Nadia compares the weights, in grams, of some apples and oranges. She finds the median and


interquartile range of the weights.



Apple sample: median=150 interquartile range=8



Orange sample: median=130 interquartile range=11



1. Which sample has a greater typical value, or median?



2. Which sample has a greater variability, or spread?



3. According to these measures, is it possible the the heaviest piece of fruit in the two samples was an orange? Explain why or why not.



I need an answer soon

A 95% confidence interval for the true population proportion of people who received flu vaccinations this year is  0.067 < p < 0.133.

To construct a 95% confidence interval for the true population proportion of people who received flu vaccinations, we can use the formula:

CI = p ± z√((p(1-p))/n)

where:

CI is the confidence interval

p is the sample proportion (33/300 = 0.11)

z is the z-score associated with a 95% confidence level, which is approximately 1.96

n is the sample size (300)

Substituting the values, we get:

CI = 0.11 ± 1.96√((0.11(1-0.11))/300)

CI = 0.11 ± 0.043

CI = (0.067, 0.133)

Therefore, the 95% confidence interval for the true population proportion of people who received flu vaccinations is 0.067 < p < 0.133.

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Patrick's method of depositing $300 as the principle amount with an interest rate of 6% compounded quarterly results in more money after two years, with a final amount of $337.95.

To compare the two methods, we need to calculate the total amount of money each person will have after 2 years.

For Patrick:
The formula for compound interest is: A = P (1 + r/n)^(nt)
Where:
A = the total amount of money after t years
P = the principle amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

So for Patrick, we have:
A = 300 (1 + 0.06/4)^(4*2)
A = 300 (1.015)^8
A = 300*1.1265 = 337.95

After 2 years, Patrick will have $337.95.

For Brooklyn:
Using the same formula, we have:
A = 300 (1 + 0.05/12)^(12*2)
A = 300 (1.004167)^24
A = 300 * 1.10495 = 331.485

After 2 years, Brooklyn will have $331.485.

Therefore, Patrick's method of depositing $300 as the principle amount with an interest rate of 6% compounded quarterly results in more money after two years. Patrick will have $337.95, which is slightly more than Brooklyn with $331.485.

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The value of x is [tex]\sqrt{\frac{2}{6} }[/tex]

A function can be defined as a law or expression showing the relationship between two variables.

From the information given, we have that;

f(x) = x ^ 2 + 1

g(x) = 3x

To determine the composite function, substitute the value of the function inside the bracket and the value of x in the other function, we have;

fg(x) = (3x²) + 1

expand the bracket

fg(x) = 9x² + 1

Then,

gf(x) = 3(x² + 1)

expand the bracket

gf(x) = 3x² + 3

Equate the functions, we have;

9x² + 1 = 3x² + 3

collect the like terms

6x² = 2

Divide the value

x = [tex]\sqrt{\frac{2}{6} }[/tex]

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The set that includes ONLY rational numbers that are also integers is:

{-3, -2, -1, 0, 1, 2, 3, ...}

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Answer:

20 tanks

Step-by-step explanation:

if each tank holds 6 fish and there are 115 fish, you need to divide the amount of fish total by amount that go in 1 tank:

115/6 = 19.1666666667

Now we round up bc we cant leave any fish out right?

So your answer is 20 tanks will be needed to hold 115 fish if it’s 6 fish per tank.

Check this by multiplying the tanks and fish in every tank:

20 x 6 = 120

Meaning that 115 fish go into 20 tanks, one of the tanks just having 1 fish :D

Answer: 20 is the correct option.

Step-by-step explanation:Given that a pet store has 115 fish that need to be placed into fish tanks and each tank hold 6 fish.

We are to find the number of tanks that the store need.

We will be using the UNITARY method to solve the given problem.

Number of tanks needed to store 6 fishes = 1.

So, number of tanks needed to store 1 fish will be [tex]\frac{1}{6}[/tex]

Therefore, number of tanks needed to store 115 fishes is given by

[tex]\frac{1}{6}[/tex] × 155 =[tex]\frac{115}{6}[/tex]= 19 [tex]\frac{1}{6}[/tex] = 19.16.

Since we cannot have 0.16 tank, so we need one tank more than 19 to store all fishes.

Thus, the store needs 20 tanks for 115 fishes.

Hope this helps :)

the probability of choosing H or P in either selection is 0.84

Two random letters are selected from the word Happy, and we want to find the probability of choosing H or P in either selection.

There are 5 letters, 1 is an H, 2 are P's.

Then the probability of selecting one of these 3 in the first selection is:

p = 3/5 = 0.6

And if we don't chose any of these in the first selection we had the probability:

q = 2/5 = 0.4 (choosing one of the a's)

the probability of choosing one of the p's or the H in the second is again:

q' = 3/5 = 0.6

The joint probability is:

Q = q*q' = 0.4*0.6 = 0.24

Then the total probability is:

p + Q = 0.6 + 0.24 = 0.84

The correct option is the second one.

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To predict how many students might enjoy swimming during the summer break, we will use the information from Mrs. Baker's survey. According to her survey, 21 out of 30 students preferred to go swimming during the summer break.

Step 1: Find the fraction representing the proportion of students who preferred swimming:
21 students preferred swimming / 30 total students = 21/30

Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3:
[tex](21 ÷ 3) / (30 ÷ 3) = 7/10[/tex]

Step 3: Use the simplified fraction to predict the number of students who might enjoy swimming in a school with 1200 students:
[tex]7/10 * 1200 = (7 * 1200) / 10[/tex]

Step 4: Perform the calculations:
[tex]7 * 1200 = 8400[/tex]
8400 / 10 = 840

Your answer: Based on Mrs. Baker's survey, we predict that approximately 840 students out of the total 1200 students might enjoy swimming during the summer break.

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The test statistic (or standard score) would be 1.72.

To convert the outcome of the pulse rate data to a standard score, we would need to calculate the z-score. The formula for the z-score is: (sample mean - population mean) / (standard deviation / square root of sample size).

In this case, the sample mean is 76, the population mean (according to the report) is 72, the standard deviation is 13, and the sample size is 85. Plugging these values into the formula, we get:

(76 - 72) / (13 / sqrt(85)) = 1.72.

Therefore, the test statistic (or standard score) is 1.72. This indicates that the sample mean of 76 is 1.72 standard deviations above the population mean of 72. This information can be used to conduct a statistical test of significance and determine whether the difference between the sample mean and population mean is statistically significant.

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A) Irene pays $44 for the earrings.

B) Irene’s friend received $22 as credit.

C) Percent change from what Irene paid and what her friend returned it for is 50%

A) Cost of earing = $55

Discount coupon = 20%

Total cost Irene pay = 55 - (20% of 55)

Total cost Irene pay  = 55 - ( 55 × 20/100)

Total cost Irene pay = 55 - 11

Total cost Irene pay = 44

B) Credit given by store = 50%

Credit received = 50% of 44

Credit received = 44 × 50/100

Credit received = 22

C) Percent change = [tex]\frac{final - initial }{initial}[/tex] × 100

Percent change = [tex]\frac{44-22}{44}[/tex] × 100

Percent change = 50%

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To solve this equation, we first simplify both sides of the equation by using the distributive property to expand the right-hand side:

4x + 5 = 6(x + 3) - 20 - 2x

4x + 5 = 6x + 18 - 20 - 2x

Next, we can combine like terms on the right-hand side:

4x + 5 = 4x - 2

Now, we can subtract 4x from both sides to isolate the variable on one side of the equation:

4x - 4x + 5 = 4x - 4x - 2

5 = -2

This is a contradiction since 5 cannot be equal to -2. Therefore, there is no solution to this equation.

In other words, the equation is inconsistent and there is no value of x that can make it true.

Answer:41,160 meters in 2 minutes at the speed of 343 meters per second.

Step-by-step explanation:

The speed of sound varies depending on the medium it's traveling through, but assuming you meant the speed of sound in air at room temperature, it's approximately 343 meters per second.

To find out how far sound will travel in 2 minutes (120 seconds), we can simply multiply the speed of sound by the time:

Distance = Speed x Time

Distance = 343 m/s x 120 s

Distance = 41,160 meters

Therefore, sound will travel approximately 41,160 meters in 2 minutes at the speed of 343 meters per second.

Miguel will wait for 6 minutes in line, there are 6 employees working.

Joni will wait 3 minutes to order when 8 employees are working.

Here are the steps to answer your questions:

1. If Miguel waits 6 minutes in line to order, predict the number of employees working:

We have the trend line equation y = -1.5x + 15, where y is the waiting time in minutes, and x is the number of employees. We are given that Miguel waits for 6 minutes, so we'll plug y = 6 into the equation and solve for x:

6 = -1.5x + 15

To solve for x, first subtract 15 from both sides of the equation:

6 - 15 = -1.5x
-9 = -1.5x

Now, divide both sides by -1.5:

x = -9 / -1.5
x = 6

So, when Miguel waits 6 minutes in line, there are 6 employees working.

2. Joni arrives at the restaurant when 8 employees are working. Predict the amount of time Jodi will wait to order:

We'll use the same trend line equation and plug in x = 8 to find the waiting time for Joni:

y = -1.5(8) + 15

Multiply -1.5 by 8:

y = -12 + 15

Now, add 15:

y = 3

Joni will wait 3 minutes to order when 8 employees are working.

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The angle in degrees used to indicate the b region is 70.

The total number of students= Sum of the number of students with different grades and the failed ones.

                                          = 50+75+114+98+50

                                          = 387

Now,

The number of students in b region, that is, those who got b's

=75      (given)

We know that,

The sum of all angles due to different grades in the pie chart = 360 degrees.

So the distribution of degrees to b region in the pie chart will be in proportion to the number of students in b region out of total students

Let x degrees be used to indicate the "b" region.

∴ x/360=75/387              (because of the same proportion)

⇒x=75/387×360

⇒x=69.76≅70

Hence, the angle in degrees used to indicate the b region is 70.

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The nth term of the sequence 4 5 6 7 5 6 7 8 is given by a_n = 3 + (n-1)/2 for odd n and a_n = 4 + (n-2)/2 for even n.

To find the nth term of the given sequence, we need to observe the pattern in the sequence. We can see that the sequence consists of two parts:

the first part is a consecutive sequence of integers starting from 4, and the second part is a consecutive sequence of integers starting from 5, where the second part starts right after the first part ends.

So, we can express the nth term of the sequence as follows:

If n is odd, then the nth term is given by:

a_n = 3 + (n-1)/2

If n is even, then the nth term is given by:

a_n = 4 + (n-2)/2

Using this formula, we can find any term of the given sequence by plugging in the corresponding value of n. For example:

When n=1, the first term is 4: a_1 = 4.

When n=6, the sixth term is 6: a_6 = 6.

When n=7, the seventh term is 7: a_7 = 7.

When n=8, the eighth term is 8: a_8 = 8.

Note that this formula works only for n = 1, 2, 3, 4, 5, 6, 7, 8, ... , since the sequence has only 8 terms.

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Alex will have to put money in his savings account for 15 more weeks at a rate of $8 per week.

Alex purchased a cell phone for $200 using money from his savings account. He plans to replace the money in his savings account at the rate of $8 per week. He has already replaced $80, which means he needs to replace $120 more to have the entire amount. Since he is replacing the money at a rate of $8 per week, he will need 15 more weeks to replace the remaining amount. Therefore, he will have to put money in his savings account for 15 more weeks to replace the entire $200 he spent on the cell phone. By doing so, he will be able to maintain his savings and avoid any financial loss.

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The directional derivative of f(x, y, z) = z³ – x²y at the point (3,-1, -2) in the direction of the vector v=(-1,-4,-4) is -234/√33.

The function is f(x, y, z) = z³ – x²y

We have to find directional derivative at the point (3, -1, -2)

In the direction vector v = (-1, -4, -4)

The gradient of the function is

∇f(x, y, z) = ∂f/∂x [tex]\hat{i}[/tex] + ∂f/∂y [tex]\hat{j}[/tex] + ∂f/∂z [tex]\hat{k}[/tex]

∇f(x, y, z) = ∂/∂x(z³ – x²y) [tex]\hat{i}[/tex] + ∂/∂y(z³ – x²y) [tex]\hat{j}[/tex] + ∂/∂z(z³ – x²y) [tex]\hat{k}[/tex]

∇f(x, y, z) = -2xy[tex]\hat{i}[/tex] - x²y[tex]\hat{j}[/tex] + 3z²[tex]\hat{k}[/tex]

At the point (3, -1, 4).

∇f(3, -1, 4) = -2(3)(-1)[tex]\hat{i}[/tex] - (3)²(-1)[tex]\hat{j}[/tex] + 3(4)²[tex]\hat{k}[/tex]

∇f(3, -1, 4) = 6[tex]\hat{i}[/tex] + 9[tex]\hat{j}[/tex] + 48[tex]\hat{k}[/tex]

The length of the vector is

|v| = √[(-1)² + (-4)² + (-4)²]

|v| = √[1 + 16 + 16]

|v| = √33

To normalize the vector we have

n = (-√33/33, -4√33/33, -4√33/33)

The directional derivative is

∇f(x, y, z) · n = (6, 9, 48) · (-√33/33, -4√33/33, -4√33/33)

∇f(x, y, z) · n = -6√33/33 - 36√33/33 - 192√33/33

∇f(x, y, z) · n = (-6 - 36 - 192)√33/33

∇f(x, y, z) · n = -234√33/33

∇f(x, y, z) · n = -234/√33

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The height of the second bridge that Armando needs to design is 40 feet (Option C).

To get the height of the second bridge designed by Armando, we need to maintain the same ratio between the length and height as in the first suspension bridge drawing. The first bridge has a length of 230 ft and a height of 50 ft.
First, find the ratio of the height to the length of the first bridge:
50 ft (height) / 230 ft (length) = 5/23
Now, we know the length of the second bridge is 184 ft. To get the height of the second bridge, we will use the same ratio (5/23) and multiply it by the length of the second bridge:
(5/23) * 184 ft = 40 ft
So, the height of the second bridge that Armando needs to design is 40 feet (Option C).

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John is approximately 68.26 km away from his starting point after riding 68 km south and then 6 km west.

To find out how far John is from his starting point after riding 68 km south and then 6 km west, we will use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we will consider the 68 km south as one side, and the 6 km west as the other side, with the distance from the starting point being the hypotenuse.

Step 1: Square the lengths of the two given sides.
68^2 = 4624
6^2 = 36

Step 2: Add the squared values together.
4624 + 36 = 4660

Step 3: Find the square root of the sum to get the length of the hypotenuse (distance from the starting point).
√4660 ≈ 68.26 km

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The statistics indicate that the assumption that the four populations have the same standard deviation has been broken.

a. This research was done via observation.

False, as this is a test. (unlike what Alex89 says). The response variable (minutes of rest) is then recorded because the researcher randomly assigns the fruit flies to one of the treatments, using a TREATMENT, and records the response variable.

b. The statistics indicate that the assumption that the four populations have the same standard deviation has been broken.

False: There is no deviation from the equality of standard deviations. We DO NOT need to test this assumption when the sample sizes are equal. Even if we did, 29.61/19.08 = 1.55 2 means that the greatest standard deviation is less than twice the lowest standard deviation. We are therefore okay.

c. Because ANOVA needs sample sizes, it may be applied to this data are equal.

False - The ANOVA does NOT require equal sample sizes.

3. The correct option is D, For this example, we notice that 3) None of the above

(4) The correct is option A, which states that 4) the population mean rest is the same for all four caffeine concentrations.

Statistics provides a framework for making informed decisions based on data by using methods such as probability theory, hypothesis testing, regression analysis, and statistical modeling. The importance of statistics lies in its ability to transform raw data into meaningful information that can be used to make decisions, develop policies, and solve problems in a wide range of fields, including business, healthcare, government, and social sciences.

Statisticians use various tools and techniques to summarize and describe data, identify patterns and relationships, and make predictions and inferences. They also play a critical role in designing experiments, surveys, and observational studies, ensuring that they are statistically sound and produce reliable results.

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Complete Question:-

An experiment to help determine if insects sleep gave caffeine to fruit flies to see if it affected their rest. The three treatments were a control, a low caffeine dose of 1 mg/ml of blood, a medium dose of 3 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest measured over a 24-hour period was recorded. The data follow.

Treatment Minutes of rest

Control 450 413 418

Low dose 466 422 435

Medium dose 421 453 419

High dose 364 330 389

Assume the data are three independent SRSs, one from each of the four populations of caffeine levels, and that the distribution of the yields is Normal.

A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups.

One-way ANOVA: Rest versus Caffeine

Source DF SS MS F P

Caffeine 11976

Error 538.75

Total

Level N Mean StDev

Control 3 427.00 20.07

Low 3 441.00 22.61

Medium 3 431.00 19.08

High 3 361.00 29.61

3. For this example, we notice that 3) __________

a. this is an observational study.

b. the data show evidence of a violation of the assumption that the four populations have the same standard deviation.

c. ANOVA can be used on these data because ANOVA requires the sample sizes are equal.

d. None of the above

4. The null hypothesis for the ANOVA F test is that 4) __________

a. the population mean rest is the same for all four levels of caffeine.

b. the population mean rest is increasing as the caffeine level gets larger.

c. the population mean rest is decreasing as the caffeine level gets larger.

d. the population mean rest is largest for the high level of caffeine.

Using the compounding interest formula:

a) His ending balance after the year will be $7,658.91.

b) The amount of interest he will earn is $358.91.

c) His annual percentage yield is 4.9166%.

a) To calculate the ending balance after one year, we'll use the compound interest formula: A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal ($7,300), r is the interest rate (4.85% or 0.0485), n is the number of compounding periods per year (4 for quarterly), and t is the number of years (1).

A = 7300(1 + 0.0485/4)^(4*1) = 7300(1.012125)⁴ = 7300*1.049166 = $7,658.91

b) To find the interest earned, subtract the principal from the ending balance: Interest = A - P

Interest = $7,658.91 - $7,300 = $358.91

c) To calculate the annual percentage yield (APY), we'll use the formula: APY = (1 + r/n)^(n) - 1

APY = (1 + 0.0485/4)⁴ - 1 = 1.049166 - 1 = 0.049166 or 4.9166%

Paul's ending balance after one year is $7,658.91, he earns $358.91 in interest, and his annual percentage yield is 4.9166%.

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Answer:

Angle C also measures 64°.

The spherical coordinates for the given rectangular coordinates (7, 7, 2/7) are (ρ, θ, φ) = (10, 45°, 88.57°) or (10, π/4, 1.545) in radians.

We'll need to find ρ (rho), θ (theta), and φ (phi) using the given rectangular coordinates (x, y, z). Here's the step-by-step process:

1. Calculate ρ (rho): ρ is the distance from the origin to the point in 3D space. You can find it using the formula: ρ = √(x² + y² + z²)

In this case, x = 7, y = 7, and z = 2/7.

Plugging these values into the formula: ρ = √(7² + 7² + (2/7)²) ρ = √(49 + 49 + 4/49) ρ = √(98 + 4/49) ρ = √(4900/49) ρ = 10

2. Calculate θ (theta): θ is the angle in the xy-plane, measured from the positive x-axis. You can find it using the formula: θ = arctan(y/x)

In this case, x = 7 and y = 7.

Plugging these values into the formula: θ = arctan(7/7) θ = arctan(1) θ = 45° (in degrees) or π/4 (in radians)

3. Calculate φ (phi): φ is the angle between the positive z-axis and the line connecting the origin to the point. You can find it using the formula: φ = arccos(z/ρ)

In this case, z = 2/7 and ρ = 10.

Plugging these values into the formula: φ = arccos((2/7)/10) φ = arccos(1/35) φ ≈ 88.57° (in degrees) or ≈ 1.545 (in radians)

So, the spherical coordinates for the given rectangular coordinates (7, 7, 2/7) are (ρ, θ, φ) = (10, 45°, 88.57°) or (10, π/4, 1.545) in radians.

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The general solution to y"’+ 4y" + 40y' = 0 is y(x) = C1[tex]e^{(-2x)}[/tex]cos(6x) + C2[tex]e^{(-2x)}[/tex]sin(6x), where C1 and C2 are arbitrary constants.

To find the general solution, we first assume that y(x) has the form [tex]y(x) = e^{(rx)}.[/tex]

Substituting this into the differential equation, we get the characteristic equation r³ + 4r² + 40r = 0.

Factoring out r, we get r(r² + 4r + 40) = 0. The quadratic factor has no real roots, so we can write r = 0, -2 ± 6i.

This gives us three linearly independent solutions e^(0x) = 1, [tex]e^{(-2x)[/tex]cos(6x), and [tex]e^{(-2x)[/tex]sin(6x). Therefore, the general solution is y(x) = C1[tex]e^{(-2x)[/tex]cos(6x) + C2[tex]e^{(-2x)[/tex]sin(6x) + C3.

Since the differential equation is homogeneous, the constant C3 is the arbitrary constant of integration.

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An equation to model this situation will be S(t) = 4 * 10^(t). The average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.

a. Let S(t) be the number of shares of the video at time t in minutes after Steph Curry shared it with his friends. The initial number of shares is 4 (the 4 friends he shared it with), and the number of shares increases by a factor of 10 every minute. Therefore, we can model this situation with the exponential function:

S(t) = 4 * 10^(t)

b. The average rate of change for the number of shares from 2 minutes to 4 minutes can be calculated by finding the slope of the line connecting the points (2, S(2)) and (4, S(4)) on the graph of S(t). Using the equation S(t) = 4 * 10^(t), we have:

S(2) = 4 * 10^(2) = 400

S(4) = 4 * 10^(4) = 40,000

The slope of the line connecting these two points is:

(S(4) - S(2)) / (4 - 2) = (40,000 - 400) / 2 = 19,800

Therefore, the average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.

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Answer:

Sarah will have $937.28 and Claire will have $928.

Step-by-step explanation:

All my work is provided in the screenshots that are attached to my answer! Drop questions in the comments and I'll try to respond if I remember/see them lol.

Have a great day!

The height of the flagpole is approximately 23.7 feet.

We can use the tangent function to solve this problem. Let's call the height of the flagpole "h". From the ground, we have a right triangle with the flagpole height as the opposite side, the distance to the flagpole as the adjacent side, and the angle of elevation as the angle opposite the flagpole height.

Using the tangent function, we can write:

tan(39°) = h/32

Solving for h, we get:

h = 32 * tan(39°)

h ≈ 23.7 feet

Therefore, the height of the flagpole is approximately 23.7 feet when viewed from a distance of 32 feet at an angle of elevation of 39°.

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Answer:

Step-by-step explanation:

The possible outcomes of rolling a fair six-sided die are the numbers 1, 2, 3, 4, 5, and 6, each of which has an equal probability of $\frac{1}{6}$ of appearing.

The probability of rolling a number greater than 1 is $\frac{5}{6}$, since there are five out of six possible outcomes that satisfy this condition (namely, 2, 3, 4, 5, and 6).

The probability of rolling a number less than 3 is $\frac{2}{6}=\frac{1}{3}$, since there are two out of six possible outcomes that satisfy this condition (namely, 1 and 2).

To find the probability of both events happening (rolling a number greater than 1 and then rolling a number less than 3), we can multiply their respective probabilities:

$\frac{5}{6}\cdot\frac{1}{3}=\frac{5}{18}$

Therefore, the probability of rolling a number greater than 1 and then rolling a number less than 3 is $\boxed{\frac{5}{18}}$.