Answer:
The maximum revenue is $320,000
Step-by-step explanation:
To find the maximum of a function f, the procedure is as follows:
Find the first derivative of f.Equate the derivative to 0. Solve the resulting equation to get the critical points.Try all the critical points in the original function and select the one that maximizes it.The revenue function for a bicycle shop is
R(x)=xp(x), where p(x)=800-0.5x. Substituting:
[tex]R(x)=x(800-0.5x)=800x-0.5x^2[/tex]
Find the first derivative of R:
R'(x)=800-x
Equate to 0:
800-x=0
Solve:
x=800
There is only one critical point. Substitute it into the revenue function:
[tex]R(800)=800(800)-0.5(800)^2=320,000[/tex]
The maximum revenue is $320,000
A dad has three sons. He shares an amount of $30,000 among his three sons. One son deposited his amount in a bank that provides him interest at the rate of 7%. The second son deposited his sum in a mutual fund that gave him returns at a rate of 8%. The third son invested his in another bank that provided him an interest rate of 6%. The second sons share is 1000 more than that of the third son. The total interest that they got was $2110. Calculate each person's share if the first sons share is equal the second son and the third son put together.
Answer:
First son receives $15000
Second son receives $8000
Third son receives $7000.
Step-by-step explanation:
Let first son receive $x and deposit it at 7%
Second son receive $y and deposit in 8%
Third son receive $z and deposit in 6%
Now, let's set up equation using the given information.
The second son share is 1000 more than the third son.
So, we can set up equation as
y= 1000+z
First son share is equal the second son and the third son put together.
So, x=y+z
And we can set up equation for total 30000 as
x+y+z=30000
Plug in y as 1000+z and x as y+z
We get third equation as
y+z+1000+z+z=30000
Plug in again y as 1000+z
It gives,
1000+z+z+1000+z+z=30000
Combine like terms,
2000+4z=30000
Subtract both sides 2000
4z=28000
Divide both sides by 4
z=7000
Now, plug in z as 7000 into y=1000+z to get y =8000
Now, x =y+z plug in the y and z values
x= 8000+7000=15000
Let's check with interest,
15000(7%)+8000(8%)+7000(6%)=2110
1050+640+420= 2110
2110=2110.
Yes! The calculations are correct!
A family of five went out to dinner at HogTastic Pit BBQ. They all ordered the buffet and drink at $12.80 each. They left a 15% gratuity for the waitress on the after-tax bill. Based on a tax rate of 7.5%, they ended up paying a total of $ for dinner.
Answer:
$79.12
Step-by-step explanation:
Given the following :
Cost per order = $12.80
Number of people = 5
Gratuity left for waitress = 15%
Tax rate = 7.5%
Total bill before tax:
$12.80 * 5 = $64
Bill after tax:
$64 * (1 + 7.5%)
64 - 4.8
= $68.80
Final amount paid:
After tax bill + (after tax bill * Gratuity rate)
$68.80 + (68.80 * 15%)
= $79.12
SPEED QUESTION!!!
the first person that answers this and gives step by step explanation gets 50 points plus brainliest answer!
GOOD LUCK!!!
Answer:
x>13 (C)
Step-by-step explanation:
1) simplify -> 2x+7>33
2) subtract 7 from both sides -> 2x+7-7>33-7 = 2x>26
3) divide both sides by 2 -> 2x/2>26/2
x>13
If you were to multiply 3X25, you would have a product of 75.
Explain 2 ways you could rewrite 25 and using the distributive property still obtain a product of 75.
Include one example using addition and the other example using subtraction. For example, if I were to rewrite the integer 72, I could choose (70 + 2) or (80 – 8).
An example with addition is 3x(20+5) as 20 plus 5 is still 25, and an example with subtraction is 3x(30-5), as 30 minus 5 is 25.
Write the equation of a line the line that passes through (3, 9) and is parallel to the line y = 5x - 15.
Answer:
Y=5X-6
Step-by-step explanation:
Y=mx+b
m=5
when x=3 and y=9 b= -6
Which equation represents the unit fraction shown in the diagram? A grid model with 100 squares. 20 squares are shaded. StartFraction 20 Over 100 EndFraction = one-fifth StartFraction 20 Over 100 EndFraction = two-fifths StartFraction 20 Over 100 EndFraction = one-half StartFraction 20 Over 100 EndFraction = StartFraction 1 Over 10 EndFraction
Answer:
the anserw is c
Step-by-step explanation:
i took the test
Taylor multiplied 8.25 x 104 and 0.4 x 104 and got 8.65 x 104
Explain Taylor's mistake and give the correct answer. (1 pt. for the explanation and 1 pt. for the correct answer.)
Answer:
Taylor added. The correct answer is 3.3*10^8
Step-by-step explanation:
Taylor haven't consider the exponents properties and multiplication was also incorrect.
What are exponents?Exponent refers to how many times a number multiplied by itself.
Given:
8.25 x [tex]10^{4}[/tex] and 0.4 x [tex]10^{4}[/tex]
Now, multiplying by considering exponents as
a^m * a^n = a^( m+ n)
So,
=8.25 * 0.4 * [tex](10) ^{4+4}[/tex]
= 3.3 * [tex]10^8[/tex]
Hence, Taylor haven't consider the exponents properties and multiplication was also incorrect.
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A car rental service charges a one-time fee of $19.99 in addition to $0.29 per mile drive. If the final total for renting the car is $73.93, select which equation best represents the situation. Let m represent the number of miles driven.
*Answer Choices*
19.99m + 0.29m = 73.93
19.99m + 0.29m = 73.93
(19.99 + 0.29)m = 73.93m
19.99 + 0.29m = 73.93
Answer:
Your answer is: D) 19.99+0.29m=73.93
We are trying to find the miles driven so therefore 0.29$ is per mile. So we have to see how many 0.29$ along with 19.99$ can fully add up to 73.93$
Step-by-step explanation:
Hope this helped : )
A technician is launching an aerial firework from a tower. The height of the firework is measured in feet and the time is measured in seconds. A function that models the fireworks vertical distance with no respect to time,x, is f(x)=-16x^+96x+112 What information does this form of equation give about the firework
Answer:
The equation gives only the total vertical distance traveled by the firework or maximum height reached by the firework
Step-by-step explanation:
Given;
A function that models the fireworks vertical distance with no respect to time,x, as;
f(x)=-16x^+96x+112
The equation gives only the total vertical distance traveled by the firework, it does not account for the position of the firework at a particular time.
Thus, with the given function we can only estimate the maximum height reached by the firework.
Under very specific instructions, a jeweler made one ring for the queen and one ring for the princess. The gem on the queen's ring weighed 9/10 of a carat and the stone on the princess's ring weighed 7/10 of a carat. How much heavier was the stone on the queen's ring than the stone on the princess's?
Answer: 1/5
Step-by-step explanation:
From the question, we are informed that the gem on the queen's ring weighed 9/10 of a carat and the stone on the princess's ring weighed 7/10 of a carat.
To calculate how heavier the stone on the queen's ring was than the stone on the princess will be:
= 9/10 - 7/10
= 2/10
= 1/5
Solve this Proportion. If necessary round to the nearest hundredth:
5/a = 30/54
a. 7
b. 3.5
c. 5
d. 10
Answer:
I think with all the savings o will rather go with, a will I make some research
One gym has offers. Write out an equation to join and set it equal to your budget. Budget = 275, membership fees = 25 per month, flat discount = 75. How many months of a gym membership I can afford. its for 8th grade so dnt give a very complicated one thx
Answer:
8 months
Step-by-step explanation:
Given that,
Total budget = 275
Membership fee = 25 per month
Flat discount = 75
We need to find for how many months of gym membership I can afford. The equation will look like :
25x=275-75
25x=200
x = 8 months
Hence, he can afford gym membership for 8 months.
(02.01)
Solve 4(x + 1) = 4x + 4. (1 point)
Select one:
a. No solution
b. 0
c. All real numbers
d. 1
Answer:
the answer is Any Real Number
because 4(x + 1) = 4x + 4 for all value of x
Step-by-step explanation:
Ed training for a race. He ran 12.56 miles on one day, 12.98 miles the second day, and 13.04 miles on the third day.what is his combined distance for the first three days
Ed's combined distance for the first three days is 38.58 miles.
Given that, Ed ran 12.56 miles on one day, 12.98 miles the second day, and 13.04 miles on the third day.
What are decimal numbers?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.
The total distance can be determined as follows:
Total distance = 12.56+12.98+13.04
= 38.58 miles
Hence, Ed's combined distance for the first three days is 38.58 miles.
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Half the product of two numbers x and y minus five times a third number z
Answer: (X times Y) 1/2 - 5 ( Z/3 )
Step-by-step explanation:
Which ones are equivalent?
40/1000 and 40%
6/5 and 120%
50/33 and 117%
1/8 and 12.5%
1/3 and 30%
Answer:
1/8= 0.125
To have a percentage, multiply by 100
0.125 x 100 = 12.5%
Hope this helps ! : )
What number is 2/3 of 15
Step-by-step explanation:
2/3 of 15
2*5(3*5=15)
10
What is 3x+4=10 solve for x
Answer:
x=2
Step-by-step explanation:
3x+4=10
3x=6
x=2
Answer:
x=2
Step-by-step explanation:
3x+4=10
3x=6 by subtracting the 4
x=2 by dividing the 3
A student walks 2 km in 30 minutes. What is the student’s average speed in km/m?
Answer:
4km per hour
Step-by-step explanation:
Simplify -2√18
Would appreciate an explanation!
Answer:
-6√2
Step-by-step explanation:
Since the largest square root in 18 is 9 we can separate it out as shown:
√18 = √9√2
We can then solve this out to 3√2
Since we have a negative two on the outside, we would multiply it by 3 ( from the 3√2).
Work:
-2√18
-2√9√2
-2(3)√2
-6√2
Answer:
Step-by-step explanation:
Prime factorize 18
[tex]-2\sqrt{18}=-2*\sqrt{3*3*2}= -2*3\sqrt{2} \\\\ = -6\sqrt{2}[/tex]
College student makes decorative Styrofoam Lions and Husky's which she sells each year. Each one uses 8 oz of Styrofoam and takes 35 minutes to make. Each husky uses 12 oz of Styrofoam and takes 20 minutes to me. Furthermore, each line brings in a profit of $2.50 while each husky brings in a profit of $3. If she only has 3840 ounces of Styrofoam to work with and has 9650 minutes, how many of each animal should she make in order to maximize profits? What is the maximum profit possible?
Answer:
She should make 122 Styrofoam lions and 268 Styrofoam Husky's
The maximum profit, she makes is $1109
Step-by-step explanation:
The given information are;
The volume required to make each lion = 8 oz
The time it takes to make each lion = 35 minutes
The amount of profit each lion brings = $2.50
The volume required to make each Husky = 12 oz
The time it takes to make each Husky = 20 minutes
The amount of profit each Husky brings = $3
Let the number of lion Styrofoam cups she makes = x
Let the number of Husky Styrofoam cups she makes = y
Therefore, we have;
x × 35 + y × 20 = 9650..........(1)
x × 8 + y × 12 = 3840.............(2)
Dividing equation (2) by 8 and making x the subject, we get;
x × 8/8 + y × 12/8 = 3840/8
x + 4/3·y = 480
x = 480 - 4/3·y
Substituting the value of x in equation (1) gives;
(480 - 4/3·y) × 35 + y × 20 = 9650
16800 - 80/3·y = 9650
y = 268.125
x = 480 - 4/3·y = 480 - 4/3×268.125 = 122.5
Therefore, she can make 122 Styrofoam lions and 268 Styrofoam Husky's
The maximum profit, she makes is therefore given by the following equation;
The maximum profit = 122 × 2.5 + 268 × 3 = $1109.
The number of users of social media has increased significantly since the year 2001. In fact, the approximate number of users has tripled each year. It was reported that in 2005 there were 3 million users of social media.
a. Assuming that the number of users continues to triple each year, for the next three years, determine the number of users in 2006, 2007, and 2008.
How many users were there in 2006?
Answer:
9 million
Step-by-step explanation:
3 million × 3 = 9 millionI hope this helps!
The number of users in 2006, 2007, and 2008 will be 9 million, 27 million, and 51 million respectively.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the approximate number of users has tripled each year and in 2005 there were 3 million users of social media.
The number of users in 2006 = 3 × number of users in 2005]
The number of users in 2006 = 3 × 3 million
The number of users in 2006 = 9 million
The number of users in 2007 = 3 × number of users in 2006
The number of users in 2007 = 3 × 9 million
The number of users in 2007 = 27 million
Thus, the number of users in 2006, 2007, and 2008 will be 9 million, 27 million, and 51 million respectively.
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pls help!!!!!!!!!!!!!!
Why is graphite soft
Answer:
because it has a weak inter molecular forces between its layers
Answer:
Its compound
Step-by-step explanation:
How many kg in 12980 g ?
Help?
Answer:
12.98
Step-by-step explanation:
Which of this following is an expression
Answer:
Step-by-step explanation:
expressions dont have an equal sign but they have either a plus, minus, multiplying or dividing sign
which expression is equivalent to 2(n-1)-2s(-2n-3)
A) 4sn+6s +2n-2
B)-n-3-4sn+3s
C)2+[tex]s_7[/tex] ×n+6n
D)2+8n+6sn
(01.02 LC)Simplify 5 − (−1).
Answer:
Your answer is: 6
Simplify the expression.
6
Step-by-step explanation:
Hope this helped : )
Answer:
6
Step-by-step explanation:
5- (-1), the negative signs will be positive signs, 5 + 1, so we'll get 6.
11=3−4/3x solve for x
11 = 3 - 4/3x
11 = (9 - 4x)/3
33 = 9 - 4x
24 = -4x
24/4 = - x
x = -6