MATHEMATICS MIDDLE SCHOOL

Evaluate the expression when a = 4. 2a^3

A.
14

B.
24

C.
128

D.
512

Answers

Answer 1

Answer:

2(4)^3

2(64)

=128 Your final answer would be C

Answer 2

Answer: 2a^3
2(4)^3
2(64)
128
The answer is C

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You are paid $82.50 for 71212 hours of work. What is your rate of pay?

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:

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

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 $\boxed{a_(n) = -2^(n)}$ .

3x(5x2)=(3x5)x2 which property of multiplication does the equation show

Answers

The Associative Property

Can someone help me with this pattern? And the rule.

Answers

Each output is (double the input) plus 1 .

Is 50 a multiple of 5

Answers

Yes it is just count by 5's

50 is a multiple of 5 because 5x10=50

The triangular prism has a triangular base with length 12cm and hieght 8cm.the hieght of the prism is 11cm. What is the surface area of the prism

Answers

surface area of triangular prism
has 2 bases with same area (both triangles)
3 rectangle sides that are height 11 and we need to find the other sides

we need the sides of the base to find the rectangles
12/2=6
pythagoren theorem
6^2+8^2=c^2
36+64=c^2
100=c^2
10=c
2 sides are 10

so

bases are 1/2 times 12 timm es8 times 2 since 2 bases=96

sides
height for all is 11
legnth is 12 for 1 and 10 for other 2
11*12+11*10+11*10=352

add
96+352=448

answer is 448cm^2

What is the mixed number and improper fraction for 4.8