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3 years ago

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

Mathematics

2 answers:

krek1111 [17]3 years ago

6 0

Answer:

x=28

Step-by-step explanation:

We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.

x 42

---------- = ----------

x+10 42+15

Simplify

x 42

---------- = ----------

x+10 57

Using cross products

57x = 42 (x+10)

Distribute

57x = 42x+420

Subtract 42x from each side

57x-42x = 42x-42x +420

15x = 420

Divide each side by 15

15x/15 = 420/15

x=28

MariettaO [177]3 years ago

5 0

Answer: The value of x is 28 units.

Step-by-step explanation:

Since we have given that

DC ║ PA

So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.

So, it becomes,

$\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28$

Hence, the value of x is 28 units.

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There are blue, red and green pencils in the box—20 pencils total. There are 6 times more green pencils than blue pencils. There

lana [24]

Answer:

You have to take 15 pens to get at least one red pencil.

Step-by-step explanation:

If there were one red and 6 green pens, there would be more red than green pens.

If there were 3 or more blue and thus 18 or more green pens, the number of pens would be over 20.

So there must be 2 blue, 12 green and thus 6 red pencils. So you have to take at least 15 pens to be sure that you got a red one.

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3 years ago

The mean annual income for people in a certain city is 37 thousand dollars, with a standard deviation of 28 thousand dollars. A

Aloiza [94]

Answer:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the annual income of a population, and for this case we know the following info:

$\mu=37$ and $\sigma=28$ and we are omitting the zeros from the thousand to simplify calculations

We select a sample size of n=50>30.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want to find this probability:

$P( 31 < \bar X< 41)$

And we can ue the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using this formula we got for the limits:

$z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515$

$z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01$

So we want to find this probability:

$P(-1.515$

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3 years ago

mote1985 [20]

The answer should be A

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3 years ago

What is the common difference of the arithmetic sequence 5,8,11,14?

allsm [11]

Answer:

Step-by-step explanation:

8-5= 3

11-8= 3

14-11= 3

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3 years ago

Read 2 more answers

How will the graph of y=a* change when the function is transformed to y = 2a* + 9? Please state how the 2

goldenfox [79]

Y = 2y + 9. A = y, 2 means multiply yhe variable y two times, and u just add 9. Btw y = -9

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