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2 years ago

2 lines intersect. A line with points R, S, U intersects a line with points V, S, T at point S.

Mathematics

1 answer:

Dima020 [189]2 years ago

7 0

Step-by-step explanation:

here is your answer

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What is the exact volume of the cone? Radius is 9cm and the height is 6cm.

masha68 [24]

Answer:

The volume of the cone is 508.94

8 0

4 years ago

The cereal box shown below is a rectangular prism.

joja [24]

Answer:

Surface area is found:

Surface Area = 1700 cm²

Step-by-step explanation:

(The cereal box is shown in the ATTACHMENT)

The surface area of a rectangular prism can be found by added the areas of all 6 sides of the rectangular prism.

L = length = 20 cm

H = height = 30 cm

W = Width = 5 cm

Side 1:

A(1) = L×H

A(1) = 20×30

A(1) = 600 cm²

Side 2:

As the measurements of the side at the back of side 1 has the same measurement of side 1. then:

A(2) = 600 cm²

Side 3:

A(3) = L×W

A(3) = 20×5

A(3) = 100 cm²

Side 4:

As the measurements of the side at the back of side 4 has the same measurement of side 4. then:

A(4) = 100 cm²

Side 5:

A(5) = H×W

A(5) = 30×5

A(5) = 150 cm²

Side 6:

As the measurements of the side at the back of side 5 has the same measurement of side 5. then:

A(6) = 150 cm²

Surface Area:

Adding areas of all the sides

A(1) + A(2) + A(3) +A(4) + A(5) + A(6) = 600 + 600 + 100 +100 + 150 +150

Surface Area = 1700 cm²

3 0

3 years ago

In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$