Answer:
x = -4/3
Step-by-step explanation:
8^(x+3)=32
2^3 = 8
2^5 = 32
3( x + 3 ) = 5
3x + 9 = 5
3x = -4
x = -4/3
Tell me if I am wrong.
Can I get brainliest
Answer: x= -1 1/3 as a mixed number
Step-by-step explanation:
graph the function
h(x)= 6(4/3)^x
Graph of the function h(x)= 6(4/3)ˣ will be a positive exponential.
What is an exponential function?A mathematical function with the formula f (x) = eˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, which equates to about, is the exponential-function basis that is most frequently encountered.
One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function.
The exponential function increases quickly, as shown in the graph of f above. The simplest kinds of dynamical systems have solutions in the form of exponential functions. For instance, straightforward models of bacterial development produce an exponential function.
Growth or decay can both be described by an exponential function. The function h(x)= 6(4/3)ˣ
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One package of blueberries costs $3.
How many packages of blueberries can
you buy with $12?
Answer:
4
Step-by-step explanation:
Because 3×4=12
Answer:
4
Step-by-step explanation:
Simply divide 12 dollars into 3 dollars and you should get 4 :D
what is the value of x for the equation x+2/4 + 1/3 = 2x-1/6
Answer:
1
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x+24+13=2x−16
x+ 1 2 + 1 3 =2x+ −1 6
(x)+( 1 2 + 1 3 )=2x+ −1 6 (Combine Like Terms)
x+ 5 6 =2x+ −1 6
x+ 5 6 =2x+ −1 6
Step 2: Subtract 2x from both sides.
x+ 5 6 −2x=2x+ −1 6 −2x
−x+ 5 6 = −1 6
Step 3: Subtract 5/6 from both sides.
−x+ 5 6 − 5 6 = −1 6 − 5 6
−x=−1
Step 4: Divide both sides by -1.
−x −1 = −1 −1
x=1
Answer:
The answer to your question is x = 1
Step-by-step explanation:
Data
Equation x + 2/4 + 1/3 = 2x - 1/6
-Subtract 2x in both sides x + 2/4 + 1/3 -2x = 2x - 2x -1/6
-Simplify - x + 2/4 + 1/3 = -1/6
-Subtract 2/4 and 1/3 in both sides -x + 2/4 - 2/4 + 1/3 - 1/3 = -1/6 - 2/4 - 1/3
-Simplify -x = -1/6 - 2/4 - 1/3
-x = (-2 - 6 - 4)/12
-x = -12/12
-x = -1
-Result x = 1
In a deck of cards, what's the probability of selecting a Red Card and then selecting a Face Card, WITH replacement?
Question 3 options:
A. 3/26
B. 5/26
C. 1/2
D. 1/5
a salesman makes $35,000 per year plus $400 for each large appliance he sells. write and solve an equation to determine how many large appliances he sold if he made $57,400 this year.
Answer:
The salesman sold 56 large appliances.
Step-by-step explanation:
$57,400 - $35,000 = $22,400
He made $22,400 off the appliances.
To find how many appliances, you can divide 22,400 by 400.
The equation should be ($57,400 - $35,000)/400 = x
Here x represents the amount of large appliances sold. If you run the equation, the answer you should get is 56.
The salesperson vended 56 large appliances this time. The equation used to break this problem is
35,000$ 400x = $ 57,400, with' x' representing the number of appliances vended.
To determine how numerous large appliances the salesman vended, we can set up an equation grounded on the given information. Let's denote the number of large appliances he vended as x. The total earnings from these deals would be$ 400 times x. His periodic payment is$ 35,000, so the total quantum he made in the time, including his payment and the earnings from deals, is$ 57,400. thus, the equation to represent this situation is
$ 35,000$ 400x = $ 57,400
To break for x, we abate$ 35,000 from both sides
$ 400x = $ 57,400-$ 35,000
$ 400x = $ 22,400
Now, we divide both sides by$ 400 to find the number of appliances
x = $ 22,400/$ 400
x = 56
The salesperson vended 56 large appliances.
Check Plagiarism Check Grammar
Which fraction is closest to 1 1/2?
Answer:
7/13
Step-by-step explanation:
To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2. Since 1/26 is closest to zero, 7/13 is closest to 1/2.
Answer:
4/2
THATS ITTT
select the interval where h(x)<0
A. -3.5
B. -2
C. 2.5
Answer:
-2 < x < -1
Step-by-step explanation:
Karinas science test scores for this quarter are 84,86,90 and 68. What score does she need on her fifth science test to get a test average of at least 84
Answer:
Karina must score atleast 92 on the fifth test to get a average of atleast 84.
Step-by-step explanation:
We are given the following in the question:
84, 86, 90, 68
We want the average score to be atleast 84.
Let x be the score on fifth test.
Formula:
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
Thus, we can write the equation:
[tex]\dfrac{84+86+90+68+x}{5}\geq 84\\\\\Rightarrow 84+86+90+68+x \geq 420\\\Rightarrow 328+x \geq 420\\\Rightarrow x \geq 92[/tex]
Thus, Karina must score atleast 92 on the fifth test to get a average of atleast 84.
Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $160 in interest after two years. How much money should he deposit?
Answer: he should deposit $5000
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount of money deposited.
P represents the principal or amount of money deposited.
R represents interest rate on the deposit.
T represents the duration of the deposit in years.
From the information given,
I = $160
R = 1.6%
T = 2 years
Therefore,
160 = (P × 1.6 × 2)/100
160 = 0.032P
P = 160/0.032
P = $5000
Suppose that 200 flies are ee, 150 flies are ee, and 150 flies are ee. calculate the frequencies of the 3 genotypes for this population. do not leave your answers as fractions!
Complete Question
Imagine a large Source [tex](S_o)[/tex] population of 500 files at a particular time we will call [tex]T_s[/tex].The files have brown ebony bodies. Suppose that 200 flies are ee, 150 flies are Ee, and 150 flies are EE. calculate the frequencies of the 3 genotypes for this population. do not leave your answers as fractions!
Answer:
The frequency of genotype ee is [tex]f_{ee}= 0.4[/tex]
The frequency of genotype Ee is [tex]f_{Ee} = 0.3[/tex]
The frequency of genotype EE is [tex]f_{EE} = 0.3[/tex]
Step-by-step explanation:
From the question we are told that
The number of files with genotype ee is [tex]ee = 200[/tex]
The number of files with genotype Ee is [tex]Ee = 150[/tex]
The number of files with genotype [tex]EE[/tex] is [tex]EE = 150[/tex]
The frequency of genotype ee is mathematically evaluated as
[tex]f_{ee} = \frac{200}{500}[/tex]
[tex]f_{ee}= 0.4[/tex]
The frequency of genotype Ee is mathematically evaluated as
[tex]f_{Ee} = \frac{150}{500}[/tex]
[tex]f_{Ee} = 0.3[/tex]
The frequency of genotype EE is mathematically evaluated as
[tex]f_{EE} = \frac{150}{500}[/tex]
[tex]f_{EE} = 0.3[/tex]
URGENT HELP!! You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills. Your friend solves the system of inequalities x + y < 60 and 7x + 12y > 450 and tells you that a possible solution is (-3, 50). Is this a possible solution, why or why not?
Answer:
Is not a possible solution
Because the number of hours can not be negative
Step-by-step explanation:
Let
x------> the number of hours in the dog walking job
y-----> the number of hours in the sales job
we know that
-----> inequality A
------> inequality B
Remember that
If a ordered pair is a solution of the system of inequalities
then
the ordered pair must satisfy both inequalities
we have
------> Is not a possible solution
Because the number of hours can not be negative
Final answer:
Yes, (-3, 50) is a possible solution
Explanation:
The given system of inequalities is:
x + y < 60
7x + 12y > 450
To check if the solution (-3, 50) is possible, we substitute the values of x and y into the inequalities and check if the inequalities are true.
For the first inequality: (-3) + 50 < 60
47 < 60. This inequality is true.
For the second inequality: 7(-3) + 12(50) > 450
-21 + 600 > 450
579 > 450. This inequality is also true.
Since both inequalities are true when x = -3 and y = 50, we can conclude that (-3, 50) is a possible solution.
You want to construct an enclosed rectangular region using the side of a building as part of one side of the enclosed region. The building is 56 feet wide. You have 544 feet of fencing to use. Find the area of the largest region that you can enclose using these requirements
Answer:
13664 square feet
Step-by-step explanation:
Width of the Building=56 feet
Let the length of the building=L
Area of the building = LW=56L
A=56L
Available Perimeter for Fencing= 544 feet
Since we are using the side of the building as one part,
Perimeter = 2L+56=544
2L=544-56=488
L=244 feet
The area of the largest region that can be enclosed using theses requirements is given as:
Area = 244 X 56 =13664 square feet
To find the area of the largest region that can be enclosed with 544 feet of fencing alongside a 56-foot wide building, one sets up an equation for the fencing and solves for the width of the enclosure. The widest possible enclosure has a width of 244 feet, leading to a maximum area of 13,664 square feet.
To find the area of the largest rectangular region that can be constructed using the side of a building and a given amount of fencing, one must use the perimeter formula for a rectangle. Let's designate the widths of the rectangle that are not attached to the building as x, and the length that is attached to the building as 56 feet. Since two of the widths and one length will be enclosed by the fence, the total fencing used will be 2x + 56 feet.
Given that there are 544 feet of fencing available, we can set up the following equation:
2x + 56 = 544
Solving for x gives the width of the two sides not attached to the building:
2x = 488
x = 244 feet
The largest enclosed area will then be obtained by multiplying the length (alongside the building) by the width (the calculated x):
Area = 56 feet × 244 feet = 13664 square feet.
This calculation provides the largest possible rectangular area that can be enclosed with the given fencing, using the building as one side of the enclosure.
What is the slope of the line that passes through the points (-9, -3) and (1, -3)?
Write your answer in simplest form.
Answer:
The slope is 0.
Step-by-step explanation:
m= (y2-y1)/(x2-x1).
y2 is -3, y1 is -3.
x2 is 1 and x1 is -9.
m= -3 -(-3)/ 1- (-9)
m= 0/10
m=0
The slope of the line that passes through the points (-9, -3) and (1, -3) is 0 because the y-coordinates of both points are the same and this results in a 'change in y' of 0.
Explanation:In mathematics, the slope of a line passing through two given points can be calculated by the formula: (y2 - y1) / (x2 - x1). Where y2 and y1 represent the y-coordinates of the two points and x2 and x1 represent the x-coordinates of the two points. However, in this particular case, we see that the y-coordinates of both points (-9, -3) and (1, -3) are the same as -3.
This means our 'change in y', or (y2 - y1), is equal to zero (-3 - -3 = 0). Any fraction with 0 as the numerator (0 divided by any number) is itself equal to 0. Therefore, the slope of the line that passes through the points (-9, -3) and (1, -3) is 0.
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Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.
cos−1(StartFraction 6.9 Over 12 EndFraction)
cos−1(StartFraction 9.8 Over 12 EndFraction)
sin−1(StartFraction 6.9 Over 12 EndFraction)
sin−1(StartFraction 9.8 Over 12 EndFraction)
tan−1(StartFraction 6.9 Over 9.8 EndFraction)
To find measure of angle BAC in a right triangle, we can use the trigonometric functions cos⁻¹(6.9/12), sin⁻¹(6.9/12), and tan⁻¹(6.9/9.8), corresponding to the sides AC and CB with respect to the hypotenuse AB.
Explanation:To find the measure of angle BAC in triangle ABC where angle ACB is a right angle, we can use the trigonometric ratios involving the sides of the triangle. Given that AB is the hypotenuse, CB is the adjacent side to angle BAC, and AC is the opposite side to angle BAC, we can use the following expressions:
cos⁻¹(⅓6.9/12): This represents the cosine of angle BAC, since cosine is the ratio of the adjacent side to the hypotenuse.sin⁻¹(⅓6.9/12): This represents the sine of angle BAC, since sine is the ratio of the opposite side to the hypotenuse.tan⁻¹(⅓6.9/9.8): This represents the tangent of angle BAC, since tangent is the ratio of the opposite side to the adjacent side.Using any of these trigonometric functions, we can calculate the measure of angle BAC by inputting the ratios into a calculator that has the capability to compute the inverse trigonometric functions.
A play started at 2:35 P.M after the play was over , Jamie talked to a friend for 15 minutes She left the theatre at 4:10 P.M how long was the play? Would fine this super helpful thank you so much
Answer:
1 hour 20 minutes
Step-by-step explanation:
The play started at 2:35 PM.
After the play, Jamie talked to her friend for 15 mins and then left the theater at 4:10 PM.
She started talking to her friend once the play was over, hence, to find the time she started talking, we subtract 15 mins from 4:10 PM:
H M
04 : 10
- 00 : 15
03 : 55
She started talking around 3:55 PM.
Hence, to find how long the play lasted:
H M
03 : 55
- 02 : 35
01 : 20
Hence, the play lasted for 1 hour 20 minutes.
Our school had a pizza party.The school ordered 847 slices of pizza for the party. The students ate 628 slices. How many slices of pizza are left over?
Answer:
209
Step-by-step explanation:
837-628
A right cylinder has a radius of 2 units and a height of 5 units.
A right cylinder has a radius of 2 units and a height of 5 units.
What is the volume of the cylinder? Round to the nearest tenth.
a
31.4 cubic units
b
62.8 cubic units
c
157.1 cubic units
d
314.2 cubic units
Answer:
The volume of the cylinder is 62.8 cubic units.
Step-by-step explanation:
The volume of a cylinder is given by the following formula:
volume = (base area)*h
base area = pi*r²
volume = pi*r²*h
In order to solve this problem we need to apply the data given to the formula above as shown below:
volume = 3.14*(2)²*5 = 3.14*4*5
volume = 62.8 cubic units
The volume of the cylinder is 62.8 cubic units.
Answer:
The correct answer is option (b) 62.8 cubic units
Step-by-step explanation:
Solution
Recall that,
A right cylinder has a radius of = 2 units
Height of = 5 units
Now,
We define the volume of a cylinder, which is represented below.
Recall that,
A right cylinder has a radius of = 2 units
Height of = 5 units
Now,
We define the volume of a cylinder, which is represented below.
Volume of the cylinder is defined as = base * height
The base=Pi*radius*radius, or π* r
Where,
The base=3.1416*2*2,
The height=5
Thus,
The Volume=3.1416*2*2*5
Volume =62.8 cubic units.
Therefore the volume of the cylinder is 62.8 cubic units.of the cylinder is = base * height
The base=Pi*radius*radius, or π* r
Where,
The base=3.1416*2*2 ,
The height=5
Thus,
The Volume=3.1416*2*2*5
Volume =62.8 cubic units.
Therefore the volume of the cylinder is 62.8 cubic units.
Each bookshelf at a library holds 100 books. How many bookshelves are needed if the library stocks 12,400 books?
shelves
Answer:124
Step-by-step explanation:
12400/100=124
To stock 12,400 books with each bookshelf holding 100 books, 124 bookshelves are required.
To determine how many bookshelves are needed for 12,400 books, where each shelf holds 100 books, we perform a simple division:
Number of bookshelves = Total number of books ÷ Books per bookshelf
Number of bookshelves = 12,400 books ÷ 100 books per shelf
Number of bookshelves = 124 shelves
Therefore, 124 bookshelves are needed to stock 12,400 books.
Use the formula A = h(b1 + b2).
What is the area of the trapezoid?
square units
Answer:
75 square units
Step-by-step explanation:
The area of the trapezoid is 75 sq.units.
What is a Quadrilateral?A quadrilateral is a polygon with four sides.
It is of various types,
Trapezoid, which have one pair of parallel sides,
Parallelogram, it has two pairs of parallel sides,
Rhombus, it has all sides equal,
Rectangle, opposite sides are parallel and equal, and,
Square, all sides are equal and opposite sides are parallel, and all angles have measure of 90 degree.
The quadrilateral ABCD with lengths of three of its sides is 16, 6, and 14.
The height of the quadrilateral is 5.
The area of the quadrilateral has been asked to determine using the formula,
A = (1/2) h ( b1 + b2)
The parallel sides are 14 and 16, so b1 = 14 and b2 = 16, h = 5
The area is determined using the formula
A = (1/2) * 5 * ( 14+16)
A = (1/2) * 5 * ( 30 )
A = 75 sq.units
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A couple plans on having three children. Which of the following represents the sample space for the genders of the three children? To simplify this question, we will use the binary definition of gender, with representing boy and representing girl. A (68B, BBG, BGG, GGG) B.(B,G) C.(BB, BG, GB, GG) D. (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG) E. (BG, BG, BG)
The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How fast did Sean drink the slushy?
The initial amount of slushy in the cup is 600 mm.
A linear equation has the following form:
y = mx + b
where y and x are variables, m represents the rate of change, and b represents the initial value of y.
Let y be the amount of slushy remaining in the cup (in milliliters) and x the time (in seconds).
The y intercept on the graph is 600.
As a result, the initial amount of slushy in the cup is 600 mm.
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The following question may be like this:
Sean drank a slushy as fast as he could.
The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How much slushy was initially in the cup?
PLEASE HELP 50 POINTS
Assume the whole pizza was 12 inches across and cut into 8 pieces.
Answer:
14.14 inches squared
Step-by-step explanation:
We basically just want to find the area of one slice of pizza.
We know that the whole pizza was 12 inches across, which means its diameter was 12. Radius is 1/2 of the diameter, so r = 12/2 = 6 inches.
The area of a circle (the pizza, I assume, was circular) is: [tex]A=\pi r^2[/tex], where r is the radius. Here, r = 6, so:
[tex]A=\pi r^2[/tex]
[tex]A=\pi *6^2=36\pi[/tex]
But this is the area of the entire pizza. We need to divide it by 8:
[tex]36\pi /8[/tex] ≈ 14.14 inches squared
Hope this helps!
Answer:
14.13 in²
Step-by-step explanation:
Diameter: 12 inches
Radius: 12/2 = 6 inches
Area of the entire pizza:
pi × r²
3.15 × 6²
113.04 in²
Area of each slice:
113.04/8
14.13 in²
A local boys club sold 196 bags of mulch and made a total of $549. It sold two types of mulch: hardwood for $3.00 a bag and pine bark for $2.75 a bag. How many bags of each kind of mulch did it sell?
What is the formula to find the vertex of a parabola?
Answer:
y = a(x - h)^2 + k (please give branliest)
Step-by-step explanation:
(h,k) are coordinates of a point on the parabola
this is derived by ax^2 + bx + c
The formula to find the vertex of a parabola is x = -b/(2a) and y = f(x). The vertex of a parabola is represented by the coordinates (x, y).
Explanation:The formula to find the vertex of a parabola is x = -b/(2a) and y = f(x). In the equation of a parabola y = ax² + bx + c, the vertex can be found by substituting the x-coordinate from the formula into the equation to get the y-coordinate. So, the vertex of a parabola is represented by the coordinates (x, y).
I do not understand probability no matter how many ways are taught to me I still don’t understand I need a simpler or easier way to understand to find probability
Answer:
Step-by-step explanation:
Probability is basically the chance of something happening.
For example:
If you flip a coin there is a 1/2 chance to get heads and a 1/2 chance to get tails. If you were asked to find the probability of getting 3 tails in a row, you would multiply the fraction 1/2 3 times. Thus giving you 1/8.
Final answer:
Probability is the chance of an event occurring, calculated by dividing the number of ways an event can occur by the total number of possible outcomes. Karl Pearson's coin toss experiment demonstrates the law of large numbers, where the outcome over many trials approaches theoretical probability. To solve probability problems, understanding the question and systematically applying probability rules is essential.
Explanation:
Probability is a concept in mathematics that measures the likelihood of an event happening. It is calculated by dividing the number of ways an event can occur by the total number of possible outcomes. For example, when flipping a coin, there are two possible outcomes: heads or tails. Since these outcomes are equally likely, the probability of getting heads is 1 divided by 2, or 50%. This is known as theoretical probability.
Karl Pearson's experiment, where he flipped a coin 24,000 times, illustrates the law of large numbers, showing that the more times a random event is repeated, the closer the experimental results will come to the expected theoretical probability. In Pearson's case, he got heads 12,012 times, which is very close to the expected 50%, demonstrating that the probability predicts the outcome over a large number of trials, even though individual results may vary.
The relative frequency of an event is calculated by dividing the number of times the event occurs by the total number of trials. The example of Pearson's coin toss shows that the relative frequency (.5005) closely aligns with the theoretical probability (.5) when a large number of trials are conducted.
Systematic approaches to solving probability problems often involve reading the problem carefully, understanding the terminology, and using a clear process to calculate the probability. This could include determining the sample space, identifying the desired event, and calculating conditional probabilities if necessary.
To carry out probability calculations, it is essential to be able to express both the certainty and the variability of outcomes. In the case of rolling a die, while we may not predict with certainty which number will appear on any single roll, over a large number of rolls, the probability of rolling any given number, such as a three, is 1/6.
what the value of the expression -2(-7/9 divided 1/3)
Answer:
lol i need
Step-by-step explanation:
ez calps plue
Answer:
14/27
Step-by-step explanation:
let me know if this is right
A triangle has a base of 12 and one-third centimeters and height of 3 centimeters. Which expression could be used to determine the area of the triangle shown? One-half + 12 and one-third + 3 One-half (3) (12) (one-third) 12 and one-third times 3 One-half (12 and one-third) (3)
Answer:
One-half (3) (12) (one-third)
Step-by-step explanation:
Area of a triangle bus expressed as shown.
Area of a triangle = 1/2bh
B is the base
H is the height
Given base = 12 1/3xm
Height =3cm
Area =>1/2 (3) 12(1/3)
Area = One-half (3) (12) (one-third)
Answer:
One-half (12 and one-third) (3) option D/ the last one
Step-by-step explanation:
I took it and got it right on e2020
Circle V is shown. Line segments Y V and W V are radii. Tangents Y X and W X intersect at point X outside of the circle. The length of V Y is 5. Angle V is a right angle. What is the measure of circumscribed ∠X? A 45 B 50 C 90 D95
Answer:
The correct option is;
C 90°
Step-by-step explanation:
Here we have;
Angle V = 90°
Whereby, YX and WX are tangents, and YV and WV are radii then ;
Angle Y = 90° and
Angle W = 90°
Therefore we have sum of angles V, Y, W and X given by the following relation;
V + Y + W + X = 360° (Sum of interior angles of a polygon angle)
Therefore;
90° + 90° + 90° + X = 360°
270° + X = 360
X = 360° - 270° = 90°
Hence the correct option is X = 90°.
Answer:
Correct answer is C
student opened her math book and computed the sum of the numbers on two facing pages. Then she turned to the next page and computed the sum of the numbers on these two facing pages. Finally, she computed the product of the two sums, and her calculator displayed the number 69,165. What were the four page numbers?
Answer:
130, 131, 132, 133
Step-by-step explanation:
Let the first page numbe be x, the next x+1, x+2, x+3
The sum of the first two will be x+x+1=2x+1
The sum of the last two will be x+2+x+3=2x+5
Product will be (2x+1)(2x+5)
Since the product equals 69165
(2x+1)(2x+5)=69165
[tex]4x^{2}+10x+2x+5=69165\\4x^{2}+12x+5=69165\\4x^{2}+12x-69160=0\\x^{2}+3x17290\\(x-130)((x+130)=0\\x=130, -133[/tex]
Therefore, x=130
Next pages are 131, 132, 133
A motel finds it can rent 180 rooms when the room rate is $ 60 per day. For each $ 2 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .
Answer:
$7,200
Step-by-step explanation:
r=p × n
where
r=revenue
p = price per item
n = number of items sold
A change in price changes quantity ( number sold)
Variable x changes with price, then
Let
p+x=a dollar price increase
p-x= a dollar price decrease
n+x= an increase in quantity sold
n-x= a decrease in quantity sold
Therefore,
A $2 dollar increase in price=p+2x
2 decrease in room quantity sold= n-2x
Substituting in the above equation
r=(p+2x)*(n-2x)
P=$60
n=180
Then
r=(60+2x)*(180-2x)
r=10,800-120x+360x-4x^2
r=-4x^2-240x+10,800
Solve the quadratic equation
The maximum value of x in the vertex = - b/2*a
Where
b=240
a=-4
Value of x=-240/2*(-4)
X=30
r=-4x^2-240x+10,800
=-4(30)^2-240(30)+10,800
=-4(900)-7200+10,800
=3,600-7200+10800
=$7,200
The rate that maximises revenue=$7,200
Answer:
The rate that maximizes revenue is $14,000
Step-by-step explanation:
First of all, you should know that the income equation is:
R = p * n
where:
p = price per item n = number of items soldOn the other hand, if p + x means a price increase, while n - x means a decrease in the number of an item sold.
In this case, reference is made to rooms, where 60 + 2x is the increased price and 180-2x is the decrease in rooms for rent.
So:
R=(60+2x)*(180-2x)
Expressing this in another way, applying distributive property:
R=60*180+60*(-2)x+2x*180+2x*(-2)x
R=10,800+240x-4x² equation (A)
This is a quadratic equation that is graphically represented by a parabola. If a, the coefficient that accompanies the term x², has a positive value, the parabola will be oriented upwards. On the contrary, if a has a negative value, the parabola will be oriented downwards. In this case, the value of a is -4, with the parabola facing down. The vertex is a point that is part of the parabola, which has the value as ordered minimum or maximum function. In this case, since the parabola faces downward, the vertex will be its maximum value.
The value of x in the vertex is [tex]-\frac{b}{2*a}[/tex]. In this case:
a=-4b=240Replacing:
[tex]x=-\frac{240}{2*(-4)}[/tex]
Solving:
x=40
To find the rate that maximizes income you simply replace this value in equation (A)
R=10,800+240*40-4*(40)²
R=14,000
The rate that maximizes revenue is $14,000