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The given function is a rational function

We will find the zeros of the denominator

The end behavior of the function will be as follows:

The graph of the function is as follows:

Answer:

Given the data set of height (inches) for 12 students, calculate the mean: 60, 64, 66, 68, 70, 71, 72, 73, 78, 71, 65, 69

We are to create a data set of 4

that is a, b, c, d

mode means a number that occur the most

Median means the middle number

Mean means the average number

in the set, we must have a mode of 3

3, 3,

to get a median of 6, we need a number when we add to three and divide by 2 will give us 6

the number is 9

3 + 9 / 2

12/ 2 =

3, 3 , 9, d

the last number is d and it is unknown

since means is 10

mean = summation of all the numbers in the data set / the total number

the total number is 4

mean = 10

10 = 3 + 3 + 9 + d / 4

cross multiplication

10 x 4 = 3 + 3 + 9 + d

40 = 6 + 9 + d

40 = 15 + d

isolate d

d = 40 - 15

d = 25

therefore, the data set with a mode of 3, median of 6 and a mean of 10 are

3 , 3 , 9, 25

Answer:

Let flour, sugar, raisins be 3x, 1.5x, x grams respectively.

Total Mass = 550g 3x+1.5x + x = 550g

5.5x = 550 x = 100g

Flour = 3x= 3 x 100 = 300g

Hence, flour in mixture is 300g

The amount of the remaining balance of the car loan is $26293.1103.

Given,

The initial loan amount, P = 27000

The rate of interest, r = 6.2%

Time period, t = 5 years

Interest is compounded monthly.

The 20th payment of the loan = $524.50

We have to find the  remaining balance of the car loan.

Here,

Amount, A = P[1 + r/n]^nt

Where,

A is the total amount = principal amount + compound interest

P is the principal amount

r is the rate of interest

n is the number of times compounded

t is the time period

So,

A = P[1 + r/n]^nt

A = 27000 × [1 + 6.2/100/12]^12 × 5

A = 27000 × [12.062/12]^60

A = 27000 × [1.005166]^60

A = 27000 × 1.362

A = 36783.1103

The total amount should be paid after 60 months is $36783.1103

Now,

The 20th payment = $524.50

That is,

524.20 × 20 = 10490

$10490 is paid and the balance amount;

36783.1103 - 10490 = 26293.1103

Therefore,

The amount of the remaining balance of the car loan is $26293.1103.

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Answer:

To use the given table to find product of the two polynomials.

Given that,

Explanation:

Using the table, we get it as,

we get,

we get,

Answer is:

We will solve as follows:

First: We will use the i, j, k vector notation to describe each point as a vector:

Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).

Second: We determine the speed from A to B:

Third: We now determine the value of C:

So, we would have that the coordinates of C are:

Each theater sold tickets at ($7.50 a piece, if each theater received the same number of moviegoers, each theater make $6192.85 using arithmetic operations.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or more quantities. They cover topics like the study of numbers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry. Without applying the laws of arithmetic operations, we are unable to solve the issue. The four fundamental rules of mathematics are addition, subtraction, multiplication, and division.

Let the amount of each theater get be x,

No. of theaters are = 7

Cost of each ticket = $7.50

No. of people = 5780

Then we can say,

7x = 5780 ×7.50

x = [tex]\frac{5780\times7.50}{7}[/tex]

= $6192.85

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The trigonometric functions tangent, sine and cosine are related by the following equation:

In this case, the angle is y°, so:

Since we want the cosine, we can solve for it ans substitute the given tangent and sine:

This corresponds to the third alternative.

Answer:

g(x) = x + 7

Step-by-step explanation:

f(x) = x^9

g(x) = x + 7

f(g(x)) = (x + 7)^9

Answer:

C.

Step-by-step explanation:

540

Answer:

540

Step-by-step explanation:

you can use this equation to find the sum of angles for a shape
(n-2)180 with n being the number of sides. Since a pentagon has 5,
its 5-2= 3 then times 180 is 540

Answers:

Q1.a: 11g

Q1.b: 3m

Q1.3: [tex]-k^{2}[/tex]

Q2.a:  8x + 11y

Q2.b: 2a + b - 2c

Q3.a: 5q + 7

Q3.b: 6r + 3s + 7t

Step-by-step explanation:

Q1) simplify each of these expressions:

a. [tex]4g + 6g + g[/tex]

= g(4 + 6 + 1)

= 11g

____________

b. [tex]4m - m[/tex]

= m(4 - 1)

= 3m

____________

c. [tex]5k^{2} -4k^{2} -2k^{2}[/tex]

= [tex]k^{2} (5 - 4 - 2)\\[/tex]

= [tex]-1k^{2}[/tex]

= [tex]-k^{2}[/tex]

__________________________________

Q2) copy and complete the workings to simplify these expressions:

a. [tex]5x + 3x+6y+5y\\[/tex]

= x(5 + 3) + y(6 + 5)

= 8x + 11y

____________

b.[tex]2a+4b+6c-3b-8c[/tex]

combine terms b:

2a + b + 6c - 8c

combine terms c:

= 2a + b - 2c

__________________________________

Q3) simplify these expressions by collecting like terms:

a.[tex]9q-4q+15-8[/tex]

combine terms q:

5q + 15 - 8

combine numbers:

= 5q + 7

____________

b. [tex]8r+2s+4t-2r+s+3t[/tex]

combine terms r:

6r + 2s + 4t + s + 3t

combine terms s:

6r + 3s + 4t + 3t

combine terms t:

= 6r + 3s + 7t

h = 20inches

The formula for calculating the volume of a cone is expressed as:

where:

r is the radius

h is the height

Given the following

r = 12 inches

V = 3014.4 cubic inches

Substitute to determine the height

Hence the height of the cone will be 20inches

First let's find the ratio of the sequence, by dividing one term by the term before:

So the ratio is 1/5 and the first term is 75.

Now, we can use the following formula for the nth term of a geometric sequence:

Where q is the ratio and a1 is the first term. So we have:

Substituting an by the function f(n), we have:

So the correct option is b)

Given -

f(x) = x⁵ - 4x³ + 7x² + 3x - 5

To Find -

How many positive real zeroes does f(x) have =?

Step-by-Step Explanation -

We have

f(x) = x⁵ - 4x³ + 7x² + 3x - 5

where the signs of coefficients are:

+ - + + -

We can see there are three changes in the sign in f(x).

So, from

Descarte's rule,

there are either 3 0r 1 positive real roots

Now,

f(-x) = -x⁵ + 4x³ + 7x² - 3x - 5

Signs: - + + - -

So, here f(-x) has two sign changes.

From this we can conclude there is at least 1 real root and either 4, 2 or 0 imaginary roots.

Final Answer -

Positive real zeroes f(x) have =

Minimum = 1

Maximum = 3

The place value of 6 in 205.876 is 6 thousandth

Point of B is ( -10 , 0) is midpoint of AB .

What is midpoint of a segment?

The midpoint of AB =  ( – 5, 4) = ( x ,y)

A = (0, – 9) ⇒ ( x₁ , y₁)

Let B = ( x₂, y₂ )

midpoint of AB ⇒ x =  x₁ + x₂/2 ,  y = y₁ + y₂/2

                              -5 = 0 + x₂/2  , -9 = -9 + y₂/2

                              x₂ = -10  , y₂ = 0

point of B is ( -10 , 0)

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The probability of a student living off campus is 0.35.

It should be noted that probability simply means the likelihood that something will occur.

Remember the multiplication rule for conditional probability: P(B AND A)=P(B/A)P(A)

Rearranging, we find that P(A)=P(B AND A)P(B/A)

So if we think of A= the event a student lives off campus and B = event a student eats at the cafeteria, then we can plug in the known information to find:

P(A)=0.07 / 0.20

= 0.35

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What is the solution to the given equation?

x= 20

How is the equation in the bar diagram solved?

3.5x + 12.5x =320

16x = 320

x = 20

What is a bar diagram?

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The value of 1936 divided by 8 in long division is 242.

Long Division is a method for dividing large numbers that divides the task into numerous phases that follow a sequence. Just like in conventional division problems, the dividend is divided by the divisor, yielding the quotient and, in some cases, a remainder.

The steps are:

Step 1: Take the first digit of the dividend from the left.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend

Using the above step the division is 242.

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Check the picture below.

let's recall that twin sides stemming from a common vertex, make twin angles at the base.

a. Since GC bisects FGH and the angle FGH = 122°, we know that the angle FGC = 122/2 = 61°

b. Since GC bisects FGH and the angle CGH = 42°, we know that the angle FGH = 2*42 = 84°

The inequlaity is ;

And the solution is;

Let the number be x

The number divided by 3

That is x/3

less two means minus 2

x/3 - 2

Is at most 2 means it is less than or equal to 2

so the inequality is;

It is an ongoing function. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

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two thousand people attend the theater during the week of a movie's release (option A)

The equation:

y = -50x + 2000

y = number of people in the theater

x = number of weeks since the movie release

2000 will be the number of people in the theater at the begining of the movie release

y-intercept of an equation represent the value of y when x is zero

The 2000 is the number of people in the theater at week zero.

Hence, y-intercept indicate two thousand people attend the theater during the week of a movie's release (option A)

Keisha needs 3/2 of potato per guest ( i.e one guest is equivalent to 3/2 potato)

Thus, for 15 guests

she needs;

Keisha needs 45/2 potatoes for 15 guests

The given function of the height of the diver is

h is the height in feet

t is the time in seconds

To find the time for the whole motion equate h by 0, as when the diver inter the water his jumper height will be zero. (The surface of the water is the initial position)

Switch the 2 sides and change all signs to opposite

Now, we have a quadratic equation, then we will use the calculator to find the values of t

Since time can NOT be a negative value, then we will ignore the 2nd value of t

The answer should be about 15.44 seconds to the nearest 2 decimal place

everything u need id in the picture

The first step of substitution method for given system is put x = 3y +3 in place of x into the equation 2x+3y=-12 .

The system of the equations in two variables x and y consists of two equation of the form a₁ x + b₁ y = c₁

and a₂ x + b₂ y = c₂

where a₁, a₂, b₁, b₂ , c₁, c₂ are constants

For substitution method, first expression of one variable is found from one equation and then put this expression in another equation to create a linear equation in second variable. Solve the linear equation in one variable for second variable and then put the value of second variable in first equation to solve for first variable

Given system of equations is :

2x + 3y = -12       .....(1)

x = 3y + 3          .....(2)

So the first step will be take expression for one variable from one equation and put it into another equation.

Take x = 3y +3 which is an expression for x from equation (2),

Then put it into equation (1)

⇒ 2 (3y +3 ) + 3 y = -12 , This is the first step of substitution method for this variable

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We will determine the arch lenght (In radians) as follows:

*First: We transform the measure of the angle from degrees to radians, that is:

*Second: We find the arc length:

So, the arc length for CT is 88pi/15 radians.

*Third: We find its measure in feet:

So, the arch length for CT in feet is approximately 18.43 feet.