MATHEMATICS MIDDLE SCHOOL

Need help ASAP1) A new truck that sells for $42,000 depreciates 11% each year. write a function that models the value of the truck. Find the value of the truck after 8 years. Round to the nearest dollar.

2) Earl mows lawns one weekend. He earns $15 for each lawn that he mows. He spends $50 on gas and other supplies. What function equation represents Earl's profit from mowing x lawns?

A)f(x)=50x-15
B)f(x)=50x+15
C)f(x)=15x-50
D)f(x)=15+50

3) find the common geometric series.
-2,-4,-8,-16.....

Answers

Answer 1

Answer:

Answer:

$\boxed{1) V = 40 000(0.89)^(n), \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_(n) = -2^(n)}$

Step-by-step explanation:

1) Depreciation

The formula for the value V of an asset after depreciation by an annual percentage rate is

V = P(1 - r)ⁿ

where

P = present value

r = annual percentage rate

n = number of years

Data:

V = 40 000

r = 11 % = 0.11

n = 8 yr

Calculations:

(a) Function model

V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ

The function model is $\boxed{ V= 40 000(0.89)^(n) }$

(b) Future value

V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746

In eight years, the truck will be worth $\boxed{ \text{\$15 476}}.$

2) Profit function

Income from 1 lawn = $15

Income from x lawns = 15x

Less gas and supplies = -50

Net income = 15x – 50

The function is $\boxed{f(x) = 15x - 50}$ .

3) Geometric series

(a) Calculate the common ratio

a₁ = -2

a₂ = -4

a₃ = -8

a₄ = =16

The ratios of consecutive pairs are

a₄/a₃ = -16/(-8) = 2

a₃/a₂ = -8/(-4) = 2

a₂/a₁ = -4/(-2) = 2

All adjacent pairs have the same common ratio r = 2.

(b) Write the formula for the series

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

If a₁ = -2, the formula for the series is

aₙ = -2(2)ⁿ⁻¹ = -2ⁿ

The formula for the series is $\boxed{a_(n) = -2^(n)}$ .

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What is the area of a rectangle with the height of 25mm, and the length of 12mm? After you get the product, turn it into feet.

Answers

Area = (length) x (width) = (25mm x 12mm) = 300 square millimeters

You can't convert 'square millimeters' to feet. One is a unit of area,
but the other is a unit of length.

You can convert square millimeters to square feet, though.

(300 mm²) x (1 ft / 304.8 mm)² = 0.00323 square foot (rounded)

300 feet is the answer

A pool has some initial amount of water in it. Then it starts being filled so the water level rises at a rate of 666 centimeters per minute. After 202020 minutes, the water level is 220220220 centimeters. Graph the relationship between the pool's water level (in centimeters) and time (in minutes).

Answers

Answer:

$y=6x+100$

The graph is drawn below.

Step-by-step explanation:

Let the minutes passed be $x$ and height of water level be $y$ cm.

Given:

Rate of rise of water level, $m = 6\textrm{ cm/min}$

When $x=20\textrm{ min},y=220\textrm{ cm}$

Therefore, the relationship can be expressed using the point-slope form of an equation if a line.

The point-slope form is given as:

$y-y_(1)=m(x-x_(1))$

Here, $m=6,x_(1)=20,y_(1)=220$

Therefore, the relationship is given as:

$y-220=6(x-20)\ny-220=6x-120\ny=6x-120+220\ny=6x+100$

Therefore, the relationship between the pool's water level (in centimeters) and time (in minutes) is $y=6x+100$ .

The graph is shown below.

Answer: Points are (20, 220) and (15, 190)

Step-by-step explanation: I had the same quiz question.

What is 17/30 simplifying please please please help me

Answers

you can't simplify the 30 has no common factors

Is 31.010 greater or less or equal to 31.01

Answers

Well, lets look at it this way ... tell me if this does anything for you:

-- Take the number 31.01 .

-- Stick a zero on the end and make it 31.010 .

-- Zeros at the end of a number after the decimal point don't change
the value of the number. So you haven't changed the value of 31.01 .

-- But now it looks exactly like the other number !

-- They must be equal.

Does this float your boat at all ?

31.010 is = to 31.01

the reason being that the 0 on the end of 31.010 is just there for to hold an unwanted place value.

Ex. 0.70 is the same as 0.7 because the zero is just holding a place value. It's not wrong to put in the zero but its better if you don't.

How long does a horse take to run a distance of 6 miles at 16 miles/hour