Answer:
$192
Step-by-step explanation:
The cost function is given as:
C(x)=18x+240
The price function is given as:
p(x)= 90 - 3x
The revenue R(x) is the product of the price and the number of products. It is given by:
R(x) = xp(x) = x(90 - 3x) = 90x - 3x²
The profit P(x) is the difference between the revenue and the cost of production. Therefore:
P(x) = R(x) - C(x) = 90x - 3x² - (18x + 240) = 90x - 3x² - 18x - 240
P(x) = -3x² + 72x - 240
The standard equation of a quadratic equation is ax² + bx + c. The function has a maximum value at x = -b/2a
Since P(x) = -3x² + 72x - 240, the maximum profit is at:
x = -72/2(-3) = 12
at x = 12, the profit is:
P(12) = -3(12)² + 72(12) - 240 = -432 + 864 - 240 = $192
The table below shows the students in an Algebra 1 class. What is the probability that a randomly chosen student will be a girl? (Note: If your fraction will reduce, you need to reduce it.)
Someone plz Help its due now!!! In a histogram, if I have 0-2 does this count everything up to 2, or does this count 2?
Answer:
everything
Step-by-step explanation:
because in statistics we represent data in classes and you can't have a class of one number since the histogram a class has to have limits hope it helps
What is the real interest rate if the nominal interest rate is 1 when the rate of inflation is 2
Answer:
Real interest rate = -1%
Step-by-step explanation:
Real interest rate=Nominal interest rate - inflation rate
From the above,
Nominal interest rate=1%
Inflation rate=2%
Real interest rate=Nominal interest rate - inflation rate
=1% - 2%
= -1%
Real interest rate = -1%
Real interest rate shows you what it really costs borrowers to pay back their loans.
if the real interest rate is greater than zero, the amount you pay back is worth more in real terms than the money you borrowed.
if the real interest rate is below zero as in the above case, the amount you will pay back is less worth in real terms than the money you borrowed.
Determine whether the data set is a population or a sample. Explain your reasoning. The temperature in four state capitals out of 50 Choose the correct answer below. A. Population, because it is a collection of temperatures for all of the state nbspcapitals. B. Sample, because it is a collection of temperatures for all of the state nbspcapitals comma but there are other countries. C. Sample, because the collection of temperatures for four state capitals is a subset of all state capitals. D. Population, because it is a subset of all state capitals.
Answer:
The correct answer is C. Sample, because the collection of temperatures for four state capitals is a subset of all state capitals.
Step-by-step explanation:
we cannot fully understand this answer without first defining the parameters that are involved in the questions, the two key terms are; Population or sample.
Population: a population contains all the set of data which is in consideration and
Sample: Sample is the range of values in an experiment.
The main difference between a population :A population basically includes all the elements from a set of data while a sample only consists of one or more observations drawn from the population.
we can say safely that a sample is a subset of a population.
Since we it have been stated that the temperatures of from four states capitals out of 50 states then our explanation supports our answer.
Identify the true statement about a curvilinear relationship. Multiple Choice The variables vary independently of one another. The relationship results in a flat line when graphed. The relationship is sometimes referred to as a monotonic function. The direction of the relationship changes at least once.
Answer:
The direction of relationship changes at least once.
Step-by-step explanation:
Curvilinear relationship is a relationship between two variables where if one variable increases the other variable also increases but up to certain point after which one variable increases and other decreases. This type of relationship is referred as non monotonic function.
Rearrange this formula Α= πr2 for the area of a circle to solve for r in-terms of A.
What is the new formula?
Answer:
sqrt( A / pi ) =r
Step-by-step explanation:
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
Answer: A/2pi = r
all you have to do is single out the r to get the new equation
I dont know how to solve this question using proportions:
212.7 = 16.8% of
Answer:
17,725/14.
Step-by-step explanation:
Let's say that the blank is represented by x.
Since the question asks what is 16.8% of x, we can set up a proportion where 16.8 out of 100 is equivalent to 212.7 out of x. The 100 represents the "whole" number, which corresponds to x. The 212.7 IS the 16.8 of x.
[tex]\frac{16.8}{100} =\frac{212.7}{x}[/tex]
16.8 * x = 212.7 * 100
16.8x = 21,270
x = 21,270 / 16.8
x = 212,700 / 168
x = 17,725 / 14 = 1,266.071429
To check our work, 1,266.071429 * 0.168 = 212.7.
Hope this helps!
in the circle, m∠S=33°, mRS=120, and RU is a tangent. the diagram is not drawn to scale. what is m∠U? Please help!
Answer:
27°
Step-by-step explanation:
arc RT = 66
1/2(120 - 66) = 27
Answer:
∠ U = 27°
Step-by-step explanation:
The inscribed angle S is half the measure of its intercepted arc, thus
arc RT = 2 × ∠ U = 2 × 33³ = 66°
The secant- tangent angle U is half the measure of the difference of the measures of the intercepted arcs, that is
∠ U = 0.5( RS - RT) = 0.5(120 - 66)° = 0.5 ×54° = 27°
PLEASE SHOW YOUR WORK!!! ASAP best answer gets brainliest
Answer:
weak positive
Step-by-step explanation:
it is positive because it is going up to the right and weak because no points are together
Paige launched a ball using a catapult she built. The height of the ball (in meters above the ground) ttt seconds after launch is modeled by h(t)=-5t^2+40th(t)=−5t 2 +40th, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 40, t Paige wants to know when the ball will hit the ground. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) How many seconds after launch does the ball hit the ground? seconds
Answer:
1) Factor form : [tex]h(t)=-5t(t-8)[/tex]
2) 8 second after launch.
Step-by-step explanation:
The height of the ball (in meters above the ground) t seconds after launch is modeled by
[tex]h(t)=-5t^2+40t[/tex]
To find the time when ball hit the ground, we need to find the factor form of the given function.
[tex]h(t)=-5t(t-8)[/tex]
When ball hi the ground, then height of the ball from the ground is 0.
[tex]h(t)=0[/tex]
[tex]-5t(t-8)=0[/tex]
Using zero product property, we get
[tex]-5t=0\Rightarrow t=0[/tex]
[tex]t-8=0\Rightarrow t=8[/tex]
Ball hit the ground at t=0 and t=8. It means ball hit the ground in starting and 8 second after launch.
Answer:
-5t(t - 8) and it hit 8 seconds after launch.
Find SP when CP=Rs.400 and proft%=4%
Answer:
[tex]\boxed{Selling\ Price = Rs.\ 424}[/tex]
Step-by-step explanation:
Cost Price = Rs. 400
Profit = 4 % of Cost Price
=> [tex]\frac{4}{100} * 600[/tex]
=> 4 * 6
=> Profit = Rs. 24
Now, Selling Price = Cost Price + Profit
Selling Price = 400+24
Selling Price = Rs. 424
Answer:
Selling price = ₹ 416
Step-by-step explanation:
Cost Price = ₹ 400
Profit% = 4 %
Profit = 4 % of cost price
= [tex]\frac{4}{100}*400\\\\[/tex]
= 4 * 4
= ₹ 16
Selling price = Cost price + profit
= 400 + 16
= ₹ 416
The measure of one base angle is an isosceles triangle is 20 degree. the measure of the largest angle in the triangle is
Answer:
140°
Step-by-step explanation:
Every triangles angles when combined equals 180°
In an isosceles triangle there are 2 acute angles and one obtuse angles.
It was given that the base angle/acute angle is 20°
This brings us to our equation. 20° + 20° + x = 180°
20 + 20 = 40
40 + x = 180
Now we solve algebraically:
180-40= 140
Therefore the answer is x = 140°
I hope this helps!
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year?
Answer: Pam's total salary is $41666.666
Step-by-step explanation:
Assume her total earning or salary per year = y
Personal expenses spent yearly = $7500
Personal expenses yearly ($7500) = 18% of y
100%y =
18% of y = 7500
(18/100)y = $7500
100% y = Total salary
0.18y = $7500 - - - - - - - (1)
1y = Total salary
(Total salary * 0.18y) = (7500 * y)
Total salary = 7500y / 0.18y
Total salary = 7500/0.18
Total salary = $41666.666
Please help ill rate 5 stars and give brainlyest
Answer:
Option C.
Step-by-step explanation:
It is given that, a menu at a local diner has
Appetizers = 12
Entrees = 8
Choice of desserts = 4
We need to find the different meal combinations which are possible if you select one appetizer, one entree and one dessert form the menu.
Total ways to select an Appetizers = 12
Total ways to select an entrees = 8
Total ways to select a desserts = 4
Now,
Total combinations for different meal [tex]=12\times 8\times 4=384[/tex]
Therefore, the correct option is C.
Answer:
see below
Step-by-step explanation:
the answer is c
A collection of 108 coins containing only quarters and nickels is worth $21. A table titled Coin Collection showing Number of Coins, Value, and Total. The first row shows Nickels, and has n, 0.05, and 0.05 n. The second row shows, Quarters, and has q, 0.25, and 0.25 q. The third row shows total, and has not entries. Which value could replace q on the chart? 21 108 21 – n 108 – n
Answer:
q = 108-n
Step-by-step explanation:
Given: 108 coins containing only quarters and nickels
q = 108-n
since total number of coins is 108, and n= number of nickels
If you want to know how many of each kind of coin, read on:
First solve the number of quarters and nickels.
If all 108 coins are quarters, the value is 108*0.25 = $27
Since this value exceed the actual by 27-21 = $6,
we replace a number of quarters by nickels.
Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.
So it will take 6/0.2 = 30 replacements.
Therefore there are 108-35 = 78 quarters and 30 nickels.
The solution is : q = 108-n, is the value could replace q on the chart.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Given:
108 coins containing only quarters and nickels
q = 108-n
since total number of coins is 108, and n= number of nickels
If you want to know how many of each kind of coin, read on:
First solve the number of quarters and nickels.
If all 108 coins are quarters, the value is 108*0.25 = $27
Since this value exceed the actual by 27-21 = $6,
we replace a number of quarters by nickels.
Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.
So it will take 6/0.2 = 30 replacements.
Therefore there are 108-35 = 78 quarters and 30 nickels.
The solution is : q = 108-n, is the value could replace q on the chart.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ7
A village P is 10km from a lorry station,Q on a bearing 065°.another village R is 8km from Q on a bearing 155°.calculate; a.the distance of R from P to the nearest kilometer and b.the bearing of R from P to the nearest degree.
Answer:
RP = 12.8 km
38 degrees
Step-by-step explanation:
RP = [tex]\sqrt{8^{2} + 10\\^{2} } \\[/tex]
RP = 12.8 km
angle = Inv sin = 8/12.8
angle 38.7°
Expand. Your answer should be a polynomial in standard form. 3x(x to the second power, -5x+6)
Answer:
3x³ - 15x² + 18x
Step-by-step explanation:
Given
3x(x² - 5x + 6) ← distribute the parenthesis by 3x
= 3x³ - 15x² + 18x ← in standard form
Can someone help fast please
Answer:
B
Step-by-step explanation:
Just reduce your x's and y's. The x^-1 cancels with the x^5, and the y^-9 and y^-3 get simplified. After some basic simplifying, you get answer B.
What is the solution to the system of equations?
2/3x - 1/3y = -2
-2x + y = -6
There is no solution.
There are infinitely many solutions.
There is only one solution, (2, –2).
There is only one solution, (–2, –10).
Answer:
There is no solution.
Rewrite -2x + y = -6 so it starts with y =...
y = 2x - 6
Substitute that in 2/3x - 1/3y = -2 gives:
2/3x - 1/3*(2x -6) = -2
2/3x - 2/3x + 2 = -2
0 + 2 = -2
This statement is not true, and that means there is no solution.
3. Show how √5 can be represented on the number line.
Answer:
Take a line segment AB = 2 units (consider 1 unit = 2 cm) on x-axis.
Draw a perpendicular on B and construct a line BC = 1 unit length.
Join AC which will be √5 (Pythagoras theorem). Take A as center, and AC as radius draw an which cuts the x-axis at point E.
The line segment AC represents √5 unit
How many natural 4-digit numbers exist in which all of the digits are even?
Answer:
256
Step-by-step explanation:
the first digit cannot be 0, so there are only 4 even numbers
For the second, third, and fourth digits, there are 5 available numbers.
Thus, the number of 4-digit numbers containing only even digits is 4 x 5 x 5 x 5 = 500
2nd place ( hundred place) can also be filled up by 4 number : 2, 4, 6, 8 and same logic applies to 3rd ( 10th ) and 4th( unit) .
so number of ways is 4*4*4*4= 256 ways .
Oscar says to Vanesa: "I am five times the age you were when I was the age you are; and when you are the age I am, our ages will add up to 72 years." How old is Vanessa? Please
Answer:
Vanessa is 60 and the other person is 12
Step-by-step explanation:
X + 5x = 72
6x = 72
x = 12
12 x 5 = 60
vanessa is 60
the other person is 12
60 + 12 = 72
Answer:
18
Step-by-step explanation:
Let's say x is Oscar's age, and y is Vanessa's age.
When Oscar was Vanessa's age, Vanessa was y−(x−y) = 2y−x years old. Oscar is five times older than this:
x = 5 (2y − x)
x = 10y − 5x
6x = 10y
3x = 5y
When Vanessa is Oscar's age, Oscar will be x+(x−y) = 2x−y years old. The sum of their ages will by 72.
2x−y + x = 72
3x − y = 72
Substituting:
5y − y = 72
4y = 72
y = 18
Vanessa is 18. Which means Oscar is 30.
Let's check our answer. When Oscar was 18, Vanessa was 6. Oscar is 5 times older than that (30). When Vanessa is 30, Oscar will be 42, and their ages will add up to 72.
Text: these two triangles are similar
Values from left to right: 10, 12, 9
What is the area of the shaded area
Answer:
26.25 cm²
Step-by-step explanation:
The area of the shaded part is the area of the shaded triangle subtract the area of the white triangle.
Since the triangles are similar then the ratios of corresponding sides are equal.
let the height of the white triangle be h, then
[tex]\frac{12}{9}[/tex] = [tex]\frac{10}{h}[/tex] ( cross- multiply )
12h = 90 ( divide both sides by 12 )
h = 7.5
shaded area = [tex]\frac{1}{2}[/tex] × 12 × 10 - [tex]\frac{1}{2}[/tex] × 9 × 7.5 = 60 - 33.75 = 26.25 cm²
PLEASE HELP ASAPPPP!!!
Solve the right triangle given that mA =30°, mC = 90° and a = 15. Then round your result to ONE decimal place
Answer:
m∠B = 60°
b = 26 units
c = 30 units
Step-by-step explanation:
In a right triangle ACB,
By applying Sine rule,
[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{SinC}{c}[/tex]
m∠A = 30°, m∠C = 90°
m∠A + m∠B + m∠C = 180°
30° + m∠B + 90° = 180°
m∠B = 180° - 120°
m∠B = 60°
Therefore, [tex]\frac{\text{Sin30}}{15}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]
[tex]\frac{1}{30}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]
[tex]\frac{1}{30} =\frac{1}{c}=\frac{\frac{\sqrt{3}}{2}}{b}[/tex]
[tex]\frac{1}{30}=\frac{1}{c}=\frac{\sqrt{3}}{2b}[/tex]
[tex]\frac{1}{30} =\frac{1}{c}[/tex] ⇒ c = 30 units
[tex]\frac{1}{30}=\frac{\sqrt{3}}{2b}[/tex]
b = 15√3
b = 25.98
b ≈ 26 units
11. John has a life insurance policy that will pay his family $32,000 per year if he dies. If interest rates are at 2.5% when the insurance company has to pay, what is the amount of the lump sum that the insurance company must put into a bank account?
Answer:
$1280000
Step-by-step explanation:
Given that :
John has a life insurance policy that will pay his family $32,000 per year if he dies
If interest rates are at 2.5% when the insurance company has to pay
The amount of the lump sum that the insurance company must out into a bank account can be determined by the division of the amount to be paid by the interest rate.
i.e
the amount of the lump sum = $32000/2.5%
the amount of the lump sum = $32000/0.025
the amount of the lump sum = $1280000
PLEASE help me...! I am really stuck on this question.
Answer:
D
Step-by-step explanation:
the domain of 3^x is (-∞,∞) and the range is (0,∞)
the domain of 3^x-5 is (-∞,∞) and the range is (-5,∞)
the domain doesn't change, the range (-5,∞)
Follow the steps to solve for the variable in this two step equation 5x-10=0
Answer:
x = 2
Step-by-step explanation:
5x = 10
x = 2
Answer:
x = 2
Step-by-step explanation:
5x-10=0
Add 10 to each side
5x-10+10=0+10
5x = 10
Divide by 5
5x/5 = 10/5
x = 2
A pair of dice is rolled. What is the probability that the sum is 9 or that the first number is a 2? Please show you're work!
Answer:
5/18
Step-by-step explanation:
There are 36 possible outcomes
There are 6 with a 2 as the first roll
There are 4 with a sum of 9
P( sum is 9 or that the first number is a 2)
= sum is 9 or that the first number is a 2/total
( 6+4) / 36
=10/36
=5/18
What is the 52nd term of -11,-2,7,16,25,34
Answer:
448
Step-by-step explanation:
Formula
tn = a + (n - 1)d
Givens
a = - 11
n = 52
d = 9
Solution
t52 = -11 + (51)*9
t52 = - 11 + 459
t52 = 448
3 3/8 divided by 9 =
Answer:
0.375
Hope this helps....
Have a nice day!!!!
Answer:
3/8
Step-by-step explanation:
Hey there!
[tex]\frac{3}{8} = \frac{3*8+3}{8} = \frac{24 + 3}{8} = \frac{27}{8}[/tex]
[tex]\frac{27}{8} = \frac{27 / 9}{8} = \frac{3}{8}[/tex]
= 3/8
Hope this helps :)