let be the probability density function (pdf) for the diameter of trees in a forest, measured in inches. what does represent?

Answer:

Step-by-step explanation:

An equation which is the inverse of y = 2x² - 8 include the following: B. [tex]y= \pm \sqrt{\frac{x+8}{2} }[/tex]

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

f(x) = y = 2x² - 8

x = 2y² - 8

2y² = x + 8

By dividing both sides of the equation by 2, we have the following:

y² = (x + 8)/2

By taking the square root of both sides of the equation, we have the following:

y = √[(x + 8)/2]

[tex]y= \pm \sqrt{\frac{x+8}{2} }[/tex]

Read more on inverse function here: brainly.com/question/23626757

#SPJ1

A container size of at least 66.03 ounces will ensure that overflow occurs only 0.5% of the time.

To make sure overflow occurs only 0.5% of the time, we would have to find the container of size "c" such that the amount of distilled water dispensed by the machine does not exceed c with a probability of 0.995 (or 1-0.005).

Let X be the amount of distilled water dispensed by the machine. Then X ~ N(64, 0.78^2).

We want to find c such that P(X ≤ c) = 0.995.

We can standardize X to a standard normal distribution:

Z = (X - μ) / σ

Z = (c - 64) / 0.78

Then we can find the value of Z such that P(Z ≤ z) = 0.995, where z is the z-score associated with the 0.995 percentile of the standard normal distribution.

Using a standard normal distribution table or a calculator, we can find that z ≈ 2.576.

Therefore, 2.576 = (c - 64) / 0.78. Solving for c, we get:

c = 64 + 2.576 * 0.78 ≈ 66.03

So a container size of at least 66.03 ounces will ensure that overflow occurs only 0.5% of the time.

Learn more about standard normal distribution on

https://brainly.com/question/29509087

#SPJ4

Equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites; 5 packages of brownie bites and 15 packages of cookies needed to serve one dessert per person for a total of 75 attendees.

We can use the following equation to calculate the total number of packages of each dessert that the club treasurer must purchase:

Total packages of brownie bites (b) + Total packages of cookies (c) = Total number of attendees (75)

We know that brownie bites come in packages of 15, so the total number of packages of brownie bites the treasurer needs to purchase would be:

b = ceil(75/15) = 5

where "ceil" refers to the ceiling function, which rounds to the nearest integer. In this case, we need at least 5 packages of brownie bites to have one dessert per person.

To find the number of packages of cookies needed, we can substitute the value of b into the equation:

c + 12b = 75

c + 12(5) = 75

c + 60 = 75

c = 15

However, this value is not reasonable since 15 packages of cookies would provide 180 cookies, which is more than 2 cookies per person. Therefore, the treasurer would need to adjust the number of packages of cookies based on the actual number of cookies in each package to ensure that they have exactly one dessert per person.

To learn more about Equation, visit:

brainly.com/question/29514785

#SPJ9

The principal should then survey the selected students to gather their opinions on the new dress code.

To answer your question, the principal should choose a sample of students that is both representative and random. This will ensure that the opinions gathered are an accurate reflection of the entire high school population.

How the principal can achieve this:
Determine the sample size:

The principal should decide on a suitable sample size based on the total number of students in the high school.

A larger sample size will yield more accurate results, but it may not be feasible to survey too many students.

To ensure representativeness, the principal should divide the high school population into different strata, such as grade levels or other relevant demographic categories.

This will help ensure that the sample includes a balanced mix of students from different backgrounds and groups.
Select a random sample:

Within each stratum, the principal should choose a random sample of students.

The principal should then survey the selected students to gather their opinions on the new dress code.
By following these steps, the principal can select an appropriate sample of students that will provide an accurate representation of the high school's overall opinion on the new dress code.

For similar question on opinions.

https://brainly.com/question/25607827

#SPJ11

The following statements are accurate conclusions:

The null hypothesis is: The proportion of California college students who currently drink alcohol is the same as the proportion nationwide (p = 0.60).

The alternative hypothesis is: The proportion of California college students who currently drink alcohol is different from the proportion nationwide (p ≠ 0.60).

p in the hypotheses represents the proportion of college students who currently drink alcohol.

The Z-score is calculated as:

Z = (0.66 - 0.60) / 0.023 = 2.61

The P value can be obtained from a standard normal distribution table or calculator:

P = 0.0045 (for a two-tailed test)

We reject the null hypothesis and come to the conclusion that there is a statistically significant difference between the proportion of drinkers in the population of California college students and the proportion of drinkers in the American adult population because the P value (0.0045) is less than the significance level (which is not stated in the question) (0.66).

For the given question:

The following statements are accurate conclusions:

The result that "There is a 0.06 difference in the proportion of drinkers when we compare the US adult population to the population of CA college students" is untrue since the hypothesis test is not concerned with proportional differences.

The complete question is:-

Normal Distribution Calculator Drag the orange flag left or right to change the Z-score Alternatively, enter a Z-score into the textbox and click enter. Enter 8 -1 Z-score: -1.000 0 Z-score The area to the left of the Z value is 0.1587 The area to the right of the Z value is 0.9413 Question 1 6 pts California College Students Who Drink According to the Centers for Disease Control and Prevention, 60% of all American adults ages 18 to 24 currently drink alcohol. Is the proportion of California college students who currently drink alcohol different from the proportion nationwide? A survey of 450 California college students indicates that 66% currently drink alcohol. The null hypothesis is (Select] The alternative hypothesis is Select] p in the hypotheses represents [Select) The standard error is 0.60(1-0.60) 450 = 0.023 The Z-score is (Select] The P value is Select) The conclusion is Select Question 2 4 pts For the previous example, which statements are accurate conclusions? The proportion of drinkers in the population of CA college students is not 0.60. There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinknes in the population of CA college students A larger proportion of CA college students drink alcohol compared to the adults nationwide When we compare the American adult population to the population of CA college students, there is a 0.06 difference in the proportion of drinkers

To learn more about the null hypothesis, refer:-

https://brainly.com/question/28920252

#SPJ1

The required simplified value of x in the △RQP (triangle RQP) is given as x = 12 centimeters.

Similar triangles:

Two triangles are similar if their corresponding sides have the same ratio and if the corresponding pairs of angles are equal. Two or more figures having the same shape but different sizes are called similar figures. Consider a hula hoop and a bicycle wheel, both objects are similar in shape because they have the same shape. Similar triangles are those triangles that have similar properties, i.e. angles and proportionality of sides.

Here,

△RST ~ △RQP

So, the Property of similar triangle states that the ratio of the corresponding side of the triangle is equal.

PQ/ST = PR/RT

From the given data n the question,

8/x = 12 / 18

⇒ x = 8 × 18 / 12

⇒ x = 12

Thus, the required simplified value of x in the △RQP is given as x = 12.

Complete Question:

Given △RST ~ △QRP. Triangle P Q R. Side P Q is 8 centimeters and side P R is 12 centimeters. Triangle S R T. Side S T is x centimeters and side R T is 18 centimeters. What is the value of x?

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ4

Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress, which can be useful in calculating the total cost of fabric required for a certain number of doll dresses.

Given that Ellie uses 27 lengths of fabric for 48 doll dresses, we can calculate the amount of fabric she uses for one dress by dividing the total yards of fabric by the number of dresses.

Dividing 27 by 48, we get 0.5625 yards, or approximately 9/16 of a yard, for one doll dress. This means that each dress requires a little more than half a yard of fabric.

This information can be useful in calculating the cost of fabric required to make a certain number of doll dresses. If we know the cost of fabric per yard, we can multiply it by the number of yards required to determine the total cost of fabric. In this case, if the cost of fabric is $5 per yard, the cost of fabric for one doll dress would be approximately $2.81.

In conclusion, Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress.

To learn more about lengths please click on below link        

https://brainly.com/question/30100801

#SPJ1

The denominators of fractions that are the same are known as common denominators. Think about the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 Since the fractions' denominators are the same in both instances, it is simple to calculate the solution.

Davi's nail is 3/4 inch long, and Theo's nail is 3/8 inch long. To find how much longer Davis's nail is than Theo's, we need to subtract the length of Theo's nail from the length of Davis's nail:

3/4 inch - 3/8 inch

To subtract these fractions, we need to find a common denominator. The smallest common denominator for 4 and 8 is 8, so we need to convert the fractions:

3/4 inch = 6/8 inch

3/8 inch = 3/8 inch

Now we can subtract:

6/8 inch - 3/8 inch = 3/8 inch

Therefore, Davis's nail is 3/8 inch longer than Theo's nail.

To know more about common differences visit :

https://brainly.com/question/29775115

#SPJ9

Dorothy should have received $45.84 in change.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To find out how much change Dorothy should have received, we need to first calculate the total cost of the energy drink and the bag of chips:

Total cost = Cost of energy drink + Cost of the bag of chips

Total cost = $2.34 + $1.82

Total cost = $4.16

Next, we need to subtract the total cost from the amount paid by Dorothy to get the change:

Change = Amount paid - Total cost

Change = $50 - $4.16

Change = $45.84

Therefore, Dorothy should have received $45.84 in change.

To learn more about the equivalent expression visit:

https://brainly.com/question/2972832

#SPJ9

The calculated surface area of the figure is 152 square feet

From the question, we have the following parameters that can be used in our computation:

The triangular prism

The surface  area is calculated as

SA = hp + 2B

Where

h = height

p = perimeter of base

B = base area

From the figure, we have

B = 1/2 * 6 * 4 = 12

p = 5 + 5 + 6 = 16

h = 8

So, we have

SA = 8 * 16 + 2 * 12

Evaluate

SA = 152

Hence, the surface area is 152 square feet

Read more about surface area a

https://brainly.com/question/26403859

#SPJ1

Using area formula, we can find that the diagonal length is not 10ft. So, Jordan should not buy the pen.

A square's area is a measurement of the volume or surface that it takes up. It is equivalent to the two sides' combined lengths. Since the product of a square's two sides determines its size, the area is expressed in square units.

Here in the question,

Jordan wants an area that is of 35 ft² and 10ft diagonal length.

Now in the figure,

Dimensions of the pen are:

Length, l = 6ft.

Width, w = 6ft.

Height, h = 6ft.

So, it's a square.

Area that the puppy pen will provide = l × w

= 6 × 6

=36ft².

Diagonal of the pen is: (As per Pythagoras theorem)

√ (6² + 6²)

= √ (36+36)

= √ 72

= 8.48

The pen does provide 35ft² of area as it has 36ft², but it does not have a diagonal length of 10ft.

Therefore, Jordan should not buy the puppy pen.

To know more about area, visit:

https://brainly.com/question/1658516

#SPJ9

The complete question is:

Jordan wants a collapsible puppy pen that gives his puppy at least 35 square feet of area and at Least 10 feet of diagonal length. Should Jordan buy the pen shown? Explain.

We may determine that the diagonal length is not 10 feet using the area formula. Jordan shouldn't buy the pen.

The volume or area that a square occupies is determined by its area. It is equal to the sum of the lengths of the two sides. The area is given in square units since a square's size is determined by the product of its two sides.

Jordan requests a 35ft² square foot area with a 10-foot diagonal.

Now look at the figure.

The pen is the following size:

Length, l = 6ft.

Width, w = 6ft.

Height, h = 6ft.

So, it's a square.

The area that the puppy kennel will offer

= 6 × 6

=36ft².

Diagonal of the pen is:

= √ (6² + 6²)

= √ (36+36)

= √ 72

= 8.48

The pen has 36ft² square feet, so it does offer 35ft² square feet, but it lacks a 10 foot diagonal.

Jordan shouldn't purchase the Puppy pen as a result.

To know more about length, visit:

https://brainly.com/question/2217700

#SPJ9

The complete question is attached below,

If you want a square pen with each side measuring 6 feet:
- Perimeter = 6 feet x 4 = 24 feet
- The best length would be 24 feet, as it exactly matches the perimeter.
- No fencing needs to be cut off in this case, as the chosen fencing length fits the pen perfectly.

To determine the best length for the puppy pen, you will first need to know the dimensions of the desired pen. Assuming the pen is a square, follow these steps:
1. Measure the length and width of the area you want to fence.
2. Calculate the perimeter of the pen by adding the lengths of all four sides (since it's a square, the length and width are equal, so just multiply one side by 4).
3. Compare the perimeter to the available fencing lengths (12 feet, 24 feet, and 30 feet).
4. Choose the fencing length that is closest to, but not less than, the calculated perimeter.
5. Calculate the excess length by subtracting the perimeter from the chosen fencing length. This is the amount that needs to be cut off.

For similar question on square.

https://brainly.com/question/24657062

#SPJ11

Answer:

10%

Step-by-step explanation:

Percent proportion:

$28 - 100%

$8,40 - x%

Cross-multiply to find x:

[tex]x = \frac{8.40 \times 100\%}{28} = \frac{840}{84} = 10 \: \%[/tex]

Answer  30%

Step-by-step explanation:

To find what percentage $8.40 is of $28, we can use the following proportion:

part/whole = percent/100

Let x be the percentage we are trying to find, then we can write:

8.40/28 = x/100

To solve for x, we can cross-multiply:

28x = 8.40 * 100

Dividing both sides by 28, we get:

x = (8.40 * 100) / 28 = 30

Therefore, $8.40 is 30% of $28.

Using the line plot graph, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.

A line plot is a type of graph that shows the frequency of each value together with the data using symbols above a frequency number-line. It is used to organise the information simply and is very easy to comprehend.

In the given graph we can see that the distance values are given.

So, in the first instance the number of times the distance is used = 2.

The 2nd distance has been used = 3.

The 3rd distance has been used = 2.

The 4th distance has been used = 4.

The 5th distance has been used = 5.

The 6th distance has been used = 2.

The 7th distance has been used = 2.

The 8th distance has been used = 2.

Hence, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.

To know more about line plot, visit:

https://brainly.com/question/29573088

#SPJ1

The best interpretation of the 95% confidence interval to estimate the percentage of young men in your community who are living at home is 0.40 and 0.60.What is confidence interval?

A confidence interval is a range of values in which an estimated population parameter lies. The value of this parameter is inferred from sample data with a certain level of confidence. To calculate the confidence interval, the margin of error and the sample mean are combined.

A confidence interval expresses the uncertainty around the estimated parameter of a population. Confidence intervals are useful for determining the reliability of an estimate. In statistical inference, confidence intervals can be used to quantify the level of certainty regarding an estimated population parameter.

What is a 95% confidence interval?A 95% confidence interval implies that if we run the same survey many times, calculating the 95% confidence interval for each survey, 95% of those intervals will contain the true value of the population parameter. It is the most common confidence level used in surveys and statistical studies.

for such more questions on  reliability

https://brainly.com/question/29305718

#SPJ11

The staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags

To determine the number of bags of each color that the staff should order, we need to use the information from the sample of 120 students and make an inference about the entire population of 800 students.

If we assume that the sample of 120 students is representative of the entire population, we can use the proportions from the sample to estimate the number of bags of each color that the staff should order.

Let's use the following proportions from the sample:

40% of the students prefer blue bags (0.40 x 120 = 48)

45% of the students prefer black bags (0.45 x 120 = 54)

15% of the students prefer gray bags (0.15 x 120 = 18)

Therefore, based on this sample, the staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags.

However, it's important to note that this is just an estimate based on a sample, and there may be some variability or uncertainty in the actual preferences of the entire population.

To know more about  proportions  here

https://brainly.com/question/1496357

#SPJ1

Answer:

$134 per month

Step-by- step explanation:

Simply divide 536 by 4, and you get 134.

Answer:

6 degrees Celsius

Step-by-step explanation:

The temperature at 2am was 3.7 degrees C.

Since the temp dropped 1.15 degrees each hour, at 1am the temp was 3.7+1.15 = 4.85 degrees

So at midnight, 12am, the temp was 4.85+1.15 = 6 degrees Celsius

The sight distance for the driver on the given road with the mentioned conditions is calculated to be approximately 860.8 ft.

To calculate the sight distance for the driver, we need to use the horizontal curve sight distance formula. The formula is:

SD = 2/3 × ((h + R)² / (2 × R - f))

Where:

SD = sight distance

h = height of driver's eye above the roadway surface (in feet)

R = radius of the curve (in feet)

f = distance from the driver's eye to the object or obstacle (in feet)

First, we need to determine the height of the driver's eye. A typical height for a driver's eye above the roadway surface is 3.5 feet. Therefore, we will assume that h = 3.5 ft.

Next, we need to determine f, which is the distance from the driver's eye to the concrete wall. Since the wall is located 70 feet from the center line of the roadway, we can determine f as follows:

f = (W / 2) + S

Where:

W = width of the roadway (in feet)

S = distance from the center line to the wall (in feet)

Substituting the given values, we get:

f = (8 × 11 / 2) + 70 = 114 ft

Now, we can plug in the values for h, R, and f into the sight distance formula:

SD = 2/3 × ((3.5 + 1176)² / (2 × 1176 - 114))

Simplifying the formula, we get:

SD ≈ 860.8 ft

Therefore, the sight distance for the driver on this roadway with a horizontal curve of radius 1176 ft and a concrete wall built at 70 ft from the center line is approximately 860.8 ft.

Learn more about Horizontal Curve :

https://brainly.com/question/29366319

#SPJ4

Be 95% confident that the true percentage of young women infected with at least one STDs in your community is between 12% and 28% based on the random sample of 100 young women in your community.

The national estimate for the proportion of young women in the United States who are infected with at least one of the most prevalent sexually transmitted diseases is 26% based on the information provided. The study also predicts that the standard error for findings from 100 young women's random sample will be 0.04 percent.

It is discovered that 20% of 100 young women in your community who were chosen at random are infected with at least one of the most prevalent STDs. A 95% confidence interval can be used to calculate the proportion of young women in your community who have at least one of the most frequent STDs.

If the same sample is obtained multiple times, the true value will, in 95% of cases, fall within the computed interval, according to a 95% confidence interval. The range of 12% to 28% is the predicted 95% confidence interval for the proportion of young women in your town who have at least one of the most prevalent STDs.

We therefore have a 95% confidence level that the true percentage of young women infected with at least one of the most prevalent STDs in your community is between 12% and 28% based on the sample of 100 young women in your community. This indicates that there is a chance that the proportion could be either higher or lower than the 26% national estimate.

Learn more about random sample here:

https://brainly.com/question/29852583

#SPJ1

The true statements about the sample are a, c, d and e.

Serial codes in the resample may differ from those in the initial sample. The histogram of the resample may vary significantly from the histogram of the initial sample due to the small sample size. The number of copies of each serial number in the resample can be zero, one, or more. Furthermore, each serial number for every German aircraft is present in the initial sample precisely once.

Using resampling methods like bootstrapping or permutation tests, a new resample is created by arbitrarily selecting some of the initial sample. Therefore, depending on the precise resampling technique employed, the sample amount of the resample may be the same as the initial sample or it may be smaller or bigger.

Complete Question:

which of the following statements are true?

a. the resample can contain serial numbers that are not in the original sample.

b. the original sample can contain serial numbers that are not in the resample.

c. because the sample size is small, the histogram of the resample might look very different from the histogram of the original sample.

d. the resample has either zero, one, or more than one copy of each serial number.

e. the original sample has exactly one copy of each serial number for every German plane.

f. the resample has exactly the same sample size as the original sample.

Read more about sample on:

https://brainly.com/question/15212314

#SPJ4

Answer:

Sure, I can help you with that geometry problem! To find the center of a circle given two points on its circumference, we need to find the perpendicular bisector of the line segment connecting those two points. Let's first find the midpoint of line segment PQ. Midpoint M = ( (1+7)/2 , (-2+1)/2 ) M = (4, -1/2) The slope of the line PQ is: Slope of PQ = (1-(-2)) / (7-1) Slope of PQ = 3/2 The slope of the perpendicular bisector of PQ is the negative reciprocal of the slope of PQ. Slope of perpendicular bisector = -2/3 Now we can find the equation of the perpendicular bisector of PQ in point-slope form using the midpoint M:

The target population for this survey is the registered voters in the city of Raleigh who are eligible to vote in the upcoming city council election.

The target population for a survey refers to the specific group of people that the survey is intended to represent or provide information about. In this case, the survey was conducted to gather information about the voting preferences of registered voters in the city of Raleigh for the upcoming city council election. Therefore, the target population for this survey would be the registered voters in the city of Raleigh who are eligible to vote in this election.

It's important to note that the target population is not the same as the sample population. The sample population refers to the group of people who actually participated in the survey, while the target population refers to the larger group of people that the sample population is intended to represent. In this case, the sample population was the 350 randomly selected registered voters who participated in the telephone poll.

Learn more about target population here

brainly.com/question/30019807

#SPJ4

The missing entries are (a) $686, (b) $635, (c) $1035, (d) $1010, (e) $938.88 and (f) $447.37.

A debit card is one that a person owns, and when they use it to make a purchase, the money is instantly withdrawn from or added to their account.

A table listing Gino's debit card purchases is provided.

He has made a $778.19 starting deposit.

The disparity between the old balance and the payment will be the new balance in the account.

He spent $92.19 on the bat.

a = $778.19 - 92.19 = $686

He bought gas for $51.00.

b = $686 - $51 = $635

He deposited $400.

c = $635 + $400 = $1035

He paid $25 for gas.

d = $1035 - $25 = $1010

Dinner at Spooner's on the shore cost him $71.12.

e = $1010 - $71.12 = $938.88

He spent $491.51 on books for the entire term.

f = $938.88 - $491.51 = $447.37

The missing records are thus discovered.

To know more about debit card, visit:

https://brainly.com/question/28877487

#SPJ1

Answer: 1/8 or 0.125 in decimal form

Step-by-step explanation: Reduce the expression by cancelling the common factors.

Even if the sample is representative and the survey questions are well-crafted, there is a possibility that the findings will differ from those of the actual population due to sampling error.

Sampling bias: The survey sample may not be representative of the community, resulting in an imbalance between the representation of some groups in the sample. As a result, there may be inaccuracies in the findings because the sample may not fairly represent the population's diversity. There are a number of factors why survey results might not be a reliable indicator of what the population will actually do. The following claims may help to clarify this:

Non-response bias: A biassed sample may result if some members of the sample decide not to take part in the poll. If the non-response rate is high among specific groups, such as minority groups or low-income households, this may be a particular issue.

Social preference bias: Respondents may be influenced to provide answers that make them appear more desirable.Instead of being fully honest, I'll be polite. As a result, socially acceptable behaviour may be overreported while socially unacceptable behaviour may be underreported.

topic wording: How a topic is worded can have an impact on the responses it receives. It's possible that ambiguous or deceptive questions don't accurately represent the respondent's true viewpoint.

Response options: How respondents react to a survey can also be influenced by the response options that are offered. Respondents might feel under pressure to select a response that doesn't accurately represent their opinions, for instance, if the choices are few or don't include a "neutral" option.

Learn more about population here:

https://brainly.com/question/27991860

#SPJ1

Answer:

Let the radii of two cylinders be 4x and 5x and their heights be 7y and 6y respectively. The lateral surface area of a cylinder is given by the formula 2πrh where r is the radius and h is the height. The lateral surface area of the first cylinder is 2π(4x)(7y) = 56πxy. The lateral surface area of the second cylinder is 2π(5x)(6y) = 60πxy. Therefore, the ratio of their lateral surface area is 56πxy : 60πxy which can be simplified to 14:15. Hence, the ratio of their lateral surface area is 14:15.

Answer:

8. c ≈ 7,2 cm

9. b ≈ 6,7 in

Step-by-step explanation:

Use the Pythagorean theorem for each of these problems:

8.

[tex] {c}^{2} = {6}^{2} + {4}^{2} = 36 + 16 = 52[/tex]

[tex]c > 0[/tex]

[tex]c = \sqrt{52} ≈7.2[/tex]

.

9.

[tex] {b}^{2} = {7}^{2} - {2}^{2} = 49 - 4 = 45[/tex]

[tex]b > 0[/tex]

[tex]b = \sqrt{45} ≈6.7[/tex]