MATHEMATICS COLLEGE

8. The initial value of an investment is $12,000. If the investment earns an annual interest rate of 2.2%, what is its value in 10 years?a. $14,917.30
b. $14,640.00
c. $14,627.93
d. $87,655.58

Answers

Answer 1

Answer:

Amount get after 10 year is $14,640

Given information:

Initial amount invested = $12,000

Annual interest rate = 2.2%

Number of year = 10 year

Find:

Amount get after 10 year

Computation:

Amount of interest = Initial amount invested × Annual interest rate × Number of year

Amount of interest = 12,000 × 2.2% × 10

Amount of interest = $2,640

Amount get after 10 year = Initial amount invested + Amount of interest

Amount get after 10 year = 12,000 + 2,640

Amount get after 10 year = $14,640

Learn more:

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Answer 2

Answer:

Answer:

$14,917.30

Step-by-step explanation:Step 1: To calculate your interest rate, you need to know the interest formula I/Pt = r to get your rate. Here,

I = Interest amount paid in a specific time period (month, year etc.)

P = Principle amount (the money before interest)

t = Time period involved

r = Interest rate in decimal

Step 2: Once you put all the values required to calculate your interest rate, you will get your interest rate in decimal. Now, you need to convert the interest rate you got by multiplying it by 100. For example, a decimal like .11 will not help much while figuring out your interest rate. So, if you want to find your interest rate for .11, you have to multiply .11 with 100 (.11 x 100).

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A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.4 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Answers

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

$(AD)/(AB) = (DE)/(BC)$

$(8)/(12) = (2)/(y)$

8y = 24

y = 24/8

y = 3 meters

Let take an integral look at the distance of the man from the building as x, therefore the distance from the spotlight to the man is 12 - x

∴

$(12-x)/(12)=(2)/(y)$

$1- (1)/(12)x = 2* (1)/(y)$

To find the derivatives of both sides ;we have:

$- (1)/(12)dx = 2* (1)/(y^2)dy$

$- (1)/(12) (dx)/(dt) = 2* (1)/(y^2) (dy)/(dt)$

During that time ;

$(dx)/(dt )= 1.4 \ m/s$ and y = 3

So; replacing the value into above ; we have:

$-(1)/(12)(1.4) = - (2)/(9) (dy)/(dt)$

$(dy)/(dt) = \frac{\frac{ 1.4} {12 } }{ (2)/(9)}$

$(dy)/(dt) = {\frac{ 1.4} {12 } }*{ (9)/(2)}$

$(dy)/(dt) =0.525 \ m/s$

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Will mark brainliest, 60 points

Answers

Answer:

$\boxed{ \bold{ \sf{ \: 1. \: \: \: \: \: 198}}}$

$\boxed{ \bold{ \sf{2. \: \: \: \: \: - 8}}}$

$\boxed{ \bold{ \sf{ 3. \: \: \: \: \: (64)/(343) }}}$

Step-by-step explanation:

1. Given, u = 20 , x = 4 , y = 7 , z = 10

$\sf{ (u)/(z) + x {y}^(2) }$

⇒ $\sf{ (20)/(10) + 4 * {7}^(2) }$

⇒ $\sf{ (20)/(10) + 4 * 49}$

⇒ $\sf{ (20)/(10) + 196}$

⇒ $\sf{ (20 + 196 * 10)/(10) }$

⇒ $\sf{ (20 + 1960)/(10) }$

⇒ $\sf{ (1980)/(10) }$

⇒ $\sf{198}$

2. $\sf{4( - 2)}$

Multiplying or dividing a positive integer by any negative integer gives a negative integer

= -8

3. $\sf{( (4)/(7) ) ^(3) }$

⇒ $\sf{( \frac{ {4}^(3) }{ {7}^(3) } })$

⇒ $\sf{ (4 * 4 * 4 )/(7 * 7 * 7)}$

⇒ $\sf{ (64)/(343) }$

Hope I helped!

Best regards! :D

Answer:

$\Huge \boxed{\mathrm{18. \ \ \ 198}} \n\n\n \Huge \boxed{\mathrm{19. \ \ \ -8}} \n\n\n \Huge \boxed{\mathrm{20. \ \ \ (64)/(343) }}$

$\rule[225]{225}{2}$

Step-by-step explanation:

18.

$\displaystyle (u)/(z) +xy^2$

u = 20, x = 4, y = 7, and z = 10.

$\Rightarrow \displaystyle (20)/(10) +(4)(7)^2$

$\Rightarrow \displaystyle 2+(4)(49)$

$\Rightarrow 2+196$

$\Rightarrow 198$

19.

$4(-2)$

Rewriting.

$\Rightarrow -(4*2)$

Multiplying.

$\Rightarrow -8$

20.

$\displaystyle ( (4)/(7) )^3$

Distributing the cube sign to the numerator and the denominator.

$\Rightarrow \displaystyle (4^3 )/(7^3 )$

$\Rightarrow \displaystyle (64)/(343)$

$\rule[225]{225}{2}$

Twice the area of a square is 72 square miles. What is the length of each side of the square?

Answers

Answer:

6 miles

Step-by-step explanation:

Let's say the length of the sides of the square is x.

The area of a square is denoted by: A = x².

Here, we're given that twice the area of the square is 72, so we can write this is 2 times the area, which is 2 * x². Set this equal to 72 and solve:

2x² = 72

x² = 36

x = 6

Thus the answer is 6 miles.

Answer:

6 miles

Step-by-step explanation:

2A = 72

A = 72/2

A = 36

Area = s²

36 = s²

s = 6 miles

Why is underfind the square root of a negative number?

Answers

Answer:

The square root of a negative number is undefined, because anything times itself will give a positive (or zero) result. Note: Zero has only one square root (itself). Zero is considered neither positive nor negative

Answer:

sjshzhshshdhdgdgdhdhdgshshshshshwywhwhw

Estimate the product by rounding 4×472

Answers

4*500=2000

Answer = 2000

Answer:

i think it would be 2000

Step-by-step explanation:

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (–5, –5), (4, 6) L2 : (–9, 8), (–18, –3)

Answers

Answer: The lines L1 and L2 are parallel.

Step-by-step explanation: We are given to determine whether the following lines L1 and L2 passing through the pair of points are parallel, perpendicular or neither :

L1 : (–5, –5), (4, 6),

L2 : (–9, 8), (–18, –3).

We know that a pair of lines are

(i) PARALLEL if the slopes of both the lines are equal.

(II) PERPENDICULAR if the product of the slopes of the lines is -1.

The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by

$m=(d-b)/(c-a).$