Answer:
R(x) = -50x2 + 300x + 2000
Maximum revenue of $2450 with x = 3
Step-by-step explanation:
For each 1$ reduced of the price, he sells 50 more candle sets, so if he reduces x times the price by 1$, the final price will be:
price = 10 - x
And the number of sets sold will be:
sets = 200 + 50x
If the revenue is the price times the number of sets sold, we have that:
R(x) = (10 - x) * (200 + 50x)
R(x) = 2000 + 500x - 200x - 50x2
R(x) = -50x2 + 300x + 2000
To find the value of x that gives the maximum revenue, we use the formula of the vertex of the quadratic equation:
x_v = -b / 2a
x_v = -300 / (-100) = 3
And the maximum revenue is:
R(x_v) = -50*3^2 + 300*3 + 2000 = $2450
Find the slope of the line
Answer:
3/5
Step-by-step explanation:
m = change in y / change in x
m = 3 / 5
Suppose the time to process a loan application follows a uniform distribution over the range 77 to 1515 days. What is the probability that a randomly selected loan application takes longer than 1414 days to process
Answer:
The probability is approximately 0.2222
Step-by-step explanation:
The correct question is as follows;
Suppose the time to process a loan application follows a uniform distribution over the range 7 to 15 days. What is the probability that a randomly selected loan application takes longer than 14 days to process
Please check attachment for solution to question
What are the Odds of an event happening if the probability of the event happening is (Event
0.25]?
Answer:
odds and probably are the same. If there is 0.25 chance that means there is basically a 25% chance the event will happen or 1/4 chance.
Step-by-step explanation:
Identify the equation for the graph shown.
A)
y = x - 4
B)
y = 5x - 2
4-3x6
D)
y = 2x - 5
Answer:
(D) y = 2x - 5
Step-by-step explanation:
First locate where the line touches the y axis or vertical axis. Then find the rise over run or rate of change (slope) by using the triangle method.
I call this the triangle method because it involves drawing vertical(up, and down), and horizontal(left, and right) lines from the original or diagonal line (hypotenuse or longest line) to create a right (90 degree, because the angle between them forms a square) triangle. First draw a line going to the right from a point on the original line, and form a triangle by connecting the next point with a line going up, and down (vertical line) with the line going to the right (horizontal line)
Then count the units of the vertical line and divide them by the units counted by the horizontal line.
This is k(for constant) or m(slope or steepness of a graph ) = change in or rise of y divided by the change in or rise of x = ∆y(change in or rise of y)/∆x(change in or run of x).
For this graph, starting from -5 or the point where the line touches the y axis. Draw a line going up 1 square to the right, and another going up 2 squares. Repeat this, and you will realise that it's the same pattern every time. Because the line goes up 2 squares, every time it goes to the right 1 square. There is a change of 2 in y every change of 1 in x or rise of 2 for every run of 1. Therefore, the slope is 2/1 = 2. Then since we know the graph touches the y axis at -5, y = 2x - 5
In a certain college,20% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that exactly 7 belong to an ethnic minority?
Answer:
0.000786432
Step-by-step explanation:
In a certain college,20% of the physics majors belong to ethnic minorities
The proportion p = 20%
= 0.2
q = 1 - 0.2 = 0.8
1f 10 students are selected at random from the physics majors
n = 10
x = 7
The formula for Binomial Probability is
= nCx × p^ x × (1−p)^ n−x .
= 10C7 × p⁷ × (0.8) ^10 - 7
= 0.000786432
The probability that exactly 7 belong to an ethnic minority is 0.000786432
Circle O has a circumference of approximately 44 in.
What is the approximate length of the diameter, d2
7 in
14 in
22 in
44 in
Answer:
14 in
Step-by-step explanation:
Given:
Circumference of circle = 44 in
Required:
The length of the diameter of the circle.
SOLUTION:
Circumference of circle = πd
Circumference = 44 in
π = 3.14
d = ?
Plug the values into the formula
44 = 3.14*d
Divide both sides by 3.14
44/3.14 = d
14.01 = d
d ≈ 14 in
Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 112 inches and standard deviation σ = 10 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 22nd percentile of the tree heights. (b) Find the 80th percentile of the tree heights. (c) Find the first quartile of the tree heights. (d) An agricultural scientist wants to study the tallest 1% of the trees to determine whether they have a certain gene that allows them to grow taller. To do this, she needs to study all the trees above a certain height. What height is this? Part: 0 / 40 of 4 Parts Complete Part 1 of 4 Find the 22nd percentile of the tree heights. The 22nd percentile of tree heights is inches.
Answer:
Explained below.
Step-by-step explanation:
Let X represents the tree heights.
It is provided that X follows a normal distribution with mean μ = 112 inches and standard deviation σ = 10 inches.
(a)
Compute the 22nd percentile of the tree heights as follows:
[tex]P(X<x)=0.22\\\\P(Z<z)=0.22[/tex]
The z-score for the corresponding probability is, z = -0.77.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.77=\frac{x-112}{10}\\\\x=112-(0.77\times 10)\\\\x=104.3[/tex]
Thus, the 22nd percentile of the tree heights is 104.3 inches.
(b)
Compute the 80th percentile of the tree heights as follows:
[tex]P(X<x)=0.80\\\\P(Z<z)=0.80[/tex]
The z-score for the corresponding probability is, z = 0.84.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.84=\frac{x-112}{10}\\\\x=112+(0.84\times 10)\\\\x=120.4[/tex]
Thus, the 80th percentile of the tree heights is 120.4 inches.
(c)
Compute the first quartile of the tree heights as follows:
[tex]P(X<x)=0.25\\\\P(Z<z)=0.25[/tex]
The z-score for the corresponding probability is, z = -0.67.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.67=\frac{x-112}{10}\\\\x=112-(0.67\times 10)\\\\x=113.3[/tex]
Thus, the first quartile of the tree heights is 113.3 inches.
(d)
The tallest 1% of the trees, i.e. P (X > x) = 0.01.
That is, P (X < x) = 0.99.
⇒ P (Z < z) = 0.99
The corresponding z-value is, z = 2.33.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.99=\frac{x-112}{10}\\\\x=112+(0.99\times 10)\\\\x=121.9[/tex]
Thus, the tallest 1% of the trees are more than 121.9 inches tall.
help needed please answer asap
What is the least common multiple of six and eight?
Answer:
24
plz mark me as brainliest :DD
Answer:
The LCM for 6 and 8 = 24
Step-by-step explanation:
Because 24 is the first multiple they have in common.
6 | 8
12| 16
18 | 24 <-- 24
24 | 32
^
24 Least Common Multiple
Pls i beg you help meeeeeee
Answer:
is thisssssssssssssssssss right????????????????????????????
Same Thing as the first one
Let M = 18,526.6 find the smallest power of 10 that will exceed M
A. 10^6
B. 10^ -1
C. 10^5
Please help me with this!
I will give you a thanks!
Ming makes 6 trays of muffins. Each tray requiers 1.75 pounds of apples. How many pounds of apples does ming use?
Answer:
10.5
Step-by-step explanation:
Answer:
He would use 10.5 lbs of apples.
If b^2 = 25 then b= Answer it please
Answer:
b = 5
mark me as brainliest plz!! :DD
The standard normal distribution has a mean of
and a standard deviation of
The standard normal distribution has a mean of 0 and a standard deviation of 1
??????????number line
Answer:
A. 6 B. 8 min C. yes
Step-by-step explanation:
200 students ate lunch today. 37% of the students ate soup how many students ate soup?
Answer:
74
Step-by-step explanation:
Answer:74 students ate soup
Step-by-step explanation:
37% of 200 = 74
or
.37 x 200 = 74
what are the two consecutive odd integers whose product is 99.
Answer:
9and 11
Step-by-step explanation:
it also can be -9 and -11
Can I please have answer
Answer:start on -4 go over 3 right and up 4
Step-by-step explanation:
Answer:
Start at -4 on the y axis(the axis that goes up and down). Then draw a line from this point that goes to the right 3 squares, and up 4 squares. Then just continue the line with the same movements to the right, and opposite movements to the left.
Step-by-step explanation:
Magic
The cost of a ticket t will be no more than 26$
Answer: What's the question?
Step-by-step explanation:
In 2 /3 ÷ 4 /5 the is 2/ 3 .
Answer:
5/9
Step-by-step explanation:
2/3 • 5/2 • 2/3
1/3 • 2/5 • 2/3
multiply 1/3 for 5/2
5
-----------
3 • 2
multiply 3 for 2
5/6 • 2/3
anular el factor común 2
5/3 • 1/3
multiply 5/3 for 1/3
5
------------
3 • 3
multiply 3 for 3
5/9
the result
5/9
form decimal
0.5
Kim sold a house for $250,000 and made a 2% commission. How much money did Kim make from commission for selling the house?
$250.00
$5,000.00
$255,000.00
$500,000.00
Answer:
5000
Step-by-step explanation:
2% of 250,000 is 5000
7th grade math help me plzzz
Answer:
a. -7 + 3
b. draw 7 negatives + 7 positives
Step-by-step explanation:
Answer:
3.a) -7 + 3
3.b) 4
I hope this helps!
A= 1,321 +0.3433m
The equation above can be used to estimate the body surface area A, in square centimeters, of a child with mass
m, in grams, where 3,000 sms 30,000 Which of the following statements is consistent with the equation?
O a
A. For each increase of 1 gram in mass, A increases by approximately 0.3433 square centimeter.
Ob
B. For each increase of 0.3433 gram in mass, A increases by approximately 1 square centimeter.
Ос
C For each increase of 1 gram in mass, A increases by approximately 1,321 square centimeters.
Od
D. For each increase of 1,321 grams in mass, A increases by approximately 1 square centimeter.
Answer:
Option A: For each increase of 1 gram in mass, A increases by approximately 0.3433 square centimeter.
Step-by-step explanation:
We are given the function;
A= 1321 + 0.3433m
To find the rate of increase of the area, we will find the derivative of the function. Thus;
dA/dm = 0.3433
This means that the area increases at the rate of 0.3433 Sq.metre for each additional 1 gram added to the mass.
Looking at the given options, the one that corresponds to our answer is Option A
The following is an excerpt from a soccer magazine. Read and answer the question The ball should weigh between 410–450 g (14–16 oz), with a circumference of 68–70 cm (27–28 in). The ball's weight must be in the range of 410 to 450 g (14 to 16 oz) and inflated to a pressure of 0.6 and 1.1 bars (8.7 and 16.0 psi) at sea level. Create a compound inequality for the weight using min and max weight values, leave units out, just the numerical answer.
Answer:
A) 410 ≤ x ≤ 450 AND 68 ≤ y ≤ 70
B) 410 ≤ x ≤ 450 AND 0.6 ≤ x ≤ 1.1
Step-by-step explanation:
In the first statement we are told that the ball should weigh between 410–450 g (14–16 oz), with a circumference of 68–70 cm (27–28 in).
If the weight is x, it means we have the inequality as;
410 ≤ x ≤ 450
If the circumference is denoted as y, we have;
68 ≤ y ≤ 70
Compound inequality is when we join two inequalities with the word "OR" or the word "AND.
Thus, the compound inequality is;
410 ≤ x ≤ 450 AND 68 ≤ y ≤ 70
Similar to he first statement, in the second statement, we have;
410 ≤ x ≤ 450
If the inflated pressure is denoted by z, then we have;
0.6 ≤ x ≤ 1.1
Like in the first statement, the compound inequality can be represented as;
410 ≤ x ≤ 450 AND 0.6 ≤ x ≤ 1.1
please answer this The cost of 2.5 pounds of cheese is $5.60.
D. How could you find the cost for 5 pounds of cheese without finding the cost per pound? Type your answer in the box.
Answer:
$11.20
Step-by-step explanation:
you just double the cost of 2.5 pounds because 2.5 +2.5 is 5
Answer:20.16
Step-by-step explanation:
That is we want the price of
9
pounds (lets call it
$
x
) to be such that
$
5.60
:
2.5
pounds
is the same as
$
x
:
9
pounds
or written as fractions, we want
$
5.60
2.5
pounds
=
$
x
9
pounds
That is
XXX
$
x
=
$
5.60
2.5
pounds
×
9
pounds
XXXXX
=
$
50.40
2.5
=
$
20.16
. The article "Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive" (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144–154) presents a study of the failure pressures of roof panels. Following are the failure pressures, in kPa, for five panels constructed with 6d smooth shank nails. These data are consistent with means and standard deviations presented in the article. 3.32 2.53 3.45 2.38 3.01 Find a 95% confidence interval for the mean failure pressure for this type of roof panel.
Answer:
The 95% confidence interval is [tex] 2.354 < 3.526 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 5
The sample data is 3.32 2.53 3.45 2.38 3.01
Gnerally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{n}[/tex]
=> [tex]\= x = \frac{3.32+ 2.53 +3.45+ 2.38+ 3.01 }{5}[/tex]
=> [tex]\= x = 2.94 [/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{ \frac{ \sum (x_i - \= x )^2}{n-1} }[/tex]
=> [tex]s = \sqrt{ \frac{ ( 3.32 - 2.94 )^2 + ( 2.53 - 2.94 )^2+ \cdots + ( 3.01 - 2.94 )^2}{5-1} }[/tex]
=> [tex]s = 0.472 [/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n-1[/tex]
=> [tex]df = 5-1[/tex]
=> [tex]df = 4 [/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 4 [/tex] is
[tex]t_{\frac{\alpha }{2} ,df } = 2.77[/tex]
Generally the margin of error is mathematically represented as
[tex]E =t_{\frac{\alpha }{2} ,df } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.77 * \frac{0.472 }{\sqrt{5} }[/tex]
[tex]E = 0.586 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
[tex]2.94-0.586 < 2.94 + 0.586[/tex]
[tex] 2.354 < 3.526 [/tex]
The inside of an oven is set to rise to a temperature of 298°F. So far it has risen 76% If this amount.
Which would be the best way to estimate the number of degrees Fahrenheit the inside of the oven has risen so far?
Answer:
226.48°F
Step-by-step explanation:
Temperature of the oven = 298°F
if it has risen 76% of this amount so far, the number of degrees Fahrenheit the inside of the oven has risen so far can be expresses as:
= 76% of 298
= 76/100 * 298
= (76*298)/100
= 0.76*298
= 226.48°F
The temperature inside the oven so far is 226.48°F
The data set below represents the total number of home runs that a baseball player hit each season for 11 seasons of play. What is the interquartile range of the data? 14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28 12 16 22 28
Answer:
The interquartile range of the data is 12
Step-by-step explanation:
Data : 14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28 12 16 22 28
Data in ascending order : 12 ,14 ,15 ,16 ,16 ,19 ,21 ,22 ,22 ,25 ,27 ,28 ,28 ,30 ,32
Lower quartile :12 ,14 ,15 ,16 ,16 ,19 ,21
Q1 is the median of lower quartile
n = 7
Median =[tex]\frac{n+1}{2} \text{th term}=\frac{7+1}{2}=4 \text{th term}[/tex]=16
Upper quartile :22 ,25 ,27 ,28 ,28 ,30 ,32
Q3 is the median of upper quartile
n = 7
Median =[tex]\frac{n+1}{2} \text{th term}=\frac{7+1}{2}=4 \text{th term}[/tex]=28
IQR = Q3-Q1=28-16= 12
Hence the interquartile range of the data is 12
Answer:
A: 12
Step-by-step explanation:
edg2020
