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3 years ago

What is the value of x? Enter your answer in the box.

Mathematics

2 answers:

nignag [31]3 years ago

7 0

Answer:

Step-by-step explanation:

The whole triangle and the small triangle are similar. Therefore the sides are in proportion.

We have the equation:

$\dfrac{(2x+10)+3}{40+5}=\dfrac{3}{5}\\\\\dfrac{2x+13}{45}=\dfrac{3}{5}\qquad\text{cross multiply}\\\\5(2x+13)=(45)(3)\qquad\text{divide both sides by 5}\\\\2x+13=(9)(3)\\\\2x+13=27\qquad\text{subtract 13 from both sides}\\\\2x=14\qquad\text{divide both sides by 2}\\\\\boxed{x=7}$

olchik [2.2K]3 years ago

4 0

Answer:

The value of x is 7

Step-by-step explanation:

In order to find this, we must create a proportion using the smaller triangle (right/left) and then the whole triangle (right/left)

5/3 = 45/2x+13

Now cross multiply to solve

5(2x + 13) = 45*3

10x + 65 = 135

10x =- 70

x = 7

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Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118. If a recent test-taker

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Answer:

Probability that the student scored between 455 and 573 on the exam is 0.38292.

Step-by-step explanation:

We are given that Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118.

<u><em>Let X = Math scores on the SAT exam</em></u>

So, X ~ Normal( $\mu=514,\sigma^{2} =118^{2}$ )

The z score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean score = 514

$\sigma$ = standard deviation = 118

Now, the probability that the student scored between 455 and 573 on the exam is given by = P(455 < X < 573)

P(455 < X < 573) = P(X < 573) - P(X $\leq$ 455)

P(X < 573) = P( $\frac{X-\mu}{\sigma}$ < $\frac{573-514}{118}$ ) = P(Z < 0.50) = 0.69146

P(X $\leq$ 2.9) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{455-514}{118}$ ) = P(Z $\leq$ -0.50) = 1 - P(Z < 0.50)

= 1 - 0.69146 = 0.30854

<em>The above probability is calculated by looking at the value of x = 0.50 in the z table which has an area of 0.69146.</em>

Therefore, P(455 < X < 573) = 0.69146 - 0.30854 = <u>0.38292</u>

Hence, probability that the student scored between 455 and 573 on the exam is 0.38292.

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