Three common shapes can be made out of equilateral triangles. What are they?

Given that tan D = 0.28 To approximate the value of D, we can use the inverse tangent function tan⁻¹(0.28) on a calculator:

D ≈ 15.9° (rounded to one decimal place)

Therefore, the measurement of angle D to the nearest tenth of a degree is approximately 15.9°.Explanation:We know that tangent of angle D is 0.28.tan D = 0.28 To find the value of D, we need to take the inverse tangent of 0.28.

i.e, D = tan⁻¹(0.28)We use a calculator to evaluate this expression.

D ≈ 15.9° (rounded to one decimal place)

Therefore, the measurement of angle D to the nearest tenth of a degree is approximately 15.9°.

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The line tangent to the graph of f at x and to the graph of g at x is given by yx.

To find the line tangent to the curves at x, we can determine the slopes of the curves at that point. The slope of the tangent line to the graph of f at x is equal to the derivative of f evaluated at x. Similarly, the slope of the tangent line to the graph of g at x is given by the derivative of g evaluated at x. Since both tangent lines have the same slope, the derivatives of f and g must be equal at x. By finding the common derivative, we can obtain the slope of the tangent line, and by using the point-slope form, we can determine the equation of the line.

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Consider two functions, f(x) and g(x), with graphs in a coordinate plane. Suppose there exists a point (x, f(x)) on the graph of f, where the tangent line to f at that point is represented by the equation y = x. Additionally, suppose the same tangent line, y = x, is also the tangent line to the graph of g at the point (x, g(x)). Find the equation of the tangent line to each of the following curves at the given x-values.

Expression for the number of points Arnav scored is (1/4)P + 6, where P represents the number of points Arnav's team scored.

Let P represent the number of points Arnav's team scored.

So, Arnav scored 6 more than one fourth of P.

In the last basketball game, Arnav scored 6 more than one fourth of his team's points.

Therefore, the points that Arnav scored is given by (1/4)P + 6, where P represents the number of points Arnav's team scored.

The expression (1/4)P + 6 represents the number of points Arnav scored in the last basketball game, where P is the number of points Arnav's team scored.

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Answer:

27 1/2 inch

Step-by-step explanation:

If Robert has a container in the shape of a cube with an edge length of 6.1 cm, we can calculate various properties of the cube.

Volume of the cube: The volume of a cube is calculated by cubing the length of its edges. In this case, the volume would be: Volume = (6.1 cm)^3 = 226.651 cm³ (rounded to three decimal places). Surface area of the cube: The surface area of a cube is calculated by multiplying the area of one face by the total number of faces (which is six for a cube). Since all the faces of a cube have the same area, we can find the area of one face and then multiply it by six.  Surface Area = 6 * (6.1 cm)^2 = 223.092 cm² (rounded to three decimal places). Diagonal of the cube: The diagonal of a cube can be found using the Pythagorean theorem. In this case, Diagonal = √(6.1 cm)^2 + (6.1 cm)^2 + (6.1 cm)^2 = √(3 * (6.1 cm)^2) = √(3 * 37.21 cm²) ≈ 9.622 cm (rounded to three decimal places).

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The measure of angle DBC is half the measure of its intercepted arc AD. Therefore, if arc AD measures 118 degrees, angle DBC measures 59 degrees.

To find the measure of angle DBC, we need to use the properties of angles formed by intersecting chords and arcs in a circle.

In this case, we are given that the measure of arc AD is 118 degrees. By the Inscribed Angle Theorem, the measure of angle DBC is equal to half the measure of its intercepted arc, which is arc AD.

Therefore, the measure of angle DBC is 118 degrees divided by 2, which is 59 degrees.

Thus, the measure of angle DBC is 59 degrees.

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Tori and her two friends listened to music for a total of 2 hours and 2/5 of an hour (or 2.4 hours) in all.

Tori and her two friends each listened to music for 4/5 of an hour.

To find out how long they listened to music in total, we need to multiply the duration by the number of people.

Since Tori and her two friends listened to music for the same amount of time, we can simply multiply the duration by 3 (to account for Tori and her two friends).

Duration per person: 4/5 hour

Total duration: (4/5) [tex]\times[/tex] 3 = 12/5 hour

To simplify the fraction, we can express 12/5 as a mixed number.

Since 5 goes into 12 evenly twice, with a remainder of 2, the total duration can be written as 2 2/5 hours.

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Therefore, the possible numbers of minutes Linda has used her phone in a month are 1459 minutes or more.

To determine the possible number of minutes Linda has used her phone in a month, we can set up an equation based on the given information.

Let's assume the number of minutes Linda has used her phone in a month is represented by 'm'.

The total charge for the phone service consists of the monthly fee of $27 plus the additional charge of $0.07 per minute:

Total charge = $27 + $0.07 * m

According to the given information, the least amount Linda has been charged in a month is $129.13. So we can set up the following equation:

$27 + $0.07 * m ≥ $129.13

Now we can solve this equation to find the possible range of values for 'm'.

$0.07 * m ≥ $129.13 - $27

$0.07 * m ≥ $102.13

m ≥ $102.13 / $0.07

m ≥ 1459

Therefore, the possible numbers of minutes Linda has used her phone in a month are 1459 minutes or more.

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The surface area of the roof of the kennel, including the bottom face, is 51 square feet. The correct answer is D. 51 square feet.

To calculate the surface area of the roof of the kennel, including the bottom face, we need to find the area of the triangular prism. The surface area of a prism can be calculated by adding the areas of all its faces. In this case, the triangular prism has two triangular faces and three rectangular faces.

First, we calculate the area of the triangular faces. The formula for the area of a triangle is (base * height) / 2. Since the triangular prism has a bottom face included, the triangular faces share the same base. Let's assume the base of the triangle is 6 feet and the height is 8 feet. The area of one triangular face is (6 * 8) / 2 = 24 square feet. Since there are two triangular faces, the total area of the triangular faces is 2 * 24 = 48 square feet.

Next, we calculate the area of the rectangular faces. Let's assume the length of the kennel is 8 feet, the width is 4 feet, and the height is 6 feet. The area of one rectangular face is length * width, which is 8 * 4 = 32 square feet. Since there are three rectangular faces, the total area of the rectangular faces is 3 * 32 = 96 square feet.

Finally, we add the areas of the triangular faces and rectangular faces to get the total surface area of the roof: 48 + 96 = 144 square feet. However, since the question asks for the surface area of the roof, including the bottom face, we subtract the area of the bottom face, which is the same as the area of one rectangular face: 32 square feet. Thus, the final surface area is 144 - 32 = 112 square feet, which corresponds to option D: 51 square feet.

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Answer: To determine how much Thomas and Candice charged to mow a lawn, we can compare their total earnings (including tips) to the number of lawns they mowed.

Thomas mowed 35 lawns and received $150 in tips. Let's denote the amount Thomas charged to mow a lawn as "x."

Total earnings for Thomas = Earnings from lawns + Tips

Total earnings for Thomas = (35 * x) + $150

Similarly, Candice mowed 30 lawns and received $275 in tips. Let's denote the amount Candice charged to mow a lawn as "y."

Total earnings for Candice = Earnings from lawns + Tips

Total earnings for Candice = (30 * y) + $275

Since both Thomas and Candice charged the same amount per lawn, we can set their total earnings equations equal to each other:

(35 * x) + $150 = (30 * y) + $275

Now, we can solve this equation to find the amount they charged per lawn.

35x + $150 = 30y + $275

Rearranging the equation:

35x - 30y = $275 - $150

35x - 30y = $125

To simplify the equation, we need to know the specific values of x and y, which are the amounts they charged per lawn. Without additional information, we cannot determine the exact values of x and y or how much they charged to mow a lawn.

Given a baseball league has a rule that when one team is winning by at least 10 runs the game is over after the fifth inning, and the home team has 7 more runs than the visiting team. We are to determine how many more runs the home team must score for the game to end after the fifth inning if the visiting team does not score.

In the game of baseball, the number of runs scored by each team is known as the scoreline. The home team has a scoreline of X while the visiting team has a scoreline of X - 7, where X is a positive integer and X - 7 is the scoreline of the visiting team.

Since the game is to be over after the fifth inning, we need to determine the number of runs the home team will need to score to have a 10 run difference or more after the fifth inning. Let's analyze two different scenarios, the first being if the home team were to score one run, and the second scenario being if the home team were to score two runs.

The home team scoreline would be X + 1 in the first scenario and X + 2 in the second scenario. In both cases, the visiting team does not score any additional runs. Thus, the scoreline of the visiting team remains X - 7 in both scenarios.

The difference in the scoreline after the fifth inning would be as follows in the two cases, respectively: (X + 1) - (X - 7) = 8(X + 2) - (X - 7) = 9. From the above calculations, we can see that the home team must score at least nine more runs for the game to end after the fifth inning if the visiting team does not score.

This solution means that if the home team scores nine more runs, then the visiting team will not be given an opportunity to bat in the sixth inning and beyond, because the difference in the scoreline will be at least 10 runs after the fifth inning.

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The third quartile of the dataset is 6.5

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

3,4,3,9,3,5,8,5

Sort the number in ascending order

So, we have

3, 3, 3, 4, 5, 5, 8, 9

Split the number into equal halves

So, we have

3, 3, 3, 4,

5, 5, 8, 9

The third quartile is the median of the second half

so, we have

The third quartile = (5 + 8)/2

Evaluate

The third quartile = 6.5

Hence, the third quartile is 6.5

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The quadratic formula can be easily programmed into a TI-84 Plus by following these simple steps. This can save a lot of time and effort when solving quadratic equations, and can help you to quickly find the roots of these equations.

The quadratic formula is a useful mathematical formula that can be programmed into a calculator like the TI-84 Plus. This formula can be used to find the roots of a quadratic equation, which can be useful in solving various types of problems. Here's how to program the quadratic formula into a TI-84 Plus:
1. Press the "PRGM" button on your calculator.
2. Select "NEW" and give your program a name (e.g. "QUAD").
3. Enter the following code:
:Prompt A,B,C
:((-B+√(B²-4AC))/(2A))->X1
:((-B-√(B²-4AC))/(2A))->X2
:Disp X1,X2
4. Save your program and exit.
This code prompts the user to enter the values of A, B, and C (which are the coefficients of the quadratic equation), and then calculates the two roots of the equation using the quadratic formula. The roots are then displayed on the screen.
Note that the "√" symbol is entered by pressing the "MATH" button and selecting "1:√( )" from the menu. Also, the "->" symbol is entered by pressing the "STO->" button.
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The value of X is 7/10 and the measure of angle O is 14. Angle O must also be equal to 14, as it corresponds to angle B in the congruent triangle DOG.

To find the value of X and the measure of angle O, we need to use the information provided about the congruent triangles BAT and DOG and the measures of angles B, G, and O.

Given that BAT is congruent to DOG, we know that their corresponding angles are equal.

From the given information, angle B is equal to 14 and angle G is equal to 29.

Therefore, angle O must also be equal to 14, as it corresponds to angle B in the congruent triangle DOG.

We are also given that angle O is equal to 10X + 7.

Setting up an equation, we have:

10X + 7 = 14

To solve for X, we subtract 7 from both sides:

10X = 14 - 7

10X = 7

Dividing both sides by 10:

X = 7/10

Thus, X is equal to 7/10.

Therefore, the value of X is 7/10 and the measure of angle O is 14.

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The rational subgroup concept is a subset of data where variation is due to common causes only. This type of subgroup is used in control chart analysis to make sure that variation in the process is predictable and does not include any special causes of variation.

Control charts are graphical representations of process data over time. They help in detecting the changes or variations in the process and identify the root cause of the variation. Control charts are used to analyze process performance and identify areas where improvement is needed. The rational subgroup concept plays an essential role in the control chart analysis as it helps in selecting the appropriate data to plot on the control chart.To use control charts, a subgroup of data must be selected. The rational subgroup concept ensures that the data in the subgroup is due to common causes only and does not include any special causes of variation. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention.

Control charts are graphical representations of process data over time. They help in detecting the changes or variations in the process and identify the root cause of the variation. Control charts are used to analyze process performance and identify areas where improvement is needed.The rational subgroup concept plays an essential role in the control chart analysis as it helps in selecting the appropriate data to plot on the control chart. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention. The rational subgroup concept ensures that the data in the subgroup is due to common causes only and does not include any special causes of variation. This ensures that the control chart is an accurate representation of the process performance and helps in identifying areas where improvement is needed.Overall, the rational subgroup concept is a critical part of the control chart analysis. It ensures that the control chart accurately reflects the process performance and helps in identifying areas where improvement is needed. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention.

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The trigonometric functions are: sin(x) = 7/14.8; Cos(x) = 13/14.8; Tan(x) = 7/13; Cosecant (csc): 14.8/7

sec(x) = 14.8/13; cot(x) = 13/7

To find the trigonometric functions for angle x in the given right triangle, we can use the ratios of the sides.

Sine (sin): Opposite/Hypotenuse

sin(x) = 7/14.8

Cosine (cos): Adjacent/Hypotenuse

cos(x) = (Leg adjacent to x)/Hypotenuse

cos(x) = 13/14.8

Tangent (tan): Opposite/Adjacent

tan(x) = (Leg opposite to x)/(Leg adjacent to x)

tan(x) = 7/13

Cosecant (csc): 1/Sine

csc(x) = 1/sin(x)

= 14.8/7

Secant (sec): 1/Cosine

sec(x) = 1/cos(x)

= 14.8/13

Cotangent (cot): 1/Tangent

cot(x) = 1/tan(x)

= 13/7

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Answer: :p

The question implies so, otherwise, then p=>r

Step-by-step explanation:

Both is true because p, q, and r are variables and can be any number id k if you have any answer choices tho.

Answer:

The law of syllogism tells us that if p → q and q → r then p → r is also true.

Step-by-step explanation:

. The value for R that is closest to the expected proportion based on the conditional variables is 0.10. This indicates a potential association between the variables.



In the given table, we are looking for a value for R that suggests an association between the conditional variables. To assess this, we consider the proportions in each column.

The first column labeled A has a total of 0.12 + 0.78 + 0.10 = 1.00. The second column labeled B also has a total of 0.12 + 0.78 + 0.10 = 1.00. The fourth column labeled C has a total of 0.10 + 0.78 + 0.10 = 0.98.

Since the totals for columns A, B, and C are all 1.00, we can expect the totals in the fifth column to also be 1.00 for each entry. Thus, the expected proportion for R should be 0.10, as it completes the total of 1.00.

Therefore, the value for R that most likely indicates an association between the conditional variables is 0.10.

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In a game of luck, a turn consists of a player rolling 12 fair 6-sided dice. Let X equals the number of dice that land showing "1111" in a turn.A 6-sided die has 1, 2, 3, 4, 5, and 6. the probability of rolling four "1's" in a turn is 0.077%.

Thus, the possible outcomes for rolling a 6-sided die are: [tex]{1, 2, 3, 4, 5, 6}[/tex]To find the probability of rolling a "1" on a 6-sided die, you divide the number of favorable outcomes (1) by the total number of possible outcomes (6).Probability of rolling a 1 on a 6-sided die: P(1) = 1/6Therefore, the probability of rolling four "1's" in a turn (X = 4) can be found by the following formula:[tex]P(X = 4) = (1/6)⁴ x (5/6)⁸[/tex]

Hence, probability of rolling four "1's" in a turn (X = 4) can be found by the following formula:[tex]P(X = 4) = (1/6)⁴ x (5/6)⁸Therefore, P(X = 4) = (1/6)⁴ x (5/6)⁸ = 0.0007716[/tex] or 0.077%

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In Park City, Utah, approximately 45% of the annual rainfall falls in the months of November through February. Given that the annual rainfall is 43.8 inches, we can calculate how much rain falls during those months.

To find out how much rain falls in November through February, we need to calculate 45% of the annual rainfall. We can do this by multiplying the annual rainfall by 0.45:

Rainfall in November through February = 43.8 inches * 0.45 = 19.71 inches.

Therefore, approximately 19.71 inches of rain falls in Park City, Utah during the months of November through February. This calculation is based on the assumption that the distribution of rainfall is consistent throughout the year.

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If Laura had 2 good pictures for every 3 bad pictures, we can calculate the total number of pictures she took by considering the ratio between good and bad pictures.

Let's assume x represents the number of bad pictures Laura took. According to the given ratio, she had 2 good pictures for every 3 bad pictures. Therefore, the number of good pictures can be expressed as (2/3) * x.

Since we know that Laura took a total of 72 good pictures, we can set up the equation:

(2/3) * x = 72

To solve for x, we can multiply both sides of the equation by (3/2):

x = (72) * (3/2)

x = 36 * 3

x = 108

Therefore, Laura took a total of 108 bad pictures.

To find the total number of pictures she took in all, we can add the number of good and bad pictures:

Total pictures = Good pictures + Bad pictures

Total pictures = 72 + 108

Total pictures = 180

Therefore, Laura took a total of 180 pictures.

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Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.

Janet cut a total of 9 pieces of ribbon, each measuring 0.4 meters, and 5 pieces of ribbon, each measuring 0.6 meters.

To find the total length of ribbon Janet cut, we need to calculate the sum of the lengths of all the individual pieces.

For the 9 pieces of ribbon measuring 0.4 meters each, we can multiply the length of each piece by the number of pieces: 9 * 0.4 = 3.6 meters.

Similarly, for the 5 pieces of ribbon measuring 0.6 meters each, we can calculate the total length: 5 * 0.6 = 3 meters.

To find the total length of ribbon Janet cut, we add the lengths of the two sets of ribbons together: 3.6 + 3 = 6.6 meters.

Therefore, Janet cut a total of 6.6 meters of ribbon by combining the 9 pieces of 0.4-meter ribbon and the 5 pieces of 0.6-meter ribbon.

In summary, Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.

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The approximate volume of the model volcano can be calculated using the formula for the volume of a cylinder. Given its height of 12 inches and diameter of 12 inches, we can approximate the value of pi as 3.14 and calculate the volume in cubic inches.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.

In this case, the diameter is given as 12 inches, so the radius would be half of that, which is 6 inches.

Using the value of pi as 3.14, we can substitute the values into the formula: V = 3.14 * (6^2) * 12.

Simplifying this equation gives us the approximate volume of the model volcano in cubic inches. Calculating the expression will provide the final answer.

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Trevor needs to make 10 equal payments of £1,204 each.

To calculate the amount of each of the 10 payments Trevor needs to make, we first need to determine the total cost of the boat including VAT.

The cost of the boat before VAT is £14,200. VAT is applied at a rate of 20%, so the VAT amount is:

VAT = 20% of £14,200 = £2,840

The total cost of the boat including VAT is the sum of the cost before VAT and the VAT amount:

Total cost = £14,200 + £2,840 = £17,040

Trevor has already paid a deposit of £5,000, so he needs to pay the remaining amount in 10 equal payments.

Remaining amount = Total cost - Deposit = £17,040 - £5,000 = £12,040

To find the amount of each payment, we divide the remaining amount by the number of payments:

Amount of each payment = Remaining amount / Number of payments = £12,040 / 10 = £1,204

Therefore, Trevor needs to make 10 equal payments of £1,204 each.

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Answer:

The volume of the cone is 22 cubic inches.

Step-by-step explanation:

To find the volume of the cone, we need to use the formula for the volume of a cone:

Volume of a cone = (1/3) * π * r^2 * h

Given that the height and base area of the cylinder and cone are the same, we can assume that the radius of the cylinder's base is equal to the radius of the cone's base.

We know that the volume of the cylinder is 66 cubic inches, so we can set up the equation:

66 = π * r^2 * h

To find the volume of the cone, we need to express its height in terms of the radius of the cylinder's base. The height of the cone will be equal to the height of the cylinder.

Now, let's solve for h in terms of r using the given information:

66 = π * r^2 * h

h = 66 / (π * r^2)

Substituting this value of h into the volume formula of the cone:

Volume of the cone = (1/3) * π * r^2 * (66 / (π * r^2))

Volume of the cone = (1/3) * 66

Volume of the cone = 22

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The amount of money that Ben gets is £140.

Let's denote the amount Abby gets as 2x. Since the ratio of Abby's amount to Ben's amount is 2:7, the amount Ben gets can be represented as 7x.

Chloe and Denesh each get 1.5 times the amount Abby gets, which means they each get 1.5 * 2x = 3x.

The total amount shared between Abby, Ben, Chloe, and Denesh is £360. So we can write the equation: 2x + 7x + 3x + 3x = £360.

Simplifying the equation, we have: 15x = £360.

Dividing both sides by 15, we find that x = £24.

Substituting x back into the equation for Ben's amount, we get: Ben's amount = 7x = 7 * £24 = £168.

Therefore, Ben gets £140.

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The sampling distribution of the sample minimum, in this case, consists of the values 2, 4, 6, 30, and 32, each occurring three times, and represents the range of possible minimum ages when randomly selecting two family members.



The sampling distribution of the sample minimum represents the distribution of all possible sample minimum values that can be obtained by randomly selecting two family members from the given family. To determine this distribution, we need to consider all possible combinations of two family members and calculate the minimum age within each combination.

In this case, we have five family members with ages 2, 4, 6, 30, and 32. To calculate the sample minimum, we consider all possible combinations of two family members: (2, 4), (2, 6), (2, 30), (2, 32), (4, 6), (4, 30), (4, 32), (6, 30), (6, 32), (30, 32). Within each combination, we determine the minimum age.The resulting sample minimums are: 2, 2, 2, 2, 4, 4, 4, 6, 6, 30.

The sampling distribution of the sample minimum is the distribution of these values. In this case, it is a discrete distribution with ten possible outcomes: 2, 4, 6, 30, each occurring three times, and 32 occurring once. This distribution describes the range of possible sample minimums that can be obtained by randomly selecting two family members from the given family.

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73% of mature maple trees are between 60 and 90 feet. The required percentage is 73%

Given that the heights of mature maple trees are approximately normally distributed with a mean of 80 feet and a standard deviation of 12.5 feet.

The formula for the z-score is given by:

z = (X - μ)/σ, where X = 60, μ = 80, and σ = 12.5

Substitute the values, we get

z = (60 - 80) / 12.5

= -1.6

The z-score for 60 feet is -1.6.

The formula for the z-score is given by:z = (X - μ)/σ, where X = 90, μ = 80, and σ = 12.5

Substitute the values, we get

z = (90 - 80) / 12.5= 0.8

The z-score for 90 feet is 0.8.

To find the proportion of mature maple trees between 60 and 90 feet, we need to find the area under the standard normal curve between z = -1.6 and z = 0.8.

Using the standard normal distribution table or calculator, we can find the area under the curve as follows:

Area = 0.7881 - 0.0516= 0.7365

Therefore, the proportion of mature maple trees between 60 and 90 feet is 73% (rounded to the nearest whole percent).

Hence, the correct answer is option (D).

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9/16

I think you first add all the ratios then use the answer you got as a dinominator then the ratio of the yellow counter as you nominator

Let's solve the new math question you provided.

To simplify the product (√14 - √3)(√12 √7), we can apply the distributive property.

(√14 - √3)(√12 √7) = √14 * √12 √7 - √3 * √12 √7

To simplify the square roots, we can use the property √(a * b) = √a * √b.

= √(14 * 12) * √7 - √(3 * 12) * √7

= √168 * √7 - √36 * √7

Now, we can simplify the square roots further. √168 = √(4 * 42) = 2√42, and √36 = 6.

= 2√42 * √7 - 6√7

= 2√(42 * 7) - 6√7

= 2√294 - 6√7

Therefore, the simplified product is 2√294 - 6√7.

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