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2 years ago

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Tammy has planted a small, young tree in her yard. To allow for the tree’s growth, she needs 15 feet in all directions around th

e base of the tree to remain open and unplanted. Which best describes the section of ground surrounding the base of the tree that should remain unplanted?

1 answer:

astraxan [27]2 years ago

7 0

Answer:

First, remember that a circle of radius R centered in the point (a, b) can be written as:

(x - a)^2 + (y - b)^2 = R^2

Suppose that we can model the yard as a rectangular coordinate axis.

And the tree is planted in the point (a, b)

If we want to have 15 feet in all directions around the base of the tree (15 ft around the point (a, b))

The section that must remain unplanted is:

(x - a)^2 + (y - b)^2 ≤ R^2

Where the ≤ symbol is used because all the interior of the circle must remain unplanted (border included)

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A small school with 60 total students records how many of their students attend on each of the 180 days in a school year. the ma

horrorfan [7]

Answer:

For the sampling distribution,

a) Mean = μₓ = 55.0 students.

b) Standard Deviation = 1.8 students.

Step-by-step explanation:

The complete Question is attached to this solution.

The Central limit theorem explains that for the sampling distribution, the mean is approximately equal to the population mean and the standard deviation of the sampling distribution is related to the population standard deviation through

σₓ = (σ/√n)

where σ = population standard deviation = 4

n = sample size = 5

Mean = population mean

μₓ = μ = 55 students.

Standard deviation

σₓ = (σ/√n) = (4/√5) = 1.789 students = 1.8 students to 1 d.p

Hope this Helps!!!

5 0

2 years ago

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

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".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Part 1

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

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 $ME =\pm 0.1$ 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 that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

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

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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 $ME =\pm 0.04$ 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 that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22$

And rounded up we have that n=426

3 0

2 years ago

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav

Georgia [21]

<em><u>The intervals included in solution are:</u></em>

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

<em><u>Solution:</u></em>

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

<em><u>Given inequality is:</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}$

<em><u>We have to solve the inequality</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x} - 10\geq \frac{2}{24}$

$\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0$

$\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0$

$\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}$

When we multiply or divide both sides by negative number, then we must flip the inequality sign

$\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0$

$\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\$

This is attached as figure below

From the attached table,

$\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0$

<em><u>Therefore, solution set is given as</u></em>:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

8 0

2 years ago

Read 2 more answers

The mean of a list of 80 numbers is 230. If four numbers 145,156,210, and 255 are added, what is the mean of the list of numbers

anygoal [31]

Add 145, 156, 210. and 255 then divide by 4. The mean equals 184.

7 0

2 years ago

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Using the extended Euclidean algorithm, find the multiplicative inverse of a. 135 mod 61 b. 7465 mod 2464 c. 42828 mod 6407

rodikova [14]

Answer:

(a)1≡47 mod 61

(b)1≡2329 mod 2464

(c)Does not exist

Step-by-step explanation:

The operation a(mod b) has an inverse if the the two integers (a,b)

are co-prime. i.e. their g.c.d is 1.

(a)Given 135 mod 61

We first reduce it to its lowest form.

135 mod 61=13 mod 61

61=13(4)+9 ==> 9=61-13(4)

13=9(1)+4 ==> 4=13-9(1)

9=4(2)+1 ==> 1=9-4(2)

4=1(4)

Next we rewrite 1 as a linear combination of 13 and 61.

1=9-4(2)

=9-(13-9(1))2

=9(3)-13(2)

=(61-13(4))(3)-13(2)

=61(3)-13(12)-13(2)

1=61(3)-13(14)

1=61(3)+13(-14)

1≡-14 mod 61≡(-14+61)mod 61

1≡47 mod 61

(b)7465 mod 2464

Reducing it to its lowest form

7465 mod 2464=73 mod 2464

2464=73(33)+55 ==>55=2464-73(33)

73= 55(1)+18 ==> 18=73-55(1)

55=18(3)+1 ==>1=55-18(3)

18=1(18)

Rewriting 1 as a linear combination of 73 and 2464.

1=55-18(3)

=2464-73(33)-(73-55(1))(3)

=2464-73(33)-73(3)+55(3)

=2464-73(36)+55(3)

=2464-73(36)+(2464-73(33))(3)

=2464-73(36)+2464(3)-73(99)

=2464(4)-73(135)

1=2464(4)+73(-135)

Therefore:

1≡-135 mod 2464

1≡(-135+2464)mod 2464

1≡2329 mod 2464

(c)42828 mod 6407

The two numbers are not co-prime. In fact their g.c.d is 43.

Therefore their inverse does not exist.

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2 years ago

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