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Strike441 [17]
3 years ago
11

William says to Gracie, "If you give me $7.50,we will have and equal amount of money. "Grace responds, "That may be true, but if

you give me $ 7.50 instead, I will have twice as much money as you. "How much money did William and Grace each have in the beginning?
Please show work
Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

The amount that William has at the beginning is $37.50 and the amount that Gracie has at the beginning is $52.50

Step-by-step explanation:

Let

x ---> amount that William has at the beginning

y ---> amount that Gracie has at the beginning

we know that

William says to Gracie, "If you give me $7.50,we will have and equal amount of money

so

x+7.50=y-7.50

y=x+15.00 ----> equation A

"Grace responds, if you give me $ 7.50 instead, I will have twice as much money as you

2(x-7.50)=(y+7.50)

2x-15.00=y+7.50

2x-y=22.50 ----> equation B

substitute equation A in equation B

2x-(x+15.00)=22.50

solve for x

x=22.50+15.00=37.50

Find the value of y

y=37.50+15.00=52.50

therefore

The amount that William has at the beginning is $37.50 and the amount that Gracie has at the beginning is $52.50

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Matrix has 5 rows and 3 columns.

So it's order is 5x3.

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Step-by-step explanation:

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3 years ago
Which statement is NOT a step used when constructing an inscribed hexagon?
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Answer:

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Step-by-step explanation:

We want to determine which statement is NOT a step used when constructing an inscribed hexagon?  

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3. Place the compass on the point where the circle and radius intersect. True

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3 0
2 years ago
An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample
valentina_108 [34]

Answer:

t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626    

The degrees of freedom are given by:

df=n-1=8-1=7  

The p value would be given by:

p_v =P(t_{(7)}  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

Replacing we got:

\bar X=58.875 represent the mean

s=5.083 represent the sample standard deviation for the sample  

n=8 sample size  

\mu_o =60 represent the value that we want to test

\alpha=0.1 represent the significance level

t would represent the statistic

p_v represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:  

Null hypothesis:\mu \geq 60  

Alternative hypothesis:\mu < 60  

The statistic would be given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

Replacing the info we got:

t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626    

The degrees of freedom are given by:

df=n-1=8-1=7  

The p value would be given by:

p_v =P(t_{(7)}  

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

3 0
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zheka24 [161]

Answer:

284.625

Step-by-step explanation:

Arrange the numbers highest to lowest.

Find the middle value in the arrangement.

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