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3 years ago

12

The hypotenuse of a right triangle is 6 inches, and the side opposite to angle theta, one of the non-right angles, is three squa

re root 3 inches long. What is the measure of angle theta?

1 answer:

Anton [14]3 years ago

6 0

Answer:

theta = 60°

Step-by-step explanation:

sin theta = 3 √3 / 6 = √3 / 2

theta = 60°

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Simplify the expression: <br> 6x ^ 2 + 7x - 3x ^ 2 - 2x

yaroslaw [1]

Answer:

3x²+5x

Step-by-step explanation:

8 0

3 years ago

The sales tax for an item was $19.20 and it costs $480 before tax. Find the sales tax rate. Write your answer as a percentage

Zigmanuir [339]

Answer:

sales tax rate = 4%

Step-by-step explanation:

In this problem formula to express one term in percentage is used

To express x as percentage of y is given by (x/y*100) %

______________________________________________

Cost of item = $480

sales tax = $19.20

we have to find sales tax rate.

sales tax rate is percentage of cost price which will levied as tax .

thus, we have to find sales tax as percentage of cost price.

using the percentage cost as given above

sales tax as percentage = sales tax/ cost of item *100

sales tax as percentage = 19.20/480 *100 = 4%

Thus, sales tax rate is 4%.

It means that if cost price of item is $100 then $4 will be the sales tax for the item.

5 0

3 years ago

In a popular tale of wizards and witches, a group of them finds themselves in a room with unmarked doors which change position,

SSSSS [86.1K]

Answer:

Expected number of hours before the the group exits the building = E[Number of hours] = 3.2 hours

Step-by-step explanation:

Expected value, E(X) is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Let X represent the number of hours before exiting the building taking each door. Note that D = Door

D | X | P(X)

1 | 3.0 | 0.2

2 | 3.5 | 0.1

3 | 5.0 | 0.2

4 | 2.5 | 0.5

E(X) = (3×0.2) + (3.5×0.1) + (5×0.2) + (2.5×0.5) = 3.2 hours

Hope this Helps!!!

7 0

3 years ago

Explain which variables would be included when using technology to calculate the present value of a lump sum and to calculate th

koban [17]

Answer:

a. Present value of a lump sum =

PV = FV / ( 1 + i )ⁿ

b. Present value of an annuity =

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)

Step-by-step explanation:

a. Present Value of a Lump sum =

PV = FV / ( 1 + i )ⁿ

Where variables in the formula are explained as follows

PV = Present Value of the given amount today

FV = Future Value of the given amount

i = Discount rate

n = Number of periods

b. Present value of an annuity is given as:

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)

The variables in the equation are explained as the follows:

P = the present value of annuity

PMT = Payment per period or the amount in each annuity payment

r = the interest or discount rate

n = total number of periods or the number of payments left to receive

8 0

3 years ago

A bag contains 8 red marbles, 7 blue marbles, and 6 green marbles. Adam randomly picks out a marble from a bag. What is the theo

alexandr1967 [171]

Answer:

⅓

Step-by-step explanation:

8+7+6

total= 21

blue= 7÷21

1/3

7 0

3 years ago

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