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3 years ago

A wooden board is leaning against a house

Mathematics

1 answer:

kobusy [5.1K]3 years ago

6 0

Answer:

24.4 feet

Explanation:

Let x be the length of the wooden board as shown in the diagram.

Using trigonometry ratio, we can write

$\cos(35)=\frac{20}{x}$

$\implies0.819= \frac{20}{x}$

cross multiplying we get:

$0.819 \times x = 20$

Diving through by 0.819, we obtain

$x = 24.42$

To the nearest tenth, x=24.4 feet.

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A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have accepta

VikaD [51]

Answer: Our required probability is 0.167.

Step-by-step explanation:

Since we have given that

n = 15

Probability of success p = 80% = 0.8

Probability of failure q = 20% = 0.2

We need to find the probability that at least fourteen will work.

So, by Binomial distribution, we get that

$P(X\geq 14)=P(X=14)+P(X=15)\\\\P(X\geq 14)=^{15}C_{14}(0.8)^{14}(0.2)+^{15}C_{15}(0.8)^{15}\\\\P(X\geq 14)=0.167$

Hence, our required probability is 0.167.

4 0

3 years ago

1) The variable x represents a value in the set ( 4, 6, 7, 8). Which value of x makes 2 (x-4) +3 =7?

sammy [17]

Answer:

x=6

Step-by-step explanation:

2 (x-4) +3 =7

Subtract 3 from each side

2 (x-4) +3-3 =7-3

2(x-4) =4

Divide each side by 2

2(x-4)/2 = 4/2

x-4 = 2

Add 4 to each side

x-4+4 =2+4

x=6

8 0

3 years ago

A box weighs 90 grams.<br>Write down, in terms of b, the weight of b boxes.

Drupady [299]

Answer:

Let B = the weight of box B

Let 2B = the weight of box A

Let 2B + 30 = the weight of box C

B + 2B + 2B + 30 = 640

5B = 610

B = 122 pounds, weight of box B

2B = 2(122) = 244 pounds, weight of box A

2B + 30 = 2(122) + 30 = 274 pounds, weight of box C

hope this helps

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7 0

3 years ago

Change this fraction into a decimal: 20/25

marissa [1.9K]

.8

20/25 = 4/5 = 80% = .8

3 0

3 years ago

Read 2 more answers

A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviat

Mnenie [13.5K]

Answer:

B. Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

35 gas ovens

A consumer group has determined that the distribution of life spans for gas ovens has a mean of 15.0 years and a standard deviation of 4.2 years. This means that:

$\mu_G = 15, \sigma_G = 4.2, n = 35, s_G = \frac{4.2}{\sqrt{35}} = 0.71$