Find the y-coordinate of the y-intercept of the polynomial function defined below.

f(x) = 3 + 5x² + 4x^4 - 3x³ - 6x

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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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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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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According to the concept of polynomial division, the equivalent expression is option (a). x+7 + 26/(x-3)

Polynomial division

Polynomial division refers the process of dividing one polynomial with another.

Given,

Here we have the expression (x² + 4x + 5) / x - 3.

Now, we have to find the equivalent polynomial expression when x - 3 is not equal to 3.

In order to find the equivalent expression, we have to do the following steps:

1. Divide the first term of the dividend by the first term of the divisor

2. Write down the calculated result x in the upper part of the table.

3. Multiply it by the divisor

4. Subtract this result from the dividend

Repeat this 4 steps until no further division.

This process is illustrated below.

According to this process, the equivalent fraction for the given fraction is

x + 7 + 26/(x - 3)

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Answer:

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

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 translated function is g(x)= 8x+0

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is an association between inputs in which each input is connected to precisely one output. A domain,  range exists for every function.

An example of a rule is a function, which produces one output for a single input.

Given:

f(x)= 8x - 10

Now,  translation 10 units up

Thus, g(x)= f(x) + 10

g(x)=  8x - 10+ 10

Hence, g(x)= 8x+0

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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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Answer:

a=3

Step-by-step explanation:

To find a, you plug the known numbers into the given equation (coordinates). f(x) is the same as the y-coordinate.

With that, you get:

5=a(-1)^2+2

Then you solve for a

3=a(-1)^2

3=a(1)

3=a

The final cost of the necklace if the customer bought it on February 28th or March 1st is $96.05 or $113, respectively.

The final cost of the necklace purchased on February 28th includes the markup and excludes the promotional and coupon discounts, before adding the sales tax.

Similarly, the final cost of the necklace purchased on March 1st includes the markup and excludes the coupon discount, before adding the sales tax.

Cost price to the store = $75

Markup =55%

Marked-up selling price = $116.25 ($75 x 1.55)

February sales discount = 15%

Promotional price during February = $98.81 ($116.25 x 1 - 15%)

Discount coupon rate = 10%

Discounted price = $88.93 ($98.81 x 1 - 10%)

Sales tax = 8%

Final selling price = $96.05 ($88.93 x 1.08)

Cost price to the store = $75

Markup =55%

Marked-up selling price = $116.25 ($75 x 1.55)

Discount coupon rate = 10%

Discounted price = $104.63 ($116.25 x 1 - 10%)

Sales tax = 8%

Final selling price = $113 ($104.63 x 1.08)

Thus, the customer pays an additional $16.95 if they purchase the necklace on March 1st without the promotional discount, instead of February 28th.

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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]

y=4/5x-2/5 is the equation used to plot the graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given equation is 4x−5y=1

Four times of x minus five times of y equal to one

4x−5y=1

Let us write this equation in slope intercept form

-5y=1-4x

5y=-2+4x

y=-2/5+4/5x

y=4/5x-2/5

x       0         1        2         3

y       -2/5    2/5    6/5     10/5

y       -0.4     0.4     1.2     2

by using these points we plot the graph.

Hence y=4/5x-2/5 is the equation used to plot the graph.

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Answer:

It is B

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

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 cards that are needed to ensure that you have 12 cards of the same color is of:

43 cards.

The highest number of cards for which at least one color having 12 cards is not guaranteed is obtained as follows:

Hence the number is:

11 + 11 + 11 + 10 = 3 x 11 + 10 = 33 + 10 = 43 cards.

With the next card, that is, the 44th card, it will be ensured that at least one color will have 12 cards.

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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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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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The slope of the line, 8x + 3y = 8 – 2x, is -10/3

From the question, we are to determine the slope of the given equation.

The given equation is

8x + 3y = 8 – 2x

To determine the slope of the line, we will express the equation in the general form of the slope-intercept form of the equation a line.

The general form of the slope-intercept form of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Expressing the equation in the slope-intercept form of a line

8x + 3y = 8 - 2x

Subtract 8x from both sides of the equation

8x - 8x + 3y = 8 - 2x - 8x

3y = 8 - 10x

3y = -10x + 8

Divide through by 3

3y/3 = -10x/3 + 8/3

Y = -10/3 x + 8/3

By comparison,

m = -10/3

Hence, the slope is -10/3

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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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Answer: The answer is -4

If you use the chips to help illustrate your point, here's a good way to explain it:

Let's say that there are five -1 chips and one +1 chip. In order to use chips, you would have to subtract the chips from each other. Put a -1 chip and a +1 chip together and then take them away (as to subtract them). This would leave you with four -1 chips, thus giving you your answer.

Hope this helps!

Answer:

when two different signs are in numbers if +or_ you I'll substruct or +or+ you I'll added ok

Answer: 8 books

Step-by-step explanation:

First, she has 40 books.

1) Then she fills 4/5 of it. 4/5 of 40 is 32.

2) (4/5) x (40) = 32.

3) 40 - 32 = 8

4) So she needs to add 8 books.

Hope this helps :)

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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The statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.

We are given;

h(x) = -x^3 - 9x^2 + 4x + 96

The function is a cubic function.

Since the leading coefficient is negative the graph start from second quadrant.

So, the graph must be positive in the second quadrant.

Let us check the option D;

The graph is positive on the intervals (- ∞ , - 8) and (- 4, 3).

The graph is positive in the second quadrant. So, (- ∞ , - 8) satisfy.

Let's choose any point between -4 to 3 and substitute in the given equation.

Put x = -1 in the given equation;

h(x) = -(-1)^3 - 9(-1)^2 + 4(-1) + 96 = 1 - 9 - 4 + 96 = 84

So, h(x) is positive.

So, option D is correct.

Thus, the statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.

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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

The total loss of yards is 10yards(-10yards)

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

There are positive integers e g 1,2,3,5,7,8,11,16 and negative integers -1,-2,-4, -22 e t c

The addition of a negative and positive integers of the same number will give 0 .i.e -5+(+5)=0

similarly -6+(+6)= 0

if the lost yards are represented by negative and the gained yards by positive then,

-5yards-9yards-8yards = -22yards

+12 yards is gained

therefore the total yards lost or gained is

-22+12= -10yards

since it is -10yards then the yards are lost yards.

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Answer:shanikas height

Step-by-step explanation:

The equation that will be used to illustrate the information regarding the total cost is C = 50 + 75h.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Initial fee = 50

Amount charged by hour = 75

Number of hours = h

The total cost will be:

= Initial fee + Amount for each hour

= 50 + 75(h)

= 50 + 75h

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Answer:

The answer is 6.5

Step-by-step explanation:

The equation is y=3x-1. Plug in 2.5 as the value for x and solve.

3×2.5=7.5

7.5-1=6.5