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Crank
3 years ago
10

A garden table and a bench cost $781 combined. The garden table costs $69 less than the bench. What is the cost of the bench?

Mathematics
2 answers:
Arlecino [84]3 years ago
6 0

Answer:

$425

Step-by-step explanation:

x = bench

x - 69 = garden table

x + (x - 69)=781

x + x - 69 =781

2x - 69 = 781

2x -69 +69 = 781 + 69

2x = 850

2x/2 = 850/2

x = 425

Bench = 425

lutik1710 [3]3 years ago
3 0

Answer: £425?

Step-by-step explanation:

x = bench

x - 69 = garden table

x + (x -69) = 781

2x - 69=781

+ 69 both sides

2x = 850

x = 425

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A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95. and a standard deviation
lubasha [3.4K]

Answer:

127.95-1.685\frac{24.03}{\sqrt{40}}=121.55    

127.95 +1.685\frac{24.03}{\sqrt{40}}=134.35    

So on this case the 90% confidence interval would be given by (121.55;134.35)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=127.95 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=24.03 represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=40-1=39

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,39)".And we see that t_{\alpha/2}=1.685

Now we have everything in order to replace into formula (1):

127.95-1.685\frac{24.03}{\sqrt{40}}=121.55    

127.95 +1.685\frac{24.03}{\sqrt{40}}=134.35    

So on this case the 90% confidence interval would be given by (121.55;134.35)    

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3 years ago
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