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Elis [28]
3 years ago
14

The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have r

adii of 1 meter. The cost of every mirror is proportional to the cube of the mirror's radius. What is the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors? Express your answer as a common fraction
Mathematics
1 answer:
pogonyaev3 years ago
5 0

Answer: 1:5

Step-by-step explanation:

Given: The cost of every mirror is proportional to the cube of the mirror's radius.

i.e. \dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}

Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.

Then,

\dfrac{\text{Cost of smallest mirror}}{\text{Cost of  largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}

The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:

\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}

Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .

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2 years ago
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 p
Elina [12.6K]

Answer:

2.25

Step-by-step explanation:

The total frequency is:

20 + 12 + 6 + 2 = 40

Calculate the probability of each score:

P(X=3) = 20/40 = 0.50

P(X=2) = 12/40 = 0.30

P(X=1) = 6/40 = 0.15

P(X=0) = 2/40 = 0.05

So the expected value is:

E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)

E = 2.25

5 0
3 years ago
A car moved at a speed of 90km/hr for 3 minutes.What distance did it cover?​
aniked [119]

Answer:

270kilometers

Step-by-step explanation:

To find the distance, all you have to do is the speed · time

In these types of distance time and word problems, you multiply the other factors, 90 and 3, The time(T) · The speed(S)

So. 90(S) · 3(T) = 270(D)

5 0
3 years ago
For questions 8 – 10, answer the questions about tangent-tangent angles.
olchik [2.2K]

Answer:

m(arc ZWY) = 305°

Step-by-step explanation:

8). Formula for the angle formed outside the circle by the intersection of two tangents or two secants is,

Angle formed by two tangents = \frac{1}{2}(\text{Difference of intercepted arcs})

                                                   = \frac{1}{2}(220-140)

                                                   = \frac{1}{2}(80)

                                                   = 40°

9). Following the same rule as above,

Angle formed between two tangents = \frac{1}{2}(\text{Difference of intercepted arcs})

125 = \frac{1}{2}[m(\text{major arc})-m(\text{minor arc})]

250 = [m(\text{arc ZWY})-m(\text{arc ZY})]

250 = m(arc ZWY) - 55

m(arc ZWY) = 305°

Therefore, measure of arc ZWY = 305° will be the answer.

10). m(arc BAC) = \frac{1}{2}([m(\text{arc BDC})-m(\text{arc BC})])

                          = \frac{1}{2}(254-106)

                          = \frac{148}{2}

                          = 74°

4 0
2 years ago
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of b is negative. The value of a is not
sergejj [24]

Answer:

Quadrant III ( C )

Quadrant IV ( D )

Step-by-step explanation:

Ordered pair ( a, b )

gives a point P on the coordinate plane

( a, b ) = ( x, y )

given : b = negative ( y-axis )

           a ≠ 0 ( i.e. a = negative or positive ) ( x -axis )

Therefore point P is located in the : Third and fourth quadrants

8 0
3 years ago
Read 2 more answers
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