Leroy's total employee compensation was $50,150 last year. His total job expenses for traveling and for professional developement for the year were $3,500. Which of the following represents his total job benefits?
a.
$53,650
b.
$50,150
c.
$46,650
d.
$47,650


Answer is :
a.
$53,650
100% correct

sally can have 3 pairs of full outfits

Answer:

150

Step-by-step explanation:

Because, 5 x 3 x 10 = 150.

10 x 3

10 20 30

1    2   3

( add 10 every time )

30 60 90 120 150

1    2   3     4     5

( add 30 every time )

I tried to explain well.

The obtuse angle is 165 degrees.

You find this by subtracting 15 from 180
180 - 15 = 165
This works because the two angles (15 and 165) are supplementary. They add to 180 degrees and form a straight angle.

Answer: 6 < x < 18.9

Justification

1) An acute angle is less than 90° and greater that 0°, i.e. 0 < angle < 90°.

2) The lower bound of the third side is when the angle approaches to zero, this is both sides 10 and 16 almost overlap.

Under this condition the lenght of the third side approaches (never gets to) 16 - 10 = 6.

From this you conclude x > 6.

3) The upper bound of the third side is when the angle approaches 90°, this is the triangle is almost a right triangle. In this case, the upper limit of x is the value of the hypotenuse of a triangle withs legs 10 and 16.

=> x^2 < 10^2 + 16^2

=> x^2 < 100 + 256

=> x^ 2 < 356

=> x < 18.86

So the range is 6 < x < 18.86

Answer:

B 12.5 < x < 18.9

Step-by-step explanation:

subtract:
189.95 - 45.00 = 144.95

the cost = 144.95

Answer:

Cost price of an item = $144.95

Step-by-step explanation:

Cost price is the price at which the article is purchased .

It includes all the expenses incurred on that item till the time it is owned by us .

Selling price is the price at which the item is sold to the customer .

Market price is the price marked on the product . It is basically the current price of the item .

We know that selling price - market price = cost price

Given :

Market price of an item =  $45.00

Selling price of an item = $189.95

To find : cost price of an item

Solution :

Cost price = $189.95 - $45.00 = $144.95

passover extra words to make 20 characters lol

     

Answer: -135

Explanation:

1) I will use synthetis division

2) Write the coefficients of the divisor in order

   1    -3    7    5

3) Dividing by x + 4 => use x = - 4

4) Division:

      | 1     -3       7       5
      |
 - 4 |       -4    +28   - 140
-------------------------------
        1    -7      35    - 135

5) The last number is the remainder: - 135

Let's use syntethic division
The dividend is x^3-3x^2+7x+5
Write the coefficients in decresing order:
x^3   x^2   x   Independent term
1       -3     7      5

Let's do the synthetic division with x=-4
    ! 1   -3      7          5
-4 !___-4__28__-140_
      1   -7    35     -135

The remainder is the last term: -135

The graph of f is reflected across the y-axis to create the graph of g. (C)

You are basically assigning the same y-value to the opposite x-values to make g(x). So, for the point (x, 31), on f(x), x is -2, but on g(x), x is 2. Thinking about this visually, you can imagine that this represents a reflection of f across the y-axis.

(Side note: Later in math, this symmetry will be formalized so that you can find it algebraically. It's called "even" symmetry.)

As g(x) is a function that is multiplied by - 1 with f(x) D. They are reflections of each other over x = y.

What is a graph?

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, g(x) is a function that is multiplied by - 1 with f(x).

∴ f(x) = - g(x).

So, They are reflections of each other over x = y.

learn more about graphs here :

https://brainly.com/question/2288321

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Selection C is appropriate for a fence that extends x feet away from the house and utilizes the full 30 ft width of the house.

Try this solution (see the attachment).

Final answer:

The general solution to the differential equation (8 + x)y' = 3y is y = C(8+x)³, where C is a constant and can be found by integrating and rearranging the separated variables.

Explanation:

To find the general solution of the differential equation (8 + x)y' = 3y, we can separate variables and integrate both sides. First, we divide both sides by (8 + x) and then by y to get [tex]\frac{ y'}{y} = \frac{3}{8 + x}[/tex]

Next, we integrate both sides:

Integrate LHS: [tex]\int \frac{dy}{y} = ln|y| + C_1[/tex]

Integrate RHS: [tex]\int \frac{3dx}{8 + x} = 3ln|8+x| + C_2[/tex]

Now, we can combine the two constants (C₁ and C₂) into a single constant C by writing C = C₂ - C₁. So our solution looks like ln|y| = 3ln|8+x| + C. We can exponentiate both sides to solve for y:

[tex]y = e^{3ln|8+x|+C}[/tex]

Remembering that [tex]e^{ln|a|} = a[/tex], we can simplify this to:

y = C(8+x)³ where C is a constant.

This is the general solution to the differential equation.

Answer:
100 times bigger 

Explanation:
The given number is:
35.3186

Let's take a look at the first 3 on the left (the one in bold).
We will find that this 3 is in the tens position (10)

Now, let's take a look at the other 3 (the one directly after the point).
We will find that this 3 is in the tenth position (0.1)

Now, when multiplying the digit in the tenth position by 100, this digit would be in the tens position.
This means that the difference between the two positions is 100

Based on this:
The 3 in the tens position is 100 times greater than the 3 in the tenth position.

Hope this helps :)

She read 5 pages

8÷4=2+3=5

Final answer:

To find the total number of pages they have read so far, add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class. The total number of pages they have read so far is 5 pages.

Explanation:

To find the total number of pages they have read so far, we need to add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class.

Mrs. Ross read 1/4 of the chapter, which is 8 x 1/4 = 2 pages.

Mrs. M read 3 pages to the class.

Therefore, the total number of pages they have read so far is 2 + 3 = 5 pages.

Note: The explanation of problems b) and c) are attached as images because of the maximum limit of 5,000 characters.

Answers:

a) [tex]y = -\frac{1}{32} x^2 + \frac{49}{8}[/tex]
b) [tex] \frac{49}{8} \text{ meters} [/tex]
c) [tex]y = -\frac{1}{32} (x-14)^2 + \frac{49}{8}[/tex]

Explanations:

a) Note that the path where the ball travels when kicked off the ground is the parabola. 
Let (h,k) be the vertex of the parabola. Since the vertex is in y-axis, the x-coordinate of the vertex is 0. So, h = 0. 
The equation of the parabola with vertex (h, k) is given by
 [tex]y = a(x - h)^2 + k[/tex]   (1) Since h = 0, we can replace this to equation (1) so that 
 [tex]y = a(x - h)^2 + k\\ y = a(x - 0)^2 + k\\ y = ax^2 + k[/tex]   (2)

To solve for a and k, we need to get the coordinates of the points of parabola. In the problem, it is possible to determine the coordinates of the points where the ball is kicked off from the ground and where the ball ended hitting the ground and the point where the ball hits the tree which are points of the parabola.
Since the ground is in x-axis and the ball is kicked off from the ground and ended hitting the ground, the parabola intersects the x-axis at the points where the ball is kicked off from the ground and where the ball ended hitting the ground. 
Let

A = point where the ball is kicked off from the ground
B =  point where the ball ended hitting the ground
M be the midpoint of A and B.

Note that the x-coordinate of the vertex of the parabola is the same as the x-coordinate of M. Since the x-coordinate of the vertex of the parabola is 0, the x-coordinate of M is 0. Moreover, since the ground is in x-axis, A and B are in the x-axis and so M is in x-axis. So, the y-coordinate of M is 0 because the y-coordinate of any points of x-axis is 0. Thus, the coordinates of M are (0,0).
As mentioned earlier, the y-coordinate of any points in x-axis is 0. Since A and B both lie in x-axis, their y-coordinate is 0. Now, we let j be the x-coordinate of A and k be the x-coordinate of B so that (j, 0) are the coordinates of A and (k, 0) are the coordinates of B.

Since the ball traveled with a horizontal distance of 28 meters when it is kicked off until it hit the ground, the horizontal distance from A to B is 28. Since the coordinates of A and B are (j, 0) and (k, 0) respectively, using the distance formula the distance from A and B is given by 

[tex]d = \sqrt{(j-k)^2 + (0 - 0)^2} \\ 28 = \sqrt{(j-k)^2} \\ (j-k)^2 = 28^2 \\ \boxed{j - k = \pm 28}[/tex]

Since A is the point where the ball is kicked off and B is the point where the ball hits the ground, A is in the left of B. Since A and B are both in x-axis and j and k are the x-coordinates of A and B respectively, j < k. Thus, j - k is negative and so

j - k = -28      (3)

Because M is the midpoint of A and B, the x-coordinate of M is [tex] \frac{j+k}{2}[/tex]. Since the x-coordinate of M is 0,

[tex]\frac{j+k}{2} = 0[/tex]     (4)

Multiplying both sides of equation (4) by 2, we have

j + k = 0   (5)

Now, we add equations (3) and (5) so that 

2j = -28
j = -14

Substituting the value of j in (5), we have

j + k = 0
-14 + k = 0
k = 14

Hence the coordinates of A are (-14,0) and the coordinates of B are (14,0). Since point A is in parabola, we can substitute its coordinates of A in equation (2) with x = -14 and y = 0 so that 

[tex]y = ax^2 + k \\ 0 = a(-14)^2 + k \\ 0 = 196a + k \\ \boxed{196a + k =0} [/tex]      (6)

Note that, if we substitute the coordinate of B, we also arrive at equation (6), which is useless.

So, we need to determine the coordinates of another point of parabola, which is the point where the ball hits the tree. We call this point C. Since the tree is 3 meters high and the ground is in x-axis, the y-coordinate of point C is 3. Let c be the x-coordinate of C. Since the ball hits the tree after travelling a horizontal distance of 24 meters, the horizontal distance from A to C is 24. Moreover, the horizontal distance is the difference of x-coordinates of two points. Since C is the right of A and the x-coordinate of A is -14

c - (-14) = 24
c + 14 = 24
c = 10

Hence, the coordinates of C are (10, 3). Substituting this to equation (2), we have

[tex]y = ax^2 + k \\ 3 = a(10)^2 + k \\ 3 = 100a + k \\ \boxed{100a + k =3} [/tex]       (7)

Subtracting equation (6) to (7), we have

[tex](196a + k)-(100a + k) = 0-3 \\ 96a = -3 \\ \boxed{a = -\frac{1}{32} }[/tex]

Substituting the value of a in equation (6) we have

[tex]196a + k = 0 \\ 196(-\frac{1}{32}) + k = 0 \\ \\ -\frac{49}{8} + k =0 \\ \\ \boxed{k = \frac{49}{8} } [/tex]

Using equation (2) and the values of a and k, the equation of the parabola is given by 

[tex]\boxed{y = -\frac{1}{32} x^2 + \frac{49}{8} }[/tex]

The surface area of a cone consists of the area of lateral side and the area of the base. The area of lateral side is determined using (π × r × s), s represents the slant height. The area of the base is determined using the formula of the area of a circle.

area of lateral side + area of base = surface area
(π × r × s) + (π × r²) = surface area

Input the numbers
(π × r × s) + (π × r²) = surface area
(π × 10 × s) + (π × 10²) = 150π
10πs + 100π = 150π
10πs = 150π - 100π
10πs = 50π
s = 50π/10π
s = 5
The slant height is 5 inches

(The vertex formula is derived from the completing-the-square process, just as is the Quadratic Formula. In each case, memorization is probably simpler than completing the square.) For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k

i DONT HAVE THE TABLE THAT MENTIONED IN PROBLEM 

We observe that the function is a parabola that grows upwards.
 For this case, we must first graph the function to observe the behavior of the same.
 We see that the vertex of the function is located at the point:
 (x, y) = (- 2, -3)
 The point is a minimum.
 Answer:
 (x, y) = (- 2, -3)
 It is a minimum.
 See attached image.

x / x-2 + 7x / x + 5
 What you must do in this case is a sum of fractions.
 Step 1:
 Common factor x in the numerator
 Step 2:
 Make addition of fractions
 Step 3:
 Rewrite the expression.
 See attached image.
 Answer:
 c. 8x ^ 2-9x / x ^ 2 + 3x-10

Final answer:

The sum of the rational expressions is found by obtaining a common denominator, combining the numerators, and simplifying the resulting expression. The correct answer is [tex](8x^2-9x)/(x^2+3x-10).[/tex]

Explanation:

The sum of the rational expressions [tex]x/(x-2) + 7x/(x+5)[/tex] requires finding a common denominator before the sum can be calculated.

The common denominator for these two fractions is the product of the individual denominators (x-2) and (x+5), which is [tex]x^2+3x-10.[/tex]

Once we have a common denominator, we can combine the numerators and simplify the expression as follows:

Multiply the first term by (x+5)/(x+5) and the second term by (x-2)/(x-2) to create a common denominator.

Combine the numerators: [tex]x*(x+5) + 7x*(x-2)[/tex]

[tex]= x^2+5x + 7x^2-14x[/tex]

[tex]= 8x^2-9x.[/tex]

Place the combined numerator over the common denominator: [tex](8x2-9x)/(x^2+3x-10).[/tex]

Therefore, the correct sum of the given rational expressions is option c. [tex](8x2-9x)/(x^2+3x-10).[/tex]

1/2 divided by 3 is 1/6.
So your answer is 1/6 pounds each person.

3 friends equally shared 1/2 pound of trail mix, during the hike.

Total quantity of trail mix = 1/2 pound

Quantity shared by each friend is 1/3 rd of the trial mix

= 1/3 * 1/2 pound

= 1/6 pound

Therefore, during the hike, each friend shared 1/6 pound of the trail mix.

Hope this helps ..!!

Thank you :)

You have 6 sides
2 are 2*1 = 2*2*1 square feet.
2 are 4*1 = 2*4*1 square feet
2 are 4*2 = 2*4*2
The total is 4 + 8 + 16 = 28 square feet.

First, draw the number line and assign the values of the real numbers that correspond (See the figure attached).
  Now, let's represent the mixed numbers given in the problem.

 Let's start with 8 2/5: This mixed number is located between 8 and 9. The numerator 2 of the fractional part, tells us how far from 8 it will be located  and the denominator 5 indicates how many parts we must divide the space between these two numbers (8 and 9). 

 Now, to plot 2 3/4 on the number line, we have to follow the same proccedure: It is located between the numbers 2 and 3. The numerator 3 of the fractional part, tells us how far from 2 it will be located  and the denominator 4 indicates how many parts we must divide the space between 2 and 3.

The above is an estimation question. Estimation is when you judge the results obtained from a sample and make a rough calculation. The answer obtained might not be exactly right, its based on a judgement.

In this a sample was taken and out of 80 books, 6 of them were history books.
The assumption made then is that for every 80 books taken randomly , 6 of them will be history. Using this assumption ;
21 360 books in the library,
for every 80 books - 6 history books
then for 21 360 books - 6 / 80 * 21360
                                   =  1602 history books

11 is divisible by three three times with a remainder of two so the mixed number would be 3 2/3

3 2/3 would be the answer

I FOND YOUR COMPLETE QUESTION IN ANOTHER SOURCE.
 PLEASE SEE ATTACHED IMAGE.

 The width of the rectangle in this case will be given by:
 w = x + 5 + x
 Rewriting:
 w = 2x + 5
 The length of the rectangle will be given by:
 L = x + 10 + x
 Rewriting:
 L = 2x + 10
 Answer:
 w = 2x + 5
 L = 2x + 10

55 degrees is your answer

Answer:

55 degree

Step-by-step explanation:

By the Law of cosines: a2 = b2 + c2 – 2bccos(A)

That is the image. :-）

6050(.14)=847
150+847=997
He made $997

I have attached a picture that shows the computation with an explanation for each number. The main idea is to represent the situation with the retail price, multiplied by the percent you'll pay after 20% has been deducted, multiplied by the percent you will pay after the additional 15% is taken off for store A. For store B it will be the retail price multiplied by the price you pay after the 35% has been taken off. You can see that store C will be a lower price after the discounts.

3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?

The domain of a function is the complete set of possible values of the independent variable.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

2x+3y=18

For this equation, domain and range both would be all real numbers.

3x-4y>16

Here domain and range both will be all real numbers.

FIND LOT AREA:
Area = length * width
A= 18 feet * 45 feet
A= 810 feet squared

FIND # OF YARDS:
1 yard= 3 feet

Divide number of square feet by number of feet per yard.
Yards= 810 ÷ 3
Yards= 270

FIND PRICE OF SOD:
multiply number of yards by price per square yard.
Price= 270 yards * $12/yard
Price= $3,240

ANSWER: Cindy will pay $3,240 to cover the lot with sod.

Hope this helps! :)

The actual answer to this problem is (4.8,7.6)

Using the internal division formula the coordinates of the ball are (4.8,7.6).

Let us assume the x-axis as the goal line and the y-axis as the sideline

So, coordinates Messi≡(3,4)

Similarly, coordinates Suarez≡(6,10)

Let us suppose the ball is somewhere in between Messi and Suarez

Suppose coordinates of the ball ≡(a,b)

Since the ratio between the distance between Messi and the ball to the distance between Suarez and the ball is 3/2.

This means ball is internally dividing Messi and Suarez in 3:2

So, applying the internal division formula for a straight line.

What is the internal division formula for a straight line?

If a point (a,b) is internally dividing a line segment with coordinates of endpoints as (x₁,y₁) and (x₂,y₂) in the ratio m:n then

[tex]a= \frac{m_{1}x_2+m_2x_1 }{m+n}[/tex]

[tex]a= \frac{m_{1}y_2+m_2y_1 }{m+n}[/tex]

So, [tex]a = \frac{3*6 + 2*3}{3+2}[/tex]

[tex]a=4.8[/tex]

[tex]b= \frac{3*10+2*4}{3+2}[/tex]

[tex]b=7.6[/tex]

So, the coordinates of the ball≡(4.8,7.6)

Therefore, Using the internal division formula the coordinates of the ball are (4.8,7.6).

To get more about straight lines visit:

https://brainly.com/question/13284474

Each frame costs $12. Since you are ordering 15 frames, the price of the frames is 15 * $12 = $180.
Shipping is $8 for the entire order, not for each frame, so just add $8 to the price of the frames.
$180 + $8 = $188
Answer: The total cost of the order is $188.

Answer:

$188

Step-by-step explanation:

Well, 50% of 15 is 7.5 , so you should say something a little less than that. The real answer is 7.35

Answer:

9 + 7 + 6 + 2 + 2 + 1 = 27 ÷ 6 = 4.5

4.5 - 9 = 4.5

4.5 - 7 = 2.5

4.5 - 6 = 1.5

4.5 - 2 = 2.5

4.5 - 2 = 2.5

4.5 - 1 = 3.5

4.5 + 2.5 + 1.5 + 2.5 + 2.5 + 3.5 = 17 ÷ 6 = 2.83 or 2.8

so our MAD is 2.83 or 2.8!