Answer:
Step-by-step explanation:
Given the Revenue in dollars modelled by the function R(x) = 60x-0.5x²
Cost in dollars C(x) = 3x+5
Profit function = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 60x-0.5x²-(3x+5)
P(x) = 60x-0.5x²-3x-5
P(x) = -0.5x²+57x-5
The rate of change of total revenue = dR(x)/dt
dR(x)/dt = dR(x)/dx * dx/dt
dR(x)/dx = 60-2(0.5)x²⁻¹
dR(x)/dx = 60-x
Given x = 40 and dr/dx = 15 units per day
dR(x)/dt = (60-x)dx/dt
dR(x)/dt = (60-40)*15
dR(x)/dt = 20*15
dR(x)/dt = 300dollars
Rate of change of revenue = 300dollars
For the rate of change of cost;
dC(x)/dt = dC(x)/dx * dx/dt
dC(x)/dt = 3dx/dt
dC(x)/dt when dx/dt = 15 will give;
dC(x)/dt = 3*15
dC(x)/dt = 45 dollars.
Rate of change of revenue = 45dollars
For the profit;
Profit = Rate of change of revenue - rate of change of cost
Profit made = 300-45
profit made = 255 dollars
What is the correct slope and y-intercept for the following: y=-3x+8
━━━━━━━☆☆━━━━━━━
▹ Answer
Slope = -3
Y-intercept = 8
▹ Step-by-Step Explanation
y = mx + b
mx represents the slope.
b represents the y intercept.
therefore,
y = -3x + 8
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
[tex]\boxed{\mathrm{Slope:}-3 \: \: \: \:\: \mathrm{Y \: intercept:}8}[/tex]
Step-by-step explanation:
The general form of slope-intercept:
[tex]y=mx+b[/tex]
[tex]m:slope\\b:y \: intercept[/tex]
[tex]y=-3x+8[/tex]
[tex]m=-3\\b=8[/tex]
The slope is -3.
The y-intercept is (0, 8) or 8.
Find the 10th term of the following geometric sequence.
2, 10, 50, 250, ...
Answer:
3906250
Step-by-step explanation:
We can notice that the ratio is 5. 10/2 = 5
Each term gets multiplied by 5 to get the next term.
250 × 5 = 1250 (5th term)
1250 × 5 = 6250 (6th term)
6250 × 5 = 31250 (7th term)
31250 × 5 = 156250 (8th term)
156250 × 5 = 781250 (9th term)
781250 × 5 = 3906250 (10th term)
The 10th term of the geometric sequence is 3906250.
Which best describes the meaning of the statement if A then B
Answer:
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
Step-by-step explanation:
You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as "negation of a" or " b" in mathematical terms is written like this
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
You can show that they are logically equivalent because they have the same truth table.
The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t) = -16t^2 + 32t +128. How long will it take the projectile to hit the ground?
Answer:
It takes 4 seconds for the projectile to hit the ground
Step-by-step explanation:
The height of the projectile after t seconds is given by the following equation:
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
How long will it take the projectile to hit the ground?
It happens when [tex]h(t) = 0[/tex]
So
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
[tex]-16t^{2} + 32t + 128 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-16t^{2} + 32t + 128 = 0[/tex]
So [tex]a = -16, b = 32, c = 128[/tex]
[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]
[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]
[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]
Time is a positive measure, so:
It takes 4 seconds for the projectile to hit the ground
This function to calculate the area of a rectangle is not very readable. Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? Tip: a function that calculates the area of a rectangle should probably be called rectangle_area, and if it's receiving base and height, that's what the parameters should be called.
Answer:
Here is the refactored function:
def rectangle_area(base, height):
area = base * height
return area
print("The area is ", rectangle_area(5,6))
Step-by-step explanation:
The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.
print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:
The area is 30
Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.
which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?
Answer:
y = -3.5x² + 2.7x -8.2
Step-by-step explanation:
the quadratic equation is set up as a² + bx + c, so just plug in the values
Answer:
[tex]-3.5x^2 + 2.7x -8.2[/tex]
Step-by-step explanation:
Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].
So, we can use your values of a, b, and c, and plug them into the equation.
A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].
B is 2.7, so the second term is [tex]2.7x[/tex]
And -8.2 is the C, so the third term is [tex]-8.2[/tex]
So we have [tex]-3.5x^2+2.7x-8.2[/tex]
Hope this helped!
Please answer in the form of a number
Answer:
d ≈ 8.3
Step-by-step explanation:
This is kind of like the pythagorean theorem, but with one extra value. Thus, [tex]d^2=l^2+w^2+h^2[/tex].
Plug in the values to get:
[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]
Thus d ≈ 8.3
which is bigger 4 or
[tex] \frac{12}{7} [/tex]
obviously 4 is bigger coz 12/7 will yeild you 1.71
Witch table represents a linear function ?
Answer:
If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.
Remember that the slope between any two points (x1,y1), (x2,y2) is
slope = ( y2 - y1 ) / (x2 - x1)
Step-by-step explanation:
If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.
Remember that the slope between any two points (x1,y1), (x2,y2) is
slope = ( y2 - y1 ) / (x2 - x1)
Find the probability of picking 1 consonant and 4 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles.
Answer:
Ok, we have a total of 26 letters, and we want to select 5 of them.
Of the 26 letters, 21 are consonants and 5 are vowels.
Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.
p = 21/26
now a letter has been selected, so in the set, we have 25 letters left.
In the next 4 selections, we must select vowels.
In the second selection the probability is:
p = 5/25
in the third, the prob is:
p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)
The fourth selection:
p = 3/23
and the last selection:
p = 2/22
The total probability is equal to the product of all the individual proabilities, so we have:
P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)
Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:
P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) = 0.0018
4.5/y = 12.5/4 PLEASE HELP!!! SOS
Answer:
y = 1.44
Step-by-step explanation:
What are you aiming to do here? Please share all instructions with each problem.
If you want to solve 4.5/y = 12.5/4 for y: Multiply both sides by 4y:
18 = 12.5y. Then y = 1.44
how many two third ounce slice of cheese in twenty four ounce package
Answer: 36
Step-by-step explanation:
Simply do 24/(2/3) to get 36 2/3 ounce slices.
Hope it helps <3
PLEASE HELP
Divide. Write your answer using the smallest numbers possible. 47 pounds 13 ounces divided by 15 = ___pounds ___ounces
Answer:
3 pounds
51 ounces
Step-by-step explanation:
Solve for y in terms of x.
IN
2
y - 4 = x
Oy= = x + 6
Oy
y = -x + 4
Oy
y = -x + 6
O
y =
X+ 4
Answer:
[tex]\boxed{\mathrm{Option \ 4}}[/tex]
Step-by-step explanation:
Given that
[tex]y-4 = x[/tex]
Adding 4 to both sides
[tex]y-4+4 = x+4\\[/tex]
[tex]y = x+4[/tex]
BRAINLIEST ANSWER GIVEN Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. The length of a rectangle is 2 feet longer than the width. The perimeter is 20 feet. Find the dimensions of the rectangle. Length= ?; width=?
Answer:
length = 6 feetwidth = 4 feetStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
The length of the rectangle is 2 feet longer than the width is written as
l = 2 + w
Perimeter = 20feet
So we have
20 = 2( 2 + w ) + 2w
20 = 4 + 2w + 2w
4w = 16
Divide both sides by 4
w = 4
Substitute w = 4 into l = 2 + w
That's
l = 2 + 4
l = 6
length = 6 feetwidth = 4 feetHope this helps you
Answer:
w = 4 and L = 10
Step-by-step explanation:
perimeter of a rectangle = 2(l+w)
p = 20
L = 2 + w
w = ?
20 = 2(2 + w + w)
20 = 2(2 + 2w)
20/2 = 2 + 2w
10 = 2 + 2w
10 - 2 = 2w
8 = 2w
w = 8/2 = 4
L = w + 2
L = 4 +2 = 6
w = 4 and L = 10
What is the next number in the series: 4, 5, 9, 25, 89, ___
Answer:
345
Step-by-step explanation:
1 + 4 = 5
4 + 5 = 9
16 + 9 = 25
64 + 25 = 89
1, 4, 16, and 64 are powers of 4. The next power of 4 is 256.
256 + 89 = 345
The answer is 345 (don’t ask why)
Dunno these answers
Answer:
its 9
Step-by-step explanation:
Answer:
c. 9i.
Step-by-step explanation:
[tex]\sqrt{-81}[/tex]
= [tex]\sqrt{-1 * 9 * 9}[/tex]
= [tex]\sqrt{-1 * 9^2}[/tex]
= [tex]9\sqrt{-1}[/tex]
The square root of -1 is the same thing as i.
= [tex]9i[/tex]
So, your answer is C.
Hope this helps!
If four times the brother's age is subtracted from three times the sister's age, the difference is 17. Give an equation that represents this statement using bbb as the age of the brother and s as the age of the sister.
Answer:
3s-4bbb=17
Step-by-step explanation:
brother=4bbb
sister=3s
3s-4bbb=17
what is the slop of y= -5+4x
Hey there! :)
Answer:
m = 4.
Step-by-step explanation:
We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)
Where 'm' is the slope and 'b' is the y-intercept. Therefore:
y = -5 + 4x becomes y = 4x - 5
The 'm' value is equivalent to 4, so the slope of the equation is 4.
Answer:
4
Step-by-step explanation:
because of y= mx + b where m is the slope
m= 4 in the equation
What is the equation of the line perpendicular to y=5x-3 that passes through the point (3, 5)?
Answer:
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]
Step-by-step explanation:
Hey there!
Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.
Look at the image below ↓
By looking at the image we can conclude that the equation for the perpendicular line is,
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].
Hope this helps :)
Answer:
[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]
Step-by-step explanation:
Part 1: Finding the new slope of the line
Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.
Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].
Part 2: Using point-slope formula and solving in slope-intercept form
Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].
Then, use the point-slope equation to get b, or the y-intercept of the equation.
[tex](y-y_{1})=m(x-x_{1})[/tex]
[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]
4, 12, 36,what is 3 other remaining sequence
Answer:
108, 324, 972
Step-by-step explanation:
This sequence is multiplying by ✖️3.
4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972
Hope this helps!
if -2x = -14 what is the value of x
Answer: x= 7
Step-by-step explanation:
-2x= -14 Divide both sides by -2
x= 7
check
-2(7) = -14
-14 = -14
Answer:
x = 7
Step-by-step explanation:
-2x = -14
Divide each side by -2
-2x/-2 = -14/-2
x = 7
The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answer:
[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
Step-by-step explanation:
[tex]Volume = Base \ Area\ * Height[/tex]
[tex]Height = \frac{Volume}{Base \ Area}[/tex]
Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]
Putting in the formula
[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]
Doing long division, we get
[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
This is the simplifies form and it can't be further simplified.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
find the maximal area of a right triangle with hypotenuse of length 8
Answer:
Max area is 16
Step-by-step explanation:
If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.
So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.
The maximal area of a right triangle is 90.496
What is differentiation?Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given:
let the perpendicular be 'x'
and base be 'y'
Using Pythagoras theorem
x² + y² = 8²
x² + y² = 64
y²= 64- x²
y = √64-x²
Now, Area of triangle
= 1/2* base* height
=xy/2
=x *√64-x²*1/2
On differentiating both side
A' = 64-2x²/√64-x²*1/2
Setting derivative function equal to zero,
64= 2x²
32=x²
x=5.656
So, Area of triangle = x *√64-x²*1/2
= 90.496
Learn more about differentiation here:
https://brainly.com/question/24898810
#SPJ2
Applications of exponential functions
Answer:
a simple interest rate of 4.5%
You are mandated to pick 45 units per hour. You work 8.5 hours a day (minus a 1/2 hour lunch), Monday to Friday. How many units should you be picking each week?
Answer:
1912.5 unitsStep-by-step explanation:
Firstly let us calculate the amount of hours you will have to work in a week.
Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.
Hence in a week you will work 8.5*5= 42.5 hours in a week
Since in 1 hours you are mandated to pick 45 units
Hence in 42.5 hours you will pick 42.5*45= 1912.5 units
PLEASE HELP ME UNDERSTAND!! ok, when i looked at other people converting sin, cos, tan, i realized this; cos(x) = y/z z = y cos(x) which is weird. why would you multiply cos by y instead of dividing cos by y?
Answer:
the real deal is that you mistook if
cos(x)=y/z gives y=zcos(x)
A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.
(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.
Answer:
Step-by-step explanation:
From the information given:
mean life span of a brand of automobile = 35,000
standard deviation of a brand of automobile = 2250 miles.
the z-score that corresponds to each life span are as follows.
the standard z- score formula is:
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
For x = 34000
[tex]z = \dfrac{34000 - 35000}{2250}[/tex]
[tex]z = \dfrac{-1000}{2250}[/tex]
z = −0.4444
For x = 37000
[tex]z = \dfrac{37000 - 35000}{2250}[/tex]
[tex]z = \dfrac{2000}{2250}[/tex]
z = 0.8889
For x = 3000
[tex]z = \dfrac{30000 - 35000}{2250}[/tex]
[tex]z = \dfrac{-5000}{2250}[/tex]
z = -2.222
From the above z- score that corresponds to their life span; it is glaring that the tire with the life span 30,000 miles has an unusually short life span.
For x = 30,500
[tex]z = \dfrac{30500 - 35000}{2250}[/tex]
[tex]z = \dfrac{-4500}{2250}[/tex]
z = -2
P(z) = P(-2)
Using excel function (=NORMDIST -2)
P(z) = 0.022750132
P(z) = 2.28th percentile
For x = 37250
[tex]z = \dfrac{37250 - 35000}{2250}[/tex]
[tex]z = \dfrac{2250}{2250}[/tex]
z = 1
Using excel function (=NORMDIST 1)
P(z) = 0.841344746
P(z) = 84.14th percentile
For x = 35000
[tex]z = \dfrac{35000- 35000}{2250}[/tex]
[tex]z = \dfrac{0}{2250}[/tex]
z = 0
Using excel function (=NORMDIST 0)
P(z) = 0.5
P(z) = 50th percentile
a. The z score of each life span should be -0.4444, 0.889, and 2.2222.
b. The percentile of each life span should be 0.0228, 0.8413 and 0.5000.
Given that,
mean life span of 35,000 miles, with a standard deviation of 2250 miles.The calculation is as follows:(a)
The z score should be
[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]
The tire with life span of 30000 miles would be considered unusual
(b)
The percentile should be
[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]
p(Z1 < -2) = NORMSDIST(-2) = 0.0228
[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]
p(Z2 < 1) = NORMSDIST(1) = 0.8413
[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]
p(Z3 < 0) = NORMSDIST(0) = 0.5000
Find out more information about standard deviation here:
https://brainly.com/question/12402189?referrer=searchResults
please please
please
please help
me. i am desperate
Answer:The answer is c
Step-by-step explanation:
WHY CAN'T ANYONE HELP ME: ( Two computer disks and three notebooks cost $29. However, five computer disks and four notebooks cost $48. Find the price of each.
Answer:
Disks = $4 each and Notebooks = $7 each
Step-by-step explanation:
-4(2D + 3N = 29)
3(5D + 4N = 48)
-8D - 12N = -116
15D + 12N = 144
7D = 28
D = $4
2(4) + 3N = 29
8 + 3N = 29
3N = 21
N = $7