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3 years ago

8

Marie can find the volume of a cube by using the formula V = s³, where s represents the side length of the cube. If Marie’s cube

has a side length of 2 1 2 centimeters, what is the volume of her cube? Show your work. Write your answer as a fraction and a decimal.

1 answer:

lana [24]3 years ago

8 0

Answer: 7 1/2 cubic cm

Step-by-step explanation:

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Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments fo

svp [43]

Answer:

Step-by-step explanation:

From the given information:

The present value of the house = 128000

interest rate compounded monthly r = 7.8% = 0.078

number of months in a year n= 12

duration of time t = 30 years

To find their regular monthly payment, we have:

$PV = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}} \end {bmatrix}$

$128000 = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

128000 = 138.914 P

P = 128000/138.914

P = $921.433

∴ Their regular monthly payment P = $921.433

To find the unpaid balance when they begin paying the $1400.

when they begin the payment ,

t = 30 year - 5years

t= 25 years

$PV= 921.433 \begin {bmatrix} \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

PV = $121718.2714

C) In order to estimate how many payments of $1400 it will take to pay off the loan, we have:

$121718.2714 = \begin {bmatrix} \dfrac{1300 (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}} \end {bmatrix}$

$121718.2714 = 200000 \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$\dfrac{121718.2714}{200000 } = \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$0.60859 = \begin {bmatrix} (1 - \dfrac{12}{12.078}))^{nt} \end {bmatrix}$

$0.60859 = (0.006458)^{nt}$

$nt = \dfrac{0.60859}{0.006458}$

nt = 94.238 payments is required to pay off the loan.

How much interest will they save by paying the loan using the number of payments from part (c)?

The total amount of interest payed on $921.433 = 921.433 × 30(12) years

= 331715.88

The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)

= 177795.38

The amount of interest saved = 331715.88 - 177795.38

The amount of interest saved = $153920.5

6 0

4 years ago

Plz Help, and solve. Show your work. I will give Brainliest. A - 7 = -13 solve and show your work 10X - 8 = 9X + 8 Can a right t

likoan [24]

Answer:

A - 7 = -13

Add 7

A = -6

10X - 8 = 9X + 8

Add 8

10X = 9X + 16

Subtract 9X

X = 16

In a right triangle, where a and b are the shorter sides, and c is the longer side a^2+b^2=c^2

Thus, plug in the values.

12^2+16^2=20^2

144+256=400

400=400.

Because the equation is true, 12, 16, and 20 can be a right triangle

<em>Hope it helps <3</em>

3 0

4 years ago

Read 2 more answers

I need help fast plss

Marysya12 [62]

Answer:

a = 1√6

b = -2

Step-by-step explanation:

Hello,

To solve this trigonometric problem, we need to convert this values into fractions

a).

Sin45° = 1/√2

cos30° = √3/2

Sin60° = √3/2

Sin45° / (cos30° + sin60°) = [(1/√2) ÷ (√3/2 + √3/2)]

(1/√2) ÷ (√3/2 + √3/2)

Add √3/2 + √3/2

1/√2 ÷ 2√3/2

1/√2 × 2/2√3

2/2√(2×3)

2/2√6

1/√6

b

Cos 180° = -1

Sin150° = ½

Tan135° = -1

2cos180° - 2sin150° - tan135°

(2 × -1) - (2×½) - (-1)

-2 - 1 + 1 = -2

3 0

3 years ago

A square pyramid with a height of 7 inches has volume of 47.25 cubic inches. Find the side length of the square base

mixas84 [53]

Hello,
Volume of the square pyramid=
1/3×B×h where B represent Base and h represent height

Now, substitute the information that we had from this problem into the formula.
47.25=1/3×B×7
Times 3 from both side
141.75=7B
Divide B from both side
B=20.25 square inches
B=s^2
Square root it to get
s=4.5 inches. As a result, the side length of square base is 4.5 inches. Hope it help!

7 0

3 years ago

Write the equation of the line that passes through the points (-1, -2), (2, 7).

mote1985 [20]

Answer:

y+2=3(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(7-(-2))/(2-(-1))

m=(7+2)/(2+1)

m=9/3

m=3

y-(-2)=3(x-(-1))

y+2=3(x+1)

7 0

3 years ago