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yaroslaw [1]
3 years ago
15

What is the volume of the triangular prism shown below?

Mathematics
1 answer:
liberstina [14]3 years ago
8 0

Answer:

B

Step-by-step explanation:

The volume (V) of the triangular prism is calculated as

V = area of triangular face × length

Area of triangle = \frac{1}{2} bh ( b is the base and h the height )

Here b = 6 and h = 8, thus

Area = \frac{1}{2} × 6 × 8 = 3 × 8 = 24 units², thus

V = 24 × 20 = 480 units³ → B

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A circle has been split into 8 sectors each of which can be colored as 4 different colors, and no consecutive sectors are colore
Eva8 [605]

Answer:

5832 ways

Step-by-step explanation:

Since the circle has 8 sectors and there is 4 colour,

Assuming the sectors are numbered 1 to 8,

Sector 1 : can be coloured with any of the 4 colour in 4 ways

Sector 2 can be coloured with any of the remaining 3 colours in 3 ways

Sector 3 in 3 ways without using the colour in sector 2

Sector 4 in 3 ways without using the colour in sector 3

Sector 5 in 3 ways without using the colour in sector 4

Sector 6 in 3 ways without using the colour in sector 5

Sector 7 in 3 ways without using the colour in sector 6

Sector 8 in 2 ways without using the colours in sector 1 and 7

Number of ways of colouring = 4*3*3*3*3*3*3*2 = 5832 ways

3 0
3 years ago
Which expression is NOT equivalent to 12 * −3 2/3? Drag this expression to the box. select all that apply
Evgen [1.6K]

Answer:

Step-by-step explanation:

6

4 0
4 years ago
Read 2 more answers
A basketball team starts 5 of its 12 available players at random every week. What is the probability that for two consecutive we
tatiyna

Answer:

There is a 58% chance. I think.

Step-by-step explanation:

You add 7 and 7 together to get your numerator (14). Then you add 12 and 12 together to get 24 which is your denominator. Next you divide 14/24 to get .58333333. Finally you move the decimal 2 places to the right to get your percentage.

3 0
3 years ago
A referee moves along a straight path on the side of an athletic field. The velocity of the referee is given by v(t) = 4(1-6)cos
stepan [7]

Answer:

(A). 3.93

Step-by-step explanation:

You need to find the following integral

{\displaystyle  \int\limits_{2}^{6} 4(t-6)\cos(2t+5) \, dt } = 3.93

Therefore the answer is (A). 3.93

6 0
4 years ago
Let
Digiron [165]

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

5 0
3 years ago
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