Answer: See below
Step-by-step explanation:
a)
[tex]$$The total revenue R(x) is obtained as:\begin{align*} R\left( x \right) &= xp\left( x \right)\\ &= x\left( {100 - x} \right)\\ &= 100x - {x^2} &$$$ R(x) = 100x - {x^2} \end{align*}[/tex]
[tex]$$Thus, {R\left( x \right) = 100x - {x^2}[/tex]
b)
[tex]$$The total profit is obtained as: \begin{align*} P\left( x \right) &= R\left( x \right) - C\left( x \right)\\ &= 1000x - {x^2} - 3000 - 20x\\ &= - {x^2} + 980x - 3000 \end{align*}[/tex]
[tex]$$Hence, P\left( x \right) = - {x^2} + 980x - 3000[/tex]
c)
[tex]$$For maximum profit dP/dx should be equal to zero: \begin{align*} \dfrac{{dP}}{{dx}} &= 0\\ - 2x + 980 &= 0\\ x &= 490 \end{align*}[/tex]
[tex]$$So, the required units to maximize profit is 490[/tex]
d)
[tex]$$The maximum profit is calculated as: \begin{align*} P\left( x \right) &= - {x^2} + 980x - 3000\\ P\left( {490} \right) &= - {490^2} + 980 \times 490 - 3000\\ &= 237100 \end{align*}[/tex]
[tex]$$Accordingly, the maximum profit is \$237100.[/tex]
e)
[tex]$$Calculating the price at maximum profit as: \begin{align*} p\left( x \right) &= 1000 - x\\ p\left( {490} \right) &= 1000 - 490\\ &= 510 \end{align*}[/tex]
[tex]$$Consequently, the price at the maximum profit is \$510.[/tex]
If the following line segment is reflected across the y-axis, what are the coordinates of the new endpoints?
A. (1, 6) and (3, 2)
B. (-1, -6) and (-3, -2)
C. (6, -1) and (2, -3)
D. (-6, 1) and (-2, 3)
Answer:A
Step-by-step explanation: im right im a god at answering these kind of equations.
please help!
elect the correct answer.
Which statement is true?
A.
The function is an odd function because its graph is symmetric about the y-axis.
B.
The function is an even function because .
C.
The function is an odd function because .
D.
The function is an even function because its graph is symmetric about the origin.
The true statement is The function f(x)= tan(x) is an odd function because f(-x) = -f(x).
What is odd function?When x is substituted with -x, the odd functions are those that return their negative inverse. When f(-x) = -f(x), it follows that f(x) is an odd function (x). The trigonometric sine function, tangent function, cosecant function, etc. are a few examples of odd functions.
If f(x) = f(x), then the function is odd for all x. An odd function's graph will be symmetrical in all directions around the origin. Consider how unusual f(x) = x³ is. In other words, the function on one side of the x-axis is graphically symmetric about the origin or sign inverted with respect to the other side.
As, we know for the
even function: f(-x) = f(x)
odd function: f(-x)= -f(x)
and, using Trigonometry
tan x = sin x / cos x
Then,
f(-x) = sin (-x) / cos (-x)
= -sin (x) / cos (x)
= -tan (x)
= -f(x)
Thus, tan (x) is an odd function.
Hence, the function f(x)= tan(x) is an odd function because f(-x) = -f(x).
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WHICH ANIMALS IS FOUND IN THE TAIGA FOREST
Answer:
1.) foxes
2.) lynxes
3.) bears
4.) minks
5.) squirrels
Step-by-step explanation: hope this helps ^^ pls mark me brainliest
Find the area of the shape based on the provided measurements
Answer:
375 units²
Step-by-step explanation:
A = bh/2
A = (75)(10)/2
A = 750/2
A = 375
OLZ HELP ILL MARK AS BRAINLEST
find the slope
Answer:
-1
Step-by-step explanation:
A radio station has a broadcast area in the shape of a circle with equation x2+ y2=5,625, where the constant represents square miles.
A.
B.
C.
Highlight answers + work shown pls
I'll give brainliest
47. Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.
Use the Midpoint Rule Kelly travels 12m/s more than Chris does during the first ten seconds.
What is the midpoint rule?The midpoint rule is the rule that follows the median of a set of values which is the middle value when the values are written in numerical order.
From the table above, the midpoint for the velocity of Chris car = 81, while the midpoint for the velocity of Kelly's car = 93
Therefore, the Kelly's car travelled 93-81 = 12 m/s farther than Chris does during the first ten seconds.
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please help! a point is chosen at random in the square, what percent of the time will the point be in the circle,round to the nearest tenth of a percent?
Answer:
78.5%
Step-by-step explanation:
You take the area of the circle which is pie*r^2
and divide it by the area of the square
HELPPP PLS IM GIVING 60 POINTSSSSS IT'S EASYYYYYY 6TH GRADE MATHH
Explain how you would create and use a spinner to simulate the probability of an event with the following probabilities:
Percent chance: 20% green, ¼ blue, ⅖ yellow, and 15% orange
To simulate the probability in a spinner divide the spinner into colors depending on the probability each color represents.
What does the word "probability" mean?This word refers to the likelihood for an event to occur. Moreover, it is often expressed either as a fraction, a percentage, or a number.
How to create a spinner to simulate probability?In this case, each of the colors represents a probability:
Green 20%Blue 1/4 or 25%Yellow 2/5 oe 40%Orange 15%Due to this, the best is to divide the spinner by colors and considering the percentanges of each color. For example 40% of the spinner should be red, while 15% should be orange.
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Here are the chorus datz: {0, 10, 10, 20, 20, 20, 20,30, 30, 40) What is the mean?
Answer:
7 is 20
8 is 40
Step-by-step explanation:
Mean is the total of all the numbers divided by the amount of numbers
7. 20
8. 40
Add them all up divide by the total amount of them
Please help!! What do I do
Answer:
a(5) = 1.080
a(10) = 0.393
a(20) = 0.122
Step-by-step explanation:
Take the derivative of velocity v(t) -> acceleration a(t)
v(t) -> a(t)
Quotient Rule: [tex]\frac{u*dv-du*v}{u^2}[/tex]
[tex]120*\frac{x}{5x+13}[/tex]
Make u= 5x+13 and v=x
[tex]120*\frac{x'*(5x+13)-x*(5x+13)'}{(5x+13)^2}\\\\120*\frac{1*(5x+13)-x*(5)}{(5x+13)^2}\\\\120*\frac{(5x+13)-5x}{(5x+13)^2}\\120*\frac{13}{(5x+13)^2} \\\\a(t)=\frac{1560}{(5x+13)^2}[/tex]
Now Subsitute your a(5) , a(10) , a(20). Also, round to 3 decimal place.
a(5) = 1.08033241 = 1.080
a(10) = 0.3930461073 = 0.393
a(20) = 0.122170826 = 0.122
Answer:
(a) 1.080 ft/s²
(b) 0.393 ft/s²
(c) 0.122 ft/s²
Step-by-step explanation:
Acceleration is the derivative of velocity. You are being asked to differentiate the given function and evalutate the derivative at three different times. The function is a rational function, so the formula for the derivative of a ratio is applicable.
(u/v)' = (vu' -uv')/v²
__
For the given velocity function, the accleration is ...
v(t) = (120t)/(5t +13)
a(t) = v'(t) = ((5t +13)(120) -(120t)(5))/(5t +13)² = 1560/(5t +13)²
(a)At t=5, the acceleration is ...
a(5) = 1560/(5·5 +13)² = 1560/1444 ≈ 1.080 . . . ft/s²
(b)At t=10, the acceleration is ...
a(10) = 1560/(5·10 +13)² = 1560/3969 ≈ 0.393 . . . ft/s²
(c)At t=20, the acceleration is ...
a(20) = 1560/(5·20 +13)² = 1560/12729 ≈ 0.122 . . . ft/s²
_____
Additional comment
Many graphing calculators are capable of finding the numerical value of the derivative of a function.
Use formula A=LW to find the length of a rectangle when the width is 35 ft and the area is 1,750 sq ft
Answer:
the length of the rectangle is 50 ft
Step-by-step explanation:
A-LW
1,750=L(35)
divide both sides by 35
L= 50
the least common multiple of 9 and 6 is 54
Answer:
18
Step-by-step explanation:
The multiples of 9 are 9,18,27,36,45,54,63,...
The multiples of 6 are 6,12,18,24,30,36,42,...
one ounce of gold can be purchased for $1,195.80.one ounce of silver can be purshased for $16.08.what is the difference between the cost of 5 ounces of gold and 5 ounces of silver?
Answer:
Step-by-step explanation:
Remark
This is a proportion question a proportion is 2 equal ratios equated to each othe. If three parts are known the 4 can be found.
Givens
1 oz silver costs 16.08
1 oz Gold costs 1195.80
Silver
16.08/1 = x / 5 Multiply both sides by 5
5*16.08 = 1*x
80.4 =x
Gold
1195.80/1 = x/5
5 * 1195 = 1 * x
5979 = x
Answer
Difference = Cost of Gold - Cost of Silver
Difference = 5979 - 80.4
Answer Difference = 5898.60Which fraction make comparison 3/4
Answer:
6/8, 12/16, and so on. I wasn't sure how you wanted this question to be answered, but 3/4 is also 0.75
Step-by-step explanation:
find x.
please help whoever egts right gets brainliest
Answer:24
Step-by-step explanation:
a^2+b^2=c^2
c^2 has to be 26 because it is the hypotinuce. 10 could take the place of a^2 or b^2, it dose not matter.
a^2+10^2=26^2
a^2+100=676
subtract 100 from both sides
a^2=576
sqrt576
a=24
x=a
x=24
I need help with this please.
Answer:
1782 cm²
Step-by-step explanation:
the required surface area =1782
units= cm²
Which of the following describes the polynomial function?
8
==
4
-2
2
09
00
8
X
1
-5
do
9
The function has a negative leading coefficient.
O The function has an even degree.
O The function has zero turning points.
The function has one x-intercept.
Answer:
the function has one x intercept is the correct answer of given statement
Pls help with this ;w;
Answer:
79-83= 2
84-88 =4
89-93= 5
94-98=2
Step-by-step explanation:
put in order then you can just count them
HELPPP Pleaseeee
Last year, Dan opened an investment account with $6600. At the end of the year, the amount in the account had increased by 26.5%. How much is this increase
in dollars? How much money was in his account at the end of last year?
Answer:
1,749
8,349
Step-by-step explanation:
We can multiply 6,600 by 1.265 to get 8,349. To get the percentage all we have to do is multiply 6,600 by .265 and get 1,749.
Hope this helps
Function or not a function pls help giving brainlest
Answer:
function
Step-by-step explanation:
For every value of 'x' ....there is only ONE value of 'y'
so it IS a function
Mike paid $492.60 for 4 new tires for his truck. If each tire cost the same, What was the cost for 1 tire?
Can someone help me with it, plase? :(
Answer:
123.15
Step-by-step explanation:
3. In a sample of 250 high school seniors,
5 stated that they have red hair. What is
the sample proportion?
Answer choices:
0.02
0.05
0.12
Answer:
0.02 (the first option)
Step-by-step explanation:
This is because a proportion means there is division going on. If 5 out of the 250 students have red hair, this creates a fraction of [tex]\frac{5}{250}[/tex] and when you divide this out: 5 ÷ 250, you get 0.02
helpp pppppppppp ppp
Step-by-step explanation:
use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
and therefore also
sin(A)/a = sin(B)/b = sin(C)/c
where the lines and corresponding angles are always opposite of each other.
and remember, the sum of all angles in a triangle is always 180°.
and sin(x) = sin(180-x).
so, we have
sin(32)/43 = sin(B)/53
sin(B) = 53×sin(32)/43 = 0.653156302...
B = 40.77999844...° ≈ 41°
C = 180 - 32 - 40.77999844... = 107.2200016...° ≈ 107°
43/sin(32) = c/sin(107.2200016...)
c = 43×sin(107.2200016...)/sin(32) = 77.507143... ft
≈ 78 ft
B' = 180 - B = 139.2200016...° ≈ 139°
C' = 180 - 32 - 139.2200016... = 8.779998438...° ≈ 9°
43/sin(32) = c'/sin(8.779998438...)
c' = 43×sin(8.779998438...)/sin(32) = 12.38595519... ft
≈ 12 ft
Help me pls lol
I don’t understand
[tex]J'= (-5,-6)[/tex]
[tex]K'=(-5,-1)[/tex]
[tex]L'=(-10,-2)[/tex]
See graph below.
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]Have[/tex] [tex]a[/tex] [tex]good[/tex] [tex]day![/tex] [tex]:)[/tex]
Convert the decimal 3.88888… to a fraction.
Answer:
The answer is 35/9
Step-by-step explanation:
PLEASE help me violate brainly communityWrite in index form 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12
Answer:
[tex]\sf{12^{8} }[/tex]
Step-by-step explanation:
12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 = [tex]\sf{12^{8} }[/tex]
[tex]\sf{12^{8} }[/tex] = 429,981,696
An easy way to think of this is that there are 12 is being multiplied by itselg 8 times (there are 8 12s). Similar to how squared numbers work...
Hope this helps! If you need further explanation, let me know!
- profparis
Answer:
12⁸
Step-by-step explanation:
Index forms are used to show how many times a number or variable has been multiplied by itself.
Here, 12 is being multiplied by itself eight (8) times.
The index form would be:
12⁸
Hope this helps!
A random survey found that 6
prefer blueberry candies from
of the 27 people surveyed prefer blueberry candies. Based on those results, about how many people
a population of 108 people?
A. 24
B. 18
C. 30
D. 12
Answer:
A
Step-by-step explanation:
108/24 finds you the ratio from people surveyed to population
gets you 1:4
so for the 6 who prefer candies you sub it it
6:(4*6)
6:24
so its 24 = A :)
Write a propotion that can be used to convert 50 meters into kilometers. Then solve
Answer:
0.5km
[tex]1km = 1000m \\ x = 50m \\ \\ 50m \times 1km = 1000 \times x \\ x = 0.5km[/tex]