Consider the following linear equation.

y=−43x+2
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.

The car which covers 28 miles on 1 gallon of gas that car will take 9 gallons of gas and drives 252 miles.

We know that the relation between distance, speed, and time is given by:

distance = speed * time

speed = distance / time

We are given;

Distance covered by the car = 252 miles

Gas used to cover  252 miles = 9 gallons

We will solve the given problem using the unitary method.

Since for 9 gallons of gas, the car covered a distance of 252 miles.

So, for 1 gallon of gas, the car covered a distance of 252 / 9 miles = 28 miles.

So, the car will drive 28 miles per gallon.

Thus, a car which covers 28 miles on 1 gallon of gas that car will take 9 gallons of gas and drives 252 miles.

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The greatest common factor of 30, 72, and 54 would be 6.

Answer:shanikas height

Step-by-step explanation:

The variables that the scatter plot is most likely to represent are:

c. The number of siblings a person has and the person's GPA.

A scatter plot is composed by a set of points in the following format:

(Input, Output).

Meaning that the objective of the scatter plot is to find a relation between the output variable and the input variable.

This relation, also classified as association, can be classified as follows:

in this problem, we have an oscillating scatter plot, meaning that it represents variables without any clear relation among themselves.

Hence, option c is correct, as there is no relation between the number of siblings that a person has and the GPA of the person.

For the other three options, they would have been represented by increasing scatter plots.

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The number of quarts of pure antifreeze that must be add to obtain a 30% antifreeze solution would be = 15 quart.

Antifreeze is defined as the solution that can be used to lower the freezing point of a liquid based substance.

The percentage solution of antifreeze 1 = 10

The quantity of quart of antifreeze 1 = 5

The percentage solution of antifreeze 2 = 30%

The quantity of quart of antifreeze 2 = x

Using the formula;

if 10% = 5

30% = X

make X the subject of formula:

X = 30×5/10

X = 150/10

X = 15 quarts.

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The rectangular design should be 2.5 m tall.

What is area of rectangle?

 A flat surface of a specific shape can be thought of as the area it occupies in space. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle is known as the area of a rectangle. The flat surfaces of laptop monitors, chalkboards, canvases, and other objects are a few instances of rectangular shapes. To determine the area that these items occupy, use the formula for a rectangle's area.

Here area of rectangle = 2[tex]m^2[/tex]

And width of the rectangle w= 4/5 m .

Using area of rectangle formula ,

=> A = h*w

=> 2= h*4/5

=> h = 10/4 = 2.5 m.

Therefore the rectangular design would be 2.5 m tall.

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a) This is a discrete probability distribution because the sum of the probabilities is of 1 and each probability is positive.

b) The distribution is represented by Graph A.

c) The mean is of: 1.559.

d) The standard deviation is of: 1.4

e) The probability that a student is involved in three activities is of 0.151.

f) The probability that a student is involved in three or four activities is of 0.28.

From the table, the distribution is presented as follows:

The sum of these probabilities is of:

0.332 + 0.186 + 0.202 + 0.151 + 0.129 = 1.

Since the sum is of one and none of the probabilities is negative, this is a valid discrete distribution shown by Graph A, as it associates each valeu of the input with it's respective probability.

The mean of the distribution is the sum of each outcome multiplied by it's probability, hence:

E(X) = 0 x 0.332 + 1 x 0.186 + 2 x 0.202 + 3 x 0.151 + 4 x 0.129 = 1.559.

The standard deviation is the square root of the sum of the differences squared between each outcome and the mean, multiplied by it's probability, hence:

S(X) = sqrt((0-1.559)² x 0.332 + (1-1.559)² x 0.186 + (2-1.559)² x 0.202 + (3-1.559)² x 0.151 + (4-1.559)² x 0.129) = 1.4.

The probabilities are given as follows:

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Answer: 2

x = 2

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

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

4 = 4

a. The part of the expression that represents the discounted price before tax is (x − 35).

b. The of the expression represent the amount of sales tax, is 0.12x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the expression 0.12x + (x − 35) models the final price of a scooter.

It should be noted that 0.12x represented the sale tax. In this case, the sales tax is 12% which was depicted as 0.12.

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The gallons of first brand is 102 gallons and that of the second brand is 68 gallons.

According to the question,

We have the following information:

The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. 170 gallons of a mixture contains 80% pure antifreeze.

Now, let's take the amount of first brand to be x gallons and that of the second brand to be y gallons.

So, we have the following expressions:

x+y = 170

x = 170-y ....(1)

70x/100 + 95y/100 = (80*170)/100

70x+95y = 13600

Now, putting the value of x from equation 1:

70(170-y)+95y = 13600

11900-70y+95y = 13600

11900+25y = 13600

25y = 13600-11900

25y = 1700

y = 1700/25

y = 68

Now, putting this value of y in equation 1:

x = 170-68

x = 102

Hence, the gallons of first brand is 102 gallons and that of the second brand is 68 gallons.

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Through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.

It is given to us that -

Each carton of food will feed 11 people

Each carton of clothing will help 4 people

Each 20-cubic-foot box of food weighs 40 pounds

Each 5-cubic-foot box of clothing weighs 20 pounds

The total weight per carrier cannot exceed 23,000 pounds

The total volume must be no more than 9000 cubic feet

We have to find out the number of cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped.

Let us say that -

The number of cartons of food = x

The number of cartons of clothing = y

According to the given information, the constraints on weight and size can be represented as -

Constraints on weight:

[tex]40x+20y\leq 23000\\= > 20y\leq 23000-40x\\= > 20y\leq -40x+23000\\= > y\leq -2x+1150[/tex]------ (1)

Constraints on size:

[tex]20x+5y\leq 9000\\= > 5y\leq 9000-20x\\= > 5y\leq -20x+9000\\= > y\leq -4x+1800[/tex]----- (2)

We also know that

[tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]

The equation for the help that will be provided with each carton of food and clothing can be represented as -

[tex]11x+4y[/tex] ---- (3)

From equation (1), for weight graph, we have

[tex]y\leq -2x+1150[/tex]

For [tex]x=0[/tex], [tex]y\leq 1150[/tex]

For [tex]y=0, x\leq 575[/tex]

From equation (2), for size graph, we have

[tex]y\leq -4x+1800[/tex]

For [tex]x=0, y\leq 1800[/tex]

For [tex]y=0, x\leq 450[/tex]

For (0,1150), the equation (3) becomes

[tex]11x+4y[/tex]

[tex]= 11*0+4*1150\\= 4600[/tex]

For (360, 550), the equation (3) becomes

[tex]11x+4y\\= 11*360 + 4*550\\= 6160[/tex]

For (450,0), the equation (3) becomes

[tex]11x+4y\\= 11*450 + 4*0\\= 4950[/tex]

Thus, through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.

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As per the concept of distance-speed-time formula, the speed of Rachel is 38 meters per second

Distance-speed-time formula

The general time formula to calculate the distance-speed-time for any task is given as

[Time = Distance ÷ Speed].

And the SI unit of time is seconds (s).

Given,

Rachel is a stunt driver, and she's escaping from a building that is about to explode! And the variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.

The function of d=-38t+220

Now, we have to find the speed of Rachel.

We already know that the speed is calculated as,

=> v = dx/dt

Here we have the distance is a function of time,

Now, we have to apply it one the given formula then we get,

=> v = d/dt( 38t + 220)

After the differentiation we get the value of

=> v = 38 m/s

Here the derivative of a constant (here 220) is zero.

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Employee: "Great! I make $12.00 per hour now, and that extra 10% would put me at $13. 20 per hour."

The supervisor says that should an employee work the late shift, they would be paid 10% more than they are paid now.

This increase in the wage rate is:

= Current wage rate x Increase for late shift

= 12 x 10 %

= $1. 20

The new wage rate for the employee would therefore be:

= Wage rate per hour + Extra if late shift is worked

= 12 + 1. 20

= $13. 20

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Answer:

apples 19%, bananas 38%, oranges 36%, and other fruits 7%

Answer:

i think the denominator of 5,12,3,8, is 24

Answer: 2.5 miles

We are given that

Total length of path=10 mile

Han runs at a pace=12 minutes per mile

Tyler runs at a pace=15 minutes per mile

We have to find the distance run by Han after a half hour.

Half hour=30 minutes

Using unitary method

Han runs distance in 12 minutes=1 mile

Han runs distance in 1 minute= mile

Han runs distance in 30 minutes= miles

Hence, Han runs 2.5 miles after half hour.

Step-by-step explanation:

The solution after the multiplication of 0.01 x 4066.61 is 40.6661

Multiplication

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. And the word multiply means the repeated addition of groups of equal sizes.

Given,

Here we have the operation 0.01 x 4066.61

Now we have to perform the multiplication operation in it.

While we looking into the given operation, we have identified that there are  4 total decimal places in both numbers.

First, we have to ignore the decimal places and complete the multiplication as if operating on two integers.

The the calculation for the multiplication is shown in the following image.

Now, we have to rewrite the product with 4 total decimal places.

Then we get the answer is 40.6661

Therefore, 0.01 × 4066.61 = 40.6661

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The ordered pair which s included in the solution to this system of inequality y ≥ 2/3x + 2, y < - 1/3x + 1 is (-6, -2) and (-6, 3).

The correct answer option is option B and C

y ≥ 2/3x + 2

y < - 1/3x + 1

Check all that applies:

(x, y) = (−6, −3)

(x, y) = (−6, −2)

(x, y) = (−6, 3)

(x, y) = (−6, 4)

y ≥ 2/3x + 2

substitute x = -6 into the inequality

y ≥ 2/3(-6) + 2

y ≥ -12/3 + 2

y ≥ - 4 + 2

y ≥ - 2

(x, y) = (-6, -2)

y < - 1/3x + 1

substitute x = -6 into the inequality

y < -1/3(-6) + 1

y < 6/3 + 1

y < 2 + 1

y < 3

(x, y) = (-6, 3)

So therefore, the solution to the system of inequality is (-6, -2) and (-6, 3).

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Answer:

-1/2

Step-by-step explanation:

(-1-(-5)/(1-9)

(-1 + 5)/-8

4/-8

- 1/2

To calculate the distance between two points, we have to:

We have that the points are: (x₁ = 9, y₁ = -5) and (x₂ = 1,y₂ = -1). To calculate the slope, we apply the following formula:

 [tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{y_2-y_1}{x_2-x_1} }}[/tex]

Substitute data into the formula and solve:

                          [tex]\boldsymbol{\sf{m=\dfrac{-1-(-5) }{1-9 }=\dfrac{4}{-8}=-0.5000 }}[/tex]

Yes, they justified giving us a ticket, even though we were not caught speeding, because we drove at a speed higher than the posted speed limit.

It is given that we are driving down a straight country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road, tracking vehicle speeds, and are in contact with each other. At the first officer’s position, we drive by going 39 miles per hour. At the second officer’s position, 63 seconds later, we drive by, going 38 miles per hour.

The second officer pulls us over and gives us a ticket. We will use the mean value theorem to check whether getting a ticket was justified or not. Let the maximum speed be "v" that we reach between the officers at time "c". Let the function f(t) denote the distance at time "t".

f'(c) = [f(b) - f(a)]/(b - a)

v = (1 - 0)/(63 - 0)

v = 1/63 miles per second

We need to convert the speed into miles per hour.

v = 3600/63 = 57.143 miles per hour

The speed is higher than the posted speed limit. Hence, they justified giving us a ticket, even though we were not caught speeding.

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Answer:

It is B

Tangent theta is undefined when cosine theta equals zero. Remember that identity.

The regular selling price per unit for the laptop is $298.6.

Let the regular price per unit be x.

The expense is 19% of the selling price and profit is 25% of the selling price. This will be illustrated as:

x + (19% × x) + (25% × x) = 430

x + 0.19x + 0.25x = 440

1.44x = 430

Divide

x = 430 / 1.44

x = 298.6

The price is $298.6

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The portion that were taking summer classes in 2016 is 31.4%.

From the information, the portion of students taking summer classes decreased 6.3% from 2015 to 2016 and it was stated that 38% of students took summer classes in 2015.

In this case, the portion of the people taking dinner classes will be:

= Original percentage - Reduction in percentage

= 38% - 3.6%

= 31.4%

The percentage is 31.4%

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Answer: $429

Step-by-step explanation:
$6600 + 6.5% = $7029
$7029 - $6600 =$ 429

The determination of the gross profit for April and the ending inventory on April 30, using the FIFO, LIFO, and weighted average cost methods, is as follows:

                                 Gross Profit    Ending Inventory

FIFO                                 $45                  $342

LIFO                                 $37                  $334

Weighted Average         $41                   $338

The gross profit is the difference between the net sales revenue and the cost of goods sold.

It is the first profit point in the income statement which measures the financial performance of an entity during a period.

The ending inventory is the difference between the cost of goods available for sale and the cost of goods sold, depending on the inventory method in use.

Some of the inventory methods include FIFO, LIFO, Weighted Average, and Specific Identification.

Item       Beta          Units    Cost

April 2   Purchase      1       $165

April 15  Purchase      1        169

April 20 Purchase      1        173

April 27 Sales          1                  $210

Total                           3    $507

Average cost per unit $169 ($507 ÷ 3 units)

Cost of goods available for sale = $507

a) First-in, First-out (FIFO):

Ending inventory = $342 ($169 + $173)

Cost of goods sold = $165 ($507 - $342)

Gross profit = $45 ($210 - $165)

b) Last-in, First-out (LIFO):

Ending inventory = $334 ($165 + $169)

Cost of goods sold = $173 ($507 - $334)

Gross profit = $37 ($210 - $173)

c) Weighted average cost method:

Ending inventory = $338 (2 x $169)

Cost of goods sold = $169 (1 x $169)

Gross profit = $41 ($210 - $169)

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The equation of the quadratic model is f(x) = -16x^2+99x+6.

From the given table:

A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150.

we know that:

regression equation = ax^2 + bx + c.

a∑x^4+b∑x^3+c∑x^3 = ∑x^2y

a∑x^3+b∑x^2+c∑x = ∑xy

a∑x^2+b∑x+cn = ∑y

After substituting and solving these three equations we get:

a = -15.714

b = 98.857

c = 5.571

Approximate values

a = -16

b = 99

c = 6

substitute these values

f(x) = -16x^2+99x+6.

Therefore the equation of the quadratic model is f(x) = -16x^2+99x+6.

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Answer:

d = V- x

Step-by-step explanation:

To make 'd' as the subject, isolate 'd'.

To isolate d, subtract 'x' from both sides,

              d +x = V

        d + x - x = V - x

                  d = V - x

The formula using d as the subject is d = V-x.

The formula is d+x = V

The subject of the formula is nothing but a variable that is being worked out. Here, we have to convert the given formula to describe d as the subject.

According to the property of equality, the two sides of the equation should be balanced. To solve the given expression, we use the subtraction property of equality.

The subtraction property of equality refers to balancing an equation by using the subtraction operation on both sides of the equation.

Therefore, subtract x on both sides of the given formula,

[tex]\begin{aligned}d+x&=V\\d+x-x&=V-x\\d&=V-x\end{aligned}[/tex]

Therefore, the final answer is d=V-x.

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Answer:

4x^2 + 16x - 48

Step-by-step explanation:

A quadratic equation with roots 2 and -6 has to have factors of (x - 2) and (x + 6) since both equal 0 when either 2 or 6 are plugged in. To get a leading coefficient of 4, multiply the product of the two factors by 4. When the 4 is distributed it becomes the leading coefficient:

4(x - 2)(x + 6)

4(x^2 + 4x - 12)

4x^2 + 16x - 48

By taking the difference between the final distance and the initial distance we will see that the change in the distance is -23/24 feet.

First, we should define the system we will use.

Notice that "distance" is defined positive, then when you are behind your friend and when you are ahead, the distances are in both cases positive.

First, you are at (4 + 5/8) feet from your friend, and then you are at (3 + 2/3) feet from your friend.

The difference is given by the final distance minus the initial distance, so we have:

d = (3 + 2/3) ft -  (4 + 5/8) ft

We can decompose the mixed numbers into wholes and fractions, so we get:

d = (3 + 2/3)ft - (4 + 5/8) ft

d = (3 - 4)ft + (2/3 - 5/8)ft

d = (-1)ft + (16/24 - 15/24)ft

d = -1 ft + 1/24ft = -23/24ft

So the change in the distance between the end and the beginning is:

d = -23/24ft

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