Based on the fixed costs and the equilibrium point, the function for total costs would be TC = 300 + 100VC
What s the function for total cost?The total cost that a company incurs for making a good or service is a combination of both the fixed cost and the variable cost.
The total variable cost is found as:
= Number of units produced x variable cost per unit
= 100 units x vc
= 100vc
The total cost would therefore be:
= Fixed cost + Total variable cost
= 300 + 100vc
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A tower has a revolving restaurant 785 feet above the ground. The restaurant makes a
complete revolution every 90 minutes. While a visitor was at the tower, the restaurant
rotated through 82°. How long was the visitor at the tower?
The visitor was at the tower for ______
minutes.
Answer:
1 revolution is 360 degrees
1 hour = 60 minutes
360/60 = 6
so it rotates 6 degrees every minute
135/6 = 22.5 minutes
Factor 2x² + 8x - 90 completely.
O a
Ob
OC
Od
(2x +9)(x - 5)
(2x-9)(x - 5)
2(x + 9)(x - 5)
2(x-9)(x - 5)
A
Please helppp
Factors of the polynomial 2x² + 8x - 90 is Option (c) 2(x + 9)(x - 5).
What is Factorization?Factorization is the method used to discover the factors of a given value or mathematical statement. A factor is an integer that is multiplied by another to create the original number. For instance, 2, 3, 6, 9, and 18 are the factors of 18. Likewise, in the case of polynomials, the factors are the polynomials that are multiplied to create the initial polynomial.
Given Equation: 2x² + 8x - 90
Step 1: Pull out like factors from the equation
⇒ 2x² + 8x - 90 = 2 • (x² + 4x - 45)
Step 2: Factorize by splitting the middle term of the equation (x² - 4x - 45)
⇒ x²+ 9x - 5x - 45
Step 3: Take Common factors from the two pairs of the equation
⇒ x(x + 9) - 5(x + 9)
Step 4: Rewrite the polynomial in factored form
⇒ 2(x + 9)(x - 5)
Therefore the factorization result is 2(x + 9)(x - 5).
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You are buying a house and will borrow $330,000 on a 25-year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.15 percent. Alternatively, she tells you that you can “buy down” the interest rate to 3.8 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
The number of points the borrower needs to buy down interest rate to 3.8% is 0.350 points
What is the desired annual percentage rate for the borrower?
The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%
difference in interest rate=4.15%-3.8%
difference in interest rate=0.35%
We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point
number of points required to buy down interest=1 point*0.35%
number of points required to buy down interest=0.350
In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%
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Can someone help wit this problem I’m confused on it
Answer:
1/9
Step-by-step explanation:
When the quantities are proportional, you are able to find the constant of proportionality by y/x. If you take each one of the y's listed and divide it by x, you will get 1/9.
For example 1 2/9 ÷11
1 2/9 is the same at 9/9 + 2/9 or 11/9
[tex]\frac{11}{9}[/tex] ÷ 11 is the same as [tex]\frac{11}{9}[/tex] ÷ [tex]\frac{11}{1}[/tex] To divide with fractions, you multiply by the reciprocal.
[tex]\frac{11}{9}[/tex] x [tex]\frac{1}{11}[/tex] The 11 can cancel out and we are left with [tex]\frac{1}{9}[/tex]
Answer: r = [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
y = rx
finding r (substitute y and x):
5 = r x 45
5/45 = r
r = [tex]\frac{5}{45} = simplify = \frac{1}{9}[/tex]
checking:
rx = y
[tex]\frac{1}{9}[/tex] x 11 = 1 [tex]\frac{2}{9}[/tex]
[tex]\frac{11}{9}[/tex] = 1 [tex]\frac{2}{9}[/tex]
convert mixed fraction into improper fraction
[tex]\frac{11}{9}[/tex] = [tex]\frac{11}{9}[/tex]
correct
Four fifths is equal to ten sixteenths of a number.
The Four-fifths is equal to ten-sixteenths of a number is x=32/25.
Given the statement is four-fifths is equal to ten-sixteenths of a number.
A mathematical statement is a meaningful component of words that can be true or false. Simply, they are known as a statement.
Let us assume the given number be x.
According to the given statement,
Four fifths means 4/5. ......(1)
And ten sixteenths means 10/16.
It is also given that ten sixteenths of a number means is (10/16)x. .......(2)
Now, we will equate equation (1) and equation (2) according to the given statement is
4/5=(10/16)x
Further, we will cross multiply both sides, we get
4×16=10x×5
64=50x
Now, we will divide both sides by 50, we get
64/50=50x/50
64/50=x
32/25=x
Hence, the number for the given statement "Four fifths is equal to ten sixteenths of a number" is 32/25.
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Please Help Me ;-;
[tex]||3x-1|+5|\ \textless \ 1[/tex]
The value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.
How to illustrate the information?It should be noted that an equation is simply used to show the relationship between the expression or variables.
From the information, 3x - 1 + 5 < 1.
Collect like terms
3x - 1 + 5 < 1.
3x < 1 + 1 - 5
3x < -3
Divide
3x / 3 < -3 / 3
x < 1
Therefore, the value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.
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(LOTS OF POINTS ANSWE FAST) multiply (5 4/7) (-2 2/5)
Answer:
-13 13/35
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation: Just took it
Evalute f(x) = x² + 1 for f(10)
Answer:
101
Step-by-step explanation:
Because if f(x) = [tex]x^{2}[/tex] + 1 and f(x) is f(10), this means that x = 10. If x = 10, then you can plug that into the equation, getting you [tex]10^{2}[/tex] + 1. [tex]10^{2}[/tex] is 100, plus 1 is 101.
Hope this helps!
A spherical tank has a capacity of 750 gallons. Using the fact that one gallon is about 0.1337 , find the radius of the tank to the nearest hundredth of a foot.
The radius of the spherical tank of capacity 750 gallons to the nearest hundredth is 2.88 ft.
How much s a gallon?
In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L[1] (231 cubic inches); and the US dry gallon ("usdrygal"), which is defined as 18 US bushel (exactly 4.40488377086 L).
Given data: 1 gallon ≈ 0.1337 ft³
Then, 750 gallons = 0.1337 x 750 ≈ 100.275 ft³
We know, Volume of sphere, [tex]V=\frac{4}{3}\pi r^{3}[/tex]
then, r = [tex]\sqrt[3]{\frac{3}{4\pi }V }[/tex]
= [tex]\sqrt[3]{\frac{3}{4\pi } 100.275}[/tex]
= [tex]2.88 ft.[/tex]
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The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation’s central office during the year. A random sample of 25 clerical workers reveals the following: Absenteeism: days, days. 12 clerical workers were absent more than 10 days. Construct a 95% confidence interval estimate for the mean number of absences for clerical workers during the year. Interpret. (Assume that the population is normally distributed)
The 95% confidence interval estimate for the mean number of absences for clerical workers during the year is (8.132, 11.268).
What is confidence interval?It should be noted that the mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given a = 0.05, Z(0.025) = 1.96 (from standard normal table).
The 95% confidence interval will be:
xbar +/- Z*s/vn
= 9.7 +/- 1.96*4/✓(25)
= (8.132, 11.268)
Therefore, the 95% confidence interval is (8.132, 11.268).
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On a map of the Thunderbird Country Club golf course, 1.5 inches equals 15 yards. How
long is the 15th hole if the map shows 17.5 inches?
175 yards long is the 15th hole if the map shows 17.5 inches.
hole = c yards
1.5 / 15 = 17.5 / c
1.5 c = 15 * 17.5
1.5 c = 262.5
c = 175 yards
A length unit equal to 36 inches, or 3 feet (see foot), in the United States Customary System, or 0.9144 metre in the International System of Units. A cloth yard is 37 inches long, and it was also the standard length for arrows.
The yard is an English unit of length that equals 3 feet or 36 inches in both the British imperial and US customary measurement systems. Since 1959, it has been standardized as 0.9144 meter by international agreement. One mile is equivalent to 1,760 yards. The survey yard in the United States is slightly longer.
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write in a number in which the value of the 8 is ten times greater than the value of the 8 in 8304?
Thee number in which case has the value of the 8 ten times greater than than the value of the 8 in 8304 as required in the task content is; 83450.
Which number has the value of the 8 is ten times greater than the value of the 8 in 8304?It follows from the task content that the number which satisfies the condition that, the value of its 8 is ten times greater than the value of the 8 in 8304 is to be determined.
It follows from place value that the 8 in 8304 has a value of; 8 × 1000 = 8000.
Hence, an example of a number that is ten times greater is; 10 × 80,000.
Ultimately, an example of the required number as in the task content is; 83450 where it's 8 digit is ten times greater than that in 8304.
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What are the coordinates for the image of the figure E(0,4), F(2,2), G(0,0), D(-4,3) if it has been dilated with a scale factor of 1/4
Answers:
E ' = (0, 1)
F ' = (0.5, 0.5)
G ' = (0, 0)
D ' = (-1, 0.75)
Notes: 0.5 = 1/2 and 0.75 = 3/4
================================================
Explanation:
Assuming the origin is the center of dilation, then we multiply each coordinate by the scale factor of 1/4 = 0.25
For instance, the point E(0,4) moves to E ' (0, 1) since
x coordinate: 0*0.25 = 0y coordinate: 4*0.25 = 1Do the same for the other points.
4 friends buy 16 pizzas. Each pizza is cut into
12 pieces. Each person eats the same number
of pieces.
How many pieces does each person eat?
-Solve the system. y - 10=3x
(2y=6x+20
infinite solutions
no solution
(10,40)
(2,13)
Step-by-step explanation:
[tex]y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20[/tex]
you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.
Yossi used to have a square garage with 250 ft 2 of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Answer:
5√10 ≈ 15.81 ft5√15 ≈ 19.36 ft22.47%Step-by-step explanation:
You want to know the length of the sides of a 250 ft² square, and one with an area 50% larger. You also want to know the percentage change in side length.
Side lengthThe area of a square is given by the formula ...
A = s²
Solving for the side length (s), we find ...
s = √A
The side length of a square with 250 ft² area is ...
s = √250 ft = 5√10 ft ≈ 15.81 ft . . . side length
The area of a square that has 50% more area is ...
(250 ft²) × (1 +50%) = 375 ft²
The side length of that square is ...
√375 ft = 5√15 ft ≈ 19.36 ft . . . side length
Percentage changeThe percentage change can be found from ...
percentage change = ((new value)/(old value) -1) × 100%
= ((5√15)/(5√10) -1) × 100% = (√1.5 -1) × 100% ≈ 22.47%
The percentage increase in the length of one side is about 22.47%.
Type an equation for the following pattern.
PLS HELP RUNNING OUT OF TIME
The x-intercept of a line is -5 and the y-intercept of the line is -2. What is the equation of the line?
A. y = - 5/2x -5
B. y = 2/5x + 2
C. y = 5/2x - 2
D. y = -2/5x - 2
The equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)
How to derive the equation of a line based on information about two intercepts
Lines are represented by first grade polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept of the line, and x and y are the independent and dependent variables, respectively.
We can find the values of the slope and the y-intercept by knowing the location of two distinct points on Cartesian plane. If we know that (x₁, y₁) = (- 5, 0) and (x₂, y₂) = (0, - 2), then the equation of the line is:
- 5 · m + b = 0 (1)
b = - 2 (2)
The solution to the system of linear equations is (m, b) = (- 2 / 5, - 2). Lastly, the equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)
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-10/17 divided by (-15/17)
Answer:
0.66
Step-by-step explanation:
Please help me! I have a fe of this for me to finish my homework! Please
Jasmine received a $140 paycheck from her job at the supermarket today. If she spends $10 every day at Starbucks, in how many days will she have exactly $30 left? Represent and solve this problem by creating a table graph and equation.
what is an equivalent fraction for 6/10
Answer:
3/5, 9/15 - some equivalent fractions for 6/10
I=Prt. You borrow $10,000 from the bank at a 8% rate for 5 years. Find
the simple interest you will pay on this loan.
Answer:14 000
Step-by-step explanation:
Simple interest formula: A=P(1+in)
A= amount after interest is added
P= initial amount (10000)
i= interest rate (8%)
n= number of periods (5 years)
Now substitute what you have into the simple interest formula:
A=P(1+in)
A=10000(1+(8/100)(5))
A= 14 000
The reason why 8 is divided by 100 is that 8 is a percentage. Unless you have a percentage function on your calculator, I'd strongly encourage you to ALWAYS divide your percentages by 100.
Last month, Alma was able to volunteer in a community pet shelter for 2,760 minutes. How many hours did she volunteer?
The number of hours Alma volunteered is 46 hours.
What is time conversion?
The process of time conversion changing or converting the unit of time from one unit to another.
For example, it can be converting seconds to minutes, converting minutes to hour or converting hours to minutes or hours to seconds.
Basically, time can be converted from one unit to another.
The number of hours Alma volunteered is calculated as follows;
60 minutes = 1 hour
2,760 minutes = ?
= (2760 x 1) / 60
= 46 hours
Thus, the number of hours Alma volunteered is 46 hours.
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Answer:
Step-by-step explanation:
46
Expand and simplify 4(2x - 1) + 3(2x + 5)
Answer:
14x+11
Step-by-step explanation:
A triangle has a perimeter of 13. If it has
sides of x/2,( x – 5), and (x - 2) lengths,
then:
a) find the value of x
b)find the length of the longest side
find the value of x.
find length of the longest side.
Step-by-step explanation:
perimeter=s+s+s
p=x/2+x-5+x-2
13=x/2+x-5+x-2
26=x+x+x-10-4
26=3x-14
26+14=3x
3x/3=40/3
x=13.3cm
b.
x/2=6.65
x-5=8.3
x-2=11.3
longest side=11.3cm
In an orchard, there are 15 apple trees, 23 orange trees, and a cherry tree. What is the ratio of apple trees to orange trees?
Can you please help me
Answer:1=a
2=b
3=c
Step-by-step explanation:
Factorize this does it have Any breaking form??
4a^2+4a-5
Answer:
[tex](2a + 1+\sqrt{6})(2a + 1-\sqrt{6})[/tex]==========================
Identities we will use:
[tex]a^2+2ab+b^2=(a+b)^2[/tex][tex]a^2-b^2=(a+b)(a-b)[/tex]===========================
Given expression:
[tex]4a^2+4a-5[/tex]Factorize it by completing the square and setting the difference of squares:
[tex]4a^2+4a + 1-6=[/tex][tex](2a)^2+2*1*2a + 1^2-6=[/tex][tex](2a+1)^2-6=[/tex][tex](2a + 1+\sqrt{6})(2a + 1-\sqrt{6})[/tex]Suppose a deep sea diver dives from the surface to 206 feet below the surface. He then dives down 18 more feet. Use integers to represent this situation. Then find the diver's present depth. (Simplify)
Answer:
Step-by-step explanation:
