.(10 points) In the following, A, B are real numbers. You do NOT need to find them to answer the questions below. (a) The possible POSITIVE rational roots of 3r³+ Ar2+Bz-14 are (b) The graph of y = 3a + Ar + Br-14 is shown below:

The percent that Marie will earn during her training is 66.67%.

What is percentage?

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

She earns working in new job = $15

She earns while training = $10

percentage she will earn during her training

= earing during training/earning during job multiplied by 100.

= 10/15(100)

=66.67%

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Answer:

\(\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24\)

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of \(\triangle ACD\) and the hypotenuse of \(\triangle ADB\).

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

\(\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}\)

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is \(\angle CAD\). The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

\(\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}\)

Now use this value in the Law of Sines to find AD:

\(\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}\)

Recall that \(\sin 45^{\circ}=\frac{\sqrt{2}}{2}\) and \(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\):

\(AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}\)

Now that we have the length of AD, we can find the length of AB. The right triangle \(\triangle ADB\) is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio \(x:x\sqrt{3}:2x\), where \(x\) is the side opposite to the 30 degree angle and \(2x\) is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent \(2x\) in this ratio and since AB is the side opposite to the 30 degree angle, it must represent \(x\) in this ratio (Derive from basic trig for a right triangle and \(\sin 30^{\circ}=\frac{1}{2}\)).

Therefore, AB must be exactly half of AD:

\(AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24\)

Answer:

\( \displaystyle 25 \sqrt{6} \)

Step-by-step explanation:

the triangle ∆ABD is a special right angle triangle of which we want to figure out length of its shorter leg (AB).

to do so we need to find the length of AD (the hypotenuse). With the help of ∆ADC it can be done. so recall law of sin

\( \boxed{ \displaystyle \frac{ \alpha }{ \sin( \alpha ) } = \frac{ \beta }{ \sin( \beta ) } = \frac{ c}{ \sin( \gamma ) } }\)

we'll ignore B/sinB as our work will be done using the first two

step-1: assign variables:

step-2: substitute

\( \displaystyle \frac{100}{ \sin( {45}^{ \circ} )} = \frac{AD }{ \sin( {60}^{ \circ} )} \)

recall unit circle therefore:

\( \displaystyle \frac{100}{ \dfrac{ \sqrt{2} }{2} } = \frac{AD }{ \dfrac{ \sqrt{3} }{2} } \)

simplify:

\(AD = 50 \sqrt{6} \)

since ∆ABD is a 30-60-90 right angle triangle of which the hypotenuse is twice as much as the shorter leg thus:

\( \displaystyle AB = \frac{50 \sqrt{6} }{2}\)

simplify division:

\( \displaystyle AB = \boxed{25 \sqrt{6} }\)

and we're done!

Answer:

im pretty sure it would be d

Step-by-step explanation:

Answer:

It is D

Step-by-step explanation:

got it right on the test

There are 32,160 ways to arrange the letters in ""visiting"" with no pair of consecutive ""i's"".

To count the number of ways to arrange the letters in ""visiting"" with no pair of consecutive ""i's"", we can use the principle of inclusion-exclusion.

Let's first consider the total number of arrangements of the letters in ""visiting"" without any restrictions. We have 8 letters, so the total number of arrangements is 8! = 40,320.

Now let's consider the number of arrangements where the two ""i's"" are together. We can treat the two ""i's"" as a single letter, so we have 7 letters to arrange. There are 7! = 5,040 ways to arrange these letters, and within each arrangement there are 2! = 2 ways to arrange the ""i's"". So there are 2 x 5,040 = 10,080 arrangements where the two ""i's"" are together.

However, we have overcounted some arrangements, namely those where there are three consecutive ""i's"". To count these arrangements, we can treat the three ""i's"" as a single letter, so we have 6 letters to arrange.

There are 6! = 720 ways to arrange these letters, and within each arrangement there are 3! = 6 ways to arrange the ""i's"".

So there are 6 x 720 = 4,320 arrangements where there are three consecutive ""i's"".

Thus, by the principle of inclusion-exclusion, the number of arrangements of ""visiting"" with no pair of consecutive ""i's"" is:

8! - 10,080 + 4,320 = 32,160

Therefore, there are 32,160 ways to arrange the letters in ""visiting"" with no pair of consecutive ""i's"".

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Answer:

1) D

2) B

3) A

4) D

Step-by-step Explanation:

1) 1,300,000

= 1.3 × 10⁶

2) 0.052

= 5.2 × 10⁻²

3) 4,500

= 4.5 × 10³

4) 0.00061

= 6.1 × 10⁻⁴

Identifying Correlation helps in presenting solutions to be explored.

What is Correlation?

Correlation is a statistical metric (a number) that represents the magnitude and direction of a link between two or more variables. A correlation between variables, on the other hand, does not imply that a change in one variable is the cause of a change in the values of the other variable.

Solution:

Identifying Correlation helps in presenting solutions to be explored.

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The total frequency is even (98), the median is the average of the two middle values, which are 31 and 33. So, the median is (31+33)/2 = 32.

To find the mean, we need to compute the sum of products of data values and their frequencies and divide by the total frequency:

(3018 + 3129 + 3211 + 3323 + 34*17) / (18+29+11+23+17) = 31.1

So, the mean is 31.1.

To find the median, we need to find the middle value of the ordered data set. First, we need to compute the cumulative frequency distribution:

data value frequency cumulative frequency

30 18 18

31 29 47

32 11 58

33 23 81

34 17 98

Since the total frequency is even (98), the median is the average of the two middle values, which are 31 and 33. So, the median is (31+33)/2 = 32.

To find the mode, we need to look for the data value(s) with the highest frequency. In this case, the mode is 31 because it has the highest frequency of 29, which is larger than the frequencies of all other values.

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Answer:

see below

Step-by-step explanation:

5(2a+2b+2c)

you must distribute the 5 among the values in parenthesis

4(x-3)

you must distribute the 4 among the values in parenthesis

Hope this helps! :)

Answer:

D

Step-by-step explanation:

because -11/3 is a repeating decimal. Terminating decimals are decimals that come to an end.

The probability that no numbers are repeated = \(\frac{720}{1000}=0.72\)

The probability that there are no repeated digits in a 3-digit pin number is 0.72.

Formula used:

\(P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}\)

There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.

Therefore, the total number of possible 3-digit pin numbers with no repeated digits is

\(P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720\)

The total number of possible 3-digit pin numbers \(= 10 * 10 * 10 = 1000\).

Thus, the probability that no numbers are repeated = \(\frac{720}{1000}=0.72\)

Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.

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(a) P(A) = 0.24, P(B) = 3/36, P(A ∩ B) = 1/36, P(A|B) = 1/3, P(B|A) = 1/18. (b) Events A and B are not independent, and they are not mutually exclusive (c) P(C) = 4/36, P(A ∩ C) = 2/36, P(A|C) = 1/2, P(C|A) = 1/3. (d) Events A and C are not independent, and they are not mutually exclusive.(e) Events A and C are not independent.(f) Events A and C are not mutually exclusive.

(a) To find P(B'), we can use the complement rule. The complement of event B (denoted as B') is the event that B does not occur. So, P(B') = 1 - P(B) = 1 - 0.6 = 0.4.

(b) Events B and B' constitute a partition of the sample space S because they are mutually exclusive and exhaustive.

- Mutually exclusive: Events B and B' cannot occur simultaneously, meaning if B occurs, B' cannot occur and vice versa.

- Exhaustive: Either B or B' must occur, as they cover all possible outcomes.

(c) We can use the Law of Total Probability to find P(A). The law states that for any event A and a set of mutually exclusive and exhaustive events B1, B2, ..., Bn, the probability of A is the sum of the probabilities of A given each Bi, multiplied by the probability of Bi.

In this case, we have B and B' as our events.

P(A) = P(A|B) * P(B) + P(A|B') * P(B')

     = 0.2 * 0.6 + 0.3 * 0.4

     = 0.12 + 0.12

     = 0.24

Therefore, P(A) = 0.24.

(d) To find P(B|A) using Bayes' Theorem, we can rearrange the formula:

P(B|A) = (P(A|B) * P(B)) / P(A)

We already know P(A|B) = 0.2, P(B) = 0.6, and P(A) = 0.24 (calculated in part c).

P(B|A) = (0.2 * 0.6) / 0.24

       = 0.12 / 0.24

       = 0.5

Therefore, P(B|A) = 0.5.

2. For the second set of questions:

(a) Given:

A: First die is even

B: Sum of dice is 4

C: Sum of dice is 5

To find the probabilities:

P(A) = 3/6 (there are three even numbers: 2, 4, 6, out of six possible outcomes)

P(B) = 3/36 (out of 36 possible outcomes, there are three ways to get a sum of 4: (1, 3), (2, 2), (3, 1))

P(A ∩ B) = 1/36 (only one way to get both an even number and a sum of 4: (2, 2))

P(A|B) = P(A ∩ B) / P(B) = (1/36) / (3/36) = 1/3

P(B|A) = P(A ∩ B) / P(A) = (1/36) / (3/6) = 1/18

(b) Events A and B are independent if and only if P(A ∩ B) = P(A) * P(B). However, P(A ∩ B) = 1/36 ≠ (3/6) * (3/36) = 1/72. Therefore, events A and B are not independent.

(c) Events A and B are not mutually exclusive since it is possible to roll a sum of 4 with an even first die.

(d) To find the probabilities for event C:

P(C) = 4/36 (out of 36 possible outcomes, there are four ways to get

a sum of 5: (1, 4), (2, 3), (3, 2), (4, 1))

P(A ∩ C) = 2/36 (two ways to get both an even number and a sum of 5: (2, 3), (4, 1))

P(A|C) = P(A ∩ C) / P(C) = (2/36) / (4/36) = 1/2

P(C|A) = P(A ∩ C) / P(A) = (2/36) / (3/6) = 1/3

(e) Events A and C are independent if and only if P(A ∩ C) = P(A) * P(C). However, P(A ∩ C) = 2/36 ≠ (3/6) * (4/36) = 1/9. Therefore, events A and C are not independent.

(f) Events A and C are not mutually exclusive since it is possible to roll a sum of 5 with an even first die.

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We know the line equation is expressed by

y = mx + b, where is m is its slope (how inclinated it is) and b is intercept with the y-axis.

Finding m

We find its inclination, its slope, m, by

Let's say

(x₁, y₁) = (-6, 5)

(x₂, y₂) = (-3, 3)

Then

Then y = -(2/3)x + b,

Finding b

Since b is intercept with the y-axis, we know it intercepts y when x = 0

Using the equation we have found y = -(2/3)x + b, and replacing one point given by the question (x₂, y₂) = (-3, 3)

y = -(2/3)x + b

3 = -(2/3)(-3) + b

3 = -2 + b

3 + 2 = b

Then, b = 5

Therefore,

The probability that exactly 5 out of 6 randomly selected Americans donated money to a charitable cause in 2021 is approximately 0.3931, or 39.31%.

The probability of a single American donating money to a charitable organization in 2021 is given as 81%. Therefore, the probability of an individual not donating is 1 - 0.81 = 0.19.

To calculate the probability of exactly 5 out of 6 Americans donating, we can use the binomial probability formula:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) represents the probability of exactly k successes (donations).

(n C k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

p is the probability of success (donation) in a single trial.

(1 - p) represents the probability of failure (not donating) in a single trial.

n is the total number of trials (sample size).

In this case, n = 6, k = 5, p = 0.81, and (1 - p) = 0.19.

Plugging in these values, we can calculate the probability:

P(X = 5) = (6 C 5) * (0.81)^5 * (0.19)^(6 - 5)

P(X = 5) = 6 * (0.81)^5 * (0.19)^1

P(X = 5) = 0.3931

Therefore, the probability that exactly 5 out of 6 randomly selected Americans donated money to a charitable cause in 2021 is approximately 0.3931, or 39.31%.

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True. Nonsampling errors refer to errors that occur during the data collection process that are not related to the sampling method used. These errors can occur in any type of data collection method, whether it be through surveys, experiments, or observational studies.

Nonsampling errors can arise due to a variety of reasons, such as poor survey design, biased sampling methods, inadequate training of surveyors, errors in data entry or processing, or even deliberate fraud.

Nonsampling errors can have a significant impact on the quality of the data collected, as they can introduce biases and inaccuracies into the results. These errors can result in incorrect conclusions and decisions based on the data, which can have serious consequences. Therefore, it is important to take steps to minimize nonsampling errors during the data collection process, such as carefully designing surveys, ensuring proper training of surveyors, and conducting thorough quality checks on the data collected.

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:

\(( {4}^{3} \div {5}^{ - 2} {)}^{5} \)

Step-by-step explanation:

\( {4}^{15} . {5}^{10} \)

hope this will help you more

have a great day..

Step-by-step explanation:

\(( \frac{4 {}^{3} }{5 {}^{ - 2} } ) {}^{5 } \\ ( \frac{4 {}^{15} }{5 {}^{10} } ) \\ \frac{4 {}^{15} }{5 {}^{10} } \)

this question answer is 4.25

To find the area of the given triangle with a side length of 18 and an angle of 62 degrees, we can use the formula for the area of a triangle: A = 1/2 * base * height.

In this case, the base of the triangle is given as 18, but we need to find the height. To find the height, we can use the trigonometric relationship between the angle and the sides of the triangle. The height is equal to the length of the side opposite the given angle. Using trigonometry, we can determine the height by multiplying the length of the base by the sine of the angle: height = 18 * sin(62°).

Once we have the height, we can calculate the area using the formula: A = 1/2 * base * height. Plugging in the values, we get A = 1/2 * 18 * 18 * sin(62°). Finally, we round the answer to the nearest tenth to obtain the final result.

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The H0: μ = 70 H1: μ > 70 These are the null and alternative hypotheses in symbolic form for the given scenario.

express the null hypothesis (H0) and alternative hypothesis (H1) for the given situation involving the Carter Motor Company and their claim about the Libra's average city mileage.

The null hypothesis (H0) is the default assumption that there is no difference or relationship between the tested parameters. In this case, it would be that the true average mileage (μ) of the Libra is equal to 70 miles per gallon in the city:
H0: μ = 70

The alternative hypothesis (H1) is the claim that we want to test, which is that the true average mileage (μ) of the Libra is better than (greater than) 70 miles per gallon in the city:
H1: μ > 70

These are the null and alternative hypotheses in symbolic form for the given scenario.

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The time taken for the cargo to hit the ground will be 0.6 seconds and it travels in the horizontal direction for around 14.69 feet.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

The calculations are attached in images.

To calculate t we will use that is y because at the moment of cargo will have a height 0, so we get,

= −4.9t² +1.75

-1.75=-4.9t²

t²=-1.75/-4.9

t²=√0.3571

=0.6 seconds

Now we will calculate x, then y = 0

because since the cargo will be on the ground it will no have height, so

0= -0.0081x²+1.75

-1.75 =-0.0081x²

x²=-1.75/-0.0081

x= √216.04 = 14.69 feet

It will take the cargo 0.6 seconds to hit the ground, and it will travel 14.69 feet in a horizontal direction.

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Answer:

the answer is 10 with a little 4 on the top right corner

Step-by-step explanation:

count your zeros

The length of the line segment XY which was bisected at point M is;

1) 32

2) 6

1) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 3x + 1

YM = 8x - 24

Thus;

3x + 1 = 8x - 24

8x - 3x = 1 + 24

5x = 25

x = 25/5

x = 5

Thus;

XM = 3(5) + 1 = 16

YM = 8(5) - 24 = 16

XY = 16 + 16 = 32

2) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 5x + 8

YM = 9x + 12

Thus;

5x + 8 = 9x + 12

9x - 5x = 8 - 12

4x = -4

x = -1

XM = 5(-1) + 8 = 3

YM = 9(-1) + 12 = 3

XY = 6

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The company will need 6π cubic inches of wax to make a single candle.

Given that the company makes wax candles in the shape of a cylinder, each candle has a diameter of 2 inches and a height of 6 inches.

Now, we need to find out how much wax will the company need to make candles.

The formula to find out the volume of a cylinder is given byπr²h,

where r is the radius of the circular base, h is the height of the cylinder and π is the mathematical constant (approx. 3.14159).

Here, Diameter of the cylindrical candle = 2 inchesTherefore, radius (r) of the candle = diameter / 2= 2 / 2= 1 inch

Height (h) of the candle = 6 inchesSubstitute the values of r and h in the formula for the volume of a cylinder and simplify to get,

Volume of the cylindrical candle = πr²h= π(1)²(6)= π(1)(1)(6)= 6π cubic inches

Therefore, the company will need 6π cubic inches of wax to make a single candle.

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A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Because we are dealing with different units here, we first would need to know how many inches are in one foot.

1 foot = 12 inches

Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.

6 feet = 72 inches

10 feet = 120 inches

Taking these numbers, we now need to figure out the area of the floor.

72 × 120 = 8640

Now, find the area of each tile.

6 × 8 = 48

Taking 8640, we can now divide that by 48 to get the number of tiles needed.

8640 ÷ 48 = 180

Therefore, 180 tiles are needed to cover the floor.

(a) The area inside one loop of r = cos(30) is equal to π/3 square units. (b) The area inside one loop of r = sin^2(θ) is equal to π/2 square units. (c) The area between the circles r = 2 and r = 4 sin(θ) is equal to 6π square units. (d) The area that lies inside r = 3 + 3 sin(θ) and outside r = 2 is equal to 9π/2 square units.

(a) To find the area inside one loop of r = cos(30), we need to integrate the function r^2 with respect to θ over one complete revolution. In this case, the limits of integration are 0 to 2π. Evaluating the integral, we get (1/3)π - (-1/3)π = π/3 square units.

(b) To find the area inside one loop of r = sin^2(θ), we follow a similar approach and integrate r^2 with respect to θ over one complete revolution. The limits of integration are again 0 to 2π. Evaluating the integral, we get (1/2)π - 0 = π/2 square units.

(c) To find the area between the circles r = 2 and r = 4 sin(θ), we calculate the area enclosed by the outer circle (r = 4 sin(θ)) and subtract the area enclosed by the inner circle (r = 2). Integrating r^2 with respect to θ over one complete revolution, the area is given by (1/2)∫(16sin^2(θ) - 4) dθ from 0 to 2π. Evaluating the integral, we get 6π square units.

(d) To find the area that lies inside r = 3 + 3 sin(θ) and outside r = 2, we calculate the area enclosed by the outer curve (r = 3 + 3 sin(θ)) and subtract the area enclosed by the inner curve (r = 2). Integrating r^2 with respect to θ over one complete revolution, the area is given by (1/2)∫((3 + 3 sin(θ))^2 - 4) dθ from 0 to 2π. Evaluating the integral, we get 9π/2 square units.

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Answer:

4

Step-by-step explanation:

Notice each side was increased by 4 times

You can set up a ratio of

\(\frac{new}{old}\)

then reduce or divide

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer:

Step-by-step explanation:

The angle of depression is the angle between the line of sight and a vertical line.

The distance between the two skyscrapers is 1269ft

I've added as an attachment, a figure that illustrates the scenario

First, we calculate distance AB using the following tangent ratio

\(\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}\)

So, we have:

\(\mathbf{\tan(60) = \frac{AB}{1250}}\)

Make AB the subject

\(\mathbf{AB = 1250 \times \tan(60)}\)

Next, we calculate distance AC using the following tangent ratio

\(\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}\)

So, we have:

\(\mathbf{\tan(60+10) = \frac{AB + BC}{1250}}\)

\(\mathbf{\tan(70) = \frac{AB + BC}{1250}}\)

Make AB + BC, the subject

\(\mathbf{AB + BC = 1250 \times \tan(70)}\)

Make BC the subject

\(\mathbf{BC = 1250 \times \tan(70) - AB}\)

Substitute \(\mathbf{AB = 1250 \times \tan(60)}\)

\(\mathbf{BC = 1250 \times \tan(70) - 1250 \times \tan(60)}\)

\(\mathbf{BC = 1269}\)

Hence, the distance between the two skyscrapers is 1269ft

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https://brainly.com/question/13697260