Answers
Answer:
B. -15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Swapping Limits]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^3_{-1} {[2g(x) + 4]} \, dx = 22[/tex]
[tex]\displaystyle \int\limits^{-1}_{10} {g(x)} \, dx = 12[/tex]
[tex]\displaystyle \int\limits^{10}_{3} {g(x)} \, dx = z[/tex]
Step 2: Redefine
Manipulate the given integrals.
[Integrals] Combine [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^{-1}_{10} {g(x)} \, dx + \int\limits^{10}_3 {g(x)} \, dx = \int\limits^3_{10} {g(x)} \, dx[/tex][Integrals] Rewrite: [tex]\displaystyle \int\limits^3_{10} {g(x)} \, dx = \int\limits^{-1}_{10} {g(x)} \, dx + \int\limits^{10}_3 {g(x)} \, dx[/tex][Integrals] Substitute in variables: [tex]\displaystyle \int\limits^{-1}_3 {g(x)} \, dx = 12 + z[/tex][Integrals] Rewrite [Integration Property - Swapping Limits]: [tex]\displaystyle -\int\limits^3_{-1} {g(x)} \, dx = 12 + z[/tex][Integrals] [Division Property of equality] Isolate integral: [tex]\displaystyle \int\limits^3_{-1} {g(x)} \, dx = -(12 + z)[/tex][Integrals] [Distributive Property] Distribute negative: [tex]\displaystyle \int\limits^3_{-1} {g(x)} \, dx = -12 - z[/tex]Step 3: Solve
[Integral] Rewrite [Integration Property - Addition]: [tex]\displaystyle \int\limits^3_{-1} {2g(x)} \, dx + \int\limits^3_{-1} {4} \, dx = 22[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 2\int\limits^3_{-1} {g(x)} \, dx + 4\int\limits^3_{-1} \, dx = 22[/tex][Integral] Substitute in integral: [tex]\displaystyle 2(-12 - z) + 4\int\limits^3_{-1} \, dx = 22[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle 2(-12 - z) + 4(x) \bigg| \limits^3_{-1} = 22[/tex][Integral] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle 2(-12 - z) + 4(3 - -1) = 22[/tex][Integral] (Parenthesis) Simplify: [tex]\displaystyle 2(-12 - z) + 4(3 + 1) = 22[/tex][Integral] (Parenthesis) Add: [tex]\displaystyle 2(-12 - z) + 4(4) = 22[/tex][Integral] Multiply: [tex]\displaystyle 2(-12 - z) + 16 = 22[/tex][Integral] [Subtraction Property of Equality] Subtract 16 on both sides: [tex]\displaystyle 2(-12 - z) = 6[/tex][Integral] [Division Property of Equality] Divide 2 on both sides: [tex]\displaystyle -12 - z = 3[/tex][Integral] [Addition Property of Equality] Isolate z term: [tex]\displaystyle -z = 15[/tex][Integral] [Division Property of Equality] Isolate z: [tex]\displaystyle z = -15[/tex][Integral] Back-Substitute: [tex]\displaystyle \int\limits^{10}_{3} {g(x)} \, dx = -15[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
Related Questions
Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycle? Round your answer to two decimal places, if needed.
Answers
Answer:
17 mphStep-by-step explanation:
Miguel's speed = m, Raul's speed = rGivenm = 4rDistance = 68 milesTime difference = 3 hoursSolutiontime = distance/speedSubstitute values and solve for r the equation of the time difference:
68/m + 3 = 68/r68/4r + 3 = 68/r17/r + 3 = 68/r17 + 3r = 683r = 68 - 173r = 51r = 17Raul's speed is 17 mph
Answer:
[tex] \huge \boxed{ \boxed{ \red{ \tt17 \: mph}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:equationequation word problemsPEMDASgiven:Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycletips and formulas:t=d/sto findhow fast can Raul ride his bicyclelet's solve:let's the speed of Raul be x
likewise
Miguel can drive 4 times as fast as Raul can ride his bicycle
therefore
4x
according to the question
[tex] \sf \frac{68}{4x}+3=\frac{68}{x}[/tex]
[tex] \implies \sf \frac{68 + 12x}{4x} = \frac{68}{x} [/tex]
[tex] \sf factor \: out \: 4 \: and \: reduce \: it : \\ \sf \implies \frac{4(17 + 3x)}{4x} = \frac{68}{x} \\ \\ \implies\sf \frac{17 + 3x}{x} = \frac{68}{x}[/tex]
[tex] \sf multipy \: both \: sides \: by \: x : \\ \sf \implies (\frac{17 +3 x}{x} )x = (\frac{68}{x} )x \\ \implies \sf 17 + 3x = 68[/tex]
[tex] \sf cancel \: 17 \: from \: both \: sides : \\ \implies \sf 17 - 17 + 3x = 68 - 17 \\ \implies \sf 3x = 51[/tex]
[tex] \sf divide \: both \: side s \: by \: 3 : \\ \sf \implies \frac{3x}{3} = \frac{51}{3} \\ \therefore x = 17[/tex]
Mr. Ryan had 8 meters of cable. He used 300 centimeters to hook up the television in his living room. Then he used 400 centimeters to hook up the television in his office. How many meters of cable did Mr. Ryan have left?
Answers
Answer:
1 meter left
Step-by-step explanation:
100 cm makes up a meter so 300 + 400 is 700 which is 7 meters so he has 1 meter left
Answer:
Mr. Ryan has 1 meter or 100 centimeters ethier (answer is correct)
Step-by-step explanation:
How many meters of cable did Mr. Ryan have left?
Let's start here with that for every meter(m) there is 100 centimeters(cm) so in other words 1 meter = 100 centimeters
300 cm=3 m 400 cm=4 m
3m+4m=7m 300cm+400cm=700cm
__________________________________________________________800cm-700cm=100cm
8m-7m=1m
Write the exponent for 4^? = 64 What number is the question mark? *
Answers
As 4^3 = 64
4x4x4= 64
Simplify completely''''
Answers
Answer:
[tex]\displaystyle \frac{2(x + 3)}{5x - 2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{2x^2 + 16x + 30}{5x^2 + 13x - 6}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{2(x + 3)(x + 5)}{5x^2 + 13x - 6}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{2(x + 3)(x + 5)}{(x + 3)(5x - 2)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{2(x + 3)}{5x - 2}[/tex]John bought a video game that was 20% off. The game was originally $60. What was the sale price of the game?
Answers
Answer:
it was $48
Step-by-step explanation:
$60X0.2
=$48
You welcome
What number does x stand for in this equation?
-7x + 6= 27
A
21
B
2
C
-3
D
-7
Answers
Answer:
C. -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
-7x + 6 = 27
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 6 on both sides: -7x = 21[Division Property of Equality] Divide -7 on both sides: x = -3Why is California at higher risk for earthquakes than North Dakota
( Also i know this isnt math but people answer faster when its in math )
Answers
Answer:
Step-by-step explanation:
Because calfornia is right next to Ocean
Nathan buys 8 bottles of iced tea at the grocery store. He has coupons for $0.35 off the regular price of each bottle. After using the coupons, the total cost of the drinks is $7.20.
Which equation can be used to find the regular price, p, of each bottle of iced tea?
Answers
Answer:
$1.25
Step-by-step explanation:
0.35 x 8 = 2.80
7.20 + 2.80 = 10
10 divided by 8 = 1.25
Thank you :)
The equation that can be used to determine the regular price of iced tea is p = 1/8($7.20 - $2.80).
Description of couponsCoupons reduce the price of an item. An item becomes cheaper when coupons are used. Thus, Nathan would buy the iced teas at a cheaper price as a result of the coupons.
Equation that represents the regular price of the iced tea.Discounted price = regular price - discount
$7.20 = p - ($0.35 x8)
$7.20 = p - $2.80
p = $7.20 - $2.80
Price of each bottle = p = 1/8( $7.20 - $2.80)
To learn more about how to calculate discounts, please check: https://brainly.com/question/26061308
Divide 4/5 * 1/10
Blank 1:
Answers
Reciprocal of
1
10
:
10
1
Now, multiply it with the dividend
So,
4
5
÷
1
10
=
4
5
×
10
1
=
4 × 10
5 × 1
=
40
5
After reducing the fraction, the answer is
8/1
Use the drop-down menu to identify what each label shows.
Answers
Answer:
please put a picture so i can awnser
Step-by-step explanation:
Answer:
where is the picture ?
Step-by-step explanation:
.4^3Grafting, the uniting of the stem of one plant with the stem or root of another, is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety. Suppose grafts are done one at a time. A graft fails with probability 0.4, independently of the others. Given there were no failed grafts in the first seven done, what is the probability that there will be at least one failed graft in the next three done
Answers
Answer:
0.784 = 78.4% probability that there will be at least one failed graft in the next three done
Step-by-step explanation:
To solve this question, we need to understand the binomial probability distribution and conditional probability.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: No failed grafts in the first seven
Event B: At least one fail in the next three.
Intersection of events A and B:
Since the probability of a graft failling is independent of other grafts, we have that:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)*P(B)}{P(A)} = P(B)[/tex]
So we just have to find the probability of one fail in three trials.
Three trials means that [tex]n = 3[/tex].
The probability is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.4)^{0}.(0.6)^{3} = 0.216[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.216 = 0.784[/tex]
0.784 = 78.4% probability that there will be at least one failed graft in the next three done
what does m represent in the equation y = mx+b?
Answers
Answer:
In the equation y = mx + b for a straight line, the number m is called the slope of the line
Step-by-step explanation:
Use intercepts to graph the linear equation
-2 + 2y = 7.
Answers
Answer:
2y=7+2
2y=9
y=9/2
4.5
i hope to help you
pls help due in one min
Daniel hiked
4
5
8
miles on Saturday and
4
1
2
miles on Sunday. How many miles did he hike in all?
A.
8
3
5
miles
B.
8
3
4
miles
C.
9
1
8
miles
D.
9
1
2
miles
Answers
Answer:
the answer isnt on there it would be 870 miles
Step-by-step explanation:
Answer:
c.
Step-by-step explanation:
Here is a long-division calculation of 917:7.
1 31
7
9 1 7
- 7
2 1
- 2 1
- 7
0
There is a 7 under the 9 of 917. What does this 7 represent?
Answers
Answer:
Step-by-step explanation:
it means that 7 goes into 9 one time, and its seven.
a line that separates the plane into two regions
Answers
Answer:
Two-Half Planes. Or, You can Call it a Boundary line.
Step-by-step explanation:
Answer:
half-planes or boundary region
Step-by-step explanation:
In the first year of a 10,000 investment the interest rate was 6%. All earned interest remained invested for the second year, and the interest rate increased to 7%. What was the percent increase of the entire investment after two years?
Answers
Answer:
13.4%
Step-by-step explanation:
First year:
$10,000*6% = $600
New balance = $10,600
Second Year:
$10,600*7% = $742
$10,600+ $742 = $11,342
Total Return:
Final Balance - Initial balance
$11,342 - $10,000 = $1,342
$10,000*x ÷ $1,342
x = $1,342/$10,000
x = 0.1342
0.134 = 13.4%
I RESLLY NEED THIS NOW
The simple interest owed on a loan of $5,600 after 4 years is $1,008. What percent
represents the annual interest rate on the loan? Record your answer on the grid.
Answers
What are the 3 equivalent fraction 75/100
Answers
Answer:
3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator. GCD of 75 and 100 is 25.
75 ÷ 25100 ÷ 25.
Reduced fraction: 34. Therefore, 75/100 simplified to lowest terms is 3/4.
Answer:
three equivalent fractions to 75/100 are 3/4 , 6/8 , & 12/16
ALGEBRA 1 PLS HELP ASAP
Answers
A college basketball player makes 70% of his free throws. At the end of a game, his team is losing by two points. He is fouled attempting a three-point shot and is awarded three free throws. Assuming each free throw is independent, what is the probability that he makes at least two of the free throws?
a. 0.784
b. 0.700
c. 0.216
d. 0.441
Answers
Answer:
B.
Step-by-step explanation:
If he makes 70% then 70% as a decimal would be 0.700 which is B
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability that he makes at least two of the free throws is 0.0700.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head when a coin is tossed is 1/2
We have,
Each free throw is independent of the other.
Percentage of making free throws = 70%
The probability that he makes at least two of the free throws.
= 70%
= 70/100
= 0.07
This can be written as 0.0700.
Thus,
The probability that he makes at least two of the free throws is 0.0700.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ2
58 + 18 =
78-58=
335+415
Answers
Answer:
78
20
750
Step-by-step explanation:
I’ve been trying to figure out this question but I am not able to please help
Answers
Answer:
its C
Step-by-step explanation:
ik
Answer:
D
Step-by-step explanation:
Since the total degrees of a circle is 360 and half of a circle is 180, 1/4 of a circle is 90 or less, D is the answer :)
write 7% as a Vulgar fraction
Answers
Answer:
7/100
Step-by-step explanation:
This is literally what the percent sign means: "per hundred".
Thirty-seven is less than the difference of seven and ten times a number.
Answers
Answer:
37< 10x-7
Step-by-step explanation:
Find all the zeros and their multiplicities for the function. d(x)=x^3+3x^2-4x-12
Answers
Step-by-step explanation:
1) x³+3x²-4x-12=x²(x+3)-4(x+3)=(x²-4)(x+3)=(x-2)(x+2)(x+3).
2) zeros of the given functions are: -3; -2; 2.
Make a conjecture. What properties do you think stay the same after a translation? Check all that Apply.
Angle measures
Length
Orientation
Shape
Size
Answers
Answer: ALL OF THE ABOVE
Step-by-step explanation:
a translation doesn't change any of the above, they all remain the same. it's a trick question :P
the square root of a number increased by 9 is 27 find the number
Answers
Answer:
4.24264
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
I don't know how to explain. •-• Sorry!
What are the next three terms in the sequence 4,8,12,16?
Answers
Answer:
20,24,28
Step-by-step explanation:
It is increasing by 4 each time
Mark me brainliest please :)
Answer:
20, 24, 28
Step-by-step explanation:
yeah
Is anyone smart enough to answer this correctly?
Answers
Answer:
C. 55 square centimetre
Step-by-step explanation:
Area of the triangle on the top= 1/2 * 2 * 3 cm^2
= 3 cm^2
Area of the rectangle in between= 8 * 2 cm^2
= 16 cm^2
Area of the parallelogram at the bottom
= 12 * 3 cm^2
= 36 cm^2
Therefore, Area of the figure
= (3+16+36) cm^3
= 55cm^2
Hope you got the answer ☺️