Answer:
C
Step-by-step explanation:
Exponential form is y = b^x, with b as the base, and logarithmic form is x = log_b(y).
In this case, 10 is the base, 4 is x, and 10,000 is y. In logarithmic form, this can be changed into 4 = log_10(10,000). Logarithms with base 10 can also be written as 4 = log(10,000). Therefore C is the correct answer.
A stereo manufacturer determines that in order to sell x units of a new stereo, the price per unit , in dollars, must be p(x) = 100 - x. The manufacturer also determines that the total cost of producing x units is given by C(x) = 3000 + 2x. a. Express the total revenue function R as a function of x. b. Express the total profit P as a function of x. c. How many units must the company produce and sell in order to maximize profit d. What is the maximum profit? e. What price per unit must be charged in order to make this maximum profit .
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]
How many kilograms are in 242,000 milligrams? The solution is
Answer:
i am from afghanistan and you
Answer:
.242 Kilograms
Step-by-step explanation:
To convert milligrams to kilograms multiply the value by .000001 or move the decimal mark 6 places to the left.
Please help on the question as attached by providing detailed steps. Tq
Answer:
Step-by-step explanation:
in the table below x represents miles traveled and y represents the cost to travel by train what is the y intercept of this function?
Answer:
im pretty sure its 2.25...
Step-by-step explanation:
hope this helps:)
what is 36x - 28 equal
Answer:
[tex]36x-28[/tex]
Rewrite 36 as 4*9 & Rewrite 28 as 4*7
[tex]4\cdot \:9x-4\cdot \:7[/tex]
Now, u can factor out the common term 4
[tex]4\left(9x-7\right)[/tex]
Can you just answer question 23!!! i need help!!!
Answer:
It is Graph A because it has the properties of a cubic graph.
please mark as brainliest thank you
NO LINKS!! Please help
Answer:
FJ = 32
IJ = 24
FG = 48
Step-by-step explanation:
Getting Started with FG
[tex]\frac{IH}{AB} =\frac{FG}{ED}[/tex]
[tex]\frac{72}{36} =\frac{FG}{24}[/tex]
[tex]\frac{FG}{24} =2[/tex]
[tex]FG=24(2)=48[/tex]
The proportion between polygons is 2:1
[tex]IJ=2CB[/tex]
[tex]IJ=2(12)=24[/tex]
[tex]FJ=2BC=2(16)=32[/tex]
Hope this helps
Answer:
FJ = 32
IJ = 24
FG = 48
Step-by-step explanation:
Given: HGFJI ~ AEDCB
From inspection of the diagram, the corresponding sides are:
HG~AE
FG~DE
FJ~DC
IJ~CB
IH~BA
The only pair of sides that both have side lengths are IH and BA. Therefore, we can use these to figure out the scale factor of dilation.
IH = 72 and BA = 36
⇒ IH/BA= 72/36 = 2
Therefore, HGFJI is an enlargement of AEDCB by a scale factor of 2
If HG = 56
⇒ AE = 56 ÷ 2 = 28
If DE = 24
⇒ FG = 24 × 2 = 48
If DC = 16
⇒ FJ = 16 × 2 = 32
If CB = 12
⇒ IJ = 12 × 2 = 24
Write the inverse variation function given that y varies inversely with x, and y = 0.5 when x = 24.
[tex]\large{\text{Refer\:to\:explanation\:pls}}[/tex]
Calculation ↓If y varies inversely with x, we divide :
y = [tex]^k/_x[/tex]
Where
k = constant of proportionality
We are given that :
y = 0.5
x = 24
So we write :
0.5 = [tex]\Large\text{$^k/_{24}$}[/tex]
Multiply by 24 on [tex]\Large{\text{both\:sides\::}}[/tex]
12=k
[tex]\Large{\text{The\:constant\:of\:proportionality\:is\:12.}}[/tex]
So we havey = 12/x
[tex]\footnotesize{\text{hope\:helpful}}[/tex]
519.6 x 10.86
by process.
Answer:
5642.856
Step-by-step explanation:
Multiply 5196 x 1086 without the decimal points
Then you will get the ans 5642856 then count how many decimal points are there altogether which is three points.
So go behind three numbers and put the point.
Final Answer - 5642.856
What is the measure of angle ACB? (geometry)
Answer:
30°Step-by-step explanation:
The angle between two secants is half the difference of intercepted arcs.
m∠ACB = 1/2(mAB - mDE)Substitute the arc values and calculate
m∠ACB =1/2(80° - 20°) = 1/2(60°) = 30°Answer:
∠ACB = 30°
Step-by-step explanation:
Finding ∠ACB :
∠ACB = 1/2 x (∡AB - ∡DE)∠ACB = 1/2 x (80° - 20°)∠ACB = 1/2 x 60°∠ACB = 30°Find the following given f(x) = - 9x - 2.
a. f(4)
b. f( - 3)
c. f(0)
D. F(1/7)
Answer:
the answer for {a} is -38
Step-by-step explanation:
fill in the number for x then simplify
f(x)=-9x - 2
f(4) = -9 (4) - 2
= -36 - 2 = -38
Use the same process for the other questions.
A self-serve car wash charges $5.52 to use its facilities, plus an additional $0.95 for each minute the customer is at the self-serve
car wash. If Tiffany was at the car wash for 5 minutes, how much was she charged?
A. $10.52
B. $6.47
C. $10.27
D. $4.75
a bike requires 2 hours of assembly and a swing 3 hours. a maximum of 250 hours of assembly time are available. the profit is $50 on a bike and $20 on a swing. if no more than 100 items can be produced how many of each should be assembled for maximum profit?
The assemble for maximum profit is mathematically given as
For maximum profit, 100 tire and 0 strings must be assembled.
How many of each should be assembled for maximum profit?Generally, the equation for the max number is mathematically given as
Mx=50x+20y
Therefore
2x+3y \leq 250
x1+x\leq=100
Therefore
with cordinates of
(0,0)
(100,0)
(50,50)
(0,250/3)
In conclusion, The mx of 50x+20y is (100,0)
Hence, for maximum profit 100 tire and 0 strings must be assembled.
Read more about Arithmetic
https://brainly.com/question/22568180
-27 w3 + 125 factorize
[tex]-1(3w-5)(9w^{2} +15w+25)[/tex]
(3+2a)² alguien sabe la respuesta?
Answer:
3(3+2a)+2a(3+2a)
9+6a+6a+4a^2
9+12a+4a^2
ANS 4a^2+12a+9
If the area of a rectangle is x4 + 3x3 - 2x2 - 200 and the width is x + 5, find its length.
Answer:
Step-by-step explanation:
Area = 4x + 9 - 4 - 200
= 4x - 195
Since Area is lw, let the width be x + 5 and y be the unknown length.
Therefore (x + 5) (y) = 4x - 195
Answer:
x³ - 2x² + 8x - 40
Step-by-step explanation:
Area = length · width
(x⁴ + 3x³ - 2x² + 0x¹ - 200) = length · (x + 5)
length = (x⁴ + 3x³ - 2x² + 0x¹ - 200) ÷ (x + 5)
BRAINLIEST please if this helped!Use the function below to find f(3)
F(x) = (1/4)x
Please help!!
Case Study 2: Maxing out Matched Savings
Chen's employer will match 50% of their $250 monthly contributions to their 401(k). This
means that Chen's employer will put 50% of $250 = $125 into Chen's 401(k) account each
month in addition to Chen's $250. Free money-- Nice! (this is common!)
How much will Chen have after 40 years of saving $250 their own money if the account
compounds monthly at 3% APR?
hint: Use the TVM Solver on the Tl or this website. Remember, ignore the - sign. Don't forget
about the matching!
Type answer as a number without the $ symbol rounded to the hundredths. Example, if it
the answer was $1234.5687, you would enter 1234.57.
Answer:
The computation of the given question is shown below:-
Total Contributions = Monthly contribution + Amount invested in Ferdinand’s 401(k)
= $250 + $125
= $375
1. Future Value = PMT [((1 + r)n - 1) ÷ r
Future value = 375 × ((1 + 0.03 ÷ 12) × 12 × 40 - 1) ÷ (0.03 ÷ 12)
= $347,272
2. Ferdinand deposit = Given Amount × Total number of months in a year × Number of years
= $250 × 12 Months × 40 Years
= $120,000
3. The Amount put in by the employer = 50% of $250 ×Total number of months in a year × Number of years
= $125 × 12 Months × 40 Years
= $60,000
4. Interest = Future value - Ferdinand deposit - The Amount put in by the employer
= $347,272 - $120,000 - $60,000
= $167,272
Step-by-step explanation:
Use the picture attached.
How many lines of symmetry does the picture have?
A.
1
B.
3
C.
2
D.
0
Answer: look honestly I am not sure but Probably it is choice c which is 2 lines of symmetry .
Step-by-step explanation: 2 lines of symmetry because one line is horizontal and the other is vertical . One line will be in the middle of the flower which is vertical and the other line is horizontal as they will make equivalent sides . HOPE IT HELPS BUDDY .
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
(3, 2)
Explanation:
y = −2x + 8 ....equation 1y = x − 1 ....equation 2======================
substitute equation 2 into 1
x − 1 = −2x + 8x + 2x = 8 + 13x = 9x = 3find y
y = x − 1y = 3 − 1y = 2solution
(x, y) ⇒ (3, 2)Answer:
(3, 2)
Step-by-step explanation:
Given
Equation 1: y = -2x + 8
Equation 2: y = x - 1
Solving by Substitution
Substitute Equation 2 into Equation 1 and solve for x:
⇒ x - 1 = -2x + 8
Add 2x to both sides:
⇒ 3x - 1 = 8
Add 1 to both sides:
⇒ 3x = 9
Divide both sides by 3:
⇒ x = 3
Now substitute the found value of x into Equation 2 and solve for y:
⇒ y = 3 - 1
⇒ y = 2
Therefore, the solution is (3, 2)
How many hours would it take to watch 170 episodes of a show, each episode is about 23 minutes long.
Answer:
Around 65 hours(2 days and 17 hours)
Each episode is 23 minutes long, and there's 170 episodes, so multiply 23 by 170 being 23 minutes for each episode.
[tex]23 * 170 = 3,910[/tex]
Now, convert 3,910 minutes to hours by dividing for every 60 minutes.
[tex]3,910 / 60 = about~65[/tex]
Therefore, the answer is ≈65
the exact value is 65.16667
Let Vector a = LeftAngleBracket 3, 11, negative 8 RightAngleBracket. and Vector b = LeftAngleBracket 2, negative 3, c RightAngleBracket. . If Vector a minus vector b = LeftAngleBracket 1, 14, negative 3 RightAngleBracket., what is the value of c?
–11
–5
5
11
Answer:
c.5
Step-by-step explanation:
Need help with math please
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = (x-7)2 + (x-7)-1
A. F(x)=(x-7)2 and G(x)=(x-7)-1
B. F(x)=x²+x-1 and G(x) = x-7
C. F(x)=(x-7)-1 and G(x)=(x-7)²
D. F(x)= x-7 and G(x)=x²+x-1
SUBMIT
Answer:
The answer is D.
Step-by-step explanation:
will mark brainliest
Answer:
0.5
Step-by-step explanation:
total no. of tiles
= 3 + 6 + 3
= 12
probability of tile being green
= 6 / 12
= 1/2
= 0.5
hope this helps!
I need help ASAP!!!! Worth 20 points!
Answer:
x in (-oo:+oo)
(5/4)*x-(3/7) = 0
(5/4)*x-3/7 = 0
5/4*x-3/7 = 0 // + 3/7
5/4*x = 3/7 // : 5/4
x = 3/7/5/4
x = 12/35
x = 12/35
Step-by-step explanation:
Carter deposited $146.00 into a new savings account that earns 13% interest compounded
quarterly. How long will it take for the balance to grow to $239.00?
Round your answer to the nearest month.
___ years and ___ months
Answer:
it should be around 4 months I believe
Step-by-step explanation:
146.00(1+0.13/4)^(4×4)
What’s 1+2?
Answer fasttttt
I will mark you as branly
Answer:
3
Step-by-step explanation:
uhhhhhhhhhhhhh yeah
Look at the following ratio:
3:8
Write an equivalent ratio if it was three times greater:
24 out of 50 children prefer the color blue. what
percentage of children prefer the color blue?
Answer:
48%
Step-by-step explanation:
as a fraction is 24/50
make denominator 100 so times by 2
24 x 2 = 48 so
48/100 = 48%