Work Shown:
Complementary angles add to 90 degrees.
A+B = 90
(3x+18)+(2x+17) = 90
5x+35 = 90
5x = 90-35
5x = 55
x = 55/5
x = 11
Then we can determine each angle:
angle A = 3x+18 = 3*11+18 = 33+18 = 51 degrees is the final answerangle B = 2x+17 = 2*11+17 = 22+17 = 39 degreesAs a check: A+B = 51+39 = 90 to confirm the answer.
ngberg Company installs lawn sod in home yards. The company’s most recent monthly contribution format income statement follows:
Amount Percent of Sales
Sales $ 90,000 100%
Variable expenses 36,000 40%
Contribution margin 54,000 60%
Fixed expenses 40,500
Net operating income $ 13,500
Required:
1. What is the company’s degree of operating leverage?
2. Using the degree of operating leverage, estimate the impact on net operating income of a 7% increase in unit sales.
3. Construct a new contribution format income statement for the company assuming a 7% increase in unit sales.
1. The company’s degree of operating leverage is 4.
2. The degree of operating leverage is 3.34.
3. The new contribution is $17, 280.
What is degree of operating leverage?How much a company's operating income alters in reaction to a change in sales is measured by the level of operating leverage.
1. Degree of operating leverage = Contribution /Net Operating Income
and, Contribution = 54,000
Net Operating Income = $13,500
Thus, operating Leverage = 54000/ 13500 = 4
2. If Company's sales increase by 7% then contribution also increases by 7%,
Revised Contribution = $54000 + 7% = $57780
and, Revised net Operating income = $57780- $40500
= 17280
Degree of operating leverage = 57780 / 17280 = 3.34
3. Contribution format income statement:
Sales = $90000+ 7% = $96,300
Less: Variable Cost 36, 000 + 7% = $38520
So, New Contribution = 57780 - 40500 = $17, 280.
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Cala rolls a biased dice 40 times. It comes up with a three 14 times. Calculate the relative frequency of rolling a three.
The relative frequency of rolling a three is 14/40 or 0.35.
Answer14/40 or 0.35
Step-by-step explanation:
Number of times dice is rolled= 40
Number of times three comes up= 14
Relative frequency(Probability) = 14/40 or 0.35
The sum of three numbers is 54. The difference of the largest and the smallest is 46, and the sum of the two smaller numbers is 13. Find the numbers?
These values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.
What is a three-variable linear equation?
When a, b, and c are constants, a linear equation in two variables has the form ax + by + c = 0. (real numbers). Similar to this, a three-variable linear equation has the form ax by c z plus d = 0, where a, b, c, and d are constants.
Let's call the three numbers x, y, and z, where x is the largest number and z is the smallest number. Then, we have the following information:
x + y + z = 54
x - z = 46
y + z = 13
From the second equation, we can find z:
z = x - 46
Substituting this into the third equation:
y + x - 46 = 13
y = 13 + 46 - x
Substituting both of these into the first equation:
x + (13 + 46 - x) + (x - 46) = 54
Expanding the parentheses:
2x = 154
Dividing both sides by 2:
x = 77
Substituting this value of x into the equation for z:
z = x - 46 = 77 - 46 = 31
And substituting it into the equation for y:
y = 13 + 46 - x = 13 + 46 - 77 = -18
Note that these values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.
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. Describe the graph of the function. Y=sqrt x-7 +8
Tracy bought a wristwatch for $845.00. She made a down-payment of $95.00 and financed the rest with six monthly payments of $128.75. Find the total installment price and total interest.
10
Complete the equation for the line
shown in the graph.
6.67 y
-6.67
(0,2)
(1,-2)
10
y=[?]x + [ ]
Answer:
y= -4x+2
Step-by-step explanation:
diff in y / diff in x = slope
so the slope is (-2-2) /(1-0) = -4
intercept is whatever is on Y axis, it's 2
so y= -4x+2
Answer:
Step-by-step explanation:
Divide 100 by 16 and write the answer as a mixed number. Reduce the
fraction part of the mixed number. 6 1/4 here u go.
Natalia bought 3 boxes of pencils and 9 reams of paper for $75. Ronnie bought 8 boxes of pencils and 5 reams of paper for $67. Set up and solve a system of equations by elimination to determine the cost of a box of pencils and a ream of paper.
The cost of a box of pencils is $4.
The cost of a ream of paper is $7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 1 = 6 is an equation.
We have,
Pencils = x
Reams of paper = y
Now,
Natalie:
3x + 9y = 75 _____(1)
Ronnie:
8x + 5y = 67 _____(2)
From (1) and (2)
Multiply 8 on (1)
Multiply 3 on (2)
24x + 72y = 600
24x + 15y = 201
(-) (-) (-)
57y = 399
y = 7
Now,
3x + 9y = 75
3x + 9 x 7 = 75
3x + 63 = 75
3x = 75 - 63
3x = 12
x = 4
Thus,
The cost of a box of pencils and a ream of paper are $4 and $7.
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Find the length of JM
The length of JM is 24 units.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
<H= <K= <N= 90
and, GH || JK || MN
then, Using proportion
GL/ GM = HK/ HN
18/ (18+ x) = 15/ (15+20)
18(15+20) = 15(18+x )
18 . 20= 15 x
x= (18)(20)/ 15
x= 24
Hence, the length is 24 units.
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Approximately how many downloads were there between 3 p.m. and 4 p.m.?
Answer: If you can explain the question a little bit more i would be happy to help!
Step-by-step explanation:
Please help will mark Brainly
The total amount of Investment A is $6,348.58.
What is the compound interest?
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
To find the total amount of investment A, you can use the formula for compound interest:
A = P * (1 + r/n)⁽ⁿᵗ⁾
Where P is the initial investment ($5,000), r is the annual interest rate (6%), n is the number of times interest is compounded per year (2 times), and t is the number of years invested (4).
A = 5000 * (1 + 0.06/2)⁽²*⁴⁾
= 5000 * (1 + 0.03)⁸
= 5000 * 1.03⁸
= 5000 * 1.269716
= $6,348.58
Hence, The total amount of Investment A is $6,348.58.
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Last April, it rained in Danville on ten days. This graph shows how much rain fell on each day.
The difference in rainfall between the wettest and driest days is 3/8 inches.
3.0 inches of rain—is that a lot?The intensity of the rain is typically categorized as light, moderate, or heavy. Light precipitation is defined as less than 0.10 inches per hour. Rainfall that is considered moderate ranges from 0.10 to 0.30 inches per hour. More than 0.30 inches of rain per hour is considered heavy rainfall. under 0.5 mm per hour. Greater than 0.5 mm per hour but less than 4.0 mm per hour is considered moderate rain. Greater than 4 mm per hour but less than 8 mm per hour is considered heavy rain. greater than 8 mm per hour of extremely intense rain.
Rainfall in Rainiest day = 5/8
Rainfall in driest day = 2/8
So, The Difference = 5/8 - 2/8 = 3/8 inches
Hence, rainfall on the rainiest day 3/8 more than driest day
Proper fraction = 3/8
Mixed fraction = 8/2 inches.
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Can you answer ASAP PLEASE
Need help with solution please
Answer: The definition of a solution is a value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x2 = 4 are 2 and -2. I hope this helped!
g(x) =8x²-5x³+7-12x total roots
The given cubic equation has no roots.
What are cubic equations?Traditionally, a cubic problem can be solved by converting it into a quadratic equation, which can then be solved by factoring or the quadratic formula. A cubic equation has three roots, just like a quadratic equation has two. Three real roots or one real root and two imaginary roots are both possible for a cubic equation. Cubic equations must also always be arranged in their standard form first.
The following strategies can be used to resolve a cubic equation:
Using Graphical Method to Find Integer Solutions with Factor Lists
Given that the cubic equation is: 8x²-5x³+7-12x
Regrouping the equation in standard form:
- 5x³ + 8x² - 12x + 7
Here, the constant is 7. Take the factors of the constant.
7 = 1, 7
Substitute the value of the factors as follows:
G(1) = - 5(1)³ + 8(1)² - 12(1) + 7 = -5 + 8 - 12 + 7 ≠ 0
G(7) = -5(7)³ + 8(7)² -12(7) + 7 = -1715 + 392 - 84 + 7 ≠ 0
Hence, the given cubic equation has no roots.
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Look at the figure. Find TW.
VIEW THE IMAGE ATTACHED.
Answer:
TW = 9
Step-by-step explanation:
WY is the perpendicular bisector of TZ with TY ≅ ZY , then
Δ TWZ is isosceles with ZW ≅ TW , that is
3x = x + 6 ( subtract x from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Then
TW = x + 6 = 3 + 6 = 9
The two rectangles above are similar. If b = 18 mm, and c = 24 mm, and d = 36 mm, what is the length of a?
Answer:
The length of a is 36 mm.
Step-by-step explanation:
Similar rectangles have the same shape, but can have different sizes. The ratio of the lengths of corresponding sides of similar rectangles is always the same.
Given that b = 18 mm, c = 24 mm, and d = 36 mm, the ratio of the lengths of corresponding sides of the two rectangles is c/d = 24/36 = 2/3.
So, the length of a is equal to b * (c/d) = 18 * (2/3) = 36 mm.
g (-9) if g(x) = -6x + 6
Another operation that can be defined on sets A and B is the difference of the sets, denoted by
A − B.
Here is the formal definition of the difference of sets A and B.
A − B = {x | x is in A and x not in B}
Thus
A − B
is the set of elements that belong to A but not to B. For instance, let
A = {1, 2, 3, 7, 8}
and
B = {2, 7, 11}.
Then
A − B = {1, 3, 8}.
Determine the difference, given that
U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {2, 4, 6, 8},
and
B = {1, 4, 6, 9}.
(Enter your answers as a comma-separated list.)
A − B'
Answer:
Step-by-step explanation:
To find the difference A - B', we need to first find the complement of B, denoted by B', which is the set of all elements in U that are not in B.
Given that U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
B = {1, 4, 6, 9},
then B' = {2, 3, 5, 7, 8}.
Next, we find A - B' by looking for the elements that belong to A and not to B':
A - B' = {2, 4, 6, 8} - {2, 3, 5, 7, 8} = {4, 6, 8}.
54) If a spring stretches 6 meters when a 8-kilogram weight is attached to it, how much will it stretch when a 56-kilogram weight is attached to it?
The length of the spring stretched is given by the proportion A = 42 meters
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the length of the spring stretched when 56 kg weight is attached be A
Now , the equation will be
The length of the spring when 8 kg is attached to it = 6 meters
So , the proportion is
A / 56 = 6 / 8
On simplifying the equation , we get
Multiply by 56 on both sides of the equation , we get
A = ( 6 x 56 ) / 8
On further simplification , we get
A = 6 x 7
A = 42 meters
Therefore , the value of A is 42 meters
Hence , the equation is A = 42 meters
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Find all the missing angles in the diagram below. Explain how you used at least two different angle theories to find some of these angles.
Answer:
Angle A is 90, angle B is 50, angle C is 90, and angle D is 40.
Answer:
<A = 90
<B = 50
<C = 90
<D = 40
Step-by-step explanation:
C:
vertical angles are congruent so the angle left of C is 40. The angle right to C is 50 because alternate interior angles are congruent
The three angles together are supplemental
180 - 50 - 40 = 90
A:
A = C vertical angles are congruent
A = 90
D:
A, D and 50 are supplemental
180 -90-50 = 40
B
The sum of the interior angles of a triangle are 180
180 - 40 - 90 = 50
Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180°.
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 28° more than the measure of the second angle.
What is themeasure of each angle?
Answer:
The first one is 76°, second one is 38°, third one is 66°
Step-by-step explanation:
Suppose the second one is x, given the first one is twice of the second one, so the first one is 2x.
2x+x+(28°+x)=180°
4x=152°
x=38
So, the first one is 76°, second one is 38°, third one is 66°
What is the slope and y-intercept of this line?
y = –6x + 2
Answer:
the slope is -6
the y-intercept is 2
Step-by-step explanation:
y=mx+b where m is the slope and b is the y-intercept
a) Slope: -6;
b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).
Step-by-step explanation:Given equation: [tex]y = -6x + 2[/tex].
Here's a little tip that will help you quickly find the slope and y-intercept.
First, solve the equation for "y". This equation is already solved for "y", this is called "slope-intercept form". Now, take a look at the attached image and identify the values. As you can tell, for the given equation, values are:
a) Slope: -6;
b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).
You may verify this information using the algebraic methods (slope formula and substituting "x" by 0 and calculate "y"). It'll give you the same answer, this is just a faster way to find the values.
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If
p
=
2
and
q
=
5
, evaluate the following expression:
40
2
q
−
p
Answer:
398
Step-by-step explanation:
40*2q-p
=40*2*5-2
=400-2
=398
Answer:
2008
Step-by-step explanation:
since p=2
q=5
therefore, 402(q)-p
=402(5)-2
=2,010-2
=2008
Which equation is more appropriate for modeling this DATA?
The equation which is more appropriate for modeling this DATA is y = 64 × (1.25)^x
The correct answer choice is option A.
Which equation is more appropriate for modeling this DATA?y = 64 × (1.25)^x
when,
x = 1
substitute into the equation
y = 64 × (1.25)¹
= 64 × 1.25
= 80
y = 79 × 1.25^x
when x = 1
= 79 × 1.25¹
= 79 × 1.25
y = 98.75
79 + 1.25x
when x = 1
= 79 + 1.25(1)
= 79 + 1.25
= 80.25
64 + 22x
when x = 1
= 64 + 22(1)
= 64 + 22
= 86
Therefore, y = 64 × (1.25)^x is the equation which is more appropriate to represent the data.
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Even salaried employees can be paid by the hours they clocked in/out.
A) True
B) False
Answer:
B
Step-by-step explanation:
There are two types in this good ol' world, Salary and Hourly.
Hourly gets paid by, well, the hour
Salary has a set amount. Let's say there around is $1000 a week. If they work 70 hours, they get paid $1000, if they work 30 hours, they get paid $1000
what is the answer for
−7x−y=0
Answer: y=-7x-0 if solving for literal y or x=y+0/-7 if solving for literal x.
Step-by-step explanation:
-7x-y=0
add (+) 7x to both sides
-y=7x+0
then divide by -1
y=-7x-0
-------------------------------------
for literal X
-7x-y=0
add y to both sides
-7x=y+0
then divide by -7\
x=y+0/-7
A person invested $7500 for 1 year, part at 6%, part at 9%, and the remainder at 15%. The total annual income from these investments was $867. The amount of money invested at 15% was $100 more than the amounts invested at 6% and 9% combined. Find the amount invested at each rate.
Answer: The amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.
Step-by-step explanation:
Let's denote the amount invested at 6% as "x". Then, the amount invested at 9% would be "y", and the amount invested at 15% would be "z".
According to the problem, we have the following information:
x + y + z = $7500 (the total amount invested)
0.06x + 0.09y + 0.15z = $867 (the total annual income)
And,
z = x + y + $100 (the amount invested at 15% was $100 more than the amounts invested at 6% and 9% combined)
We can substitute the third equation into the first equation to get:
x + y + x + y + $100 = $7500
Simplifying:
2x + 2y + $100 = $7500
2x + 2y = $7400
Next, we can substitute "z = x + y + $100" into the second equation:
0.06x + 0.09y + 0.15(x + y + $100) = $867
Expanding:
0.06x + 0.09y + 0.15x + 0.15y + 0.15 * $100 = $867
0.21x + 0.24y + $15 = $867
0.21x + 0.24y = $852
Finally, we can solve for x and y using the equations "2x + 2y = $7400" and "0.21x + 0.24y = $852".
We can use elimination method to find x:
2x + 2y = $7400
0.21x + 0.24y = $852
Multiplying the first equation by 0.21:
0.42x + 0.42y = $1557.8
Subtracting the second equation from the first:
0.42x + 0.42y - 0.21x - 0.24y = $1557.8 - $852
0.21x - 0.03y = $705.8
Dividing both sides by 0.21:
x = $705.8 / 0.21 + 0.03y / 0.21
x = $3357.14 / 0.24 + y
Finally, substituting x back into the equation "2x + 2y = $7400":
2($3357.14 / 0.24 + y) + 2y = $7400
Expanding:
$6714.29 + 2.24y = $7400
Solving for y:
2.24y = $7400 - $6714.29
y = $685.71 / 2.24
y = $306.13
And finally, substituting y back into the equation "x = $3357.14 / 0.24 + y":
x = $3357.14 / 0.24 + $306.13
x = $1393.57
Therefore, the amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.
Express it to mathematical phrase:
Three added to four times a number
Answer:
4x + 3 = y
Step-by-step explanation:
Answer:
4x+3
there is no actual explanation
Three added= +3
four times a number= 4*x=4x
Kate has a collection of 20 buttons. Each button has a diameter of either 2 or 3
centimeters. The combined diameters of all buttons is 48 cm. If x is the number of 2 cm
buttons, and y is 3 cm buttons, which system below represents the situation?
x+y=20
3x+2y=48
x+y=20
5xy=48
x+y=20
2x+3y=48
x+y=48
2x+3y=20
The solution is, the system represents the situation is, x+y= 20
and, 2x+3y = 48.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Each button has a diameter of either 2 or 3 centimeters.
The combined diameters of all buttons is 48 cm.
If x is the number of 2 cm buttons,
and y is 3 cm buttons.
Kate has a collection of 20 buttons.
So, the system represents the situation is,
x+y= 20
and, 2x+3y = 48.
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An game is on sale for $28, which is 30% off the original price. What was the original price?
a$19.60
b$40.00
c$84.00
d$98.33
The solution is the original price was 93.33.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
An game is on sale for $28, which is 30% off the original price.
let,
the original price was x
ATQ,
x*30% = 28
x = 280/3
x=93.33
Hence, The solution is the original price was 93.33.
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