The solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]
Given;
To evaluate the value of a given integral;
[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex]
Let;
[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex]
Now, assume u = x² + 4
→ [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex] = [tex]2\cdot \int \frac{u^3}{2}du[/tex]
→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]
→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]
→ [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]
By adding constant C;
[tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]+ C
Hence, the solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]
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A certain brand of coffee comes in two sizes. An 11.5-ounce package costs 3.19. A 30.6-ounce package costs 7.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
The size that is the better one is 30.6-ounce package costs 7.98.
How to calculate the cost?The 11.5-ounce package costs 3.19. The price per package will be:
= 3.19 / 11.5
= 0.27
A 30.6-ounce package costs 7.98. The cost per package will be:
= 7.98 / 30.6
= 0.26
In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.
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Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complementary, then the sum of their measures is 90°.
The Law of detachment states that if m then n and m is true then q is true.
If two angles are complementary, then the two angles' sum is 90 degrees.
This is m∠E + m∠F = 90.
Option C is the correct answer
What is the law of detachment?The Law of detachment states that if m then n and m is true then q is true.
We have,
If two angles are complementary, then the sum of their measures is 90°.
This is in the form of,
If M then N and if M is true then N must be true.
So,
If two angles are complementary, then the two angles' sum is 90 degrees.
If the two angles are m∠E and m∠F.
m∠E + m∠F = 90
Thus,
If two angles are complementary, then the two angles' sum is 90 degrees.
This is m∠E + m∠F = 90.
Option C is the correct answer
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a fruit basket contains apples, oranges, and tangerines in the ratio 3:2:5, respectively. what is the total number of apples, oranges, and tangerines in the fruit basket?
The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x
In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.
The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.
Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.
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Please answer this question, URGENT 50 POINT
Answer: Use your brain aka 12 and 7
Step-by-step explanation:isn't this urgent?
Math trigonometry non right angle help please
ong please guys
well, as I said a while back, Heron's Area formula works for any triangle, so long we have all sides, and in this case we do, since it's not a right-triangle SOH CAH TOA won't work, so let's plug the values in Heron's
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a = 12\\ b = 8\\ c = 6\\ s=\frac{12+8+6}{2}\\ \qquad 13 \end{cases} \\\\\\ A=\sqrt{13(13-12)(13-8)(13-6)} \implies A=\sqrt{13(1)(5)(7)} \\\\\\ A=\sqrt{455}\implies {\Large \begin{array}{llll} A\approx 21.33 \end{array}}~cm^2[/tex]
a sample survey interviews an srs of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months. what is the probability that 72% or more of the women in the sample have been on a diet? report your answer using 4 decimal places.
The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.
p = 0.69
1 - p = 0.31
n = 209
μp = p = 0.69
σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199
= 1 - p(p < 0.72)
= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)
= 1 - p(z < 0.94)
= 1 - 0.8264
= 0.1736
Hence, the probability is 0.1736.
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Find the component form of the vector that translates (3, − 2) to ′(− 1, 4)
The vector that translates P to P' is (-4 , 6)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
The points are given;
[tex]{P = (3, -2)}\\{P' = (-1, 4)}[/tex]
The translation rule is calculated as:
{(x,y) = P' - P}
So, we have:
{(x,y) =(− 1, 4) - (3, − 2)}
Combine the terms;
{(x,y) = (-1 -3 , 4 + 2)}
{(x,y) = (-4 , 6)}
Express as vectors;
(x, y) = (-4 , 6)
Hence, the vector that translates P to P' is (-4 , 6)
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wer:
Find the slope of the line that passes through the given points.
(-3, 7.2) and (2,-2.3)
Answer:
Step-by-step explanation:
this slope of a line question is such a common question. I feel like math teachers all over don't understand how to teach this subject. Just so you know, I answer a question like this about 10 times a day when I am on here. It's like one of the most common questions.
Here is my copy and paste answer for this...
point P1 (-3,7.2) in the form (x1,y1)
point P2(2,-2.3) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
m = (-2.3-7.2) / (2-(-3))
notice all the minus signs and how i'm being very careful to keep close track of them. Also, who ever has written this question is intentionally trying to trip you up by putting in all the minus signs, there is no need for so many minus signs to teach this well. Anyway...
m = -8.5 / 5
m = - 1.7
the problem question ends there , but there is a common place this question is supposed to take you. to the point slope formula. but for another question.
The slope of (-3, 7.2) and (2, -2.3) is -1.9.
Consider,
(x1, y1) = (-3, 7.2)
(x2, y2) = (2, -2.3)
slope = (y2 - y1)/(x2-x1)
slope = ((-2.3) - (7.2))/((2) - (-3))
slope = (-9.5)/(5)
slope = -1.9
Therefore, the slope of the given points (-3, 7.2) and (2, -2.3) is -1.9.
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Jacob reduced the size of a painting to a width of 3. 2 inches. What would be the new height if the painting was originally 42. 88 inches in width and 33. 5 inches tall?.
The new height of painting by Jacob will be 2.5 inches.
The ratio and proportion will be used to relate the original and reduced dimensions of painting. The original width and height = 42.88/33.5. Let us assume the new height be x. So, new width and height = 3.2/x. Equating these two fractions -
42.88/33.5 = 3.2/x
Rewriting the equation according to x
x = (3.2 × 33.5) ÷ 42.88
Performing multiplication in numerator
x = 107.2 ÷ 42.88
Performing division on Right Hand Side of the equation
x = 2.5
Thus, the new height will be 2.5 inches.
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How much would you subtract from the grouping?
(4 – 2)4 – 42 × 4
Answer:
-160 I think so
Step-by-step explanation:
(2)4-168
8-168
-160
Which of the following is NOT a solution to -4x + 9 > -3
A: -3
B: -1
C: 3
D:5
Answer:
D
Step-by-step explanation:
-4x + 9 ≥ -3 Subtract 9 from both sides
-4x ≥ -12 Divide both sides by -4. When you divide both sides by a negative number, you must flip the inequality sign.
x ≤ 3
D: 5 is not a solution.
Answer:
D) 5
Step-by-step explanation:
To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?
How do you isolate a variable?
Here's an example.
x+3=18
What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.
x + 3 - 3= 18 - 3
Combine like terms.
x = 21
That's how you solve for an equation.
Next, an example with division.
3x = 21
How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.
[tex]\frac{3x}{3} =\frac{21} {3}[/tex]
Simplify:
3x/3 means 3 times x divided by 3. 3/3 = 1
1x = 21/3
21/3 = 7
x = 7
Now lets get to the problem.
[tex]-4x + 9 \geq -3[/tex]
The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.
[tex]-4x + 9 -9\geq -3 - 9[/tex]
Simplify.
[tex]-4x \geq -12[/tex][tex]-4x \geq -12[/tex]
Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:
A [tex]\geq , \leq , > , or < B[/tex]
If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!
When you multiply/divide by a negative number or both sides in an equality:
[tex]\leq[/tex] [tex]\geq[/tex]
[tex]\geq[/tex] [tex]\leq[/tex]
> <
< >
So, we currently have:
[tex]-4x \geq -12[/tex]
Divide by -4 on both sides.
[tex]\frac{-4x}{-4} \geq \frac{-12}{-4}[/tex]
Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).
[tex]x \geq 3[/tex]
Flip the sign (This is a crucial step!)
[tex]x \leq 3[/tex]
Now, [tex]x \leq 3[/tex] means any number equal to or lower than 3 satisfies the conditions of the inequality.
Is -3 lower than or equal to 3?
Yes; Lower
Is -1 lower than or equal to 3?
Yes;
Is 3 lower than or equal to 3?
Yes; Equal
Is 5 lower than or equal to 3?
No; Greater
D, 5 is your answer as it does not satisfy the inequality.
What is the converse of the conditional statement "If the streetlights are on, then the sun has gone down."?
O If the sun has gone down, then the street lights are on.
O If the streetlights are not on, then the sun has gone down.
O If the streetlights are not on, then the sun has not gone down.
If the sun has not gone down, then the streetlights are on.
The converse of the conditional statement "If the streetlights are on, then the sun has gone down" is If the sun has not gone down, then the streetlights are on and is denoted as option D.
What is Converse of the conditional statement?This is referred to as the type of sentence which is formed when the hypothesis and the conclusion are interchanged.
In this scenario, "If the streetlights are on, then the sun has gone down" when interchanged will be If the sun has not gone down, then the streetlights are on which therefore makes option D the correct choice.
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Eric rode his small motor bike 5 4/5 miles in 1/3 of an hour what is his average speed per mile
The Average speed is 17.4 mph.
What is Average speed?The average speed is calculated by dividing the total distance travelled by the total amount of motion time.
The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Average speed = Distance travelled/ Time taken
Given:
Distance = 5 4/5 = 29/5 miles
Time= 1/3 hours
So, Average speed = Distance travelled/ Time taken
Average speed= 29/5 x 3/1
= 87/5
= 17.4 mph
Hence, the Average speed is 17.4 mph.
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after begging his parents for 3 years, jason is finally going to clown college! on the first day, his juggling instructor divides a box of bean bags equally among the 16 clowns in jason's class. each clown gets 6 bean bags. which equation can you use to find the number of bean bags b in the instructor's box?
The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.
Given,
In the question:
His juggling instructor divides a box of bean bags equally among the 16 clowns in Jason's class. each clown gets 6 bean bags.
Now, According to the question:
The equation that can be used to determine the number of bean bags in the instructor's box is b = 16 x 6.
The number of bean bags in the instructor's box is 96.
What is multiplication?
Multiplication is a mathematical operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.
Hence, The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.
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if amy has 17 apples and gave 9 to jacob how may does amy hve if she goes to the store and buys 78 more?
Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86
find the distance when r=55 mi/hr and t =3
The distance when r = 55 mi/hr and t = 3 hours is 165 miles .
In the question ,
it is given that ,
r = 55 mi/hr which means the speed is 55 mi /hr
t = 3 hours , which means time = 3 hours .
we need to find the distance when r=55 mi/hr and t =3 hours .
the formula to calculate the distance is written as
distance = Speed × time
Substituting the value of speed = 55 and time = 3 ,
we get ,
distance = 55 × 3
distance = 165 miles .
the distance is 165 miles .
Therefore , The distance when r = 55 mi/hr and t = 3 hours is 165 miles .
The given question is incomplete , the complete question is
Find the distance when r=55 mi/hr and t = 3 hours ?
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Please help me please
The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.
We know that,
Sum of all angles of triangle = 180°.
Therefore, m∠3 + 42° + 25° = 180°.
m∠3 = 180° - 67°
m∠3 = 113°
Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.
We know that,
Vertical or opposite angles have equal measures.
So, 42° and m∠2 are vertical or opposite angles.
Therefore, the value of m∠2 = 42°.
Similarly, for m∠3, We know that,
Sum of all angles of triangle = 180°.
∴ ∠1 + ∠2 + 50° = 180°.
=> ∠1 + 42° + 50° = 180°
=> m∠1 = 88°.
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Find the nth term of the sequence 90,81,72,63
Answer: 9.
Step-by-step explanation:
These are all multiples of 9, meaning that they can all be divided by 9 into a whole number.
90/9 =10
81/9 =9
72/9 =8
63/9 =7
Answer:
9:N
Step-by-step explanation:
90-9=81
81-9=72
72-9=63
The same number (9) is used to fing the sum of the next number in the sequence therefore that is your nth term
Shawn had some nickels in a jar. He put 147 nickels in the jar. Now there are 435 nickels in the jar. How many nickels were in the jar at the start?
Responses
A 288288
B 218218
C 312312
D 398398
Answer:
A
288 nickels
Step-by-step explanation:
There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.
435 - 147 = 288
So, there were 288 nickels in the jar at the start.
Davis digs a hole at a rate of 3/4 feet every 10 minutes. After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
Enter your answer as a simplified fraction. NOT MIXED NUMBER
The elevation of the hole after placing the bush in the hole is 17/8 feet
How calculate the elevation of the hole after placing the bush in the hole?
Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes
After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole
This involves subtraction and multiplication of fractions
Since the rate of digging = 3/4 feet every 10 minutes
Thus, after digging for 40 minutes, the depth will be:
3/4 × 4 = 3 feet
If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:
3 feet - 7/8 feet = 17/8 feet
Therefore, after placing the bush in the hole, the elevation of the hole is 17/8 feet
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8x + 5° + 3x + 8° =90
Solve for x pls <3
Answer: x=7°
Combine like terms and divide.
8x+5°+3x+8°=90°
(8x+3x)+(5°+8°)=90°
11x+13°=90°
-13° -13°
11x=77°
[tex]\frac{11x}{11} =\frac{77}{11}[/tex]
x=7°
princeton pretzels picks a package box A 6in 7in 6in box B 3in 8in 9in calculate the volume of each box answer
Answer:
box a - 252 inches squared (6 x 7 x 6)
box b - 216 inches squared (3 x 8 x 9)
Step-by-step explanation:
Find f(x) +g(x) if f(x)=10-3 and g(x)=-x+3
Answer:
10 - x
Step-by-step explanation:
Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:
10 - 3 - x + 3
7 - x + 3
10 - x
Erin wants to buy a dictionary that costs $12, a dinosaur book that costs $16, and a
children's cookbook that costs $11. She has saved $29 from her allowance. How much
more money does Erin need to buy all three books?
Answer:
Erin would need $10 more dollars in order to buy all three books.
Step-by-step explanation:
Step one: find the cost of all books
12 +16 +11 = 39
Step two: subtract
39 -29 = 10
Step two: Get your Answer!
Erin would need $10 more dollars in order to buy all three books.
5,10,20 Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
The given sequence is geometric sequence not arithmetic.
What is arithmetic sequence?An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant
What is the geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.
Difference between arithmetic and geometric sequence:
An arithmetic sequence has a constant difference between each consecutive pair of terms
while
A geometric sequence has a constant ratio between each pair of consecutive terms.
Here, we have a sequence 5,10,20.
So a₁ = 5, a₂ = 10, a₃ = 20
Difference = a₃- a₂ = 20 - 0 = 10
a₂ - a₁ = 10 - 5 = 5
Since the difference is not constant, therefore the given sequence is not arithmetic.
Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.
Therefore, the sequence is geometric sequence.
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Today, Austin's age
is 1/4 of Stephanie's
age. In 4 years,
Austin's age will be
2/5 of Stephanie's age.
How old is Stephanie
today?
Answer: Steph is 16 today
Step-by-step explanation:
Austin age today = x
Austin in 4 years = x+4
Steph age today = 4x (because Austin is 1/4 her age today)
Steph age in 4 years is 4x + 4
In 4 years Austin's age is 2/5 of Steph's, so:
2/5 (x+4) = 4x + 4
Now solve for x!
x+4 = (8/5)x + 8/5
12/5 = (3/5)x
Therefore Austin is 4 years old today (x=4) and...
Steph age today = 4x = 4x4 = 16
1-8: MathXL for School: Practice & Problem Solving
0 Assignment is past due (10/27/22 11:59pm)
Question Help
The populations of Cities A and B are 3.7 x 105 and 2,115,000, respectively. The population of City C is twice the population
of City B.
The population of City C is how many times the population of City A?
1.8.PS-15
The population of City C is times the population of City A.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest tenth as needed.)
Answer:
11
Step-by-step explanation:
You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.
EvaluationThe ratio of interest is ...
2B/A = 2(2115000)/(3.7×10⁵)
A calculator provides an easy answer to the value of this expression. (See attached.)
City C is about 11 times the population of City A.
__
Additional comment
If you want to work this out "by hand", you will need to find the quotient of ...
4230000/370000 = 423/37 = 11 17/37 ≈ 11
because 17/37 < 1/2.
I need help please!!!!!!!
the slope of the given point is m=9
What is the slope of the line represented by the equation 2x-5y=9
The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
In the question ,
it is given that ,
the equation of the line is 2x - 5y = 9 .
we know that the equation of the line is represented as y = mx + c ,
where slope of the equation is "m" .
So , rewriting 2x - 5y = 9 in the form of y = mx + c ,
w get ,
2x - 5y = 9
5y = 2x - 9
dividing both sides of the equation 5y = 2x - 9 by 5 ,we get
y = 2/5x - 9/5
y = (2/5)x - 9/5
the slope is = 2/5 .
Therefore , The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
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In Cedarburg, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 12 kilometers and
the distance between the courthouse and the city pool is 13 kilometers, how far is the library
from the community pool?
kilometers
The library is 5 kilometres far from the community pool.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.
The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle
So, using Pythagoras theorem, we get
[tex]13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km[/tex]
So, the library is 5 kilometres far from the community pool.
Therefore, the distance between the library and the community pool is 5 kilometres.
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