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1 year ago

If PQ=RS, which of the following must be true?

Mathematics

1 answer:

maw [93]1 year ago

4 0

Answer:

If PQ=RS then PQ and RS have the same length. Hence option D is correct

Solution:

Given that, pq = rs

And, we have to find which of the given options are true.

a) pq and rs form a straight angle

We can’t decide the angle in between pq and rs just by the statement pq = rs.

So this statement is false.

b) pq and rs form a zero angle.

We can’t decide the angle in between pq and rs just by the statement pq = rs.

So this statement is false.

c) pq and rs are same segment. 

If two things equal then there is no condition that both represents a single item.

So this statement is false.

d) pq and rs have the same length

As given that pq = rs, we can say that they will have the same length

Hence, option d is true.

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What is the sum of the distinct prime factors of 315

Nuetrik [128]

Answer: The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 315 has exactly 12 factors.

Step-by-step explanation: First, the exponents in the prime factorization are 2, 1, and 1. Then adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Finally, 315 has exactly 12 factors.

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1 year ago

An inspector checks 98 cell phones and finds that 2 of them are defective. A company has 850 of these phones. How many of the co

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Answer:

Step-by-step explanation:

As 2 phones are defective from a group of 98 that were checked, you can determine a percentage:

2/98= 2%

This indicates that 2% of the phones are likely to be defective and because of that you can find 2% of 850:

850*2%= 17

According to this, 17 phones are likely to be defective.

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2 years ago

Imagine you have a data set with 9,987 names. The data set is sorted alphabetically. You want to find out if the name "David Joy

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Answer:

Step-by-step explanation:

David Joyner might be the first name, so you may only have to check 1 name.

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1 year ago

A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

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1 year ago

Nancy used 14 yards of fabric to make flags for one third of the drill team. How much fabric would Nancy need to make flags for

Kipish [7]

If all the flags use material at the same rate, Nancy will need 3 times the fabric to make 3 times the number of flags. Nancy needs 3×(14 yd) = 42 yd for the whole team.

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1 year ago

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