Answer:
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
Step-by-step explanation:
Given
[tex]Rooms = 240[/tex]
[tex]Price= \$40[/tex]
[tex]Increment = \$2[/tex]
First, we calculate the revenue.
[tex]Revenue (r) = Price (p) * Number\ of\ Rooms(n)[/tex]
[tex]r = p*n[/tex]
Let x be the change in rate.
i.e.
For every 2x increment in price (p) i.e. p + 2x
There will be 4 fewer rooms (n) i.e. n - 4x
So, the revenue is updated as:
[tex]r = (p + 2x) * (n - 4x)[/tex]
[tex]Price = 40[/tex]
So:
[tex]r = (40 + 2x) * (n - 4x)[/tex]
[tex]Rooms = 240[/tex]
So:
[tex]r = (40 + 2x) * (240 - 4x)[/tex]
Expand
[tex]r = 40 * 240 - 40 * 4x + 2x * 240 - 2x*4x[/tex]
[tex]r = 9600 - 160x + 480x - 8x^2[/tex]
Reorder
[tex]r = -8x^2 - 160x + 480x + 9600[/tex]
[tex]r = -8x^2 +320x + 9600[/tex]
The maximum of a function is calculated as:
[tex]Max = -\frac{b}{2a}[/tex]
In: [tex]r = -8x^2 +320x + 9600[/tex]
[tex]a = -8[/tex] [tex]b = 320[/tex] [tex]c = 9600[/tex]
So:
[tex]Max = -\frac{b}{2a}[/tex]
[tex]Max = -\frac{320}{-8}[/tex]
[tex]Max = \frac{320}{8}[/tex]
[tex]Max = 40[/tex]
To get the maximum revenue;
Substitute 40 for x in [tex]r = -8x^2 +320x + 9600[/tex]
[tex]r = -8(40)^2 + 320 * 40 + 9600[/tex]
[tex]r = 9600[/tex]
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
fill in the blank:
5/7 of ... is 1/7
Answer: 1/3
5/7 x X=1/7 35x= 7
X=7/35 simplified version 1/3
(HELP ME )Jolie played dodgeball in PE. In one game, Jolie threw a total of 75 balls at her
opponents in one day of dodgeball. She hit 30 of her opponents. What percent of her
targets did she hit?
Answer:
40%
Step-by-step explanation:
A percent is;
[tex]\frac{part}{whole} = \frac{x}{100}[/tex]
It is given that Jolie the 75 dodgeballs in total, hence the whole is 75. It is also given that 30 of the dodgeballs hit the target, so the part is 30. Now all one has to do is solve for "x".
[tex]\frac{30}{75} = \frac{x}{100}[/tex]
Simplify [tex]\frac{30}{75}[/tex] by dividing the numerator and denominator by 15.
[tex]\frac{2}{5}[/tex]
Now the equation is;
[tex]\frac{2}{5}=\frac{x}{100}[/tex]
Typically, one would solve a proportion by doing cross products, but in this case, it is easier to think about it intuitively. Since 5 is a factor of 100 (5 * 20 = 100), then all one has to do is multiply [tex]\frac{2}{5}[/tex] by 20 to get the answer (on the numerator).
x = 40
Answer:
40%
Step-by-step explanation:
30/75 = 0.40
0.40*100 = 40
75 * 40% = 30
Addison has 124,234,281,284 cartons of milk, she dropped like 456,789,098,345,678,987,654,568 of them, how many did bruh bruh bruh 21 haha lebron james
Answer:
Lebron James = bruh bruh bruh
Step-by-step explanation:
Answer:
Lol free points
Step-by-step explanation:
I need help finding the slope, identifying the initial value and writing An equation for a linear function and finding the X answer Y intercept PLEASE HELP PLEASE
Answer/Step-by-step explanation:
✔️Slope (m) using the two points (2, 4.58) and (5, 4.28):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4.28 - 4.58}{5 - 2} = \frac{-0.3}{3} = -0.1 [/tex]
Slope (m) = -0.1
✔️Initial Value = y-intercept = b
To find b, substitute x = 2, y = 4.58, and m = -0.1 into y = mx + b.
(Note: y is P(t) and x is t).
Thus:
4.58 = (-0.1)(2) + b
4.58 = -0.2 + b
Add 0.2 to both sides
4.58 + 0.2 = b
4.78 = b
b = 4.78
Initial value = 4.78
✔️Equation for the linear function:
Substitute b = 4.78, and m = -0.1 into P(t) = mt + b
Thus the equation would be:
P(t) = -0.1t + 4.78
✔️The y-intercept = initial value = 4.78
✔️The x-intercept = the value of t when P(t) = 0.
To get this, substitute P(t) = 0 into P(t) = -0.1t + 4.78.
Thus:
0 = -0.1t + 4.78
Add 0.1t to each side
0.1t = 4.78
Divide both sides by 0.1
t = 47.8
x-intercept = 47.8
3(x + 1) + 2(x + 5)
Whats the answer to this
Let's simplify step-by-step.
3(x+1)+2(x+5)
Distribute:
=(3)(x)+(3)(1)+(2)(x)+(2)(5)
=3x+3+2x+10
Combine Like Terms:
=3x+3+2x+10
=(3x+2x)+(3+10)
=5x+13
PLEASE HELPPPPPPP
Arun ran without stopping, which is closest to the benchmark fraction ___. On Tuesday, he ran 7/15 without stopping, which is the closest benchmark fraction ___. Arun ran about ____ mile(s) over the two days.
A. 1/2, 1/2, 1
B 1/4, 1/2, 3/4
C. 0/4,3/4,3/4
Answer:
Option C is correct answer
Can you Simplify
5a - a
Answer:
4a is the answer.
Step-by-step explanation:
5a - a
= 4a
Answer:
It is 4a.
Step-by-step explanation:
=5a-a
=4a
Hope it helps you..
10 (1/2x+2)-5=3(x-6)+1
Answer:
x = -16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
10(1/2x + 2) - 5 = 3(x - 6) + 1
Step 2: Solve for x
Distribute: 5x + 20 - 5 = 3x - 18 + 1Combine like terms: 5x + 15 = 3x - 17Subtract 3x on both sides: 2x + 15 = -17Subtract 15 on both sides: 2x = -32Divide 2 on both sides: x = -16Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 10(1/2(-16) + 2) - 5 = 3(-16 - 6) + 1Multiply: 10(-8 + 2) - 5 = 3(-16 - 6) + 1Add/Subtract: 10(-6) - 5 = 3(-22) + 1Multiply: -60 - 5 = -66 + 1Subtract/Add: -65 = -65Here we see that -65 does indeed equal -65.
∴ x = -16 is the solution of the equation.
The GCF of 15 and 27 is _____. Numerical Answers Expected! Answer for Blank 1:
Answer:
the answer is 3 i just did the test and btw i like your profile pick anyways not the point just know the answer is 3
Step-by-step explanation:
passes through (6. -6), slope = 5
Answer:
well you need to rise/run. so rise 5 and over 1 to find your answer. repeat the process if needed
Step-by-step explanation:
Given
n, find the value of x.
I think the answer is 109 but I’m not sure
Answer:
x=35 hope it helps see ☜☆☞
Shannon's rectangle countertop is 3 feet wide.it is 3 times as long as it is wide.Find the length and the area of Shannon’s countertop.
AnswerArea: 27 square feet Length: 9 Feet
Step-by-step explanation:
So, first we need to find the length.
If the length is 3 times the width, we need to multiply the width times 3 to get the lenght. So, 3*#=9/ So the lenght is 9
Now, we need to find the area.>
We need to multiply length times width, so-
9*3=27
Write
3√2 +6
√2-1
in the form a +b√√2, where a and b are integers.
Step-by-step explanation:
Solution
3(√2+2)
Alternative Form
≈ 10.24264
Please help me out!
Brainiest will be given to the most accurate answer
Answer:
g(x) = -3x
Step-by-step explanation:
g(x)=3x reflected about x - axis is g(x) = -3x. It's kind of hard to explain but that's the right answer i'm pretty sure
Find the missing number so that the equation has infinitely many solutions.
3(-x + 3) = -3x +?
Answer: 9
Step-by-step explanation: First, solve the left side. Using the distributive property, the left side would be -3x + 9. The right side is the same, but missing the 9. Adding the 9 will make the value of x not matter (essentially infinite solutions).
Starting at 300 feet away, a car drives towards you. IT then passes you by at a constant speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds is given by the equation d=|300-48t|. AT what times is the car 60 feet from you?
The car is 60 feet away from you after___seconds and after _____ seconds.
Explain what 48t represents in the given equation.
The car is at 60ft from you 5 seconds after it starts moving and 7.5 seconds after it starts moving.
The 48*t part means the number of feet that the car moves in t seconds
At what times is the car at 60ft from you?We know that the absolute value equation that models the distance is:
d(t) = |300 - 48*t|
Then what we need to solve is d(t) = 60, this is:
d(t) = 60 = |300 - 48*t|
That absolute value equation can be represented in two forms:
300 - 48*t = 60
300 - 48*t = -60
Solving these two we get the two times at which the car is at 60ft from you.
-48*t = 60 - 300
t = (60 - 300)/(-48) = 5
t = (-60 - 300)/(-48) = 7.5
So the car is at 60ft from you 5 seconds after it starts moving and 7.5 seconds after it starts moving.
The 48*t part means the number of feet that the car moves in t seconds.
If you want to learn more about absolute value equations:
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Put a ring around the number with the largest value. 113 0.3030 0.0330 3 10 33%
Answer:
Step-by-step explanation: big aye
solve by the matrix method , x+y/5 -1=y-x
10x - 4y = 5 (if it requires shorten)
Step-by-step explanation:
x + y/5 - 1 = y - x
<=> (5x + y - 1.5)/5 = 5(y - x)/5
<=> 5x + y - 5 = 5y - 5x
<=> 5x + 5x + y - 5y = 5
<=> 10x - 4y = 5
Can someone help with this please?
Answer:
<4 = 81
Step-by-step explanation:
we know that all the interior angles of a triangle will equal 180
so <1 + <2 + <3 = 180
we know that <4 is the exterior angle to <3
the exterior angle is equal to the angles opposite to its interior
<3 is the interior angle to <4
<1 and <2 are the angles opposite to <3
so <4 = <1 + <2
<4 = 42 + 39
<4 = 81
I need help plss
Hola
Subtract
3-9 = ???????
Answer:
-6
Step-by-step explanation:
come on
3 ( k - 5 ) = - 16.
Answer:
k = -1/3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(k−5)=−16
(3)(k)+(3)(−5)=−16(Distribute)
3k+−15=−16
3k−15=−16
Step 2: Add 15 to both sides.
3k−15+15=−16+15
3k=−1
Step 3: Divide both sides by 3.
3k /3 = −1 /3
k = −1 /3
As labor costs, an electrician charges
$36.50 per hour for himself, and $27.50
for his assistant. What would be the
total labor cost for a job taking 6 1/2 hours?
giving brainliest
Answer:
h=416$
Step-by-step explanation:
36.50h+27.50h= 64
64x6 1/2=
416 $
Answer:
416
Step-by-step explanation:
36.50+27.50=64
64*6=384
and then add 32 for the half an hour
384+32=416
Find the value of x by filling the blanks in the provided statement-reason solutions
Answer:
no picture?
Step-by-step explanation:
Find the distance between 6 and -2 on a number line
Answer:
8
Step-by-step explanation:
The distance between 6 and -2 is 8
(draw a number line and from 6 to -2 is 8 steps)
Consider the circle centered at the origin and passing through the point (-8,0) give the equation of the circle
Answer:
Step-by-step explanation:
The equation of circle that passes through origin is given by
And the given circle passes through (-8,0).
Substituting -8 for x and 0 for y, we will get
Order from least to greatest
11. 357
2. 1.02
13. .80
4. .002
15. .05
16. .40
Answer:
0.002 , 0.05 , 0.40 , 0.80 , 1.02 , 2 , 4 , 11 , 13 , 15 , 16 , 357
Step-by-step explanation:
11 , 357 , 2 , 1.02 , 13 , .80 , 4, .002 , 15 , .05 , 16 , .40
Jim wants to save money to open a tutoring center. He buys an annuity with a quarterly payment of 56$ that pays 3.7 interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 9 years.
Answer:
$78.01
Step-by-step explanation:
solve the equation 56(1+.037÷4)^4×9
ends up being 56(1.00925)^36
56(1.3930133899)
=78.0087
The total value of the annuity in 9 years is: $78.00
We have the following information available from the question is:
He buys an annuity with a quarterly payment of $56 that pays 3.7 interest, compounded quarterly.
Payments will be made at the end of each quarter.
We have to find the total value of the annuity in 9 years.
Now, According to the question:
The total value of the annuity in 9 years :
The equation will be :
[tex]= > 56(1+ \frac{3.7}{4} )^4^(^9^)[/tex]
=>56(1.3930)
=$78.00
Learn more about Compound interest at:
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Triangle MRN is created when an equilateral triangle is folded in half. What is the value of x?
A. 2√3 units
B. 4 units
C. 4√3 units
D. 8 units
Answer:
C. 4√3 units
Step-by-step explanation:
Edge 2021
The value of x is 4.
Option B is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
From ΔRMN,
NM² = RN² + RM²
8² = y² + x²
64 = y² + x² ______(1)
And,
From ΔRNS,
RN² = RS² + SN²
y² = z² + 6²
y² = z² + 36 ______(2)
And,
From ΔRMS,
x² = z² + 2²
x² = z² + 4 _______(3)
From (1), (2), and (3).
x² = y² - 36 + 4
x² = 64 - x² - 36 + 4
2x² = 64 - 36 + 4
2x² = 68 - 36
2x² = 32
x² = 16
x = 4
Thus,
The value of x is 4.
Learn more about the Pythagorean theorem here:
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GIVING OUT BRAINLIEST!!! PLS HELP ASSAPPP!!!!
Which statement is correct when solving the expression 5y^2-3y^2?
Add the coefficients (5 + 3).
Subtract the exponents (2 – 2).
Add the exponents (2 + 2).
Subtract the coefficients (5 – 3).
Answer:
C. Add the exponents (2+2)
D. Subtract the coefficients. (5-3)
2y^4
I hope this helped! :))