Domain and range of f^-1?

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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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:

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: See attachment (enlarge line)

Step-by-step explanation:

y = 2x

When x = -1

y = 2(-1)

y = -2

When x = 2

y = 2(2)

y = 4

Plot the points on the graph (-1, -2) and (2, 4)

Answer: The answer should be A, Isosceles

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

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

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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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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We want a circle that has center (-1,4) and just skims y=2. We can find the equation of the circle knowing its center and its radius. Knowing that it skims y=2 the radius=4-2=2 (Do you know why? Think visually). Then, the standard form of a circle is given by (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius. So the equation is (x+1)^2+(y-4)^2=4

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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The expression in terms of x and/or y for

a) angle OAC = y

b) angle OBA = 2x

A circle is a shape consisting of all points in the plane that are at a specified distance from a specified point (center). Correspondingly, it is a curve drawn by points moving in the plane at a constant distance from a point. The distance from any point of the circle to the center is called the radius. Normally the radius should be a positive number.

Specifically, a circle is a simple closed curve that divides a plane into two regions inside and outside. In everyday use, the term "circle" can be used interchangeably to refer to the entire shape, including the boundary or interior of the shape. In strict technical usage the circle is just the boundary and the whole figure is called the disk.

In ΔOCA;

OC = OA  [Radius of circle]

So, m∠OCA = m∠OAC

y = m∠OCA

y = m∠OAC

Similarly in ΔAOB;

m∠OAB = 2x

m∠OAB = m∠OBA

2x = m∠OBA

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The complete question is as follows:

The diagram shows a circle with centre O.

Write an expression in terms of x and/or y for

a) angle OAC.

b) angle OBA.

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:

The area of the rectangle is 24x^5 y^2.

Step-by-step explanation:

To find the area of a rectangle when the length is represented by 8x³y² and the width is represented by 3x²yº, you need to multiply the length by the width.

8x³y² represents the length and 3x²yº represents the width.

Therefore, the area (A) of the rectangle can be calculated as:

A = length x width

A = 8x³y² x 3x²yº

To simplify this expression, you can use the laws of exponents:

A = 8x³y² x 3x²y°

A = 8 x 3 x x³ x x² x y² x yº

A = 24x^(3+2) y^(2+0)

Simplifying further:

A = 24x^5 y^2

Therefore, the area of the rectangle is 24x^5 y^2.

Answer:

I'm going to make it more simple for you so you don't have to read his book (no offence to that guy)

the area of the rectangle is 24x^5 y^2.

Therefore, the length of LM is 85.5.

Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.

Since LM is the midsegment of ABCD, it is parallel to both AB and DC, and its length is equal to the average of the lengths of AB and DC.

The length of LM can be found using the formula:

[tex]LM = (AB + DC) / 2[/tex]

Substituting the given values, we get:

[tex]LM = (46 + 125) / 2[/tex]

[tex]LM = 171 / 2[/tex]

[tex]LM = 85.5[/tex]

Therefore, the length of LM is 85.5.

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Answer:

238

Step-by-step explanation:

Formula: 2(aXb + bXc + cXa)

let, a = 7 m

     b = 7 m

     c = 5 m

then,

      2(7X7 +7X5 + 7X5)

      = 2(49 + 35 + 35)

      = 2 X 119

      = 238

Answer:

These triangles are congruent by AAS.

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:

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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Based on the data given, the probability of the next roll of the die being a 4 is 30%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability of rolling a 4 on the next roll, we need to divide the number of times 4 was rolled by the total number of rolls. In this case, 4 was rolled 9 times out of a total of 30 rolls.

So the probability of rolling a 4 on the next roll is:

9/30 = 3/10 = 0.3 = 30%

Therefore, based on the data given, the probability of the next roll of the die being a 4 is 30%.

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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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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.

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()

Answer: x = 8

Step-by-step explanation:

x^2 + y^2 = c^2
x^2 + 6^2 = 10^2
x^2 + 36 = 100
100 - 36 = x^2
x^2 = 64

x = root 64
x = 8

Answer:

172.5

Step-by-step explanation:

1/2(perimeter)(Apothem)

10+10+10+10+10=50

1/2(50)(6.9)

172.5

Answer:

x = -10

Step-by-step explanation:

To solve the equation:

x - 4 = 16 + 3x

Collect like terms:

x - 3x = 16 + 4

Then solve:

-2x = 20

x = -10

Answer: x is -10

Step-by-step explanation:

x - 4 = 16+3x

Transposing the x, and arranging in one side of equation

x - 3x = 16 + 4

now we changed the positions of x and we can simplify it.

so,

x - 3x = -2x -----------------(1)

16 + 4 = 20 ----------------(2)

Therefore the x - 3x = 16 + 4 will change into -2x = 20

Then x = 20 ÷ -2 = -10

x = -10

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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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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