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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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The subjects of a study by Dugoff et al. (A-5) were 10 obstetrics and gynecology interns at the University of Colorado Health Sc

astra-53 [7]

Answer:

The 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn is (19.1269, 32.6730).

Step-by-step explanation:

Intern No. of Breast

Number Exams Performed X²

1 30 900

2 40 1600

3 8 64

4 20 400

5 26 676

6 35 1225

7 35 1225

8 20 400

9 25 625

10 20 400

 ∑ 259 ∑ 7515

Mean= X`= ∑x/n= 259/10= 25.9

Variance = s²= 1/n-1[∑X²- (∑x)²/n]

= 1/0[7515- (259)²/10]= 1/9[7515- 6708.1]

= 806.9/9=89.655= 89.66

Standard Deviation= √89.655= 9.4687

Hence

The value of t with significance level alpha= 0.05 and 9 degrees of freedom is t(0.025,9)= 2.262

The 95 % Confidence interval is given by

x`±t(∝,n-1) s/√n

So Putting the values

25.9± 2.262( 9.4687/√10)

= 25.9 ±2.262 (2.9943)

= 25.9 ± 6.7730

= 25.9 +6.7730=32.6730

25.9 -6.7730= 19.1269

= 19.1269, 32.6730

The 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn is (19.1269, 32.6730).

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2 years ago

The following chart shows a store?s records of coat sales over two years. 2 circle graphs. A circle graph titled 2006. Top coats

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Answer:

The correct answer is A. 16.5%

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly and to calculate the trend:

2006 2007 Trend

Top Coats 297 223 -24.92%

Parkas 210 210 + 0%

Jackets 213 285 +33.80%

Raincoats 137 259 +89.05

Trench coats 103 127 +23.30%

Total 960 1,104 +15%

2. If the trend shown in these graphs stays constant, what percent of the market will parkas occupy in 2008?

Let's calculate the percent of the market occupied by parkas.

In 2006 = 210/960 = 21.88%

In 2007 = 210/1,104 = 19.02%

In 2008 = 210/1,270 = 16.54% (210 + 0 = 210; 1,104 + 15% = 1,270)

The correct answer is A. 16.5%

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Suppose 1000 people enter a chess tournament. Use a rooted tree model of the tournament to determine how many games must be play

Vlada [557]

Answer: 999 games

Step-by-step explanation:

There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.

We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.

The sum of the figures in the third column is 999.

We could also use the formula for rooted trees to calculate the number of games that would be played.

$i=\frac{l - 1}{m - 1}$

where i is the number of "internal nodes," which represents the number of games played for an "m-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.

The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by

$i=\frac{l - 1}{m - 1} = i=\frac{1000 - 1}{2 - 1} = \frac{999}{1} =999$

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