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777dan777 [17]
2 years ago
15

Let

Mathematics
1 answer:
Digiron [165]2 years ago
5 0

What I gather from the question is that X has second moment E(X^2)=81 and variance V(X) = 58, and you're asked to find the expectation and variance of the random variable Y=2X+10.

From the given second moment and variance, we find the expectation of X :

V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}

Expectation is linear, so

E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}

Using the same variance identity, we have

V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2

and

E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}

so that

V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}

Alternatively, we can use the identity

V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232

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A regulation basketball has a diameter of about 9 in. What is the best approximation for the volume of this ball? 3050 in³ 382 i
Mandarinka [93]

The best apporximation for the volume of this ball is 382 cubic inches.

<h3>What is the volume of the ball?</h3>

The volume of the ball is calculated by the formula V = 4 / 3πr³. This formula is the same in the whole world.

Given

A regulation basketball has a diameter of about 9 in.

The radius of the ball is;

\rm Radius = \dfrac{Diameter}{2}\\\\Radius=\dfrac{9}{2}\\\\Radius=4.5\ inches

The volume of the ball is;

\rm Volume =\dfrac{4}{3}\pi r^3\\\\Volume=\dfrac{4}{3} \times 3.14 \times 4.5^3\\\\Volume =\dfrac{144.53}{3}\\\\Volume = 381.51\\\\Volume = 382 \ In^3 \ apporx

Hence, the best apporximation for the volume of this ball is 382 cubic inches.

To know more about volume click the link given below.

brainly.com/question/10647788

4 0
2 years ago
What is 3.2 × 10−4 m/h in centimeters per second? A. 8.889 × 10−6 cm/s B. 8.889 × 10−5 cm/s C. 1.152 × 10−5 cm/s D. 1.152 × 10−7
atroni [7]
3.2 x 10^{-4} x  \frac{100}{3600} = 8.888 x  10^{-6}

therefore ur answer is OPTION A 8.889 x 10-6 cm/s
4 0
2 years ago
I will give brainliest
ruslelena [56]

Answer:

w is the length

Step-by-step explanation:

length squared is always the area of a square

8 0
3 years ago
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Find the value of the variable if P is between J &amp; K. A) JP = 8z - 17 B) PK = 5z + 37 C) JK = 17z - 4
Daniel [21]
<span>We cannot deduce about the exact location of P between J and K. But we can conclude: segment JP + segment PK = line JK.
</span><span>JP + PK = JK.
</span><span>Substitute first each.
(8z - 17) + (5z + 37) = 17z - 4
Combine like terms.
13z + 20 = 17z - 4
Isolate the variable z.
4z = 24
z = 6
The value of the variable z is then 6 units.</span>
3 0
3 years ago
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it is 3,452 miles round trip to craig's aunt's house.if he travels to her house 3 times this year, how many miles did he travel
sveta [45]
(3,452 * 2) = round trip = 6,904.

6,904 * 3 = total distance = 20,712.

Therefore, the final answer is 20,712 miles.
8 0
3 years ago
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