Hattie is on a boat 74 metres away from the foot of a vertical cliff. The height of the cliff is 94 metres. Calculate the angle of depression of the boat from the top of the cliff.​

The scaled values sum up to 1/10.

        k subscript 1 + k subscript 2 = 1

        E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k  subscript 1 E[theta with hat on top subscript 1] + 10 k subscript 2 E[theta with hat on top subscript 2]

        E[theta with hat on top subscript 1] = theta

        E[theta with hat on top subscript 2] = theta

        E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k subscript 1 theta + 10 k subscript 2 theta = theta (10 k subscript 1 + 10 k subscript 2) = theta

        k subscript 1 + k subscript 2 = 1

        10 k subscript 1 + 10 k subscript 2 = 10

       k subscript 1 + k subscript 2 = 1

       k subscript 1/10 + k subscript 2/10 = 1/10

Therefore, their sum is equal to 1, and their scaled values sum up to 1/10.

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Answer: To check if the rates form a proportion, we need to calculate the rate (sit-ups per minute) for both Eric and John.

Eric's rate: 70 sit-ups / 2 minutes = 35 sit-ups per minute

John's rate: 108 sit-ups / 3 minutes = 36 sit-ups per minute

Now we can set up the proportion:

35/1 = 36/1

The rates do not form a proportion since they are not equal.

Step-by-step explanation:

Step-by-step explanation:

The coefficient of C in the inequality 56C+64R<9000 represents the rate of fuel consumption while flying through clear skies. From the inequality, we can see that the rate of fuel consumption while flying through clear skies is 56 gallons per minute.

To find the initial fuel capacity of the airplane, we need to set the values of C and R to zero in the inequality 56C+64R<9000, since this represents the scenario where the plane flies entirely through clear skies and does not encounter any rain clouds.

56(0) + 64(0) < 9000

Simplifying the inequality, we get:

0 < 9000

This means that the inequality is true for any positive value of C and R, including C = 0 and R = 0. Therefore, the airplane has more than 0 gallons of fuel before takeoff, but the exact amount is not specified in the given information.

The given inequality is:

56C + 64R < 9000

We know that the airplane consumes fuel at a constant rate while flying through clear skies. Let the fuel consumption rate be F (in gallons per minute) and let the amount of fuel the airplane has before takeoff be T (in gallons).

We need to find the values of F and T that satisfy the given inequality.

First, we can simplify the inequality by dividing both sides by 8:

7C + 8R < 1125

Next, we can use the fact that the airplane consumes fuel at a rate of 64 gallons per minute while flying through rain clouds to write an expression for the total fuel consumption during R minutes:

64R

Similarly, the total fuel consumption during C minutes while flying through clear skies is:

FC

The total fuel consumption during both C and R minutes can be expressed as:

FC + 64R

We know that the total fuel consumption must be less than the initial amount of fuel, which is T. Therefore, we can write:

FC + 64R < T

Substituting FC = F * C, we get:

F * C + 64R < T

We can rearrange this inequality to solve for T:

T > F * C + 64R

Now we can use the inequality 7C + 8R < 1125 to solve for F and T.

Let's assume the airplane has enough fuel to fly for 1 hour (60 minutes) in clear skies and no rain clouds. Then C = 60 and R = 0. Substituting these values into the inequality, we get:

56(60) + 64(0) < 9000

3360 < 9000

This is true, so our assumption is valid.

Using the assumption that the airplane has enough fuel to fly for 1 hour in clear skies, we can solve for F and T:

T > F * C + 64R

T > F * 60 + 64(0)

T > 60F

Since we assumed the airplane has enough fuel to fly for 1 hour in clear skies, T must be greater than the amount of fuel consumed during that time:

T > F * 60

Combining these two inequalities, we get:

60F < T < 60F + 3360

Now we can choose any value of F between 0 and 64 that satisfies the inequality, and choose a value of T that is greater than 3360 + 60F. For example, we can choose:

F = 30 (assuming a fuel consumption rate of 30 gallons per minute in clear skies)

T = 4000 gallons (initial amount of fuel)

Substituting these values into the inequality, we get:

56C + 64R < 9000

56(60) + 64R < 9000

3360 + 64R < 9000

64R < 5640

R < 88.125

Therefore, the airplane can fly for 88.125 minutes (or approximately 1 hour and 28 minutes) through rain clouds before consuming all of its fuel, if it is flying at a rate of 64 gallons per minute. And if the airplane consumes fuel at a rate of 30 gallons per minute while flying through clear skies, it has 4000 gallons of fuel before takeoff

Answer:

x = y + 3

Step-by-step explanation:

y = x - 3 ( add 3 to both sides )

y + 3 = x , that is

x = y + 3

Answer:

First, we can calculate the discount from the sale. The sweater costs $65.99, and with a 40% discount, the price is reduced by:

$65.99 x 0.40 = $26.40

So the sale price of the sweater is:

$65.99 - $26.40 = $39.59

Next, we can apply Carson's $10 coupon to the sale price:

$39.59 - $10 = $29.59

Therefore, Carson pays $29.59 for the sweater after the discounts.

To calculate the total discount that Carson receives, we can first find the amount of the 40% discount on the sweater, which is:

40% of $65.99 = 0.4 x $65.99 = $26.40

Then, we can add the additional $10 coupon discount to get the total discount:

$26.40 + $10 = $36.40

Therefore, the total discount that Carson receives on the sweater is $36.40.

To find the final price that Carson pays after the discounts, we can subtract the total discount from the original price:

$65.99 - $36.40 = $29.59

Therefore, Carson pays $29.59 for the sweater after the discounts.

Answer:

Step-by-step explanation:

x^2-2xz+xy-2yx^2+xy-xz-yz =x^2+xy+xy-yz-2xz-xz-2yx^2

=x^2+xy+xy-yz-2xz-xz-2yx^2

=x^2+2xy-yz-3xz-2x^2y

The director of fitness for a large corporation with over 5,000 employees recorded the resting heart rate, in beats per minute (bpm), for 35 employees who were known to wear activity trackers. The following boxplot summarizes the results.

The director wants to estimate the resting heart rate for all employees with a confidence interval. Have all conditions for inference been met?Solution:Yes, all conditions for inference have been met.The given boxplot represents the resting heart rate, in beats per minute (bpm), for 35 employees who were known to wear activity trackers.

As the sample size is greater than 30, we can use the normal distribution to create a confidence interval. Additionally, there are no outliers in the data, which suggests that the data is normally distributed. Therefore, we can conclude that all conditions for inference have been met.

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The required number of elements in set A and set B as per given elements of A, B , and A ∪ B is equal to |A ∩ B| = 3.

Number of elements in set A,  |A| = 97

Number of elements in set B, |B|  = 16

Total number of elements in set A or set B,  |A ∪ B| = 110

Use the formula for the size of the union of two sets,

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A| represents the number of elements in set A,

|B| represents the number of elements in set B,

And |A ∩ B| represents the number of elements in the intersection of sets A and B.

Rearrange the formula to solve for |A ∩ B|,

|A ∩ B| = |A| + |B| - |A ∪ B|

⇒|A ∩ B| = 97 + 16 - 110

⇒|A ∩ B| = 3

Therefore, the number of elements in sets A and B have 3 elements in common.

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The formula one-half(a° - b°) is derived from the fact that the exterior angle of a triangle is equal to one-half the difference between the measures of the two remote interior angles.

The formula that would be used to find the measure of angle 1 is one-half(a° - b°). This formula applies to a situation where angle 1 is an exterior angle of a triangle, and a° and b° are the measures of the two remote interior angles of the triangle that are adjacent to angle 1. The exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Mathematically, this can be expressed as:

angle 1 = a° - b°

To find the measure of angle 1 using the formula one-half(a° - b°), we would simply plug in the known values of a° and b°, and perform the necessary arithmetic operations.

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According to the figure the value of x is

The value of x is solved using the intersecting secant tangent theorem

The theorem have the formula

12^2 = 9 * (9 + x)

solving for x

144 = 81 + 9x

9x = 63

9x / 9 = 63 / 9

x = 7

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As a result, the product property can be used to manipulate and equation statements containing 2xy, as well as to express 2xy in terms of its factors.

An equation is a statement that shows the equality between two mathematical expressions. It is a fundamental concept in mathematics and is used to describe relationships between quantities.

The purpose of an equation is to find the value of the unknown variable(s) that make the equation true. This is typically done by applying algebraic operations to manipulate the equation, with the goal of isolating the variable on one side of the equal sign.

[tex]2xy = 2 * x * y[/tex]

[tex]2xy = 2x * y = 2y * x = x * 2y = y * 2x = x * y * 2[/tex]

[tex]4x^2y * 3xy^2 = (4 * x * x * y) * (3 * x * y * y)[/tex]

[tex]= 12 * x^3 * y^3[/tex]

As a result, the product property can be used to manipulate and simplify statements containing 2xy, as well as to express 2xy in terms of its factors.

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The probability that a randomly selected part is not defective is 47/50.

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here Total number of parts machine makes = 50

Number of parts defective out of 50 = 3

Then number of parts not defective out of 50 = 50-3 = 47.

Now using probability formula:

Probability = No of favorable item/ Total no of item

Now probability that a randomly selected part is not defective is,

= 47/50.

Hence the probability that a randomly selected part is not defective is 47/50.

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According to given information, Joanna bought 6 notebooks and 8 pencils with total cost $20.94, which is answer choice A.

What is cost?

cost refers to the amount of money required to purchase or produce a particular item or service.

Let's assume that Joanna bought x notebooks and y pencils. We know that she bought a total of 14 items, so:

x + y = 14

We also know that the total cost of her purchase was $20.94, so:

2.05x + 1.08y = 20.94

We can use the first equation to solve for x:

x + y = 14

x = 14 - y

Substitute this expression for x in the second equation:

2.05x + 1.08y = 20.94

2.05(14 - y) + 1.08y = 20.94

28.7 - 2.05y + 1.08y = 20.94

-0.97y = -7.76

y = 8

Substitute this value of y back into the equation x + y = 14:

x + 8 = 14

x = 6

So, Joanna bought 6 notebooks and 8 pencils, which is answer choice A.

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The coordinates of the image is at

The coordinates of the image is solved by applying the translation rule which is

(x, y) → (x + 6, y - 4)

This is applied as follows

preimage coordinates    translation        image coordinates

(-9, 2)                 →             (-9 + 6, 2 - 4) → (-3, -2)

(-9, 4)                 →             (-9 + 6, 4 - 4) → (-3, 0)

(-7, 4)                 →             (-7 + 6, 4 - 4) → (-1, 0)

(-5, 2)                →             (-5 + 6, 2 - 4) → (1, -2)

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Decreasing the circumference of a tire by 20% would increase the number of rotations required to travel a given distance.

What is Circumference ?

Circumference is the distance around the outside of a circle or a curved object. It is the measurement of the boundary line or the perimeter of the circular object. The circumference of a circle is calculated using the formula C = 2πr, where "C" is the circumference, "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.

The number of rotations of a tire depends on its circumference, which is the distance around the outside of the tire. If the circumference of a tire decreased by 20%, it means that the distance around the outside of the tire would be 20% less than it was before. This would cause the tire to cover less ground in each rotation, which would result in an increase in the number of rotations needed to travel a given distance. Specifically, the number of rotations would increase by 20% for the same distance traveled, as the tire would need to rotate more times to cover the same distance due to the reduced circumference.

Therefore, decreasing the circumference of a tire by 20% would increase the number of rotations required to travel a given distance.

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At least one child made fewer than 2 greeting cards.

For a fundraiser, the children in the art club made greeting cards and kept track of how many they produced.

Children made fewer than 2 greeting cards:

To find out how many children made fewer than 2 greeting cards we need to use the data available.

Assume that there are n children in the art club who participated in the fundraiser.

For each child, the number of greeting cards that they produced is given.

The first step is to set up an inequality for each child that expresses the number of greeting cards they made.

The inequality for the ith child is given by: gᵢ ≥ 0,

where gᵢ is the number of greeting cards made by the ith child.

The second step is to add up the inequalities for each child.

This gives you the following inequality: g₁ + g₂ + ... + gₙ ≥ 0.

The third step is to use the data given in the question.

It is known that each child made fewer than 2 greeting cards.

Therefore, you can substitute 2 for each gᵢ.

This gives you the following inequality:2 + 2 + ... + 2 ≥ 0

Simplifying, we get: 2n ≥ 0

The final step is to solve for n, which is the number of children who participated in the fundraiser.

Dividing both sides of the inequality by 2, you get: n ≥ 0

Since n is a positive integer, the answer is: n ≥ 1.

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By graphing the solution to the inequality x - 4 < 15 on a number line. The graph demonstrates that any number less than 19 satisfies the given inequality, allowing you to quickly verify the solution set.

To justify the answers from the video by graphing the solution to the inequality x - 4 < 15 on a number line, follow these steps:

1. Start by isolating the variable, x. To do this, add 4 to both sides of the inequality: x - 4 + 4 < 15 + 4, which simplifies to x < 19.

2. Now, you need to represent the inequality x < 19 on a number line. Begin by drawing a horizontal line and marking it with evenly spaced points. Label each point with consecutive integers, ensuring that 19 is among them.

3. Since the inequality is "less than" (x < 19) and not "less than or equal to," place an open circle at 19 on the number line. An open circle indicates that 19 is not included in the solution set.

4. To show that the solution consists of all values less than 19, draw an arrow starting from the open circle at 19 and extending to the left. This visually represents all the numbers that are smaller than 19.

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Let's start by using the formula for the total labor cost:

Total labor cost = Fixed cost + (Number of employees x Cost per employee)

We know that the fixed cost is $32,782.00, and the cost per employee is $31,009.00. Let's represent the number of employees with the variable "x". So we have:

$3,133,682.00 = $32,782.00 + (x * $31,009.00)

Simplifying the equation:

$3,133,682.00 - $32,782.00 = x * $31,009.00

$3,100,900.00 = x * $31,009.00

x = $3,100,900.00 / $31,009.00

x ≈ 100

Therefore, the company intends to employ approximately 100 people next year.

Answer: The answer should be A, Isosceles

Step-by-step explanation: Have a great day!

The transformation of the function f(x) = log2(x) involves shifting 2 units up and vertically compressing by a factor of 0.4.

Which function represents the transformation g(x)?

The following equation can be used to represent the transformation:

g(x) = 0.4*log2(x) + 2

Therefore, the function that represents the transformation g(x) is:

g(x) = 0.4*log2(x) + 2

To understand the transformation of the function f(x) = log2(x) into g(x), we need to first understand the individual transformations involved.

Vertical compression: When a function is vertically compressed by a factor 'a', its output values get multiplied by 'a'. This means that the function's range gets compressed by a factor of 'a'. In this case, the function f(x) = log2(x) is vertically compressed by a factor of 0.4. So, the output values of f(x) get multiplied by 0.4, which compresses the range of the function by a factor of 0.4.

Vertical shift: When a function is shifted 'b' units up or down, its output values get increased or decreased by 'b'. This means that the function's range gets shifted up or down by 'b'. In this case, the function f(x) = log2(x) is shifted 2 units up. So, the output values of f(x) get increased by 2, which shifts the range of the function 2 units up.

Putting these two transformations together, we get the transformation of the function f(x) = log2(x) into g(x) as follows:

g(x) = 0.4*log2(x) + 2

This equation represents a vertical compression of the function f(x) by a factor of 0.4, followed by a vertical shift of 2 units up.

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Complete question:

This means that half of the schools requested more than 87.5 seedlings and half requested less than 87.5 seedlings.

To find the median number of seedlings requested by the 9 schools for Earth Day, we need to first arrange the number of seedlings requested by each school in ascending or descending order. Let's assume the following number of seedlings were requested by each school:

School 1: 50 seedlings
School 2: 60 seedlings
School 3: 75 seedlings
School 4: 80 seedlings
School 5: 85 seedlings
School 6: 90 seedlings
School 7: 100 seedlings
School 8: 120 seedlings
School 9: 150 seedlings

Now, to find the median, we need to find the middle value. In this case, there are 9 schools, so the middle value will be the average of the 5th and 6th values. The 5th value is 85 and the 6th value is 90, so the median is (85 + 90) / 2 = 87.5 seedlings.

Therefore, the median number of seedlings requested by the 9 schools for Earth Day is 87.5.

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The answer is option b. confidence coefficient.

To explain this, let's start by defining interval estimation. Interval estimation is a statistical method used to estimate an unknown population parameter (such as the population mean or proportion) by constructing a range of values, called a confidence interval, that contains the true value of the parameter with a certain level of confidence.

The level of confidence refers to the percentage of times that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated. For example, a 95% confidence level means that if we were to repeat the interval estimation procedure many times, we can expect to obtain a confidence interval that contains the true population parameter 95% of the time.

The confidence coefficient, on the other hand, is the probability that a particular confidence interval actually contains the true value of the population parameter. It is the complement of the significance level, which is the probability of making a Type I error (rejecting a true null hypothesis). For example, if we have a 95% confidence level, then the confidence coefficient is 0.95, and the significance level is 0.05.

Therefore, the confidence coefficient represents the probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated. It is a measure of how confident we are that the estimated interval contains the true population parameter.

In conclusion, the confidence coefficient is a crucial concept in interval estimation that reflects the probability of obtaining a confidence interval that includes the true population parameter. It provides a measure of the reliability and accuracy of the interval estimation procedure and helps researchers interpret the results of their analyses.

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Answer:

If u mean 312 inches then the answer is 12480in^3

Step-by-step explanation:

To solve volume do LxWxH which is Length times width time height.

Answer:

D: Left side

Step-by-step explanation:

The measure of angle K is 47.2° ( nearest tenth)

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

From the rule;

c² = a²+b²+2abcosC

to find K we must find angle J

22² = 15²+15²+ 2× 15 × 15cos J

484 = 225+225+ 450cosJ

484 = 450+450cos J

450cos C = 484-450

450cos C = 34

cos J = 34/450

cos J = 0.075

J = cos^-1( 0.075)

J = 85.7°

The sum of angle in a triangle is 180°

x+x + 85.7 = 180

2x = 180-85.7

2x = 94.3

x = 94.3/2 = 47.2(nearest tenth)

therefore the measure of K is 47.2°

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Answer:

Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions.

The length 53.1°, 90°, and 39.9°,vertical length: 3/5 ,length of vertical: 4/5 1 hypotenuse.

Angle is a geometric concept that describes the relative difference between two straight lines or planes that meet at a common point. It is measured in degrees, radians or grads, and is often represented by the symbol θ. An angle can be acute, right, obtuse, straight, reflex, or full. Angles can be used to measure the size of a triangle, to calculate the area of a figure, and to determine the position of a point in a coordinate system.

We possess that

Angle = 53.1°

Vertical length = 3/5 (this is the adjacent cathetus)

Vertical length equals 4/5 (this is the opposite cathetus)

We can use it to check this.

tg(angle) = adjacent/opposite:

tg(53.1) = 1.33

and

(4/5)/(3/5) = 4/3 = 1.33

This makes sense, then.

Using the relationship, we can now identify the hypotenuse:

Sin(angle) = the antipode or hypotenuse

sin(53.1) = (4/5)/H

H = (4/5)/sin(53.1) = 1

Hence, there is always a 90° angle in a triangle or rectangle.

We may get the final angle using the fact that the sum of a triangle rectangle's three interior angles is always 180 degrees.

A + 53.1° + 90° = 180°

A = 90° - 53.1° = 36.9°

Now that we have located every missing part of the triangle.

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To complete her journey Ann needs to run for (120/3) = 40 minutes in order to travel at an average speed of 5 km/h.

We can start by using the formula:

average speed = total distance ÷ total time

Let's first calculate the total distance Ann covers:

distance walked = speed x time = 4 km/h x (8 km / 4 km/h) = 8 km

distance run = speed x time

Let's call the time Ann runs for "t". Then:

distance run = 8 km/h x (t/60) h = (8t/60) km

Total distance = distance walked + distance run = 8 km + (8t/60) km = (480 + 8t) / 60 km

Now, let's find the total time:

total time = time walked + time run

time walked = distance ÷ speed = 8 km ÷ 4 km/h = 2 h

time run = t/60 h

total time = 2 h + t/60 h = (120 + t)/60 h

Now we can substitute the values we have found into the formula for average speed:

5 km/h = [(480 + 8t)/60 km] ÷ [(120 + t)/60 h]

Simplifying the right-hand side, we get:

5 km/h = (480 + 8t) / (120 + t)

Multiplying both sides by (120 + t), we get:

600 + 5t = 480 + 8t

Subtracting 480 and 5t from both sides, we get:

120 = 3t

Therefore, Ann has to run for (120/3) = 40 minutes to have an average speed of 5 km/h over her complete journey.

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The function that they can use to determine how strongly related are two of the variables is equals to the cor() which stands for correlation. So, the correct choice for answer is option (c).

The function cor() returns the correlation between two variables. In R language, the cor() function is used to determine the correlation coefficient between two

vectors. Correlations may be generated

using the cor() function, while covariance

can be generated using the cov() function. In statistical, correlation shows us how strong the relationship is between two variables. It describes the degree to which two variables are linearly connected (meaning they change together at a constant rate). In case of symmetry, the correlation between A and B is the same as the correlation between B and A. The most used correlation coefficients are Pearson, Spearman, and Kendall.

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Complete question:

A data analyst is using statistical measures to get a better understanding of their data. What function can they use to determine how strongly related are two of the variables?

A) sd()

B) mean

C) cor()

D) bias()