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Sergio039 [100]
3 years ago
9

Which of the following expressions could give the total amount of a $45 restaurant bill with a 15% tip added on?

Mathematics
1 answer:
vazorg [7]3 years ago
4 0

Answer:

$51.75

Step-by-step explanation:

Given

Total amount of bill, x= $45

Tip Percent=15%

⇒15% on $45 is to be paid extra as tip, other than the already paying $45

⇒Tip=\frac{15}{100}\times x=\frac{15}{100}  \times45=6.75

So <em>total amount to be paid</em>= Bill+ tip

= x + tip=x+\frac{15}{100} x=1.15x=1.15\times45

=$51.75

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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume
Lynna [10]

Answer:

a) 21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

b) ME=2.58\frac{52}{\sqrt{350}}=7.17

c) ME=2.58\frac{52}{\sqrt{100}}=13.42

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".  

Part a

\bar X=21 represent the sample mean  

\mu population mean (variable of interest)  

\sigma=52 represent the population standard deviation  

n=350 represent the sample size  

99% confidence interval  

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

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58  

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

21-2.58\frac{52}{\sqrt{350}}=13.83  

21+2.58\frac{52}{\sqrt{350}}=28.17  

So on this case the 99% confidence interval would be given by (13.83;28.17)  

Part b

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{350}}=7.17

Part c

The margin of error is given by:

ME=2.58\frac{52}{\sqrt{100}}=13.42

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0
3 years ago
Which ordered pairs are solutions to the inequality x+3y≥−8?
crimeas [40]
(-6,0)
(-1,-2)
(-5,-1)
4 0
3 years ago
Read 2 more answers
What is the definition of mean???
Scilla [17]
Mean, in terms of math, is the total added values of all the data in a set divided by the number of data <em>in</em> the set. Make sense? If not, here' an example...

Let's say this is my data set:
1, 2, 5, 4, 3, 8, 7, 4, 6,10

To find the mean...
Step 1: Add all of them together.
1+2+5+4+3+8+7+4+6+10 is what? 50. Now that you have this number...
Step 2: Divide by the amount there are. Basically, count up all of the numbers. How many are there? There are 10. Finally...
Step 3: Divide. 50/10 is 5, so the mean of this data set would be 5. Get it? I sure hoped this helped :)
3 0
3 years ago
Use the graph to evaluate the function.<br> f(-5) =<br> y<br> -8 -6
DENIUS [597]

Answer:

-4

Step-by-step explanation:

Go to x value of -5 and go down until you touch line.

3 0
3 years ago
The area of a square mat is 125 square inches. The best approximation of its length is inches. If the length of each side is inc
gtnhenbr [62]
The area of a square is simply the side length squared and we are given that the area is 125 so:

s^2=125

s=√125

s=5√5

Now using the area equation again, and adding 1 inch to s we have:

A=(s+1)^2, and using s found above we have:

A=(5√5+1)^2

A=125+10√5+1

A=126+10√5 in^2

A≈148.36 in^2  (to nearest hundredth of a square inch)
4 0
3 years ago
Read 2 more answers
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