Answers
Part (a)
[tex]\int\limits^6_0 {f(x)} \, dx =\int\limits^3_0 {f(x)} \, dx +\int\limits^6_3 {f(x)} \, dx =8+(-7) = 1[/tex]
Part (b)
[tex]\int\limits^3_6 {f(x)} \, dx =-\int\limits^6_3 {f(x)} \, dx =-(-7) = 7\\[/tex]
Part (c)
[tex]\int\limits^3_3 {f(x)} \, dx =0[/tex]
Part (d)
[tex]\int\limits^6_3 {-5f(x)} \, dx =-5* \int\limits^6_3 {f(x)} \, dx=-5 * -7 =35[/tex]
Hope that helps!
Related Questions
You are mixing two kinds of candy to make 10 pounds of a mixture worth $5.50 per pound. One kind is $6 per pound and the other is $4 per pound. How many pounds of each should you use? Show all your work.
Answers
Answer:
5.60 pounds each
Step-by-step explanation:
This is the dry mixture problem.
Let x = the number of pounds of the first type of candy
Therefore, number of pounds of second type of candy = 10-x
Value of first candy + value of second candy = value of mixture
Value of any candy = cost per pound of candy * weight of candy
Thus:
4x + 6(10 - x) = 5.60(10)
4x + 60 - 6x = 56
-2x + 60 = 56
-2x = -4
x = -4/-2
x = 2
Therefore, the number of pounds of first type of candy = 2 pounds
The number of pounds of second type of candy = 10 - 2 = 8 pounds
Check
$4(2) + $6(8) =
8 + 48 = $5.60(10)
$56 = $56
Gotten two different answers…is it 18 or 55
Answers
Answer:
18.2%
Step-by-step explanation:
For this, you want to take the amount of 70 year old men that will die in the next 10 years and divide it by the total amount of men.
The table states "number out of 1,000 men" so this means there are 1000 total men in this study.
So:
182/1000 = 0.182 = 18.2%
Suppose that the volume of a right circular cylinder is 500 A cubic
centimeters and the radius of its base is 5 centimeters. What is the
height of the cylinder?
Answers
The height of the right circular cylinder with volume of 500π cubic centimetre and radius of 5 centimetre is 20 cm.
Volume of a cylindervolume = πr²h
where
r = radiush = heightTherefore,
volume = 500π cm³
r = 5 cm
Therefore,
volume of the cylinder = πr²h
500π = 5²πh
500π = 25πh
divide both sides by 25π
500π / 25π = 25πh / 25π
h = 20 cm
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Answer:
A) 20 cm
Step-by-step explanation:
If 15 percent of cars are blue and an observer's observation is 80 percent accurate, what is the probability that a car is, in fact, blue when the witness reports it as blue
Answers
The probability that a car is blue is the likelihood of the car being blue
The probability that a car is, in fact, blue when the witness reports it as blue is 12%
How to determine the probability?The given parameters are:
P(Blue) = 15%
P(Accurate) = 80%
The probability that a car is blue, and the observation is accurate is calculated as:
P(Blue and Accurate) = P(Blue) * P(Accurate)
This gives
P(Blue and Accurate) = 15% * 80%
Evaluate the product
P(Blue and Accurate) = 12%
Hence, the probability that a car is, in fact, blue when the witness reports it as blue is 12%
Read more about probability at:
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Sandra makes and sells bracelets. It costs her $2 to make each bracelet, plus a one-time cost of $15 for supplies. She plans to sell each bracelet for $5. Let x represent the number of bracelets. Which equation can be used to find the number of bracelets she needs to sell to break even?
2 x minus 5 x = 15
2 x + 5 x = 15
2 x + 15 = 5 x
5 x + 15 = 2 x
Answers
The number of animal in a park increase by 60% every month. By the end on December the number of animals is 2560, how many animals would have been there by the end of November?
Answers
Answer:
1,600
Step-by-step explanation:
I did a bit of guessing becuase I don't know the exact way to reverse the formula, but here is what I did!
I guessed around 1,550 at first, but it was too low. I kept increasing the base number until I reached 1,600, and came to the conclusion by doing the equation;
1,600(0.6)=960
Then, since it increases each month by 60% of the previous month's value, you do
1,600+960=2,560
Zoey purchased a new car in 1992 for $28,000. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $9,600 in the year 1996, then what would be the predicted value of the car in the year 1998, to the nearest dollar?
Answers
Answer:
V = V0 e^-k t where V is the value of the car and t the time in years
ln (V/V0) = - k t
k = -1/4 ln (96/280) = .268
V = V0 e^-k t = 28000 e^-.268 * 6 = 28000 e^-1.606 = $5621
1
6
of the fruits at a warehouse were apples and the remaining fruits were oranges. There were 291 more red apples than green apples and there were 3455 oranges in the warehouse. How many red apples were there?
Answers
Answer:
491 red apples
Step-by-step explanation:
1/6 are apples
then 5/6 are oranges
red apples = green apples + 291
there are 3455 oranges
total amount of fruits is :
3455 / (5/6) = (3455 x 6)/5 = 4146
4146 - 3455 = 691 apples ( total )
so red + green = 691
and red - green = 291
add the two equations
red + red + green - green = 691 + 291
2red = 982
red = 982 / 2 = 491 red apples
green = 691 - 491 = 200 green apples
so red is 291 more than green
then red = 491
I need step by step written answer for this
Answers
Answer:
-1/2
Step-by-step explanation:
2/5 * - 3/7 - 1/14 - 3/7 * 3/5
= - 6/35 - 1/14 - 9/35
= - (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)
= - 12/70 - 5/70 - 18/70
= (-12 - 5 - 18)/70
=- 35/70
= - 1/2
- 6/35 - 1/14 - 9/35
- (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)
- 12/70 - 5/70 - 18/70
= (-12 - 5 - 18) /70
=- 35/70
- 1/2
The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.
Answers
Answer:
9.852
Step-by-step explanation:
First, Graph all three functions and find where they intersect and the shape that they make through their intersection. Note that since the shape does not touch the y= -1 line, we will use the "washer" method (where the volume equals [tex]\pi\int\limits^a_b {R(x)\x^{2} - r(x)^{2} } \, dx[/tex].
The next step is to find a and b. Since the function that the area is going to be rotated about is a " y =" equations, the boundaries will be the x coordinates where the three functions intersect, b=1 for (1,1) and a=3 for (3,1).
Next we have to find R(x) and r(x). In this case, R(x) is the difference between the function furthest away from the axis of rotation and the function of the axis of rotation (or visa versa depending on which is on top), and r(x) is the difference between the function closest to the axis of rotation and the function of the axis of rotation (or visa versa depending on which is on top.
For this problem R(x) = 1 - (-1) and r(x) = 1/x - (-1) since when you look at the graph, Y = 1 is further from y = -1 than y = 1/x is, and both functions are on top of y = -1.
Finally plug in R(x) and r(x) and solve either using a calculator or through integration. If you solve through integration you should get [tex]\pi (-2ln(3) + \frac{16}{3} )[/tex].
Find the numbers whose difference is five and whose product is 266
Answers
Answer: 19 and 14
Step-by-step explanation:
19-14 = 5
19x14 =266
Tim will buy a pair of shoes that cost $120.He received a 35% discount coupon. Luckily his friend Mario gets an additional 15% discount being an employee of the store. If Mario buys the shoes for Tim, how much will Mario pay if the tax is 8%? Round your answer to the nearest centavo
Answers
Answer: 55.20$
Step-by-step explanation:
1. Add up 35% with the 15% since Mario is paying for it
2. Multiply 120(the cost without any discount/tax) with the new discount percentage
3. Now with the answer from multiplying subtract it from 120.
4. With the answer, multiply the tax percentage(0.08)
5. Now add It to the discounted price.
6. Round it to the nearest hundredth
R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.
Answers
Answer:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Step-by-step explanation:
If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.
[tex]\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)[/tex]
[tex]\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)[/tex]
[tex]\sf =(-2, 2)[/tex]
Equation of a circle: [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the center and r is the radius)
Substituting found center (-2, 2) into the equation of a circle:
[tex]\sf \implies (x-(-2))^2+(y-2)^2=r^2[/tex]
[tex]\sf \implies (x+2)^2+(y-2)^2=r^2[/tex]
To find [tex]\sf r^2[/tex], simply substitute one of the points into the equation and solve:
[tex]\sf \implies (-3+2)^2+(1-2)^2=r^2[/tex]
[tex]\sf \implies 1+1=r^2[/tex]
[tex]\sf \implies r^2=2[/tex]
Therefore, the equation of the circle is:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Find the value of the expression 1/2x+3 if x=12
Answers
Answer:
The answer is 9.
Step-by-step explanation:
1/2 * 12 = 6
6+3=9
Answer:
9
Step-by-step explanation:
x = 12
1/2 · 12 = 6
6 + 3 = 9
5/6 of a number is 65.
Find the number.
Answers
Answer:
78 is the number
Step-by-step explanation:
(65*6)÷5 = 78.
5/6 of a number is 65.
And the number is 78.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A phrase: 5/6 of a number is 65.
To find the number:
Let the number be n.
Applying multiplication operation,
5/6 of n is 65.
(5/6)n = 65.
Applying cross multiplication,
n = 65 x 6/5
n = 390/5
n = 78.
Therefore, the number is 78.
To learn more about multiplication;
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The length of a rectangle is 3 inches more than it’s width.If the perimeter is 42 inches,find the dimensions of the rectangle.
Answers
Answer: Length = 9 in
Width = 12 in
Step-by-step explanation:
Length L = 3 + W
Perimeter P = 42 in
Perimeter = 2L + 2W
plugin values:
42 = 2(3 + W) + 2W
42 = 6 + 2W + 2W
42-6 = 4W
W = 36 / 4
W = 9
solve L by substituting the value of W=9 into the equation:
L = 3 + W
L = 3 + 9
L = 12
therefore, the dimensions of the rectangle:
Length = 9 in
Width = 12 in
Answer:
Answer:
length = 9 in
width = 12 in
Step-by-step explanation:
You have to use the formula for the perimeter of a rectangle
P=2(l+w)
Need help with his geometry question. Find the value of x
Answers
Answer:
Step-by-step explanation:
Vani has a collection of vintage action figures that is worth $140. If the collection
appreciates at a rate of 15% per year, which equation represents the value of the
collection after 2 years?
OV = 140(0.85)
Submit Answer
O V = 140(0.15)
V = 140(1 - 0.15)2
V = 140(1 + 0.15)?
Answers
The equation represents the value of the collection after 2 years is V = 140(1 + 0.15)^2.
What equation represents the value of the collection?
When the value of an asset appreciates,it means that the price of the item increases with the passage of time.
The formula for calculating future value with appreciation is:
FV = P (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of yearsV = 140(1 + 0.15)^2.
To learn more about future value, please check: https://brainly.com/question/18760477
Answer:
Step-by-step explanation:
V=140(1+0.15)
2
what is the value of x if x over 5=3
Answers
Answer:
x = 15
Step-by-step explanation:
the easiest way to do this is 5 times 3 and with that we get 15 :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
Step-by-step explanation:
answer: x = 15
explanation in picture
You need to buy insulation to cover the inside of a shipping container. The container is a rectangular prism that is 15 feet long, 8 feet wide, and 7 feet high. How much insulation do you need to buy if you want to insulate all the inside surfaces of the shipping container except the floor?
Answers
Answer:
442 ft²
Step-by-step explanation:
The amount of insulation needed is the amount that covers the area of the side walls and the ceiling. The area of the side walls is the product of the perimeter and height. The area of the ceiling is the product of length and width.
__
Lateral area = Ph = 2(L+W)h = 2(15 ft +8 ft)(7 ft) = 322 ft²
Ceiling area = LW = (15 ft)(8 ft) = 120 ft²
__
Insulation needed = lateral area + ceiling area = 322 ft² +120 ft²
Insulation needed = 442 ft²
Select the correct answer from each drop-down menu.
Look at the expression below.
Where could parentheses be placed in the expression for it to equal 4?
Where could parentheses be placed in the expression for it to equal 358?
Answers
F(x)=4x^2 and g(x)=x+1, find (f x g)(x)
Answers
Answer:
option b
Step-by-step explanation:
It is option b
Your answer is 4(x+1)²
Answer:
B
Step-by-step explanation:
Given functions:
[tex]f(x)=4x^2[/tex][tex]g(x)=x+1[/tex][tex](f \circ g)(x) & =f[g(x)][/tex]
This means substitute the x of f(x) with the function g(x).
[tex]\implies f[g(x)]=4(x+1)^2[/tex]
Help help help help help help math
Answers
Answer:
55
Step-by-step explanation:
Area=LxW
so, Area=11x5
=55
Answeri think its 55
Step-by-step explanation:
you have to multiply 5x11 and thats 55 which is simple becaused i suck at explaining stuff
Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations.
A. 5 × 3 = 15
B. 1/5 × 1/3= 1 /15
C. 1/5 × 3 = 3/5
D. 5 ÷ 1/3 =15
E. 1/3 ÷ 5 = 1/15
Answers
Answer :D
A (or) 5 * 3= 15
Question explanation:
5 pears.
3 pieces
[tex](1 * 3) + (1 * 3) + (1 * 3) + (1 * 3) + (1 * 3)[/tex]
Which is:
[tex](3) * (3) * (3) * (3) * (3)[/tex]
Which, simplified:
[tex]3 * 5[/tex]
Which equals:
[tex]3 * 5 = 15[/tex]
Hope this helps :) - Answered by Lilo
Find the slope of the line that passes through \left(10,8\right)(10,8) and \left(1,9\right)(1,9).
Slope ==
Answers
Answer:
m = -1/9
Step-by-step explanation:
Michelle is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 16 meters away from the hook. If Michelle is 20 meters away from the fish, how far below Michelle is the hook?
Answers
Answer:
12 meters
Step-by-step explanation:
You have to use the inverse of the pythagorean theorem to do this so you do square root of (20x20-16x16) which is 12
what is 65% of (102/2)
Answers
Answer:
33.15
Step-by-step explanation:
65% is 0.65
102/2=51
0.65*51=33.15 which is the answer
PLEASE HELP ASAP!!!!!
a lower auto insurance deductible usually means a higher __
a.) maintenance cost
b.) max out of pocket
c.) premium
d.) ticket.
Answers
The deductible is the amount one pays towards the auto insurance
The complete statement is: a lower auto insurance deductible usually means a higher premium
What is deductible?When an insured loss or disaster happens, the amount one pay towards the loss is referred to as the deductible
As a general rule, the more the deductible, the lower the premium; and vice versa.
This means that: a lower auto insurance deductible usually means a higher premium
Hence, the text that completes the statement is premium
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Find the missing number if the average is 8.8 and _____
A) 4
B) 8
C) 12
D) none of the above
Answers
Answer:
none of the above
Step-by-step explanation:
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
The following refers to a purchase of a machine by a company on January 1, 2021:
Salvage Value: $7,500
Life: 6 years
Desired Rate of Return 4%
Interest Compounded: semi-annually
Maximum amount the company can pay $32,348
What is the semi-annual net cash flow the company must achieve in order for the purchase to be made?
Answers
The semi-annual net cash flow that the company must achieve in order for the purchase to be made is $5041.
How to calculate the cash flow?Maximum amount that can be invested = $32348.
Less: Present value of salvage value = $5927
Present value of cash inflow = $32348 - $5927 = $26421.
Net cash flow will be:
= $26421 / PV factor
= $26421/5.242
= $5041
In conclusion, the correct option is $5041.
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