This company’s revenue function is given by −0.25x³ - 4x² + 1000x + 16,000.
How to determine company's revenue function?Mathematically, the amount of revenue that's being generated by a company or business organization can be calculated by using the following function (expression):
Revenue = price × demand
R(x) = p(x) × d(x)
The demand (d) for this company’s product at cost (x) is given by this demand function:
d(x) = −0.25x² + 1,000
Also, the price (p) in dollars that this company can charge for its product is given by this price function:
p(x) = x + 16
Substituting the parameters into the revenue function, we have;
Revenue function, R(x) = p(x) × d(x)
Revenue function, R(x) = (−0.25x² + 1,000) × (x + 16)
Revenue function, R(x) = −0.25x³ - 4x² + 1000x + 16,000.
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Complete Question:
Suppose demand, d, for a company's product at cost, x, is predicted by the function, d(x) = −0.25x² + 1,000, and the price, p, that the company can charge for the product is given by p(x) = x + 16. Find the company's revenue function.
5. For which values of x and y is line p parallel to line q? (1 point)
R
(26y)⁰
Ox= 5, y = 3
Ox= 1, y = 5
Ox=3, y=5
Ox=3, y=6
(16x + 2)°
(45x-51
Answer:
x = 3 and y = 5
Step-by-step explanation:
1st: The sum of the same side interior angles equal 180°. Use this to solve for x.
45x - 5 + 16x + 2 = 180
61x - 3 = 180
61x - 3 + 3 = 180 + 3
61x/61 = 183/61
x = 3
2nd: find the measure of angle 16x + 2
16x + 2
16(3) + 2
48 + 2
50°
3rd: the sum of the 50° angle and the angle 26y° is 180 since they make a straight angle. Make an equation and solve for y.
50 + 26y = 180
50 - 50 + 26y = 180 - 50
26y = 130
26y/26 =130/26
y = 5
The rental price of a dacha was $9000. At the end of each month
the price is increased by 6%.
a) Find the price of the house after 1 month.
b) Find the price of the house after 3 months.
c) Find the price of the house after 10 months
a) The price (amount) of the house after 1 month = $9540
b) The price (amount) of the house after 3 months = $10719.14
c) The price (amount) of the house after 10 months = $16117.629
a ) How to find the rental price of the house after 1 month ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 1
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]
The rental price of the house after 1 month = $9540
b ) How to find the rental price of the house after 3 months ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 3
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]
The rental price of the house after 3 months = $10719.14
c ) How to find the rental price of the house after 10 months ?
The rental price of a dacha =Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 10
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]
The rental price of the house after 10 months = $16117.629
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X 2 4 6 8 10
Y 1, 3, 5 , 7, 9
(a) Is it a function?
(b) Domain:
(c) Range:
Answer:B
Step-by-step explanation:
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
Answer: 19
Step-by-step explanation:
[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]
A package contains 11 resistors, 2of which are defective. If 4 are selected find the probability of getting the following results.P(1 defective)=
From the given values, we know there are 2 defective resistors and 9 not defective. then, we have
[tex]P(1\text{ defective)=}\frac{C^9_3\times C^2_1}{C^{11}_4}[/tex]where
[tex]C^9_3[/tex]denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,
[tex]C^2_1[/tex]denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.
Then, we have
[tex]P(1\text{ defective)=}\frac{84\times2}{330}[/tex]then, the answer is
[tex]P(1\text{ defective) =}0.509[/tex]Two cars are initially 10 miles parat on the same straight road and are moving towards each other. One car is going 30 miles per hour and the other car is going 36 miles per hour. How far apart are the two cars 2 minutes later?
Answer:
Let's break down the given information.
Car A
Speed - 30 mph
Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.
Car B
Speed - 36 mph
The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.
Initial distance between the cars is 10 Miles
Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.
Hence to calculate the distance between the 2 cars we need to calculate
Initial distance - Distance travelled by Car A - Distance traveled by Car B
Which is
10 - 1 - 1.2
7.8 Miles distance between the 2 cars
Create a system of equations and use algebra to write a quadratic equation with points (-3,-4), (3,14), and (0,-4). Equations 1: -4=9a-3b+c Equation 2: 14=9a+3b+c Equation 3: -4=c
what is the resultiNg of b?
In the system of equations, the value of the variable 'b' will be 3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the equations is given below.
Equations 1: - 4 = 9a - 3b + c
Equation 2: 14 = 9a + 3b + c
Equation 3: - 4 = c
Put the value of c in equations 1 and 2, then we have
- 4 = 9a - 3b - 4
9a - 3b = 0 ...4
14 = 9a + 3b - 4
9a + 3b = 18 ...5
Subtract equation 4 from 5,
9a + 3b - 9a + 3b = 18 - 0
6b = 18
b = 3
In the system of equations, the value of the variable 'b' will be 3.
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5. Estimation What is the greatest possible integer solution of the inequality
3.806x< 19.902?
The greatest possible integer of the inequality is 19.902.
What is the inequality?
In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, as to if it is less than or greater than. The different inequality symbols, properties, and methods for resolving linear inequalities inside one variable and two variables will all be covered in this article along with examples.
Given that,
3.806< 19.902
In which, less than inequality is used.
The given numbers are in decimal form.
comparison be between the given numbers and check which one is greater.
3.806< 19.902
19.902 is the greater than 3.806
Hence, the greatest possible integer is 19.902.
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The lines represented by the equations
12
y
−
4
x
=
84
12y−4x=84 and
y
=
−
3
x
+
8
y=−3x+8 are
The two linear equations are perpendicular.
What are the lines?
Here we have the two linear equations:
12y - 4x = 84
y = -3x + 8
If we write both of them in the slope-intercept form (as the second one) we will get:
12y - 4x = 84
12y = 4x + 84
y = (4x + 84)/12
y = (1/3)*x + 7
Now, if we take the product of the slopes of the two lines, we get:
p = -3*(1/3) = -1
when this product is -1, the lines are perpendicular, so that is the relation between our lines.
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Please help! Consider the following diagram where the regular polygon ABCDE has center at M, polygon DEHGF is irregular, and point D is on CF.Which of the following statements are correct? Select all that apply.
Solution:
From the given diagram;
The statements that are correct about the given diagram are
b)
[tex]m\angle EDC=108\degree\text{ \lparen Interior angle of a regular pentagon\rparen}[/tex]d) The sum of exterior angles of a polygon is 360°,
Hence, the sum of the exterior angles of polygon ABCDE and the sum of exterior angles of polygon DEHGF is 720°
e)
[tex]m\angle ABM=m\angle DCM[/tex]apesville is a utopian island of 5000 square kilometers. there are currently 250,000 inhabitants of the island. last year, there were 12,000 new children born and 10,000 people were recorded as deceased. in how many years will the population of apesville double?
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Given vectors a=(3, 2) and b=(-5, 6), find – 3a+2b.Write your answer in component form.-3a + 2b =
Vector a = (3, 2), then;
[tex]-3a=-3(3,2)\text{ = (-9,-6)}[/tex]Also, vector b = (-5, 6), then;
[tex]2b=2(-5,6)=(-10,12)[/tex]Then, -3a + 2b = (-9, -6) + (-10, 12)
[tex]\begin{gathered} -3a+2b=(-9+(-10),-6+12)_{} \\ -3a+2b=(-19,6) \end{gathered}[/tex]The answer is (-19,6)
a container of milk contains 8 cups of milk. if paul sets aside $1\frac{2}{5}$ cups of milk for use in a recipe and divides the rest evenly among his three children, how much milk should each child receive? express your answer as a mixed number.
Each child will receive the 1.1 cup of milk.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;
8 - [tex]1\frac{2}{5}[/tex] = 8 - 7/5
= 40- 7/5
= 33/5
= 6.6
The the rest cups of milk = 6.6
Then the rest evenly among his three children 6.6/3 = 1.1
Hence, Each child will receive the 1.1 cup of milk.
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I need this answered please
The rate of the slowest car is 86 km/hr using the concept of relative velocity.
What is Relative velocity?Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.
Let the speed of 1st car is v₁.
Let the speed of 2nd car is v₂.
v₁- v₂ = 18 km/hr --- (1)
And using the concept of relativity.
S(rel) = D(rel)/time
S(rel) = 360 / 2
S(rel) = 190
v₁ + v₂ = 190 --- (2)
Adding equations 1 and 2 we get
v₁ = 104 km/hr
v₂ = 86 km/hr
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Which of the following rational functions is graphed below?
Answer: A.
Step-by-step explanation:
1. The function is even (symmetric about the y-axis)
2. The function F(x) is positive
[tex]\displaystyle\\Hence,\\F(x)=\frac{1}{x^2}[/tex]
I need this answered please
Answer:
76 child tickets were sold
Step-by-step explanation:
let a represent number of adults and c number of child tickets sold, then
a + c = 165 → (1)
5.8a + 8.9c = 1192.6 → (2)
multiplying (1) by - 5.8 and adding to (2) will eliminate a
- 5.8a - 5.8c = - 957 → (3)
add (2) and (3) term by term to eliminate a
0 + 3.1c = 235.6
3.1c = 235.6 ( divide both sides by 3.1 )
c = 76
that is 76 child tickets were sold that day
Jamie has 8/10 of a
candy bar leftover. He
wants to split it into 4
pieces. How big will
each piece be?
Answer: 1/5
Step-by-step explanation: It might be first easier to put it in decimal form so 8/10 is 0.8 and 0.8 divided by 4 is 0.2. 0.2 as a fraction is 1/5.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
convert element to fraction: 4 = [tex]\frac{4}{1}[/tex]
= [tex]\frac{8}{12}[/tex] ÷[tex]\frac{4}{1}[/tex]
The fraction rule: a/b ÷ c/d = a/b x d/c
= [tex]\frac{8}{12}[/tex] × [tex]\frac{1}{4}[/tex]
Cross - cancel common factor: 4
= [tex]\frac{2}{12}[/tex]
Cancel the common factor: 2
= [tex]\frac{1}{6}[/tex]
A fair coin is flipped 10 times. Each flip is independent.
What is the probability of getting exactly eight heads?
Answer:
8 out of 10.
Step-by-step explanation:
if you flip a coin independent then it doesn't matter what the other outcomes are. So if it's a one out of two chance every time then it's 8 /10.
A laptop computer originally priced at $1,700 now sells for $1,800. What is the percent of increase?%.The percent of increase is(Type an integer or decimal rounded to one decimal place as needed.)
EXPLANATION:
We are given the original price of a laptop computer at $1,700.
Now the price has been increased to $1,800.
Note that there is a $100 increase over the original price.
For us to calculate the percent increase we shall use the ratio of the increase over the original price and calculate as a percentage.
[tex]\begin{gathered} Original\text{ price}=1700 \\ Increase=100 \\ Percent=x \end{gathered}[/tex]We can now set up the following equation;
[tex]\frac{100}{1700}=\frac{x}{100}[/tex]We now cross multiply;
[tex]\frac{100\times100}{1700}=x[/tex][tex]\frac{10000}{1700}=x[/tex][tex]x=5.8823...[/tex]Rounded to one decimal place, the percent increase is;
ANSWER:
[tex]Increase=5.9\%[/tex]Assuming a direct proportion between the distance and time, how far would they travel in 5 hours?
A family taking a road trip vacation travels 126 miles in 3 hours.
We can calculate the constant of proportionality as:
[tex]\frac{126\text{ miles}}{3\text{ hours}}=42\text{ miles/hour}[/tex]Then, in 5 hours they would travel:
[tex]d=5\text{ hours}\cdot\frac{42\text{ miles}}{1\text{ hour}}=210\text{ miles}[/tex]In 5 hours they would travel 210 miles.
What is the equation to this graph? pls help
Answer is y=1/2x+2 because the slope is 1/2 and the starting point is +2
There is a negative correlation between the number of years in college and earnings.
Please select the best answer from the choices provided
Or T
F
Answer:
F (false)
Step-by-step explanation:
i hope this helps! Have a good day! c:
A bag contains:• 3 red marbles• 2 2 orange marbles• 1 yellow marble• 4 green marblesA marble is drawn from the bag and replaced 150times. How many times can you predict that a greenmarble or yellow marble will be drawn?
The probability of getting a green of a yellow marble can be determined like this:
Probability = (yellow marbles + green marbles) / total number of marbles
Probability = (1 + 4) / 10
Probability = 5 / 10
Probability = 1/2
By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:
Number of predictions = 150 × 1/2
Number of predictions = 75
Then, the answer is 75 times
Answer:
75 times.
Step-by-step explanation:
There are a total of 10 marbles in the bag.
Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.
In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.
Probability a yellow marble is drawn (in 1 draw) = 1/10.
In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.
So, the number of times for a green or yellow marble
= 60+15= 75.
Jenna bought a new car for $29,000. She paid a 10% down payment and financed
the remaining balance for 48 months with an APR of 4.5%. Determine the monthly
payment that Jenna pays.
If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.
How to find the monthly payment?Using this formula to determine the monthly payment
P = A ×r × ( 1 +r)^n ÷( 1+ r)^n -1
Where:
P = Principal = ?
A = Amount = $29,000 × ( 1- .10) = 26,100
r = Interest rate = 4.5% / 12 = 0.00375
n = number of months = 48 months
Let plug in the formula
P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1
P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 1.196814377 -1
P = 26,100 × 0.00375 × 1.196814377 ÷ 0.196814377
P = $117.1382456 ÷ 0.196814377
P = $595.17
Therefore $595.17 is the monthly payment.
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1 billion, 1 million compare and give the factor
Answer:
1000000
Step-by-step explanation:
100000000: 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5
100000: 2 2 2 2 2 5 5 5 5 5
GCF: 2 2 2 2 2 5 5 5 5 5
The Greates Common Factor (GCF) is: 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 = 100000
an airplane, flying horizontally at 200 mph at an altitude of 3 miles, passes over a radar station. what is the rate of change of the angle of elevation between the radar station and the plane 3 minutes after the plane passes over the radar station? (the angle of elevation is the angle between the horizontal and a line between the radar station and the airplane.)
The rate of change of angle of elevation between the radar station and airplane is
[tex]\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]
The airplane is flying at the speed of 200 mph
The airplane is at an altitude of 3 miles over the radar station
The distance travelled by the airplane after 3 mins
distance = speed x time
= 200 mi/hr x 3 min
Since the speed is hour let us convert it to mins
= 200 x 3 x 1/60
= 600 / 60
= 10 miles
So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles
Then the elevation angle of the between radar station and airplane can be find by
tan θ = O / A
where O is the opposite side to the angle of elevation
A is the adjacent side to the angle of elevation.
But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time
[tex]\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}[/tex]
[tex]\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}[/tex]
[tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}[/tex]
The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.
[tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}[/tex]
We had found the value of sec²θ = (hyp/adj)²
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}[/tex]
Now , let us convert in terms of rad/min
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)[/tex]
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]
Therefore , the rate of change of angle of elevation is -10/109 (rad/min)
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23 - x < 23(1 + 7x)
What does x equal???
[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]
without given any restriction x is all the numbers greater than 0.
NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
Simplify the expression, 2√54x8 - 4√24x8
Answer:
[tex]-2\sqrt{} 6x^{8}[/tex]
Step-by-step explanation:
the population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. assume the variable is normally distributed. (a) find the probability the cholesterol content for a single egg is between 210 and 220. (b) find the probability the average cholesterol content for 25 eggs is between 210 and 220. (c) find the third quartile for the average cholesterol content for 25 eggs. (d) if we are told the average for 25 eggs is less than 220 mg, what is the probability the average is less than 210 mg?
Using the normal distribution, the probabilities are given as follows:
a) Between 210 and 220 for a single egg: 0.2586 = 25.86%.
b) Between 210 and 220 for the average of 25 eggs: 0.8164 = 81.64%.
c) Third quartile for the average of 25 eggs: 213 milligrams.
d) Less than 220 if less than 210: 0.1011 = 10.11%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for the cholesterol levels are given as follows:
[tex]\mu = 215, \sigma = 15[/tex]
For item a, the probability is the p-value of Z when X = 220 subtracted by the p-value of Z when X = 210, hence:
X = 220:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (220 - 215)/15
Z = 0.33
Z = 0.33 has a p-value of 0.6293.
X = 210:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (210- 215)/15
Z = -0.33
Z = -0.33 has a p-value of 0.3707.
Hence the probability is:
0.6293 - 0.3707 = 0.2586.
For item b, we are dealing with a sample of 25, hence we apply the Central Limit Theorem as follows:
n = 25, s = 15/sqrt(25) = 3.
X = 220:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (220 - 215)/3
Z = 1.33
Z = 1.33 has a p-value of 0.9082.
X = 210:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (210 - 215)/15
Z = -1.33
Z = -1.33 has a p-value of 0.0918.
Then the probability is:
0.9082 - 0.0918 = 0.8164 = 81.64%.
The third quartile is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 215)/3
X - 215 = -0.675 x 3
X = 213.
The conditional probability in item d is calculated as follows:
P(X < 210)/P(X < 220) = 0.0918/0.9082 = 0.1011 = 10.11%.
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-5/2 can be simplified?
If it can be simplified, would the answer be a fraction or a decimal?
Answer: -2 1/2 or -2.5
Step-by-step explanation:
Yes, it can be simplified.
-5/2 can be simplified to -2 1/2 which can be as a decimal as -2.5