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2 years ago

The volume of two spheres is shown:

Mathematics

1 answer:

12345 [234]2 years ago

8 0

Answer:

≈ 1.3 inches

Step-by-step explanation:

Given that:

Sphere A = 30 cubic inches
Sphere B = 10 cubic inches

As we know, the formula to find the volume of a sphere is;

V = π $\frac{4}{3} r^{3}$

So we have:

Sphere A = 30 cubic inches

<=> π $\frac{4}{3} r^{3}$ = 30

<=> $r^{3}$ = 90/4π

<=> r ≈ 4.13

Sphere B = 10 cubic inches

<=> π $\frac{4}{3} r^{3}$ = 10

<=> $r^{3}$ = 30/4π

<=> r ≈ 2.86

So the different between the radius of sphere A and B is:

= 4.13 - 2.86

= 1.27

≈ 1.3 inches

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$\frac{7}{9} x - \frac{1}{5} = 124 \div 5$
and combine the second like-terms:
$\frac{7}{9}x - \frac{1}{5} = 24.8$
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3 years ago

What is the range of possible values for x?

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The minimum value for 2x is 0
the maximum value is achieved when A, D and C are collinear and the quadrilateral ABCD becomes an isosceles triangle ABC 
base AB = 52 and vertical angle 2x + 34° 

For the sine law 
(sin 2x)/22 = (sin ADB)/AB 
(sin 34°)/30 = (sin BDC)/BC 

is given that AB = BC, and sin ADC = sin BDC because they are supplementary, so from 
(sin ADC)/AB = (sin BDC)/BC 

it follows 
(sin 2x)/22 = (sin 34°)/30 

sin 2x = 22 (sin 34°)/30 

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2 years ago

Which expression can be used to find the surface area of the following square pyramid?

telo118 [61]

Answer:

Step-by-step explanation:

The slant height of one side of this pyramid is 5, and the base of this side is 4. Thus, the area of one slant side is (1/2)(5)(4) = 10 units^2.

There are 4 such sides. Thus, the total slant surface area is 4(10 units^2), or 40 units^2.

If you also want to include the base area, the total would be

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3 years ago

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Step-by-step explanation:

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3 years ago

In answering a question on a multiple-choice test, a student either knows the correct answer or guesses it. Let 0.7 be the proba

Dahasolnce [82]

Answer:

The probability is 0.9211

Step-by-step explanation:

Let's call K the event that the student know the answer, G the event that the student guess the answer and C the event that the answer is correct.

So, the probability P(K/C) that a student knows the answer to a question, given that she answered it correctly is:

P(K/C)=P(K∩C)/P(C)

Where P(C) = P(K∩C) + P(G∩C)

Then, the probability P(K∩C) that the student know the answer and it is correct is:

P(K∩C) = 0.7

On the other hand, the probability P(G∩C) that the student guess the answer and it is correct is:

P(G∩C) = 0.3*0.2 = 0.06

Because, 0.3 is the probability that the student guess the answer and 0.2 is the probability that the answer is correct given that the student guess the answer.

Therefore, The probability P(C) that the answer is correct is:

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Finally, P(K/C) is:

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3 years ago