Brainliest to correct answer. Please help!!! Last year, Trevor gave $5,462 to his local charity, which he calculated as 22.5% of his yearly salary. How much money does Trevor make in a year?

20 pieces of 10 5/6 inch bar can be cut from a stock 29 foot bar.

To calculate the number of pieces of 10 5/6 inch bar that can be cut from a 29 foot bar, we need to first convert the measurements to a common unit. One foot is equal to 12 inches, so 29 feet equals 348 inches.

Next, we need to determine how many 10 5/6 inch bars can be cut from the 348-inch stock bar. To do this, we can use division. First, we need to convert the mixed number 10 5/6 to an improper fraction by multiplying the whole number by the denominator and adding the numerator. This gives us 125/6 inches.

Now, we can divide the length of the stock bar (348 inches) by the length of one 10 5/6 inch bar (125/6 inches). This gives us:

348 / (125/6) = 20.736

Since we cannot cut a partial bar, we need to round down to the nearest whole number. Therefore, we can cut 20 pieces of 10 5/6 inch bar from a 29 foot stock bar.

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Answer:

The ordered pairs are;

A(3, 4), B(-3, 2), C(-2, -4), D(6, -3), and E(0, 0)

Step-by-step explanation:

An ordered pair is the coordinate definition of a point on a coordinate plane that gives the x and y values of the coordinate of the point within parenthesis separated by a comma

An ordered pair provides a visual designation of points located on a Cartesian plane.

The milliliters of blood the volunteers donate is 470 * (32 - n)

The given parameters are

Total = 32

Unqualified = n

The number of qualified volunteers would be

Qualified = 32 - n

A volunteer donates 470 ml

So, we have

Total = 470 * (32 - n)

Hence, the milliliters of blood the volunteers donate is 470 * (32 - n)

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On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Answer:

Yes!

Step-by-step explanation:

153 can be divided by 3 making 51 parakeets in each cage!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:Yes

Step-by-step explanation:Yes it can because 3 cages can hold 51 animals

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Answer:

143°

When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.

The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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Analysts use financial ratios rather than absolute numbers because ratios provide a more meaningful and comparative assessment of a company's financial performance.

Ratios allow for a standardized comparison between companies of different sizes and industries, facilitating a better understanding of their financial health, operational efficiency, and profitability.

Furthermore, ratios enable analysts to evaluate a company's performance over time and benchmark it against industry averages and competitors. Some examples of commonly used financial ratios include the current ratio, return on equity (ROE), and earnings per share (EPS).

Current Ratio: The current ratio measures a company's ability to meet its short-term obligations. It is calculated by dividing current assets by current liabilities. For example, if a company has current assets of $500,000 and current liabilities of $250,000, the current ratio would be 2 ($500,000 / $250,000). A higher current ratio indicates a stronger liquidity position, suggesting the company is better equipped to meet its short-term financial obligations.

Return on Equity (ROE): ROE measures a company's profitability relative to its shareholders' equity. It is calculated by dividing net income by average shareholders' equity and multiplying by 100 to express it as a percentage. For instance, if a company has a net income of $1 million and average shareholders' equity of $10 million, the ROE would be 10% ($1 million / $10 million * 100). A higher ROE signifies better profitability and efficient utilization of shareholders' capital.

Earnings per Share (EPS): EPS indicates the profitability of a company on a per-share basis. It is calculated by dividing net income attributable to common shareholders by the weighted average number of outstanding shares. For example, if a company has a net income of $5 million and 10 million weighted average shares outstanding, the EPS would be $0.50 ($5 million / 10 million). A higher EPS implies higher profitability for each share held by investors.

Financial ratios provide valuable insights into a company's financial performance and facilitate better comparisons and analysis. Absolute numbers alone may not convey the same level of meaningful information or allow for easy comparisons between companies. Ratios allow analysts to assess a company's financial health, profitability, liquidity, efficiency, and other key aspects relative to industry peers and historical performance.

They help identify trends, strengths, weaknesses, and potential investment opportunities or risks. While absolute numbers provide essential context, ratios offer a standardized framework for evaluation and decision-making, making them a preferred tool for financial analysis.

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The equation of the linear function represented by the table is y = 2x - 5

From the question, we are to find the equation of the linear function that is represented by the table.

Using the formula for the equation of a line with two points,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

To determine the equation, we will pick any two points from the table

Using the points (3, 1) and (4, 3) from the table.

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

(y - 1)/(x - 3) = (3 - 1)/(4 - 3)

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

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

y - 1 = 2x - 6

Writing the equation on the slope-intercept form

y - 1 = 2x - 6

Add 1 to both sides of the equation

y - 1 + 1 = 2x - 6 + 1

y = 2x - 5

Hence, the equation is y = 2x - 5

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The probability of the first two songs played being slow songs is approximately 0.5454.

The probability that the first two songs played are slow songs can be calculated by dividing the number of favorable outcomes (two slow songs) by the total number of possible outcomes.

Since there are 9 slow songs out of 12 total songs, the probability of selecting a slow song as the first song is 9/12. After the first slow song is played, there are 8 slow songs left out of the remaining 11 songs. Therefore, the probability of selecting a slow song as the second song, given that the first song was slow, is 8/11.

To find the probability of both events occurring (selecting a slow song first and then selecting a slow song second), we multiply the probabilities of each event:

P(First song slow) * P(Second song slow | First song slow) = (9/12) * (8/11) = 72/132 = 0.5454 (rounded to four decimal places).

The probability that the first two songs played are slow songs is 0.5454.

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Answer:

8 and lower

Step-by-step explanation:

72 needs to be greater than 8a.

8 x 9 = 72 so it can't be 9 or anything higher than 9

8 x 8 = 64

72 > 64

8 and anything less than 8 will result in the inequality being true

According to the given equation, the number of bottles that the vendor sold today before raising the price is; 8 bottles

In equation for the total amount collected T = 12 + 1.75n, it means that every additional bottle sold at the new price brings in $1.75 dollars:

Therefore, the per-bottle price after the $0.25 price increase would be $1.75. The per-bottle price before the price increase would be;

$1.75 - $0.25 = $1.50

When n = 0, we have;

T = 12 + 1.75(0)

T = $12

Thus, before any bottle was sold the total price collected was $12 before any bottle was sold at the new price.

Thus, the number of bottles sold at that price = 12/1.5 = 8 bottles

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Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

The area of the small figure is 6 in².

In Geometry and Mathematics, a scale factor is the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:

(Scale factor of dimensions)² = Scale factor of area

Scale factor of side lengths = 3/6 = 1/2

Therefore, the area of the small figure can be calculated as follows;

Area of small figure = (1/2)² × 24

Area of small figure = 1/4 × 24

Area of small figure = 6 in².

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Answer: x = 4

Step-by-step explanation: multiply both sides of the equation by 4. multiply 7 and 4 to get 28. add 28 and 1 to get 29. add 3 to both sides and add 29 and 3 to get 32. divide both sides by 8 then divide 32 by 8 to get 4.

The possible rational roots are

The constant is 14, and its factors are:

The lead coefficient is 1, and its factors are:

Then, the possible rational roots for this equation are

Since, 7 is a possible rational root, the answer is option C

The resulting graph of g(x)=|x|+5 is a V-shaped curve that is shifted upwards by 5 units.

What is function ?

Function can be defined in which it relates an input to output.

To graph the function g(x)=|x|+5, we start with the parent function f(x)=|x|.

First, we shift the entire graph of f(x) upwards by 5 units to get g(x). This means that the new function will take the absolute value of x and then add 5 to it.

To graph g(x), we can choose two points on either side of the y-axis and then plot the corresponding points. We can use the ray tool to draw the rays passing through these points.

Here are the steps to graph g(x)=|x|+5:

Choose a value of x on the left side of the y-axis, such as x=-3.

Substitute this value into the equation g(x)=|x|+5 to get g(-3)=|-3|+5=8. This gives us the point (-3,8).

Choose another value of x on the left side of the y-axis, such as x=-2.

Substitute this value into the equation g(x)=|x|+5 to get g(-2)=|-2|+5=7. This gives us the point (-2,7).

Draw a ray passing through the points (-3,8) and (-2,7) to represent the left side of the graph.

Choose a value of x on the right side of the y-axis, such as x=2.

Substitute this value into the equation g(x)=|x|+5 to get g(2)=|2|+5=7. This gives us the point (2,7).

Choose another value of x on the right side of the y-axis, such as x=3.

Substitute this value into the equation g(x)=|x|+5 to get g(3)=|3|+5=8. This gives us the point (3,8).

Draw a ray passing through the points (2,7) and (3,8) to represent the right side of the graph.

Therefore, The resulting graph of g(x)=|x|+5 is a V-shaped curve that is shifted upwards by 5 units.

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The paid amount including service fee, tip, and tax is $77.987.

the percentage is value per hundred.

bill value = $59.99

service fee = 3% of  $59.99 = 59.99*3/100 = $1.7997

tip = 20% of 59.99 =  $11.998

tax = 7 % of $59.99 = $4.1993

total payment = 59.99+1.7997+11.998+4.1993 = $77.987

therefore, the paid amount including service fee, tip, and tax is $77.987.

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Answer:

Step-by-step explanation:

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 58%?

Answer:

\(p=39.4\)°

Step-by-step explanation:

\(4a+4+75+p=180\) (The sum of angles on a triangle is \(180\)°)\(4a+p=180-4-75\)

\(4a+p=101\)

\(p+9a+2=180\)  (Angles of a straight line sums to \(180\)°)

\(p + 9a = 178\)

Elimination can be used to find the value of one variable:

\(p+9a-(4a+p)=178-101\)

\(5a = 77\)

\(a=15.4\)

Now, the value of \(p\) can be found by using substitution:

\(4a+p = 101\)

\(4(15.4)+p=101\)

\(p = 101-61.6\)

\(p = 39.4\)

I hope this helps :)

We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:

1.  1.6744 × 10⁻²⁴: Two electrons and 0ne proton

2. 5.021 × 10⁻²⁴: Two protons and one neutron

3. 5.0224 × 10⁻²⁴: One proton and two neutrons

4. 3.3484  × 10⁻²⁴: One electron, one proton, and one neutron

To match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to  1.6726 × 10⁻²⁴ and one electron is equal to  9.108 × 10⁻²⁸.

To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;

1.6744 × 10⁻²⁴, we would

Add 2 electrons and one proton

= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴

= 1.6744 × 10⁻²⁴

The same applies to the other combinations.

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Answer:

x<-2

Step-by-step explanation:

Since there are absolute value bars around the equation everything inside the equation is now a positive value. Then to solve we need to get x alone

Step-by-step explanation:

So it's important to define what parallel is. If one line is parallel to another line, it will never intersect the other line. This means the two lines must be changing by the same amount simultaneously. In other words, they have the same slope. It's also important to remember that same slope doesn't mean they're parallel. You also have to look at the y-intercept. If they have the same y-intercept, and the same slope, then they're the same line. So two lines are only parallel, if the slopes are the same and they have different y-intercepts.

So now that you understand what's parallel let's look at some of the problems

1. So this is kind of tricky, because as I mentioned before, parallel lines have the same slope, but in this case a slope cannot be defined. For two vertical lines to be parallel, they just have to have different a different x-constant. Because x is what's constant, and if they're different, then the two lines will never intersect. This gives us the general formula for a vertical parallel line: \(x=a\text{ where a} \ne3\) (this is specific to this problem, since the constant in the graph is x=3). Since the parallel line must pass through (-5, -4) this means that the constant for x, must be -5, because the x is constant, if it equals anything else, it will never equal -5. So the parallel line in this case will be: \(x=-5\)

2. So the equation is already in slope-intercept form, so we don't have to solve for the slope. The slope in this case is 8, which can be determined by looking at the formula. This gives us the general formula for the parallel line: \(y=8x+b\text{ where b}\ne 4\). b cannot equal 4, because if it did, then we would have two lines that are the same, not parallel, otherwise b can be anything else. Since we have a point that the parallel line goes through, we can plug this in as (x, y) to solve for b: \(21=8(4)+b \implies21=32+b\implies -11=b\). So now this gives us the complete equation: \(y=8x-11\)

3. The image is a bit low quality, although from what I can see the linear equation intersects the origin (0, 0) and (4, -1). This gives us the equation for the slope -1/4 (rise/run). which gives is the slope -1/4. So this gives us the general equation: \(y=-\frac{1}{4}x+b \text{ where b} \ne0\). b cannot equal 0, since it would then have the same y-intercept, meaning the two lines would be the same. In this case we also get some coordinates which we can plug into the equation to solve for b: \(-5=-\frac{1}{4}(12)+b\implies -5=-3+b\implies-2=b\). This gives us the complete formula: \(y=-\frac{1}{4}x-2\)

4. This is similar to the vertical line, as there is a constant value, but in this case a slope can be defined, and that slope is 0; it's 0 for all horizontal lines. So we have the general equation: \(y=0x+b \text{ where b}\ne4\). This can be simplified to: \(y=b \text{ where b} \ne4\). Since the line passes through (13, -7), that means b must equal -7, because the y does not depend on x. It's a constant value. So you have the equation: \(y=-7\)

5. \(y-6=\frac{3}{5}(x+5)\). So in this case we have the point-slope form. We don't need to convert it to the slope-intercept form, since all we need to form the parallel line is the slope, sort of. You technically do need the y-intercept, so you know what b cannot equal, so that you don't have the same line, but I'm assuming, the coordinates they're giving you, do not pass through the original line, but rather a parallel line. So we have the general equation: \(y=\frac{3}{5}x+b\). Plugging the given coordinates give you the equation: \(8=\frac{3}{5}(0)+b \implies8=b\). You didn't really need to do this, since if you noticed the coordinates have x=0, which means the y-value by definition is what b is equal to, since b is the y-intercept. So this gives you the equation: \(y=\frac{3}{5}x+8\)

The probability of getting a difference in sample means xF − xM of at least 1 minute is 0.1160 or 11.60%.

To find the probability of getting a difference in sample means xF − xM, we need to use the Central Limit Theorem.

For the female students, the sample mean running time x¯f follows a normal distribution with a mean of 8.8 minutes and a standard deviation of 3.3 minutes divided by the square root of 8 (since we are selecting 8 students). Similarly, for the male students, the sample mean running time x¯m follows a normal distribution with a mean of 7.3 minutes and a standard deviation of 2.9 minutes divided by the square root of 8.

Now, we need to find the difference in sample means xF − xM or we want to find the probability of getting a difference of at least 1 minute between the sample means of the two populations.

Using the formula for the difference in sample means, we have:

xF − xM = 8.8 - 7.3 = 1.5

The standard deviation of the difference in sample means is the square root of the sum of the variances of the two populations, which is:

sqrt[(3.3^2/8) + (2.9^2/8)] = 1.255

The z-score for a difference of 1.5 minutes is:

z = (1.5 - 0) / 1.255 = 1.195

Using a standard normal table or a calculator, we can find that the probability of getting a z-score of 1.195 or greater is approximately 0.1160.

Therefore, the probability of getting a difference in sample means xF − xM of at least 1 minute is 0.1160 or 11.60%.

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#24: The "D" in the cell name D25 refers to the column identifier in Excel.

#32: To enter a cell address in Excel, specifically for cell D3, when you want the row to always remain the same, you use the dollar sign ($) before the row number. So, the correct way to enter the cell address D3 while keeping the row fixed is "$D$3". By adding the dollar sign before both the column letter and the row number, the cell reference becomes an absolute reference, meaning it will not change when copied or filled down to other cells.

This is useful when you want to refer to a specific cell in formulas or when creating structured references in Excel tables.

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There are 560 ways to fill the 5 positions on the shelf, with the first 2 positions occupied by math books and the last 3 positions occupied by computer science books.

To determine the number of ways to fill the positions on the shelf, we need to consider the different combinations of books for each position.

First, let's select the math books for the first two positions. Since Mike has 8 different math books, we can choose 2 books from these 8:

Number of ways to choose 2 math books = C(8, 2) = 8! / (2! * (8-2)!) = 28 ways

Next, we need to select the computer science books for the last three positions. Since Mike has 6 different computer science books, we can choose 3 books from these 6:

Number of ways to choose 3 computer science books = C(6, 3) = 6! / (3! * (6-3)!) = 20 ways

To find the total number of ways to fill the positions on the shelf, we multiply the number of ways for each step:

Total number of ways = Number of ways to choose math books * Number of ways to choose computer science books

= 28 * 20

= 560 ways

Therefore, there are 560 ways to fill the 5 positions on the shelf, with the first 2 positions occupied by math books and the last 3 positions occupied by computer science books.

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