Answer:
The price that maximizes the revenue is $165
Step-by-step explanation:
We can model the price as a function of sold units as a linear relationship.
Remember that a linear relationship is something like:
y = a*x + b
where a is the slope and b is the y-intercept.
We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
For this line, we have the point (40, $110)
which means that to sell 40 units, the price must be $110
And we know that if the price increases by $11, then he will sell 2 units less.
Then we also have the point (38, $121)
So we know that our line passes through the points (40, $110) and (38, $121)
Then the slope of the line is:
a = ($121 - $110)/(38 - 40) = $11/-2 = -$5.5
Then the equation of the line is:
p(x) = -$5.5*x + b
to find the value of b, we can use the point (40, $110)
This means that when x = 40, the price is $110
then:
p(40) = $110 = -$5.5*40 + b
$110 = -$220 + b
$110 + $220 = b
$330 = b
Then the price equation is:
p(x) = -$5.5*x + $330
Now we want to find the maximum revenue.
The revenue for selling x items, each at the price p(x), is:
revenue = x*p(x)
replacing the p(x) by the equation we get:
revenue = x*(-$5.5*x + $330)
revenue = -$5.5*x^2 + $330*x
Now we want to find the x-value for the maximum revenue.
You can see that the revenue equation is a quadratic equation with a negative leading coefficient. This means that the maximum is at the vertex.
And remember that for a quadratic equation like:
y = a*x^2 + b*x + c
the x-value of the vertex is:
x = -b/2a
Then for our equation:
revenue = -$5.5*x^2 + $330*x
the x-vale of the vertex will be:
x = -$330/(2*-$5.5) = 30
x = 30
This means that the revenue is maximized when we sell 30 units.
And the price is p(x) evaluated in x = 30
p(30) = -$5.5*30 + $330 = $165
The price that maximizes the revenue is $165
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
A. Combination.
B. 17020
Step-by-step explanation:
A. Determination whether it is permutation or combination.
From the question given above, we were told that the student body of 185 students wants to elect two (2) representatives.
This is clearly combination because it involves a selecting process (i.e selecting 2 out of 185).
NOTE: Combination involves selecting while permutation involves arranging.
B. Determination of the combination.
Total number of people (n) = 185
Number of chosen people (r) = 2
Number of combination (ₙCᵣ) =?
ₙCᵣ = n! / (n – r)! r !
₁₈₅C₂ = 185! / (185 – 2)! 2!
₁₈₅C₂ = 185! / 183! 2!
₁₈₅C₂ = 185 × 184 × 183! / 183! 2!
₁₈₅C₂ = 185 × 184 / 2!
₁₈₅C₂ = 185 × 184 / 2 × 1
₁₈₅C₂ = 34040 / 2
₁₈₅C₂ = 17020
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 5% of the time if the person does not have the virus, (This 5% result is called a false positive.) Let A be the event "the person is Infected" and B be the event "the person tests positive", a) Find the probability that a person has the virus given that they have tested positive, l.e. find P(AB). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(AIB)= % b) Find the probability that a person does not have the virus given that they test negative, I.e. find P(A'B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'B') =
This question is solved using the conditional probability concept.
Using this concept, we find that:
a) P(AIB)= 5.3%b) P(A'|B') = 99.9%First, the concept is presented.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]
In which
P(A|B) is the probability of event A happening, given that B happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(B) is the probability of B happening.
----------------------------------------------------
Question a:
For relation with the formula presented above, I will change events A and B.
Event A: Person is infected.
Event B: Positive test.
Probability of a positive test:
85% = 0.85 out of 1/300 (person has the virus).5% = 0.05 out of 299/300(person does not have the virus)Thus:
[tex]P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527[/tex]
Probability of a positive test and the person is infected.
85% = 0.85 out of 1/300. Thus:
[tex]P(A \cap B) = \frac{0.85}{300} = 0.0028[/tex]
Desired probability:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053[/tex]
0.053*100% = 5.3%, thus:
P(AIB)= 5.3%
---------------------
Question b:
Event A: Does not have the virus
Event B: Test negative.
Probability of a negative test:
100% - 85% = 15% = 0.15 out of 1/300 (person has the virus).100% - 5% = 95% = 0.95 out of 299/300(person does not have the virus)Thus:
[tex]P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473[/tex]
Probability of a negative test and the person is not infected.
0.95 out of 299/300
Thus:
[tex]P(A \cap B) = \frac{0.95\times299}{300} = 0.9468[/tex]
Desired probability:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999[/tex]
0.999*100% = 99.9%, so:
P(A'|B') = 99.9%
A similar question can be found at https://brainly.com/question/24275491
I need help for this math question!
Answer:
D
Step-by-step explanation:
Assuming that the expression is referring to sin²(2πft) and not sin²(2)πft, we can solve as follows:
One trigonometric identity states that sin²x+cos²x = 1. We want to express this in terms of cos²x, so we need to solve for sin²x. Subtracting cos²x from both sides, we get 1-cos²x = sin²x. Plugging (2πft) for x, we get
1-cos²(2πft) = sin²(2πft)
We can plug that into our equation to get
P = I₀²R(1-cos²(2πft)), or D
Please help!! Can’t figure this out for the life of me.
Select the correct answer from each drop-down menu.
If _______, then AABC and ADEF are congruent by the ASA criterion.
If _______, then AABC and ADEF are congruent by the SAS criterion.
AABC and ADEF are congruent if ______
Answer:
Angle b is congruent to angle E
CA=FD
Step-by-step explanation:
If _______, then triangle ABC and triangle DEF are congruent by the ASA criterion. ASA is angle side angle . We know angle C= angle F and side CB = side FE We need to know angle B = angle E
If _______, then triangle ABC and triangle DEF are congruent by the SAS criterion. SAS is side angle side, we know side CB = side FE and then angle C= angle F then we need side CA = side FD
If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.
If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.
What are congruent figures?Two figures are said to be congruent of they have the same shape and all the corresponding sides and angles are congruent.
The HL (hypotenuse leg) congruence theorem states that if the hypotenuse and one leg of a triangle is congruent to another triangle, then both triangles are congruent.
In triangle ABC and DEF;
BC = EF and ∠ACB ≅ ∠DFE
Hence:
If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.
If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.
Find out more on congruent figures at: https://brainly.com/question/1675117
A drinks factory packed their drinks into red and yellow boxes. There were 24 more red boxes than yellow boxes. Each red box contained 60 packets of milk and each yellow box contained 75 packets of fruit juice. There were 120 fewer of milk than packets of fruit juice in all
boxes.
(a) How many yellow boxes were used ?
(b) How many packets of milk were packed into the the red boxes?
Answer:
A) 128
B) 7800
Step-by-step explanation:
Trial and error until I got to 75 x 104 and 60 x 128 (which abides by the fact that there has to be 24 more red boxes) which equals 7800 and 7680 and if you take them away from each other you get 120
5 oranges weigh 1.5 kg, 8 apples weigh 2 kg. What would be the total weight of 3 apples and 4 oranges?
Answer: oranges 1.2 Kg and apples 0.75 Kg.
Step-by-step explanation:
Oranges (4)(1.5)/5
Apples (3)(2)/8
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3 sin^2(t), y = 3 cos^2(t), 0< t<3pi
What is the length of the curve?
The length of the curve (and thus the total distance traveled by the particle along the curve) is
[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]
We have
x(t) = 3 sin²(t ) ==> x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )
y(t) = 3 cos²(t ) ==> y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )
Then
√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|
and the arc length is
[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]
Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.
Now,
• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)
• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)
so we split up the integral as
[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]
which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.
Hhhhhhhhhhhhhhhhuuiuu
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
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what is 5 2/3 - 11 1/6
Answer:
Check the photo for the answer
SOMEONE PLS HELP ME!!!
Answer:
No
Step-by-step explanation: Bye
Solve for a.
5a + 2 - 7-8 = 0
What is the root? If there is no root, choose none.
Answer:5
Step-by-step explanation: root5a+2 +7a-8 = 0
squaring both side
5a+2=7a-8
8+2=7a-5a
10=2a
a=5
Answer:
[tex]\sqrt{5a+2}-\sqrt{7a-8}=0[/tex]
Isolate a square root on the left-hand side
[tex]\sqrt{5a+2} =\sqrt{7a-}8+0[/tex]
Eliminate the radical :-
[tex]5a+2 = 7a-8[/tex]
Solve:-
[tex]2a -10 = 0[/tex]
Add 10 to both sides, then Divide both sides by 2:-
[tex]a = 5[/tex]
OAmalOHopeO
A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output.
Which of the following represents the standard deviation of the residuals?
1.223
34.55
78.712
124.13
I think it's (B), 34.55
Answer:
34.55
Step-by-step explanation:
S = 34.55 represents the standard deviation of the residuals which is the correct answer that would be option (B).
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
Students' proficiency in math and English is assessed by a particular standardized test. Ten students were chosen at random, and their math and English test results were recorded and examined.
The computer output displays the outcomes.
Predictor Coef SE Coef t-ratio p
Constant -124.13 78.712 0.046
Math 1.223 0.1966 6.220 0.000
S = 34.55 R-Sq = 82.8% R-Sq (Adj) = 83.5%
In the above ANOVA table, S = 34.55 represents the residual standard deviation.
Therefore, the correct answer is Option B = 34.55.
Option A = 1.223 represents the coefficient of the math score.
Option C = 78.712 represents the Standard Error (S.E).
Option D = 124.13 is the coefficient value.
Hence, the correct answer would be an option (B).
Learn more about the standard deviation here:
https://brainly.com/question/16555520
#SPJ2
A survey showed that, in one city, 20.7% of the population used
product X, 50% use product Y and among users Y, 36.5% use X. Randomized interview
However, a resident in that city, calculate the probability that that person
a) Use both X and Y;
b) Neither X nor Y
Answer:
Step-by-step explanation:
a) 0.5*0.365=18.25%
b) (100%-20,7%-50%)=29.3
A car is traveling at a constant speed of 60 miles per hour. How many feet does it travel in 10 seconds?
Answer:
880 ft.
Step-by-step explanation:
First! We have to establish how many feet the car travels per hour.
60 (number of miles per hour) x 5280 (number of feet in a mile) = 316,800 (number of feet in an hour)
Next, since we know that there are 60 minutes in an hour we are going to divide our "number of feet in an hour" by 60 to get the "number of feet in a minute"
316,800 ÷ 60 = 5280
Once again, we are going to divide our "number of feet in a minute" by 60 to get the "number of feet per second".
5280 ÷ 60 = 88
Finally! We will multiple our "number of feet per second" by 10 to get how many feet the car can travel in 10 seconds.
88 × 10 = 880
So! Our car can travel 880 feet in 10 seconds.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 indicating that their financial security was more than fair. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.
Answer:
hey, how you're day going
Step-by-step explanation:
.................
If there was a system where 5 points was equivalent to $1 how many points would $43 be?
Answer:
Step-by-step explanation:
5 pts = $1
$43 × (5 pts)/$1 = 43×5 pts = 215 pts
What are the first and third quartiles for the following data set?
12, 15, 18, 16, 14, 9, 12, 21
A 9 and 21
C 12 and 17
B 12 and 16
D 15 and 17
Answer:
A
Step-by-step explanation:
I guess that is it may be
How many of each coin does he have?
_____nickels
_____quarters
Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
A line passes through the point (5,6) and is parallel to the line given by the equation y = 2x - 12. Which of these is an equation for the line? O A. y-5=-264-6) B. y - 6 = -2(x - 5) C. y + 6 = 2(x + 5) D. Y- 6 = 2(x - 5)
Answer: D
Step-by-step explanation:
(lines parallel to each other have the same slope)
slope = m = 2
y = mx + b, (5,6)
6 = 2(5) + b
6 = 10 + b
b = -4
y = 2x - 4
y - 6 = 2(x - 5)
y - 6 = 2x - 10
y = 2x -4
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
What is the slope line that passes through the points (10, 8) and (-15, 18)? Write your answer in simplest form
Answer: [tex]y=-\frac{2}{5}x+12[/tex]
y = mx + b
m = slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{18-8}{-15-10}=\frac{10}{-25}=\frac{2(5)}{-5(5)}=-\frac{2}{5}[/tex]
The y-intercept(b) can be found by substituting a point into the function.
[tex]y = -\frac{2}{5}x + b \\\\8=-\frac{2}{5}(10) + b\\\\8=-4+b\\\\b=8+4=12[/tex]
Therefore, the function is:
[tex]y=-\frac{2}{5}x+12[/tex]
Geometry workkkk I need help it’s due tonightttt
Find m∠F=....................
.................................
What would it equal??
m∠F= what is it???
Answer:
45°
Step-by-step explanation:
[tex] \sin \: m\angle F = \frac{EG}{FG} \\ \\ \sin \: m\angle F = \frac{2 \sqrt{11} }{2 \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{\sqrt{11} }{ \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{1}{ \sqrt{2} } \\ \\ \sin \: m\angle F = \sin \: 45 \degree \\ \\ \huge \boxed{ \purple{m\angle F = 45 \degree }}[/tex]
The degree of the polynomial function f(x) is 4. The roots of the equation f(x) =0 are -2,-1,1 and 3. Which graph could be the graph of f(x)?
Answer:
top right
Step-by-step explanation:
roots of an equation = x-intercepts
Answer:
top right is the answer from my calculatins
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 10 .
Answer:
The probability of getting two numbers whose sum is 10 is 25%.
Step-by-step explanation:
Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:
1 = +9
2 = +8
3 = +7
4 = +6
5 = +5
6 = +4
7 = +3
8 = +2
9 = +1
9/36 = 0.25
Therefore, the probability of getting two numbers whose sum is 10 is 25%.
The acceleration of car that comes from a velocity of 10m/s in distance of 25m is
Answer:
what is the time given ???
Step-by-step explanation:
either initial velocity is 0 or final velocity is zero
V=U+AT
converting it we get
V/T = u+a
V/T - U= a
where
v= final velocity
u= initial velocity
a= acceleration
t= time
plz write the full question
The The Laplace Transform of a function , which is defined for all , is denoted by and is defined by the improper integral , as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of as a fixed constant) 1. Find (hint: remember integration by parts)
Answer:
a. L{t} = 1/s² b. L{1} = 1/s
Step-by-step explanation:
Here is the complete question
The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0
Solution
a. L{t}
L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]
Integrating by parts ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1
So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w
So, ∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]
= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]
= -1/s[(0 - 0] - 1/s²[0 - 1]
= -1/s[(0] - 1/s²[- 1]
= 0 + 1/s²
= 1/s²
L{t} = 1/s²
b. L{1}
L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]
= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[exp(-∞s) - exp(-0s)]
= -1/s[exp(-∞) - exp(-0)]
= -1/s[0 - 1]
= -1/s(-1)
= 1/s
L{1} = 1/s
PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST
Answer:
32.64°
Step-by-step explanation:
From triangle Given :
The sides of the missing angle given are the Adjacent and hypotenus.
Since the triangle is right angled, we can apply trigonometry :
cosθ = adjacent / hypotenus
Cosθ = 16 / 19
θ = Cos^-1(16/19)
θ = 32.6368
θ = 32.64°
Find the unit price of each of the following items Round your answer to the nearest tenth
frozen orange juice
16.0% at $2.01
12 oz at $1.69
Answer:
12.56 cents
14.08 cent
Step-by-step explanation:
The unit price for each of the following items could be obtained thus :
The unit price = price of one item
Therefore, given that x numbers of a certain item cost y ;
The unit price will be : y / x
frozen orange juice
16.0 oz at $2.01
12 oz at $1.69
If 16 oz cost $2.01
1 oz = $2.01 / 16 = $0.125625 * 100 = 12.56 cents
If 12 oz = $1.69
1 oz = $1.69 / 12 = $0.1408333 * 100 = 14.08 cent
