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
One winter day, the temperature in Houston is 8 Celsius. Find the temperatures in these other cities. Explain or show your reasoning.
In Orlando, it is 17 warmer than it is in Houston
In Salt Lake City, it is 18 colder than it is in Houston
In Minneapolis, it is 25 colder than it is in Houston
In Fairbanks, it is 12 colder than it is in Minneapolis
Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks.
Answers
Salt Lake city = -10° because 8-18
Minneapolis = -17° because 8-25
Fairbanks = -29° because -17-12
Houston = 8° - 37° = Fairbanks
Hence, the temperatures in these other cities are
Orlando is [tex]25[/tex] degree
Salt Lake is [tex]-10[/tex] degree
Minneapolis is [tex]-17[/tex] degree
Fairbanks is [tex]-29[/tex] degree
What is the degree?
A degree, usually denoted by °, is a measurement of a plane angle in which one full rotation is [tex]360[/tex] degrees.
Here given that,
One winter day, the temperature in Houston is [tex]8[/tex] Celsius.
In Orlando, it is [tex]17[/tex] warmer than it is in Houston.
In Salt Lake City, it is [tex]18[/tex] colder than it is in Houston.
In Minneapolis, it is [tex]25[/tex] colder than it is in Houston.
In Fairbanks, it is [tex]12[/tex] colder than it is in Minneapolis.
So, it would be
Orlando = [tex]25[/tex] degree
because [tex]17+8=25[/tex] degree
Salt Lake city [tex]= -10[/tex] degree
because [tex]8-18=-10[/tex] degree
Minneapolis [tex]= -17[/tex] degree
because [tex]8-25=-17[/tex] degree
Fairbanks [tex]= -29[/tex] degree
because [tex]-17-12=-29[/tex] degree
Hence, the temperatures in these other cities are
Orlando is [tex]25[/tex] degree
Salt Lake is [tex]-10[/tex] degree
Minneapolis is [tex]-17[/tex] degree
Fairbanks is [tex]-29[/tex] degree
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Andy had some basketball cards. After he bought 12 more, he had 48 cards. How many cards did Andy have at the start? Write an algebraic equation and solve.
Answers
Answer:
Step-by-step explanation:
Simplify. (x 3) 4 • x -3 x -36 x 9 x 4 x -21
Answers
Answer:
-1295x -21
Step-by-step explanation:
srry if it wrong
Answer:
=12x2+−3x+−1296x3+−21
Answer:
=−1296x3+12x2−3x−21
Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get? simplify your answer to a mixed number
Answers
Answer:
Step-by-step explanation:
Divide the 8 cups between 6 people: 8/6 = 1.333
As a mixed fraction, that is 1(1/3)
As an improper fraction (that you didn't ask for but whatever), it's 4/3
Each friend gets [tex]1\frac{1}{3}[/tex] cups of lemonade.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Six friends are sharing 8 cups of lemonade.
The friends share 8 cups lemonade equally.
We need to find the number of cup each friend will get.
To find this we have to divide eight by six.
In this questions we are splitting 8 cups among 6 friends.
Divide 8 by 6
8/6
Now divide numerator and denominator by 2
4/3
Now let us convert this to mixed fraction
[tex]1\frac{1}{3}[/tex]
Hence, each friend gets [tex]1\frac{1}{3}[/tex] cups of lemonade.
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What is the y-intercept of a line that passes through the points (1-7) and (5-25)?
Answers
Given:
A line passes through the points (1,-7) and (5,-25).
To find:
The y-intercept of the line.
Solution:
The line passes through the points (1-7) and (5-25). So, the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-7)=\dfrac{-25-(-7)}{5-1}(x-1)[/tex]
[tex]y+7=\dfrac{-25+7}{4}(x-1)[/tex]
[tex]y+7=\dfrac{-18}{4}(x-1)[/tex]
[tex]y+7=-4.5(x-1)[/tex]
Subtracting 7 from both sides, we get
[tex]y=-4.5x+4.5-7[/tex]
[tex]y=-4.5x-2.5[/tex]
Putting x=0, we get
[tex]y=-4.5(0)-2.5[/tex]
[tex]y=0-2.5[/tex]
[tex]y=-2.5[/tex]
Therefore, the y-intercept of the given line is -2.5 and the vertex form of (0,-2.5).
the ratio of boys to girls in the park was 4 to 5 .if 270 children were in the park.How many girl?
Answers
Answer:
150 are girls.
Step-by-step explanation:
There is an important difference between the way counts are viewed in ratio to that in fractions.
The ratio of boys : girls
4:5
so you have 4 boys and 5 girls making the whole count in its simplest form.
4+5=9
So to change the ratio proportion into fraction proportion we have:
Boys: 4/9
Girls: 5/9
It is given that the whole is 270 therefore the count of girls is:
5/9 x 270 = 150
A grocery store manager claims that 75% of shoppers purchase bananas as least once a month. Technology was used to simulate choosing 150 SRSs of size n = 100 from a population of shoppers where 75% buy bananas. The dotplot shows pˆ = the sample proportion of shoppers who bought bananas in the past month. A random sample of 100 shoppers from the store were selected and 64 bought bananas in the past month. Does this sample provide evidence that the grocery store manager overstated the true proportion? Justify your answer.
Answers
Answer:
P-value = 0.0333
At 5% level of significance;
0.0333 < 0.05
Therefore, we reject null hypothesis H₀ at 5% level of significance,
We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated
Step-by-step explanation:
Given the data in the question;
To test whether population proportion p is overstated;
Null hypothesis H₀ : p = (75%) = 0.75
Alternative hypothesis H₁ : = < (75%) < 0.75
now, sample proportion p" = 64 / 100 = 0.64
from the dot plot below, we will determine the p-value for test { P(p" < 0.64)}
so, the number of times p"<0.64 in 150 simulations is 5
Hence; P(p" < 0.64 ) = 5 / 150 = 0.0333
P-value = 0.0333
At 5% level of significance;
0.0333 < 0.05
Therefore, we reject null hypothesis H₀ at 5% level of significance,
We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated
This sample provide evidence that the grocery store manager overstated the true proportion P-value = 0.0333.
Given data in the question:
To test whether population proportion p is overstated; Null hypothesis H₀ : p = (75%) = 0.75 Alternative hypothesis H₁ : = < (75%) < 0.75Now, sample proportion p" = 64 / 100 = 0.64
From the dot plot below,
we will determine the p-value for test { P(p" < 0.64)} The number of times p"<0.64 in 150 simulations is 5Therefore:
P(p" < 0.64 ) = 5 / 150 = 0.0333 P-value = 0.0333
At 5% level of significance;
0.0333 < 0.05
Therefore, we reject null hypothesis H₀ at 5% level of significance,
We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated.
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are any two of the three triangles similar? if so write the appropriate similarity statement.
Answers
Answer:
Angle ABC is similar to PQR.
Postulate is Side side, side similarity
Step-by-step explanation:
In triangle ABC, AC:AB = 4/5 = 0.8
In triangle PQR, PR:PQ = 8/10 = 0.8
Looking at the triangle PQR carefully, we can deduce that QR = PR.
Thus; QR:PQ = 8/10 = 0.8.
Also,BC/AB = 4/5 = 0.8
Also, PR/RQ = 8/8 = 1 and AC/CB = 4/4 = 1
Both triangles have the same proportion of their sides and thus we can say they are similar.
Postulate used is Side, Side, Side similarity.
A hardware store sells 45 boxes of nails for $67.50. Assuming that each box is the same price, what is the price per box?
Answers
Answer:
$1.50
Step-by-step explanation:
You take 67.50/45= 1.50
Hope this helps! <3
What is the standard form for f(x)=7(x-1)^2+3
Answers
HELP ME !!!!?? Brainliest if right
Answers
What is the common factor in 14xy – 25yz?
1. z
2. x
3. xyz
4. y
Answers
Answer:
it would be y since both are common there
Find the area of the shape below
Answers
What is (7-2)^2+3/ 1/6
( / ) this means divide and (^) that means to the power
Answers
43
Explanation:
To start off you always handle the whatever's in your parentheses. 7-2 is 5.
Now your equation should look like this-
(5)^2 +3/1/6
5 to the power of 2 is 25 (5 times 5)
so now instead of 5 you have 25:
25 +3/1/6
To divide fractions you first have to make 3 and fraction so just put a one below it so it's still it's full value: 3/1
When dividing fractions you actually end up multiplying, you keep the first fraction the same (3/1) and you flip the second one (1/6 which is now 6/1) and then you multiply.
3/1 * 6/1 equals 18/1 which actually just equals 18 and then you get 25 + 18 from the parentheses and that equals 43 :)
Hope this helped! i'm horrible at explaining but i tried!
Answer:
ewannnnnnnnnnnnnn
Step-by-step explanation:
d q den alam d pa namin pinagaaralan yan, xenxia na godbless
Please help me 10 points reward
Answers
Answer:
Step-by-step explanation:
I re wrote the question so its easier to understand. You should now be able to solve this problem using simple math.
3² + (3×8) ÷ 2 - (2×5)
work it out in steps, using the acronym PEMDAS <3
Use the graph to solve the equation x2 - 2x - 8 = 0.
Answers
Answer:
Graph.
y = x^ 2 − 2 x − 8
y = 0
What is the ratio of the number of students who sometimes watch sports to the total number of students surveyed?
Answers
Answer:
You need to provide an image or some sort of attachment, since there is no context to this question or any data one could answer off of.
Step-by-step explanation:
^
What is the greatest common factor of 15 and 18?
A. 3
B. 60
C. 5
D. 18
Show your work/show how you got your answer
Answers
Answer:
A
Step-by-step explanation:
You write out all the factors and see which is the greatest one out of both
Can someone help me with this? Linear equation
Answers
Answer:
hope it helps
Step-by-step explanation:
x+2=6
3x=10
6+3x=22
5-3x=15
3+x=6y I'm sure about this one
5+x=y/4=23
Kimmy needs to big 48 cookies for cookie exchange party she will be 28 chocolate chip cookies and the rest will be gingerbread cookies G represent how many gingerbread cookies Kimmy needs to bake which equation models the problem? G-28=48 or 28+g=48
Answers
Answer:
28+ 20 = 48 because 48 take away 28 equals 20. so g is 20
Compare the initial values and the rates of change for Jenna's and Finn's plans. What do they mean in the problem situations?
Answers
Answer:
Step-by-step explanation:
Notah lives in Minnesota. He records the lowest temperature each day for one week. What is the mean of the temperatures? -7.3°F, - 11.2°F, 2.2°F, O⁰F, -1.7°F, 3.3°F, 0°F)
Answers
Answer:
-2.1
Step-by-step explanation:
-7.3 - 11.2 - 1.7 + 0 + 0 +2.2 + 3.3
--------------------------------------------------
7
= -2.1
Step-by-step explanation:
Answer:
Given :-
notha records the lowest temperature each day for one week
-7.3°f, -11.2°f, 2.2°f, 0°f, -1.7°f, 3.3°f, 0°f
To Find :-
MeanSolution :-
Mean = -7.3 +(-11.2) + 2.2 + 0 + (-1.7) + 3.3 + 0/7
Mean = -7.3 - 11.2 + 2.2 - 1.7 + 3.3/7
Mean = -20.2 + 5.5/7
Mean = -14.7/7
Mean = -2.1⁰ F
1 and 3/16 - 7/8????
Answers
Answer:
0.3125
Step-by-step explanation:
Answer:
5/16 or 0.3125
Step-by-step explanation:
g/5 - 9 = -4
Please answer right away
Answers
g/5 - 9 = -4
g-45 / 5 = -4
g -45 = -4×5
g = -20+45
g = 25
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AADCH ADEP
Check all that apply
A. LA
B. MAS
C. HL
D. HA
E. SAS
F. LL
Answers
D. HA
1234567890oplkjhgrewsertyuiopoiuytr
Answer:
Step-by-step explanation:
Its
D and E
A painter charges $20 for every hour that he paints. Let h represent the number of hours he paints and e represent his earnings. Select all the statements that are true.
Answers
Answer:
the 3 correct ones are b,c,e
Answer:
See below.
Step-by-step explanation:
He earns $20 per hour, so when you multiply 20 by h number of hours, you get the amount he earns for working h hours.
The equation is
e = 20h
A is false.
B
e = 20h
20h = 500
h = 25
B is true.
C is false. He earns $20 per hour, not 20h dollars per hour.
D
e = 20h
For 10 hours, h = 10.
e = 20 * 10 = 200
He earns $200 for 10 hours.
D is false.
E
If he raises his hourly rate by $2, he will earn $22 per hour. The new equation is
e = 22h
E is true.
Write 2 different word phrases for the expression (52 + 8) divided 30
Answers
Answer:
fifty two plus eight divided by thirty
eight plus fifty two divided by thirty
Step-by-step explanation:
I just switched them around.
Answer:
1) Thirty divided by (fifty-two plus eight)
2) (52+8)
30
Step-by-step explanation:
if 7y + 42 <14 then which among the following is true
Answers
Answer:
[tex]y<-4[/tex]
Step-by-step explanation:
Given
[tex]7y + 42 <14[/tex]
Required
Determine the true statement
Options are not given; but, the question can still be attempted.
[tex]7y + 42 <14[/tex]
Collect Like Terms
[tex]7y < 14 -42[/tex]
[tex]7y < -28[/tex]
Divide through by 7
[tex]\frac{7y}{7} < -\frac{28}{7}[/tex]
[tex]y<-4[/tex] -- This is true
Pleas e help me 100 points and brainliest
Answers
Answer:
this is your answer. I think it is right.
Answer:
see the answersStep-by-step explanation:
to understand thisyou need to know about:factoringlCDPEMDAStips and formulas:L.C.D=lowest common denominatorlet's solve:[tex]1) \sf\frac{7}{m - 6} \: , \frac{1}{m} \\ [/tex]
denominators are m-6,m
therefore
the lowest common denominator is
(m-6)(m)[tex] \sf\frac{1}{n - 1} \: , \frac{1}{ {n}^{2} - 2n + 1 } [/tex]
denominators n-1,n²-2n+1
step-1
factor n²-2n+1 to find the lowest common denominator
use (a-b)²=a²-2ab+b to factor n²-2n+1therefore
(n)²-2.n.1+(1)²(n-1)²therefore
the L.C.D of the second expression is
(n-1)² alternative form(n-1)(n-1)[tex]3) \tt\frac{k}{ {h }^{2} - 5h + 6} \: , \frac{3}{h -3 } [/tex]
step-1
factor out h²-5h+6 to find L.C.D
rewrite -5h as -2h-3h: h²-2h-3h+6factor out h: h(h-2)-3h+6factor out -3: h(h-2)-3(h-2)group: (h-3)(h-2)therefore
the L.C.D of the third expression is
(h-3)(h-2)Nine bands are to perform at a weekend festival. Suppose you want to determine how many different ways there are to schedule their appearances. Would you use a combination or a permutation?
Answers
Answer:
permutation
Step-by-step explanation:
Analyzing the information in the question above, it is correct to say that it is necessary to use permutation, since the ORDER matters, since there is a need to program the band's appearances.
Permutation can be understood as an arrangement in which n = p, where n is the number of elements in the set and p is the number of available elements.
Therefore, the permutation of nine bands is:
Pn = n!
P9 = 9!
p9 = 362880
