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3 years ago

13

Lou made $24 mowing lawns. David made twice as much as Lou mowing lawns, and then David made another $16 from washing windows. W

hich equation can be used to find m, the amount of money David made?

1 answer:

mixer [17]3 years ago

4 0

Answer:

64

Step-by-step explanation:

24 times 2 is 48 then add 16 it is 64

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Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

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PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

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Two runners, same time. Alan travels east at a uniform rate that is 2 mph faster than ed, who is traveling west. After two hours

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Ed is going 12 miles per hour.

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The average household income for a recent year was $30,000. five years earlier the average household income was $24,500. assume

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Using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

According to the question,

The average household income for a recent year (x₁⁻) = $30,000

The average household income for a recent year (x₂⁻) = $24,500

sample sizes n₁ = n₂ = 34

standard deviation of both samples were $24,500. Thus, s₁ = s₂ = $5928.

Null hypothesis: There is no evidence to believe that the average household income has increased.

H₀ : μ₁ ≤ μ₂

Alternative hypothesis: There is evidence to believe that the average household income has increased.

H₁: μ₁ > μ₂

To check hypothesis we have the formula

Standard error= $\sqrt{\frac{s_{1} ^{2} }{n_{1} } + \frac{s^{2} _{2} }{n_{2} } }$

= $\sqrt{2067128.4706}$

= 1437.7512

Thus, standard error is $1437.7512.

Formula for test statistic = [(x₁⁻ - x₂⁻) - (μ₁ - μ₂)]/standard error

= [(30000 - 24500) - 0]/1437.7512

= 3.8254

The critical value of z at 5% level of significance is 1.6449.

Here, the calculated value is greater than the critical value so we reject H₀.

Hence using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

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Andre and Noah started tracking their savings at the same time. Andre started with $15 and deposits $5 per week. Noah started wi

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Answer:

1. he started with 15 and 5 per week. w is week

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Step-by-step explanation:

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3 years ago

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