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ElenaW [278]
3 years ago
12

What is the surface area of the cylinder with height 8 in and radius 2 in? Round your answer to the nearest thousandth.

Mathematics
1 answer:
leonid [27]3 years ago
6 0

Answer:

2^2 = 4

4 x 3.14 = 12.56

12.56 x 2 (since there are two circles on the cylinder) = 25.12

Now let's find the circumference of one circle and multiply it by the height to get the round surface area!

2 x 3.14 x 2 = 12.56(circumference)

12.56 x 8(height) = 100.48

Now add both the surface areas!:

25.12 + 100.48 = 125.6 in2 is your answer.

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Tay–Sachs Disease Tay–Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carri
BARSIC [14]

Answer:

a) 0.0156 = 1.56% probability that all children will develop the disease.

b) 0.4219 = 42.19% probability that only one child will develop the disease.

c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The probability that their offspring will develop the disease is approximately .25.

This means that p = 0.25

Three children:

This means that n = 3

Question a:

This is P(X = 3). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156

0.0156 = 1.56% probability that all children will develop the disease.

Question b:

This is P(X = 1). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219

0.4219 = 42.19% probability that only one child will develop the disease.

c. The third child will develop Tay–Sachs disease, given that the first two did not.

Third independent of the first two, so just multiply the probabilities.

First two do not develop, each with 0.75 probability.

Third develops, which 0.25 probability. So

p = 0.75*0.75*0.25 = 0.1406

0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.

6 0
3 years ago
Solve the following equation for 0° ≤ θ < 360°. Use the "^" key on the keyboard to indicate an exponent. For example, sin2x w
Margarita [4]

Answer: 2sin^2x+sin2x+cos2x=0 ..... (1).

By using the trigonometric identities below :

sin2x=2sinxcosx

cos2x=cos^2x-sin^2x

We substitute the trigonometric identities into (1).

2sin^2x+2sinxcosx+cos^2x-sin^2x=0

By combining like terms .

sin^2x+2sinxcosx+cos^2x=0.....(2)

The equation (2) is equivalent to the following expression (3).

(sinx+cosx)(sinx+cosx)=0 .....(3).

sinx+cosx=0

cosx=-sinx

divide both sides by cosx

1=-sinx/cosx

-1=sinx/cosx

sinx/cosx=tanx

substitute

-1=tanx

tanx=-1

tangent is negative in 2nd and 4th quadrants

tan135º=-1 (one answer)

tan315º=-1 (second answer)

Step-by-step explanation:

Please refer to the trigonometric identities used and explained above .

5 0
3 years ago
Solve system of equation using elimination by addition.<br><br> Will give brainliest!!
DedPeter [7]

Answer:

x = 2, y = -3

Step-by-step explanation:

Add the 2 equations together, then solve for x.

(2x + 2y) + (3x - 2y) = (-2) + (12)\\ 2x + 3x + 2y - 2y = -2 + 12\\5x = 10\\x = 2

Now that we know the value of x, we can easily find y by substitution.

3x - 2y = 12\\3(2) - 2y = 12\\6 - 2y = 12\\-2y = 6\\y = -3

These are the answers

- Kan Academy Advance

5 0
2 years ago
The lengths of the
Dmitrij [34]

Answer:

S_{\Delta ABC} = 4·S_{\Delta EDC}

Step-by-step explanation:

From the midpoint theorem, which states that the line that a line drawn such that it joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and is equal to half the length of the third side

Therefore, the lengths of the sides of ΔDEF, drawn by joining the midpoints of ΔABC is equal to half the length of and parallel to the corresponding side of ΔABC

We therefore, have that the corresponding sides of ΔABC and ΔDEF have a common ratio and a pair of sides in each triangle form same angles, therefore;

ΔDEF is similar to ΔABC by Side, Side, Side SSS similarity.

The length of the perimeter of ΔABC, S_{\Delta ABC} = 2 × The length of the perimeter of triangle ΔEDC, S_{\Delta EDC}

S_{\Delta ABC} = 2 ×  S_{\Delta EDC}

∴  S_{\Delta ABC}  ≠ 4 ×  S_{\Delta EDC}

The statement which is incorrect is therefore;

S_{\Delta ABC}  = 4 ×  S_{\Delta EDC}.

4 0
3 years ago
Write the number with 5 hundreds and 2 thousands
mina [271]

Answer:

500 2000

Step-by-step explanation:


6 0
3 years ago
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