Answer:
C
Step-by-step explanation:
We want to evaluate the definite integral:
[tex]\displaystyle \int_0^1 (x+2)(3x^2+12x+1)^{1/2}\, dx[/tex]
Again, notice that the radicand is quite similar to the outside factor. So, we can use u-substitution again. We will let:
[tex]\displaystyle u=3x^2+12x+1[/tex]
Then:
[tex]\displaystyle \frac{du}{dx}=6x+12[/tex]
Hence:
[tex]\displaystyle du=6x+12 \, dx[/tex]
And we can divide both sides by 6:
[tex]\displaystyle \frac{1}{6}\, du=x+2\, dx[/tex]
Note that the limits of integration of our original integral (from x = 0 to x = 1) is in the domain of x. Since we changed variables, we should also change the limits of integration to u. So:
[tex]u(0)=3(0)^2+12(0)+1=1[/tex]
And:
[tex]u(1)=3(1)^2+12(1)+1=16[/tex]
Hence, our new limits of integration is from u = 1 to u = 16.
Perform the substitution:
[tex]\displaystyle =\int_{1}^{16} u^{1/2}\Big(\frac{1}{6}\, du\Big)[/tex]
Simplify:
[tex]\displaystyle =\frac{1}{6}\int_1^{16}u^{1/2}\, du[/tex]
Integrate:
[tex]\displaystyle =\frac{1}{6}\Big(\frac{2}{3}u^{3/2}\Big)\Big|_{1}^{16}[/tex]
Simplify:
[tex]=\displaystyle \frac{1}{9}\Big(u^{3/2}\Big|_1^{16}\Big)[/tex]
Evaluate:
[tex]\displaystyle =\frac{1}{9}\Big(16^{3/2}-1^{3/2}\Big)=\frac{1}{9}(64-1)=7[/tex]
The answer is C.
As you know, there are three doors. Behind one door is a fabulous prize.
Behind the other two doors are bogus prizes. When you pick the first door
another door will open and show you a bogus prize, leaving the door you
picked and the third door closed. You once again pick one of the two closed
doors. You will either get the fabulous prize or the bogus prize
Answer:
What do you mean
Step-by-step explanation:
What expression is equivalent to 4y?
Answer:
4xy=x or ?
Step-by-step explanation:
Two bags of flour have a total weight of 8 3/4 pounds. What could be their individual weight
Answer:
4 3/8 lbs.
..................
There are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The individual weights of the bags of flour must add up to a total weight of 8 3/4 pounds.
We can express 8 3/4 as an improper fraction by multiplying the whole number 8 by the denominator 4 and adding the numerator 3, giving us 35/4.
Therefore, we can set up an equation:
x + y = 8 3/4
where x is the weight of one bag of flour, and y is the weight of the other bag of flour.
We can simplify 8 3/4 to 35/4, so the equation becomes:
x + y = 35/4
We can solve for one variable in terms of the other:
x = 35/4 - y
Now we can substitute this expression for x into the original equation and solve for y:
x + y = 35/4
(35/4 - y) + y = 35/4
35/4 = 35/4
This equation is true for any value of y.
Therefore, there are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.
For example, one bag could weigh 4 pounds and the other could weigh 4 3/4 pounds, or one bag could weigh 3 pounds and the other could weigh 5 3/4 pounds, and so on.
Thus,
There are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.
Learn more about expressions here:
https://brainly.com/question/3118662
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16
15. The dimensions of a triangle
with base 4 m and height
5 m are multiplied by 3. How
is the area affected?
Answer:
It increases it by 9.
Step-by-step explanation:
Given the following data;
Base = 4m
Height = 5m
Area of triangle = ½*base*height
Area of triangle = ½*4*5
Area of triangle = 2 * 5
Area of triangle = 10 m²
Multiplying the parameters by 3, we have;
Base = 4 * 3 = 12m
Height = 5 * 3 = 15m
To find the area of triangle;
Area of triangle = ½*base*height
Area of triangle = ½*12*15
Area of triangle = 6 * 15
Area of triangle = 90 m²
Therefore, multiplying the dimensions by a factor of 3 increases the area by 9.
HELP WITH MATH!! RLLY COULD USE IT
Answer:
120 square units
Step-by-step explanation:To find the area you do length times hight or l x h. If you want you can also make the triangle and move it to the other side to create a square if thats helps :) but you always do LxH for area :)
Answer:
120
Step-by-step explanation:
Since it's a parallelogram, it has to be A = BH.
Base in this problem: 10
Height in this problem: 12
10x12=120
what is y=3x and y=2x+2 solution ??
( , )
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
Try this: (2,6)
x=2, y=6
Step-by-step explanation:
Answer:
i belive it is (-2,-6)
What is the sum of the largest and smallest recorded capacity?
Answer:
A) 3 2/4
Step-by-step explanation:
1+2 2/4= 3 2/4
The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter. Round all answers to 4 decimal places.
Required:
a. What is the probability that the amount of collagen is greater than 60 grams per.
b. What is the probability that the amount of collagen is less than 90 grams per.
c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
Answer:
a) 0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.
b) 0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.
c) 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter.
This means that [tex]\mu = 65, \sigma = 7.7[/tex]
a. What is the probability that the amount of collagen is greater than 60 grams per.
This is 1 subtracted by the pvalue of Z when X = 60. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 65}{7.7}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a pvalue of 0.2578
0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.
b. What is the probability that the amount of collagen is less than 90 grams per.
This is the pvalue of Z when X = 90.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 65}{7.7}[/tex]
[tex]Z = 3.25[/tex]
[tex]Z = 3.25[/tex] has a pvalue of 0.9994
0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.
c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?
Between Z = 1 and Z = -1, so the proportion is the pvalue of Z = 1 subtracted by the pvalue of Z = -1
Z = 1 has a pvalue of 0.8413
Z = -1 has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826*100% = 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean
If 3 inches of rain fell in 5 hours, how much rain fell each hour? *
Answer:
Step-by-step explanation:
you can divide 5 divided by 3 and your answer will be 0.6
Someone please help me find the value of X
Answer:
2
Step-by-step explanation:
Solve for x if 26 = x/2
Answer:
x=52
Step-by-step explanation:
Sine divided by Cosine is equal to Tangent. True or false?
Answer:
True
Step-by-step explanation:
A man who is 2m tall stands on horizontal ground 30m from a tree. The Angel of elevation of the top of the tree from his eyes is 28 . Fine the distance between the men eyes to the top of the tree
Answer:33.95 m
Step-by-step explanation:
Given
The height of the man is 2 m
Distance between man and tree is 30 m
the angle of elevation of the top from the eyes is [tex]28^{\circ}[/tex]
from the figure,
[tex]\Rightarrow \tan 28^{\circ}=\dfrac{h}{30}\\\\\Rightarrow h=30\tan 28^{\circ}=15.91\ m[/tex]
Using Pythagoras we can write
[tex]\Rightarrow AD^2=ED^2+AE^2\\\Rightarrow AD^2=30^2+15.91^2\\\Rightarrow AD=33.95\ m[/tex]
Thus the distance between the men eyes to the top of the tree is 33.95 m
The area of a sector of an circle of a radius 5 cm, formed by an arc of length is 3.5cm. what is the answer
Answer:
8.75cm²
Step-by-step explanation:
First we need to find the angle subtended by the arc
L = theta/360 * 2pir
3.5 = theta/360 * 2*3.14(5)
3.5 = theta/360 * 31.4
theta/360 = 3.5/31.4
theta/360 = 0.11146
theta = 0.11146 * 360
theta = 40.13 degrees
Area of the sector = theta/360 * pir^2
Area of the sector = 40.13/360 * 3.14*25
Area of the sector = 40.13/360 * 78.5
Area of the sector = 8.75cm
Hence the area of the sector is 8.75cm²
3/4 x 1/5, just double checking for a test
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer....
3/4 × 1/5 = 3/20Hope it helps you,
Mark me brainliest plz....
Follow me! :)
the 30% discount on a $49 dollhouse
Answer:
34.30
Step-by-step explanation:
$14.70 is 30% of $49 so
The total would be $34.30 after the discount
But the discount is %14.70
A poll of 803 adults in the United States found that a majority—60%—said that changes should be made in government surveillance programs. The poll reported a margin of error of 3.5%.
Explain in plain English what we can conclude from this poll.
We can conclude that most American adults want changes in government surveillance programs. But we can't conclude what specific changes in those programs they want (more surveillance? less? it doesn't say.)
A population has a mean of 125 and a standard deviation of 16. A sample of 64 observations will be taken. The probability that the sample mean will be between 122.4 and 126.1 is
Answer:
0.61204
Step-by-step explanation:
μ = 125 ; σ = 16 ; n = 64
Probability that mean will be between 122.4 and 126.1
Z = (x - μ) / σ/sqrt(n)
x = 122.4
Z = (122.4 - 125) ÷ 16/sqrt(64)
Z = - 2.6 ÷ 2 = - 1.3
P(Z < - 1.3) = 0.0968
x = 126.1
Z = (126.1 - 125) ÷ 16/sqrt(64)
Z = 1.1 ÷ 2 = 0.55
P(Z < 0.55) = 0.70884
P(Z < 0.55) - P(Z < - 1.3)
0.70884 - 0.0968
= 0.61204
PLS HELP I WILL GIVE BRAINLYEST
Answer:
hey
Step-by-step explanation:
pls help me then i help u
How do you solve 11-15?
Which expression is equivalent to (3x^2y)^2 (2x^4y^2)^2?
A. 10x^10y^6
B. 12x^24y^8
C. 24x^10y^7
D. 36x^12y^6
PLEASE ANSWER QUICK
The sum of the data values divided by the number of data values is a measure of ______ and is called the _____
FIRST BLANK'S OPTIONS = CENTER/SPREAD
SECOND BLANK'S OPTIONS = MEAN/MEAN ABSOLUTE DEVIATION/MEDIAN/RANGE
Answer:
Center... Mean
Step-by-step explanation:
The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order.
the answer is NOT.. C. please help .
Answer:
Option B
Step-by-step explanation:
First term of the given arithmetic sequence 'a' = -3
Common difference in each successive term 'd' = -8 - (-3)
d = -5
Explicit formula for an arithmetic sequence will be,
[tex]A_n=a+(n-1)d[/tex]
Here, n = number of term
[tex]A_n[/tex] = nth term of the sequence
[tex]A_n=(-3)+(n-1)(-5)[/tex]
For n = 23,
[tex]A_{23}[/tex] = -3 + (23 - 1)(-5)
= -3 - 110
= -113
Option B is the answer.
Megan Sold 3 times as many concert tickets this week as she did last week. They sold 69 tickets this week. How many did she sell the week before
Answer: 23 is how many she sold last week.
Answer:
23
Step-by-step explanation:
3 times 23 is 69
If , then what is –K
Asap!!!
Answer:
I think C
I see a pattern
Do the opposite of their signs in the same number pattern just do their opposite sign.
PLS HELP ME OUT WITH THIS
Student A: 78, 99, 80, 85, 95, 79, 85, 96
Student B: 100, 80, 79, 75, 92, 93, 75, 78, 84
Student A Mean:
Student A Mean Absolute Deviation:
Student B Mean:
Student B Mean Absolute Deviation:
Answer:
Student A Mean: 697/8=87.125
Student A Mean Absolute Deviation: 7.1563
Student B Mean: 756/9=84
Student B Mean Absolute Deviation: 7.3333
Can someone please help me?
I will try i had this unit last year, basically the diameter is 5 in this problem, which you multiply by pi (in this case I will use 3.14 as the shortened version since its on-going) which gives you 15.7, then you multiply that by 3 in this problem to get 47.1!
Answer:
Step-by-step explanation:
Volume of a cylinder formula = πr^2h
r (radius) = 5/2 = 2.5
h (height) = 3
Answer: 3π(2.5)^2 = 3π(6.25) = 18.75π cubic units
Write an equation of the line that passes through (-2, 0) and is perpendicular to the line y=-1/3x+3
Slope of y = -⅓x + 3 is -⅓ (on comparing with m of y = mx + c)
As the required line is perpendicular to this, slope of the required line = - 1 / (-⅓) = 3
Equation:
=> y - y1 = m(x - x1)
=> y - 0 = (3)(x - (-2))
=> y = 3(x + 2)
=> 3x - y + 6 = 0
an oil company bores a hole 80m deep estimate the cost of boring if the cost is £30 for drilling the first meter with an increase in cost of £2 per meter for each succeeding meter
Answer: £188
Step-by-step explanation:
Given
The depth of the hole is 80 m
For the first meter, it is £30
After that, it is £2 per meter
after a meter, it is 79 m more
The total cost is C
[tex]\Rightarrow C=30+2\times 79\\\Rightarrow C=30+158=188[/tex]
GEOMETRY!!!! Will give brainliest