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2 years ago

Which of the following statements must be true about this diagram? Check all that apply.

Mathematics

1 answer:

pishuonlain [190]2 years ago

8 0

Answer:

Options (D), (E) and (F) are the correct options.

Step-by-step explanation:

From the figure attached,

1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.

Therefore, by the property of exterior angle,

∠4 = ∠1 + ∠2

2). Since ∠4 = ∠1 + ∠2,

Therefore, ∠4 will be greater than ∠1

Similarly, ∠4 will be greater than ∠2

Therefore, Options (D), (E) and (F) are the correct options.

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A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without

sveticcg [70]

Question:

For the following exercise, determine the range (possible values) of the random variable. A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.

Answer:

Possible values are all integers from 1 to 491.

{1,2,...........491}

Step-by-step explanation:

Given:

Total number of machined parts = 500

Number that do not conform to customers requirements = 10

Number that conforms to customers requirements = 500 - 10 = 490

Since, parts are selected successively, without replacement, until a nonconforming part is obtained, the range of the random variable (number of parts selected) here will be all integers from 1 to 491 ie {1,2,...........,491}.

Here, we have a total of 490 conforming parts, and 10 non conforming parts, there must be a non-conforming part among 491 selections, considering the fact that total number of parts are 500

7 0

2 years ago

There are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. So far, 170 tickets have been

slamgirl [31]

There are 400 balcony seats in the concert hall.

Step-by-step explanation:

Step 1 :

The number of lower seats = 450 seats

Total seats = Lower seats + balcony seats

Step 2 :

Tickets sold = 170 tickets
Total tickets = x

Tickets sold = 1/5 of total tickets.

⇒ 170 = (1/5)x

⇒ x = 5 $\times$ 170

⇒ x = 850 tickets

∴ Total seats in the concert hall is 850.

Step 3 :

Total seats = 450 + balcony seats

850 - 450 = balcony seats

∴ balcony seats = 400

7 0

2 years ago

g An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the

blagie [28]

Answer:

A 90% confidence interval of the true mean is [$119.86, $123.34].

Step-by-step explanation:

We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.

Also, the standard deviation of the population was $6.36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean amount of money spent on textbooks = $121.60

$\sigma$ = population standard deviation = $6.36

n = sample of students = 36

$\mu$ = population mean

Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $121.60-1.645 \times {\frac{6.36}{\sqrt{36} } }$ , $121.60+1.645 \times {\frac{6.36}{\sqrt{36} } }$ ]

= [$119.86, $123.34]

Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].

5 0

2 years ago

In a survey of 15000 students of different schools, 40% of them were found to have tuition before the see examination. Among the

USPshnik [31]

Answer: 600 students.

Step-by-step explanation:

Ok, we start with 15,000 students.

40% of them had tuition, so the actual number of them that had tuition is:

15,000*0.40 = 6,000.

Now we want to find the number of students that studied math and science.

50% only studied math,

30% only studied science

10% studied other subjects.

So 50% + 30% + 10% did NOT studied both math and science

90% is the percentage that did not study math and mathematics as well as science, then the other 10% did.

Then, out of the 6,000 students that had tuition, 10% studied math and science, the total number is:

6,000*0.10 = 600

4 0

2 years ago

Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn

barxatty [35]

Gwen has already burned 100 calories when Tristan and Keith started, and he continues to burn 10 calories per minute. The equation for Gwen is

y = 100 + 10x

Question 2)

`Tristan is burning 125 calories every 10 minutes. His burning calories rate is 12.5 calories per minute. The equation for Tristan is

y = 12.5x

Question 3)

Keith is burning 300 calories in 30 minutes. His rate per minute is 10 calories per minute. The equation for Keith is

y = 10x

8 0

1 year ago