +72 -4

y = 32

So, the vertex of the parabola will be at (6, 32) and the vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.

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Answer:

-6

Step-by-step explanation:

-7 x -1 = 7

7 - 13 = -6

False, one can tell if a data set is close to symmetric or not by watching a histogram.

             The histogram exhibit a symmetrical distribution of given data. The data is symmetrical if we are able to draw a vertical line at some point in the histogram such that its shape on both sides of the left and the right of the vertical line exactly reflected images to each other. The mean, the median, and the mode are can be taken as examples to prove the symmetricity using histogram for these data.  

         In an altogether symmetrical distribution, the mean and the median are alike. Such as the mode has one mode (unimodal), and the mode is the alike as the mean and median.

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Answer:

D

Step-by-step explanation:

Since Δ QTS is isosceles then the base angles are congruent , that is

∠ TQS = ∠ QST = y

∠ QST and ∠ RST are a linear pair and sum to 180° , that is

∠ QST + ∠ RST = 180

y + ∠ RST = 180 ( subtract y from both sides )

∠ RST = 180 - y

the sum of the 3 angles in Δ TRS = 180° , that is

∠ RTS + ∠ TRS + ∠ RST = 180

∠ RTS + x + 180 - y = 180 ( subtract 180 from both sides )

∠ RTS + x - y = 0 ( subtract x - y from both sides )

∠ RTS = y - x

The student council sold $273$ t-shirts were sold at $\$10$ per shirt.

Let $x$ be the number of shirts sold at $\$10$

Let $y$ be the number of shirts sold at $\$12$

$x+y=661$

$10x+12y=3780$

$x=y+101$

$10y+12y=3780$

$22y=3780$

$y=172$

$x=172+101$

$x=273$

Hence $273$ t-shirts were sold at $\$10$ per shirt.

If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.

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Answer:

Option 3 ) 18x - 9 = 72

Step-by-step explanation:

Algebraic equations:

  [tex]\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\[/tex]

Multiply each term of (30x - 15) by 3/5,

    [tex]\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72[/tex]

The given equation is same as 18x - 9 = 72

The values of the variables x in the  equations are;

An equation is a mathematical statement that connects two mathematical expression with an equals sign.

x + 9 = 13

Subtracting 9 from both sides of the equation, we get;

x = 13 - 9 = 4

3•x = 12

Dividing both sides of the equation by 3, we get;

x = 12 ÷ 3

x + 5 - 9 = 0

Subtracting (5 - 9) from both sides of the equation, we get;

x = 9 - 5 = 4

2•x + 5 = 17

Subtracting 5 from both sides of the equation, we get;

2•x  = 17 - 5 = 12

2•x = 12

Dividing both sides of the equation by 2, we get;

x = 12 ÷ 2 = 6

5•x - 3 = 17

Adding 3 to both sides of the equation, we get;

5•x = 17 + 3 = 20

5•x = 20

Dividing both sides of the equation by 5, we get;

x = 20 ÷ 5 = 4

x - 3 = 1

Adding 3 to both sides of the equation, we get;

x = 1 + 3

7•x = 35

Dividing both sides of the equation by 7, we get;

x = 35 ÷ 7 = 5

[tex]\frac{4\cdot x}{4} = 4 [/tex]

Multiplying both sides of the equation by 4 and dividing the result by 4, we get;

x = 4 × 4 ÷ 4 = 4

3•(x + 4) = 15

Dividing both sides of the equation by 3, we get;

x + 4 = 15 ÷ 3 = 5

x + 4 = 5

Subtracting 4 from both sides of the equation, we get;

x = 5 - 4 = 1

8 + x - 5 = 7

Adding 5 and subtracting 8 from both sides of the equation, we get;

x = 7 + 5 - 8 = 4

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When r is made the subject of the formula we have; V + πh^3/3πh^2

The term subject of a formula has to do with the variable that we are trying to obtain in the equation. Hence the subject of the formula must be written on the left hand side of the mathematical equation.

We have;

V = πh^2(r - h/3)

We open the bracket;

V = πrh^2 - πh^3/3

Adding πh^3/3 to both sides, we have;

V + πh^3/3 = πrh^2

Then we divide both sides by πh^2

r = V + πh^3/3/πh^2

r =  V + πh^3/3πh^2

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Answer: c = 30

Step-by-step explanation:

[tex]12=\frac{c-6}{2}\\ \\12(2)=c-6\\\\24=c-6\\\\c=24+6=30[/tex]

Step-by-step explanation:

Please refer to photo for drawing

Answer:

C

Step-by-step explanation:

(-2x -9y^2) (-4x - 3)

= 8x^2+6x + 36y^2x+27y^2

Answer:

(-3,5)

Step-by-step explanation:

we just plug the solutions in the equation to see if it’s true

y<x+12

12<-4+12

12<8

Not true 12 is not less than 8

9<-7+12

9<5
not true 5 is not greater than 9

8<-5+12

8<7

Not true 8 is not less than 7

5<-3+12

5<9
true 5 is less than 9

Hopes this helps please mark brainliest

The value to the system of equations is (-10, -4)

In this case, the system of equations is given as

5x -10y = 10

x + 2y = -18

Make x the subject in the second equation

So, we have the following representation

x = -2y - 18

Substitute x = -2y - 18 in the equation 5x -10y = 10

So, we have

5(-2y - 18) -10y = 10

Open the brackets

This gives

-10y - 90 - 10y = 10

Evaluate the like terms

-20y = 80

Divide by -20

y = -4

Recall that x = -2y - 18

So, we have

x = -2 * -4 - 18

Evaluate

x = -10

Hence, the solution is (x, y) = (-10, -4)

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Answer:

the side a  is equal to 15.

Step-by-step explanation:

I entered it into my calculator.

Answer:

Yes, the relation is proportional

Step-by-step explanation:

For a proportional relation, the ratio of X/Y (and thus Y/X) should be constant. You can verify, for examply dividing each Y by the corresponding X:

9 / -3 = -3

6 / -2 = -3

-3 / 1 = -3

-6 / 2 = -3

-9 / 3 = -3

As you can see, the ratio is the same, so the relation is proportional.

Answer:

Step-by-step explanation:

EQUATION: F = km / d²100 = k(8) / (5)²100 = k 8 / 25100 ÷ 8 / 25 = k 8 / 25 ÷ 8 / 25625 / 2 = kF = (625 / 2)(2) / (15)²F = 625 / 225F = 25 / 9

Answer:

Option A

Step-by-step explanation:

We are here given that Mary spent a total of $ 355.58 for a party , $200.93 on food , and an additional charge of $30.93 for each hour of party .

So the total money spent for staying at party , will be ;

[tex]\longrightarrow \$ 355.58 - \$200.93 [/tex]

[tex]\\\longrightarrow \$ 154.65 [/tex]

We can calculate the no. of hours spent at the party by dividing this amount by the rate of staying per hour at party as ;

[tex]\\\longrightarrow \dfrac{ \$ 154.65}{\$ 30.93 / hr } [/tex]

[tex]\\\longrightarrow 5 \ hrs . [/tex]

Hence she spent 5hrs at the party .

The answer of resulting box volume = 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]

What are example and volume?

The volume of an object serves as a gauge for its capacity. For instance, if the brim of a cup can hold 100 ml of water, that cup is said to have a 100 ml capacity.. Another way to quantify volume is how much room a three-dimensional object occupies.

Volume = length x breath x height

length = 32-2[tex]x[/tex]
Breath = 18-2[tex]x[/tex]

Height = [tex]x[/tex]

Volume = (32-2[tex]x[/tex]) x (18-2[tex]x[/tex]) x ([tex]x[/tex])

= 576 - 64[tex]x[/tex] - 36[tex]x[/tex] - 4[tex]x^{2}[/tex] x ([tex]x[/tex])

= 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
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Answer:

Area under the curve f (x) = 38 on interval [88, 132]: 38 132 -3344 (Decimal: 1672)

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Check the file

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5(2)^2 - 6}[/tex]

[tex]\mathsf{= 5(2 \times 2) - 6}[/tex]

[tex]\mathsf{= 5(4) - 6}[/tex]

[tex]\mathsf{= 20 - 6}[/tex]

[tex]\mathsf{= 14}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

There is a probability of 22% that exactly 4 defective parts will be found in a sample of 100.

Probability of a machine producing a defective part is 0.05,

p = 0.05

q  = 1 - p = 1 - 0.05 = 0.95

n = 100

P(x)  = ⁿCₓ pˣqⁿ⁻ˣ

x = 4  

P(4) = ¹⁰⁰C₄(0.05)⁴(0.95)⁹⁶

P(4) = 0.215569

=  0.2156

0.2156 is the probability of finding exactly 4 defective parts from a sample of 100.

The probability of defective parts is the likelihood that a part will be defective. This can be due to a variety of factors, such as poor quality control, incorrect manufacturing process, or use of sub-standard materials. A high probability of defective parts can lead to serious problems, such as faulty products, safety hazards, and financial losses.

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Probability of choosing the biased coin if you won a prize is 0.30

Let "B" be the event of selecting biased coin and "H" be the event of getting head.

P(B) = 0.5

P(getting head when coin was biased) = 100% - 78%

= 22% = 0.22

Using conditional Probability that biased coin was selected given that you have won the prize that is getting head

we have to calculate ,

P(B | H ) = P(B∩H)/P(H)

here , P(B∩H) = P(biased coin selected and getting head) = 0.5 × 0.22

and P(H) = P(getting head)

P(getting head when coin was biased) + P(getting head when coin was unbiased) = 0.5 × 0.22 + 0.5 × 0.5

putting all together ,

P(B | H ) = P(B∩H)/P(H) = 0.5 × 0.22 / 0.5 × 0.22 + 0.5 × 0.5

cancelling 0.5 from numerator and denominator

= 0.22 / 0.5+ 0.22

= 0.22 / 0.72 = 22/72

=0.30

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n/16 lies between 4/16 and 8/16

So, n can be 5,6,7

Answer:

5, 6 , 7

Step-by-step explanation:

Change 1/4 and 1/2 to the values they would be if their denominator was 16

1/4 will become 4/16

1/2 will become 8/16

the values between these are 5/16, 6/16, 7/16

n can be 5, 6 or 7

Answer:

Yes, he is correct

Step-by-step explanation:

100% : x

62%   : 19

Cross multiply

19*100% = 62%x

19 = 0.62x

19/0.62 = x

x = 30.645

Rounds up to 31

The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:

x = 5, x = -1 + i, x = -1 - i.

The equation is defined by the rule presented as follows:

f(x) = 2x³ - 6x² - 16x - 20.

One solution for the equation is given as follows:

x = 5.

Because f(5) = 0.

Then (x - 5) is a linear factor of the function f(x), which can be written as follows:

2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).

This is because the product of a linear function and a quadratic function results in a cubic function.

Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:

2x³ - 6x² - 16x - 20 =  = ax³ + (b - 5a)x² + (c - 5b)x - 5c.

Then these coefficients are obtained comparing the left and the right side of the equality as follows:

Hence the equation is:

2x² + 4x + 4.

Using a quadratic equation calculator, the remaining zeros are given as follows:

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