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SIZIF [17.4K]
3 years ago
9

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The measure of angl

e 0 is 7pie/6 the measure of its reference angle is __ degree and sin 0 is __ .
Mathematics
2 answers:
Marta_Voda [28]3 years ago
7 0
Your answer is 71626
kompoz [17]3 years ago
5 0
The answer should be 71626
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A company makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 15 cm. If
jekas [21]

We have been given that a company makes wax candles in the shape of a solid sphere. Each candle has a diameter of 15 cm. We are asked to find the number of candles that company can make from 70,650 cubic cm of wax.

To solve our given problem, we will divide total volume of wax by volume of one candle.

Volume of each candle will be equal to volume of sphere.

V=\frac{4}{3}\pi r^3, where r represents radius of sphere.

We know that radius is half the diameter, so radius of each candle will be \frac{15}{2}=7.5 cm.

\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot (7.5\text{ cm})^3

\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot 421.875\text{ cm}^3

\text{Volume of one candle}=1766.25\text{ cm}^3

Now we will divide 70,650 cubic cm of wax by volume of one candle.

\text{Number of candles}=\frac{70,650\text{ cm}^3}{1766.25\text{ cm}^3}

\text{Number of candles}=\frac{70,650}{1766.25}

\text{Number of candles}=40

Therefore, 40 candles can be made from 70,650 cubic cm of wax.

8 0
3 years ago
The diagonals of a rectangle measure x+5 feet and 2x+1 feet what is the value of x?
vodomira [7]

The value of x is 4.

Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.

The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.

In the given figure ABCD is a rectangle.

OA=2x+1 and OD=x+5             [Given]

AC and BD are diagonals of a rectangle.

As we know that the diagonals of a rectangle are always equal.

So, AC = BD

We can also write it as,

2×OA=2×OD

2×(2x+1) =2×(x+5)

Apply the distributive property a(b+c)=ab+ac, we get

4x+2=2x+10

Subtract 2x from both sides, we get

4x+2-2x=2x+10-2x

2x+2=10

Subtract 2 from both sides, we get

2x+2-2=10-2

2x=8

Divide both sides by 2, we get

2x/x=8/2

x=4

Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.

Learn more about rectangles from here brainly.com/question/1549055.

#SPJ4

4 0
2 years ago
Annuity A pays 1 at the beginning of each year for three years. Annuity B pays 1 at the end of each year for four years. The Mac
kiruha [24]

Answer:

Calculate the Macaulay duration of Annuity B at the time of purchase is 1.369.

Step-by-step explanation:

First, we use 0.93 to calculate the v which equals 1/(1+i).

\frac{0+1*v+2v^{2} }{1+v+v^{2} } = 0.93

After rearranging the equation, we get 1.07v^{2} + 0.07v - 0.93=0

So, v=0.9

Mac D: \frac{0+1*v+2*v^{2}+ 3*v^{2} }{1+v+v^{2}+ v^{3} }

After substituting the value of v, we get Mac D = 1.369.

7 0
3 years ago
the polynomial 10x 3 + 35 x 2 -4 x -14 is Factor by grouping what is the common factor that is missing both sets of parentheses​
My name is Ann [436]

Answer:

Step-by-step explanation:

10x^3 + 35x^2 - 4x - 14

5x^2(2x + 7) - 2(2x + 7)

(5x^2 - 2)(2x + 7)

5 0
3 years ago
Find the length DE. Round your answer to the nearest tenth of a meter
Oksi-84 [34.3K]

Answer:

10.7 m

Step-by-step explanation:

5 0
3 years ago
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