Directions: Choose the best answer to the question and fill in the corresponding oval on the Multiple Choice section of the Scantron sheet provided.
1. The population of Rochester has been increasing by 5% each year for the past 7 years. What is the growth factor?
A. 7
B. 1.05
C. 50
D. 5
2. Which of the following is not a point on the graph of the function y=4 x+1.
A. (0,4)
B. (-1,1)
C. (1,16)
D. (-2,0)

Using synthetic division we get, the remainder is 24
and the quotient is [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex]

What is synthetic division?

Particularly when we need to divide the polynomial by a linear factor, the Synthetic division provides a faster method of doing so. Instead of dividing factors, it is typically employed to determine the polynomial's zeroes or roots.

Here, in the question we have [tex]\frac{-x^{4} +2x^{3}+12x^{2} -16 }{x+2}[/tex]

First we find x from the divisor,

x+2=0

x=-2

Next, we arrange it in the division form with only the coefficients of the dividend terms.

[tex]-2 | -1 \space\ \space\ 2 \space\ \space\ 12 \space\ \space\ 0 \space\ \space\ -16\\[/tex]

             [tex]2 \space\ -2 \space\ -20 \space\ 40[/tex]

 ----------------------------------

     [tex]-1 \space\ \space\ 0 \space\ \space\ 10 \space\ \space\ -20 \space\ \space\ 24[/tex]

Therefore, we get the remainder as 24

And the quotient as [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex].

To learn more about synthetic division, visit the link below:

https://brainly.com/question/28824872

#SPJ4

Answer: 17 packs

Step-by-step explanation: 16 packs of 10 equals 160 beads, and one pack of 5 will give you 164 beads with 1 left over.

first off, let's check the equation for each year.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$736.80\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ 736.80=P\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4}\implies 736.80=P\left(1+\frac{r}{100} \right)^4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$788.82\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases} \\\\\\ 788.82=P\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 7}\implies 788.82=P\left(1+\frac{r}{100} \right)^7 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{736.80=P\left(1+\frac{r}{100} \right)^4}\implies \cfrac{736.80}{\left(1+\frac{r}{100} \right)^4}=P \\\\\\ \stackrel{\textit{using the 2nd equation}}{788.82=P\left(1+\frac{r}{100} \right)^7}\implies \stackrel{\textit{substituting on the 2nd equation}}{788.82=\cfrac{736.80}{\left(1+\frac{r}{100} \right)^4}\left(1+\frac{r}{100} \right)^7}[/tex]

[tex]788.82=736.80\cfrac{ ~~ \left(1+\frac{r}{100} \right)^7 ~~ }{\left(1+\frac{r}{100} \right)^4}\implies 788.82=736.80\left(1+\frac{r}{100} \right)^3 \\\\\\ \cfrac{788.82}{736.80}=\left(1+\frac{r}{100} \right)^3\implies \sqrt[3]{\cfrac{788.82}{736.80}}=1+\cfrac{r}{100}\implies \sqrt[3]{\cfrac{788.82}{736.80}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[3]{\cfrac{788.82}{736.80}}=100+r\implies 100\sqrt[3]{\cfrac{788.82}{736.80}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{2.3}\approx r \end{array}}[/tex]

1. 177.441177

2. 354.882354

3. 118.294118

4. 473.176472

5. 236.588236

Answer: 2

Step-by-step explanation:

Answer:

C 76

Step-by-step explanation:

let x = 1st number

let x+ 2 = 2nd number

let x + 4 = 3rd number

let x + 6 = 4th number

Let x + 8 = 5th number

x + x + 2 + x+ 4 + x + 6 + x + 8 = 400  Combine like terms

5x + 20 = 400 Subtract 20 from each side

5x  = 380  Divide both sides by 5

x = 76

Check:

76 + 78 + 80 + 82 + 84 = 400

Answer:

(I will only answer one and I think my explanation can help you understand so you do it yourself) For number 8: the slope-intercept form is: y=-1/3x-11

Step-by-step explanation:

x+3y=-33
3y=-x-33(take away x from both sides of the = sign)

y=-1/3x-11(divide 3 on both sides of the = sign)

Answer:

Z=3

Step-by-step explanation:

1 1/2+1 1/2= 2+1=3

Answer:

I believe it is positive although I am not 100% sure.

Step-by-step explanation:

The arrows tend to go upwards even though it does have a curve at the bottom. It is still going upwards.

By using the concept of function, it can be calculated that-

(g.f)(x) = 8x - 5

(g - f)(x) = -2x - 5

(g + f)(3) = 13

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

a) The given functions are

   f(x) = 4x

  g(x)= 2x - 5

  (g.f)(x) = g(f(x)) = 2(4x) - 5 = 8x - 5

   (g - f)(x) = g(x) - f(x) = 2x - 5 - 4x = -2x - 5

    (g + f)(x) = g(x) + f(x) = 2x - 5 + 4x = 6x - 5

     (g + f)(3) =  6 [tex]\times[/tex] 3 - 5 = 13

To learn more about function, refer to the link -

https://brainly.com/question/22340031

#SPJ4

By solving the following trigonometric function of m(x)= x cos(-x) we get m(x) = cos(x).

What is trigonometry ?

Given that;

              m(x) = x cos(-x)

              m(x) = x cos (x)    [ we know that cos(-x) = cos(x) ]

           m(x)/x = x cos(x)/x   [divide both sides by x]

                   m = cos(x)

Therefore, m(x)=x cos(-x) ⇒cos(x)

To learn more about the trigonometry check the given link

brainly.com/question/13729598

#SPJ4

Answer:

B) Elias sold one-fourth the number of books Lena sold.

Step-by-step explanation:

How is this the answer? Well after I looked at the problem again, I realized what I needed to do. I needed to do 4,832*1/4 which is 1208.

I got this from the line that says "Elias sold 4,832 times one-fourth copies"

I hope this helps!!!!

The diagonal of a rectangle with a width of 12 units and a length of 16 units is 20 units

From the question, we are to determine the length of the diagonal of the rectangle

From the given information,

The width of the rectangle is 12 units

and

The length of the rectangle is 16 units,

The diagonal, D, of a rectangle is given by

D = √(l² + w²)

Where l is the length of the rectangle

and w is the width of the rectangle

l = 16

w = 12

Thus,

The diagonal of the rectangle is

D = √(16² + 12²)

D = √(256 + 144)

D = √400

D = 20

Hence, the diagonal is 20 units

Learn more on Calculating the diagonal of a rectangle here: https://brainly.com/question/15728315

#SPJ1

Answer:

B

Step-by-step explanation:

Assuming these 4 are the only possibilities:

A: This cannot be correct because if 181 were divisible by 9, it would not be prime, as the problem suggests.

C: This cannot be correct because 181/9 is 21.11, which is not a whole number

D: This cannot be correct because 181/3 is 60.333, which is not a whole number

Thus, the answer is B.

FUN FACT:

When seeing whether a number is divisible by 3, add up its digits, and if they are divisible by 3, so is the number. Example: 36 is divisible by 3 because   3 + 6 = 9, and 9 is divisible by 3. 181 is not, however, because 1+8+1=10, and 10 is not divisible by 3.

Same with 9! 459 is divisible by 9 because 4+5+9 = 18, which is divisible by 9. 181 is not, however, because 1+8+1 = 10, which is not divisible by 9.

I hope this helps!

Answer:

B. 181 is prime because its only factors are 1 and itself.

Step-by-step explanation:

Prime number

A whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).  

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.

Composite number

A number that is divisible by a number other than 1 and itself (so it has more than 2 factors).  

An example of a composite number is 6 as its factors are 1, 2, 3 and 6.

The factors of 181 are 1 and 181.

Therefore, it is prime because its only factors are 1 and itself.

Answer:

Exact area = 81π ft²

Approximate area = 254 ft²

Step-by-step explanation:

A = πr²

A = π × (9 ft)²

A = 81π ft²

A = 81(3.14) ft²

A = 254 ft²

[tex] \Large{\boxed{\sf A = 81 \pi \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]

[tex] \\ [/tex]

The area of a circle is given by the following formula:

[tex] \Large{\sf A = \pi \times r^2 } [/tex]

Where:

[tex] \\ [/tex]

We know that the diameter of a circle is twice its radius. Therefore, we can find the value of the circle's radius by dividing its diameter by 2.

[tex] \sf Diameter =2 \times radius \Longleftrightarrow radius = \dfrac{Diameter}{2} \\ \\ \\ \star \: \sf r = \dfrac{18 \ ft}{2} = \boxed{\sf 9 \ ft} [/tex]

[tex] \\ [/tex]

Now, substitute the value of the radius into the formula:

[tex] \sf A = \pi \times (9 \ ft)^2 = \boxed{\boxed{\sf 81 \pi \ \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

▪️Learn more about the area of a circle here:

↣https://brainly.com/question/27912608

Answer:

Below

Step-by-step explanation:

WOW! THIS is not 'jogging' :

4 miles / 1/5 hr = 20 m/hr

Answer:

31 [tex]\frac{3}{5}[/tex] miles per gallon.

Step-by-step explanation:

[tex]\frac{39\frac{1}{2} }{1\frac{1}{4} }[/tex]

39 [tex]\frac{1}{2}[/tex] ÷  1 [tex]\frac{1}{4}[/tex]

[tex]\frac{79}{2}[/tex] ÷ [tex]\frac{5}{4}[/tex]

[tex]\frac{79}{2}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{158}{5}[/tex] = 31 [tex]\frac{3}{5}[/tex] miles per gallon or 31.6 miles per gallon

(A) Positive

When z and y are both positive, the expression{ [tex]\frac{-z}{-y}[/tex] }is equal to [tex]\frac{-z}{-y}[/tex]. Since both z and y are positive, -z is negative and -y is negative, so the expression [tex]\frac{-z}{-y}[/tex] is equal to the positive number [tex]\frac{z}{\\y}[/tex].

Therefore, the sign of {-z}/{-y} when z>0 and y>0 is positive.

So the correct answer is:

(A) Positive

What is sign?

In mathematics, a sign is a symbol that is used to represent the relative size or value of a number or expression. The most common signs used in mathematics are the plus (+) and minus (-) signs, which are used to represent positive and negative numbers, respectively.

For example, the number 5 is a positive number, and it is represented using the plus sign. On the other hand, the number -5 is a negative number, and it is represented using the minus sign.

In addition to the plus and minus signs, there are also other signs used in mathematics, such as the equal sign (=), which is used to indicate that two quantities are equal, and the inequality signs (>, <, ≥, ≤), which are used to indicate that one quantity is greater than or less than another.

Overall, signs play a vital role in mathematics as they help to indicate the size and value of numbers and expressions, and they are essential for performing various mathematical operations and solving mathematical problems.

To learn more about positive expression follow link : https://brainly.com/question/14504072

#SPJ1

Answer:

1st

Step-by-step explanation:

-400 degrees can also be seen as positive 40 degrees

Answer:

[tex]f(x)=3^{x+1}-3[/tex]

Step-by-step explanation:

The curve of the graph shows it is Exponential:  [tex]f(x)=b^{x-h}+k[/tex]

To find b, h, and k, we need to "un-transform" the graph from  [tex]f(x)=b^{x}[/tex]

1. h = horizontal shift/translation;  k = vertical translation:

  (0,1) ⇒ (-1,-2), so h = -1  and  k = -3  and  [tex]f(x)=b^{x+1}-3[/tex]

2. Given the points (-1,-2), (0,0), and (1,6), use one of them to find b:

     [tex]f(x)=b^{x+1}-3\\0=b^{0+1}-3\\0=b^{1}-3\\3=b^1\\3=b[/tex]

3. Place b, h, and k in their correct places in the function.

0.53.The elements left over after the given set's components have been eliminated from the universal set are the complement of the set.

Explanation:

P(event E)=0.47

Consequently, P(not E)=1P(E) [P(E)+P(not E)=1] =10.47 =0.53

To learn more about Probability refer to:

https://brainly.com/question/13604758

#SPJ1

Answer:

5 i think

Step-by-step explanation:

1) The growth rate is 40%

2) The number of bacteria initially present is 990

3) The number after four hours is  4904

4) The function in terms of time is written as F(t) = 120e^-1.6t

We know that the number of the bacteria can be obtained on the basis of the function that we have. We know that the process of exponential increase of decrease would have to be modelled by the use of an exponential equation. In this case, we have the equation; n(t) = 990e^0.4t

We know that in this case, the time of the multiplication of the bacterial is t, the percent growth rate of the bacteria is 40% and the initial number of the bacteria is 990.

After 4 hours we have;

n(4) = 990e^0.4(4)

n(4) = 4904

b) Given that the initial temperature  if the system is 120°F and the rate of the cooling is 1.6, the formula is written as;

F(t) = 120e^-1.6t

Learn more about exponential function:https://brainly.com/question/14355665

#SPJ1

Answer:

Below

Step-by-step explanation:

$ 5   for the first one   <=== a fixed constant ....admission charge

.25  per minute   <===== charges dependent on the number of minutes

Answer:

pls rate brainliest

Step-by-step explanation:

the entrance fee to the skating rink=$5

each minute the skater uses the rink costs=$0.25

HOPE IT HELPED YOU

The quantities we need circumference for are: A and C.

The quantities we need area for are: B and D.

The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.

On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².

Therefore:

For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.

For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.

Learn more about area and circumference on:

https://brainly.com/question/402655

#SPJ1

The value of each variable iS

x = 6

y = 4

What is angle bisector theorem?

The angle bisector theorem in geometry is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into. It compares their proportional lengths to the proportional lengths of the triangle's other two sides.

Apply the angle bisector theorem to solve for x and y respectively.

✔️4/(9 - x) = 8/x

Cross multiply

4*x = 8(9 - x)

4x = 72 - 8x

Add 8x to both sides

4x + 8x = 72

12x = 72

12x/12 = 72/12

x = 6

✔️y/2 = 6/3

Cross multiply

3*y = 6*2

3y = 12

3y/3 = 12/3

y = 4

To learn more about angle bisector theorem visit:https://brainly.com/question/10433817

#SPJ1

The band have to sell 76 tickets for each concert to meet the goal

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

P = 850 + 5x

Also, we have

Bonus = $50

This means that

Cost = 850 + 5x + 50x

So, we have

Cost= 850 + 55x

When they earn $5000, we have

850 + 55x = 5000

Evaluate the like terms

55x = 4150

Divide

x = 76

Hence, the number of tickets is 76

Read more about linear equation at

https://brainly.com/question/4074386

#SPJ1

The measure of angle TQU is 41.1°

What is angle of measure?

The measure of the angle is formed by the two lines or arms having a same vertex.

Solution:

We know that,

PQ² + PT² = QT²   -------- By Pythagoras theorem

∴QT = √10

∵ PT + TU + US = 4

∴ TU = 4 - PT - US

TU = 4 - 1 - 1

∴TU = 2

Now, using Pythagoras theorem in triangle PQU

PQ² + PU² = QU²

∴ QU =√ 3² + 3²         (∵PU = PT + TU = 1 + 2)

∴ QU = 3

Now using Heron's formula in triangle TQU

Semi-perimeter = (2 + √10 + 3)/2

                          = 4.08

Area of the triangle = [tex]\sqrt{S(S-TQ)((S-TU)(S-QU)}[/tex]

                                = [tex]\sqrt{4.08(0.92)(2.08)(1.08)}[/tex]

                                = 2.903 unit²

Now, we know that

Area of a scalene triangle = ab/2 × sin c

∴ 2.903 = (√10×3/)2 × sin T

∴ sin T = 2.903×2/3√10

  sin T  = 0.61

∴  ∠T = [tex]sin^{-1}[/tex](0.61)

∴∠T = 93.9°

Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)

∠U + ∠T + ∠Q  = 180°

∴ ∠Q = 180 - 93.9 - 45

∴∠Q  = 41.1°

To learn more about  measure of angle of a triangle click on the link below:

https://brainly.com/question/25716982

#SPJ4

The measure of angle TQU is 41.1°

What is angle of measure?

The measure of the angle is formed by the two lines or arms having a same vertex.

We know that,

PQ² + PT² = QT²   -------- By Pythagoras theorem

∴QT = √10

∵ PT + TU + US = 4

∴ TU = 4 - PT - US

TU = 4 - 1 - 1

∴TU = 2

Now, using Pythagoras theorem in triangle PQU

PQ² + PU² = QU²

∴ QU =√ 3² + 3²         (∵PU = PT + TU = 1 + 2)

∴ QU = 3

Now using Heron's formula in triangle TQU

Semi-perimeter = (2 + √10 + 3)/2

                         = 4.08

Area of the triangle = 2.903 unit²

Now, we know that

Area of a scalene triangle = ab/2 × sin c

∴ 2.903 = (√10×3/)2 × sin T

∴ sin T = 2.903×2/3√10

 sin T  = 0.61

∴  ∠T = (0.61)

∴∠T = 93.9°

Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)

∠U + ∠T + ∠Q  = 180°

∴ ∠Q = 180 - 93.9 - 45

∴∠Q  = 41.1°

To learn more about  angle of a triangle :

brainly.com/question/25716982

#SPJ4

The diagram that shows a valid approach to the given construction is option a for the perpendicular bisector.

A perpendicular bisector is a section of a line that divides a straight segment into two congruent or equal segments. At exactly its midpoint, they split the line section. With the line segment it divides, a perpendicular bisector produces a 90° angle. A line segment that bisects another line segment at an angle of 90 degrees is referred to as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal pieces by intersecting it at a 90° angle. The term "perpendicular bisector" refers to a precise drawing in which a line is accurately divided in half by another line that is perpendicular to the first line. To divide into two equal portions, or bisect, is a verb.

Therefore, The diagram that shows a valid approach to the f=given construction is option a.

To know more about perpendicular bisector, visit:

https://brainly.com/question/24753075

#SPJ1