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pochemuha
3 years ago
8

Mitch is buying candy bars for his friends. He wants to give 2 bars to each friend, and he wants to have 10 spare bars. He can a

fford to buy 16 candy bars.What is the algebraic sentence that will help him figure out how many friends he can treat? Let f= the number of friends (1. 1/2f-10=16 (2. 2f-10=16 (3. 2f+10=16 (4. 1/2f+10=16
Mathematics
1 answer:
Olenka [21]3 years ago
5 0
The answer is 2.2f-10=16
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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
3 years ago
Define a function f on a set of real numbers as follows: f(x) = 3x − 1 x , for each real number x ≠ 0 Prove that f is one-to-one
dalvyx [7]

Answer with Step-by-step explanation:

We are given that

f(x)=\frac{3x-1}{x}

For each real number x\neq 0

To prove that f is one -to-one.

Proof:Let x_1 and x_2 be any nonzero real numbers such that

f(x_1)=f(x_2)

By using the definition of f to rewrite the left hand side of this equation

f(x_1)=\frac{3x_1-1}{x_1}

Then, by using the definition of f to rewrite the right hand side of this equation  of f(x_1)=f(x_2)

f(x_2)=\frac{3x_2-1}{x_2}

Equating the expression then we get

\frac{3x_1-1}{x_1}=\frac{3x_2-1}{x_2}

3x_1x_2-x_2=3x_2x_1-x_1

3x_1x_2-3x_1x_2+x_1=x_2

x_1=x_2

Therefore, f is one-to-one.

6 0
3 years ago
The low temperature on Monday was 5 F. During the day, the temperature rose 20. What was the high temperature on Monday?
maria [59]

Answer:

the temp rose up 15 dgrs

Step-by-step explanation:

7 0
3 years ago
Divide.<br><br> 11.02 ÷ 3.8<br><br> Enter your answer, as a decimal, in the box.
AnnyKZ [126]

Answer:

2.9

Step-by-step explanation:

11.02÷3.8= 2.9

4 0
3 years ago
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How may weeks are there in a year?​
Zanzabum

Answer:

There are exactly 52.142857142857 weeks in the year 2019. This is equivalent to 52 weeks and 1 extra day, since there are 365 total days in 2019. Most years have 365 days, but a leap year has 366 days. That adds up to 52 weeks (where each week is exactly 7 days) PLUS 1 or 2 additional days.There are 52 complete weeks in a year. The year has 365 days, leaving one extra day. A leap year has 366 days, adding a second extra day. This makes 52 1/7 weeks in a normal year and 52 2/7 weeks in a leap year..

7 0
3 years ago
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