Write an equation for the line graphed below.

At age 58, the investor will have (Future Value) $571,816.64 in their savings account after accumulating $150,000 and then adding $100 monthly for five years and $200 monthly for fifteen years.

The future value at age 58 can be computed in two tranches.

The first step is to compute the future value using the present value of the accumulated funds in addition to the periodic monthly investments.

The second step computes the future value using the present value of the funds after 5 years in addition to the periodic monthly savings.

N (# of periods) = 60 months (5 x 12)

I/Y (Interest per year) = 6%

PV (Present Value) = $150,000

PMT (Periodic Payment) = $100

FV = $209,304.53

Sum of all periodic payments = $6,000 (60 x $100)

Total Interest = $53,304.53

N (# of periods) = 180 months (12 x 15 years)

I/Y (Interest per year) = 6%

PV (Present Value) = $209,304.53

PMT (Periodic Payment) = $200

Results:

Future Value (FV) = $571,816.64

Sum of all periodic payments = $36,000 ($200 x 180 months)

Total Interest = $326,512.11

Thus, you will have $571,816.64 as the future value in your savings account when you turn 58.

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Answer: 10,000

Step-by-step explanation:

Solution

For this case we can do the following:

And then the solution for this case would be:

18v^9 y^5

If we need to determine the surface area of a prims we would have to add the areas of each of the faces of the prism, therefore, we would also require to know the length of the prism.

From the question given,

The formula to find the test statistics mean is given below as,

Where,

Given the values of the above below,

Substituting the values into the formula of test statistics t above,

Hence, the test statistics, t = -3.24 ( two decimal places)

Here, we want to make a unit conversion

Since we want to move from Fahrenheit to celsius, we are going to use the first formula

We simply are going to substitute the value of F = 35 into the equation

Thus, we have it that;

Answer

The length of the missing leg = 12 m

Explanation

The triangle presented is a right angled triangle because one of its angles is equal to 90 degrees.

The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

Hypotenuse side = 15 m

a = 9 m

b = d = ?

a² + b² = (hyp)²

9² + d² = (15)²

81 + d² = 225

d² = 225 - 81

d² = 144

d = √144

d = 12 m

Hope this Helps!!!

Answer:

We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem,

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

If one leg is 9 , that's our a value.

If the hypotenuse is 15 , that's our c value.

Now we just have to find the b value.

Plugging in the variables,

[tex] {9}^{2} + {b}^{2} = {15}^{2} [/tex]

[tex] {9}^{2} = 81 \\ {15}^{2} = 225 \\ 81 + {b}^{2} = 225[/tex]

Subtract 81 from both sides.

[tex] {b}^{2} = 144[/tex]

Square root both sides.

[tex] \sqrt{ {b}^{2} } = b \: and \: \sqrt{144 = 12 } [/tex]

so b = 12

Let's draw the ramp to better understand the problem:

For us to be able to determine how long the ramp will be, we will be using the Cosine Function.

We get,

Therefore, the answer is 57.2165 feet.

4 ---> 48

x ---> 96

answer: 8 hours

To the nearest hundred thousand, we must first determine the number in the hundred thousand position. This is the digit 1. Now consider the number next to it. This is 2. Since two is not up to 5, we would round off all other nuber to zero.

Hence to the nearest hundred thousand, 126,945 is 100,000

Answer: 56

To solve this problem, we will use the formula for Combination which goes by

From the problem, we know that:

n = 8

r = 3

Since there are a total of 8 different movie soundtracks and we only need 3.

Substituting it on the formula,

Therefore, there are 56 possible selections of movie soundtracks at the music store.

The new coordinates after the dilation are as follows;

Here, we want to perform a dilation

Given a pre-image with coordinates (x,y) and a scale factor of k, the coordinates of the image will be;

Applying this to the given coordinates, we have;

a number : w

A number w divided by 5: w/5

equals (=) 6

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

On the given dataset, if we ignore the outlier of the dataset, all those measures are going to be similar, but since we have a high frequency on the middle of our dataset and the presence of an outlier value, the most likely to describe the center of the dataset is the mode.

2 blams ----------------- 15 droms

5 droms ----------------- 28 klegs

1 blam ------------------ ? klegs

5 droms ------------------- 28 klegs

15 droms -------------------- x

x = (15 x 28) / 5

x = 84 klegs

2 blams ------------------------- 84 klegs

1 blam --------------------------- ? klegs

x = (1 x 84)/2

x = 42 klegs

There are 42 klegs in 1 blam

Answer:

hope it helps

Step-by-step explanation:

Answer:

C  -8/3

F  8/3

Step-by-step explanation:

9x² - 64 = 0

==> 9x² = 64

==> x² = 64/9

x = ±√(64/9) = ±√64/√9 = ±8/3

Tax amount = 5% of $16.38

Let's us tabulate the data that is on the scatterplot.

As you can see in the fourth column, "Sold More Trucks than Cars?", some rows say "Yes" and some say "No".

Let's take a look at Employee No.1. Employee No.1 sold 4 trucks and sold 2 cars. Therefore, employee no.1 was able to sell more trucks than cars and thus, the answer to the fourth column is "Yes."

The same is done for all the employees.

In the end, there are 6 employees who were able to sell more trucks than cars.

The first 4 terms of given recursive formulas will be as follows

The recursive expression provides two pieces of information:

the first term in the sequence.

the pattern rule that takes each term from the previous term.

As we have G(1) = 18, G(n) = 2 · G(n − 1).

It's A geometric sequence with r as 2

∴ G(2) = 2 · G(2 − 1) = 2 · G(1) = 2(18) = 36.

∴ G(3) = 2 · G(3 − 1) = 2 · G(2) = 2(36) = 72.

∴ G(4) = 2 · G(4 − 1) = 2 · G(3) = 2(72) = 144.

As we have H(1) = 3, H(n) = 5 · H(n − 1).

It's A geometric sequence with r as 5

H(2) = 5 · H(2 − 1) = 5 . H(1) = 5(3) = 15.

H(3) = 5 · H(3 − 1) = 5 . H(2) = 5(15) = 75.

H(4) = 5 · H(4 − 1) = 5 . H(3) = 5(75) = 325.

As we have J(1) = 3, J(n) = J(n − 1) + 5

It's an arithmetic sequence with d as 5

J(2) = J(2 − 1) + 5 = J(1) + 5 = 3+5 = 8.

J(3) = J(3 − 1) + 5 = J(2) + 5 = 8+5 = 13.

J(4) = J(4 − 1) + 5 = J(3) + 5 = 13+5 = 18.

As we have M(1) = 3, M(n) = 2 · M(n − 1)

It's A geometric sequence with r as 2

M(2) = 2 · M(2 − 1) = 2 · M(1) = 2(3) = 6.

M(3) = 2 · M(3 - 1) = 2 · M(2) = 2(6) = 12.

M(4) = 2 · M(4 - 1) = 2 · M(3) = 2(12) = 24.

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The value of y is π/9 or 7π/9 for the range 0 ≤ y ≤ π.

cosec 3y /( cot 3y + tan 3y) = 0.5

Trigonometry formula is:

cosec Ф = 1/ sin Ф

cot Ф = cos Ф/ sinФ

tan Ф = sinФ/ cos Ф

[tex]\frac{\frac{1}{sin 3y} }{\frac{cos 3y}{sin 3y} +\frac{sin 3y}{cos 3y} }[/tex]  = 0.5

[tex]\frac{\frac{1}{sin 3y} }{\frac{cos 3y^{2} + sin 3y^{2} }{sin 3y cos 3y} }[/tex] = 0.5

sin² 3y + cos ² 3y = 1

1/ sin 3y × sin 3y cos 3y = 0.5

cos 3y = 0.5 = 1/2

cos π/ 3 = 1/2

For 0≤ y ≤π

0 ≤3y ≤ 3π

So 3y = 2kπ + π/3 , k = 0, 1

y = π/ 9 or 7π/ 9

Therefore the value of y is π/9 and 7π/ 9 for the given range.

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The total surface area will be given by:

Where:

Therefore:

Answer:

248 in²

We are given a table that shows the number of zombies over a 4 day period.

a) What is the initial value?

The initial value means an initial population that is the number of zombies at day 0

From the table, we see that the initial population is 2

Initial value = 2

b) What is the growth/decay factor?

The growth/decay factor can be found by finding the ratio of the consecutive terms

r = 512/128 = 4

r = 128/32 = 4

r = 32/8 = 4

r = 8/2 = 4

As you can see, we have got the same ratio.

Since the ratio is greater than 1 then it is a growth factor.

If it was less than 1 then it would have been a decay factor.

Therefore, the growth factor is 4

Initial value = 2

Growth factor = 4

Solution

Given the following below

To find the 90% confidence interval, the formula is

Substituting values into the formula above

Solve the above

At 90% confidence interval, the population mean will be between 121.16 and 130.84 (121.16, 130.84)

Given:

Length of the park, l=4 inches

Width of the park, w=6 inches.

Here, 1 inch is equal to the 30 miles.

To find the actual area of the park:

Area of the park is, A=lw

That is,

In miles,

Hence, the area of the park in miles is 720 miles.