Answer:
Part A: The maximum of the graph is the highest point which is at (2.5, 2531.25). Since xx is the decrease in price and yy is the profit, the maximum of (2.5, 2531.25) means that the maximum profit is $2531.25 and occurs when the price of the t-shirts is decreased by $2.50.
Part B: The yy-intercept is when the graph intersects the yy-axis which occurs at about (0, 2500). The yy-intercept then means that the profit is $2500 if the price of the t-shirts does not decrease.
Part C: The solution of a graph is its xx-intercept(s). The graph crosses the xx-axis at (25,0) so this point is the solution. The solution means that the profit will be $0 if the price is decreased by $25.
Step-by-step explanation:
9. Gross Margin equals $50,000, operating expenses equals $23,000, income
taxes equals $5,400 and sales is $110,000. What is the company's net income?
Answer:
$21600
Step-by-step explanation:
Net income is calculated by deducting all company expenses from its total revenue. Net income is given by the formula:
Net income = Revenue - cost of goods sold - operating expenses - tax.
But Gross margin = gross profit = Revenue - cost of goods sold. Hence:
Net income = Gross margin - operating expenses - tax.
Substituting gives:
Net income = $50000 - $23000 - $5400
Net income = $21600
19) Albert says that the two systems of equations shown have the same solutions.
FIRST SYSTEM
6x + y= 2
-x-y=-3
SECOND SYSTEMS
2x-3y = -10
-X-y= -3
A) Agree, because the solutions are the same
B) Agree, because both systems include -x-y= -3
C) Disagree, because the solutions are different
D) Cannot be determined
Answer:
option A) Agree, because the solutions are the same is correct.
Step-by-step explanation:
FIRST SYSTEM
[tex]6x + y= 2[/tex]
[tex]-x-y=-3[/tex]
solving the system
[tex]\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18[/tex]
[tex]\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}[/tex]
adding the equation
[tex]-6x-6y=-18[/tex]
[tex]+[/tex]
[tex]\underline{6x+y=2}[/tex]
[tex]-5y=-16[/tex]
so the system becomes
[tex]\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}[/tex]
solve -5y for y
[tex]-5y=-16[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]
simplify
[tex]y=\frac{16}{5}[/tex]
[tex]\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]
[tex]6x+\frac{16}{5}=2[/tex]
subtract 16/5 from both sides
[tex]6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}[/tex]
[tex]6x=-\frac{6}{5}[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{-\frac{6}{5}}{6}[/tex]
[tex]x=-\frac{1}{5}[/tex]
Therefore, the solution to the FIRST SYSTEM is:
[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]
SECOND SYSTEM
[tex]2x-3y = -10[/tex]
[tex]-x-y=-3[/tex]
solving the system
[tex]\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6[/tex]
[tex]\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}[/tex]
[tex]-2x-2y=-6[/tex]
[tex]+[/tex]
[tex]\underline{2x-3y=-10}[/tex]
[tex]-5y=-16[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}[/tex]
solve -5y for y
[tex]-5y=-16[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]
Simplify
[tex]y=\frac{16}{5}[/tex]
[tex]\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]
[tex]2x-3\cdot \frac{16}{5}=-10[/tex]
[tex]2x=-\frac{2}{5}[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{-\frac{2}{5}}{2}[/tex]
Simplify
[tex]x=-\frac{1}{5}[/tex]
Therefore, the solution to the SECOND SYSTEM is:
[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]
Conclusion:
As both systems of equations have the same solution.
Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.
Hence, option A) Agree, because the solutions are the same is correct.
Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror car
be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. Where should she place the
bulb to ensure a perfect beam of light?
(0
1)
(0, 4)
(1, 0)
(4, 0)
Answer:
Step-by-step explanation:
0,1
The bulb should be placed at (1,0).
What is Parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.
Given:
Suppose the equation of parabolic mirror is y² = 4ax.
The given data in the is x = 1 and y = 2
So, the value is y² = 4ax
4 = 4 a (1)
a = 1
So x = 1
and, the focus is at (x, y) is (1,0).
Learn more about parabola here:
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Which of the following is equal to 7 1/4
Answer:
D. [tex]\sqrt[4]{7}[/tex]
Step-by-step explanation:
Answer:
d.
Step-by-step explanation:
Write an Inequality to represent a graph.
Answer:
nun of the 3 you gave use so the last one the 4th
Step-by-step explanation:
2,704 rounded to the nearest thousand
Answer:
3000,
Step-by-step explanation:
5 or above round up, 4 and below keep it the same
Measurement A equals 6X - 35°
Answer:
............the answer is 97
what is the slope in the equations: y = 4x + 3
Answer:
4
Step-by-step explanation:
y = mx + b
m represents the slope, and as we can see in the equation, the number 4 is there instead of m, so therefore 4 is the slope
In the expression -3g + 12, how many terms are in the expression? *
1
2
3
4
Which expression has three terms? *
5x + kr
3ab
6 + x - 2y
4p + 2
Answer:
There are 1 terms.
5x+kr has 3 terms
Step-by-step explanation:
-3g has 1 term. 12 has none. so it is 1
5x has 1 term and kr has 2 terms and 2+1 is 3 terms.
Who ever Answers first gets a good review
Answer:
Do we do all of them???
Step-by-step explanation:
There are 12 basketball players on the team. In order to complete the main composition of the team for the
game, the coach can choose any 5 players from the team. How many different combinations of the main
compositions the coach can complete?
I get 792 but why is the answer 7.92. Kinda don't understand.
Step-by-step explanation:
We have been given that a basketball team has 12 players and the coach wants to pick which 5 players will start today's game.
We will use combinations formula to solve our given problem. , where,
n = Number of total items,
r = Number of items being chosen at a time.
Upon substituting our given values in combinations formula we will get,
Therefore, the coach can choose from 792 combinations
6. 1350 = 5 = find the quotient
Answer:
this question is of high school or collage
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of 0.2 (to 2 decimal places)
Answer:
69.04
Step-by-step explanation:
Given that:
Mean (m) = 69.0
Standard deviation (s) = 2.8
Zscore = 0.2
Find the corresponding height (x) ;
Using the relation :
Zscore = (x - m) / s
0.2 = (x - 69.0) / 0.2
0.04 = x - 69.0
0.04 + 69.0 = x
69.04 = x
Hence, the height of a man with a Zscore of 0.2 is 69.04
what is 9/10 ÷ 3/5 will give brainlist
Answer:1.5
Step-by-step explanation:
Anastasia is grocery shopping list is 60% done and she only has 12 items, how many items does she have on the list?
Answer:
She has 20 items on the list
Step-by-step explanation:
Answer:
if she is 60% done shopping and has a total of 12 items, then the list will have 8 items left or 20 in total.
hey um, so i’m learning ab percentages in my math class so can someone please explain to me how to solve percent problems if that’s ok? thank you.
Answer:
It's pretty simple. For example, if it says there is a percentage increase on something like there is a jacket for $25 and there was a 15% increase, you multiply 25 by 1.15 to see what the new price is. But say if the same $25 jacket is on sale for 15%, then you can multiply 25 by .15, then subtract that from 25 or originally subtract the 15% from 100 which is 85 and multiply 25x.85 and get the answer directly.
Hope this helps! But this would be easier to explain with an example
At time t ≥ 0, the velocity of a body moving along the s-axis is v = t² -5t +4. When is the body moving backwards
Check comments for multiple choice answers
Answer:
A
Step-by-step explanation:
The velocity of a moving body is given by the equation:
[tex]v=t^2-5t+4 ,\, t\geq0[/tex]
Is the velocity is positive (v>0), then our object will be moving forwards.
And if the velocity is negative (v<0), then our object will be moving backwards.
We want to find between which interval(s) is the object moving backwards. Hence, the second condition. Therefore:
[tex]v<0[/tex]
By substitution:
[tex]t^2-5t+4<0[/tex]
Solve. To do so, we can first solve for t and then test values. By factoring:
[tex](t-4)(t-1)=0[/tex]
Zero Product Property:
[tex]t=1, \text{ and } t=4[/tex]
Now, by testing values for t<1, 1<t<4, and t>4, we see that:
[tex]v(0)=4>0,\, v(2)=-2<0,\,\text{ and } v(5)=4>0[/tex]
So, the (only) interval for which v is <0 is the second interval: 1<t<4.
Hence, our answer is A.
In a flower basket, the ratio of red roses to white roses is 2 to 3. There are a total of 20 roses in the basket. How many red roses are in the basket?
Stephanie spends $15 each month to belong to a photography club. As a member of the club she can develop rolls of film for $2.50 each. Write and solve an equation to find the total amount Stephanie will spend this month if she develops 5 rolls of film.
Answer:
2.5*5= 12.5
15-12.5=2.5
So in order to pay the 15 dollars in the photography club, she only has to pay 2.50
Drag and drop each pair of lines into the correct category to indicate whether the pair of lines are parallel, perpendicular, or neither.
1/7x + y = 9; y = -7x
y = 3x - 3; 12x - 4y = 12
7y = 2x + 1; 14x + 4y = 12
x - 4y = 18; y = x + 4
3x - 4y = -1; 3y = -4x + 5
Parallel Perpendicular Neither
Answer:
Step-by-step explanation:
(1). [tex]\frac{1}{7}[/tex] x + y = 9 and y = - 7x ( Neither ) ; lines intersect.
(2). y = 3x - 3; 12x - 4y = 12 ( Neither ) ; Lines are overlapped or both equation are of the same line.
(3). 7y = 2x + 1; 14x + 4y = 12 ( Perpendicular ) ; [tex]m_{1}[/tex] = [tex]\frac{2}{7}[/tex] and [tex]m_{2}[/tex] = - [tex]\frac{7}{2}[/tex] , slopes are opposite reciprocals.
(4). x - 4y = 18; y = x + 4 ( Neither ) ; lines intersect.
(5). 3x - 4y = - 1; 3y = - 4x + 5 ( Perpendicular ) ; [tex]m_{1}[/tex] = [tex]\frac{3}{4}[/tex] and [tex]m_{2}[/tex] = - [tex]\frac{4}{3}[/tex] , slopes are opposite reciprocals.
A travel agency is advertising a vacation package that includes $250 fora $40a day for hotel. The agency also offers the option of eating breakfast and lunch at the hotel for
$10 a day for the length of the hotel stay.
Answer:
V(d) = 50d + 250 us the answer
The equation for the function V(d) is V(d) = 5d + 250 if the travel agency is advertising a vacation package that includes $250 for $40a day for a hotel.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that,
A travel agency is advertising a vacation package that includes $250 for $40a day for a hotel.
The agency also offers the option of eating breakfast and lunch at the hotel for $10 a day for the length of the hotel stay.
The equation for the function can be framed as follows:
Per day expense = 40 + 10 = 50
Fixed expense = 250
V(d) = 5d + 250
Thus, the equation for the function V(d) is V(d) = 5d + 250 if the travel agency is advertising a vacation package that includes $250 for $40a day for a hotel.
Learn more about the function here:
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Allan bought a sweater
for $78 and a shirt for
$29. How much more did
the sweater cost than
the shirt
Answer:
$49
Step-by-step explanation:
78 - 29 = 49
To get 49, I subtracted 29 from 78.
please solve:
2(X+3)=8-3(x-4)
x-3(x-2)=3(2-x)
question from equation and inequality.
Answer:
i) x = 2.8
ii) x = 2
Convert:
5 m = ________mm
Answer:
5m = 5000 mm
Step-by-step explanation:
9/12 +3/12 =?
A. 1
B. 6/12
C. 11/12
D.1/2
9/12 + 3/12 = 12/12 = 1
Therefore, 1 is your answer.
Answer:
Solving [tex]\frac{9}{12}+\frac{3}{12}[/tex] we get 1.
Option A is correct answer.
Step-by-step explanation:
We need to solve [tex]\frac{9}{12}+\frac{3}{12}[/tex]
For solving fractions we need to take LCM of denominators.
The LCM of 12, 12 is 12
So, solving:
[tex]\frac{9}{12}+\frac{3}{12}\\=\frac{9*1+3*1}{12}\\=\frac{9+3}{12}\\=\frac{12}{12}\\=1[/tex]
So, solving [tex]\frac{9}{12}+\frac{3}{12}[/tex] we get 1.
Option A is correct answer.
What is the equation of the line that passes through the points (-3, -2) and (1, 6)?
Answer:
y = 2x +4
Step-by-step explanation:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~
(1, 6)
(- 3, - 2)
m = 2
y - 6 = 2 ( x - 1 ) <------ ( point-slope form )
y = 2x + 4 <------- ( slope-intercept form )
2x - y = - 4 <------ ( standard form )
How do I simplify 25.3(2.4)
Answer:
60.72
Step-by-step explanation:
you multiply 25.3 by 2.4
Alexandra spends 1/3 of her daysleeping and 3/8 of her day at work. What fraction of Alexandra’s day is occupied by sleep or work?
Answer:
17/24
Step-by-step explanation:
Change the denominators to match
8/24 + 9/24 = 17/24
X=number of hours
Y=number of tents made
X=0,1,2,3,4,5,6,7,8
Y=6,7,8,9,10,11,12,13,14
What is the slope? What does it represent?
Given:
X=number of hours
Y=number of tents made
Table of value.
To find:
The slope and its interpretation.
Solution:
Consider any two points from the table, i.e., (0,6) and (1,7).
The slope is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{7-6}{1-0}[/tex]
[tex]m=\dfrac{1}{1}[/tex]
[tex]m=1[/tex]
Therefore, the slope is 1 and it represent that the number of tents made are increasing by 1 units in each hour.
Drag the simplified value into the box to match each expression.
23+1⋅4−3
20+10−4⋅2
3+52−6⋅4
Answer:
Step-by-step explanation:
9
3
4
Answer:
1. 9
2. 3
3. 4
Step-by-step explanation:
I have taken the test and got 100% on it so I hope this helped you!