Given f(x) = (2 - x)}, what is the value of f(18)?

Answer:

6 cm and 18 cm.

Step-by-step explanation:

We are given that:

The perimeter of any rectangle is:

To determine the dimensions of the rectangle, we need to determine the value of "x". The word "dimensions" are the length and the width of the rectangle. Since the question has not stated the length and width, we can consider the length as x and the width as 3x.

It is also given that the perimeter of the rectangle is 48 cm. Thus, the formula with the length and the width substituted is equivalent to 48 cm.

It is required for the expression on the left hand side to be simplified. This can be done by combining like terms.

Then, we can divide 8 both sides to isolate the coefficient from "x". Once the coefficient of "x" is isolated, we will obtain the value of "x".

Finally, substitute the value of "x" into the length and the width. We considered the length to be "x" and the width to be "3x". Therefore,

Thus, the dimensions of the rectangle are 6 cm and 18 cm.

Now

B=6

L=3(6)=18

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.

A comparison between two items by means of a number. (arithmetic) comparing two quantities' relative magnitudes (usually expressed as a quotient).

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys.

Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B. Your ratio will be 5/10, for instance, if A is 5 and B is 10.

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Answer:

The answer was obtained by first taking the measurement for the temperature drop, the duration of the temperature drop, and the rate at which the temperature is dropping which are -28 F, 4 hours, and dropping at a steady rate.

The measured temperature drop of -28 F, is then divided by the duration of the drop which is 4 hours, to get the amount the temperature drop each our as -28F/4 = -7 F per hour

Step-by-step explanation:

The rate at which the local meteorologist claims that the temperature is going to drop = Steady rate

The duration over which the local meteorologist states that the temperature is going to drop = 4 hours

The amount by which the temperature is observed to drop = -28F

The rate at which the temperature is observed to drop = The same amount each hour

Therefore, the temperature drop per hour = -28F/4 = -7 F per hour

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

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Answer:

518000 if it increases 8% per year

Step-by-step explanation:

8 times 5, because there are 5 years, is 40%

we take 40% out of 370000 and we get 148000 then we add 370000 and 148000 together and we get 518000

The range of sample mean is that it defines the middle 95% of the distribution of sample mean is from 68.2 to 81.8. This means that if we were to take multiple random samples of size 16 from the population, 95% of the sample means would fall within this range.

To find the range of sample means that defines the middle 95% of the distribution of sample means, we can use the formula:
range = (X - zα/2 * σ/√n, X + zα/2 * σ/√n)
where X is the sample mean, σ is the population standard deviation, n is the sample size, and zα/2 is the z-score that corresponds to the desired confidence level and is found using a standard normal distribution table.
For a 95% confidence level, zα/2 = 1.96. Substituting the given values into the formula, we get:
range = (75 - 1.96 * 20/√16, 75 + 1.96 * 20/√16)
range = (68.2, 81.8)
Therefore, the range of sample means that defines the middle 95% of the distribution of sample means is from 68.2 to 81.8. This means that if we were to take multiple random samples of size 16 from the population, 95% of the sample means would fall within this range.
To find the range of sample means that defines the middle 95% of the distribution of sample means, we need to use the Central Limit Theorem and calculate the standard error.
Given a normal distribution with mean (μ) = 75, standard deviation (σ) = 20, and sample size (n) = 16, we can calculate the standard error (SE) using the following formula:
SE = σ / √n
SE = 20 / √16
SE = 20 / 4
SE = 5
Now, we need to find the critical z-score for a 95% confidence interval. For a 95% confidence interval, the critical z-score (z*) is approximately ±1.96.
Next, we'll use the critical z-score to find the margin of error (ME):
ME = z* × SE
ME = 1.96 × 5
ME = 9.8
Finally, we'll calculate the range of sample means:
Lower limit = μ - ME = 75 - 9.8 = 65.2
Upper limit = μ + ME = 75 + 9.8 = 84.8
The range of sample means that defines the middle 95% of the distribution of sample means is approximately 65.2 to 84.8.

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Answer:

1. B

2. E

3. D

4. B

5. C

6. B

7. E

8. D

9. D

10.D

11. E

Young people respond more favorably to literature that reflects their cultural customs, and this is because of the importance of cultural background in children’s reading development. Ethnic and cultural differences play an essential role in the children's reading development.

Children's cultural and ethnic background has a considerable impact on their learning, and thus the type of literature they respond to. Children tend to read more when they find that the stories and books reflect their cultural customs and identity. This enhances their literacy and reading skills, which in turn leads to an increased interest in reading and a better understanding of what they are reading.

Cultural diversity can help children become more empathetic and accepting of differences, and can help them to learn about new cultures. Therefore, it is crucial to provide children with access to a range of culturally diverse literature to help them understand the experiences of others. Children learn more effectively when they can make connections between what they are learning and their own experiences.

In conclusion, children's reading development is influenced by their ethnic and cultural background. Young people respond more favorably to literature that reflects their cultural customs, which can help them to become more empathetic and accepting of differences, as well as develop their literacy and reading skills. Therefore, it is essential to provide children with a range of culturally diverse literature to help them learn about new cultures and understand the experiences of others.

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Answer:

Elizabeth had 30 stamps originally.

Step-by-step explanation:

Let,

x be the number of stamps Elizabeth have.

Number of stamps given to John = 1/6 of x = \(\frac{1}{6}x\)

Remaining stamps = \(x-\frac{1}{6}x = \frac{6x-1x}{6} = \frac{5}{6}x\)

Stamps given to Peter = 1/5 of remainder = \(\frac{1}{5}*\frac{5}{6}x = \frac{1}{6}x\)

Number of stamps left = 20

Now,

\(\frac{1}{6}x + \frac{1}{6}x + 20 = x\\\\\frac{1x+1x+120}{6} = x\\\\\frac{2x+120}{6} = x\\\\2x + 120 = 6x \\\\120 = 6x - 2x \\\\120 = 4x \\4x = 120\)

Dividing both sides by 4

\(\frac{4x}{4}=\frac{120}{4}\\x=30\)

Hence,

Elizabeth had 30 stamps originally.

1 (7/24) cups of condensed soup were in the can.

Given,

There is a can of condensed soup .

The amount of milk  Alen mixes with the condensed soup = 1 1/3

Subtract amount of milk from total cups of soup:

2 ( 5/8 ) – 1 ( 1/3 )

Make the fraction in same form to make the subtraction easy.

2 ( 5/24 ) – 1 ( 8/24 )

Now solve

2 (15/24 ) – 1 ( 8/24 )= 1 ( 7/24 )

Here, there is 1 ( 7/24 ) cups of condensed soup in the can.

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The question is incomplete. And the corrected question is given below.

Alan mixes 1 1/3 cups of milk with a can of condensed soup. he makes a total of 2 5/8 cups of soup. how many cups of condensed soup were in the can?

Answer:

x=34

Step-by-step explanation:

132-64=

68/2=

34

PLEASE MAKE ME BRAINLIEST

The percent of the variance in the dependent variable unexplained by the independent variable is 81%

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.

The correlation coefficient is therefore represented as follows:

\(r = 0.3\)

The explained variance is found using the following formula:

\(R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9\)

Thus, 81% of the variance remains unexplained by variations in the independent variable.

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By using the properties of angle,

The proof of ∠1 ≅ ∠3 has been given below

What is angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle

1. ∠2 ≅ ∠4 [Given]

2. m∠2= m∠4 [Angle Congruence Postulate]

3. ∠2 and ∠3 are supplementary [Given]

4. m∠2+m∠3 = 180° [Definition of Supplementary angles]

5. ∠1 and ∠4 are supplementary [Angle on a straight line]

6. m∠1+m∠4 = 180° [Definition of supplementary angles]

7. m∠1+m∠4 = m∠2+ m∠3 [ Substitution from 4 and 6]

8. m∠1+m∠4 = m∠4+m∠3 [Substitution from 2]

9. m∠1=m∠3 [Cancellation property]

10. ∠1 ≅ ∠3 [Converse of angle congruence theorem]

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Answer:

$3.50

Step-by-step explanation:

Divide the price of 6 books ($21) by the number of books bought (6)

$21 divided by 6 = $3.50

So the price of 1 book is $3.50

Hope this helps :)

Answer:$3.50

Step-by-step explanation:

x=4 and that it's the answer

Answer:

12$!❤️

Step-by-step explanation:

A research design is a crucial component of any research study as it provides a framework for conducting the investigation.

It encompasses the planning and organization of the research process, including the specification of research questions, data collection methods, and data analysis procedures.

The research design outlines the specific research questions that the study aims to answer, guiding the focus and scope of the research. It also determines the methods and techniques that will be employed to gather data, such as surveys, interviews, observations, or experiments.

The design further delineates the timeline and sequencing of data collection, determining when and how data will be gathered from participants or sources.

Overall, a well-constructed research design ensures that the research questions are addressed effectively, the data is collected appropriately, and the analysis is conducted in a rigorous and systematic manner, enhancing the validity and reliability of the research findings.

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EXPLANATION

Let's see the facts:

shoot = 20 feet

goal = 5 foot

Let's draw the statement:

Since we are finding the side opposite the given angle and know the side adjacent, we can use the Pythagoras Theorem to find the needed value.

Replacing terms:

Isolating x:

Switching sides and simplifying:

The player will not score because 5.4 is greater than 5

Answer:

P(x)= x^3 - 4x^2 + 16x - 64

Step-by-step explanation:

First, let’s find all of the zeroes. If the question is asking for a degree 3 polynomial, than there has to be more than 2 zeroes. The complex conjugates theorem states that if a+bi is a zero, than a-bi has to be a zero as well. So if 4i is a zero, than -4i has to be a zero as well. By looking at the zeroes, you can write them as a linear factorization.

(x-4)(x+4i)(x-4i)

If you foil all of it, you will get x^3 - 4x^2 + 16x - 64.

hello, first we need to know what color represents each line segment.

Look at the figure: CD is represented in green, and C'D is represented in blue.

Now, let's look at the points of each one:

CD: (2,1) and (3(-4)

C'D': (-1,2) and (4,3)

To solve this question, we need to rotate the green line segment to the same position as the blue line segment.

So, if we rotate 90 degrees in the clockwise, we will have:

(-2, 1) and (-3, -4)

If we rotate 90 degrees in the counterclockwise, we will have:

(-1,2) and (4,3). This are the same points of the line segment C'D'

Answer:

(4th option) 164; Two real solutions

Step-by-step explanation:

Please see the attached picture for the full solution.

b² -4ac > 0

➣2 real and distinct roots

b² -4ac = 0

➣ 1 repeated root/ 2 real and equal roots

b² -4ac < 0

➣ No real roots

*Roots is another name for the solutions of a quadratic equation.

The discriminant of the quadratic equation is 164 and two real solutions are present.

Mathematically, the discriminant of the quadratic equation is \(D=b^2-4ac\).

The given quadratic equation is \(x^2+14x+8=0\).

Here, b=14 and c=8.

So, the discriminant is-

\(D=(14)^2-4\times 1\times 8\\=196-32\\=164\)

As the discriminant is positive so, the roots of the solutions are real and distinct.

Thus, the discriminant of the quadratic equation is 164 and two real solutions are present.

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Answer:

2636.5

Step-by-step explanation:

because he saved alot but uncle sam only took alittle

Answer:

y = 3x + 3

Step-by-step explanation:

As x increases, y increases by 3. Therefore, the slope of the function is 3.

Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).

Overall, the function rule for the given data set is y = 3x + 3.

In quadrant II, if cosθ=-12/13, then cscθ=-13/5 and cotθ=5/12.

In quadrant II, if secθ=-5/3, then cotθ=-3/5 and sinθ=4/5.

(a) The terminal side of θ lies in quadrant III. (b) The terminal side of θ lies in quadrant IV.

Since cosθ is negative in quadrant II, sinθ will be positive. Using the Pythagorean identity sin^2θ + cos^2θ = 1 and the fact that cosθ=-12/13, we can solve for sinθ to get sinθ=5/13. Therefore, cscθ=1/sinθ=-13/5 and cotθ=cosθ/sinθ=-12/5.

Similarly, since secθ is negative in quadrant II, cosθ will be negative. Using the Pythagorean identity cos^2θ + sin^2θ = 1 and the fact that secθ=-5/3, we can solve for cosθ to get cosθ=-3/5. Therefore, sinθ is positive and sinθ=√(1-cos^2θ)=4/5. Thus, cotθ=cosθ/sinθ=-3/5.

(a) Since sinθ<0 and cotθ<0, we know that sinθ is negative in quadrant III and cotθ is negative in quadrant II and IV. Therefore, the terminal side of θ can only lie in quadrant III or IV. To determine which quadrant it lies in, we can look at the signs of both sinθ and cotθ. Since both are negative in quadrant III and only cotθ is negative in quadrant IV, we conclude that the terminal side of θ lies in quadrant III.

(b) Since cosθ>0 and cscθ<0, we know that cosθ is positive in quadrant I and IV, and cscθ is negative in quadrant III and IV. Therefore, the terminal side of θ can only lie in quadrant III or IV. To determine which quadrant it lies in, we can look at the signs of both cosθ and cscθ. Since both are negative in quadrant III and only cscθ is negative in quadrant IV, we conclude that the terminal side of θ lies in quadrant IV.

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Answer:

x=13

Step-by-step explanation:

9x+15+3x+9=180

12x+24=180

12x=156

x=13

Answer:

x=13

Step-by-step explanation:

(3x+9)+(9=180

12x+24=180

12x=156

x=13

Adding one more worker to the plant will result in a savings of approximately $78.05 per month.

To find dy/dx, we need to take the partial derivative of P with respect to y, keeping x constant, and then divide by the partial derivative of P with respect to x, keeping y constant.

Taking the partial derivative of P with respect to y, we get:

∂P/∂y = 0.3x^0.7y^(-0.7)

Keeping x constant at x=100 and y=300,000, we have:

∂P/∂y = 0.3(100)^0.7(300,000)^(-0.7) ≈ 0.000164

Taking the partial derivative of P with respect to x, we get:

∂P/∂x = 0.7x^(-0.3)y^0.3

Keeping y constant at y=300,000 and x=100, we have:

∂P/∂x = 0.7(100)^(-0.3)(300,000)^0.3 ≈ 0.0128

Therefore, dy/dx at x=100 and y=300,000 is:

dy/dx = (∂P/∂y)/(∂P/∂x) ≈ (0.000164)/(0.0128) ≈ 0.0128/0.000164 ≈ 78.05

So, dy/dx ≈ $78.05 per worker.

Interpretation: The result means that for Snappy Hardware to maintain a constant production rate, it needs to decrease its monthly budget by approximately $78.05 for each additional worker it hires at an employment level of 100 workers and a monthly operating budget of $300,000.

In other words, adding one more worker to the plant will result in a savings of approximately $78.05 per month.

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