For the following exercises, find the decomposition of the partial fraction for the irreducible nonrepeating quadratic factor. 4x^2/(x+5)(x^2+7x-5)

Answer:

A, C, D

Step-by-step explanation:

This is because the ratio between te consecutive terms are constant, that is ×2, ×0.5 and ×3 respectively

Answer:

Step-by-step explanation:

x/13=10

We have to get rid of the 13. (the denominator)

How?

By multiplying 2 sides by 13

Remember the Rules of Maths:

1. Whatever you do to one side, you must do to the other.

2. Use the opposite operation.

So, we used Rule 2 to get rid of the 13.

Now:

x=10*13

(On the left side, the 13s cancel)

x=130

It is always a great idea to double-check

Does 130 divided by 13 equal 10?

Of course it does!

Have a great day!!

I hope everything is clear!

Line passing through AB is perpendicular. A pair of angles that are linear have an angle sum of 180 degrees. The lines are therefore shown to be perpendicular to one another because the angles are 90 degrees in size.

Two lines intersect to generate perpendicular lines, and the angle formed between the two lines must be 90 degrees (right angle).

Given,

Create another line perpendicular to AB passing through C on AB..

Line passing through AB is perpendicular.

Two lines are perpendicular if they cross at a point where a pair of linear congruent angles results. In a plane, a transversal is perpendicular to the other line if it is parallel to one of the two parallel lines.

A pair of angles that are linear have an angle sum of 180 degrees. The lines are therefore shown to be perpendicular to one another because the angles are 90 degrees in size. The linear pair perpendicular theorem is demonstrated by this.

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Answer:

To calculate the total amount, first find out how much you contribute and then add the amount your employer contributes.

Your contribution: 10% of $50,000

= ($50,000 * 10) / 100

= $5,000

Employer's contribution: 3% of $50,000

= ($50,000 * 3) / 100

= $1,500

Total contribution:

= Your contribution + Employer's contribution

= $5,000 + $1,500

= $6,500

So, the total amount being put away in your account each year is $6,500.

Step-by-step explanation:

The measure that would be used to compute the average gender of subjects is the mean. Option a) mean is the correct answer.

The mean is calculated by adding up all of the values in a set of data and dividing by the number of values. In this case, if we assign a value of 0 to represent male and a value of 1 to represent female, we can calculate the mean by adding up all of the values and dividing by the total number of subjects.

However, it is important to note that gender is a binary category and using numerical values to represent it may not be appropriate or respectful. Additionally, the concept of an "average" gender may not be meaningful or relevant in all contexts.

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Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x  (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y  (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

The length of the hypotenuse is 1.

We have,

Let's denote the unknown leg of the right triangle as x.

Since we have a 45-45-90 triangle, we know that the two legs are congruent.

So,

We can set up the following equation:

1/6 = x/c, where c is the length of the hypotenuse.

To solve for c, we can cross-multiply:

x = 1/6 x c

c = 6x

Now, we also know that the hypotenuse is equal to the cotangent of both angles a and b.

Since the two acute angles in a 45-45-90 triangle are congruent, we only need to find the cotangent of one of the angles.

The cotangent of an angle is equal to the ratio of the adjacent side to the opposite side.

In a 45-45-90 triangle, the two legs are congruent, so the adjacent and opposite sides are equal.

So, the cotangent of each acute angle is equal to 1.

So we have:

c = cot(a) = cot(b) = 1

Substituting this value of c into the equation we found earlier:

6x = 1

x = 1/6

Now,

The length of the hypotenuse is:

c = 6x = 6(1/6) = 1

Thus,

The length of the hypotenuse is 1.

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Since the median for both areas is 2 hours or more, at least 50% of the subscribers surveyed spent 2 hours or more per week watching cable TV. Correct options are: a. True, b. False, c. False, d. False

In statistics, mean refers to  average value of  set of numbers. It is calculated by adding up all  numbers in  set and then dividing by  total number of values in  set.

a. True

b. False

c. False

d. False

a. True. Since the median for both areas is 2 hours or more, at least 50% of the subscribers surveyed spent 2 hours or more per week watching cable TV.

b. False. The range for Area A is 3 hours, while the range for Area B is 4 hours, indicating that there is more variability in the data for Area B.

c. False. The number of subscribers surveyed is not given and cannot be determined from the given information.

d. False. The mean number of hours spent watching cable TV is 3 for Area A and 2.5 for Area B, indicating that subscribers in Area A spent more time watching cable TV on average than subscribers in Area B.

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Answer:

(3x - 5) (x + 3)

Step-by-step explanation:

Multiply the coefficient of the first term by the constant:

3 x -15 = -45

Find two factors of -45 that equals 4:

-5 + 9 = 4

Rewrite the polynomial splitting 4 using -5 and 9:

3x2 - 5x + 9x - 15

Add up the first 2 terms, pulling out like factors:

x • (3x-5)

Add up the last 2 terms, pulling out common factors:

3 • (3x-5)

Add everything up:

Answer

(x+3) (3x-5)

This question is incomplete. Find attached to this answer the required diagram.

Answer:

16√3 cm³

Step-by-step explanation:

Volume of a pyramid = 1/3 × Base area × Height

The base area is given as 12√3 cm²

But the height is not given

From the attached diagram an angle was given

Using Trigonometric function of Tangent

tan = Opposite/Adjacent

Opposite = Height of the pyramid

Adjacent = base length of the pyramid = 4√3

Hence,

tan 30° = opposite/4√3

Cross multiply

Opposite = tan 30° × 4√3

Opposite = Height of the pyramid = 4 cm

Volume of a pyramid = 1/3 × Base area × Height

= 1/3 × 12√3 × 4

= 16√3 cm³

Answer:

B. 16√3 cm³

Step-by-step explanation:

Just took the Pre-Test on Edg (2020-2021)!!

A customer can select the meal in 960 ways

Permutations: The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to a variety of possible arrangements or orders. With permutations, the arrangement's sequence is important. Permutations come in three varieties, one without repetition and two with repetition. In contrast to combinations, where data is selected from a group and the order is irrelevant, permutations choose data from a group.

Number of appetizers offered = 6

Number of salads offered = 4

Number of entrees offered = 8

Number of desserts offered = 5

Total number of choices = 6*4*8*5 = 960 ways

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Answer:

i think its d

Step-by-step explanation:

Answer:

23.333....

Step-by-step explanation:

The distance of the ball from the foot of the tower is : 35.18m

The ball would be moved 57.2m away from the foot of the tower for the Angle of elevation to be halved.

Angle of elevation is the angle formed between the horizontal and the  line of view from the vertical.

Analysis:

The height of the tower and the distance of the ball from the foot of the tower form a right angle triangle.

so we use trigonometry.

a) let distance of the ball from foot of tower be x.

  so that, tan 52 = 45/x

  x = 45/tan52

  x = 45/1.279 = 35.18m

b) let the distance of the ball in the new position from the foot of the tower be y.

if the angle of elevation is halved, then new angle is 52/2 = 26°

 tan 26 = 45/y

y = 45/tan26 = 45/0.487 = 92.4m

distance moved from old position to new position = 92.4 - 35.18 = 57.2m

In conclusion, the distance of the ball from the foot of the tower and the distance the ball should move to make its elevation 26° are 35.18m and 57.2m respectively.

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Answer:

they are 11 pints vertically apart and 3 points horizontally apart.

Step-by-step explanation:

The time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d). So the answer is d. 40 minutes

Let's set up the equation based on the given information:

1/24 is the rate at which Sean and Colleen work together (clearing the yard in 24 minutes).

Let's denote the time it takes Colleen to clear the yard alone as c minutes. According to the given information, it would take Sean 20 minutes longer than Colleen to clear the yard alone, so Sean's time is (c + 20) minutes.

To set up the equation, we can combine their individual rates of work:

1/c is Colleen's rate of work (clearing the yard in c minutes).

1/(c + 20) is Sean's rate of work (clearing the yard in c + 20 minutes).

Given that their combined rate is 1/24, we can set up the equation:

1/c + 1/(c + 20) = 1/24

To solve this equation and find the value of c, we can multiply both sides by the common denominator of 24c(c + 20):

24(c + 20) + 24c = c(c + 20)

Simplifying and rearranging the equation:

24c + 480 + 24c = c^2 + 20c

48c + 480 = c^2 + 20c

Rearranging the terms and setting the equation equal to zero:

c^2 - 28c - 480 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. By factoring, we find:

(c - 40)(c + 12) = 0

This gives two possible values for c: c = 40 or c = -12.

Since time cannot be negative, we discard the solution c = -12.

Therefore, the time it would take Colleen alone to clear the yard of leaves is 40 minutes (option d).So the answer is d. 40 minutes.

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Answer:

Z,X,Y,Z

Step-by-step explanation:

Answer:

Length=15cm

Hope this answer is right!!

Step-by-step explanation:

Length be 3 cm longer than the breadth.

So, x=y+3

Perimeter = 2(x+y)54

So, x+y=27 =>x=15

x-y=3 =>x=12

So, length is 15 cm

Answer:

19.6 is the answer

use sine law

22/sin90= x/sin63

The map's scale is 1/2 mile = 1 inch.

The distance between the junior college and high school in real life is 3 miles and on the map, it is 6 inches away. Thus,1 inch = 3/6 miles 1 inch = 1/2 miles.

So, the map's scale is 1/2 mile = 1 inch.

To get the scale of the map, divide the distance on the map by the actual distance. The scale of a map is defined as a proportion of actual size and map size. This proportion might be provided in different ways like a fraction, ratio or bar scale etc.

For example, 1:50,000 means that one unit on the map represents 50,000 units on the actual land. This scale shows a small area with great detail. It is usually used for geological and topographical maps.

The scale of a map determines the degree of detail and amount of information that can be displayed on the map. It is important to select a scale that is appropriate for the purpose of the map. A larger scale will show a greater level of detail but cover a smaller area, while a smaller scale will show less detail but cover a larger area.

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The line which has points (5,7),(-4,-2) is slanting upward.

Given that the line has points (5,7) and (-4,-2).

We are required to find whether the line is upward sloping, downward , horizontal or vertical.

The slope or gradient of a line is basically a number that describes both the direction and the steepness of the line.

Slope between two points \((x_{1} ,y_{1} ),(x_{2} ,y_{2} )\) is equal to \((y_{2} -y_{1}) /(x_{2} -x_{1} )\).

Slope between (5,7) and (-4,-2)=(-2-7)/(-4-5)

=-9/-9

=1

Because the slope is positive so it is an upward sloping line means the difference between the y coordinates and the difference between the x coordinates are equal.

Hence the line which has points (5,7),(-4,-2) is slanting upward.

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To evaluate the integral ∫1−1(|2x|+2) dx exactly using the technique of example 2 in the text, we first split the integral into two parts:

∫1−1(|2x|+2) dx = ∫1^0 (-2x + 2) dx + ∫0^-1 (2x + 2) dx

Next, we can simplify the absolute values:

∫1^0 (-2x + 2) dx + ∫0^-1 (2x + 2) dx = ∫1^0 (-2x + 2) dx + ∫0^-1 (-2x + 2) dx

Now we can integrate each part:

∫1^0 (-2x + 2) dx + ∫0^-1 (-2x + 2) dx = [-x^2 + 2x]1^0 + [-x^2 + 2x]0^-1

Simplifying further, we get:

[-1^2 + 2(1)] - [0^2 + 2(0)] + [0^2 + 2(0)] - [-(-1)^2 + 2(-1)]
= 1 + 1 + 1 = 3

Therefore, the exact value of the integral ∫1−1(|2x|+2) dx is 3.
To evaluate the integral ∫₁₋₁ (|2x|+2) dx, we first need to split the integral into two parts due to the absolute value function.

For x >= 0, |2x| = 2x, and for x < 0, |2x| = -2x.

Now, we split the integral into two parts:

∫₁₋₁ (|2x|+2) dx = ∫₀₋₁ (-2x+2) dx + ∫₁₀ (2x+2) dx.

Now, we evaluate each integral separately:

∫₀₋₁ (-2x+2) dx = [-x²+2x]₀₋₁ = (1-2)-(0) = -1.

∫₁₀ (2x+2) dx = [x²+2x]₁₀ = (1+2)-(0) = 3.

Finally, we add the two results together:

∫₁₋₁ (|2x|+2) dx = -1 + 3 = 2.

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The most the salon would be willing to pay that groomer is $25×4 = $100.

The unitary method is a technique that determines the worth of a single unit from value of multiple units, as well as the quality of multiple units from value of a single unit.

Some key features regarding the unitary method are-

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Answer:

Zero

Step-by-step explanation:

A number divisible by 2 must be positive.  Example: 2, 4, 6, 8

A number divisible by 5 must have either 5 or 0 in the ones place.  Example: 15, 200, 3985, 4500

A number divisible by 9 must have numbers that add up to one of the multiples from nine.  Example:  279 (2+7+9=18), 612 (6+1+2=9)

The digit that all numbers have in common is zero.  Zero is considered positive, is one the numbers required for 5, and, with other numbers, can be divisible by 9.

Apply:

Where (h,k) is the center of the circle, and r= radius.

Since the center is on (0,0) , h=0 and k=0

Since it passes through the point (0,-2) = (x,y)

Solve for r^2

The final equation is:

The gradient of the straight line passing through two points D and E is -8/6 or -4/3.

According to the question,

We have the following information:

The coordinates of the points D and E are (-1, 13) and (5, 5) respectively.

We know that gradient of the line means that we have to find the slope of the line.

We also know that following formula is used to find the slope of line passing through two points:

m = (y2-y1)/(x2-x1)

In this case, we have x1 = -1, y1 = 13, x2 = 5 and y2 = 5.

m = (5-13)/{5-(-1)}

m = -8/(5+1)

m = -8/6

m = -4/3

Hence, the gradient of the straight line passing through two points D and E is -8/6 or -4/3.

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Answer:

5/28

Step-by-step explanation:

5/4 / 7     =  5/4 * 1/7  = 5/28

Answer:

5/28

Step-by-step explanation:

it could also be 0.17 in decimal form

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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