All categories

2 years ago

Find the value of X in the diagram below.

Mathematics

1 answer:

Maru [420]2 years ago

4 0

Answer:

The answer to your question is x = 2

Step-by-step explanation:

Process

1.- Use proportions to solve this problem

$\frac{4x + 2}{23} = \frac{2x + 16}{23 + 23}$

2.- Solve for x

46(4x + 2) = 23(2x + 16)

Expand

184x + 92 = 46x + 368

Simplify

184x - 46x = 368 - 92

138x = 276

x = 276/138

Result

x = 2

You might be interested in

When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic

andriy [413]

Answer:

<em>Statistical inference</em>

Step-by-step explanation:

The confidence interval is used to give a range of values for a target population while applying the law of probability. Inferential statistics makes use of data obtained from a given population to predict and make a conclusion on a study.

Statistical inference is the process of applying the tools for inferential statistics to analyze data gotten from a given fraction of the population. This process is based on probability and random sampling.

<em>When a confidence interval is used to conclude a population study, it is certainly based on probability. Therefore the correct option is statistical inference. </em>

3 0

2 years ago

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Sati [7]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

Step-by-step explanation:

When the distribution is normal, we use 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.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

$\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

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

$Z = \frac{135 - 128}{23}$

$Z = 0.3$

$Z = 0.3$ has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

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

$Z = \frac{141 - 128}{23}$

$Z = 0.565$

$Z = 0.565$ has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

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

$Z = \frac{125 - 128}{23}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483

X = 120

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

$Z = \frac{120 - 128}{23}$

$Z = -0.35$

$Z = -0.35$ has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

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

$1.28 = \frac{X - 128}{23}$

$X - 128 = 1.28*23$

$X = 157.44$

157.44mmHg

6 0

2 years ago

If the median of the score distribution on this pop quiz is more than 170, the teacher will drop the next pop quiz. The pop quiz

MAVERICK [17]

The median of a set of data is obtained by arranging the data from lowest to highest. In this pop quiz scores, the arrangements is as follows:

110, 125, 138, 144, 152, 153, 162, 163, 164, 174, 174, 175, 177, 180, 183, 185, 186, 187, 194, 195, 196, 198.

There are 22 items in the list and the median is located in the middle position. In this case, it is the average of 174 (11th) and 175 (12th). Thus, the median is 174.5.

4 0

2 years ago

Read 2 more answers

Find the area of the shaded sector. Leave your answer in terms of π.

bearhunter [10]

Answer:

d=10m

r=10/2=5m

The Area is:

(πr^{2}) /2

(π5^2) / 2

=25π/2

=12.5π

8 0

1 year ago

Read 2 more answers

The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0). The focus of the reflector

sattari [20]

Answer:

1.26 feets

Step-by-step explanation:

Given the following :

Vertex (0, 0)

Focus of reflector = 6 feets

Extension = 5.5 feets

Equation to obtain conic section of a parabola:

(x - h)² = 4p(y - k)

Vertex (0, 0)

h =0 ; k = 0, p = 6, x = 5.5

(5.5 - 0)² = 4*6(y - 0)

30.25 - 0 = 24(y - 0)

30.25 = 24y

y = 30.25 / 24

y = 1.26

Hence, depth of reflector = 1.26 feets

5 0

2 years ago