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3 years ago

If 3,x,y,18 are in arithmetric progression , find the value of x and y

1 answer:

6 0

Given:
arithmetic progression
a₁ = 3
a₂ = x
a₃ = y
a₄ = 18

Solution:
The arithmetic progression has general formula to determine nth term
a₁ + d(n - 1) = an
a₁ represents first term, d represents difference, n represents number of terms, an represents nth term

First we should find out the value of d, by submitting a₄ to the formula
a₁ + d(n - 1) = an
a₁ + d(4 - 1) = a₄
3 + d(3) = 18
3 + 3d = 18
3d = 15
d = 5
The difference of the sequence is 5

Second, determine x and y
x = a₂
x = a₁ + d(2 - 1)
x = 3 + 5(1)
x = 8

y = a₃
y = a₁ + d(3 - 1)
y = 3 + 5(2)
y = 13

The value of x is 8, the value of y is 13

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Jason needs to explain to his class how to use mental math to find the product of 400,000×50,000 how would u explain that

elena55 [62]

You would do 5 times 4 which is 20. then count how many zero's there are and put them after the 20.

4 0

3 years ago

Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages (x) Price (y) A

belka [17]

Answer:

a) $y=0.00991 x +1.042$

b) $r^2 = 0.7503^2 = 0.563$

c) $r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

$y = mx +b$

Wehre

$m=\frac{S_{xy}}{S_{xx}}$

And:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2595100-\frac{4210^2}{7}=63085.714$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625$

And the slope would be:

$m=\frac{625}{63085.714}=0.00991$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429$

$\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7$

And we can find the intercept using this:

$b=\bar y -m \bar x=7-(0.00991*601.429)=1.042$

And the line would be:

$y=0.00991 x +1.042$

Part b

The correlation coefficient is given by:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=7 $\sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354$

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

The determination coefficient is given by:

$r^2 = 0.7503^2 = 0.563$

Part c

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

4 0

3 years ago

What is the measure of ZNMR?<br>[Not drawn to scale]

ss7ja [257]

Answer:

The answer is 63°

Step-by-step explanation:

The lines intersect so opposite angles are congruent.

7 0

3 years ago

Select strong association, weak association, or moderate association to correctly classify the correlation coefficient.

11Alexandr11 [23.1K]

Answers:

0.45 is a moderate association

0.95 and -0.8 are both strong association

0.10 is weak association

Explanation:

This is the interpreation of the correltaion coefficient:

1) The correlaion coefficient assesses the relationship between two variables in a scatter plot.

2) If the sign of the correlation coefficient is positive means that the two variables trend to grow or decrease in the same sense. This is an uphill line or curve: if variable X grows, variable Y grows, and if variable X decreases variable Y grows.

If the sign of the correlation coefficient is negative means that the two variables go in opposite direction. This is a downhill line or curve.

3) A correlation coefficient of +1 or -1 is a perfect association. The two variables are totally associated.

4) A correlation coefficient less that +1 but greater than 0.7 is a strong association. The same with a coefficite between - 0.7 and -1.

5) A correlation coefficient arroun +0.5 or -0.5 is a moderate association.

6) A correlation coefficient of 0 is a nill association.

7) A correlation coeffiicient between 0 and 0.3 is a weak association. The same when the correlation coefficient is between -3 and 0.

4 0

3 years ago

Read 2 more answers

Write an equation of the line passing through point p that is perpendicular to the given line. p(3,1), y=13x−5

Anarel [89]

You know two lines y=ax+b and y=mx+n that are perpendicular, so we have the product a*m=-1

+ This line is perpendicular to y=13x-5, so it has equation: y=-1/13x+b
+ And it passes through the point (3;1), so we have x=3, y=1. So 1=-1/13 *3+b
and b= 1+3/13= 16/13
And we have y=-1/13x+16/13
Have fun

7 0

3 years ago