A triangle has side lengths x, 10, and 7. What are the possible values of x?

anzhelika [568]

The last one.

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6 0

3 years ago

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one part

Sergeu [11.5K]

Answer:

The standard deviation increased but there was no change in the interquantile range

Step-by-step explanation:

We are given the following data in the question:

320, 411, 348, 537, 420, 449, 462, 403, 454, 517, 515, 358, 438, 541, 387, 368, 502, 437, 431, 428.

n = 20

a) Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{8726}{20} = 436.3$

Sum of squares of differences =

13525.69 + 640.09 + 7796.89 + 10140.49 + 265.69 + 161.29 + 660.49 + 1108.89 + 313.29 + 6512.49 + 6193.69 + 6130.89 + 2.89 + 10962.09 + 2430.49 + 4664.89 + 4316.49 + 0.49 + 28.09 + 68.89 = 75924.2

$S.D = \sqrt{\frac{75924.2}{19}} = 63.21$

Sorted Data = 320, 348, 358, 368, 387, 403, 411, 420, 428, 431, 437, 438, 449, 454, 462, 502, 515, 517, 537, 541

$IQR = Q_3 - Q_1\\Q_3 = \text{upper median},\\Q_1 = \text{ lower median}$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

$Median = \frac{431 + 437}{2} = 434$

$Q_1 = \frac{387 + 403}{2} = 395\\\\Q_3 = \frac{462 + 502}{2} = 482$

IQR = $482 - 395 = 87$

b) After changing the observation

0, 411, 348, 537, 420, 449, 462, 403, 454, 517, 515, 358, 438, 541, 387, 368, 502, 437, 431, 428

$Mean =\displaystyle\frac{8406}{20} = 420.3$

Sum of squares of differences =

176652.09 + 86.49 + 5227.29 + 13618.89 + 0.09 + 823.69 + 1738.89 + 299.29 + 1135.69 + 9350.89 + 8968.09 + 3881.29 + 313.29 + 14568.49 + 1108.89 + 2735.29 + 6674.89 + 278.89 + 114.49 + 59.29 = 247636.2

$S.D = \sqrt{\frac{247636.2}{19}} = 114.16$

Sorted Data = 0, 348, 358, 368, 387, 403, 411, 420, 428, 431, 437, 438, 449, 454, 462, 502, 515, 517, 537, 541

$Median = \frac{431 + 437}{2} = 434$

$Q_1 = \frac{387 + 403}{2} = 395\\\\Q_3 = \frac{462 + 502}{2} = 482$

IQR = $482 - 395 = 87$

Thus. the standard deviation increased but there was no change in the interquantile range.

5 0

3 years ago

Alexa has finished her culinary training program and is now working full-time as a chef in a hotel resort restaurant. She has tr

otez555 [7]

Answer: The budget of Alexa is increased by $100.

Explanation:

It is given that the current income of Alexa is 3 times of her previous income.

Her previous salary was $800 and current salary was $2400.

Expenses = Rent + Utilities + Groceries + Savings + Bus

The sum of previous expenses is,

Previous expenses = $300 + $60 + $200 + $100 + $30 = $690

The sum of current expenses is,

Current expenses = $300 + $60 + $250 + $150+ $30 = $790

Effect of income on expenses is the difference of current expenses and previous expenses.

Effect of income on expenses = $790 - $690 = $100

Therefore, the budget of Alexa is increased by $100.

3 0

3 years ago

Read 2 more answers

Select all of the following sets of angle measures that would form a triangle. You must chose more than one.

mario62 [17]

Here ... I'll give you all the help you need to answer this question
on your own:

-- The three angles inside any triangle always add up to exactly 180 degrees.

-- Simply examine each group of numbers in the question.
Any set that adds up to 180 can be the three angles of a triangle.
Any set that doesn't, can't.

Go to it !

4 0

3 years ago

15 POINTS!! PLEASE HELP ASAP!!

insens350 [35]

Answer:

Total number of kilometers in the ride = 5 km

Number of kilometers Garret has already biked = k km

Number of kilometers Garret left to ride = 5 - k km

Number of minutes Garret takes per kilometer = 4 minutes.

Step-by-step explanation:

1. It takes 4 minutes for Garret to go a kilometer. Then

Number of minutes Garret takes per kilometer = 4 minutes.

2. Suppose the variable $k$ is the number of kilometers Garret has already biked.

3. Garret is partway through a 20-minute bike ride. It takes 4 minutes for him to go a kilometer. Then

Total number of kilometers in the ride is

$20\div 4=5\ km$

4. Suppose the variable $k$ is the number of kilometers Garret has already biked. Then $5-k$ km is the number of kilometers Garret left to ride.

6 0

3 years ago