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3 years ago

52. A 33-tt ladder leans against a building so that the angle between the ground and the ladder is 80". How high does the

Mathematics

1 answer:

Ulleksa [173]3 years ago

3 0

9514 1404 393

Answer:

32.5 ft

Step-by-step explanation:

The length of the side opposite the given angle is found using the sine relation:

Sin = Opposite/Hypotenuse

height on building = (33 ft)·sin(80°) ≈ 32.5 ft

The ladder reaches about 32.5 feet up the side of the building.

_____

Additional comment

The maximum angle compliant with OSHA safety rules is 75.5°.

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A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight ident

Fudgin [204]

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, 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.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that $p = 0.9$

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when $n = 4$ . So

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

$P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486$

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that $n = 8$

It will operate if at least 4 components are working correctly, so we want:

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0$

$P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex][tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0$

$P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004$

Then

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996$

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

5 0

3 years ago

Please answer the 2 questions

hammer [34]

the correlation between the days and weight is that when the number of days goes up, the weight goes up too.

The puppy gained about 2.5 pounds during this time.

6 0

3 years ago

Please help me with this one to as soon as possible!

Naily [24]

Answer: A

Step-by-step explanation: Alright so- it says that Justin is both in half of his friends photos (which would be 15 photos) and half of his family's photos (6 photos). The total amount of photos period is 50 photos and 15 is greater than 6. Therefore I would say A.

8 0

3 years ago

Substitutions y=x+4 y=3x+0

cluponka [151]

Answer:

x = 2

Step-by-step explanation:

since both equal y, you can set them equal to each other

x + 4 = 3x + 0

subtract x on both sides

4 = 2x

divide by 2 on both sides

2 = x

♡♡ hope this helped ♡♡

4 0

3 years ago

Read 2 more answers

9/11 - 1/2 in it's simplest form

Murrr4er [49]

Answer:

7/22

Step-by-step explanation:

Step 1: Define/explain.

To subtract fractions with different denominators, you must first find the least common denominator (LCM).

You can do this by listing the multiples of each denominator.

Step 2: Solve.

11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

22 is the LCM.

Now, we change the fractions to where they both have denominators of 22.

**REMEMBER: WHICHEVER NUMBER YOU MULTIPLY THE DENOMINATOR BY, YOU MULTIPLY IT BY THE NUMERATOR AS WELL!!**

$9/11*2/2=18/22$

$1/2*11/11=11/22$

Now, subtract as normal.

$18/22-11/22=7/22$

$7/22 (simplified).$

Step 3: Conclude.

Therefore, 9/11 - 1/2 = 7/22.

5 0

3 years ago