Answer: B. −8x − 12y − 18q − 42p
The profit for a certain commodity, n, where n is in units, is given by the functionP(n) =25n^2 + 300n + 1125At the break-even point, the profit is zero, i.e., P(n) = 0. Find the number of units where the break-even point is located, i.e., find n when P(n) = 0.The number of units, n, where the break-even point is located, isHint: Did you factor the GCF? Then reduce your equation to smaller coefficients?
Given the function:
[tex]P\mleft(n\mright)=-25n^2+300n+1125[/tex]You know that "P" is the profit for a certain "n" commodity (in units).
You need to find the value of "n" when:
[tex]P(n)=0[/tex]In order to find it, you can follow these steps:
1. Substitute this value into the function:
[tex]P(n)=0[/tex]Then:
[tex]\begin{gathered} 0=-25n^2+300n+1125 \\ \\ -25n^2+300n+1125=0 \end{gathered}[/tex]2. Divide both sides of the equation by -25:
[tex]\begin{gathered} \frac{-25n^2}{(-25)}+\frac{300n}{(-25)}+\frac{1125}{(-25)}=\frac{0}{(-25)} \\ \\ n^2-12n-45=0 \end{gathered}[/tex]3. Factor the equation by finding two numbers whose Sum is -12 and whose Product is -45. These are 3 and -15, because:
[tex]\begin{gathered} 3-15=-12 \\ \\ (3)(-15)=-45 \end{gathered}[/tex]Then:
[tex](n+3)(n-15)=0[/tex]4. Set up these two equations:
[tex]\begin{gathered} n+3=0\text{ (Equation 1)} \\ \\ n-15=0\text{ (Equation 2)} \end{gathered}[/tex]5. Solving form "n" from each equation, you get:
[tex]\begin{gathered} n+3=0\text{ }\Rightarrow n_1=-3 \\ \\ n-15=0\Rightarrow n_2=15 \end{gathered}[/tex]Since the number of units cannot be negative, the answer is:
[tex]n=15[/tex]←
The formulas below are the cost and revenue functions for a company that manufactures and sells small radios.
C(x)=90,000 +42x and R(x) = 47x
a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios.
b. Find the company's profit if 23,000 radios are produced and sold.
***
Answer:
(a) The profit function is P(x) = 89x - 90,000.
(b) The company's profit at x=23,000 is 1,957,000.
Step-by-step explanation:
Given,
The cost function of the company is C(x)=90,000 +42x and
The revenue function is R(x) = 47x
where x is the number of radios.
(a)
The company's profit function, P, is from producing and selling x radios is
The formula for profit:
Profit (P) = Revenue (R) - Cost (C)
P = R - C
P = 47x - 90,000 + 42x
P = (47x + 42x) - 90,000
P = 89x - 90,000
For (a), The company's profit function, P, from producing and selling x radios is P = 89x - 90,000
(b)
The radios produced and sold are 23,000
So, x = 23,000
putting x value in the profit function, P
P = 89x - 90,000
P = 89 x 23,000 - 90,000
P = 2,047,000- 90,000
P = 1,957,000
For (b), the company's profit at x = 23,000 is 1,957,000.
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HELP ASAP Arrange the dot plots in descending order based on standard deviation
Answer:
its true because standard deviation is the only way out to find any solution
At their going out business sale, Bill’s Bikes sold 36 bikes and had 58 left. Which equation could be used to find x, the number of bikes the store had originally.
The equation that could be used to find x, the number of bikes the store had originally, is (x-94) = 0.
According to the question,
We have the following details:
Bill has sold 36 bikes and is left with 58 bikes more.
Now, the number of bikes the store had originally is given to be x.
So, we have:
x = Number of bikes sold + Number of bikes left
x = 36+58
x = 94
x-94 = 0 (94 was positive on the right hand side. So, it is negative on the left hand side.)
Hence, the equation that could be used to find number of original bikes in Bill's store is x-94 = 0.
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y+3 = 2(x+3) how do i solve it
Answer 2xy3
Step-by-step explanation: you basic combine 2(x+3) to get 2x + 6
i have 2 mins pleaseeeee
Answer: 179.07 this is ur answer
Step-by-step explanation:
rewrite y=1/4x+3 solving for x. what feature of the line can easily be found using the rearranged equation?
x intercept is x = -12
What is linear equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
x = 4y - 12
y = 0
x intercept is
x = -12
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please please answer
1: which measure represents the SA (surface area) in square inches, of the right square pyramid.
a:196
b:217
c:322
d:385
- — - — - - - - - - — — - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -—
The total surface area of the prism is 217 square inches.
In geometry, a prism is a polyhedron with n sides made of polygons, a second base that is a translation of the first base, and n additional faces that must all be parallelograms and connect the effective distribution of the two bases.
The bases are translated into all cross-sections that are parallel to them.A solid object's surface area is a measurement of the overall space that the object's surface takes up.The base is a square with area = 49 square inches
Length of 1 side = √49 = 7 inches
Area of the triangular sides is given by the formula (1/2) × base × height
Area of each side
= (1/2) × base × height
= (1/2) × 7 × 12
= 42 square inches.
Total surface area
= 42 × 4 + 49
=217 square inches
Therefore the total surface area is 217 square inches
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Points A and B are on a circle with centre O and radius n so that AOB = (360/n). Sector AOB is cut out of the circle. Determine all positive integers n for which the perimeter of sector AOB is greater than 20 and less than 30
The integer n = 25 is the only value so that the sector AOB is greater than 20 and less than 30.
How to find the positive integers associated to the diameter of a circle
In this problem we find the sector generated by line segments OA and OB, where O is the center of the circle and the points A and B are on the circle:
20 < 360 / n < 30
20 · n < 360 < 30 · n
First, we determine the factorial decomposition of 360:
360 = 2³ × 3² × 5
Second, find the value of n associated to each limit of the inequality:
Lower limit
360 = (2² × 5) × (2 × 3²)
360 = 20 × 18
n = 18
Upper limit
360 = (2 × 3 × 5) × (2² × 3)
360 = 30 × 12
n = 12
Third, find the values that are between 12 and 18:
x = 2³ × 3
x = 24
n = 360 / 24
n = 15
The only integer that satisfies the inequality is 15.
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Write an inequality that represents the velocity of an object that has a mass of 30 kilograms and creates a momentum of at least 15 kg(m/s)
The inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .
The relation between the mass(m) of an object with momentum(p) and velocity(v) is given by the equation
p=m × v .
In the question,
it is given that
the mass of the object = 30 Kg
the momentum required is at least 15 Kg(m/s).
let the velocity of the object " v " .
Substituting values in the formula ,
we get ,
15 = 30×v
the word at least in inequality is represented by " ≥ " .
So , the inequality becomes
15 ≥ 30×v
Therefore , the inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .
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Decrease 58 by 41%.
Give your answer to 2 decimal places.
Answer: 34.22
Find 41% of 58 first.
[tex]58*0.41=23.78[/tex]
The problem asks to decrease it, meaning you would subtract the percentage from 58.
[tex]58-23.78=34.22[/tex]
34.22
Solve the equation b over 24 equals negative 6 for b.
Answer:
b=-144
Step-by-step explanation:
b/24=-6
cross multiplication
b=24×-6
=-144
Solve the following Radical Equation (Square root). Show all work.
Find the equation of the line that goes through the points (-15,70) and (5,10).
[tex](\stackrel{x_1}{-15}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{70}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-15)}}} \implies \cfrac{-60}{5 +15} \implies \cfrac{ -60 }{ 20 } \implies - 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{70}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-15)}) \implies y -70= -3 (x +15) \\\\\\ y - 70 = -3x - 45\implies {\Large \begin{array}{llll} y = -3x+25 \end{array}}[/tex]
The information is in the photo. Please help. Goodnight .
The ratio of hexagons to triangles is 2/1.
What are Ratios?The ratio is the relationship or comparison between two amounts of the same unit to determine how much larger one number is than the other. A ratio is a mathematical term that compares two comparable or dissimilar numbers by division. If you want to compare one data point (A) to another data point (B), your formula would be A/B.Given:
In the figure,
Number of hexagons = 4
Number of triangles = 2
We have to determine the ratio of hexagons to triangles.
Ratio = Number of hexagons/Number of triangles
Ratio = 4/2
Reducing it we get,
Ratio = 2/1
Therefore, the required ratio is 2/1.
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Find the values of the variables and the measure of the angles.
Since ∠GFE is a right triangle, we can conclude:
[tex]\begin{gathered} b+32=90 \\ b=90-32 \\ b=58 \end{gathered}[/tex]the sum of the internal angles of a triangle is 180, therefore, for the triangle GHF:
[tex]\begin{gathered} 55+a+b=180 \\ \text{ Since b=58} \\ 55+a+58=180 \\ a+113=180 \\ a=67 \end{gathered}[/tex]Finally, for the triangle GEF:
[tex]\begin{gathered} a+90+d=180 \\ 67+90+d=180 \\ 157+d=180 \\ d=180-157 \\ d=23 \end{gathered}[/tex]The tangent line to the graph of y=h(x) at the point (-1,4) passes through the point (3,6). Find h(-1) and h'(-1).
The value for h(-1) is 4
The value for h'(-1) is 1
Given the tangent line to the graph of y=h(x) at the point (-1,4) passes through (3,6), to get h(-1) and h'(-1), we should calculate the following:
Gradient of the tangent line:
Gradient=change in y axis/change in x axis=Δy/Δx
Using the x and y coordinates (-1,4) and (3,6)
Gradient=(6-4)/(3--1)
=2/4
=1/2
Gradient=1/2 or 0.5
Equation of the tangent line:
This should be in the form of y=mx+c, where m is the gradient of the line
We use the gradient and one of the x and y coordinates get the equation of the tangent line
Gradient=change in y axis/change in x axis=Δy/Δx, and gradient was found as 1/2
Δy/Δx=1/2
(y-4)/(x--1)=1/2
(y-4)/(x+1)=1/2
2y-8=x+1
y=(1/2)x+4.5
Equation of the tangent line is y=(1/2)x+4.5 or y=0.5x+4.5
And y=h(x)
So, h(x)=0.5x+4.5
Calculate h(-1), here x=-1:
h(x)=0.5x+4.5
h(-1)=(0.5*-1)+4.5
=4
h(-1)=4
Calculate h'(-1), x=-1:
Here we get the derivative of the equation of the tangent line h(x)=0.5x+4.5,
h'(x)=0.5x^0+0
h'(-1)=1+0
h'(-1)=1
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Thaddeus wants to attend a sports camp this spring that costs $180.00 for the week. He rakes leaves during the fall and earns
$58.35. He shovels snow during the winter and earns $82.80. How much more money does Thaddeus need to earn to pay for
the sports camp? Write your answer as a decimal.
Thaddeus needs to earn $
Answer:
$38.35
Step-by-step explanation:
take $180 subtract $58.35 that will leave you with $125.65 then subtract $82.80 then that will leave you with $38.35
Determine the slope of a line passing through the given points. If the slope is undefined, write undefined. Enter your answer as a decimal if necessary. a. ( 5 , − 4 ) and ( 0 , 1 ) b. ( − 1 , 8 ) and ( 7 , 10 ) c. ( − 4 , 12 ) and ( − 4 , 5 ) Tools are not currently accessible
The slope of the given line that runs through the points are:
1. Defined
2. Defined
3. undefined.
What is an Undefined Slope of a Line?An undefined slope of a line can be described as the slope of a vertical line that has no run but only rise. That is, the x-coordinates do not change even though the y-coordinates of the line are changing.
Thus, the change in x-coordinates is always 0.
Slope = change in y / change in x.
a. (5 , − 4) and (0 , 1):
Slope = (-4 - 1)/(5 - 0)
Slope = -5/5 = -1 [the slope is defined]
b. (−1 , 8) and (7 , 10):
Slope = (10 - 8)/(7 -(-1))
Slope = 2/8
Slope = 1/4
c. (-4, 12) and (-4, 5)
Slope = (12 - 5)/(-4 -(-4))
Slope = 7/0 [cannot divide, therefore, the slope is undefined]
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Garrett is a member of The Mighty Manatees, an outdoor swim team. Every practice, his coach tells him to swim a target number of laps. One day, Garrett swims 31 laps before practice is canceled due to a thunderstorm. Garrett still has 29 laps left to reach his target number.
Find the measure of EG.
Thank you :)
Measure of EG is 9.5 cm.
Define triangles.A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A triangle's third side is always equal to the sum of any two of its sides' lengths. Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle. As a polygon, a triangle.
Given Data
Lengths
EH = 24, GH = 24
The third side of a triangle is always equal to the sum of the lengths of any two of its sides.
24 = 9.5 + x + 24
9.5 = x
Measure of EG is 9.5 cm.
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If f(x)=5x^2-x-4 and g(x)=x-6What (f+g)(x)=And(f+g)(9)=
Explanation
given
[tex]\begin{gathered} f(x)=5x^2-x-4 \\ g(x)=x-6 \end{gathered}[/tex]Step 1
a) (f+g) (x)
here we need to find a new function ( f+g) (x), this is the sum of the functions f and g, so to find it just add g(x) to f(x)
hence
[tex]\begin{gathered} (f+g)(x)=5x^2-x-4+x-6 \\ add\text{ like terms} \\ (f+g)(x)=5x^2-10 \end{gathered}[/tex]so
[tex](f+g)(x)=5x^{2}-10[/tex]Step 2
now, we have to evaluate that function for x= 9
so
[tex]\begin{gathered} (f+g)(x)=5x^{2}-10 \\ evaluate\text{ for x=9} \\ replace\text{ and calculate} \\ (f+g)(9)=5(9)^2-10 \\ (f+g)(9)=5(81)-10=405-10 \\ (f+g)(9)=395 \end{gathered}[/tex]so
[tex](f+g)(9)=395[/tex]I hope this helps you
what is 3 (6+99) - 45
Given:
[tex]3(6+99)-45[/tex]Shelby prepared 9 kilograms of dough after working 3 hours. How many hours did Shelby work if she prepared 15 kilograms of dough? Assume the relationship is directly proportional.
Shelby works for 5 hours to prepare 15 kgs of dough.
Here, we are given that Shelby prepared 9 kilograms (kgs) of dough after working 3 hours.
from this information we can calculate the amount of dough she can prepare in 1 hour.
3 hours ⇒ 9 kgs
1 hour ⇒ 9/3 kgs
9/3 = 3
Thus, she will prepare 3 kgs of dough in 1 hour.
Now, we are given that Shelby prepares 15 kgs of dough in all.
we have, 3 kgs ⇒ 1 hour
Thus, 15 kgs ⇒ 15/3 hours
15/3 = 5
Thus, Shelby works for a total of 5 hours to prepare 15 kgs of dough.
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Solve the word problem below. Enter your answer, using the slash (/) as the
fraction bar.
Students were asked to choose their favorite season and 3/10 chose either spring or summer. If 1/10 chose spring, what fraction chose summer? (Please show a solution)
When asked which season they preferred, just 3/10 of the students selected either spring or summer. 2/5 fraction went with summer if 1/10 chose spring.
Given that,
When asked which season they preferred, just 3/10 of the students selected either spring or summer.
We have to find what fraction went with summer if 1/10 chose spring.
To find the fraction we have to add the students selected in spring or summer.
3/10+1/10
Denominator are equal numerator can add
(3+1)/10
By adding
4/10
By doing the division
2/5
Therefore, the fraction is 2/5.
2/5 fraction went with summer if 1/10 chose spring.
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Which angle pairs include the named angle?
Select all that apply.
Which of the following are equal to 450?
300 increased by 50%
240 increased by 25%
250 increased by 50%
225 increased by 100%
Answer:
300
Step-by-step explanation:
H(-1, 3), X(7, -1) midpoint
Answer: (3,1)
Step-by-step explanation:
Ashley saved money every month last year. The table below shows how much money she saved each month.
Dollars Saved
Month Money Saved (in dollars)
January
96
February
38
March
162
April
65
May
178
June
112
July
57
August
143
September
135
October
104
88
22
November
December
What is the mean absolute deviation of amounts she saved?
A.18
B.39
C.23
D.156
The mean absolute deviation of the amount $39
What is Mean Absolute Deviation?
The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set. A measure of variance in a data set is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.
Given,
The amount she saved throughout the year
January 96
February 38
March 162
April 65
May 178
June 112
July 57
August 143
September 135
October 104
November 88
December 22
The mean of the data will be = 96+38+162+65+178+112+57+143+135+104+88+22/12
= 1200/12
=100
The mean would be 100
|data - mean value| = 96-100 = 4
38-100 = 62
162-100 = 62
65-100 = 35
178-100 = 78
112-100 = 12
57-100 = 43
143-100 = 43
135-100= 35
104-100 = 4
88-100 = 12
22-100 = 78
Now, sum of |data - mean values| = 468
The mean absolute deviation:
= sum of |data - mean values| / number of values
= 468 / 12
= 39
Hence, the mean absolute deviation of amounts she saved is $39
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Rewrite as a simplified fraction.3.16
The decimal number 3.16 in the form of the simplest fraction is 79/25.
The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.
Consider the decimal number,
Let x = 3.16
Then,
x = 3.16 = 316/100
The fraction then can be simplified as,
x = ( 158 × 2)/ (50 × 2)
x = 158/50
x = ( 79 × 2)/ ( 25 × 2 )
x = 79/25
Hence, the number 3.16 in the simplest fraction is 79/25.
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