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4 years ago

80% of Vanessa's final grade is based on the average score of her quizzes, which is 73.

1 answer:

8 0

80% of quizzes + 20% of final = final grade

80% * 73 + 20% * x = 70

0.8 * 73 + 0.2x = 70

58.4 + 0.2x = 70

0.2x = 11.6

x = 58

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Set A of six numbers has a standard deviation of 3 and set B of four numbers has a standard deviation of 5. Both sets of numbers

Alenkinab [10]

Given:

$\sigma_A=3$

$n_A=6$

$\sigma_B=5$

$n_B=4$

$\overline{x}_A=\overline{x}_B$

To find:

The variance. of combined set.

Solution:

Formula for variance is

$\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}$ ...(i)

Using (i), we get

$\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}$

$(3)^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$9=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$54=\sum (x_i-\overline{x}_A)^2$

Similarly,

$\sigma_B^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{n_B}$

$(5)^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$25=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$100=\sum (x_i-\overline{x}_B)^2$

Now, after combining both sets, we get

$\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}$

$\sigma^2=\dfrac{54+100}{6+4}$

$\sigma^2=\dfrac{154}{10}$

$\sigma^2=15.4$

Therefore, the variance of combined set is 15.4.

7 0

3 years ago

Stacy and Neil painted 280 ft of their living room wall with 4/5 gallon of paint. How many square feet can they paint with 3 gal

barxatty [35]

Step-by-step explanation:

4/5 gallons for 280 ft² (the ² is missing in the question ...).

3 gallons would be 15/5.

so, what do I need to multiply 4 with to get 15 ?

4×x = 15

x = 15/4

multiplying now also 280 ft² with this factor gives us the answer :

280 × 15/4 = 70 × 15 = 1050 ft²

they can paint 1050 ft² with 3 gallons of paint.

6 0

2 years ago

Help please it’s for home work

Dmitry [639]

Slope would be 2
Y intercept would be 2
y = 2x + 2

6 0

3 years ago

MUSIC Randall recorded 8 songs on his most recent CD. The total length of the CD is 49 minutes. Find a unit rate to represent th

Juliette [100K]

Answer: 6.13

Step-by-step explanation:

From the question, we are informed that MUSIC Randall recorded 8 songs on his most recent CD and that the total length of the CD is 49 minutes.

The unit rate to represent the average length per song on the CD will be calculated by dividing 49 by 8. This will be:

= 49 minutes / 8

= 6.125 minutes per song

= 6.13 to nearest hundredths

6 0

2 years ago

What is the length of the third side of the window frame ??

drek231 [11]

A^2+b^2=c^2
A=63
B=?
C=87
63^2+b^2=87^2
3969+b^2=7569
-3969 both sides
B^2=3600
Square root both sides
B=60in

5 0

3 years ago

Read 2 more answers