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Maths!

Ber [7]

Answer:

(1) Variance = 4.5 and Standard deviation = 2.121.

(2) Variance = 4.5 and Standard deviation = 2.121.

(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.

Step-by-step explanation:

We are given with the following set of data below;

X $X-\bar X$ $(X-\bar X)^{2}$

5 5 - 8 = -3 9

8 8 - 8 = 0 0

10 10 - 8 = 2 4

9 9 - 8 = 1 1

6 6 - 8 = -2 4

Total 72 36

Firstly, the mean of the above data is given by;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{72}{9}$ = 8

(1)Now, the variance of the given data is;

Variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$

= $\frac{36}{9-1}$ = 4.5

So, the standard deviation, (S.D.) = $\sqrt{\text{Variance}}$

= $\sqrt{4.5}$ = 2.12

(2) Now, each value is added by 2; so the new data set is given by;

X $X-\bar X$ $(X-\bar X)^{2}$

7 7 - 10 = -3 9

10 10 - 10 = 0 0

12 12 - 10 = 2 4

11 11 - 10 = 1 1

8 8 - 10 = -2 4

Total 90 36

Firstly, the mean of the above data is given by;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{90}{9}$ = 10

(1)Now, the variance of the given data is;

Variance = $\frac{\sum (X-\bar X)^{2} }{n-1}$

= $\frac{36}{9-1}$ = 4.5

So, the new standard deviation, (S.D.) = $\sqrt{\text{Variance}}$

= $\sqrt{4.5}$ = 2.12

(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.

4 0

3 years ago

It took emily 25 min to rideHer bicycle to the repair shop in one hour and 15 minutes to walk back home. If Emily her bicycle to

s2008m [1.1K]

Answer:the repair shop is 5km from her house.

Step-by-step explanation:

Let x represent the distance of the repair shop from her house.

Let y represent Emily's speed when riding.

Distance = speed × time

It took Emily 25 min to ride her bike to the repair shop. Converting 25 min to hours, it becomes 25/60 = 5/12 hours.

Distance covered,

x = y × 5/12 = 5y/12

It took her 1h 15 min to walk back home. Converting to hours, it becomes 1 + 15/60 = 1 1/4 = 5/4

If she can ride her bike 8km/h faster than she can walk, it means that her speed while walking would be y 8 8

Therefore,

Distance covered,

x= 5/4(y - 8) = (5y - 40)/4

Since the distance remains the same, then

5y/12 =(5y - 40)/4

Crossmultiplying, it becomes

5y × 4 = 12(5y - 40)

20y = 60y - 480

60y - 20y = 480

40y = 480

y = 480/40 = 12

x = 5y/12 = 5 × 12/12 = 5 km

6 0

3 years ago

Solve each system using substitution: 1. 4x - 5y= -15 y= -3x + 22

Bumek [7]

4x - 5y = -15
y = -3x + 22

Plug in your y= equation into the y variable in the other equation

4x - 5 (y) = -15
^^
y = (-3x + 22) = -15

4x - 5 (-3x + 22) = -15

Distribute

4x + 15x - 110 = -15

Combine like terms and add 110 over to -15

19x = 95

Then, divide the whole equation by 19

x = 5

Then, plug in your x into your y= equation

y = -3 (5) + 22
y = -15 + 22
y = 7

x = 5
y = 7
(5, 7)

3 0

3 years ago

In the diagram, lines and intersect at E. If m∠AED = 3x + 11 and m∠CEB = 125, find x. A. 19 B. 38 C. 42 D. 55

Lady_Fox [76]

3X+11=125

3X=125-11

3X=114

X=114/3

X=38

So the answeris B 38

7 0

3 years ago

20% of a spring basket is peeps. There are 8 peeps. What is the total number of items in the basket?

murzikaleks [220]

8*100=20*x
800 =20x
40 =x
40 items are in the basket

5 0

4 years ago

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