Please use law of cosines to answer the question with your work shown. Wrong answers will be reported.
Thx

a) The perimeter of the cross is: P = 4a = 4(c - b) = 4c - 4b

b) The area of the cross is:[tex]A= 2cb - 2b^2 \ cm^2[/tex]

c) b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]

What is area and perimeter?

The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.

a) The perimeter, P, of the cross is equal to the sum of the lengths of its four arms.

The length of one arm of the cross can be found by subtracting the length of one rectangle from the length of the other rectangle. Since each rectangle has dimensions c cm × b cm, the length of one arm is:

a = c - b

Therefore, the perimeter of the cross is:

P = 4a = 4(c - b) = 4c - 4b

b) The area, A, of the cross is equal to the area of the two rectangles minus the area of the four triangles formed by the arms of the cross.

The area of each rectangle is:

[tex]Area_{rect} = c * b[/tex]

The area of each triangle is:

[tex]Area_{tri} = (a * b) / 2 \\\\= \frac{[(c - b) * b]}{2} \\\\= \frac{ (c * b - b^{2} )}{2}[/tex]

Since there are four triangles, the total area of the triangles is:

[tex]4A_{tri} = 2cb - 2b^2\ cm^2[/tex]

Therefore, the area of the cross is:

[tex]A = 2A_{rect} - 4A_{rect} \\\\ = 2cb - 2b^2[/tex]

c) c) To find b in terms of A and C, we can use the formula for the area of the cross that we found in part b:

[tex]A = 2cb - 2b^2[/tex]

We can rearrange this equation to put it in the form of a quadratic equation:

[tex]2b^2 - 2cb + A = 0[/tex]

This is a quadratic equation in standard form, with a = 2, b = -2c, and c = A. We can use the quadratic formula to solve for b:

b = (-b ± sqrt(b^2 - 4ac)) / 2a

b = (2c ± sqrt((2c)^2 - 4(2)(A))) / (2 × 2)

[tex]b=\frac{-b ± \sqrt{(b^2 - 4ac)} }{2a} \\\\b= \frac{2c ± \sqrt{(2c^2 - 4(2)c)}}{4} \\\\b= \frac{2c ± \sqrt{(4c^2 - 16A)}}{4} \\\\b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]

Therefore, b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]

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The equation AB=BC for [tex]A=BCB^{-1}[/tex].

The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is

We have to solve the equation

AB = BC given that these all are square matrices and B is invertible.

Write the required Equation:

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

⇒[tex]ABB^{-1} =BCB^{-1}[/tex]

⇒[tex]AI=BCB^{-1}[/tex]

⇒[tex]A=BCB^{-1}[/tex]

Therefore, the solution of AB = BC is [tex]A=BCB^{-1}[/tex].

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The required inequality, which represents the possible values for the number of apples and bananas purchased is 2a + 0.6b ≤10.

What is inequality?

Inequality can be defined as the relation of the expression containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

Let, the number of apples purchased, a, and the number of bananas purchased, b.

According to the question, Each apple costs $1.25 and each banana costs $0.60. London has a total of $10 to spend on apples and bananas.

So,

1.25a + 0.6b ≤10

Thus, the required inequality, that represents the possible values for the number of apples and bananas purchased is 1.25a + 0.6b ≤20.

Answer:

10 miles; it represents the original distance of the bird from its nes

Step-by-step explanation:

The probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John is 0.60 or 60%

We can find the probability that a person does not believe Marilyn Monroe had an affair with John F Kennedy by dividing the number of people who responded "no" by the total number of people who responded to the survey:

Probability of "no" = Number of "no" responses / Total number of responses

Total number of responses = Number of "yes" responses + Number of "no" responses

Total number of responses = 110 + 163 = 273

Probability of "no" = 163 / 273

Simplifying the fraction, we get:

Probability of "no" = 0.5967 or approximately 0.60

So, the probability that if a person is chosen at random, he does not believe Marilyn Monroe had an affair with John F Kennedy is approximately 0.60, or 60%.

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0.75 times the amount of miles+the base fee

Answer:

Y=0.75X+3

Answer:

25%

Step-by-step explanation:

x + 0.25x = y

y - 0.25x = x

If the size of a circle increases by 25% and then decreases back down to it's original size it's going to be the same percentage 25%.

Answer:

140 ° , because it is vertically opp to angle 4 and angle 4 is corresponding 8 .

Sarah's age now is 18.

Ratio is defined as the relationship between two quantities for which it tells how much one quantity is contained in the other.

Normally, the ratio of two quantities a and b is denoted as a : b.

Given in the question that,

The ratio of Sarah's age to her father's age now is 1:3.

Suppose that x is the age of Sarah now.

Then, from the information given, father's age now = 3x

After 6 years,

Sarah's age = x + 6

Father's age = 3x + 6.

Given that, In 6 years' time, the ratio becomes 2:5.

So, numerically,

(x + 6) / (3x + 6) = 2 / 5

Doing the cross multiplication, we get,

5 (x + 6) = 2 (3x + 6)

5x + 30 = 6x + 12

5x - 6x = 12 - 30

-x = -18 or x = 18

Hence now, age of Sarah is x = 18.

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Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given that, Casey claims the linear equation for the relationship shown by the graph is c=25j.

We have points on it,

(1, 25), (3, 75), (5, 125) and (7, 175)

Put each point in the equation,

c = 25j

Put j = 1, 3, 5, and 7

We get the corresponding value, 25, 75, 125, 175

That means, the points are satisfying the equation,

Hence, Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.

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The given graph is :-

Answer:

Step-by-step explanation:

n

Answer:

14 oz of flour.     2 oz yeast.

Step-by-step explanation:

If you're making 40 servings of bread and using 0.35 oz of yeast, you need:

0.35 oz yeast / 1 yeast : 200 flour = 0.35 oz yeast / 1 : 200 flour = 0.00175 oz yeast/flour

So, you need 0.00175 oz yeast/flour * 40 servings * 200 flour/serving = 14 oz of flour.

If you're making 90 servings of bread and using 360 oz of flour, you need:

1 yeast : 180 flour = 360 oz flour / 90 servings / 180 flour/serving = 2 oz yeast.

8/19 or 42.1%

add all values up to a total, then find the percentage from that total.

8 + 2 + 1 + 3 + 5 = 19 balls total

8 tennis valls to 19 total.

8/19 or 42.1%

The mean absolute deviation from the given data set is 1.6

The mean absolute deviation measures how far the data points are on average from a center point. Mean, median, mode, or any other random figure can serve as the center point.

The mean is frequently used as the center point, In this situation,  The method for computing mean absolute deviation (MAD) is helpful, which represents the average of the absolute departure of the data points from the mean of the data set.

Mean = (1+5+5+6+8)/5

Mean = 25/5

Mean = 5

The distance of each value from the mean is as follows:

Value     distance from the mean 5

1               4

5              0

5              0

6              1

8              3

MAD = (4 + 0 + 0 + 1 + 3)/5

MAD = 8/5

MAD = 1.6

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Answer: 16

Step-by-step explanation:

6 ÷ 3 = 2

[tex]2^{3}[/tex] = 2 x 2 x 2

2 x 2 x 2 = 8

2 x 8 = 16

The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let the price be 'x'. Then the equivalent to the statement the price decreased by 1/2% is given as,

⇒ (1 - 0.5 / 100) x

⇒ 0.995x

The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.

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The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.

What exactly is a cone?

A cone is a shape formed by connecting a single point known as the apex or vertex to all of the points of a circular base using a series of line segments (which does not contain the apex). The distance from the vertex to the base is the cone's height. The circular base's radius has been measured. The slant height is the length of the cone from the peak to any point along the base's perimeter. The height, radius of base, and slant height of the cone in the figure define it.

Volume of cone=1/3πr²h, where r=base radius and h=cone height

Curved surface area=πrL, where L is the slant height.

Now,

Given Volume of cone to hold popcorn=9 inch³

i.e. 1/3πr²h=9

r²h=9*3*7/22

r²h=8.5943

let r=2

then h=8.5943/4

h=2.1485

Hence,

            The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.

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PPM stands for "parts per million" and is a way of expressing small concentrations of substances in a larger mixture. To calculate PPM, divide the mass or volume of the substance by the total mass or volume of the mixture and multiply by one million.

To calculate PPM, you need to know the mass of the substance in question and the total mass of the mixture. Here are the steps to calculate PPM:

1. Determine the mass of the substance in question. For example, let's say you have a mixture that contains 0.5 grams of salt.

2. Determine the total mass of the mixture. For example, let's say the total mass of the mixture is 1000 grams.

3. Divide the mass of the substance by the total mass of the mixture. In this example, 0.5 grams / 1000 grams = 0.0005.

4. Multiply the result by 1,000,000 to get the PPM. In this example, 0.0005 x 1,000,000 = 500 PPM.

So, the concentration of salt in the mixture is 500 PPM. Remember to always use the same units of measurement for both the substance and the mixture when calculating PPM.

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Answer:

Step-by-step explanation:

None of the given equations support the fact that rational numbers are closed under addition, because they all involve irrational numbers or fractions, which are not necessarily rational.

Option (A) involves the irrational number √2.

Option (B) involves adding the irrational number √6 with its negative, which results in a rational number, but it doesn't prove that all additions of rational numbers are also rational.

Option (C) involves the perfect square 9, but the square root of a non-square integer is generally an irrational number.

Option (D) involves the addition of two rational numbers, which is a valid example of the closure property of rational numbers under addition.

Therefore, the correct answer is (D) 1/3+1/3=2/3.

The equation of hyperboloid of one sheet: [tex]\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1[/tex] which is used to calculate hyperboloid.

The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.

Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.

The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.

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The simplified form of subtraction is 3/2.

The simplified form of x+7/2 subtracted by x+4/2 is 3/2.

1. Start with the original expression: x+7/2 - (x+4/2)

2. Distribute the negative sign: x+7/2 - x - 4/2

3. Combine like terms: 7/2 - 4/2

4. Simplify by subtracting: 3/2

So the simplified form is 3/2.

Subtraction is an arithmetic operation tat represents the operation of removing an object from a collection. Subtraction is indicated by a minus sign, −. For example, in the image next to it, 5 − 2 peaches—meaning 5 peaches with 2 picked for a total of 3 peaches.

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Answer: $3.32

Step-by-step explanation:

First arrange the given discrete values in ascending order.

$3.26, $3.28, $3.31, $3.31, $3.32, $3.34,$3.35, $3.38, $3.42

we will use the formula 1/2 x (n +1), where n is total number of discrete values which in this case is 9.

This formula doesn't give the answer of the second quartile, it tells which nth term in the arranged set will be the second quartile.

1/2 (9+1) = 5.

Now we will choose the 5th term of the ascending order set.

Second quartile is same as the median, that means you need the mid value.

The true statement is that the y intercept of function A is less than the y intercept of function B.

y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.

Here we have two functions.

Function A is given in the graph and function B is given in the equation form.

From the graph, the y intercept of function A is the y coordinate of the point touching the Y axis.

Line touches the Y axis at the point (0, -3).

So y intercept of function A = -3.

The equation of function B is the slope intercept form.

In the slope intercept form, y = mx + c, c is the y intercept.

From the equation y = 1/2 x + 4, 4 is the y intercept.

So 4 > -3.

Hence the y intercept of B is greater than that of A.

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The value that represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test is called the degrees of freedom (df).

It is equal to the number of categories minus one. The degrees of freedom provide a measure of the amount of information available in the sample to estimate the parameters of the distribution.

In a goodness-of-fit test, the degrees of freedom are calculated as the number of categories minus one, which represents the number of ways in which the expected classes are free to vary.

For example, if you are conducting a chi-square goodness-of-fit test to compare the distribution of a categorical variable with expected frequencies, you would have one degree of freedom for each category or class, with the exception of the last category.

The last category's frequency is determined by subtracting the sum of the observed frequencies for all other categories from the total sample size. This means that the last category is not free to vary independently, so it is not counted in the degrees of freedom calculation.

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If there were 950 countries, we could expect celebrations from 10 countries.

Groundhog Day is a popular North American tradition celebrated on February 2 in the United States and Canada. It is based on the Pennsylvania Dutch superstition that if a groundhog emerges from its burrows on this day and sees its shadow due to clear weather, it will retreat to its burrow and winter will last six weeks longer.

In our calculation, as 2 out of 195 celebrate the day, we need know  how many celebrations we could expect if there were 950 countries.

950 / 195 = 4.87179487179 = 4.87. We will multiply 4.87 by 2 country giving us 9.74, approximately 10 countries.

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The equation of the line that is perpendicular to this line and passes through the point (5, −1) is y = (9/4)x - (49/4) and the equation of the line that is parallel to this line and passes through the point (5,−1) is y = (-4/9)x + (11/9).

An equation of a line is provided: -4x - 9y = 2

                                       -9y = 4x + 2

                                    y = (-4/9)x - 2/9

The slope-intercept form of the line is y = mx + c

So, the Slope of the line is -4/9

The slope of the perpendicular line is -1/(-4/9) = 9/4

Equation of line with slope 9/4 and containing the point (5, -1):

                                  y - (-1) = (9/4)(x - 5)

                                          y = (9/4)x - (49/4)

Parallel lines have the same slope, so the equation of the line with slope -4/9 and which contains the point (5, -1) is:

                              y - (-1) = (-4/9)(x - 5)

                               y = (-4/9)x + (11/9)

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The y- coordinate for the solution to the system of equations is 4

From the question, we have the following parameters that can be used in our computation:

8x−4y=−32,

2x+2y=4

Multiply the second equation by 4

So, we have the following representation

8x − 4y = −32

8x + 8y = 16

Subtract the equations

So, we have the following representation

12y = 48

Divide by 12

y = 4

Hence, the solution is y = 4

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The y-coordinate for the solution to the system of equations is equal to 4.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-2, 4).

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Step-by-step explanation:

x = number of quarters

y = number of dimes

x + y = 34

therefore, we can say right away

y = 34 - x

0.25x + 0.1y = 4

because a quarter is worth $0.25, and a dime is worth $0.10.

now we are using the first equation in the second :

0.25x + 0.1(34 - x) = 4

0.25x + 3.4 - 0.1x = 4

0.15x + 3.4 = 4

0.15x = 0.6

x = 0.6/0.15 = 4

y = 34 - x = 34 - 4 = 30

the solution is therefore (4, 30).

she has 4 quarters and 30 dimes.

Peng has 4 quarters and 30 dimes.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Peng has $4 in quarters and dimes. She has 34 coins.

we need to find the number of quarters and dimes, does Peng have,

Let x = number of quarters and y = number of dimes

Therefore, establishing the equations :-

x + y = 34

y = 34 - x...(i)

Since, a quarter is worth $0.25, and a dime is worth $0.10.

Therefore,

0.25x + 0.1y = 4.....(ii)

Therefore,

0.25x + 0.1(34 - x) = 4

0.25x + 3.4 - 0.1x = 4

0.15x + 3.4 = 4

0.15x = 0.6

x = 0.6/0.15

x = 4

Put x = 4 in the eq(i)

y = 34 - x = 34 - 4 = 30

y = 30

Hence, she has 4 quarters and 30 dimes.

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According to the California Board of Accountancy's requirements for CPA license renewal, if the highest level of service provided during the two years prior to the renewal date was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.

Here is the breakdown of the requirements for the Accounting and Auditing Education Requirement:

- If the highest level of service provided was an audit, review, or attestation engagement, the CPA must complete 40 hours of continuing education in accounting and auditing subjects.

- If the highest level of service provided was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.

- If the highest level of service provided was preparation of financial statements, the CPA must complete 8 hours of continuing education in accounting and auditing subjects.

- If the CPA did not provide any of the above services, they are not required to complete any continuing education in accounting and auditing subjects.

In Brandon's case, since his highest level of service provided was a compilation engagement, he must complete 24 hours of continuing education in accounting and auditing subjects out of the total of 80 continuing education hours required.

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