Answer:
a) $675000
b) $289000 profit,3300 set, $190 per set
c) 3225 set, $272687.5 profit, $192.5 per set
Step-by-step explanation:
a) Revenue R(x) = xp(x) = x(300 - x/30) = 300x - x²/30
The maximum revenue is at R'(x) =0
R'(x) = 300 - 2x/30 = 300 - x/15
But we need to compute R'(x) = 0:
300 - x/15 = 0
x/15 = 300
x = 4500
Also the second derivative of R(x) is given as:
R"(x) = -1/15 < 0 This means that the maximum revenue is at x = 4500. Hence:
R(4500) = 300 (4500) - (4500)²/30 = $675000
B) Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 80x) = -x²/30 + 300x - 80x - 74000
P(x) = -x²/30 + 220x - 74000
The maximum revenue is at P'(x) =0
P'(x) = - 2x/30 + 220= -x/15 + 220
But we need to compute P'(x) = 0:
-x/15 + 220 = 0
x/15 = 220
x = 3300
Also the second derivative of P(x) is given as:
P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3300. Hence:
P(3300) = -(3300)²/30 + 220(3300) - 74000 = $289000
The price for each set is:
p(3300) = 300 -3300/30 = $190 per set
c) The new cost is:
C(x) = 74000 + 80x + 5x = 74000 + 85x
Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 85x) = -x²/30 + 300x - 85x - 74000
P(x) = -x²/30 + 215x - 74000
The maximum revenue is at P'(x) =0
P'(x) = - 2x/30 + 215= -x/15 + 215
But we need to compute P'(x) = 0:
-x/15 + 215 = 0
x/15 = 215
x = 3225
Also the second derivative of P(x) is given as:
P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3225. Hence:
P(3225) = -(3225)²/30 + 215(3225) - 74000 = $272687.5
The money to be charge for each set is:
p(x) = 300 - 3225/30 = $192.5 per set
When taxed $5, the maximum profit is $272687.5
Answer:
b) $289000 profit,3300 set, $190 per set
At a sporting goods store, Franklin tennis racquets normally sell for $110, but this week
they're selling for less than their normal price, How much has the price on each
d'acquet been lowered?
The park wanted to put up a new 500 foot fence around the rectangular playground. The length of the fence is going to be 100 foot. what will be the with of the fence?
Answer:
150 feet
Step-by-step explanation:
A rectangle has 2 pairs of equal sides.
One of the sides is 100 feet, meaning another side is 100 feet.
If we subtract 200 feet we are left with 300, which are the last two sides.
Divide 300 by 2 to get each side length.
150 feet
Ben can type 25 words in half a minute at the rate how many words can he type in 5 minutes
Answer: 250 words in 5 minutes
Step-by-step explanation:
20 POINTSS!! Choose the fraction(s) equivalent to the given fraction. -1/7 Select all that apply A. -1/7 B. 1/-7 C. 1/7 D. -1/-7
Answer:
A and B.
Step-by-step explanation:
So we want to select the fractions that equal -1/7.
Let's go through each of the answer choices.
A)
A is -1/7, the exact same.
A is correct.
B)
B is 1/-7.
We can move the negative to the top.
So, 1/-7 is equivalent to -1/7.
B is also correct.
C)
C is 1/7
There are no negatives whatsoever.
C is not correct.
D)
We have -1/-7.
Again, move the negative to the top. We will have:
-(-1)/7
The two negatives cancel:
=1/7.
So, D is not correct.
Our answers are A and B.
in abc the measure of side c is 3.9cm if def has a dilation of abc with a scale factor of 2.5
Complete Question:
In ABC, the measure of sides c is 3.9 cm If DEF is a dilation ABC with a scale factor of 2.5 what is the measure of side f
Answer:
f = 9.75
Step-by-step Explanation:
From the information given, a sketch of ∆ABC and ∆DEF with their corresponding sides and angles have been attached below.
∆DEF is a dilation of ∆ABC, which is said to be on a scale factor of 2.5.
The scale factor is a whole number, this implies that ∆DEF is an enlargement of ∆ABC.
Since side c = 3.9 cm, in ∆ABC corresponds to side f, in ∆DEF, therefore, the measure of f would be:
f = measure of c × scale factor
f = 3.9 cm × 2.5
f = 9.75
There are 180 girls in a mixed school. if the ratio of girls to Boyd is 4:3,find the total number of students in the school.
Step 1) Set up a proportion
180 girls / x boys = 4 girls / 3 boys
540 = 4x
x = 135 boys
Step 2) Add the number of boys and girls together
180 + 135 = 315
Answer: 315 total students
A solid sphere is cut into 10 equal wedges. The volume of each wedge is Solve the formula for r. 15 O Ar= V2 O B. r = 151 O c. r= 15V (27) O D. r= 15V - 27
Answer:
A. r = ∛ 15V / 2π
Step-by-step explanation:
Volume of a sphere = 4/3 π r³
And to be divided into 10 equal wedges parts.
Volume of each wedge = V = 2/15 π r³
find r
V = 2 π r³ / 15
15 V = 2 π r³
15V / 2π = r³
r = ∛ 15V / 2π
The correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]
It is given that a solid sphere is cut into 10 equal wedges , with each wedge having volume V = [tex]\frac{2}{15} \pi r^{3}[/tex]
We have to solve it to get the value of radius r.
What is the formula for volume of sphere ?
The volume of sphere is given by V = [tex]\frac{4}{3} \pi r^{3}[/tex] where , r is the radius of the sphere.
As per the question ;
Volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
To be divided into 10 equal wedges ;
Volume of each wedge of sphere will be ;
V = [tex]\frac{2}{15} \pi r^{3}[/tex]
15 V = 2[tex]\pi r^{3}[/tex]
or
r³ = [tex]\frac{15V}{2\pi }[/tex]
or
r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]
Thus , the correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]
To learn more about volume of sphere click here ;
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Find an equation of the line passing through the points (−8,2) with the slope m= 4/3
Answer:
[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]
Step-by-step explanation:
So we want to find an equation of a line passing through (-8,2) with a slope of 4/3.
To do so, we can use the point-slope form. This is:
[tex]y-y_1=m(x-x_1)[/tex]
So, substitute (-8,2) for x₁ and y₁, and let m be 4/3:
[tex]y-2=\frac{4}{3}(x+8)[/tex]
Distribute the right:
[tex]y-2=\frac{4}{3}x+\frac{32}{3}[/tex]
Add 2 to both sides. Note that 2 can be written as 6/3. Thus:
[tex]y=\frac{4}{3}x+\frac{32}{3}+\frac{6}{3}[/tex]
Simplify:
[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]
And this is our equation :)
simplify the algebraic expression 3xy+5x+2+3y+x+4
Answer:
3xy+6x+3y+6
Step-by-step explanation:
You just need to combine like terms.
5x and x are like terms so you can add them to 6x.
2 and 4 are like terms so you can add them to 6
Let
f(x) =
7x − 5, x ≤ −5
−x2, x > −5
.
Find
f(−1), f(−5), and f(−6)
Answer:
EZ
Step-by-step explanation:
EZ
PLEASE HELP !
Expand the following numbers ;
1.) 1.23 x 10^0
2.) 1.54 x 10^4
3.) 2.5 x 10^-3
4.) 5.67 x 10^-1
5.) 1.00 x 10^8
6.) 1.00 x 10^-8
Answer:
1. 1.23
2. 15400
3. 0.0025
4. 0.567
5. 100000000
6. 0.00000001
Step-by-step explanation:
you just move the decimal point left for negative and right for positive
Find the value of x in the equation below. 2x+8/6=1/3(x+4) A. x = 0 B. no real solutions C. infinitely many solutions D. x = 1
Answer:
x = 0
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x+8/6-(1/3*(x+4))=0
Simplify 1/3
Equation at the end of step 1 :
(2x + 8/6) - (1/3 * (x + 4)) = 0
STEP 2 :
Equation at the end of step 2
(2x + 8/6) - (x+4)/3 = 0
STEP 3 :
Simplify 4/3
Equation at the end of step 3 :
(2x + 4/3) - (x+4)/3 = 0
STEP 4 :
Rewriting the whole as an Equivalent Fraction
Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2x = 2x/1 = 2x*3/3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x * 3 + 4/3 = 6x+4/3
Equation at the end of step 4 :
(6x+4)/3 - (x+4)/3 = 0
STEP 5 : Pulling out like terms
Pull out like factors :
6x + 4 = 2*(3x + 2)
Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2*(3x+2)-((x+4))/3 = 5x/3
Equation at the end of step 5 :
5x/3 = 0
STEP 6: When a fraction equals zero
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, multiply both sides of the equation by the denominator.
Here's how:
5x/3*3 = 0*3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5x = 0
Solving a Single Variable Equation:
Solve : 5x = 0
Divide both sides of the equation by 5:
x = 0
Round 7/12 to the nearest hundredth
Answer:
7.00
Step-by-step explanation:
so you have to round to the narest 0.01 the easy way to do it is round to the hundreth place. And you will get your answer which is 7.00
What’s 2 1/6 - 1 5/6?
Answer:
2/6 or 1/3
Step-by-step explanation:
1 and 2/3 plus 3 and 3/4
2 and 1/5 plus 3 and 7/8
4 and 1/2 plus 2 5/7
3/4 plus 2/3 plus 1/5
anyone?
URGENT
75 points!!
Answer:
Step-by-step explanation:
1 2/3 + 3 3/4 = 1 8/12 + 3 9/12 = 4 17/12 = 5 5/12
4 1/2 + 2 5/7 = 4 7/14 + 2 10/14 = 6 17/14 = 7 3/14
3/4 + 2/3 + 1/5 = 45/60 + 40/60 + 12/60 = 97/60 = 1 37/60
Answer:
Step-by-step explanation:
boom = 1 37/60
for stella’s lemonade recipe, 18 lemons are required to make 15 cups of lemonade. at what rate are lemons being used in cups of lemonade per lemon? express your answer in simplest form.
Answer:
5/6 cups/lemon
Step-by-step explanation:
(15 cups)/(18 lemons) = (15/18) cups/lemon = 5/6 cups/lemon
for what values of x will 4^x be greater than 1 ?
Answer:
x>0
Step-by-step explanation:
We want to solve for x in the inequality:
4^x > 1
ln(4^x)=xln(4) > ln(1)=0
x > 0/ln(4) =0
x>0
So for any value of x greater than 0, you will have 4^x be greater than 1.
Pleaseeeeeeee helpppp
Answer:
point G
Step-by-step explanation:
Find the referenced points on the diagram and notice the lines between them. The point at the intersection of those lines is what is wanted.
It is point G.
Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π. Need this ASAP
Answer:
22 square feet
Step-by-step explanation:
Area of shaded region = Area of square - Area of circle. The diameter of the circle is also the length of the side of the square as the circumference of the circle is on the circumference of the square.
Area of circle = 3.14 × r × r
r = 10 ÷ 2
= 5
Area of circle = 3.14 × 5 × 5
= 78.5
Area of square = length × length
Area of square = 10 × 10
= 100
Area of shaded region = Square - Circle
= 100 - 78.5
= 21.5
= 22 (to the nearest square foot)
I hope this helps :)
The sum of the sequence of 685+678+671+664+...+6
Answer:
Sum of the sequence (Sn) = 33,859
Step-by-step explanation:
Given:
Sequence = 685+678+671+664+...+6
Find:
Sum of the sequence (Sn)
Computation:
a = 685
d = 678 - 985 = -7
an = 6
an = a+(n-1)d
6 = 685+(n-1)(-7)
-679 = (n-1)(-7)
97 = n-1
n = 98
So,
Sum of the sequence (Sn) = (n/2)[a+an]
Sum of the sequence (Sn) = (98/2)[685+6]
Sum of the sequence (Sn) = (49)(691)
Sum of the sequence (Sn) = 33,859
6x- 10=-8+3x
Solve the linear equation.
Answer:
x =2/3Step-by-step explanation:
[tex]6x-10=-8+3x\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\6x-10+10=-8+3x+10\\\\\mathrm{Simplify}\\6x=3x+2\\\\\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}\\6x-3x=3x+2-3x\\\\Simplify\\3x=2\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{2}{3}\\\\Simplify\\x=\frac{2}{3}[/tex]
Answer:
x = 2/3
Step-by-step explanation:
This equation can be solved by using conventional algebraic techniques.
We firstly want to make sure to get our constants on one side of the equation and then get our variables on the other.
6x - 10 = -8 + 3x Subtract 3x from both sides of the equation.
3x - 10 = -8 Add 10 to both sides of the equation.
3x = 2 Divide by 3 on both sides of the equation.
x = 2/3
Then, you can voluntarily check your answer.
6(2/3) - 10 = -8 + 3(2/3)
4 - 10 = -8 + 2
-6 = -6
What is the answer rounded to the nearest whole number
HELP!!!!!!!!!! AP CALCULUS AB
Answer:
[tex]\lim_{x \to 5^{-}} f(x)= 54[/tex]
[tex]\lim_{x \to 5^{+}} f(x) = -17[/tex]
Step-by-step explanation:
+ means we are approaching from the right
- means we are approaching from the left
We are given that if x < 5, it is x² + 5x + 4
So to find [tex]\lim_{x \to 5^{-}} f(x)[/tex] we would plug in 5 into that piecewise function part:
5² + 5(5) + 4 = 54
We would be approaching y = 54 if we approach from the left.
We are given that x > 5, it is -4x + 3
So to find [tex]\lim_{x \to 5^{+}} f(x)[/tex] we would plug in 5 into that piecewise function part:
-4(5) + 3 = -17
We would approach y = -17 if we approached from the right.
Answer:
[tex]\lim_{x \to 5^-}f(x)=54\\\lim_{x \to 5^+}f(x)=-17[/tex]
Step-by-step explanation:
So, we have the function:
[tex]f(x)=x^2+5x+4,x<5\\f(x)=8,x=5\\f(x)=-4x+3,\text{ otherwise}[/tex]
And we want to show that this has a jump discontinuity.
As directed, calculate the limit at x=5 from the left and from the right. Thus:
[tex]\lim_{x \to 5^-}f(x)[/tex]
To calculate this, since we're coming from the left, x is less than 5. So, use the first equation:
[tex]\lim_{x \to 5^-}f(x)\\= \lim_{x \to 5^-}(x^2+5x+4)\\[/tex]
Use direct substitution:
[tex]=(5)^2+5(5)+4\\=25+25+4\\=54[/tex]
Thus, as the limit approaches f(5) from the left, the function approaches 54.
Now, calculate the limit at x=5 from the right. Since we're coming from the right, use the third equation:
[tex]\lim_{x \to 5^+}f(x)\\= \lim_{x \to 5^+}(-4x+3)[/tex]
Direct substitution:
[tex](-4(5)+3)\\=-20+3\\=-17[/tex]
Thus, as the limit approaches f(5) from the right, the function approaches -17.
As you can picture, there's a huge gap between y=54 and y=-17. The limits are not equal and both of the limits do exist. Thus, we have jump discontinuity.
Help it’s not b what is the answer plz help
Answer:
c
Step-by-step explanation:
Please see attached picture for full solution.
a company has $25,000 in cash. next month the company anticipates sales revenue of $10,000, equiptment expense of $2,500, insurance costs of $100, and $200 in licensing fees. what is the projected cash flow at the end of the month?
Answer:o
Step-by-step explanation:
No sé cómo hacerlo. Y me gustaría que me ayudaran con él proceso?
Answer:
BC=11
Step-by-step explanation:
we need to find BC
and we know that
AB= x+2
AC=13
BC=2x+11
A, B and C are collinear
that means that
AB+BC=AC
x+2+2x+11=13
3x+13=13
3x=0
x=0
so BC=2(0)+11
BC=11
please assist me with this problem: part 10
Answer:
c
Step-by-step explanation:
Given
sinN = [tex]\frac{a}{b}[/tex] ( multiply both sides by b ) , then
a = bsinN → (a)
And
sinM = [tex]\frac{a}{y}[/tex] ( multiply both sides by y ), then
a = ysinM → (b)
Thus a is both (a) and (b)
Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why?
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs 38 12
Subject Is Not a drug user 19 29
Answer:
0.193877
Step-by-step explanation:
The data given to us is
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs: 38 12
Subject Is Not a drug user: 19 29
Now the total of this is = 38+19+12+29= 98
Now the probability of false positive is = 19/98= 0.193877
The Subject Is Not a drug user would suffer from a false positive. He is not a user and has a positive result.
Two pieces of fabric
are 143/4 inches and
207/8 inches long. To
form a single piece in
length, 3/8 inch of
each masonry piece
was sewn together to
create a seam. What
is the final length of
the fabric after the
two pieces are sewn?
Answer:
487/8 inchesStep-by-step explanation:
[tex]\left(\dfrac{143}{4}-\dfrac38\right)+\left(\dfrac{207}{8}-\dfrac38\right)=\dfrac{286}{8}-\dfrac38+\dfrac{204}{8}=\dfrac{283}{8}+\dfrac{204}{8}=\dfrac{487}{8}[/tex]
7) A jet travels 440 miles in 2 hours. At this rate, how far could the jet Hy
12 hours? What is the rate of speed of the jet?
Answer:
2,640 miles in 12 hours.
Step-by-step explanation:
440/2=220mph
220*12 hours=2,640
rate of speed=220pmh