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2 years ago

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A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. Using the 45°

-45°-90° triangle theorem, find the value of h, the height of the wall. 6.5 ft ft 13 ft ft

2 answers:

Radda [10]2 years ago

8 0

A wall is in the shape of a trapezoid and it can be divided into a rectangle and a triangle. A triangle is with angles 45°- 45° - 90°. The hypotenuse of that triangle is 13√2 ft.Using the 45° - 45° - 90° theorem, sides of that triangle are in the proportion:x : x : x√2, and since that x√2 = 13√2 ( hypotenuse ), x = 13.Therefore h = 13 ft.We can check it: c² = 13² + 13²,c² = 169 + 169c² = 338c = √ 338 = 13√2Answer: h = 13 ft

zmey [24]2 years ago

7 0

Answer:

13 ft

Step-by-step explanation:

You might be interested in

1.How much taller Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall. 2.How many times as tall

EleoNora [17]

Answer:

Porter is $n-m$ inches taller than Henry.

Porter is $\frac{n}{m}$ times taller than henry.

Step-by-step explanation:

The difference in height can be found using subtraction.

Since Porter is taller than Henry, we'll subtract away Henry's height from Porter's height. This will leave us with only the difference between the heights.

n = Porter's height

m = Henry's height

Difference in height is thus:

$n-m$

Answer: Porter is $n-m$ inches taller than Henry.

To find out how many times taller Porter is than Henry, we can use division.

An example: if Porter was 200cm, and Henry was 100cm, Porter is obviously 2 times as tall.

If we divide Porter's height by Henry's height...

$\frac{200}{100}=2$

..we'll get 2. This is because Henry's height "fits in twice" in Porter's height. 100 fits twice in 200.

Using our values, n and m, we'll divide n by m.

$\frac{n}{m}$

Answer: Porter is $\frac{n}{m}$ times taller than henry.

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2 years ago

A hospital finds that 22% of its accounts are at least 1 month in arrears. A random sample of 425 accounts was taken. What is th

GenaCL600 [577]

Answer:

8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears

Step-by-step explanation:

For each account, there are only two possible outcomes. Either they are at least 1 month in arrears, or they are not. The probability of an account being at least 1 month in arrears is independent from other accounts. So the binomial probability distribution is used to solve this question.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.22, n = 425$

So

$\mu = E(X) = np = 425*0.22 = 93.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{425*0.22*0.78} = 8.54$

What is the probability that fewer than 82 accounts in the sample were at least 1 month in arrears

This probability is the pvalue of Z when X = 82. So

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

$Z = \frac{82 - 93.5}{8.54}$

$Z = -1.35$

$Z = -1.35$ has a pvalue of 0.0885.

8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears

8 0

1 year ago

Kristin is swimming in the ocean and notices a coral reef below her. The angle of depression is 35∘ and the depth of the ocean,

LenaWriter [7]

Answer:

Distance: 435.9 ft

Step-by-step explanation:

This is a right triangle shown in the picture.

To solve for $x$ , we can use trigonometry.

The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is $x$ (what we are seeking to find).

The ratio that relates opposite and hypotenuse is sine.

<em>We know that,</em>

$sin(angle)=\frac{opposite}{hypotenuse}$

<em>Thus we can write:</em>

$sin(35)=\frac{250}{x}$

<em>Cross multiplying and solving for $x$ gives us:</em>

$sin(35)=\frac{250}{x}\\x=\frac{250}{sin(35)}\\x=435.9$

Second answer choice is right: 435.9 ft

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1 year ago

Given log Subscript 4 Baseline 3 almost-equals 0.792 and log Subscript 4 Baseline 21 almost-equals 2.196, what is log Subscript

defon

Answer:

Step-by-step explanation:

The following is the logarithm quotient rule:

$log_{c}{a / b} = log_{c}{a} - log_{c}{b}$

Plugging in the values we have above gives us the following:

$log_{4}{21 / 3} = log_{4}{21} - log_{4}{3}$

$log_{4}{7} = 2.196 - 0.792$

$log_{4}{7} = 1.404$

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1 year ago

Read 2 more answers

Ivan used coordinate geometry to prove that quadrilateral EFGH is a square.

Thepotemich [5.8K]

Answer:

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Step-by-step explanation:

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1 year ago