What value of x makes this equation true?<br> x/3

Write an expression to represent: The sum of ten and the quotient of a number x and 6.

Minchanka [31]

Let us break it down. A sum of ten. That is just

+10

Then, we will add that to the quotient (which is the number after dividing) of a number x and 6. We can write that as

+ x/6

The slash means division here. Thus your final answer is

10 + x/6

8 0

3 years ago

A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-ra

S_A_V [24]

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

Compounds money quarterly

Double your money in 10 years

Step:1

Formula to calculate future investment with compounded quarterly,

$A =P(1+\frac{r}{n} )^{nt}$ ...............................(1)

Where, A - Future amount

P - Initial investment\

r - Rate of interest

n - No. of compounding in a year

t - No. of years

Step:2

Let, P = X

A = 2X ( Double your money )

From given, n - 4 ( for compounding quarterly )

t - 10 years

From equation (1)

$2X =X(1+\frac{r}{4} )^{(4)(10)}$

$\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}$

$2 =(1+\frac{r}{4} )^{40}$

Take root $40^{th}$ root on both side,

$\sqrt[40]{2} = (1+\frac{r}{4} )$

$1.017479692 = (\frac{4+r}{4} )$

$(1.017479692)(4) = (r+4)$

$4.06992=(r+4)$

$r = 4.06992 -4$

$r =( 0.06992)(100)$

r = 6.992 %

Result:

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

3 0

3 years ago

Ralph is painting the barn below, including the sides and roof. He wants to know how much paint to purchase.

grandymaker [24]

PART A

The barn is constructed by the following 2D shapes

Two triangles of height = 4' and base = 20'
Area = 2 × (0.5×4×20) = 80

Two rectangles of length = 20' and width = 15'
Area = 2 × 20 × 15 = 600

Two rectangles of length = 45' and width = 15'
Area = 2 × 45' × 15' = 1350

One base of length = 45' and width = 15'
Area = 45 × 15 = 675

Two rectangles on each on one side of the roof. We have the length = 45' but not the width. We can work out the width by using Pythagoras theorem

w² = 4² + 10²
w² = 16 + 100
w² = 116
w = √116 = 10.77

Area of the two rectangles on the roof part is = 2 ×10.77 × 45 = 969.33

Total area to paint = 969.33+675+1350+600+80 = 3674.33 ≈ 3700 (to the nearest hundreth)

PART B

Numbers of paint cans needed = 3700 ÷ 57 = 64.9 ≈ 65 cans

PART C

Total cost of paint = 65 × 23.50 = $1527.50

PART D

The barn is constructed by a cuboid and a rectangular prism

V of cuboid = length × width × height
V of cuboid = 20 × 45 × 15
V of cuboid = 13500

V of triangular prism = Area of cross section × depth
V = [0.5×4×20] × 45
V = 1800

Total volume = 1800 + 13500 = 15300

7 0

3 years ago

A true-false question is to be posed to a husband and wife team. Both the husband and the wife will give the correct answer with

marysya [2.9K]

Answer:

Choose either strategy both are equally successful

Step-by-step explanation:

Given:-

- The probability of success for both husband (H) and wife (W) are:

P ( W ) = 0.8 , P ( H ) = 0.8

Find:-

- Which of the following is a better strategy for the couple?

Solution:-

Strategy 1

- First note that P ( W ) & P ( H ) are independent from one another, i.e the probability of giving correct answer of husband does not influences that of wife's.

- This strategy poses an event such that either wife knows the answer and answer it correctly or the husband knows and answers in correctly.

- We will assume that probability of either the husband or wife knowing the answer is 0.5 and the two events of knowing and answering correctly are independent. So,

P ( Wk ) = P (Hk) = 0.5

- The event P(S1) is:

P(S1) = P ( Hk & H ) + P ( Wk & W )

P(S1) = 0.5*0.8 + 0.5*0.8

P(S1) = 0.8

- Hence, the probability of success for strategy 1 is = 0.8

Strategy 2

- Both agree , then the common answer is selected otherwise, one of their answers is chosen at random.

- The success of strategy 2, will occur when both agree and are correct, wife is correct and answers while husband is not or husband is correct and he answers.

- The event P(S2) is:

P(S2) = P ( H & W ) + P ( H / W' & Hk ) + P ( H' / W & Wk )

P(S2) = P ( H & W ) + P ( H / W') P ( Hk ) + P ( H' / W) P (Wk)

P(S2) = P ( H & W ) + P ( H / W')*0.5 + P ( H' / W)*0.5

P(S2) = 0.5* [ P ( H & W ) + P ( H / W') ] + 0.5* [ P ( H' / W) + P ( H & W )]

P(S2) = 0.5*P(H) + 0.5*P(W)

P(S2) = 0.5*0.8 + 0.5*0.8

P(S2) = 0.8

- Hence, the probability of success for strategy 2 is = 0.8

Both strategy give us the same probability of success.

4 0

3 years ago

Write in y= mx + b form: a line through (-3,1) having the same y-intercept as the graph of x-2y=-4

MariettaO [177]

Step-by-step explanation:

Aight, so the same intercept

$- 2y = - 4 - x = = = > \\ y = \frac{1}{2} x + 2$

m=½

$y = \frac{1}{2} x + b = = = > \\ now \: let \: us \: replace \: the \: point \\ 1 = \frac{1}{2} ( - 3) + b = = = > \\ \frac{5}{2} = b$

soooo

$y = \frac{1}{2} x + \frac{5}{2}$

7 0

2 years ago

What value of x makes this equation true? x/3 - 3 = x/9 + 3