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2 years ago

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If AB=9, the diagram blank the case of a degenerate triangle because blank. The case of a degenerate triangle justifies the use

of blank inequality symbols in the triangle inequality theorem

1 answer:

sesenic [268]2 years ago

4 0

Answer:

Step-by-step explanation:

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Fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play. Which statements are correct? Check all

Lapatulllka [165]

Answer:

(a) Yes, Fredrick’s data set contains an outlier.

(b) No, the median value is not 12 home runs.

(c) Yes, the mean value is about 12.6 home runs.

(d) Yes, the median describes Fredrick’s data more accurately than the mean.

(e) No, the mean value doesn't stay the same when the outlier is not included in the data set.

Step-by-step explanation:

We are given that Fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play.

Firstly, arranging our data set in ascending order we get;

1, 12, 12, 12, 13, 13, 14, 15, 16, 18.

(a) The statement that Fredrick’s data set contains an outlier is true because in our data set there is one value that stands out from the rest of the data, which is 1.

Hence, the outlier value in the data set is 1.

(b) For calculating median, we have to first observe that the number of observations (n) in the data set is even or odd, i.e;

If n is odd, then the formula for calculating median is given by;

Median = $(\frac{n+1}{2})^{th} \text{ obs.}$

If n is odd, then the formula for calculating median is given by;

Median = $\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}$

Here, the number of observations in Fredrick's data set is even, i.e. n = 10.

SO, Median = $\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}$

= $\frac{(\frac{10}{2})^{th} \text{ obs.}+(\frac{10}{2}+1)^{th} \text{ obs.} }{2}$

= $\frac{(5)^{th} \text{ obs.}+(6)^{th} \text{ obs.} }{2}$

= $\frac{13+13 }{2}$ = 13 home runs

So, the statement that the median value is 12 home runs is not correct.

(c) The mean of the data set is given by;

Mean = $\frac{1+ 12+ 12+ 12+ 13+ 13+14+ 15+ 16+ 18}{10}$

= $\frac{126}{10}$ = 12.6 home runs

So, the statement that the mean value is about 12.6 home runs is correct.

(d) The statement that the median describes Fredrick’s data more accurately than the mean is correct because even if the outlier is removed from the data set, the median value will remain unchanged but the mean value gets changed.

(e) After removing the outlier, the data set is;

12, 12, 12, 13, 13, 14, 15, 16, 18.

Now, the mean of the data = $\frac{12+12+ 12+ 13+ 13+ 14+ 15+ 16+ 18}{9}$

= $\frac{125}{9}$ = 13.89

So, the statement that the mean value stays the same when the outlier is not included in the data set is incorrect.

3 0

2 years ago

Read 2 more answers

What is the r-value of the following data to three decimal places?

ValentinkaMS [17]

Answer:

Option B

Step-by-step explanation:

Given that two variables in table as

Total Average

x 2 6 7 8 12 35 7

y 15 13 9 8 5 50 10

xy 30 78 63 64 60 295 59

(x-7)^2 25 1 0 1 25 52 10.4

(y-10)^2 25 9 1 4 25 64 12.8

Var x = 10.4 and std dev x = 3.225

Var Y = 12.8 and std dev Y = 3.578

Cov (xy) = E(xy)-E(x) E(Y)=59-70=-11

Correlation coefficient r

= Cov /sx sy = -11/(3.225)(3.578)=-0.9532

Round off to get

r=-0.953

Henceoption B is right.

7 0

2 years ago

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The Anza-Borrego Desert State Park is one of the best places in the United States for viewing stars. During one 50-day period, c

likoan [24]

Answer:

22

Step-by-step explanation:

I would assume that the 6% rate would carry for the rest of the year, i.e. all 365 days, 6% of those have clouds interfering with stargazing

365 * 6% = 365 * 0.06 = 21.9, and round up to 22 because you can't really have .9 of a day here.

4 0

2 years ago

Find the difference: square root of 20 - square root of 80

Mamont248 [21]

Answer:

$-2\sqrt{5}$

Step-by-step explanation:

$\sqrt{20} = \sqrt{10*2} = \sqrt{5 * 2 *2} = \sqrt{2^2 * 5} = 2\sqrt{5} \\\\\sqrt{80} = \sqrt{20*4} = \sqrt{5*4 *4} = \sqrt{4^2 * 5} = 4\sqrt{5} \\\\2\sqrt{5} - 4\sqrt{5} = -2\sqrt{5}$

8 0

2 years ago

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Which statement is true about the discontinuities of the function f(x)?

Tema [17]

Answer:

There are asymptotes at x = three-halves and x = negative one-third.

Step-by-step explanation:

f(x) = (x + 1)/ (6x^2 - 7x - 3)

= (x + 1)( / (6x^2 + 2x - 9x - 3)

= (x + 1) / (2x(3x + 1) - 3(3x + 1))

= (x + 1) / (2x - 3)(3x + 1)

Now x = 3/2 and x = -1/3 both make te denominator zero so these are both asymptotes.

6 0

2 years ago

Read 2 more answers