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jolli1 [7]
3 years ago
7

(99 POINTS) Using similarity solve for x. Show all work

Mathematics
2 answers:
ki77a [65]3 years ago
4 0

General Idea:

In any right triangle,

1. The altitude to the hypotenuse is the geometric mean between the segments into which is separates the hypotenuse.

2. Each leg is a geometric mean of the hypotenuse and the segment of the hypotenuse adjacent of the leg.

Applying the concept:

Step 1: We need to label the given diagram and set up a proportion by comparing the similar triangles as provided in attached figure.

Setting up the proportion, we get...

\frac{Shorter \; Leg}{Hypotenuse}=\frac{AB}{AC}=\frac{AD}{AB}\\\\\frac{x}{9+16}=\frac{9}{x}\\Cross \; Multiplying \; we \; get...\\\\x^2=9(9+16)\\x^2=9(25)\\x^2=225\\Take \; square \; root \; on \; both \; sides\\\\\sqrt{x^2}=\sqrt{225}\\x=15

Conclusion:

x=15 \; cm


viva [34]3 years ago
3 0

Shorter Length/Hypotenuse = ab/ac = ad/ab

x/9+16 = 9/x

x^2 = 9 x (9 + 16)

= 9 x 25

= 225

square root of 225 = 15

x = 15

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Or a very large set of data the measured mean is found to be 288.6 with a standard deviation of 21.2. assuming the data to be no
SashulF [63]

The 68-95-99.7 rule tells us 68% of the probability is between -1 standard deviation and +1 standard deviation from the mean. So we expect 75% corresponds to slightly more than 1 standard deviation.

Usually the unit normal tables don't report the area between -σ and σ but instead a cumulative probability, the area between -∞ and σ. 75% corresponds to 37.5% in each half so a cumulative probability of 50%+37.5%=87.5%. We look that up in the normal table and get σ=1.15.

So we expect 75% of normally distributed data to fall within μ-1.15σ and μ+1.15σ

That's 288.6 - 1.15(21.2) to 288.6 + 1.15(21.2)

Answer: 264.22 to 312.98


8 0
3 years ago
What is the arithmetic of the following numbers? 4,9,6,3,4,2​
Nezavi [6.7K]

Answer:

4.7

Step-by-step explanation:

Just do 28/6 and the simplify it to 14/3 and divide and get 4.6 repeating round it to 4.7

5 0
3 years ago
Plz help, answer the question below
Afina-wow [57]

\sqrt[6]{x^{16}} =\sqrt[6]{x^{12} \cdot x^{4}}=x^2\sqrt[6]{x^{4}}

5 0
3 years ago
5. Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312.
Mekhanik [1.2K]

Answer:

The actual SAT score is 2024.

The equivalent ACT score is 29.49.

Step-by-step explanation:

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

SAT score that is in the 95th percentile

Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that \mu = 1511, \sigma = 312

95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:

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

1.645 = \frac{X - 1511}{312}

X - 1511 = 1.645*312

X = 2024

The actual SAT score is 2024.

Equivalent ACT score:

The equivalent ACT score is the 95th percentile of ACT scores.

Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that \mu = 21.1, \sigma = 5.1. So

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

1.645 = \frac{X - 21.1}{5.1}

X - 21.1 = 1.645*5.1

X = 29.49

The equivalent ACT score is 29.49.

5 0
2 years ago
15 points! Please answer rigghtt
Scorpion4ik [409]

Answer:

20 hours

Step-by-step explanation:

You do 200 - 30 which gives you 170.

170 divided by 8.50 is 20.

The answer is 20.

If this helped please consider marking it brainliest :3

7 0
2 years ago
Read 2 more answers
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