Answer:
We need to assume that the relationship is linear.
a) Remember that a linear relation is written as:
y = a*x + b
then we will have:
p(x) = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:
y = (d - b)/(c - a)
In this case, we know that:
if the ticket has a price of $12, the average attendance is 25,000
Then we can define this with the point:
(25,000 , $12)
We also know that when the price is $9, the attendance is 29,000
This can be represented with the point:
(29,000, $9)
Then we can find the slope as:
a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075
Then the equation is something like:
y = (-$0.00075)*x + b
to find the value of b we can use one of the known points.
For example, the point (25,000 , $12) means that when x = 25,000, the price is $12
then:
$12 = (-$0.00075)*25,000 + b
$12 = -$18.75 + b
$12 + $18.75 = b
$30.75 = b
Then the equation is:
p(x) = (-$0.00075)*x + $30.75
b) We want to find the ticket price such that it maximizes the revenue.
The revenue will be equal to the price per ticket, p(x) times the total attendance, x.
Then the revenue can be written as:
r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )
r(x) = (-$0.00075)*x^2 + $30.75*x
So we want to find the maximum revenue.
Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.
Remember that for an equation like:
y = a*x^2 + bx + c
the x-value of the vertex is:
x = -b/2a
Then in our case, the x-value will be:
x = -$30.75/(2*(-$0.00075)) = 20,500
Then the revenue is maximized for x = 20,500
And the price for this x-vale is given by:
p( 20,500) = (-$0.00075)*20,500 + $30.75 = $15.375
which should be rounded to $15.38
Write the equation in vertex form of the parabola with the vertex (-4,-4) that goes through the point (-2,-16)
Answer:
[tex] - 3(x + 4) {}^{2} - 4[/tex]
Step-by-step explanation:
Vertex form is
[tex]a(x - h) {}^{2} + k = f(x)[/tex]
We know that h and k are both -4. Let x be -2 and y be -16.
[tex]a( - 2 + 4) {}^{2} - 4 = - 16[/tex]
[tex]a(2) {}^{2} - 4 = - 16[/tex]
[tex]4a - 4 = - 16[/tex]
[tex]4a = - 12[/tex]
[tex]a = - 3[/tex]
So the equation in vertex form is
[tex] - 3(x + 4) {}^{2} - 4[/tex]
What is the solution to log (9x)-log, 3 - 3?
O X
col 00
8
X =
3
O x=3
OX=9
Answer:
x = 8/3
Step-by-step explanation:
Log₂(9x) – Log₂3 = 3
The value of x can be obtained as follow:
Log₂(9x) – Log₂3 = 3
Recall
Log M – Log N = Log (M/N)
Thus,
Log₂(9x) – Log₂3 = 3
Log₂(9x/3) = 3
Log₂3x = 3
3x = 2³
3x = 8
Divide both side by 3
x = 8/3
William sold tooth pick for €2 a pack.On Selling 60% of his ware he still had 200 left.How much money did he collect from his entire sales?
Answer:
.......................
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 75 GPa and 1.7 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.)
Required:
a. Calculate P(79 <= P <= 81) when n = 25.
b. How likely is it that the sample mean diameter exceeds 81 when n = 36?
Answer:
a) P(79 <= P <= 81) = 0.9968
b) P( X > 81 ) = 0.0002
Step-by-step explanation:
mean value = 75 GPa
standard deviation = 1.7 GPa
a) Determine P(79 <= P <= 81)
given that : n = 25
attached below is the detailed solution
P(79 <= P <= 81) = 0.9968
b) Determine how likely the sample mean diameter will exceed 81
given that n = 36
mean diameter = 81
P( X > 81 ) = 0.0002
in how many ways can be arranged 2 different words in necklace?
Answer:
3
Step-by-step explanation:
chain by chain
parllel
series
Suppose the following data represent the ratings (on a scale from 1 to 5) for a certain smart phone game, with 1 representing a poor rating. The discrete probability distribution for the random variable x is given below:
Star Frequency
1 2140
2 2853
3 4734
4 4880
5 10,715
Required:
Construct a discrete probability distribution for the random variable X
Answer:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
Step-by-step explanation:
Given
The above table
Required
The discrete probability distribution
The probability of each is calculated as:
[tex]Pr = \frac{Frequency}{Total}[/tex]
Where:
[tex]Total = 2140+ 2853 + 4734 + 4880 + 10715[/tex]
[tex]Total = 25322[/tex]
So, we have:
[tex]P(1) = \frac{2140}{25322} = 0.0845[/tex]
[tex]P(2) = \frac{2853}{25322} = 0.1127[/tex]
[tex]P(3) = \frac{4734}{25322} = 0.1870[/tex]
[tex]P(4) = \frac{4880}{25322} = 0.1927[/tex]
[tex]P(5) = \frac{10715}{25322} = 0.4231[/tex]
So, the discrete probability distribution is:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
The absolute value inequality equation |2x – 1| > 3 will have what type of solution set?
Given:
The inequality is:
[tex]|2x-1|>3[/tex]
To find:
The solution set for the given inequality.
Solution:
We know that, if [tex]|x|>a[/tex], then [tex]x<-a[/tex] and [tex]x>a[/tex].
We have,
[tex]|2x-1|>3[/tex]
It can be written as:
[tex]2x-1<-3[/tex] or [tex]2x-1>3[/tex]
Case I:
[tex]2x-1<-3[/tex]
[tex]2x<-3+1[/tex]
[tex]2x<-2[/tex]
[tex]x<\dfrac{-2}{2}[/tex]
[tex]x<-1[/tex]
Case II:
[tex]2x-1>3[/tex]
[tex]2x>3+1[/tex]
[tex]2x>4[/tex]
[tex]x>\dfrac{4}{2}[/tex]
[tex]x>2[/tex]
The required solution for the given inequality is [tex]x<-1[/tex] or [tex]x>2[/tex]. The solution set in the interval notation is [tex](-\infty,-1)\cup (2,\infty)[/tex].
Therefore, the required solution set is [tex](-\infty,-1)\cup (2,\infty)[/tex].
5. a) Find the difference between the place values of two 5's in 95237508.
Answer:
4999500
Step-by-step explanation:
first 5 = 5000000
second 5 = 500
difference = 5000000-500
Các mô hình h i quy sau đây có ph i mô hình tuy n tính hay không? N u là môồảếếhình h i quy phi tuy n, hãy đ i v mô hình h i quy tuy n tính?ồếổềồếa) iiiuXY++=21lnββb) iiiuXY++=lnln21ββc) iiiuXY++=1ln21ββd) eiiuXiY++=21ββe) eiiu
If the price of a stapler increase from Rs 50 to Rs 54, find the percentage increase?
F(x)=x+8;g(x)=x+2. Find f=g
Answer:
f(x) can not be equal to g(x)
Step-by-step explanation:
If the result is possible:
f(x) = g(x)
x + 8 = x + 2
x + 8 - (x + 2) = x + 2 - (x + 2)
6 = 0
Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)
a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
The amount of money invested in a retirement fund is an example of which of the following?
a.
investment asset
b.
liquid asset
c.
long term asset
d.
use asset
Please select the best answer from the choices provided
Answer:
the answer is A
okay that it have a nice day
Answer:
the answer above me is correct!
Step-by-step explanation:
Edge 2021
I will give brainliest. I need help ASAP.
Answer:
\I got not answer cause im da BUDDHA
But gimme brainliest squekky plssss
Use the graphing calculator to graph the function f(x) = Vx. Which table of values contains points that lie on the
graph of the function?
9514 1404 393
Answer:
see below
Step-by-step explanation:
Assuming your Vx means √x, the values in the f(x) column will be the square root of the values in the x column. That is the case for the first table shown (also attached).
A construction crane lifts a bucket of sand originally weighing 145 lbs at a constant rate. Sand is lost from the bucket at a constant rate of .5lbs/ft. How much work is done in lifting the sand 80ft?
Answer: [tex]10,000\ lb.ft[/tex]
Step-by-step explanation:
Given
Initial weight of the bucket is [tex]145\ lb[/tex]
It is lifted at constant rate and rate of sand escaping is [tex]0.5\ lb/ft[/tex]
At any height weight of the sand is [tex]w(h)=145-0.5h[/tex]
Work done is given by the product of applied force and displacement or the area under weight-displacement graph
from the figure area is given by
[tex]\Rightarrow W=\int_{0}^{80}\left ( 145-0.5h \right )dh\\\\\Rightarrow W=\left | 145h-\dfrac{0.5h^2}{2} \right |_0^{80}\\\\\Rightarrow W=\left [ 145\times 80-\dfrac{0.5(80))^2}{2} \right ]-0\\\\\Rightarrow W=11,600-1600\\\\\Rightarrow W=10,000\ lb.ft[/tex]
5/3=12/x what does x equal?
[tex] \frac{5}{3} = \frac{12}{x} \\ = > \frac{5x}{3} = 12 \\ = > 5x = 12 \times 3 \\ = > 5x = 36 \\ = > x = \frac{36}{5} \\ = > x = 7.2[/tex]
This is the answer.
In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.
Answer:
plato screenshot!
Step-by-step explanation:
I don't personally know *how* to find the answers, but here's the screenshot of the suggested answer on Plato
Answer:
A B Slope of C Slope of Line Through C
(−5,4) (−1,−1) −1.25 (1,2) 0.8
(−5,4) (−3, 5) 0.5 (−2, 1) −2
(−4, 1) (−3, 5) 4 (−2, −2) −0.25
(−5, −2) (−1, 1) 0.75 (−4, 3) −1.33
(−5, −2) (1, −1) 0.17 (−3, 1) −6
Step-by-step explanation:
that way you can copy and paste each one but Plato
Please help me with this!
9514 1404 393
Answer:
7x -5 = 9x = 2Step-by-step explanation:
A) If we let x represent "a number", then "seven times a number" is 7x. When 5 is subtracted from that, we have ...
7x -5 . . . . . 5 subtracted from 7 times a number
This is said to be 9, so ...
7x -5 = 9 . . . . . . . 5 from 7 times a number is 9. Your equation.
__
B) To solve this, we can add 5 to both sides. This eliminates the constant term we don't want on the left.
7x = 14
Now, we can divide by 7, the coefficient of x that we don't want.
x = 14/7
x = 2
Select all the terms that can be combined with 5.
4b
14a
100
3a’2
Select the correct expressions and value.
Identify the expressions and the value that are equivalent to 6 times 5 squared.
5x 6²
6 x 5
192
6 x 5 x 5
6x5x2
150
6 + 5 x 5
Reset
Next
Answer:
✔️6 × 5²
✔️6 × 5 × 5
✔️150
Step-by-step explanation:
6 times 5 squared is written as 6 × 5²
Thus:
6 × 25 = 150
Evaluate each of the expressions given to determine whether they are equivalent to 150 or not
✔️5 × 6² = 5 × 36 = 180 (NOT EQUIVALENT)
✔️6 × 5² = 6 × 25 = 150 (EQUIVALENT)
✔️192 ≠ 150 (NOT EQUIVALENT)
✔️6 × 5 × 5 = 6 × 25 = 150 (EQUIVALENT)
✔️6 × 5 × 2 = 6 × 10 = 60 (NOT EQUIVALENT)
✔️150 = 150 (EQUIVALENT)
✔️6 + 5 × 5 = 6 + 25 = 31 (NOT EQUIVALENT)
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and three Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.
Answer:
The rental rate for the Fords is of $12 per day.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a Nissan.
y is the cost of a Ford.
z is the cost of a Chevrolet.
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.
This means that:
[tex]3x + 2y + 4z = 106[/tex]
Two Nissans, four Fords, and three Chevrolets cost $107 per day
This means that:
[tex]2x + 4y + 3z = 107[/tex]
Four Nissans, three Fords, and two Chevrolets cost $102 per day.
This means that:
[tex]4x + 3y + 2z = 102[/tex]
From the first equation:
[tex]4z = 106 - 3x - 2y[/tex]
[tex]2z = 53 - 1.5x - y[/tex]
[tex]z = 26.5 - 0.75x - 0.5y[/tex]
Replacing into the third equation:
[tex]4x + 3y + 53 - 1.5x - y = 102[/tex]
[tex]2.5x + 2y = 49[/tex]
From the second equation:
[tex]2x + 4y + 3z = 107[/tex]
[tex]2x = 107 - 4y - 3z[/tex]
[tex]x = 53.5 - 2y - 1.5z[/tex]
[tex]x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)[/tex]
[tex]x - 1.125x = 53.5 - 2y - 39.75 + 0.75y[/tex]
[tex]-0.125x = 13.75 - 1.25y[/tex]
[tex]0.125x = 1.25y - 13.75[/tex]
[tex]x = \frac{1.25y - 13.75}{0.125}[/tex]
[tex]x = 10y - 110[/tex]
Find the rental rate for the Fords.
We have to find y, so:
[tex]2.5x + 2y = 49[/tex]
[tex]2.5(10y - 110) + 2y = 49[/tex]
[tex]25y - 275 + 2y = 49[/tex]
[tex]27y = 324[/tex]
[tex]y = \frac{324}{27}[/tex]
[tex]y = 12[/tex]
The rental rate for the Fords is of $12 per day.
HELP PLEASE HELP HELP
Answer:
The first one is the only one that makes sense.
Step-by-step explanation:
hope it helps!
Consider a political discussion group consisting of 6 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Republican.
___.
(Type an integer or a simplified fraction.)
Answer:
10/16=5/8
6+6+4=16
The probability is 5/8
Pippa had 35 stickers.
She gave an equal number of stickers to 8 friends.
She gave each friend as many stickers as possible and kept the rest for herself.
How many stickers did Pippa keep for herself?
Answer: 3 stickers
Step-by-step explanation:
From the question, we know that Pippa's 8 friends have an equal amount of stickers, meaning that the number of stickers that Pippa gave out is a multiple of 8.
Also, we are able to know that Pippa gave as much as she can, meaning that she gave out the stickers until the number is the maximum multiple of 8.
First Five Multiple of 8 = 8, 16, 24, 32, 40
As we can see from the list, 8, 16, and 24 are all multiples of 8, but they are not the maximum number that could fit under 35 stickers. Similarly, 40 exceeds the number of stickers Pippa has. Thus, we are left with 32.
This means, Pippa gave out 32 stickers in total, and each friend got 4 stickers.
32 / 8 = 4 stickersAlso, this means Pippa would keep 3 stickers for herself.
35 - 32 = 3 stickersHope this helps!! :)
Please let me know if you have any questions
Four seconds pass between the first and third flash of a strobe light. The rate at which the strobe flashes is constant. How many seconds will pass between the first and the twelfth flash of the same light?
Answer:
t = 22 s
Step-by-step explanation:
If n is the number of strobe pulses
The first strobe pulse occurs at t = 0
t = 2(n - 1)
t = 2(12 - 1)
t = 2(11)
t = 22 s
2 hundreds equal how many tens?
Lets see if ya'll know the answer cause i do
Answer:
200 is equal to 20 tens I guess lol
Answer:
20 tens
Step-by-step explanation:
200÷10=20 groups of ten
Solve for X: A=2B/x+3
the answer is 2B divided by A minus 3
What is 4 × 1/7 on a numberline
Answer:
4/7
Step-by-step explanation:
When you multiply by fractions you multiply the numerators and denominators
4/1 x 1/7
Anything that doesnt have anything under it always has a 1 as its denominator
A manager for an insurance company believes that customers have the following preferences for life insurance products: 20% prefer Whole Life, 10% prefer Universal Life, and 70% prefer Life Annuities. The results of a survey of 200 customers were tabulated. Is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data
Answer:
Yes the sales manager claims can be refuted based on the calculated percentages
Step-by-step explanation:
From the table attached below
Total number of customers = 200
Calculated percentages
customers that prefer whole life insurance = 90 = 90/200 = 45%
customers that prefer universal life insurance = 15 = 15/200 = 7.5%
customers that prefer Annuities = 95 = 95/200 = 47.5
Expected percentages:
whole life = 20%
Universal life = 10%
Life Annuities = 70%
