I need to understand the solution

Two integers have a sum of 42 and a difference of 22. The greater of the two integers is

DochEvi [55]

Let
x = larger integer
y = smaller integer

The two integers (x and y) have a sum of 42 which means they add to 42

x+y = 42

solve for y to get

y = 42-x

simply by subtracting x from both sides

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The two integers have a difference of 22. This translates to "subtract the values and the result will be 22", i.e.,

x-y = 22

Plug in y = 42-x. Solve for x

x-y = 22
x-(y) = 22
x - (42-x) = 22
x - 42 + x = 22
2x - 42 = 22
2x - 42+42 = 22+42
2x = 64
2x/2 = 64/2
x = 32

If x = 32, then y is...
y = 42-x
y = 42-32
y = 10

Therefore,
x = 32
y = 10

The final answer is 10

5 0

4 years ago

Read 2 more answers

Which equation represents the line that passes through (-3,5) and is parallel to the graph of y= -2/3x+5

Nostrana [21]

Parallel to the graph of y = -2/3x + 5
means that it has the same slope

Rewrite
y = -2/3x + b
plug in the given coordinates to solve for b
5 = -2/3(-3) + b
5 = 2 + b
subtract 2 from both sides
3 = b

plug that back into the equation
y = -2/3x + b
y = -2/3x + 3

The answer is B. y= -2/3x+3

This line is parallel to y = -2/3x + 5 and it passes the point (3, 5).

Hope this helps :)

4 0

3 years ago

he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on w

stellarik [79]

Answer:

90% confidence interval is ( -149.114, -62.666 )

Step-by-step explanation:

Given the data in the question;

Sample 1 Sample 2

x"₁ = 259.23 x"₂ = 365.12

s₁ = 34.713 s₂ = 48.297

n₁ = 5 n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

$S_p^2$ = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

$S_p^2$ = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

$S_p^2$ = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [ 4 + 9 ]

$S_p^2$ = [ 4819.9692 + 20993.4 ] / [ 13 ]

$S_p^2$ = 25813.3692 / 13

$S_p^2$ = 1985.64378

Now the Standard Error will be;

$S_{x1-x2$ = √[ ( $S_p^2$ / n₁ ) + ( $S_p^2$ / n₂ ) ]

we substitute

$S_{x1-x2$ = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

$S_{x1-x2$ = √[ 397.128756 + 198.564378 ]

$S_{x1-x2$ = √595.693134

$S_{x1-x2$ = 24.4068

Critical Value = $t_{\frac{\alpha }{2}, df$ = $t_{0.05, df=13$ = 1.771 { t-table }

So,

Margin of Error E = $t_{\frac{\alpha }{2}, df$ × [ ( $S_p^2$ / n₁ ) + ( $S_p^2$ / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666 )

3 0

3 years ago

Help me please and thank you! Question is below!

yKpoI14uk [10]

Answer:

4² + b² = 8² or 8² = b² + 4² if following hypotenuse, unknown, and known leg

Step-by-step explanation:

Created by using a² + b² = c²

5 0

3 years ago

How do i use italics ??

Ber [7]

When answering, you can press crtl + i and from that point on you will type using italics.
You can also highlight a section of text that you want to italicize. This can be used to italicize words that you forgot to italicize while you were typing.

6 0

3 years ago