Help! Again..
The sales tax in your city is 8.8%, and an item costs 63 BEFORE tax.
How much tax would you pay on that item?

The correct partial fraction decomposition of\(\(\frac{6}{(x+3)(x^2+5)}\)\) is:

\(\[\frac{6}{(x+3)(x^2+5)} = \frac{A}{x+3} + \frac{Bx+C}{x^2+5}\]\)

To determine the values of A, B, and C, we can use the method of partial fraction decomposition.

We start by multiplying both sides of the equation by the common denominator, \(\((x+3)(x^2+5)\)\), to eliminate the denominators:

\(\[6 = A(x^2+5) + (Bx+C)(x+3)\]\)

Next, we expand the right side of the equation:

\(\[6 = Ax^2 + 5A + Bx^2 + 3Bx + 3C\]\)

Now, we can collect like terms and equate the coefficients of corresponding powers of x:

\(\[(1A + B)x^2 + (3B)x + (5A + 3C) = 6\]\)

Since the left side has no x term or constant term, we can set the coefficients of those terms on the right side equal to zero:

\(\[\begin{align*}1A + B &= 0 \quad \text{(coefficient of } x^2 \text{ term)} \\3B &= 0 \quad \text{(coefficient of } x \text{ term)} \\5A + 3C &= 6 \quad \text{(constant term)}\end{align*}\]\)

From the second equation, we find that B = 0. Substituting this into the first equation, we obtain A = 0 as well. Plugging B = 0 and A = 0 into the third equation, we can solve for C:

\(\[5(0) + 3C = 6 \implies C = 2\]\)

Therefore, the correct partial fraction decomposition is:

\(\[\frac{6}{(x+3)(x^2+5)} = \frac{2}{x^2+5}\]\)

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The domain is 0 ≤ x ≤ 52. The maximum number of laws that she can mow with 13 gallons is of 52, and the minimum number is of 0.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 13, hence the intercept b is given as follows:

b = 13.

When x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is:

y = -0.25x + 13.

From the intercept, the minimum amount can be mowed is given as follows:

0.

The maximum amount is given as follows:

-0.25x + 13 = 0

0.25x = 13

x = 13/0.25

x = 52.

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The measure of the remaining angle is 72 degree, the correct option is A.

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.

Given

A recycling bin is shaped like a trapezoid.

The bottom 2 angles are 108 degrees.

The top left angle is 72 degrees.

The front view of a recycle bin is shaped like a trapezoid is given by;

\(\rm \angle 1+ \rm \angle 2+ \rm \angle 3+ \rm \angle4= 360\\\\108+108+72\rm +\angle 4=360\\\\\rm 288+\angle 4 = 360 \\\\\rm \angle 4=360-288\\\\\rm \angle 4=72\)

Hence, the measure of the remaining angle is 72 degree.

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Answer: A) 72

Step-by-step explanation: I got it right

Answer:

cos(θ) = x/1

Since P is in Quadrant III, x must be negative.

We can use the Pythagorean Theorem to find x:

x^2 + (-6/7)^2 = 1

x^2 + 36/49 = 1

x^2 = 1 - 36/49

x^2 = 13/49

x = ±√13/7

Since P is in Quadrant III, x must be negative, so x = -√13/7

cos(θ) = x/1 = -√13/7

Answer:

Smallest surface area is of Cuboid B i.e 440 cm²

So, The company will choose cuboid B

Step-by-step explanation:

We need to find the surface area of all cuboids.

Surface Area of Cuboid A:

Length = 6

Breadth = 25

Height = 4

The formula used is: \(Surface \ Area \ of \ Cuboid=2((Length\times Breadth)(Breadth \times Height)+(Length \times Height)\)

Putting values and finding surface area:

\(Surface \ Area \ of \ Cuboid=2((Length\times Breadth)(Breadth \times Height)+(Length \times Height)\\Surface \ Area \ of \ Cuboid=2((6 \times 25)+(25 \times 4)+(6 \times 4))\\Surface \ Area \ of \ Cuboid=2(150+100+24)\\Surface \ Area \ of \ Cuboid=2(274)\\Surface \ Area \ of \ Cuboid=548\: cm^2\)

So, Surface Area of Cuboid A = 548 cm²

Surface Area of Cuboid B:

Length = 10

Breadth = 6

Height = 10

The formula used is: \(Surface \ Area \ of \ Cuboid=2((Length\times Breadth)(Breadth \times Height)+(Length \times Height)\)

Putting values and finding surface area:

\(Surface \ Area \ of \ Cuboid=2((Length\times Breadth)(Breadth \times Height)+(Length \times Height)\\Surface \ Area \ of \ Cuboid=2(10 \times 6)+(6 \times 10)+(10 \times 10))\\Surface \ Area \ of \ Cuboid=2(60+60+100)\\Surface \ Area \ of \ Cuboid=2(220)\\Surface \ Area \ of \ Cuboid=440\: cm^2\)

So, Surface Area of Cuboid B = 440 cm²

Surface Area of Cuboid C:

Length = 2

Breadth = 20

Height = 15

The formula used is: \(Surface \ Area \ of \ Cuboid=2((Length\times Breadth)(Breadth \times Height)+(Length \times Height)\)

Putting values and finding surface area:

\(Surface \ Area \ of \ Cuboid=2((Length\times Breadth)(Breadth \times Height)+(Length \times Height)\\Surface \ Area \ of \ Cuboid=2((2 \times 20)+(20 \times 15)+(2 \times 15))\\Surface \ Area \ of \ Cuboid=2(40+300+30)\\Surface \ Area \ of \ Cuboid=2(370)\\Surface \ Area \ of \ Cuboid=740\: cm^2\)

So, Surface Area of Cuboid C = 740 cm²

So, We get:

Surface Area of Cuboid A = 548 cm²

Surface Area of Cuboid B = 440 cm²

Surface Area of Cuboid C = 740 cm²

The company wants to choose the design having smallest surface area.

So, smallest surface area is of Cuboid B i.e 440 cm²

So, The company will choose cuboid B

Answer:

x = 5/4

Step-by-step explanation:

16x / 16 = 20 / 16

x = 5/4

Answer:

x = 5/4 or 1.2

Step-by-step explanation:

20/16 can be simplified to a smaller fraction, which is 5/4 because 20 and 16 have a common multiple of 4. 5/4 turned into a decimal is 1.2.

In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the errors come from a normal distribution.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centred on the mean, implying that data closer to the mean occur more frequently than data further away from the mean.

The normal quantile plot of the residuals in a simple linear regression model is used to establish if it is reasonable to think the errors are normal.

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To determine the value of k for which the two given lines are perpendicular, we need to find the dot product of their direction vectors and set it equal to zero. The direction vector of the first line is given by <k+2, k-2, 2k+4>, and the direction vector of the second line is <2, -10, -2>. Taking the dot product of these two vectors, we get:

(k+2)(2) + (k-2)(-10) + (2k+4)(-2) = 0

Simplifying this equation, we have:

2k + 4 - 10k + 20 - 4k - 8 = 0

Combining like terms, we get:

-12k + 16 = 0

Solving for k, we have:

-12k = -16

k = 16/12

k = 4/3

Therefore, the value of k that makes the two lines perpendicular is k = 4/3.

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Answer:

18 men = 36 tons in 6 hours

Step-by-step explanation:

3 men = 1 ton in 1 hour

6 men = 2 ton in 1 hour

9 men = 3 tons in 1 hour

with this you find a pattern

3 men = 2 tons in 2 hours

3 men = 3 tons in 3 hours

3 men = 6 tons in 6 hours

6 men = 12 tons in 6 hours

9 men = 18 tons in 6 hours

12 men = 24 tons in 6 hours

15 men = 30 tons in 6 hours

18 men = 36 tons in 6 hours

(This is how i worked it out)

Answer:

18 people

Step-by-step explanation:

Method A:

3 man-hours to stack 1 ton

36 tons is 36 times 1 ton, so it takes 36 times as long to stack.

36 * 3 man-hours to stack 36 * 1 ton, or

108 man-hours to stack 36 tons

To do the job in 6 hours instead of 108, you need to do 108/6 = 18 times as much work per hour, so you need 18 times as many people.

18 * 1 person = 18 people

Answer: 18 people

Method B:

1 person works 3 hours and stacks 1 ton. That same person works another 3 hours and stacks another ton. In a total of 6 hours, 1 person stacked 2 tons. Since you need 36 tons stacked in the same 6 hours, and 36 = 18 * 2, you need 18 times the number of people, so you need 18 people.

Answer:

answer is 20c+14

hope this helps:)

Answer:

2 1/4

Step-by-step explanation:

How many time can 4 go into 9, 2

So that is your whole number, and 2 is 8/4

the you can do 9/4 - 8/4 and you get a remainder of 1/4

so you get 2 1/4

Answer:

2 1/4

Step-by-step explanation:

if you do 9÷4 you get 2. What is left over is 1 so it would be 2 1/2 at its simplest form.

Answer:

puppy

Step-by-step explanation:

The resulting value after the subtraction of 15/57 - 6/45 is 37/285

Subtraction:

Subtraction is an arithmetic operation that represents the operation of removing the particular objects from a collection.

It is signified by the minus sign, −.

Given,

Here we need to find the value of the subtraction of 15/57 - 6/45.

The fractions have unlike denominators.

First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(57, 45) = 855

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD.

This is basically multiplying each fraction by 1.

\(\frac{15}{57}\times\frac{15}{15}-\frac{6}{45}\times\frac{19}{19}\)

Complete the multiplication and the equation becomes

=> 225/855 - 114/855

Complete the multiplication and the equation becomes

=> 111/855

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 111 and 855 using

GCF(111,855) = 3

\(= > \frac{111 \div 3}{855 \div 3} = \frac{37}{285}\)

Therefore, resulting value is 37/285.

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Angle 1 and 2 are equal because of correspondence angle

so , (78-2x) = (89-3x)

x = 89 - 78

x = 11

hence angle 1 = ( 78 - 2*11) = 56

and angle 2 = ( 89-3*11) = 56

So, both of angle is 56

hope it help and your day will full of happiness

The double integral for the function is \(\int\limits^a_b\int\limits^a_R {\frac{4x}{1+xy} (5In(5)-4} \,\)

The given integral is \(\int\limits^a_b\int\limits^a_R {\frac{4x}{1+xy} } \, d.A\)

The two sets or coordinates shall be applied during the process of integrating the first and second sets of the function

Where R is = (0,4)/x (0,1)

This can be evaluated as follow\(\int\limits^a_b \int\limits^a_R {\frac{4x}{1+xy} } \, d.xA\)

⇒\(4\int\limits^1_0 \int\limits^4_0 {\frac{1}{y-\frac{1}{y(1+xy)}} } } \, dy/dx\)

This can be simplified further as follows

= 4\(\int\limits^1_0 \frac{4/y - In(1+xy) }{x^{2} } x} \, dy\)

Applying the second integral we have

4\(\int\limits^1_0 {\frac{4}{y^{2} } {4y-[In(1+4y\\)}/4 \,\)

When we use the I V method of integration we get

4(5In(5)-4)

This is also simplified as

4(5In(5)-4

Therefore we can conclude that the second integral; is

double Integral 4x?1+xy (5In(5)-4}

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The value of double integral. ∬4x/(1+xy)dA ; R = [0, 4] × [0, 1] is -64/17.

If f(x,y) is continuous function on the region D then we can compute the double integral ∬f(x,y)dA

D

This result is known as Fubini's Theorem. We have A = xy

=> dA = dxdy

let , I = ∬f(x,y)dA =₀∫⁴ ₀∫¹4x/(1+xy)dydx

R

firstly integrated with respect to y

I = ₀∫⁴ ₀[ ln(1+xy)]⁴dx

= ₀∫⁴ [ln(1 + 4x)]dx

I = ₀[ 4/(1 + 4x) ]⁴

=> I = [ 4/(1+16) - 4/(1+0)]

=> I = 4/17 - 4 = - 64/17

Hence , required value is -64/17.

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Appendix 7.1 and Appendix 1. They have access to their professor for guidance and assistance through online channels. Additionally, the students can seek help from their classmates through the class discussion forum.

To complete the tasks, they will utilize a spreadsheet program and upload their completed workbooks to the content management system for evaluation.

The students will engage in a collaborative learning process facilitated by their instructor. By forming online groups, they can share ideas and work together on the assigned tasks. However, each student is responsible for performing the required steps individually, as outlined in Appendix 7.1 and Appendix

1. This approach allows for individual skill development and understanding of the subject matter while also fostering a sense of community and support through access to the professor and classmates. Utilizing a spreadsheet program enables them to organize and analyze data effectively.

Finally, uploading their completed workbooks to the content management system ensures easy evaluation by the instructor. Overall, this approach combines individual effort, collaboration, and technological tools to enhance the learning experience for the students.

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Answer:

  47.5 cm

Step-by-step explanation:

You want the height of a trapezoid with bases of lengths 135 cm and 105 cm, and an area of 5700 cm².

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  5700 = 1/2(135 +105)h

  5700 = 120h

  h = 5700/120 = 47.5

The height of the tabletop is 47.5 cm.

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a. The events are dependent because the outcome of one cube affects the outcome of the other cube.

b. The probability of rolling an even number on the white cube and a sum of 8 is 3/36, or 1/12.

a. The outcomes of one cube influence the outcomes of the other cube, hence the events are interdependent.

There are just a few conceivable results for the black cube if the white cube displays an even number: 2 and 6, 3 and 5, or 4 and 4.

As a result, there are fewer outcomes that could happen, making the events dependent.

b. A sum of 8 and an even number on the white cube have a probability of 1/12, or 3/36.

This is due to the fact that there are three possible outcomes when rolling an 8 with an even and an odd number (2-6, 3-5, or 4-4).

Three of the 36 potential outcomes meet the requirements. The likelihood is therefore 3/36.

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Answer:

C. y= 3(x + 2)^2 + 2

Step-by-step explanation:

A. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( 2 , − 2 )

B. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( − 2 , 2 )

C. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( − 2 , 2 )

D. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( 2 , 2 )

Answer:

did you forget to attach a photo

Answer:

5/8 * 100 = 62.5 %

Answer:

14

Step-by-step explanation:

The diagram is right angle triangle so we can use SOHCAHTOA

So in the diagram we have 62 degree opposite to x and the hypotenuse

Step 1

Sin62=x/16

Step 2

X=16sin62 by cross multiplication

Step 3

X=14.13

X=14

Answer:

Yes one pair of the opposite sides could measure 10 inches , and the other pair could measure 13 inches.

Step-by-step explanation:

A parallelogram have opposite sides parallel and congruent

the given quadrilateral is a parallelogram then

10 = x + 2 Equation A

x + 5 = 2x - 3 Equation B

Solving for Equation A:

x = 10 -2 = 8 inches

Solving for Equation B;

2x - x = 5 + 3

x = 8 inches

Value X are the same equations.

Means that

For x=8 inches opposite side

So Yes one pair of the opposite sides could measure 10 inches , and the other pair could measure 13 inches.

The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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The five-number summary for the weights of 30 preschool children is: Minimum: 25 pounds, First quartile (Q1): 27 pounds, Median (second quartile or Q2): 30 pounds, Third quartile (Q3): 34 pounds, Maximum: 38 pounds

To find the five-number summary, you need to order the data from smallest to largest and then identify the minimum, Q1, median (Q2), Q3, and maximum values. In this case, the data has already been sorted, so we just need to identify the values at each quartile.

To find the five-number summary, we need to determine the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and the maximum value.

1. Minimum: 25
2. Maximum: 38
3. Median (Q2): The middle value is between the 15th and 16th values, which are both 31. So, the median is 31.
4. First Quartile (Q1): The median of the lower half (1st to 15th values), which is between the 7th and 8th values (27.5 and 28). Q1 = (27.5 + 28) / 2 = 27.75
5. Third Quartile (Q3): The median of the upper half (16th to 30th values), which is between the 22nd and 23rd values (34.5 and 35). Q3 = (34.5 + 35) / 2 = 34.75

The five-number summary is: 25, 27.75, 31, 34.75, 38.

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Answer:

I think the first step is to group all the addition first and then you do the subtraction.

Answer:

Remember PEMDAS; parenthesis, exponents, multiplication, division, addition and subtraction.

Step-by-step explanation:

so ti will be;

2+7+5-8+13

27-8

21

The expression to be evaluated is x - 3 > 0, and there are four different expressions given as answer choices. The goal is to determine which expression, if any, is equivalent to the original expression.

To evaluate the original expression, we first need to isolate the variable x. Adding 3 to both sides of the inequality gives us x > 3. This means that any value of x greater than 3 will satisfy the inequality.

Now let's examine each of the answer choices to see if any of them are equivalent to x > 3.

a. ((!x) - 3) > 0: This expression involves the logical operator "not," which will give the opposite truth value of the statement it is applied to. However, the expression inside the parentheses is just x, so applying the "not" operator doesn't change anything. Therefore, this expression is not equivalent to the original expression.

b. (!(x - 3) > 0): This expression also involves the "not" operator, but it is applied to the entire expression (x - 3) > 0. In other words, it is checking if the inequality is not true. If we simplify the inequality as we did before, we get x > 3. The negation of this inequality is x <= 3. Therefore, expression b is equivalent to x <= 3.

c. ((!x) - (3 > 0)): This expression involves both the "not" operator and a comparison using the greater than symbol. Again, applying the "not" operator to x just gives us !x. The expression (3 > 0) is always true, so subtracting it from !x doesn't change anything. Therefore, this expression is equivalent to !x.

d. !((x - 3) > 0): This expression is the negation of the inequality (x - 3) > 0. If we simplify this inequality as before, we get x > 3. The negation of this inequality is x <= 3, which is the same as the answer we got in expression b. Therefore, expression d is equivalent to x <= 3.

In summary, expressions b and d are equivalent to the original expression x - 3 > 0, and both indicate that x must be greater than 3. Expressions a and c are not equivalent to the original expression.

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Answer:

17.74

Step-by-step explanation:

Rounded to the nearest 0.01 or

the Hundredths Place.

Answer:

C. 8x^9

Step-by-step explanation:

(2x³)³=8x^9

Answer:

Ro 90

Ro - 270

Step-by-step explanation:

Draw it to figure it out

The two possible transformations that could have taken place are:

Ro, 90°

Ro, -270°

Here, we have,

To determine which transformations could have taken place for the given vertex to be located at (2, 3) after rotation, we need to consider the change in coordinates.

The original vertex is at (3, -2), and after rotation, it is located at (2, 3).

Let's analyze the changes in the x-coordinate and y-coordinate separately:

Change in x-coordinate: From 3 to 2, there is a decrease of 1 unit.

Change in y-coordinate: From -2 to 3, there is an increase of 5 units.

Based on these changes, we can conclude that the rotation involved a combination of rotation and reflection.

The options that involve rotation are:

Ro, 90° (rotating counterclockwise by 90 degrees)

Ro, -90° (rotating clockwise by 90 degrees)

The options that involve rotation and reflection are:

Ro, 270° (rotating counterclockwise by 270 degrees, which is the same as rotating clockwise by 90 degrees with reflection)

Ro, -270° (rotating clockwise by 270 degrees, which is the same as rotating counterclockwise by 90 degrees with reflection)

Therefore, the two possible transformations that could have taken place are:

Ro, 90°

Ro, -270°

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