Answer:
The cost can be written as:
C(x) = $1.4*x
The revenue can be written as:
R(x) = $700 - $400*e^(-x/100)
And as you know, the profit is written as the difference between the revenue and the cost:
P(x) = R(x) - C(x)
P(x) = $700 - $400*e^(-x/100) - $1.4*x
Now we want to maximize this, then we must look at the zeros in the derivate of P(x)
dP/dx = P'(x) = (-1/100)*$400*e^(-x/100) - $1.4
The maximum will be when P'(x) = 0.
we can solve:
0 = (-1/100)*$400*e^(-x/100) - $1.4
$1.4 = (-1/100)*$400*e^(-x/100)
(-100)*$1.4 = $400*e^(-x/100)
$140 = $400*e^(-x/100)
($140/$400) = e^(-x/100)
0.35 = e^(-x/100)
Now we can apply the Ln() in both sides and get:
ln(0.35) = ln(e^(-x/100) ) = -x/100
-ln(0.35)*100 = x = 104.98
You should apply 104.90 pounds of fertilizer.
b) The profit per acre, is:
P(x) = $700 - $400*e^(-x/100) - $1.4*x
Then if you have 200 acres, the profit will be:
200*P(x) = 200*($700 - $400*e^(-x/100) - $1.4*x)
and the maximum profit is whit x = 104.98 pounds, then:
200*P(104.98) = 200*($700 - $400*e^(-104.98/100) - $1.4*104.98) = $82,604.98
6k - 25 = 7 -2k
what is k?
Answer: K= 16/3=5.333
Step-by-step explanation: Search up tiger algebra for other problems and the answer THEY HELP
Help please !!!!!.!!!!
Lara incorrectly placed the decimal point when she wrote 0.55 inch for the width of her e-reader. What is the correct decimal number for the width? inch(es). The correct width of the e-reader is (Type a whole number or a decimal.)
Answer:
5.5 makes more sense.
Step-by-step explanation:
The numbers on a football field indicate 10 yard increments. You walk around the perimeter of a football field between the pylons. You walk a distance of 306 2/3 yards. The playing field not including end zones perimeter and area?
Answer:
It is D.
Step-by-step explanation:
proof I just took it
Solve for z. What is the root? If there is no root, choose none.
Answer:
I dont think this has a solution to be made.. I could definitely be wrong though..
Answer:
I think the answer is none
Find the measures of the numbered angles in the figure, shown to the right. Name the theorem that justifies each
answer.
M<1=
M<2=
M<3=
M<4=
Answer:
Step-by-step explanation:
m∠1 + 75° = 180° [Linear pair of angles]
m∠1 = 180° - 75°
= 105°
m∠2 = m∠1 [Opposite angles of a rectangle are equal]
m∠2 = m∠1 = 105°
m∠2 = m∠3 = 105° [Vertically opposite angles]
m∠3 = m∠4 = 105° [Corresponding angles]
Therefore, all four angles measure the same as 105°.
The population of bluegills (type of fish) has a mean length of 152.09mm and a standard deviation of 19.62mm. What is the probability that a random sample of 25 fish has a mean length of 140mm or shorter
Answer:
0.001035
Step-by-step explanation:
Mean (m) = 152.09 mm
Standard deviation (σ) = 19.62 mm
Sample size (n) = 25
Length being 140mm or shorter (x) : x ≤ 140
Using the Zscore relation :
Zscore = (x - m) / (σ/√n)
Zscore = (140 - 152.09) / (19.62/√25)
Zscore = (140 - 152.09) / (19.62/5)
Zscore = −3.081039
P(Z ≤ −3.08) = 0.001035
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Part A:
I only see one thing that you can do. You can use transformation to move f(x) 6 units to the left
Part B:
g(x) = f(x)+1 where k = 1, and g(x) = f (x + 8) where k = 8
Part C:
g(x) = f (x) + 1, and g(x) = f (x + 8)
sorry if I got it wrong
The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds x (miles per hour).
Speed, x (mi/h) 50 55 60 65 70 75 80 85 90
Distance ,y (100m) 20 25 35 50 70 95 125 200 160
Required:
Find an equation of the quadratic function that models the data, and predict the stopping distance for the train traveling at 95 miles per hour.
The required equation is 0.1x²-9.5x+245=0
And, the stopping distance for the train traveling at 95 miles per hour is 245.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that,
Speed, x (mi/h) 50 55 60 65 70 75 80 85 90
Distance ,y (100m) 20 25 35 50 70 95 125 160 200
Now, let an quadratic equation be, ax²+bx+c=y
Putting the values of x & y we get,
2500a+50b+c=20 ....(1)
3025a+55b+c=25...(2)
3600a+60b+c=35 .....(3)
solving this we get,
a= 0.1
b=-9.5
c=245
Hence, the required equation is 0.1x²-9.5x+245=0
And, the stopping distance for the train traveling at 95 miles per hour is 245.
To learn more on function click:
brainly.com/question/21145944
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I NEED HELP ASAP!!!!!! DUE TONIGHT!!!!!! PLEASE ANSWER FULLY WITH WORK
A red ball rolls for 6 meters across a sticky level surface and slows down to a stop. the ball was rolling at 36 meters per second when it began to roll across the sticky surface. find the acceleration, velocity final, the velocity initial, the velocity average, the distance the ball rolled, and the time of the balls roll across the sticky surface
Answer:
Please find the answer in the explanation
Step-by-step explanation:
Given that a red ball rolls for 6 meters across a sticky level surface and slows down to a stop. the ball was rolling at 36 meters per second when it began to roll across the sticky surface. To find the acceleration, let us use third equation of motion
V^2 = U^2 + 2as
As the object is moving to stop, V = 0
0 = U^2 - 2as
36^2 = 2 × a × 6
1296 = 12a
a = 1296 / 12
a = 108 m/s
The velocity final = 0
The velocity initial = 36 m/s
the velocity average = (36 + 0)/2
Average velocity = 36/2 = 18m/s
the distance the ball rolled = 6m
and the time of the balls roll across the sticky surface will be achieved by using first equation of motion
V = U + at
V = 0
0 = 36 - 108t
108t = 36
t = 36 / 108
t = 0.3 seconds
Write 3.65 x 10^5 in standard notation.
Answer:
365,000Step-by-step explanation:
3.65 ⋅ 10 = 36.5
3.65 ⋅ 100 = 365
3.65 ⋅ 1000 = 3,650
3.65 ⋅ 10000 = 36,500
3.65 ⋅ 100000 = 365,000
There are 5 zeroes on the last one.
This means that 100,000 is 10 to the power of 5.
Hope this helps! <3
What is the sum of -4 1/2 and 10 1/3 show work plz
Answer:
5 5/6
Step-by-step explanation:
Change the mixed numbers to improper fractions, and you get -9/2 + 31/3, which adds up to 35/6, then divide 35 by 6, which changes it back to a mixed number, 5 5/6.
What is the correct equation of the line shown below?
Answer: Y= 3/2x + 3
Step-by-step explanation:
Using the Y =mx+b formula, you count how many units it is going up and that is the numerator. Then you count how many units it's going to the right, and that's the denominator. Then the starting point is (0, 3) so now you plug those in and b is the starting point and the fraction is mx so you are left with the answer y= 3/2x+3
Twenty employees have applied for promotions. This year 7 promotions were awarded. If a random sample of 5 applications was selected.
a. What is the probability that at most 2 employees were promoted?
b. What is the probability that no employees were promoted?
c. Find the value of the expected value and the variance of this distribution.
Answer:
a)0.764
b)0.116
c)Expected value =1.75
Variance=1.1375
Step-by-step explanation:
Total Number of employees = 20
Number of promotions awarded = 7
Probability of success p =[tex]\frac{7}{20}[/tex]
Probability of failure q = [tex]1-\frac{7}{20}=\frac{13}{20}[/tex]
We randomly select 5 applications
a) What is the probability that at most 2 employees were promoted?
We will use binomial
[tex]P(X=x)=^nC_r p^r q ^{n-r}\\P(X\leq 2)=P(X=0)+P(X=1)+P(X=2)\\P(X\leq 2)=^{5}C_0 (\frac{7}{20})^0 (\frac{13}{20})^{5-0}+^{5}C_1 (\frac{7}{20})^1 (\frac{13}{20})^{5-1}+^{5}C_2 (\frac{7}{20})^2 (\frac{13}{20})^{5-2}\\P(X\leq 2)=\frac{5!}{0!(5-0)!} (\frac{7}{20})^0 (\frac{13}{20})^{5-0}+\frac{5!}{1!(5-1)!}(\frac{7}{20})^1 (\frac{13}{20})^{5-1}+\frac{5!}{2!(5-2)!} (\frac{7}{20})^2 (\frac{13}{20})^{5-2}\\P(X\leq 2)=0.764[/tex]
b)What is the probability that no employees were promoted?
[tex]P(X=0)=^{5}C_0 (\frac{7}{20})^0 (\frac{13}{20})^{5-0}\\P(X=0)=\frac{5!}{0!(5-0)!} (\frac{7}{20})^0 (\frac{13}{20})^{5-0}\\P(X=0)=0.116[/tex]
c)
[tex]E(X)=np=5 \times (\frac{7}{20})=1.75\\Var(X)=npq=5 \times (\frac{7}{20}) \times \frac{13}{20}=1.1375[/tex]
Simplify.
5w-4(3x – 2w) + 6x
Answer:
13w-6x
Step-by-step explanation:
HELP ME PLEASE CHOOSING BRAINEST AND IM CRYING AND IM NOT JOKING
Answer:2/3
Step-by-step explanation:
rise over run and the y-intersect is 3
Margaret said the exact product of 602 and 341 is 205,282. Is she correct? Use paper and the standard algorithm to support your reasoning.
Answer:
Yes, she is. The exact product of 602 and 341 is 205,282.
Step-by-step explanation:
To determine the exact product of 602 and 341, both numbers must be multiplied, obtaining the result. To do this, said number can be decomposed, to facilitate the operation and to be able to corroborate the accuracy of the result.
So, we can multiply 602 by 300, plus 602 by 40 and 602 by 1, and add the results.
Therefore, since 602 times 300 is equal to 180,600 (602 x 300 = 180,600); that 602 times 40 is equal to 24,080 (602 x 40 = 24,080); and since 602 times 1 is equal to 602, all those values must be added.
So 180,600 plus 24,080 equals 204,680. And in turn, 204,680 plus 602 equals 205,282. Therefore, the proposed result is correct.
giving brainliest to whoever answers correctly!!
Answer:
<CBD=12 degrees
Step-by-step explanation:
Which of the following is a major benefit of working in the health sciences industry? A. The industry is very small, so you can work with the same people for most of your career. B. Most jobs in the industry are very low stress positions. C. All positions within the industry have extremely high salaries D. There is a big variety in job types, locations, and environments to choose from.
Answer:
The answer is D (There is a big variety in job types, locations, and environments to choose from.)
Answer:D because I just got it right
Step-by-step explanation:
You bought the following items at 20% off. How much did you pay total?
Tent $70, jacket $60, gloves $25, snowboard $350, goggles $30
Answer:
$524.30
Step-by-step explanation:
70+60+25+350+30= 535
535*.02(20%)
10.7
535-10.7=
524.3
Answer:
$107
Step-by-step explanation:
First you have to add up the costs and you get a total of $535
Then you need to make 535 equivalent to 100 then divide by 20 to get 107
Hope that helps and have a great day!
When a variable expression equals the exact same variable expression, what does that tell us about the solution(s)?
There is no solution.
There are 2 solutions.
There are infinitely many solutions.
There is one solution.
The Pappas family has two cats, Zeus and Athena. Together they weigh thirteen pounds. Zeus weighs 5 pounds less than Athena. How much does Athena weigh?
Given:
Combine weight of two cats, Zeus and Athena = 13 pounds
Zeus weighs 5 pounds less than Athena.
To find:
The weight of Athena.
Solution:
Let x pounds be the weight of Athena.
Zeus weighs 5 pounds less than Athena.
Weight of Zeus = x - 5 pounds
Combine weight of two cats, Zeus and Athena = 13 pounds
[tex]x+(x-5)=13[/tex]
[tex]2x-5=13[/tex]
Add 5 on both sides.
[tex]2x=13+5[/tex]
[tex]2x=18[/tex]
Divide both sides by 2.
[tex]x=\dfrac{18}{2}[/tex]
[tex]x=9[/tex]
Therefore, the weight of Athena is 9 pounds.
kori spent $46.20 on 12 gallons of gasoline. What was the price per gallon
Answer:
3.85 because you have to divide 46.20 and 12
Step-by-step explanation:
Jack received $75 for his birthday. He spent 25 on a new baseball glove, $45 on a pair of new shoes, and $5 on digital music.
a
A.what proportion of his birthday money went towards new shoes? Express the value as a simplified fraction period then, convert the fraction to a percent. show you work
B.What proportion of his birthday money went toward music? Express the value as a simplified fraction. Then, convert the fraction to a decimal. Round the decimal to the nearest hundredths or indicate it is repeating. show your work
C. bite the ratio of money Jack spent on music to money Jack spent on shoes. simplify your answer period what is the ratio mean? what fraction is equivalent to the ratio
Answer:
A) Fraction = 3/5, Percentage = 60%
B) Fraction = 1/15 , Decimal = 0.083333 ≈ 0.08
C) Ratio = 1:9, Fraction = 1/9
Step-by-step explanation:
A) The total amount of money Jack received = $75
Jack's spent on shoes = $45
The proportion he spent on shoes
= $45/$75
= 3/5
Converting this fraction to percentage
= 3/5 × 100% = 60%
B.What proportion of his birthday money went toward music?
The total amount of money Jack received = $75
Jack's spent on music = $5
The proportion he spent on music
= $5/$75
= 1/15
Converting this fraction to decimal
= 1/15 = 0.0833333333
It is a repeating decimal.
Approximately to the nearest hundredth = 0.08
C. Write the ratio of money Jack spent on music to money Jack spent on shoes.
The ratio of money spent on music to the ratio of my money spent on shoes
Music : Shoes
$5 : $45
1:9
The fraction that js equivalent to the ratio is 1/9
Please help
6x - 3y < 9
Answer:
y>2x−3
Step-by-step explanation:
:)
How do you reduce the fraction 8 to 25
What is 8.17 round to tenths
Answer:
8.2
Step-by-step explanation:
What is the area of a triangle with vertices at (-3, 3), (2, 3), and (4, 7)?
05 square units
10 square units
20 square units
040 square units
HELP ME PLEASE
Plss help me in this pre algebra question
Answer:
6, 7, and 14 feet.
Step-by-step explanation:
x+2x+x-1=27
4x-1=27
4x=27+1
4x=28
x=7
2x=14
x-1=6
So the three sides, in order, are 6, 7, and 14 feet.
1-3 Function Operations and Composition Jim was given three functions and asked to determine f + (gon). The functions were f (x) = x2 g(x) = 3x + 1, and h(x) = 2x. Jim started by writing the problem as (r + (gon))(x) = x2 + 2(3x + 1). What was Jim's mistake? What is the correct solution? O A Jim omitted the x in h(x): [ + (g = n)) = 7x2 + 2x B. Jim should have added f and g first; ( + (gon)) = 4x2 + 6x + 1 O C. Jim incorrectly performed h og instead of goh: (f + g - h)) = x2 + x + 1. OD D. Jim did not follow the order of operations, I + (g o h)) = x2 + 6x + 2.
Answer:
Step-by-step explanation:
Given the functions:
f (x) = x^2
g(x) = 3x + 1
h(x) = 2x
We are to look for f + (goh)
First we need to get the composite function goh
goh = g(h(x))
g(h(x)) = g(2x)
To get g(2x) we will substitute x in g(x) as 2x as shown below:
Given g(x) = 3x+1
g(2x) = 3(2x)+1
g(2x) = 6x+1
f + goh = x² + (6x +1)
f + goh = x² + 6x +1
Jim wrote goh as 2(3x+1) instead of 3(2x) + 1. The composite function that Jim looked for was hog not goh.
The correct solution is f + goh = x² + 6x +1