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patriot [66]
2 years ago
11

Grade 5

Mathematics
1 answer:
laila [671]2 years ago
6 0

Answer:

Here u go:

Step-by-step explanation:

6 × 1/4 = 3/2

3 × 4/5 = 12/5

5 × 2/3 = 10/3

7 × 1/2 = 7/2

4 × 8/12 =​ 8/3

Please, give a <3

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Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a
svp [43]

Answer:

Step-by-step explanation:

n = sample size = 5

a) Let us determine the sum

\sum x_i= 100+200+300+400+490=1490

\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100

\sum y_i = 237+350+419+465+507=1978

\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504

\sum x_i y_i=100  \times 237 + 200\times350+300 \times 419 + 400 \times 465 +  490 \times 507=653830

Now we can determine S_x_x, S_x_y, S_y_y

S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080

S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\

653830 - \frac{1490 \times 1978 }{5}  = 64386

S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2

The estimate b of the slope β is the ratio of S_x_y and S_x_x

b = \frac{S_x_y}{S_x_x}

\frac{64386}{96080}  = 0.67

The mean is the sum of all value divide by number of values

\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298

\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6

The estimate a of the intercept is

a = \bar y - b \bar x

= 395.6 - 0.69 \times 298\\= 195.9

General least square equation;

\bar y = \alpha + \beta x

replace alpha by a = 3 and beta by b = 0.67 in general least equation

y = a + bx

195.9 + 0.67x

b)

<em>Scatter plot is shown in the attached file</em>

x is on the horizontal axis

y is n the vertical axis

The degree of freedom of regression is 1

because we use one variable s predictor variable

d_f_R = 1

The degree of freedom of error is the sample size n decrease by 2

d_f_E =n-2= 5 - 2=3

Total df is equal to the sum  of seperate degree of freedom dfR  and dfE

total df = 1 +3  4

SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296

Total SS =Syy= 45007.2

SSE + Total SS = SSR

= 45007.2 - 43146.9296

= 1860.2705

7 0
3 years ago
The sum of twice a number and three equals five. Find the number
Anna71 [15]
2n + 3 = 5 
2n = 2
n = 1
the sum of 2 times a number and three means you add 2n + 3 and since it is equal to 5 you then solve for n.
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goblinko [34]

Answer:

Step-by-step explanation:

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Lucy paid $45 for a new sweater that was on sale. It was on sale for 25% off the original price. How much was the original price
denpristay [2]

Answer:

it was 33.75

Step-by-step explanation:

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1/4hour 1/2hour 3/4 what is the total amount of time
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1/4+1/2=1/4+1/2=3/4

1/2=2/4

3/4 is the answer
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