4. A local video store has seen good linear growth in rentals since 2005. In 2009, the store had
23,500 rentals. In 2015, the store had 28,540 rentals.
a. Find the average rate of change of the store's rentals in rentals per year.
b. Using the average rate of change, determine the number of rentals in 2005.

Option a is correct.

The first term, a is 3;

Common ratio, r = +4;

What is Geometric Series?

The total of a geometric sequence's finite or infinite terms is known as a geometric series. The analogous geometric series is a + ar + ar2 +..., arn-1 + for the geometric sequence a, ar, ar2,..., arn-1,... The word "series" is known to mean "sum." The geometric series specifically refers to the total of phrases with a common ratio between every pair of neighboring terms. Geometric series can be of two different types: finite and infinite.

In the given question, we have:

The series: 3 + 12 + 48 +

So, here the first term (a) = 3;

The second term = +12;

and, we know that the common ratio in the geometric series is the ratio of the second term and the first term.

So,

Common ratio, r = [tex]\frac{12}{3}[/tex]

r = 4;

so, The common ratio will be the same everywhere. So, It will be 4 in all the cases.

And, The first term, a is 3;

Hence,

Option a is correct.

The first term, a is 3;

Common ratio, r = +4;

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The solution to the equation given as (x - 7)² = 36 are x = 1 and x = 13

From the question, the equation is given as

(x - 7)² = 36

To start with, we take the square roots of both sides

This gives

x - 7 = ±6

Add 7 to both sides of the equation

So, we have

x = 7 ± 6

Evaluate the like terms

x = 1 and x = 13

Hence, the values of x are x = 1 and x = 13

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Answer:  

48

Step-by-step explanation:

The probability that the total duration of the 500 calls is greater than 18 hours, using the normal distribution, is of:

0.618 = 61.8%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, for the total duration of the 500 calls, in seconds, the mean and the standard deviation are given as follows:

[tex]\mu = 500 \times 130 = 65000, \sigma = 30\sqrt{500} = 670.82[/tex]

Each hour has 3600 seconds, hence the number of seconds in 18 hours is given as follows:

3600 x 18 = 64800.

The probability that the total time is greater than 18 hours is one subtracted by the p-value of Z when X = 64800, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (64800 - 65000)/670.82

Z = -0.3.

Z = -0.3 has a p-value of 0.382.

1 - 0.382 = 0.618 = 61.8% probability.

The problem says that:

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Answer:

[tex]y=-43x-173[/tex]

Step-by-step explanation:

[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]

The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.

An elevation simply means the height above sea level.

In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:

= 12.2 × 4

= 48.8 feet

He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:

= 3.6 × 10

= 36 feet.

Therefore, the change in elevation will be:

= Elevation up - Elevation down

= 36 - 48.8

= 12.8 feet.

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The measurement of angles ∠1 is 126° and ∠2 is 154°.

According to the question,

We have the following information:

We have a figure of two triangles and some of the measurements of the angles are given.

We know that the sum of three angles of a triangle is 180°.

So, for the larger triangle, we have the following expression:

96+30+third angle = 180

Third angle = 180-126

Third angle = 54°

We know that sum of angles on a straight line is 180°.

So, we have:

∠1+54 = 180

∠1 = 180-54

∠1 = 126°

Now, finding the sum of angles in smaller triangle:

126+28+third angle = 180

Third angle = 180-154

Third angle = 26°

Now, angle 2 and this angle will make a straight line.

∠2+26 = 180

∠2 = 180-26

∠2 = 154°

Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.

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The value of n is given by either 4/5 or 16/25.

Given that the positive number is n which is n<1.

Reciprocal of the number is = 1/n

Addition of the number and the reciprocal is 2.05.

So the suitable equation for this,

n + 1/n = 2.05

[tex]n^2+1=\frac{41}{20}n\\20n^2-41n+20=0\\n=\frac{41\pm\sqrt{1681-1600}}{40}=\frac{41\pm9}{40}=\frac{50}{40},\frac{32}{50}=\frac{4}{5},\frac{16}{25}[/tex]

So the number can be either 4/5 or 16/25.

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The measure of the exterior angle to triangle X is D. 97.55°.

It is important to note that the sum of the angles in a triangle is 180°.

In this case, triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6.

The exterior angle to X will be:

= Total angle - (43.85 + 38.6)

= 180 - 82.45

= 97.55°

In conclusion, the correct option is D.

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Answer:

I got the answer d when I took the test

Step-by-step explanation:

I hope this helps...

The measure of angles are

The sum of angles around a point is equal to 360 degrees

The consider the angle a

The equation will be

∠a + 312 = 360 degrees

∠a = 360 - 312

∠a = 48  degree

The angle a is less than 90 degrees then it is an acute angles

Consider the angle b

∠b + 220 = 360

∠b = 360 -220

∠b = 140 degrees

Angle b is greater than 90 degrees and less than 180 degrees then it is an obtuse angle

Consider the angle c

∠c + 36 = 360

∠c = 360 - 36

∠c = 324 degrees

Angle c is grater than 180 degrees and less than 360 degrees then it  is a reflex angle

Hence, the measure of angles are

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Answer:-48

Step-by-step explanation:

a + 85 = 48

first we need to find what a

86-48=a

a=38

now we calculate

a-86?

38 - 86 = -48

Answer:

a - 86 = -124

Step-by-step explanation:

a + 86 = 48

a = 48 - 86

a = -38

Then:

a - 86 = -38 - 86

= -124

The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.

It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:

= 16 + 15 + 16 + 8 + 17

= 72 feet

The area will be:

= Area of triangle + Area of rectangle

= (1/2 × base × height) + (length × width)

= (1/2 × 8 × 17) + (15 × 16)

= 68 + 240

= 308ft²

Therefore, the correct option is B.

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Answer: I think you would earn $8.35 per hour

Step-by-step explanation:

Answer: $880

Step-by-step explanation:

As I understand you are working 20 hours a day for 4 days.

[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880

Answer:

C. Trust me on this one, it is an easy one.

The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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Answer:

15%

Step-by-step explanation:

15%*40=46

Answer:

15%

Step-by-step explanation:

[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]

The boy was 40 inches tall so that means 40 inches is the old value

The boy is currently 46 inches tall now, so 46 is the new value

Plug these values into the equation:

[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]

Simplify:

[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]

[tex]Percent of change =\frac{600}{ 40} \\[/tex]

[tex]Percent of change =15[/tex]

I hope this answers your question :)

The solution set. for the given inequality : x-5> -10. is (-5, ∞]

An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

We need to find the solution set for  x-5> -10.

x - 5 > - 10

x > -10 + 5

x > -5

The solution set = (-5, ∞]

Therefore, the  solution set. for the given inequality : x-5> -10. is (-5, ∞]

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The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Answer:

Step-by-step explanation:

7*5

Answer:

he got 8 apples left and made a profit of 16

Step-by-step explanation:

The probability that your would get an odd number twice when the rolling is 1-8 is 12.5%

Probability is the chance of occurrence of an even (E) Over a period of time. That is, it is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

How to get the probability of the spinning?

From the analysis, the spinning is done twice from numbers 1-8

this means that in ever row, each number appears double.

The sample size is 8x8=64

1,1     1,2     1,3    1,4     1,5    1,6    1,7    1,8

2,1    2,2    2,3    2,4    2,5   2,6   2,7   2,8  

3,1     3,2    3,3   3,4     3,5   3,6   3,7   3,8

4,1    4,2    4,3   4,4    4,5   4,6    4,7   4,8

5,1      5,2   5,3   5,4     5,5    5,6    5,7  5,8

6,1      6,2    6,3  6,4     6,5    6,6   6,7   6,8

7,1      7,2     7,3   7,4    7,5    7,6   7,7  , 7,8

8,1     8,2     8,3  ,,8,4 ,,, 8,5 ,,8,6  8,7,,, 8,8

The required outcome is 8

These outcomes are

1,1  2,2   3,3   4,4   5,5   6,6  7,7  8,8=8 outcomes

Probability of and event is

P=[tex]\frac{number of required outcome}{number of possible outcome}[/tex]

P(E)=[tex]\frac{8}{64}[/tex]

P(E)=[tex]\frac{1}{8}[/tex]

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Answer: 25%

Step-by-step explanation:

You have 4/8 chances of getting an odd number on the spinner, which equals 1/2, or 50%. Now if you are going to get another odd number, you have an additional 1/2 (half your chances) or 50% of a chance of getting it after you get the first odd number. This means you must mutliply these chances. 1/2x1/2 which is 1/4 = 25%

The intervals for the concavity of the odd function are given as follows:

The definition of even and odd functions depends on the relation between f(x) and f(-x), as explained as follows:

In this problem, we have that the function is odd, hence the following statement is true:

f(-x) = -f(x) for all values of x.

This means that the concavity intervals are exchanged, hence:

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a) The linear function is:

y = 2 + 0.25x.

b) The amount of snow on the ground after 4 hours will be of 3 inches.

c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In this problem, the values of these coefficients are given as follows:

Hence the equation is:

y = 2 + 0.25x.

After four hours, the amount of snow on the ground will be of:

y = 2 + 0.25(4) = 2 + 1 = 3 inches.

The time until the amount reaches 6 inches is of:

2 + 0.25x = 6

0.25x = 4

x/4 = 4

x = 16 hours.

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Answer:

40% decrease

Step-by-step explanation:

[tex]\frac{1090-654}{1090}[/tex] = .4  x 100 to make a percent equals 40%

Answer:There is no decrease from 2,820 kilograms to 2,820 kilograms.

The percent of decrease in the size of the sugar order is 0%.

Step-by-step explanation:

The values of x and y using angle relationships are as follows:

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.

Therefore, the angle relationship can be used to find the value of x and y in the diagram.

In the diagram, l and m are parallel lines and are cut by a transversal line.

Therefore,

10.

10x - 17 = 8x + 1(alternate exterior angles are congruent)

10x - 8x = 1 + 17

2x = 18

x = 18 / 2

x = 9

8x + 1 + 6y + 29  = 180(sum of angles on a straight line is 180 degrees)

72 + 1 + 29 + 6y = 180

102 + 6y = 180

6y = 180 - 102

6y = 78

y = 78 / 6

y  = 13

11.

7x - 30 = 5x + 14(Corresponding angles)

Corresponding angles are congruent.

7x - 5x = 14 + 30

2x = 44

x = 44 / 2

x = 22

3y + 11 + 7x - 30 =  180(sum of angles on a straight line)

3y + 11 + 7(22) - 30 =  180

3y + 11 + 154 - 30 = 180

3y = 180 - 11 - 154 + 30

3y = 45

y = 45 / 3

y = 15

12.

7y - 23 = 23x - 16 (vertically opposite angles)

7y - 23x = 7

8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)

31x  - 37 = 180

31x = 180 + 37

31x = 217

x = 217 / 31

x = 7

7y - 23(7) = 7

7y = 7 + 161

7y = 168

y = 168 / 7

y = 24

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Answer:

slice it in the middle in the top and bottom or do it corner to corner.

Step-by-step explanation:

1. have 2 braincells

2. put them toghether and think.

Answer:

x      y

1      0

2     10

5     40

10   90

Step-by-step explanation:

In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).

Therefore, when x is 2, y will be 10.

To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.

Answer:

Step-by-step explanation:

(1,0)   (5,40)

Using these coordinates we find the line equation y=mx+b:

[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=\frac{40-0}{5-1} \\\\m=\frac{40}{4} \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\[/tex]

We substitute the value of coordinate (1,0) into equation (1):

[tex]0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x[/tex]

Divide both parts of the equation by 10:

[tex]10=x\\\\Thus, (10,90)[/tex]

   x   |    y

-----------------

   1    |   0    

------------------

   2   |   10

------------------

   5   |   40

------------------

  10   |  90

Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.

When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.

Hope this helps.

Step-by-step explanation:

The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d)  .

In the question ,

four set of sides is given ,

we need to find the set of side that forms a right triangle ,

we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .

Option(a)

the sides are 4 , 8 , 11.

4 + 8 = 11

16 + 64 = 121

80 = 121

we know that 80 121 ,

So , the sides do not form a right triangle

Option(b)

the sides are 6 , 8 , 13

6 + 8 = 13

36 + 64 = 169

100  169

we know that 100 169 ,

So , the sides do not form a right triangle .

Option(c)

the sides are √3, √5 , 8

√3 + √5 = 8

3 + 5 = 64

8 = 64

we know that 8  64 ,

So , the sides do not form a right triangle .

Option(d)

the sides are √3, √13 , 4

√3 + √13 = 4

3 + 13 = 16

16 = 16

Yes , the sides form a right triangle .

Therefore , The sides {√3 , √13 , 4} forms a right triangle  .

The given question is incomplete , the complete question is

Determine which set of side measurements could be used to form a right triangle ?

(a) 4, 8, 11

(b) 6, 8, 13

(c)√3, √5,8

(d)√3, √13, 4

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Answer:

27/8 or 3.375 or 3 3/8

Step-by-step explanation: