Answer:
670$ gain
Step-by-step explanation:
After accounting for both the wage increase and the increased health insurance contribution, on average, each worker experiences a net gain of $670 annually.
Explanation:The first step is to calculate the increase in wages due to the 3% increase in salary. This is calculated as follows: 3% of $39,000 is $1,170.
Next, we need to calculate the additional amount contributed toward health insurance, which has increased from 10% to 15%. This represents an increase of 5%. Thus, the added cost of health insurance is 5% of $10,000, which equals $500.
Finally, we can calculate the net change for the worker. This is achieved by subtracting the increase in health insurance contributions from the increase in wages. So, $1,170 - $500 equals $670 gain.
Hence, the correct option is (b), $670 gain.
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what decimal is equivalent to negative 3 over 8
Answer:
-9 / 24
Step-by-step explanation:
Step 1: Find an equivalent to -3/8
(-3*3) / (8*3)
-9 / 24
Answer: -9 / 24
Answer:
-0.375
Step-by-step explanation:
-3/8 is the same as saying -3 divided by 8
so just divide those puppies and you get -0.375
A triangle has side lengths of (6.2p + 4.5q) meters, (3.4p – 0.7r) meters, and (2.9r – 4.1q) meters. Which expression represents the perimeter, in meters, of the triangle?
A 9.6p + 0.4q + 2.2r
B 9.6p + 7.4q – 4.8r
C 9.6p – 1.2qr
D 10.7pq + 2.7pr – 1.2qr
Answer:
A
Step-by-step explanation:
THe perimeter is the sum of all the sides.
A triangle has 3 sides and we sum up the expressions to find the expression for perimeter.
Lets do this:
[tex](6.2p + 4.5q)+(3.4p-0.7r)+(2.9r-4.1q)\\=(6.2p+3.4p)+(4.5q-4.1q)+(-0.7r+2.9r)\\=9.6p+0.4q+2.2r[/tex]
We have added "p"s and "q"s and "r"s, together.
THe answer is Option A
What expression is equivalent to 5(2y + 8) - 12?
Multiply and simplify. Show work to earn full credit. (4 points) (7x-6)(3x^2-4x+5)
Answer:
21x³ - 46x² + 59x - 30
Step-by-step explanation:
21x³ - 28x² + 35x - 18x² + 24x - 30
= 21x³ - 46x² + 59x - 30
Step-by-step explanation:
7x ( 3x^2 - 4x + 5) - 6 ( 3x^2 - 4x +5)
21x^3 - 28x^2 + 35x - 18x^2 + 24x - 30
21x^3 - 46x^2 +59x - 30
3. Sarah's parents give her a $100.00 allowance at the
beginning of each month. Sarah spends her allowance on
comic books. The graph below represents the amount of
money Sarah spent on comic books last month.
What is the rate of change ?
What does the rate of change represent ?
Answer:
See explanation section
Step-by-step explanation:
Requirement A)
According to the graph, whenever Sarah purchased one comic book, she lost $5 from her allowance. Now the allowance remain after purchasing one comic book = ($100 - 5) = $95
Whenever she purchased three comic books, she lost $5 × 3 = $15 from her allowance. Now the allowance remain after purchasing three comic books = ($100 - 15) = $85. In that way, she lost her $50 after purchasing 10 comic books from her allowance. Therefore, the rate of change is $5.
Requirement B)
It represents that she spent $5 on her each comic book. It also represents that her each book decreases her allowance by $5.
Answer:
a) -5
Step-by-step explanation:
a) slope = (90-100)/(2-0) = -5
b) rate of change represents the deduction in amount left when one more book is purchased.. which is the cost of one book
Simplify the equations:
1.)6x+2(5x-2)
2.)7x+3(8+7)
Answer:
1) 16x -4
2) 7x + 45
Step-by-step explanation:
1 ) 6x + 2(5x -2)
we are going to open the bracket
we have,
6x + 10x - 4
16x -4
4(4x - 1).................................................... simplified
number 2
7x + 3(8+7)
7x +24 + 21
7x + 45........................................................... simplified
so therefore the solution to the first and 2nd question is
1) 16x -4
2) 7x + 45
Someone help
Plzzz I need an answer
5 and 1/2 divided by 1/4
Answer:
22
Step-by-step explanation:
5 1/2 divided by 1/4 is the same thing as times 4
5 1/2 times 4 equals 22 since 5*4 is 20 and 1/2 times 4 is 2
20+2 equals 22
Twenty minus the product of 4 and a number is 4
Answer:
20-(4*4)=4
Step-by-step explanation:
Final answer:
The number that satisfies the equation is 4.
Explanation:
To solve the equation, let's assume the number is represented by 'x'.
The product of 4 and the number would be 4*x or 4x.
Twenty minus the product of 4 and the number can be written as
20 - 4x.
According to the problem, this expression is equal to 4.
So, we can write the equation as
20 - 4x = 4.
To solve for 'x', we can isolate the variable by subtracting 20 from both sides:
-4x = 4 - 20 = -16.
Then, we divide both sides by -4:
x = -16 / -4 = 4.
Therefore, the number that satisfies the equation is 4.
A table top is in the shape of an equilateral triangle. If the perimeter of the
table top is 255 inches, what is the length of one side of the table?
A. 765 inches
B. 258 inches
C. 252 inches
D. 85 inches
Answer: The correct answer is D: 85 inches
Step-by-step explanation: The figure specified in the question is an equilateral triangle and one of it's properties is that all three sides have equal measurements.
The perimeter simply is a measurement of the lengths that runs around the entire shape. In other words the perimeter of a triangle is given as
Perimeter = 3L
Where L is the length of one side of the triangle.
If the perimeter of the table top is given as 255 inches, then we can now express it more properly as follows
255 = 3L
Divide both sides of the equation by 3
85 = L
Therefore the length of one side of the table measures 85 inches.
What is the area? Of this circle please help meeeee!!
Answer:
I'm pretty sure the answer is 1.0956.
Answer:
I think the answer is 7.065 in
Since the formula to find the area of a circle is A =
πr2
what is the value of b
b+18=-24
i need help
Answer:
the correct answer is
b=-24-18
b=-42
Answer:
-42
Step-by-step explanation:
Just do invers operation
What is another way to write x^2 *x^4
Answer:
x^6
Step-by-step explanation:
x^2*x^4=x^(2+4)=x^6
Please hurry it’s urgent
Answer:
[tex]V=\pi r^2h\\V=\pi(5)^2(10)\\V=\pi(25)(10)\\V=250\pi\\V=785.4[/tex]
Estimated
Step-by-step explanation:
Answer:
150π in^2
Step-by-step explanation:
The surface area of cylinder is calculated by 2πrh+2πr2 (r: radius, h : height)
2π×5×10 + 2π×5^2 = 150π in^2
Which of the following is the equation for the graph shown?
x squared over 20 plus y squared over 36 equals 1
x squared over 36 plus y squared over 20 equals 1
x squared over 20 minus y squared over 36 equals 1
x squared over 36 minus y squared over 20 equals 1
What is the equation of the line that passes through the point (-7,4)and has a slope of 0?
Answer:
y = 4
Step-by-step explanation:
Use point slope form: (y - y1) = m(x - x1)
(y - 4) = 0(x - (-7))
y - 4 = 0(x + 7)
y - 4 + 4 = 0 + 4
y = 4
Answer: y = 4
Which of these strategies would eliminate a variable in the system of equations?
\begin{cases} -7x + 2y = 5 \\\\ 3x - 5y = -5 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
−7x+2y=5
3x−5y=−5
The solution for given equations [tex]-7x+2y=5[/tex] and [tex]3x-5y=-5[/tex] are x = -0.517 and y = 0.6896.
Step-by-step explanation:
The given is,
[tex]-7x+2y=5[/tex]..........................(1)
[tex]3x-5y=-5[/tex]........................(2)
Step:1
Equation (1) is multiplied by 5 ( Eqn(1) × 5)
[tex]-35x+10y=25[/tex].........................(3)
Equation (2) is multiplied by -2 ( Eqn (2) × -2 )
[tex]-6x+10y=10[/tex].........................(4)
Step:2
Subtract the equation (3) and (4),
[tex]-35x+10y=25[/tex]
[tex]-6x+10y=10[/tex]
( - )
[tex](-35x+6x)+(10y-10y)=(25-10)[/tex]
[tex]-29x=15[/tex]
[tex]x = - \frac{15}{29}[/tex]
x = -0.517
From the x value equation (2) becomes,
[tex]3(-0.517)-5y=-5[/tex]
[tex]-1.551-5y=-5[/tex]
[tex]-5y = (-5+1.551)[/tex]
[tex]-5y= -3.449[/tex]
[tex]y =\frac{3.449}{5}[/tex]
y = 0.6898
Step:3
Check for solution,
[tex]-7x+2y=5[/tex]..........................(1)
[tex](-7)(-0.517)+(2)(0.6898)=5[/tex]
[tex]3.619+1.3796=5[/tex]
5 = 5
Result:
The solution for given equations [tex]-7x+2y=5[/tex] and [tex]3x-5y=-5[/tex] are x= -0.517 and y = 0.6896.
one winter, a group of students measured snowfall totals at their school. This chart shows how many inches of snow the students measured each month. How much snowfall did they receive in January and February combined?
December: 3.6
January: 8.6
February: 2.8
To calculate the total snowfall in January and February, we add the snowfall measurements for both months. The total snowfall for January (8.6 inches) and February (2.8 inches) is 11.4 inches.
Explanation:The question involves adding the amounts of snowfall for two different months, which is a basic arithmetic operation covered in mathematics. To find the total snowfall in January and February combined, we simply add the snowfall totals for each month.
According to the given information, there were 8.6 inches of snow in January and 2.8 inches in February.
Total snowfall for January and February combined is 8.6 + 2.8 = 11.4 inches.
If we consider the additional provided information, we can infer that since the schools closed and more than three inches of snowfall triggers a closure, it's reasonable to assume that in at least one of these months the snowfall was above three inches.
Which of the following data could be graphed using a dot plot? Select all that apply.
Answer:
You need to provide more information, images data etc.
Step-by-step explanation:
Answer:cars and siblings
Step-by-step explanation:
You make $32,000.00 .Using the 20% to 25% range, calculate the least and greatest amount you should spend on housing.
Answer: im am not sure but try your best
Step-by-step explanation:
To determine housing affordability based on a $32,000 annual income, calculate 20% for the least ($6,400 per year or $533.33 per month) and 25% for the greatest amount ($8,000 per year or $666.67 per month) you should allocate to housing costs.
To calculate the least and greatest amount you should spend on housing based on an income of $32,000.00 using the 20% to 25% range, you first need to determine 20% and 25% of your annual income. The formula to calculate a percentage of a number is:
(Percentage / 100) x Total Amount
For the least amount (20%): (20 / 100) x $32,000 = $6,400 per year
For the greatest amount (25%): (25 / 100) x $32,000 = $8,000 per year
To find the monthly housing cost, divide these amounts by 12:
Least amount monthly: $6,400 / 12 = $533.33
Greatest amount monthly: $8,000 / 12 = $666.67
Therefore, you should spend between $533.33 and $666.67 per month on housing, based on the 20% to 25% range of your annual income.
from a 200 ft observation tower on the beach, a man sights a whale in difficulty. the angle of depression of the whale is 7 degrees.how far is the whale from the shoreline
The whale is 24.54 feet away from the shoreline.
Step-by-step explanation:
Step 1:
The man is 200 feet from the ground and the angle at which he sees the whale is 7°.
So a right-angled triangle can be formed using these measurements. The angle of the triangle is 7° while the opposite side of the triangle measures x feet while the adjacent side of the triangle measures 200 feet.
We need to find the opposites side's length of the triangle.
Step 2:
Since we have the length of the adjacent side and need to calculate the length of the opposite side we use the tan of the given angle.
The opposite side of the triangle = x feet.
[tex]\tan \theta = \frac{opposite side}{adjacent side} , tan (7) = 0.1227,[/tex]
[tex]tan(7)=\frac{x}{200}, x = 0.1227 (200) = 24.54 feet.[/tex]
So the whale is 24.54 feet away from the shoreline.
To find the distance of the whale from the shoreline, set up a right triangle, use the observation tower height as one side, and apply the tangent function to the 7-degree angle of depression.
Explanation:To determine how far the whale is from the shoreline, we can use trigonometry, specifically the tangent function, since we have the height of the observation tower and the angle of depression. The angle of elevation from the whale to the top of the tower would also be 7 degrees. By setting up a right triangle with the observation tower as one side, the line of sight to the whale as the hypotenuse, and the distance from the whale to the base of the tower (along the shore) as the other side, we can solve for the distance to the whale using the tangent function.
The formula to use is:
Distance to the whale (d) = Height of the tower (h) / tan(angle of depression)Step-by-step solution:
Convert the angle of depression to radians if necessary (for some calculators).Use the tangent of the angle of depression, which is 7 degrees.Calculate the distance by dividing the height of the tower by the tangent of the angle: d = 200 ft / tan(7 degrees).The distance to the whale from the base of the tower is approximately 1,630.49 feet from the shoreline (considering tan(7°) = 0.12278).
Which is the closest to the height of a giraffe?
Answer:15-20 ft
Step-by-step explanation:
Find the inverse of the function. State any restrictions on the domain.
f(x) = x^2 + 9
The function is not invertible if you think of it as
[tex]f:\mathbb{R}\to\mathbb{R}[/tex]
because it is not injective: [tex]f(x)=f(-x)[/tex]
So, if we restrict the domain to the positive numbers only:
[tex]f:\mathbb{R^+}\to\mathbb{R}[/tex]
Note that the range is actually [tex][9,\infty)[/tex], so we can be more precise and write
[tex]f:\mathbb{R^+}\to[9,\infty)[/tex]
To find the inverse, we solve the expression for x:
[tex]y=x^2+9 \iff y-9=x^2 \iff x=\pm\sqrt{y-9}[/tex]
But since we restricted to positive values of x, the inverse is
[tex]x=\sqrt{y-9}[/tex]
To find the inverse of the function f(x) = x² + 9, swap x and y and solve for y. The inverse function is f^(-1)(x) = ± √(x-9), with a domain restricted to x ≥ 9.
To find the inverse of the function f(x) = x^²+ 9, we need to switch the roles of x and y and solve for y. The given function is y = x² + 9. Swap x and y to get x = y² + 9. Rearrange this equation to solve for y in terms of x: y² = x - 9. Taking the square root of both sides gives us y = ± √(x-9). Therefore, the inverse function is f^(-1)(x) = ± √(x-9), and the domain is restricted to x ≥ 9.
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Can you please help me on -6(b+3)+6b=-6(-4b+3)
Answer:
3.75=b
Step-by-step explanation:
George weeded 1/5 of the garden and Summer weeded some too. When they were done 2/3 was left of the garden. How much did Summer weed.
Answer:
Step-by-step explanation:
Step one) Figure our what peace of information you need to find and write down what information you already know.
•George weeded 1/5 of the garden.
•At the end 2/3 of the garden was left, which means that 1/3 of the garden was weeded.
•Now we need to figure out how much Summer weeded.
Step Two) Find the LCM (Lowest common multiple) of 5 and 3.
The LCM of 5 and 3 is 15.
Step three) Change the denominator of both problems to 15. Now the information you have should be:
•George weeded 3/15 of the garden. (We get the 3 on top because we multiplied 5 x 3 to get 15 so we multiply the numerator by 3 as well.)
•At the end there was 10/15 left. (We get the ten on top because the bottom was multiplied 3 x 5 to get 15, so then we take the numerator which is 2 and multiply that by 5 as well.)
•Now we know that if 10/15 weren’t picked that means that 5/15 were picked.
•We still need to figure out the amount that was picked by Summer.
Step 4)
Now we will use all the previous information to do the final step.
If a total of 5/15 were picked, and 3/15 of those were picked by George, then we do the problem:
5-3=2
Answer: Sally picked 2/15.
If 8x - 4 = 6x - 10, find the value of 5x
Answer:
5x= -15(negative)
Step-by-step explanation:
find the value of x (x= -3) add multiply by 5
If you use a cone-shaped container to fill a cylinder-shaped container with the same height and radius, how many times
will you have to empty the cone-shaped container to fill the cylinder-shaped container?
1/3
1
2
3
Answer:
3 times
Step-by-step explanation:
The volume of a cone is 1/3*pie *r^2 * h whereas the volume of a cylinder is pie*h*r^2 which means that if the height and radius are the same the volume of the cone is 1/3 of the cylinder thus you need 3 cones to fill the cylinder.
Find the volume of the cylinder in terms of . The diagrams are not drawn to scale.
43.35pi m cubed
51pi m cubed
56.78pi m cubed
73.695pi m cubed
Answer:
43.35pi m cubed
Step-by-step explanation:
Volume of a cylinder
= pi r^2 h
Where r = radius
h = height
Given r = 1.7m and
h = 15m
Volume = pi x (1.7)^2 x 15
= pi x 1.7 x 1.7 x 15
Multiply through
Volume = 43.35 pi m cubed
Alice is having her birthday party at a game center. The center charges $100 plus $20 per guest. The total cost of the party y can be
represented by the equation y = 20x + 100. What does the y-intercept represent?
a. the number of guests
b. the cost to rent the game center
c. the cost per guest
d. Alice's age
Final answer:
The y-intercept represents the fixed cost of the party, while the slope signifies the variable cost per guest.
Explanation:
The y-intercept represents the one-time fee that Alice has to pay for her birthday party at the game center, which is $100.
The slope of $20 per guest indicates the additional cost incurred for each guest that attends the party.
In the equation y = 20x + 100, 'y' represents the total cost of the party, 'x' represents the number of guests, the y-intercept is the fixed cost, and the slope is the variable cost per guest.
What is the volume of 8x12x10
Answer:
960
Step-by-step explanation:
You multiply all of the numbers together to get 960
Answer:
v = 960 (units)^3
Step-by-step explanation:
v = lwh
v = 8 * 12 * 10
v = 960 (units)^3