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2 years ago

A triangle has two sides of length 2 and 18. What is the largest possible whole-number length for the third side?

Mathematics

1 answer:

Snezhnost [94]2 years ago

6 0

Answer:

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is

difference of 2 sides < x < sum of 2 sides , that is

18 - 2 < x < 18 + 2

16 < x < 20

Then the largest possible length of the third side is 19

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The personnel files of all eight employees at the Pawnee location of Acme Carpet Cleaners Inc. revealed that during the last six

irina [24]

Answer:

a) For Pawnee:

Range = 11, Mean = 3.13, Mean deviation = 2.44

For Chickpee:

Range = 7, Mean = 4.25, Mean deviation = 1.59

b) Pawnee Location has fewer lost days.

c) variation of the Chickpee is less than Pawnee location

Step-by-step explanation:

Data given:

For Pawnee:

3 1 0 0 2 11 5 3

Max = 11

Min = 0

Range = Max - Min

Range = 11-0 = 11

Range = 11

For Chickpee:

3 6 8 4 4 5 3 1

Max = 8

Min = 1

Range = Max - Min

Range = 8 - 1

Range = 7

For mean of Pawnee:

Mean = (3 + 1 + 0 + 0 + 2 + 11 + 5 + 3)/8

Mean = 25/8

Mean = 3.125

For mean deviation, we find the difference from the mean of each point.

Note: all the negative values will be taken as 0.

Differences from the mean of each point =

(3-3.13)=0.13, (1-3.31) = 2.13 ,

(0-3.13)=0, (0-3.13)=3.13,

(2-3.13)=1.13, (11-3.13)=7.87,

(5-3.13)=1.87, (3-3.13)=0.13

So, our differences are:

(0.13, 2.13, 0, 3.13, 1.13, 7.87, 1.87, 0.13 )

Mean deviation = Sum of all differences/8

Mean deviation = (0.13+2.13+3.13+3.13+ 1.13+ 7.87+ 1.87+ 0.13)/8

Mean deviation = 2.44

For mean of Chickpee:

Mean = (3+6+8+4+4+5+3+1)/8

Mean = 34/8

Mean = 4.25

Similarly, we need to find mean deviation for Chickpee, for that we need to find the differences first as done above for Pawnee.

Note: all the negative values will be taken as 0

Differences from the mean:

(3-4.25) = 1.25, (6-4.25) =1.75,

(8-4.25) = 3.75, (4-4.25)=0.25,

(4-4.25)=0.25, (5-4.25)= 0.75,

(3-4.25)=1.25, (1-4.25) =3.25

So, the differences are:

Differences = (1.25,1.75,3.75,0.25,0.25,0.75,1.25,3.25)

Mean deviation = (1.25+ 1.75+ 3.75+ 0.25+ 0.25+ 0.75+ 1.25+ 3.25)/8

Mean deviation = 1.59

b) which location has fewer lost days:

This can be found out by the total number of days of Pawnee and chickpee.

Pawnee = Sum of values = (3 + 1 + 0 + 0 + 2 + 11 + 5 + 3) = 25 days

Chickpee = Sum of values = (3+6+8+4+4+5+3+1) = 34 days

Hence, Pawnee Location has fewer lost days.

C) which location has less variation?

Formula for variation = ∑( $\frac{x^{2} }{8}$ ) - ( $mean^{2}$ )

where x = values of the set.

For Pawnee:

$mean^{2}$ = $3.13^{2}$ = 9.8

Sum of square of all the data points of Pawnee = 169

Variation = 169/8 - 98 = 11.325

Similarly,

For Chickpee:

$mean^{2}$ = $4.25^{2}$ = 18.06

Sum of square of all the data points of Chickpee = 176

Variation = 176/8 - 18.06

Variation = 22-18.06

Variation = 4

Hence, variation of the Chickpee is less than Pawnee location

8 0

3 years ago

Joan’s washing machine tub is a cylinder with a height of 17 in. and a diameter of 22 in. Her washer was half full of water when

xxMikexx [17]

Find the volume of the cylinder and divide by 2:

V = pi * r^2 * h

V = 3.14 * 11^2 * 17

V = 6458.98

Divide by 2 since it's half full:

6458.98 / 2 = 3229.49

Now divide it by 46.2 to see how long it will take to drain out:

3229.49 / 46.2 = 69.902

So it will take approximately 70 seconds to drain out.

4 0

3 years ago

PLZ HELP ME ☻ <img src="https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bxy%7D%7Bx%20%2B%20y%7D%20%3D%201%2C%20%5Cquad%20%5Cfrac%7Bxz%7D%

Yanka [14]

Answer:

$x=\frac{12}{7} \\y=\frac{12}{5} \\z=-12$

Step-by-step explanation:

Let's re-write the equations in order to get the variables as separated in independent terms as possible \:

First equation:

$\frac{xy}{x+y} =1\\xy=x+y\\1=\frac{x+y}{xy} \\1=\frac{1}{y} +\frac{1}{x}$

Second equation:

$\frac{xz}{x+z} =2\\xz=2\,(x+z)\\\frac{1}{2} =\frac{x+z}{xz} \\\frac{1}{2} =\frac{1}{z} +\frac{1}{x}$

Third equation:

$\frac{yz}{y+z} =3\\yz=3\,(y+z)\\\frac{1}{3} =\frac{y+z}{yz} \\\frac{1}{3}=\frac{1}{z} +\frac{1}{y}$

Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":

$1=\frac{1}{y} +\frac{1}{x} \\-\\\frac{1}{3} =\frac{1}{z} +\frac{1}{y}\\\frac{2}{3} =\frac{1}{x} -\frac{1}{z}$

Combine this last expression term by term with the reduced equation 2, and solve for "x" :

$\frac{2}{3} =\frac{1}{x} -\frac{1}{z} \\+\\\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\ \\\frac{7}{6} =\frac{2}{x}\\ \\x=\frac{12}{7}$

Now we use this value for "x" back in equation 1 to solve for "y":

$1=\frac{1}{y} +\frac{1}{x} \\1=\frac{1}{y} +\frac{7}{12}\\1-\frac{7}{12}=\frac{1}{y} \\ \\\frac{1}{y} =\frac{5}{12} \\y=\frac{12}{5}$

And finally we solve for the third unknown "z":

$\frac{1}{2} =\frac{1}{z} +\frac{1}{x} \\\\\frac{1}{2} =\frac{1}{z} +\frac{7}{12} \\\\\frac{1}{z} =\frac{1}{2}-\frac{7}{12} \\\\\frac{1}{z} =-\frac{1}{12}\\z=-12$

8 0

3 years ago

The speed of a race car in mph <br><br> Discrete or continuous

Maru [420]

Answer:

Step-by-step explanation:

Discrete variables are those that can take only a finite number of values. This is not so for speed of an airplane. as it changes from time to time

4 0

3 years ago

Read 2 more answers

If a pound of bread is worth 1.75 and a orange is worth 0.50 per pound. How many pounds of oranges have an equivalent cost to 3

Alexus [3.1K]

Answer:

C. 10.5 pounds

Step-by-step explanation:

The worth of 3 loaves of bread is 3 times that of one loaf:

3 × 1.75 = 5.25

You want the number of pounds of oranges (p) at 0.50 per pound that has this same worth:

0.50p = 5.25

p = 5.25/0.50 = 10.50

10.5 pounds of oranges have an equivalent cost to 3 loaves of bread.

5 0

3 years ago