Suppose the diameter at breast height (in.) of a certain type of tree is distributed normally with a mean of 8.8 and a standard deviation of 2.8 as suggested in Aedo-Ortiz, D. M., Olsen, E. D., & Kellogg, L. D. (1997). Simulating a harvester-forwarder softwood thinning: a software evaluation. Forest Products Journal, 47(5), 36.
(a)(2pts) What is the probability that the diameter of a randomly selected tree will be at least 10 inches? Will exceed 10 inches.
(b)(3pts) What is the value of c so that the interval (8.8-c, 8.8+c) contains 98% of all diameter values.

Answer:

2-

Step-by-step explanation:

\(x = 10 \\ 3(10) + 5y = 20 \\ 30 + 5y = 20 \\ 5y = - 10 \\ y = - 2\)

Answer:

mass

Step-by-step explanation:

Answer:

\(\frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1\)

Step-by-step explanation:

The standard equation of the ellipse is

\(\frac{(x-\alpha)^2}{a^2}+\frac{(y-\beta)^2}{b^2}=1\;\cdots(i)\)

where, \((\alpha, \beta)\) is the center and a,b are semi axes of the ellipse along x-axis and y-axis respectively.

Given that, \((\alpha, \beta)=(-9,3)\) and major axis, \(2a=24\).

So, semi major axis, \(a=24/2=12\).

Now, focus of the ellipse is (-7,3).

Let \(e\) be the eccentricity of the ellipse,

So, \(e=\frac c a\)

where \(c\) is the distance between the center and focus of the ellipse.

By using the distance formula,

\(c=\sqrt{(-9-(-7))^2+(3-3)^2}=2\)

\(\Rightarrow e=\frac {2}{12}=\frac{1}{6}\;\cdots(ii)\)

Again, the relationship among \(a,b\) and \(e\) is

\(e=\sqrt{1-\frac{b^2}{a^2}\)

\(\Rightarrow \frac{1}{6}=\sqrt{1-\frac{b^2}{(12)^2}\) [from equation (ii)]

\(\Rightarrow \frac{1}{36}=\sqrt{1-\frac{b^2}{144}\) [squaring on both the sides]

\(\Rightarrow \frac{b^2}{144}=1-\frac{1}{36}\)

\(\Rightarrow b^2=\frac{35}{36}\times144=140\)

So, the value of square of semi-minir axis, \(b^2=140\).

Hence, from equation (i), the equation of required ellipse is standard form is

\(\frac{(x-(-9))^2}{144}+\frac{(y-3)^2}{140}=1\)

\(\Rightarrow \frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1\)

The equation of the ellipse is \(\frac{(x+9)^{2}}{144}+\frac{(y-3)^{2}}{140} = 1\).

The equation of the ellipse in standard form is described below:

\(\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1\) (1)

Where:

The length of the minor semiaxis (\(b\)) is found by using the following Pythagorean-like relationship:

\(b = \sqrt{a^{2}-c^{2}}\) (2)

If we know that \((h,k) = (-9,3)\), \(a = 12\) and \(F_{1}(x,y) = (-7,3)\), then the equation of the ellipse is:

\(c = \sqrt{[(-9)-(-7)]^{2}+(3-3)^{2}}\)

\(c = 2\)

\(b = \sqrt{12^{2}-2^{2}}\)

\(b = 2\sqrt{35}\)

Hence, the equation of the ellipse is \(\frac{(x+9)^{2}}{144}+\frac{(y-3)^{2}}{140} = 1\).

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Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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Answer:

Using the equation ŷ = 5.4 + 1.7x, we can say that if x is 1.2, the predicted value will be 7.44.

Step-by-step explanation:

y=5.4+1.7(1.2)

Multiply 1.7 and 1.2 to get 2.04.

y=5.4+2.04

Add 5.4 and 2.04 to get 7.44.

y=7.44

There you go!

(Sources cited from Microsoft Math Solver.)

Answer:

Step-by-step explanation:

\(8+9\div3\times6-5\\= 8+9\div \:3\times \left(6-5\right)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(6-5\right)\::\quad 1\\=8+9\div \:3\times \:1\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\div \:3\times \:1\::\quad 3\\=8+3\\\\= 11\)

\(5+3-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=5+3-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:5+3-2-2\::\quad 4\\=4\)

\(\left(5+3\right)-8\div \:4-2\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(5+3\right)\::\quad 8\\=8-8\div \:4-2\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:8\div \:4\::\quad 2\\=8-2-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:8-2-2\::\quad 4\\=4\)

The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.

This is a situation in which employable individuals look for jobs and are unable to find one.

The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.

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Answer:the answer is o.7.7

Step-by-step explanation:

Answer:

The Ramirez family has 36 eggs

Answer:

$1920

Step-by-step explanation:

Simple interest = principal x time x interest rate

8000 x 0.06 x 4 = $1920

Systematic errors are consistently in the same direction

In contrast , random errors produce different values in random directions

Random error causes a slight difference of one measurement to from the next. It is quite unpredictable in it's variation during an experiment.

Systematic error always affects measurements by the same proportion, provided that a reading is taken the same way each time. It is predictable

An example that illustrates this difference are

Systematic errors are consistently in the same direction

for example they are always 50g , 1% or 99 mm too large or too small

In contrast , random errors produce different values in random directions

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Answer:

150°

Step-by-step explanation:

2x+x+90=180

3x=90

x=30

z= 180-x = 180-30 = 150°

Answer:

The Answer is 29/18 and in mixed form it is 1 11/18

Step-by-step explanation:

Steps for adding fractions

Find the least common denominator or LCM of the two denominators:

LCM of 9 and 6 is 18

Next, find the equivalent fraction of both fractional numbers with denominator 18

For the 1st fraction, since 9 × 2 = 18,

7

9

=

7 × 2

9 × 2

=

14

18

Likewise, for the 2nd fraction, since 6 × 3 = 18,

5

6

=

5 × 3

6 × 3

=

15

18

Add the two like fractions:

14

18

+

15

18

=

14 + 15

18

= 29/18

So, 7/9 + 5/6 = 29/18

In mixed form: 1 11/18

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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The given function is the rate of change of the water depth. therefore,

W'(t) is the second derivative.

Reasons:

The volume of water in the tank is 0 at time t = 0 (the tank is empty)

The function that gives the rate at which the depth of water in the tank is

increasing at time t > 0 is W(t).

Where;

t = The time in hours

Therefore;

W'(t), the derivative of the function of the rate at which the water in the

tank is increasing in feet per hour is the rate of increase of W(t).

Which gives;

W'(2) = The rate of change of the rate at which the water level is rising (second derivative) two hours after begins to fill with water, per hour per hour.

Therefore;

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Answer:

first option is correct

Step-by-step explanation:

finding area for upper rectangle

length = 16 miles

breadth = (2x - 1) miles

area of rectangle = l*b

=16 *(2x - 1)

16*2x - 16*1

=32x - 16

finding area for another rectangle

length = (5x + 5) miles

breadth = 4 miles

area of rectangle = l*b

= (5x + 5) * 4

=5x*4 + 5*4

=20x + 20

area of the figure = area of upper rectangle + area of another rectangle

=32x - 16 + 20x + 20

= (52x + 4) sq mi

Answer:

a₉ = 11

Step-by-step explanation:

Substitute n = 9 into the nth term formula, that is

a₉ = 3(9) - 16 = 27 - 16 = 11

Answer:

Step-by-step explanation:

In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.

1. 2 outcomes (heads and tails)

2. 6 outcomes (2 outcomes * 3 tosses)

3. 60 outcomes (6 outcomes per die * 10 rolls)

4. 12 outcomes (6 outcomes per die * 2 rolls)

5. 10 outcomes (10 numbers on the pad)

6. 52 outcomes (52 cards in a regular deck)

7. 32 outcomes (32 letters in the alphabet)

8. 7 outcomes (7 letters to choose from)

9. 10 outcomes (10 letters to choose from)

10. 36 outcomes (36 crayons to choose from)

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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Answer:

24 mill

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

Distance = 6.7 units

Step-by-step explanation:

Distance formula: \(d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

\(d = \sqrt{(8.5-8.5)^{2}+(2.2-8.9)^{2}} = \sqrt{(-6.7)^{2}} = 6.7\)

Note that distance is always positive

The correct research method for the study mentioned in the question is a Field survey.

Field survey can be defined as a research method used to collect data from a target population. In this study, researchers used a survey questionnaire to gather data from participants. The research aimed to test the theory that the exposure to multiple versions of fake news on various social media platforms made people believe the news.

The researchers surveyed 1,455 participants with an average age of 27, and 42% were male. The participants were exposed to 24 false news stories, and one group was exposed to multiple versions of fake news, while the other group was only exposed to each news story once.

The findings suggested that the more familiar the news was, the more accurate and believable it was. This familiarity effect lasted for up to a month. Hence, the research method used in this study was a field survey.

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So basically everything but choices B and C are functions.

====================================

Explanation:

Answer:

October 10, hope this helps.

Step-by-step explanation:

If Nathan started biking on October 2nd, and he started swimming on October 5th, then since October 10 is the closest day to them that he will be swimming and biking, but also because their both even numbers so he will be biking and swimming on October 10th.

The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer: 47.5

Step-by-step explanation:

The upper control limit (UCL) at a 99% confidence interval with a z value of 3 is 0.165.(option c)

In statistical process control, the UCL is a key parameter used to determine the upper boundary for acceptable variation in a process. To calculate the UCL for a defect rate, we use the formula UCL = p' + z * sqrt(p'(1-p')/n), where p' is the proportion of defects in the sample, z is the z value corresponding to the desired confidence level, and n is the sample size.

In this case, we have collected 20 samples of 100 items each, and the total number of defective items is 75. Therefore, the proportion of defects in the sample is 75/2000 = 0.0375. Using the formula mentioned earlier, with a z value of 3 and n value of 100, we can calculate the UCL as follows: UCL = 0.0375 + 3 * sqrt(0.0375 * (1-0.0375)/100) ≈ 0.165.

Therefore, the correct answer is C. 0.165.

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In order to find how many drops Mark has left, we must subtract the initial amount he had at the beginning and the amount he gave away.

make both as a common denominator fraction

simplify

he has 4/3 drops of nectar left.

Answer:

$4,974.31

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.7/100

r = 0.037 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 4,000.00(1 + 0.037/1)(1)(6)

A = 4,000.00(1 + 0.037)(6)

A = $4,974.31

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $4,000.00 at a rate of 3.7% per year compounded 1 times per year over 6 years is $4,974.31.

Answer:

Solution given:

16+28=44

(4+7)=11

Answer:

The solution is 4

Step-by-step explanation:

Step 1:  Find the correct answer

I'm not really sure what you are asking but I will give it a shot.

16 + 28 = ___ (4 + 7)

44 = ___ (11)

44 / 11 = ___ (11) / 11

4 = ___

Answer:  The solution is 4