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Vinil7 [7]
3 years ago
12

The volume of the sphere is StartFraction 500 Over 3 EndFractionπ cubic units. A sphere has a radius of x units. What is the val

ue of x? 4 units 5 units 8 units 10 units
Mathematics
2 answers:
Tpy6a [65]3 years ago
4 0

Answer:

(b) Radius of the sphere = 5 units.

Step-by-step explanation:

Here, given:

The volume of the sphere  = (\frac{500}{3})\pi cubic units  ... (1)

Also, radius of the sphere  = x  units

Now, VOLUME OF SPHERE  = (\frac{4}{3}) \pi r^3

So, volume of a sphere with radius x  = (\frac{4}{3}) \pi (x)^3

But volume of sphere is given by (1).

\implies (\frac{500}{3})\pi = (\frac{4}{3}) \pi (x)^3\\\implies (\frac{500}{3}) = (\frac{4}{3}) (x)^3\\\implies x^3 = (\frac{500}{3})  \times (\frac{3}{4})  = 125\\\implies x^ 3 = 125 = (5)^3\\\implies x  = 5

Hence, radius of the sphere = 5 units.

FrozenT [24]3 years ago
4 0

Answer:

5 units

Step-by-step explanation:

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a. Yes

b. 0.35

c. 0.5

d.

E(x)=34.25

V(x)=73.1875

SD(x)=8.555

Step-by-step explanation:

a.

x      20   25   30      35   40  45 50

f(x) 0.05 0.2 0.25  0.15  0.15 0.1 0.1

This will be valid probability distribution if

1. All probabilities are between 0 and 1 inclusive.

2. Sum of probabilities must be 1.

Condition 1 is satisfied in this distribution. Now, we will check second condition

sum(f(x))=0.05+0.2+0.25+0.15+0.15+0.1+0.1=1.

As the both conditions are satisfied, thus the given distribution is a valid probability distribution.

b.

P(x≥40)=P(X=40)+P(X=45)+P(X=50)

P(x≥40)=0.15+0.1+0.1

P(x≥40)=0.35

So, the probability that Backens and Hayes LLC will obtain 40 or more new clients is 0.35.

c.

P(x<35)=P(X=20)+P(X=25)+P(X=30)

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P(x<35)=0.5

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d.

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V(x)=1246.25-(34.25)²

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Standard deviation of x=SD(x)=√V(x)

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