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2 years ago

SOMEONE PLZZ HELP

Mathematics

1 answer:

saul85 [17]2 years ago

6 0

Square root of 27.

3^(3/2) is the same as square root of 3 cubed, which is 27. so square root of 27.

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A sphere is inscribed in a cube with a volume of 64 cubic inches. What is the volume of the sphere? Round your answer to the nea

erma4kov [3.2K]

Answer:

the volume of the sphere is

$33.51 in^{3}$

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, sphere and cube.

Given data

Volume of cube v = 64 cubic inches

since we are dealing with a cube the height and the radius of the sphere is same as the sides of the cube,

we know that volume of cube is expressed as

$v= l*b*h$

$v=l^{3}$

$64= l^{3}$

$l= \sqrt[3]{64}$

$l= 4 in$

also diameter d=length l

Diameter d= $4in$

Radius r = $\frac{d}{2}$ = $\frac{4}{2}$ = ${2 in}$

Height h= $4in$

we know that the volume of a sphere is given by

$v= \frac{4}{3} \pi r^{3}$

substituting into the formula we have

$v= \frac{4}{3} \ *3.142*2^{3} \\v=\frac{4*3.142*8}3} \\v= \frac{100.54}{3} \\v= 33.52in^{3}$

8 0

2 years ago

Let A and B be events with =PA0.7, =PB0.3, and =PA or B0.9. (a) Compute PA and B. (b) Are A and B mutually exclusive? Explain. (

kvasek [131]

Answer:

a) $P(A \cup B) = P(A) +P(B) - P(A\cap B)$

And if we solve for $P(A \cap B)$ we got:

$P(A \cap B) = P(A) + P(B) -P(A\cup B)= 0.7+0.3-0.9 = 0.1$

b) False

The reason is because we don't satisfy the following relationship:

$P(A\cup B) = P(A) + P(B)$

We have that:

$0.9 \neq 0.3+0.7 =1$

c) False

In order to satisfy independence we need to have the following condition:

$P(A \cap B) = P(A) *P(B)$

And for this case we don't satisfy this relation since:

$0.1 \neq 0.7*0.3 = 0.21$

Step-by-step explanation:

For this case we have the following probabilities given:

$P(A) = 0.7, P(B) =0.7, P(A \cup B) =0.9$

Part a

We want to calculate the following probability: $P(A \cap B)$

And we can use the total probability rule given by:

$P(A \cup B) = P(A) +P(B) - P(A\cap B)$

And if we solve for $P(A \cap B)$ we got:

$P(A \cap B) = P(A) + P(B) -P(A\cup B)= 0.7+0.3-0.9 = 0.1$

Part b

False

The reason is because we don't satisfy the following relationship:

$P(A\cup B) = P(A) + P(B)$

We have that:

$0.9 \neq 0.3+0.7 =1$

Part c

False

In order to satisfy independence we need to have the following condition:

$P(A \cap B) = P(A) *P(B)$

And for this case we don't satisfy this relation since:

$0.1 \neq 0.7*0.3 = 0.21$

4 0

3 years ago

What is the value of a? -2(a-8)+6a=36

Aleksandr [31]

First we expand the brackets:

-2a + 8 + 6a = 36
4a + 8 = 36

We then need to get the a's onto one side and the numbers onto the other:

4a = 28

We can then divide to get an x by itself:

a = 28/4 = 7

6 0

2 years ago

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In the figure below, points J, K, and L are the midpoints of the sides of AXYZ.

Dima020 [189]

Answer:

28 ; 76 ; 38

Step-by-step explanation:

KL = $\frac{XY}{2}$ = $\frac{56}{2}$ = 28 units

YZ = 2 × JK = 38 × 2 = 76 units

LZ = 76/2 = 38 units

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2 years ago

Read 2 more answers

HELP TIMED PLEASE thank you :)

Readme [11.4K]

Answer:

Step-by-step explanation:

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2 years ago