Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

1. To solve 3^(2x-1)=27, we first need to simplify 27 to  power of 3: 27=3^3
3^(2x-1)=3^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
2x-1=3
Solving for x, we get:
2x=4
x=2

2. To solve 3^(x^2-3x)=81, we first need to simplify 81 to the power of 3: 81=3^4
3^(x^2-3x)=3^4
Next, we can use the property that if the bases are the same, the exponents must be equal:
x^2-3x=4
Solving for x, we can use the quadratic formula:
x=(-b±√(b^2-4ac))/(2a)
x=(-(-3)±√((-3)^2-4(1)(-4)))/(2(1))
x=(3±√(9+16))/2
x=(3±5)/2
x=4 or x=-1

3. To solve 4^(x+1)=64, we first need to simplify 64 to the power of 4: 64=4^3
4^(x+1)=4^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=3
Solving for x, we get:
x=2

4. To solve 4^(x+1)=1/64, we first need to simplify 1/64 to the power of 4: 1/64=4^(-3)
4^(x+1)=4^(-3)
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=-3
Solving for x, we get:
x=-4

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The expression that represents the number of almonds in the bag is (6x+13) - (3x-7)

What is Linear Equation?

A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation in which the highest power of the variable is one. A general linear equation can be represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Linear equations can be solved algebraically using techniques like substitution or elimination, and they can be used to model real-world situations involving linear relationships.

The expression that represents the number of almonds in the bag is (6x+13) - (3x-7) which simplifies to 3x + 20.

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The blueprint dimensions of a building that is 70 feet × 90 feet is: 4.375 inches X 5.625 inches.

Scale refers to the ratio or proportion between the dimensions of an object or a system in the real world and its representation in a model, drawing, or map. A scale is typically expressed as a ratio or a fraction, such as 1:100 or 1/4, which indicates the relationship between the size of the object in the real world and the size of its representation in the model or drawing.

Using a scale of 1 inch : 16 feet means that every inch on the blueprint represents 16 feet in the actual building. To find the blueprint dimensions of a building that is 70 feet x 90 feet, we need to divide each dimension by 16.

The blueprint dimensions are:

70 feet ÷ 16 = 4.375 inches

90 feet ÷ 16 = 5.625 inches

Therefore, the blueprint dimensions of the building are approximately 4.375 inches by 5.625 inches.

The answer is: 4.375 inches X 5.625 inches.

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The graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

For the first inequality, 2x + 3y < 9, we will start by graphing the line 2x + 3y = 9, which is the boundary line of the inequality.

To do this, we will solve for y:

2x + 3y = 9

3y = -2x + 9

Divide both sides by 3

y = (-2/3)x + 3

For the second inequality, Y≥ - 2/3x-4

Hence, the graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.

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For rational function, n < m. There is a horizontal asymptote at y = 0.

A rational function is one whose denominator is not zero and which can be expressed as the ratio between two polynomials.

f(x) = p(x) / q(x)

By examining the degrees of a numerator (n) and denominator, we can locate the horizontal asymptote (m).

Thus, For rational function, n < m. There is a horizontal asymptote at y = 0.

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dhgxjdbvsjsjjeve..nndbd

Answer: 5y²

Step-by-step explanation:

  Since 8y² and 3y² are similar terms, we can subtract the coefficients and keep the degree and variable the same.

8 - 3 = 5, so 8y² - 3y² = 5y²

The error is made because two or more shapes are said to be similar if they have common corresponding properties of sides and/ angles. The Option D is correct.

All similar shapes are two or more given shapes that share some properties in terms of their corresponding sides or angles. As a result, if the corresponding sides or angles are related, they are similar. It is important to note that similarity does not imply congruency.

When the sides and angles of the given triangles LMN and QRS are compared, it is clear that: angle Side Angle (ASA) similarity implies that the included side between two pairs of congruent angles is similar. As a result, the Option D explains the error in the diagram.

Missing options "a.Your​ friend's paper does not name the triangles correctly for them to be congruent. b. Your​ friend's paper shows that the SAS Postulate should be used to show congruence because a pair of congruent angles is included between two pairs of congruent sides. c. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the triangles do not have two pairs of congruent angles. d. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.

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Truth Table

This statement can be simplified using proportional algebra as follows: (p ∨ ∼r) ∧ (q ∨ (p ∧ r)). This can be verified using a truth table.

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The median of class A is equal to 40.

The median of class B is equal to 8.

The difference between the median of the two classes is 32.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the dot plot, the median of class A can be determined by sorting the data set in ascending order;

10, 10, 10, 20, 20, 30, 40, 40, 40, 40, 50, 50, 50, 70, 70

Median of class A = 40.

Based on the dot plot, the median of class B can be determined by sorting the data set in ascending order;

4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 16

Median of class B = 8.

For the difference, we have:

Difference = 40 - 8

Difference = 32.

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Answer:

  b (3, −2)

Step-by-step explanation:

You want the solution to the system of equations ...

We see the coefficients of d are opposites, so we can add the equations together to eliminate the d variable:

  (d +e) +(-d +e) = (1) +(-5)

  2e = -4 . . . . . . . . simplify

  e = -2

Substituting into the first equation, we have ...

  d +(-2) = 1

  d = 3 . . . . . . add 2

The solution is (d, e) = (3, -2).

__

Additional comment

We also note that the coefficients of 'e' are identical, so we can eliminate 'e' as a variable by subtracting one equation from the other. We choose to subtract the equation with the lower value coefficient of 'd'.

  (d +e) -(-d +e) = (1) -(-5)

  2d = 6 . . . . . . . simplify

  d = 3 . . . . . . . . divide by 2; matches the solution above.

The attached graph uses x and y, because those are the built-in independent and dependent variables. Your graphing calculator may let you define the variables as you wish.

Easton needs to complete 3 more jumps to reach his goal of completing 70% of the jumps on the skateboard course.

Easton's goal is to complete 70% of the jumps on the skateboard course. This means he needs to complete 70% of the total number of jumps.

We know that Easton has already completed 18 jumps out of 30, which is equivalent to completing 60% of the jumps.

The total number of jumps on the skateboard course is 30.

Easton's goal is to complete 70% of the jumps, which is:

0.7 x 30 = 21 jumps

Easton has already completed 18 jumps, so he needs to complete:

21 - 18 = 3 more jumps

So, he needs 3 more jumps

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Answer:

-3/2

Step-by-step explanation:

To find:-

Answer:-

We are interested in finding out the slope of the given line . We can see that the line passes through the points (1,0) and (-1,3) . For finding out the slope we can use the formula,

[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

Now on substituting the respective values, we have;

[tex]:\implies \sf m = \dfrac{0-3}{1-(-1)} \\[/tex]

[tex]:\implies \sf m = \dfrac{-3}{1+1}\\[/tex]

[tex]:\implies \sf \pink{m=\dfrac{-3}{2}}\\[/tex]

Hence the slope of the line is -3/2.

The classification of the variables in the question above is  as follows:

Discrete quantitative data refers to data that can be counted in whole numbers and is often used to describe things that can be categorized into groups. like the number of people in a room or the number of cars in a parking lot.

Quantitative continuous data refers to data that can be measured on a continuous scale, such as time, temperature, or weight, like the temperature of a room or the weight of a person.

Qualitative nominal data refers to data that can be categorized into groups but cannot be measured or ranked, like the type of car someone drives or the color of someone's eyes.

Qualitative ordinal data refers to data that can be categorized into groups and can be ranked or ordered, like the level of education someone has achieved or the ranking of a sports team.

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E1 x E2 x E4 = (2 0) (0 1) (1 0) (3 1)

(a) A-1 can be expressed as a product of elementary matrices by following these steps:
1. Create a matrix A' = A (2 0)
                        (0 1)
2. Create an elementary matrix E1 = (1 -2)
                                            (0  1)
3. Multiply A' and E1 to get matrix E2 = (2 -4)
                                                            (0  1)
4. Create an elementary matrix E3 = (1  0)
                                            (-3 1)
5. Multiply E2 and E3 to get matrix E4 = (2  0)
                                                                        (-6 1)
6. Create an elementary matrix E5 = (1  0)
                                            (0  2)
7. Multiply E4 and E5 to get A-1 = (2  0)
                                                                  (-3 2)
Therefore, A-1 can be expressed as a product of elementary matrices, E1 x E3 x E5 = (2 0) (-6 1) (1 0) (0 2).

(b) A can be expressed as a product of elementary matrices by following these steps:
1. Create an elementary matrix E1 = (2  0)
                                            (0  1)
2. Create an elementary matrix E2 = (1  1)
                                            (0  1)
3. Multiply E1 and E2 to get matrix E3 = (2 1)
                                                                        (0 1)
4. Create an elementary matrix E4 = (1  0)
                                            (3  1)
5. Multiply E3 and E4 to get A = (2 1) (6 4)
Therefore, A can be expressed as a product of elementary matrices, E1 x E2 x E4 = (2 0) (0 1) (1 0) (3 1).

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The inequalities that represent the regular price of eyeglass frames will be 0.4r ≤ 120 and r ≥ 4(360/5).

If we let r represent the regular price of the eyeglass frames, then we can write the following two inequalities based on the given information:

0.4r ≤ 120

This inequality represents the fact that the lowest regular price for the eyeglass frames is $120. We use 0.4 because a 60% discount means that the price paid is 40% of the regular price.

Also, r ≥ 4(360/5) as this inequality represents the fact that the highest regular price for the eyeglass frames is $360. We use 4(360/5) because a 75% discount means that the price paid is 25% of the regular price, which is equivalent to multiplying the regular price by 0.25. Then, 4 times that amount gives us the regular price, which is $360 in this case.

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The final factored form of the polynomial is b(a-b) and the category of the remaining polynomial is a binomial.

The first step in factoring out the GCF from the polynomial ab+ay-b^(2)-by is to identify the greatest common factor of all the terms. In this case, the GCF is b. Once we have identified the GCF, we can factor it out from each term by dividing each term by the GCF. This gives us:

ab+ay-b^(2)-by = b(a+y)-b(b+y) = b(a+y-b-y)

Next, we can simplify the remaining polynomial by combining like terms:

b(a+y-b-y) = b(a-b)

Finally, we can identify the category of the remaining polynomial. Since it has two terms and each term has a degree of 1, the remaining polynomial is a binomial.

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An equation passing through the points (2, 13) and (2, -11) is x = 2.

The equation of a line can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line that goes through the given points, we first need to find the slope. The slope can be calculated using the formula:

[tex]\[m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\][/tex]

Plugging in the given points, we get:

[tex]\[m = \frac{-11 - 13}{2 - 2} = \frac{-24}{0}\][/tex]

Since the denominator is 0, the slope is undefined. This means that the line is vertical. A vertical line has the equation x = a, where a is the x-coordinate of any point on the line. Since both of the given points have the same x-coordinate of 2, the equation of the line is x = 2.

Therefore, the equation with the given characteristics is x = 2.

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Answer:

No solution

Step-by-step explanation:

Use the given functions to set up and simplify f(9)

Answer:0.15 miles a minute

Step-by-step explanation:

Her pace is 6 minutes and 40 seconds a mile, she is going 0.15 miles per minute and will go 9 miles an hour

Shea needs to do 600 carpet cleaning per year to break even.

What is revenue?

Total revenue is the total amount of money earned by a business from the sale of its products or services during a particular period of time.

To break even, the total revenue Shea generates from the carpet cleaning business must be equal to the total cost of running the business.

Let's first calculate the total cost of running the business per year:

Total Cost = Fixed Costs + Variable Costs

Since the fixed plus variable costs per month total $1,500, the total cost per year would be:

Total Cost = $1,500 x 12

Total Cost = $18,000

Now, let's calculate the profit that Shea makes per cleaning:

Profit per Cleaning = Price per Cleaning - Cost per Cleaning

Profit per Cleaning = $60 - $30

Profit per Cleaning = $30

So, Shea makes a profit of $30 per cleaning.

To break even, the total profit generated by the number of cleanings Shea does per year should be equal to the total cost of running the business per year:

Total Profit = Total Revenue - Total Cost

If x is the number of carpet cleaning Shea needs to do per year to break even, then:

Total Revenue = Price per Cleaning x Number of Cleanings per Year = $60x

Total Profit = Profit per Cleaning x Number of Cleanings per Year = $30x

Setting Total Profit equal to Total Cost:

$30x = $18,000

x = $18,000 / $30

x = 600

Therefore, Shea needs to do 600 carpet cleaning per year to break even.

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Answer:

C is your answer

Step-by-step explanation:

To show that the system AX = B is equivalent to the upper-triangular system UX = Y and find the solution, we need to use the Gaussian elimination method. The Gaussian elimination method is a process of reducing a system of linear equations to an equivalent upper-triangular system.

Step 1: Write the given system of equations in matrix form:
```
| 2 -2  5 |   | x1 |   |  6  |
| 2  3  1 | * | x2 | = | 13  |
|-1  4 -4 |   | x3 |   |  3  |
```
Step 2: Use the Gaussian elimination method to reduce the matrix to an upper-triangular form:
```
| 2 -2  5 |   |  6  |
| 0  7 -9 | = |  7  |
| 0  0 9/7|   | 18/7|
```
Step 3: Write the upper-triangular system in equation form:
```
2x1 - 2x2 + 5x3 = 6
0x1 + 7x2 - 9x3 = 7
0x1 + 0x2 + 9/7x3 = 18/7
```
Step 4: Solve the system using back substitution:
```
x3 = 18/7 * 7/9 = 2
x2 = (7 + 9*2)/7 = 4
x1 = (6 + 2*2 - 5*2)/2 = 1
```
Step 5: Write the solution in vector form:
```
| x1 |   | 1 |
| x2 | = | 4 |
| x3 |   | 2 |
```
Therefore, the solution to the system AX = B is x1 = 1, x2 = 4, and x3 = 2.

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a) On average, 0.5 * 24 = 12 of the digits would be even. b)  No, you would not necessarily get exactly the number predicted in part a. This is because there is always variation from sample to sample. While the expected value is 12

a. On average, you would expect 12 of the 24 digits to be even. This is because there are an equal number of even and odd digits (0, 2, 4, 6, 8 are even and 1, 3, 5, 7, 9 are odd), so the probability of a digit being even is 0.5. Therefore, on average, 0.5 * 24 = 12 of the digits would be even.

b. No, you would not necessarily get exactly the number predicted in part a. This is because there is always variation from sample to sample. While the expected value is 12, it is possible to get more or less than 12 even digits in a sample of 24.

This is due to the randomness of the random number table and the fact that samples do not always perfectly match the population proportion.

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Answer:

The answer is B

Step-by-step explanation:

To solve this, we need to combine like terms.
(9c-8d) + (2c-6) + (-d+3)
9c + 2c - 8d - d - 6 + 3
11c - 8d - d - 6 + 3
11c - 9d - 6 + 3
11c - 9d - 3

The length and width of the toolbox are 8 feet and 5 feet respectively.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given that the volume of the toolbox is 80 cubic feet, so we can write:

V = w × h × l = 80ft³

Next, we know that the width is 3 feet less than the length, so we can write:

w = l - 3

Now we can substitute the second equation into the first equation to get an equation with just one variable:

V =  w × h × l = l(l - 3)(2) = 80

Simplifying this equation, we get:

2l² - 6l - 80 = 0

We can solve this quadratic equation using the quadratic formula:

l = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -6, and c = -80. Plugging in these values, we get:

l = (6 ± √(6² - 4(2)(-80))) / 4

l = (6 ± √(676)) / 4

We take the positive value of l since the length must be positive, so we get:

l = (6 + 26) / 4

l = 8

Now we can use the second equation (w = l - 3) to find the width:

w = l - 3

w = 8 - 3

w = 5

Therefore, the length of the toolbox is 8 feet and the width is 5 feet.

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Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

The terms of the polynomial are -5s^(7), -8s^(4), 6s^(3), 4s, and -6. The degree of each term is 7, 4, 3, 1, and 0, respectively. The degree of the polynomial is the highest degree of any of its terms, which is 7.

The leading term is the term with the highest degree, which is -5s^(7). The leading coefficient is the coefficient of the leading term, which is -5. The constant term is the term with a degree of 0, which is -6.

So, the terms are -5s^(7), -8s^(4), 6s^(3), 4s, and -6; the degree of each term is 7, 4, 3, 1, and 0; the degree of the polynomial is 7; the leading term is -5s^(7); the leading coefficient is -5; and the constant term is -6.

Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

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Answer:

a) The digit in the hundredths place in 0.453 is 3. Therefore, the value of the digit in color is 3/100.

b) The digit in the tenths place in 43.1 is 1. Therefore, the value of the digit in color is 1/10.

c) The digit in the thousandths place in 92.303 is 3. Therefore, the value of the digit in color is 3/1000.

d) The digit in the ten-thousandths place in 2.3214 is 1. Therefore, the value of the digit in color is 1/10,000.

After calculating the probability we get, there is a 7.20 percent chance that the first candidate will be identified during the fifth interview and it should take 3.33 interviews to discover the first candidate.

The quantity X of repeated trials needed to obtain r successes with p probability in a binomial experiment is known as the negative binomial distribution.

When x succeeds after n tries, the probability is given by:

P(X-x) = Cn-1, x-1*p(power x) * (1 - p)power (n-x)

The number of unique combinations of x items from a set of n elements, Cn,x, is determined by the formula below.

Cn,x = n! / x! ( n! - x! )

This problem involves that:

Let's say that 30 percent of those who apply for a certain industrial position have advanced expertise in computer programming. That follows that.

(a) We need to determine the probability that the first applicant with advanced programming training will be discovered during the fifth interview.

This is the likelihood that it will take 5 attempts to get 1 success.

So, n=5, x=1

P(X-x) = Cn-1, x-1*p(power x) * (1 - p)power (n-x)

P(X-5) = C 4,0* (0.30)(power 1) * (0.70)power (4)

= 0.0720.

During the sixth interview, there is a 7.20% chance that the first candidate with advanced programming training will be discovered.

(b) To find how many applicants should be expected to be interviewed in order to select the first candidate with advanced training, calculate

It is stated by how many trials are anticipated to result in r success:

E = r/p

Thus with the value r=1

E = r/p

= 1/0.3

= 3.33.

For the first candidate with advanced training, it will take an average of 3.33 interviews.

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The solution to this linear programming problem is (x,y) = (3,4) and f = 22.

To solve this linear programming problem, we need to find the feasible region by graphing the constraints and then use the objective function to find the maximum value of f.

1. Graph the constraints:

x + y ≤ 7 can be rewritten as y ≤ -x + 7
2x + y ≤ 12 can be rewritten as y ≤ -2x + 12
y ≤ 4

2. Find the feasible region:

The feasible region is the area that satisfies all of the constraints. In this case, it is the area bounded by the three lines and the x and y axes.

3. Use the objective function to find the maximum value of f:

f = 2x + 4y

To find the maximum value of f, we need to find the corner points of the feasible region and plug them into the objective function. The corner points are (0,4), (3,4), and (4,3).

f(0,4) = 2(0) + 4(4) = 16
f(3,4) = 2(3) + 4(4) = 22
f(4,3) = 2(4) + 4(3) = 20

The maximum value of f is 22 at the point (3,4).

Therefore, the solution to this linear programming problem is (x,y) = (3,4) and f = 22.

Answer:

(x,y) = (3,4)

f = 22

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