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3 years ago

9

Does the system shown always, sometimes, or never have a solution when a=b?

exFormula1" title="a\geq b" alt="a\geq b" align="absmiddle" class="latex-formula">? a

1 answer:

devlian [24]3 years ago

3 0

Answer:

It always has a solution until you get to imaginary numbers.

Plug in a=b for a=2

2≥2 which is true! so it will always have a solution.

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Find the mean, range, and interquartile range of the heights of plants given

Artist 52 [7]

Answer:

Mean = 30.9

Range = 80

Interquartile Range = 36

Step-by-step explanation:

The mean of a set of numbers is the sum divided by the number of terms. In other words that means 2, 22, 4, 36, 82, 44, 65, 30, 8, 16 go over a fraction like this. There are 10 numbers here so this is our denominator.

$\frac{2+ 22 + 4 + 36 + 82 + 44 + 65 + 30 + 8 + 16}{10}$

$\frac{309}{10} > 30.9$

For the range, all we do is subtract the minimum value from the maximum which is 82 - 2. That gives us 80.

For the IQ Range....

Arrange the terms in ascending order.

2, 4, 8, 16, 22, 30, 36, 44, 65, 82

Then we need to find the median which is the average of the two middle terms.

$\frac{22+30}{2} > \frac{2*11 + 30}{2} >\frac{2*11+2*15}{2} > \frac{2 * (11 + 15)}{2} > 11 + 15 > 26$

So for the lower half of data 2, 4, 8, 16, 22 we have the median of 8

And for the upper half 30, 36, 44, 65, 82 we have the median of 44.

To find the IQ Range it is the difference between the first quartile (8) and the third (44)

So 44 - 8 = 36

7 0

2 years ago

Read 2 more answers

Order the fractions from least to greatest

My name is Ann [436]

Answer:

1/4, 2/5, 1/2, 3/5, 2/3, 13/18, 7/9, 5/6, 2 6/15, 2 4/9, 2 3/5, 2 2/3, 6 3/8, 6 1/2,

6 3/4, 6 5/6

Step-by-step explanation:

I like to organize decimals more than fractions because it's easier for me, so I'm changing each of them to a decimal. You don't have to do this though.

To change a fraction to a decimal, if it is simplified, make it an improper fraction
Then, divide the numerator from the denominator. For example, 1/4 = 0.25 because 1 divided by 4 = 0.25

3/5 = <u>0.60</u>,
1/4 = <u>0.25,</u>
1/2 = <u>0.50</u>,
2/5 = <u>0.40</u>,
7/9 = 0.7 repeating or just <u>0.78 </u>rounded,
13/18 = 0.72 repeating or <u>0.73</u> rounded,
5/6 = 0.83 repeating or <u>0.84 </u>rounded,
2/3 = 0.66 repeating or <u>0.67</u> simplified,
6 3/4 = 27/4 or <u>6.75</u>,
6 1/2 = 13/2 = <u>6.50,</u>
6 5/6 = 41/6 = 6.83 repeating or <u>6.84</u>
6 3/8 = 51/8 = 6.375 or <u>6.38</u>
2 2/3 = 8/3 = 2.66 repeating or <u>2.67</u>
2 6/15 = 36/15 = <u>2.40</u>
2 3/5 = 13/5 = <u>2.60</u>
2 4/9 = 22/9 = 2.44 repeating or <u>2.45</u>

<u />

Ordering them is pretty easy, just start from the smallest and move to the greatest!

0.25 = 1/4
0.40 = 2/5
0.50 = 1/2
0.60 = 3/5
0.67 = 2/3
0.73 = 13/18
0.78 = 7/9
0.84 = 5/6
2.40 = 2 6/15
2.45 = 2 4/9
2.60 = 2 3/5
2.67 = 2 2/3
6.38 = 6 3/8
6.50 = 6 1/2
6.75 = 6 3/4
6.84 = 6 5/6

6 0

4 years ago

Can someone find The volume of the shaded portion of the cylinder??????????????????????? I have attached the picture

Yakvenalex [24]

Step-by-step explanation:

Area of circle = πr², π = 22/7 or 355/133. Here it is said to use '3.14'. I will use the same.

Volume = cross-section area * height

Cross-section area of bigger one = π(3m)²

Volume = π(3m)² * height

= 9π * 5 m³ = 45π m³

Cross-section area of smaller one= π(1m)²

Volume = π(1m)² * height

= π * 5 m³ = 5π m³

Since a large part(cylinder of 1 m is not here):

Required volume = total volume - volume of smaller circle(cylinder)

= 45π - 5π m³

= 40π m³ = 40(3.14) m³

= 125.6 m³

4 0

3 years ago

A circular garden has a radius of 3 meters. What is the area of the garden? Write your answer using π. Show your work.

Gwar [14]

Answer: 9 $\pi$

Step-by-step explanation:

Sorry the pi sign looks weird. The formula for area of a circle is $a=\pi r^2$ , so we have to substitute the radius with 3. The square of 3 is 9, so the answer is 9pi.

7 0

3 years ago

What is the length of WE?

Helga [31]

Answer: 20

Explanation:

Midsegment WE is parallel to segment RS. Recall that midsegments are half as long as the side they are parallel to. So we cut the side RS = 40 in half to get WE = (RS)/2 = 40/2 = 20.

5 0

3 years ago

Read 2 more answers