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Minchanka [31]
3 years ago
14

Allyson has 4.5 pieces of rope to use for a tire swing. If each full piece is 2 2/3 feet long, how much rope does Allyson have i

n all?
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0

Answer:

12 feet

Step-by-step explanation:

4.5 pieces of rope = 9/2 pieces in fractions

Also, 2 2/3 can be rewritten as 8/3 in fractions

So, 9/2 *8/3 = 72/6 = 12 feet

Allyson has 12 feet of rope in all.

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A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken
mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

X=1 number of citrus trees that are infected with the citrus red mite.

n=5 random sample taken

\hat p=\frac{1}{5}=0.2 estimated proportion of citrus trees that are infected with the citrus red mite.

p true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

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

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

In order to find the critical values 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 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical values would be given by:

t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96

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 0.01 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)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56  

And rounded up we have that n=6147

5 0
3 years ago
Question 2 (Essay Worth 10 points)
Soloha48 [4]

Answer:

Account A: Decreasing at 8 % per year

Account B: Decreasing at 10.00 % per year

Account B shows the greater percentage change

Step-by-step explanation:

Part A: Percent change from exponential formula

f(x) = 9628(0.92)ˣ

The general formula for an exponential function is

y = ab^x, where

b = the base of the exponential function.

if b < 1, we have an exponential decay function.

ƒ(x) decreases as x increases.

Account A is decreasing each year.

We can rewrite the formula for an exponential decay function as:

y = a(1 – b)ˣ, where

1 – b = the decay factor

b = the percent change in decimal form

If we compare the two formulas, we find

0.92 = 1 - b

b = 1 - 0.92 = 0.08 = 8 %

The account is decreasing at an annual rate of 8 %.The account is decreasing at an annual rate of 10.00 %.

Account B recorded a greater percentage change in the amount of money over the previous year.

5 0
1 year ago
8.2z^2+2.1+7z-0.1-4z+z^2
Mariulka [41]
Answer: 3z^2 + 3z +2
Hope this helps : )
4 0
2 years ago
What is the square root of 40 rounded to the nearest hundredths place
iren [92.7K]
The answer to the square root of 40 is 6.33
3 0
3 years ago
You buy a ring box as a birthday gift that is in the shape of a triangular prism. What is the least amount of wrapping paper nee
SashulF [63]
<span>If the condition means conventional/regular rectangular piece of paper, then it is, probably, 
rectangle of 8+3+3 = 14 inches wide and 3+10+3+10 = 26 inches long.</span>
7 0
3 years ago
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