Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?

The regression equation is  mathematically given as

[tex]\=Y = 5 + 0.3 X[/tex]

This is further explained below.

The line is passing through (0, 5) and (15, 10).

Generally, the equation for Slope  is  mathematically given as

[tex]S=\frac{ (10 - 5)}{(15 - 0) }[/tex]

Therefore

S= 5/15

S= 1/3

S= 0.3

Intercept = 5

In conclusion,Regression equation:

[tex]\=Y = 5 + 0.3 X[/tex]

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The measure of <2 is 60.

The tangent is defined as a line touching circles or an ellipse at only one point.

given:

VU = 80° and ST = 40°

By using theorem,

The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.

<2= 1/2 (80+ 40)

<2= 60

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Answer:

It should look like a v with the origin at +0.5

Step-by-step explanation:

hellooo

Step-by-step explanation:

so sine is 0 and (-1/3 isnt gonna positive out on the other side no is positive so ur last answer E is it

Answer:

the MEAN for class a is 72.6

the MEAN for class b is 84.0

if you take these means and compare them, you can see that on average, class B performed better.

the MEDIAN for class a is 72

the MEDIAN for class b is 85

Step-by-step explanation:

Answer:

20x^2 + 47x + 24

Step-by-step explanation:

The area of a rectangle is LENGTH * WIDTH. From the diagram, we see that  LENGTH = 4x + 3 and WIDTH = 8 + 5x. Therefore the area is:

A = LENGTH*WIDTH

  = (4x+3)(5x+8)

  = 20x^2 + 32x + 15x + 24

  = 20x^2 + 47x + 24

Answer: C. 20x²+47x+24

Step-by-step explanation: Use the FOIL Method (First, Outer, Inner, Last). Equation: (5x+8) (4x+3). Hope this helps!

The solution of the given Inequality is; D: x ≤ 6

We want to find the solution to the Inequality;

5x - 9 ≤ 21

Using Addition property of equality, add 9 to both sides to get;

5x ≤ 30

Using division property of equality, divide both sides by 5 to get;

x ≤ 6

All real numbers less than or equal to 6

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Answer:

8 * sqrt2

Step-by-step explanation:

the area of a square can be found by squaring the length of the diagonal and then dividing it by 2. 16^2 / 2 = 128. if the area of a square is 128, each side is sqrt 128 = 8 * sqrt2

The average monthly salary of the female employees is $900.

An equation is a mathematical statement that equates algebraic expression  to other algebraic expressions or constants by an equal sign that helps to determine the value of unknown variables.

It is given that

the average of the monthly salary of female and male employees is $ 2000

Let the average monthly salary of the female employees is $b

It is again given that

The average monthly salary of the male employees is $(b +200)

so , the equation can be formed as

b + b + 200  = 2000

2b + 200 = 2000

2b = 2000 - 200

2b = 1800

b = $900

The average monthly salary of the female employees is $900.

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The effective tax rate based on the assumed information is 2.5%.

Let's assume that the figures are:

Income tax expense = $50

Income before tax = $2000

It should be noted that tax rate is calculated as:

= Income tax expense / Income before tax

= 50/2000

= 0.025

= 2.5%

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The equation of the segments perpendicular bisector is; y = -¹/₂x + 2

i) Since it is a perpendicular bisector, hence point M is the midpoint. Thus;

Midpoint (AB) = [(x₁ + x₂)/2], [(y₁ + y₂)/2] = (x_m, y_m)

Slope AB will be;

m₁ = ((x₁ - x₂)/(y₁ - y₂))

Slope of perpendicular bisector is;

m₂ = -1/m₁

Equation of perpendicular bisector is;

(y - y_m) = m₂(x - x_m)

ii) Midpoint (AB) = [(-2 + 6)/2], [(3 - 1)/2] = (2, 1)

Slope AB will be;

m₁ = ((6 + 2)/(-1 - 3)) = -2

m₂ = -1/-2 = 1/2

Equation of perpendicular bisector is;

(y - 1) = -¹/₂(x - 2)

y - 1 = -¹/₂x + 1

y = -¹/₂x + 2

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The function g(x) is [tex]g(x) = (x + 7)^3[/tex]

The function f(x) is given as:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.

So, we have:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

Rewrite as:

[tex]y = \sqrt[3]{x} - 7[/tex]

Swap x and y

[tex]x = \sqrt[3]{y} - 7[/tex]

Add 7 to both sides

[tex]x + 7 = \sqrt[3]{y}[/tex]

Take the cube of both sides

[tex]y = (x + 7)^3[/tex]

This implies that

[tex]g(x) = (x + 7)^3[/tex]

Hence, the function g(x) is [tex]g(x) = (x + 7)^3[/tex]

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The statement that's is likey true about the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

It should be noted that a dot plot simply gives a pictorial representation of the information given.

In this case, the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.

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Answer: Most likely, about 40% to 60 % of the people in the town join a health club yearly.

Step-by-step explanation:

The most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations:

0.02x - 0.05y =  -0.38

0.03x + 0.04y = 1.04

We can write above equations as follows:

2x - 5y = -38

3x + 4y = 104

After solving with the substitution method:

x = 16

y = 14

-20 ≤ x ≤ 20

-15 ≤ x ≤ 15

Thus, the most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

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Answer:

-2 3/8

Step-by-step explanation:

since point A is left of 0, it means it is a negative value.

so, the positive answer options are automatically out.

then we see that point A is 2 full units and a little bit left of 0.

that means it has to be lower than -2 but higher than -3.

-22/7 = -3 1/7

so, that is too low.

-3 7/8 is too low.

so, that leaves -2 3/8 (confirmed also by the fact that A is a little bit higher than half between -2 and -3, which is the case for -2 3/8).

a. The unit rate is 9 d per t

b. Find the graph in the attachment

To graph the line, we need to find its gradient or unit rate

Since t has an increase of 0.20 units in t corresponds to an increase of 1.8 units in d.

The gradient or unit rate of change is m = change in d/change in t

= Δd/Δt

Since

So, substituting the values of the variables into the equation, we have

m = Δd/Δt

= + 1.8 units/+ 0.2 units

= 9 d per t

So, the unit rate is 9 d per t

To graph the function, we need to know the equation of the graph.

So, the equation of a graph in gradient form is

m = (y - y')/(x - x') where (x', y') = (0, 0) since the graphs both start at the origin

Since m = 9, we have

m = (y - y')/(x - x')

9 = (y - 0)/(x - 0)

9 = y/x

y = 9x

So, the equation of the line is y = 9x

Find the graph in the attachment.

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Answer:

30,000

Step-by-step explanation:

place value of 3 is tens of thousands (10,000)

therefore its total value is : 3×10,000=30,000

Answer:

z = -60

Step-by-step explanation:

1/6z= -10

To find the value for z, multiply each side by 6

6*1/6z= -10*6

z = -60

For the given right triangle, we have:

Here we have a right triangle, remember that the sum of the internal angles of a triangle must be 180°, then:

N + M + L = 180°

We can see that:

N = 37°

M = 90°

Then:

L = 180° - N - M = 180° - 37° - 90° = 53°

Also, if we step on N, the adjacent cathetus measures 6 units, then we can use the relations:

tan(37°) = (opposite cathetus)/(adjacent cathetus)

tan(37°) = ML/6

tan(37°)*6 = ML = 4.5

cos(37°) = (adjacent cathetus)/(hypotenuse)

cos(37°) = 6/NL

NL = 6/cos(37°) =  7.5

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Answer:

Step-by-step explanation:

9w^{321+15+6}

9w^{342}

The equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.

The total distance that Joe needs to cover to travel to Dallas = 320 miles {As he lives 320 miles away from Dallas}.

The distance that Joe covers after traveling for h hours at an average speed of 69 miles per hour = 69h {as Distance = Speed*Time}

Therefore, the distance left to cover by Joe, that is the distance from Dallas d can be written as the difference between the total distance needed to be covered and the distance Joe already covered.

Thus the equation is d = 320 - 69h.

Thus, the equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.

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Answer:

y = 95

Step-by-step explanation:

x + 120 = 180

25 + x + y = 180

flipping the first equation 180 - 120 = 60 so x is 60.

so plug in 60 into the second equation

25 + 60 + y =180 --> 85 + y =180 flip equation 180 - 85 = 95

so y is 95

Answer:

1) a
2) b

Step-by-step explanation:

1) Lets check all the options

a) Cannot be simplified

b) [tex](6^2)^5=6^{10}[/tex] because [tex](a^m)^n=a^{mn}[/tex]

c) [tex](2\times3)^{10}=6^{10}[/tex] fairly self-explanatory because [tex]2\times3=6[/tex]

d) [tex]2^{10}\times3^{10}=6^{10}[/tex] because [tex]a^m\times b^m=ab^m[/tex]

Hence a is the answer.

2) [tex]25\frac12\div\frac12=\frac{51}2\times\frac21=51[/tex]

Hence b is the answer

Step-by-step explanation:

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Answer:

71°

Step-by-step explanation:

So, angle A measures 66+5=71°

Using a system of equations, it is found that it would take 2 servings of macaroni and 8 servings of broccoli to get the desired amount.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Researching the problem on the internet, each serving of macaroni has 3 grams of protein, while each serving of broccoli has 2 grams. Since 22 grams of protein are needed, we have that:

3M + 2B = 22.

Each serving of macaroni has 16 grams of carbohydrates, while each serving of broccoli has 4 grams. Since 64 grams of carbohydrates are needed, we have that:

16M + 4B = 64

Simplifying by 4:

4M + B = 16 -> B = 16 - 4M

Replacing in the first equation:

3M + 2B = 22

3M + 2(16 - 4M) = 22

5M = 10

M = 10/5

M = 2.

B = 16 - 4M = 16 - 8 = 8

2 servings of macaroni and 8 servings of broccoli are needed.

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Answer:

D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)

Step-by-step explanation:

The temperature at any time t can be represented as:

D(t)=A+B*sin(2*pi*t/T)+C*cos(2*pi*t/T)

where A is the average temperature, B is the amplitude of the sine wave, C is the amplitude of the cosine wave, and T is the period.

In this case, we are given that the average temperature is 60, the high temperature is 73, and the low temperature is 47. We can therefore calculate that the amplitude of the sine wave is 23 and the amplitude of the cosine wave is 26. The period is 24 hours. Therefore, the equation for the temperature in terms of time is:

D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)

Answer:

Center of the Sphere is a fixed point in its interior which is equidistant from each point on sphere. Option A is not right because it says center is line segment. Option B is right as it says it is fixed and equidistant from point of surface.

Step-by-step explanation:

For systems A and B we have:

1) Change the first equation in A by a multiple of itself. (the multiple is 1/3).

2) Yes, the systems are equivalent.

Here we have the systems of equations:

A:

-3x + 12y = 15

7x - 10y = -2

B:

-x + 4y = 5

7x - 10y = -2

Notice that the second equation is the same in both systems, so we only need to work with the first ones.

If we take the first equation in system A:

-3x + 12y = 15

If we divide both sides by 3, we get:

-x + 4y = 5

Which is the first equation of B.

So we just need to replace the first equation in system A by a multiple of itself to get system B.

Because of that, we conclude that both systems are equivalent (because are made of the same equations) which means that both systems have the same solutions.

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Answer: C), Yes

Step-by-step explanation:

Answer:

Therefore the slope is 13

Step-by-step explanation:

Using Slope intercept formula y = mx + b.

Note : m is the slope ( the number near x).

y+6=13(x−4)

y+6 = 13x - 52

Add -6 to both sides

y+ 6- 6 = 13x- 52- 6

y= 13x -58

Therefore the slope is 13

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line y+6=13(x-4)

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

The slope of this particular graph is: the constant multiplied by the parentheses.

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=Slope \:13}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]