7. What are the coordinates of the intersection point? Does this match your answer from question 4? (2 points: 1 point each question)




8. Answer the original questions. (2 points: 1 point each question)
a) How long is each individual act?



b) How long is each group act?



9. Discussion.
Discuss the reasonableness of your answers. (2 points: 1 point for each part)
a) Is the answer you found reasonable? Does it seem like enough time?





b) Would a negative solution such as (–5, –10) be acceptable in this situation? Why or why not?

After solving the equation, the solution if the equation is -2 and -11/5.

To solve the rational equation we first express the given statement in the form of mathematical equation. After that we solve the equation.

As the statement is 5 over X + 2. It can be written as 5/(x + 2)

Then the second statement is -11 over X to the 2nd + 2X which is written as -11/(x² + 2x).

There have equal sign between both expression. So the expression is

5/(x + 2) = -11/(x² + 2x)

Now solve it.

Multiply by (x² + 2x) on both side, we get

5(x² + 2x)/(x + 2) = -11

Multiply by (x + 2) on both side, we get

5(x² + 2x) = -11(x + 2)

Now simplify using the distributive property

5x² + 10x = -11x - 22

Add 11x on both side, we get

5x² + 21x = - 22

Add 22 on both side, we get

5x² + 21x + 22 = 0

Now we factor the equation

5x² + (11 + 10)x + 22 = 0

5x² + 11x + 10x + 22 = 0

x(5x + 11) + 2(5x + 11) = 0

(5x + 11)(x + 2) = 0

Now equating equal to 0.

5x + 11 = 0                     x + 2 = 0

5x = -11                          x = -2

x = -11/5

The solution if the equation is -2 and -11/5.

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The complete question is:

Solve the rational equation 5 over X + 2 equals -11 over X to the 2nd + 2X.

Answer:

Multiply the numerator and denominator by the conjugate.

a with a small 3 b with a small 5 and check under it will be a small a and small b

Step-by-step explanation:

Answer:

Second option

Step-by-step explanation:

Check the relationship between the x digits and compare with y digits. It must be the same all through

In the second option x =2y for all the digits

4:2, 7:3.5,8:4,10:5

The expressions that are equivalent to 2(-2m+7)-9m are C: 2(-8m+6m+7)-9m and D: 2(-6m+4m+7)-9m.

To see why, let's simplify the original expression:

2(-2m+7)-9m = -4m+14-9m = -13m+14

Now let's simplify the other expressions:

(-2m+7)2-9m = -4m+14-9m = -13m+14

2(-8m+6m+7)-9m = -16m+12m+14-9m = -13m+14

2(-6m+4m+7)-9m = -12m+8m+14-9m = -13m+14

So we can see that the expressions 2(-8m+6m+7)-9m and 2(-6m+4m+7)-9m are equivalent to the original expression.

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The exact number for tan(t + 71) is -0.5846.

To find tan(t + 71), we can use the formula for the sum of two angles:
tan(t + 71) = (tan t + tan 71)/(1 - tan t * tan 71)

Given that tan t = 5, we can substitute this value into the formula:
tan(t + 71) = (5 + tan 71)/(1 - 5 * tan 71)

To find the exact number for tan 71, we can use a calculator or a table of trigonometric values. The exact value of tan 71 is approximately 2.9042.

Substituting this value into the formula, we get:
tan(t + 71) = (5 + 2.9042)/(1 - 5 * 2.9042)

Simplifying the expression, we get:
tan(t + 71) = (7.9042)/(1 - 14.521)
tan(t + 71) = (7.9042)/(-13.521)
tan(t + 71) = -0.5846

Therefore, the exact number for tan(t + 71) is -0.5846.

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The limit of the given function can be evaluated by simplifying the expression and then substituting the value of x.

First, we can factor the numerator and denominator of the expression:
lim−(x−>9)(7x−63)/(x^2−2x−63)=lim−(x−>9)(7(x−9))/((x−9)(x+7))
Next, we can cancel out the common factor of (x-9) from the numerator and denominator:
lim−(x−>9)(7)/(x+7)
Now, we can substitute the value of x=9 into the expression:
lim−(x−>9)(7)/(x+7)=7/(9+7)=7/16
Therefore, the limit of the given function is 7/16.

As for the second part of the question, we can use the result of Example 1.3 to verify the formulas. According to Example 1.3, if x+y divides x^n+y^n for n≥0, then x+y also divides x^(n+1)+y^(n+1). Using this result, we can prove that x+y divides x^2n+1+y^2n+1 for n≥0 by induction.
Base case: n=0
x^2(0)+1+y^2(0)+1=x+y, which is divisible by x+y.
Inductive step: Assume that x+y divides x^2n+1+y^2n+1 for some n≥0. We need to show that x+y divides x^2(n+1)+1+y^2(n+1)+1.
x^2(n+1)+1+y^2(n+1)+1=(x^2n+1+y^2n+1)(x^2+y^2)
Since x+y divides x^2n+1+y^2n+1 by assumption, and x+y divides x^2+y^2 by Example 1.3, x+y also divides (x^2n+1+y^2n+1)(x^2+y^2) by the distributive property. Therefore, x+y divides x^2(n+1)+1+y^2(n+1)+1 for n≥0.

Finally, for the third part of the question, we can use the fact that n is a positive integer to show that (n^3) is also a positive integer. Since n is a positive integer, n^3 is also a positive integer because the product of three positive integers is a positive integer. Therefore, (n^3) is a positive integer.

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The width of the rectangle is 4 2/3 yards.

The area of a rectangle is the measure of the total region that the rectangle occupies in two-dimensional space.

It is calculated by multiplying the length of the rectangle by its width.

The formula for the area of a rectangle is:

Here we have

The area of a rectangular tablecloth is 8 3/4 square yards.  

The width of the tablecloth is 1 7/8 yards

For simple calculation convert given fractions into improper fractions

=> 8 3/4 = 35/4 yards

=> 1 7/8 = 15/8  yards  

Let 'x' be the breadth of the rectangle

As we know Area of the rectangle = Length ×  width

=> x × 15/8 = 35/4

=> x = 35/4 × 8/15

=> x = 14/3

Here, 14/3 = 4 2/3 yards  

Therefore,

The width of the rectangle is 4 3/2 yards.

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Answer:

ABD = 75 degrees

Step-by-step explanation:

ABD is the same as ABC + CBD

ABC = 30

CBD = 45

30+45 = 75 degrees

Therfore, ABD = 75 degrees

Bob did not commit tax fraud based on the given information.

To calculate Bob's net income, we need to start with his adjusted income, which is his income minus his expenses and deductible:

Adjusted Income = Income - Expenses - Deductible

Adjusted Income = $750 - $100 - $150

Adjusted Income = $500

Next, we need to determine the amount of tax that Bob owes based on his tax bracket information:

Tax Owed on first $200 = $200 * 0.10 = $20

Tax Owed on next $300 ($200 to $500) = $300 * 0.20 = $60

Tax Owed on remaining $0 ($500 and above) = $0 * 0.40 = $0

Total Tax Owed = $20 + $60 + $0 = $80

Now, we can calculate Bob's net income by subtracting his tax owed from his adjusted income:

Net Income = Adjusted Income - Tax Owed

Net Income = $500 - $80

Net Income = $420

Finally, we can compare Bob's returned amount to his tax owed to see if he committed tax fraud:

Returned Amount - Tax Owed = $120 - $80 = $40

Since Bob's returned amount is less than his tax owed, he did not commit tax fraud. His net income after taxes is $420.

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Answer:

x = -5.5

Step-by-step explanation:

-2x - 4 + 2x + 32 - 2x - 21 = 18​

-2x - 4 + 32 - 21 = 18

-2x + 7 = 18

-2x = 11

x = -5.5

So, the answer is x = -5.5

The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Let's check all the options, then we have

A) y = 6x + 14, the equation is a linear equation because the degree is one.

B) y = x/4 + 1, the equation is a linear equation because the degree is one.

C) y = x³, the equation is a cubic equation because the degree is three.

D) y = 3/x  +2, the equation is a non-linear equation because the degree is negative one.

The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.

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Answer:

AB = 6.71

Step-by-step explanation:

The vertical leg of the right triangle

= absolute value of difference in y-coordinates between A(-1, 6) and B(5, 3)

= |6  - 3| = |3|
= 3

The horizontal leg of the right triangle
= absolute value of difference in x-coordinates between A(-1, 6) and B(5, 3)
= |- 1 - 5|
=|- 6|

= 6

By the Pythagorean theorem, the hypotenuse AB is related to each of these two legs by the formula

AB² = 3² + 6²
AB² = 9 + 36

AB² = 45

AB = √45

or

AB = 6.7082039324

= 6.71 significant to 3 significant figures

Significant figures means number of digits excluding leading and trailing zeros

The total amount will Perri need when she gets the keys for the house at closing is $41,860.

Perri is making a 7% down payment on the $364,000 purchase price of the condominium, so her down payment will be

0.07 x $364,000 = $25,480.

Perri estimates her closing costs to be 4.5% of the purchase price, which is 0.045 x $364,000 = $16,380.

Therefore, the total amount Perri will need when she gets the keys for the house at closing is the sum of the down payment and the closing costs, which is $25,480 + $16,380 = $41,860.

So the answer is (C) $41,860.

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The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it is  114 cm².

The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it can be found by calculating the area of the circle and the area of the square and then subtracting the two.

First, calculate the area of the circle using the formula

A = πr²,

where A is the area and r is the radius.

A = π(10)² = 100π ≈ 314.16 square centimeters

Next, calculate the area of the square. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. The diameter of the circle is 2r, or 20 centimeters.

Using the Pythagorean theorem, we can find the side length of the square:

s² + s² = (20)²

2s² = 400

s² = 200

s ≈ 14.14 centimeters

The area of the square is s² or (14.14)² ≈ 199.97 square centimeters.

Finally, subtract the area of the square from the area of the circle to find the difference:

314.16 - 199.97 ≈ 114.19 square centimeters

To the nearest whole, the difference in area is 114 square centimeters.

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The coordinates of point B' after the translation are given as follows:

B'(1,-2).

A translation happens when either a figure or a function are moved horizontally or vertically.

The meaning of the translation for this problem is given as follows:

The coordinates of point B are given as follows:

B(5,1).

Hence the coordinates of point B' are given as follows:

Meaning that the last option is correct.

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Answer: B

Step-by-step explanation:

answer = c

its not a or b because the range starts at y = 2

There are 8 possible ways for the first 2 finishers to complete the marathon with different genders. There are 20 possible ways for Chantal to finish the race before David.

There are a couple of different ways to approach this problem, but one common method is to use the multiplication principle, which states that if there are A ways to do one thing and B ways to do another, then there are A*B ways to do both. We can apply this principle to both parts of the question.

a) If the first 2 finishers must have different genders, then we can think about the possible combinations of boys and girls. There are 2 options for the first finisher (either a boy or a girl), and then there are 4 options for the second finisher (either a boy or a girl, but not the same gender as the first finisher).

So, using the multiplication principle, we can find the total number of ways for the first 2 finishers to complete the marathon with different genders:

2 * 4 = 8

Therefore, there are 8 possible ways for the first 2 finishers to complete the marathon with different genders.

b) If Chantal must finish the race before David, then we can think about the possible positions for Chantal and David. There are 5 possible positions for Chantal (first, second, third, fourth, or fifth), and then there are 4 possible positions for David (second, third, fourth, or fifth, but not before Chantal).

So, using the multiplication principle, we can find the total number of ways for Chantal to finish before David:

5 * 4 = 20

Therefore, there are 20 possible ways for Chantal to finish the race before David.

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The transformation applied to the function f(x) is a translation of 4 units up.

Here we can see that:

f(x) = √(x + 3)

and g(x) is a vertical translation of k units:

g(x) = f(x) + k

To get the value of k, just look how many units the graph has been translated up ( remember that each of the smalls squares in the coordinate axis represents a single unit), we can see that it is 4 units up, then k = 4

We have a vertical translation of 4 units up.

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A blue token is worth 15 points and a yellow token is worth 5 points.

Two or more expressions with an Equal sign is called as Equation.

Let b  represent the point value of a blue token and

y represent the point value of a yellow token.

We can set up two equations:

4b + 7y = 95 (Jillian's score)

4b + 3y = 75 (Jacob's score)

Subtracting the second equation from the first, we get:

4b + 7y - (4b + 3y) = 95 - 75

Simplifying this, we get:

4y = 20

Dividing both sides by 4, we get:

y = 5

So a yellow token is worth 5 points.

Now we can substitute this value of "y" into one of the original equations and solve for "b".

4b + 7y = 95

4b + 7(5) = 95

4b + 35 = 95

4b = 60

b = 15

So a blue token is worth 15 points.

Therefore, a blue token is worth 15 points and a yellow token is worth 5 points.

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Answer:

We can use the concept of percentage to solve this problem.

Let's represent the total number of cards sold for Mother's Day by "x". We know that one salesman sold 47 cards, which was 4% of the total number of cards sold. So we can set up an equation:

0.04x = 47

Solving for "x", we divide both sides by 0.04:

x = 47 / 0.04

Using a calculator, we get:

x = 1175

Therefore, the total number of cards sold for Mother's Day was 1175.

The profit is maximum when 40 lawns are mowed.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given is that Kieran is starting a lawn-mowing buisness in her neighborhood. She creates a graph to help her determine what to charge customers per lawn to maximize her profits. She uses {c} to represent the number of lawns she mows and {y} to represent her profit in dollars.

The profit is maximum when 40 lawns are mowed as at this point the the peak of the parabola occurs.

Therefore, the profit is maximum when 40 lawns are mowed.

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The permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as (A) ([1,6,2,5])([3,4]).

To find the product of disjoint cycles, we can start by looking at the first element in the first cycle, which is 1. We see that 1 maps to 6 in the given permutation, so we write ([1,6. Next, we see that 6 maps to 2, so we write ([1,6,2. Finally, 2 maps to 5, so we write ([1,6,2,5. Since 5 maps back to 1, we can close the cycle and write ([1,6,2,5]).

Next, we look at the remaining elements, which are 3 and 4. We see that 3 maps to 4 and 4 maps back to 3, so we write ([3,4]).

Therefore, the permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as ([1,6,2,5])([3,4]). The correct answer is (A) ([1,6,2,5])([3,4]).

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The multiplicative property of equality states that the same number can be added to or multiplied by both sides of an equation to obtain an equivalent equation. In this case, dividing both sides by 6 gives us u = 78/6 = 13.

The multiplicative property of equality states that if two numbers are equal, then multiplying both sides of the equation by the same number will also result in an equation that is still equal. In other words, if a=b, then ac=bc. We can use this property to solve for the variable u in the equation 78=6u.

To isolate the variable on one side of the equation, we can divide both sides by 6. This will give us:

78/6 = 6u/6

Simplifying the equation gives us:

13 = u

So the solution for u is 13.

In conclusion, the multiplicative property of equality with whole numbers was used to solve for the variable u in the equation 78=6u. The solution is u=13.

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The 95% confidence interval for the population proportion of defective calculators is (0.0015, 0.0069).

Hence, (0.0015 < p < 0.0069).

According to the given information

we can use the formula for calculating the confidence interval for a population proportion,

⇒ P ± z√(P(1-P )/n)

Where,

P = sample proportion of defective calculators = 5/1200

                                                                              = 0.0042

n = sample size = 1200

z = z-score for 95% confidence level = 1.96 (from standard normal distribution table)

Substituting the values in the formula, we get,

⇒ 0.0042 ± 1.96√(0.0042(1-0.0042)/1200)

Simplifying the expression gives us the confidence interval,

⇒ (0.0015 < p < 0.0069)

Therefore,

The 95% confidence interval for the population proportion of defective calculators is (0.0015, 0.0069).

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Simplifying the expression (2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27) will result to (x - 5)/(3x(x - 3)(x + 5)).

To simplify the given expression completely, we need to factor the numerator and denominator of each fraction, and then simplify by canceling out common factors.

(2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27)

= (2x(x² - x - 20))/(2x^2 + 5x - 12) ÷ (6x^2(x^2 - 25))/(8x^3 - 27)

= (2x(x - 5)(x + 4))/(2x² + 8x - 3x - 12) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)(4x² + 6x + 9)/(6x²(x - 5)(x + 5))

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

= (x - 5)/(3x(x - 3)(x + 5))

Therefore, the simplified expression is (x - 5)/(3x(x - 3)(x + 5)).

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Vοlume οf the Pyramid is 21 cm³

A prism is a sοlid shape with twο identical parallel bases and flat sides that cοnnect the bases. The sides οf a prism are usually rectangles, but they can alsο be triangles οr οther pοlygοns.

A pyramid is a sοlid shape with a pοlygοnal base and triangular sides that meet at a single pοint called the apex.

When a prism have same base area and height as that οf a pyramid the vοlume οf the prism is three times that οf the pyramid.

=> Vοlume οf prism = 3 Vοlume οf pyramid

Here we have

The prism and pyramid abοve have the same width, length, and height.  

The vοlume οf the prism is 63 cm³  

As we knοw,

Vοlume οf prism = 3 Vοlume οf pyramid

The vοlume οf the Pyramid = [ Vοlume οf prism ]/ 3

= [ 63 cm³]/3 = 21 cm³  

Therefοre,

Vοlume οf the Pyramid is 21 cm³

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The correct answer is O for some discrete probability distributions but not all.

This is because the probability of a random variable X being less than 8 can vary depending on the type of distribution it follows. For some discrete distributions, such as a binomial distribution, the probability of X < 8 can be calculated by summing the probabilities of all possible values of X that are less than 8. However, for other discrete distributions, such as a Poisson distribution, the probability of X < 8 may not be as straightforward to calculate. Therefore, the statement that P(X < 8) = P(X < 8) is true for some discrete distributions but not all.

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By following this process, we were able to evaluate each expression and get the answers of 590, 181, 25, and 6 respectively.

a) (fog)(4) = (f(g(4)) = f(7(4)^2+6) = 5(7(16)+6) = 5(118) = 590

b) (gof)(2) = (g(f(2)) = g(5(2)) = 7(5)^2+6 = 7(25)+6 = 181

c) (fof)(1) = (f(f(1)) = f(5(1)) = 5(5) = 25

d) (gog)(0) = (g(g(0)) = g(7(0)^2+6) = 7(0)+6 = 6

To find the expressions given, we need to first use the definition of a function composition. This means that when we have a function \(f\) composed with a function \(g\), this is represented by \(f\circ g\). When we use a function composition, we evaluate the function \(g\) first, then plug the result into the function \(f\).

For example, in part (a) we have the expression \(f\circ g(4)\). We need to first evaluate \(g(4)\), which gives us \(7(4)^2+6\). Then we plug this result into the function \(f\) to get \(f(7(4)^2+6)= 5(7(4)^2+6) = 590\). We can repeat this process for the rest of the parts. For part (b) we have \(g\circ f(2)\). Evaluating \(f(2)\) gives us \(5(2)\), which we then plug into \(g\) to get \(g(5(2))= 7(5)^2+6 = 181\).

For part (c) we have \(f\circ f(1)\), so evaluating \(f(1)\) gives us \(5(1)\) and then plugging this into \(f\) gives us \(f(5(1))= 5(5) = 25\). Finally, for part (d) we have \(g\circ g(0)\), so evaluating \(g(0)\) gives us \(7(0)^2+6\), which we plug into \(g\) to get \(g(7(0)^2+6) = 7(0)+6 = 6\).

In conclusion, we can use function composition to find the expressions given. We start by evaluating the inner function, then plugging the result into the outer function.

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The height of the building, given the angle of elevation and the distance from the top of the building, is such that he height of the building is 95 meter.

We shall assume that the building, the distance from the foot and the angle, are in a right - angled triangle.

This means that the height of the building is the opposite side and the given distance is the adjacent side.

The relevant operation would be Tan.

The height of the building would be:

Tan ( 60 ° ) = Height / 55 m

Height = Tan ( 60 ° ) x 55

Height = 95 meters

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