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lina2011 [118]
2 years ago
12

Thaddeus shakes his head as he pays $12.37 to the clerk for lunch. Complaining to a friend, Thaddeus says, “Do you realize that

is 0.2% of my monthly income?” His friend replies, “I think you made a mistake. That should be 2%. You messed up on the decimal point.” (a) Assuming Thaddeus is not wrong, what is his monthly income? (b) If Thaddeus’ friend is correct, what is Thaddeus’ monthly income?
Mathematics
1 answer:
djyliett [7]2 years ago
8 0
Pretty simple question, just set up the equation.
A) say Thad is right then equation is as follows:
X * 0.002 = 12.37
Where X is monthly income.
So to solve for X just divide 12.37 by 0.002 (0.2%)
6185$ per month. Which no offense to Thad, but means he’s probably some kind of software engineer or investment banker if he’s making that much a month. (Unlikely for Thad)

B) if he’s wrong then just set up again
X * 0.02 = 12.37
Where x = monthly income
So x= $618.5
More likely given he’s complaining about a 12$ lunch when inflation has the yelp one ($) sign restaurants charging 15 or 16 just for a meal with tip and tax.
Anyways my rant aside hope this helps.
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Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol
Dima020 [189]

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

And rounded up we have that n=2663

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".  

The population proportion have the following distribution

\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.025 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

We can assume an estimated proportion of \hat p =0.5 since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

And rounded up we have that n=2663

6 0
4 years ago
Find all points having an x-coordinate of 5 whose distance from the point (2, 6) is 5
galina1969 [7]

Answer:

(5,2) and (5,10)

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

points\ (2,6),(5,y)\\d=5

substitute in the formula

5=\sqrt{(y-6)^{2}+(5-2)^{2}}

solve for y

5=\sqrt{(y-6)^{2}+(3)^{2}}

5=\sqrt{(y-6)^{2}+9}

square both sides

25=(y-6)^{2}+9

(y-6)^{2}=25-9

(y-6)^{2}=16

square root both sides

y-6=\pm4

y=6\pm4

y=6+4=10

y=6-4=2

therefore

The points are

(5,2) and (5,10)

6 0
3 years ago
Determine if each statement is True or False. If False, determine what needs to be
kicyunya [14]

Answer:

a. False. A constant is a number on it's own, and 5 would be the coefficient of x. 8 would be the constant.

b. False. -6.5 would be the constant, since it's on its own. But actually, x would be carrying on a coefficient of 1. Letters are variables, not constants.

c. True.

8 0
3 years ago
Juan is buying flowers for his mother. He has $18 to spend and sees that roses are $3 each and carnations are $1.50 each. He wan
Irina18 [472]

Answer:

he would have 30

Step-by-step explanation:

7 0
3 years ago
How to make 15/2 into a mixed number
Mazyrski [523]
Perform division as shown here
You should get 7 1/2

3 0
3 years ago
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