Answer:
a. 18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsCalculus
Integrals
Definite IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/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]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^2_0 {x(4x^2 + 1)} \, dx[/tex]
Step 2: Integrate
[Integrand] Distribute x [Distributive Property]: [tex]\displaystyle \int\limits^2_0 {(4x^3 + x)} \, dx[/tex]Rewrite Integral [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^2_0 {4x^3} \, dx + \int\limits^2_0 {x} \, dx[/tex]Rewrite 1st Integral [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int\limits^2_0 {x^3} \, dx + \int\limits^2_0 {x} \, dx[/tex][Integrals] Reverse Power Rule: [tex]\displaystyle 4(\frac{x^4}{4}) \bigg| \limits^2_0 + (\frac{x^2}{2}) \bigg| \limits^2_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 4(4) + 2[/tex]Evaluate: [tex]\displaystyle 18[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Miguel can use all or part of his $25 gift card to make a music purchase.Each song costs $1.50, and there is a $1.00 per account activation fee
Answer:
1.5m + 1 ≤ 25
Step-by-step explanation:
Given:
Total amount of gift card Miguel have = $25
Cost of each song = $1.50
Account activation fee = $1
Find:
Inequality
Computation:
Assume;
Number of song Miguel have = m
So,
Total amount of gift card Miguel have ≥ (Cost of each song)(Number of song Miguel have) + Account activation fee
1.5m + 1 ≤ 25
Which operation will solve the following word problem? Jeff earns $14.00 per hour, Tom earns half as much as Jeff. How much does Tom earn per hour?
a.) Multiplication
b.) Subtraction
c.) Addition
d.) Division
Answer:
Multiplication
Amount Tom earns per hour = $7
Step-by-step explanation:
Amount Jeff earns per hour = $14
Amount Tom earns per hour = 1/2 × $14
Note: 1/2 = 0.5
Amount Tom earns per hour = 1/2
× $14
= 0.5 × $14
= $7
Amount Tom earns per hour = $7
18. Ingrid usually runs 12 miles in 2 hours. If she
only has 40 minutes to run today, how many
miles can she run going at the same rate?
A. 2.4 miles
B. 3 miles
4 miles
2
D. 6-miles
Answer:
4 miles
Step-by-step explanation:
120min/12miles
10min/1mile
40min/4miles
The number of miles can she run, going at the same rate will be 4 miles. Then the correct option is C.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Ingrid usually runs 12 miles in 2 hours.
2 hours = 120 minutes
Then the speed will be
Speed = 12 / 120
Speed = 0.1 miles per minutes
If she only has 40 minutes to run today.
Then the number of miles can she run, going at the same rate will be
Distance = 0.1 x 40
Distance = 4 miles
Then the correct option is C.
More about the speed link is given below.
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Apply the distributive property to create an equivalent expression.
4(x - 2 + y) =4(x−2+y)=4, left parenthesis, x, minus, 2, plus, y, right parenthesis, equals
Answer:
[tex]4x-8+4y[/tex]
Step-by-step explanation:
We are given that an expression
[tex]4(x-2+y)[/tex]
We have to find an equivalent expression using distributive property .
Distributive property:
[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]
Using the property
[tex]4(x-2+y)=4(x-2)+4\cdot y[/tex]
[tex]4(x-2+y)=4x+4(-2)+4y[/tex]
[tex]4(x-2+y)=4x-8+4y[/tex]
Hence, the equivalent expression of the given expression is given by
[tex]4x-8+4y[/tex]
PLEASE HELP ASAP! Worth 15 points!!
Which graph represents a function with direct variation?
Answer:
The bottom right photo
Step-by-step explanation:
A direct variation is an equation in the form y = kx, where k is the constant of variation. Since it is in this form, the equation will pass through the origin (0, 0)
Express sin O as a fraction in simplest form
Answer:
sin o = opposite/hypotenuse
sin o= 7/12
Simplify. Your answer should contain only positive exponents.
fraction numerator 2 b squared over denominator 2 b end fraction 2b^2/2b
A. fraction numerator 3 over denominator 4 b end fraction 3/4b
B. 3 b squared 3b^2
C. b
D. 3b
Answer:
D.6b C.v B.8squared 7b<9
In an English test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, answer the following question.
a. what is the percentile rank of the score 65?
b. what is the percentile of the score less than 70?
c. what is percent of the scores is greater than 65?
d. what percent of scores is less than 70?
e. what percent of the score is between 50 and 60?
Answer:
a) A score of 65 is in the 79.67th percentile.
b) A score less than 70 is below the 95.25th percentile.
c) 20.33% of the scores are greater than 65.
d) 95.25% of scores are less than 70.
e) 45.25% of the scores are between 50 and 60.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean is 60 and the standard deviation is 6.
This means that [tex]\mu = 60, \sigma = 6[/tex]
a. what is the percentile rank of the score 65?
This is the p-value of Z when X = 65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 60}{6}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a p-value of 0.7967.
Thus: A score of 65 is in the 79.67th percentile.
b. what is the percentile of the score less than 70?
Below the p-value of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 60}{6}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
Thus: A score less than 70 is below the 95.25th percentile.
c. what is percent of the scores is greater than 65?
The proportion is 1 subtracted by the p-value of Z when X = 65.
From item a, when X = 65, Z has a p-value of 0.7967
1 - 0.7967 = 0.2033
0.2033*100% = 20.33%
20.33% of the scores are greater than 65.
d. what percent of scores is less than 70?
The proportion is the p-value of Z when X = 70, which, from item b, is of 0.9525.
0.9525*100% = 95.25%
95.25% of scores are less than 70.
e. what percent of the score is between 50 and 60?
The proportion is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 50.
X = 60
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 60}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
X = 50
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 60}{6}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a p-value of 0.0475.
0.5 - 0.0475 = 0.4525
0.4525*100% = 45.25%
45.25% of the scores are between 50 and 60.
If AABC~ DEF and the scale factor from ABC to DEF is , what are the lengths of DE, EF, and DF, respectively?
Step-by-step explanation:
we don't see a picture, and you don't not give us any detailed information (all specific numbers like the scale factor are missing in your text). so, it is impossible to calculate anything.
but you can do it yourself very easily.
let's call the same factor "f".
that means you have to multiply the side lengths of every side of ABC by that factor f to get the cushions side lengths is the sides in DEF.
that's it.
that's all that has to be done.
so, assuming that A -> D, B -> E, C -> F
then
AB × f = DE
BC × f = EF
CA × f = FD
as I said - that's it. just use the actual numbers and multiply.
All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle ABC and DEF are similar.
And, the scale factor from ABC to DEF is 2.
Now, We get;
This means that each side of the triangle ABC were multiplied by the scale factor 2 in order to get the triangle DEF.
Based on the above, you can set up the following equations;
⇒ DE = 2AB
⇒ EF = 2BC
⇒ DF = 2CA
Finally, substituting the corresponding lengths of the triangle ABC into the equations, and then evaluating, you get the following result:
⇒ DE = 2 x 2 = 4
⇒ EF = 2 x 4 = 8
⇒ DF = 2 x 6 = 12
Thus, All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.
Learn more about the triangle visit;
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
19,10,1,...
[tex]\displaystyle\bf \underbrace{19}_910{\underbrace{1}_9} \Longrightarrow This\: is \:an \:\:arithmetic\:\: progression[/tex]
Which equation is correct?
x – 17 = 4
x – 4 = 17
x + 4 = 17
x + 17 = 4
Answer:
1 and 2.....then 3 is a different question
-4y=-20
Graph each line that represents each linear equation
Answer:
y = 5
Step-by-step explanation:
The given equation to us is
⇒ -4y = -20
⇒ y = -20/-4
⇒ y = 5
Therefore this line will pass 5 units away from y axis. For graph refer to the attachment .
More Information :-
The equation of x axis is y = 0 The equation of y axis is x = 0 .I NEED HELP WITH 2 QUESTIONSS
1.What is the mean change in the forecasted low temperatures over the next 7 days? Remember, this can be found by averaging the values in the Difference column for the low temperatures. If your answer is not an integer, explain what two integers your answer is between.
LOW TEMPTURES:
WEDNESDAY-79
THURSDAY- 79
FRIDAY- 73
SATURDAY- 73
SUNDAY - 73
MONDAY- 73
TUESDAY- 75
2. What is the mean change in the forecasted high temperatures over the next 7 days? Remember, this can be found by averaging the values in the Difference column for the high temperatures. Show your work and steps. If your answer is not an integer, explain what two integers your answer is between.
WEDNESDAY- 88
THURSDAY- 87
FRIDAY- 90
SATURDAY- 90
SUNDAY- 86
MONDAY- 88
TUESDAY-86
PLEASE ANSWER FAST!!!
If a 1 = −3 and a n = −2an − 1, what is the fifth term of the sequence?
Answer:
d
Step-by-step explanation:
o
Step-by-step explanation:
There's on;ly one way I know of that this can be done.You must start at a1 and work your way up to a5
a1 = -3n that's given
a2 =
A sheet of plastic has an area of 35 square cm. If the sheet is 5 cm thick, what is the volume?
Answer:
175 cm³
Step-by-step explanation:
Volume = área * thick
Volume = 35cm² * 5cn
Volume = 175 cm³
Answer:
7cm
Step-by-step explanation:
Area = 35cm²
Length= 5cm
Width=?
A=L×B
B=A/L
B=35/5
B=7cm
Someone help me please
Answer:
(x + 10)(2x + 5)
Step-by-step explanation:
Given
2x² + 25x + 50
Consider the factors of the product of the coefficient of the x² term and the constant term (ac) which sum to give the coefficient of the x- term (b)
ac = 2 × 50 = 100 and b = 25
The factors are + 20 and + 5
Use these factors to split the x- term
2x² + 20x + 5x + 50 ( factor the first/second and third/fourth terms )
= 2x(x + 10) + 5(x + 10) ← factor out (x + 10) from each term
= (x + 10)(2x + 5)
Question is in the image
Answer:
The answer is:
[tex]f(x)=2x^{2}-8x+6[/tex]
Step-by-step explanation:
The equation of a parabola in the intercept form is given by:
[tex]y=a(x-p)(x-q)[/tex]
Where:
p and q are x-intercepts
Now, we know the parabola intercepts at x=1 and x=3.
So we will have:
[tex]y=a(x-1)(x-3)[/tex]
Using the point (-1,16) we could find the value of a.
[tex]16=a(-1-1)(-1-3)[/tex]
[tex]16=a(-2)(-4)[/tex]
[tex]16=8a[/tex]
[tex]a=2[/tex]
Therefore, the equation is:
[tex]y=2(x-1)(x-3)[/tex]
[tex]y=2(x^{2}-4x+3)[/tex]
[tex]y=2x^{2}-8x+6[/tex]
The answer is:
[tex]f(x)=2x^{2}-8x+6[/tex]
I hope it helps you!
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (gof)(-5).
Answer:
(g ￮ f )(- 5) = - 6
Step-by-step explanation:
Evaluate f(- 5), then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
Answer:
[tex](gof)(-5)=-6[/tex]
Step-by-step explanation:
One is given the following information;
[tex]f(x)=-2x-7\\g(x)=-4x+6[/tex]
One is asked to find the following,
[tex](g o f)(-5)[/tex]
The expression ([tex]gof[/tex]) is another way to denote ([tex]g(f(x))[/tex]), in essence, substitute function (f) into function (g) in place of parameter (x). The simplify to find the resulting function;
[tex]g(f(x))\\=-4(-2x-7)+6\\=(-4)(-2x)+(-4)(-7)+6\\=8x+28+6\\=8x+34[/tex]
One is asked to evaluate the function ([tex]gof[/tex]) for (-5). Substitute (-5) into the function and simplify to evaluate;
[tex](gof)(-5)=8x+34\\=8(-5)+34\\=-40+34\\=-6[/tex]
A Warming Liquid - A liquid is taken out of a refrigerator and placed in a warmer room, where its temperature, in F, increases over time. It can be modeled using the equation Tm 74 390.87m. (a) What temperature did the liquid start at? Show the work that leads to your answer. (b) What is the temperature of the room?
Answer:
The temperature at the start is 35F
The temperature of the room is 74F
Step-by-step explanation:
Given
[tex]T(m) = 74 - 39(0.87)^m[/tex]
Solving (a): The temperature at the start.
To do this, we set: [tex]m = 0[/tex]
So, we have:
[tex]T(0) = 74 - 39(0.87)^0[/tex]
[tex]T(0) = 74 - 39*1[/tex]
[tex]T(0) = 74 - 39[/tex]
[tex]T(0) = 35[/tex]
Hence, the temperature at the start is 35F
Solving (b): The room temperature
We have:
[tex]T(m) = 74 - 39(0.87)^m[/tex]
To get the temperature of the room, we simply remove the exponential function.
So, we have:
[tex]Initial = 74[/tex]
Hence, the temperature of the room is 74F
The initial temperature of the liquid is 35 F and the room temperature is 74 F.
What is Melting Point?The melting point is the temperature at which the solid starts converting into liquid.
Given here,
[tex]T_m = 74- 39(0.87)^m[/tex]
Leat the [tex]m = 0,[/tex]
So,
[tex]T_0 = 74- 39(0.87)^0\\\\T_0 = 35 \rm \ F[/tex]
Thus the initial temperature is 35 F.
Now remove the exponential to get the room temperature,
So,
[tex]T_{RT} = 74[/tex]
Therefore, the initial temperature of the liquid is 35 F and the room temperature is 74 F.
Learn more about the Melting point:
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SOMEONE PLEASE ANSWER THIS PLZZZ
Answer:
.14
Step-by-step explanation:
A|B (or A given B)= A and B/B
So
Walk to school | senior= (walk to school and senior)/Senior
walk to school and senior= 5
senior= 25+5+5= 35
5/35= .14
What goes in the blanks? The measure of angle θ is 7π/4. The measure of its reference angle is _____°, and tan θ is ______?
Answer:
The measure of angle θ is 7π/4. The measure of its reference angle is 45°, and tan θ is -1.
Answered by GAUTHMATH
Is (0,0) a solution of the graphed inequality?
Choose 1 answer:
Yes
No
Answer:
no..........................
Someone help me with this math homework please!
Answer:
Option number B
Step-by-step explanation:
As per the statement:
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.
Given the equation as:
7h - 5 ( 3h -8 ) = -72
Using distributive property,
a ⋅ ( b + c ) = a ⋅ b + a ⋅ c
7h - 15h + 40 = - 72
Combine like terms;
-8h + 40 = -72
Subtract 40 from both sides we have;
-8h 8= -112
Divide both sides by -8 we have;
h = 14 hours
Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.
Drag the tiles to the boxes to form correct pairs
Multiply the sets of numbers and match them with their products.
[tex]( - \frac{3}{4} )( \frac{7}{8} )[/tex]
[tex] = \frac{ - 3}{4} \times \frac{7}{8} [/tex]
[tex] = \frac{ - 21}{32} [/tex]
_______________________________________
[tex]( \frac{2}{3} )( - 4)(9)[/tex]
[tex] = \frac{2}{3} \times - 4 \times 9[/tex]
[tex] = \frac{ - 72}{3} [/tex]
[tex] = - 24[/tex]
_______________________________________
[tex]( \frac{5}{16} )( - 2)( - 4)( - \frac{4}{5} )[/tex]
[tex] = \frac{5}{16} \times - 2 \times - 4 \times \frac{ - 4}{5} [/tex]
[tex] = \frac{ - 160}{80} [/tex]
[tex] = \frac{ - 16}{8} [/tex]
[tex] = - 2[/tex]
_______________________________________
[tex](2 \frac{3}{5} )( \frac{7}{9} )[/tex]
[tex] = \frac{13}{5} \times \frac{7}{9} [/tex]
[tex] = \frac{91}{45} [/tex]
Determine the value of x
2.12 units
2.02 units
12.38 units
0.49 units
Answer:
2.02
Step-by-step explanation:
Hello, I took the quiz. The correct answer is 2.02
According to class 8 please solve
Answer:
i) 4x
ii) Father's age = 3(x + 10)
Son's age = x + 10
iii) 4x + 10 = 3(x + 10)
iv) Present age of the son = x = 20
Present age of the father = 4x = 4(20)
= 80
Step-by-step explanation:
Present age of the son = x
Present age of the father = 4x
Age of the son in 10 years = x + 10
Age of the father in 10 years = 3(x + 10)
4x + 10 = 3(x + 10)
4x + 10 = 3x + 30
4x - 3x = 30 - 10
x = 20
PLEASE HELP ASAP WHAT IS THE ANSWER TO THIS QUADRATIC EQUATIONNNN
Answer:
pls i don't know
pls help im begging u..
SOMEONE PLEASE HELP ME I'M STUCK
Answer:
57%
Step-by-step explanation:
200+245+125 = 570
570/1000 = .57
Answer:
57%
Step-by-step explanation:
First find the total number of families in the sample.
Total = 350 + 200 + 245 + 125 + 66 + 10 + 4
Total = 1000
Next find the number of families that have 3, 4 or 5 people.
Total(3,4 or 5) = 200 + 245 + 125
Total(3,4 or 5) = 570
Now the % = (Total 3,4 or 5) / Total ) * 100
% = 570 / 1000 * 100
% = 57%
At a football stadium, 25% of the fans in the attendance were teenagers. If there were 190 teenagers at the football stadium, what was the total numbers of the people at the stadium?
Answer:
760
Step-by-step explanation:
25%= 190
100 = 25 × 4
100% (total number of people) = 190 × 4 = 760
