Answer:
Sorry, what's your direct question here.
Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^4, y=1 and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.
The base of the solid - call it B - is the set of points
B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}
Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².
Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².
Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,
[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]
Which of the following is NOT true of the F test? Choose the correct answer below. A. This test is very resistant to departures from normal distributions. B. This test requires that both populations have normal distributions. C. This test compares two population variances or standard deviations. D. This test uses the F distribution.
Answer:
A. This test is very resistant to departures from normal distributions.
Step-by-step explanation:
The Ftest or Fratio usually used to obtain the test statistic during hypothesis testing using the analysis of variance, is used to compare the equality or differences in population vatfuance or standard devuation. The critical values of the Ftest or Fratio is obtained using the F distribution table. When testing hypothesis using the F test, it requires that both populations follow a normal distribution.
Hence, the option, that F test is resistant to departures for normal distribution is not true of the Ftest.
What is the quotient and remainder, written as partial fractions, of 2x^3-25x+40/x^2+2x-8
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Answer:
(2x -4) +1/(x -2) -2/(x +4)
Step-by-step explanation:
The attached shows the quotient is (2x -4) and the remainder expressed as a fraction is ...
r = (8 -x)/(x^2 +2x -8)
So, the problem is to write the partial fraction expansion of this remainder. It will be of the form ...
r = A/(x -2) +B/(x +4)
where (x-2)(x+4) is the factorization of the divisor quadratic.
The value of A can be found by evaluating (x -2)r at x=2.
(x -2)r for x=2 is (8 -2)/(2 +4) = 6/6 = 1
The value of B can be found by evaluating (x +4)r at x=-4.
(8 -(-4))/(-4-2) = 12/-6 = -2
Then the quotient and remainder, written as partial fractions is ...
= (2x -4) +1/(x -2) -2/(x +4)
_____
Additional comment
In the form ...
[tex]r=\dfrac{8-x}{x^2+2x-8}[/tex]
we can see that (x -2)r will be ...
[tex](x -2)r = \dfrac{(x-2)(8-x)}{(x-2)(x+4)}=\dfrac{8-x}{x+4}[/tex]
This can be evaluated at x=2, as we have done above. Similar factor cancellation works to give (x+4)r = (8-x)/(x-2).
This method of arriving at the "A" and "B" values may not pass technical scrutiny regarding where r is defined or undefined--but it works. One could consider the work to be finding a limit, rather than evaluating a rational function at points where it is undefined.
Answer:
A. 2x-4- 2/x+4 +1/x-2
Step-by-step explanation:
Edge
five tenths percent of what number is twelve
Answer:
Step-by-step explanation:
5/10 is 1/2 or .5 As a percentage, this is .5%, and as a decimal it's .005. Using this in an equation, .005x = 12. Divide 12 by .005 to get 2400
What is the range of the data set shown below?
A. 36
B. 34
C. 32
D. 30
Answer:
b 34 the higest is 40 an the lowest 6 the diferens is 34
Step-by-step explanation:
Mark me brainlest pliz
Answer:
i would but this not my question this is theres he right A.
Step-by-step explanation:
a sequence of numbers is given by 25,30,35..............,300. find the number of terms in the sequence
Answer:
56
Step-by-step explanation:
clearly, the sequence is built by adding 5 for every new term.
so, an = an-1 + 5
a1 = 25 (the starting value)
a2 = a1 + 5 = 25 + 5 = 30
a3 = a2 + 5 = a1 + 5 + 5 = a1 + 2×5 = 25 + 10 = 35
...
an = an-1 + 5 = a1 + (n-1)×5
now, we know, the last term is 300.
when we determine for which n we get an = 300, we know that n is the number of terms in the sequence.
so,
300 = a1 + (n-1)×5 = 25 + 5n - 5 = 20 + 5n
280 = 5n
n = 56
a56 = 300
so, we have 56 terms in this sequence
Answer:
56
Step-by-step explanation:
nth term = a+d(n-1) =25+5(n-1) = 25+5n-5 = 20+5n
300 = 20 + 5n
5n = 280
n = 56
since 300 is the last term in the sequence, the total number would be 36
Solve the following system of equations by using the inverse of a matrix.
Give your answer as an ordered triple (x , y , z)
Answer:
(x, y, z) = (-8,4,-2)
Step-by-step explanation:
.......................................
If f(x) = 2(x - 5), find f(8).
04
06
O 8
16
Answer:
6
Step-by-step explanation:
f(x) = 2(x - 5)
f(8) = 2(8 - 5)
f(8) = 16 - 10
f(8) = 6
The answer is 6, hope this helps.
[tex]\boxed{ \sf{Answer}} [/tex]
[tex]\sf \: f(x) = 2(x - 5) \\ \\\sf x = 8 \\ \\\sf f(8) = 2(8 - 5) \\\sf \: f(8) = 2(3) \\ \sf \: f(8) = 2 \times 3 \\\sf f(8) =\underline 6[/tex]
Option B - 06 is the correct answer.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
in one particular suburb slacks have been reduced to $36. This price is at 90% of the original price for slacks. Given this what is the original price of the slacks
Translate To An Algebraic Expression:
S% of 1/r
Answer:
S/100r
Step-by-step explanation:
S% of 1/r = (1/r x S) : 100
(1/r x S) : 100
S/r : 100
S/100r
Two accountants for the firm of Elwes and Wright are arguing about the merits of presenting an income statement in a multiple-step versus a single-step format. The discussion involves the following 2020 information related to Bramble Company ($000 omitted).
Administrative expense
Officers' salaries
$5,006
Depreciation of office furniture and equipment
4,066
Cost of goods sold
60,676
Rent revenue
17,336
Selling expense
Delivery expense
2,796
Sales commissions
8,086
Depreciation of sales equipment
6,586
Sales revenue
96,606
Income tax
9,176
Interest expense
1,966
Common shares outstanding for 2020 total 38,960 (000 omitted).
(a) Prepare an income statement for the year 2020 using the multiple-step form. (Round earnings per share to 2 decimal places, e.g. 1.48.)
(b) The parts of this question must be completed in order. This part will be available when you complete the part above.
Answer:
73,188
Step-by-step explanation:
fees plus costs minus expenses
The ages of a group of 142 randomly selected adult females have a standard deviation of 18.1 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=18.1 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 99% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? The required sample size is
Answer:
Start with the formula for Z:
Z = (x-µ)/(σ/√n)
We want the sample mean to be within one-half year of the population mean, so we set x-µ=0.5. We are looking for a 99% confidence interval, so we set Z=2.7578. We are told to use σ=18.1. Plugging those values into the formula, we get:
2.5758 = 0.5(18.1/√n)
We can rearrange to solve for n:
((2.5758-18.1)/0.5)2 = n
Plugging that into our calculator, we get n = 964.003. Since we can't have a fraction of a person in our sample, it would be safest to round up to n=965. (But since .003 is so small, I'd also accept 964 as an answer.)Step-by-step explanation:
The required sample size for the given population distribution is; n = 8696 female ages
We are given;
Standard deviation; σ = 18.1
Confidence level; CL = 99%
Now, formula to find the margin of error is;
E = z(σ/√n)
Where;
E is margin of error
z is critical value at confidence level
σ is standard deviation
n is required sample size
Now we are told that the sample mean is within one-half year of the population mean.
Thus;
E = 0.5
z value at 99% Confidence level is;
z = 2.576
Thus, Making n the subject of the formula is;
n = (zσ/E)²
n = (2.576 × 18.1/0.5)²
n = 8695.78
Approximating to a whole number gives;
n = 8696 female ages
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a test has 20 multiple-choice questions with 5 choices each, followed by 35 true/false questions. if a student guesses on each question, how many ways can he answer the questions on the test
Answer
There are 170 ways the student can answer the test.
Explanation
If there are 20 multiple-choice questions with 5 choices each, the student has 100 choices. The first question has 5 choices to pick from. The second has 5 as well. So does the third. Hopefully now you realize that you have to multiply the number of choices by the number of questions.
The same thing goes with the true/false questions. There are 2 choices for each true/false question, and there are 35 of those. 35×2 is 70. There are 70 ways to answer on the true/false questions.
Now combine the number of choices on the first part and the second part; 100+70 is 170.
In Riverview Middle school, 20 percent of the students participate in an after school club for every 100 students how many are in an afterschool club
Answer:
What is the diferentes between and red bolos celos ?
Step-by-step explanation:
3pt b) Suggest one way that is always under the control of the researcher of making the margin of error smaller.
Answer:
By making use of a lower confidence level
Step-by-step explanation:
The margin of error is also referred to as the confidence interval and it is the system in which we use to measure the error in the result of the survey or experiment.
Now, for us to reduce the margin of error, there are different things we can do such as;
- increasing sample size
- using less data variation
- making use of a lower confidence level
- making use of a one sided confidence interval rather than a two sided confidence interval.
Looking at the above different methods of making the margin of error smaller, the one that is always under the control of the researcher is "making use of a lower confidence level".
Every other means, he does not have as much control as he has to do to lower the confidence level. That one is strictly based on his jurisdiction.
Tony invested $9538 in an account at 8% compounded daily. Identify the compound
interest C after 1 years.
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Answer:
$794.30
Step-by-step explanation:
The account balance for principal P invested at rate r compounded daily for t years is ...
A = P(1 +r/365)^(365t)
We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.
P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30
The interest earned in one year is $794.30.
eight cards are drawn from a standard deck of 52 cards. how many hands off with cards contain exactly three queens and three jacks g
Answer:
15,136 hands off with cards contain exactly three queens and three jacks.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[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]
Standard deck:
4 queens and 4 jacks.
The other 52 - 8 = 44 cards are neither queens nor jacks.
Wow many hands off with cards contain exactly three queens and three jacks?
3 queens from a set of 4.
3 jacks from a set of 4.
2 other cards(not queens neither jacks) from the other 44. So
[tex]C_{4,3}C_{4,3}C_{44,2} = \frac{4!}{1!3!} \times \frac{4!}{1!3!} \frac{44!}{2!42!} = 4*4*22*43 = 15136[/tex]
15,136 hands off with cards contain exactly three queens and three jacks.
Please helpppp me I really confused
Answer:
The answer would be D
Step-by-step explanation:
This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.
For f(x) = x2 - x + 3, find
a, f(2)
b. f(3a)
Answer:
a.5
b.3a+3
Step-by-step explanation:
in a,u need to replace 2 with x,so it will be 4-2+3
in b,replace 3a with x and so it will be6a-3a+3
Find the area of a triangle with a height of 38 and one side of 44
In triangle it is given that,
→ Height (h) = 38 cm
→ Base (b) = 44 cm
The formula we use,
→ Area of triangle = ½ × b × h
Now we have to,
find the area of the triangle,
→ ½ × b × h
→ ½ × 44 × 38
→ (44 × 38)/2
→ 1672/2 = 836 cm²
So, 836 cm² is area of triangle.
porfavor se los agradeceria mucho y de corazon :D
Answer:
1=2p+3
2=
Step-by-step explanation:
The cost of an apple has decreased from $0.50 to $0.40. Work out the decrease cost of an apple as a percentage.
Answer:
Decreased by 20%
Step-by-step explanation:
0.5 x ? = 0.4
? = 0.4/0.5
? = 0.8
1 - 0.8 = 0.2
0.2 = 20%
To check, 20% of 0.5 is 0.1. 0.5 - 0.1 is 0.4. So the answer is correct.
Write the equation of a line in the slope-intercept form that has a slope of 4
and contains the point (4, 12).
Answer:
The equation of the point (4, 12) is y=4x+12
Random samples of size 81 are taken from a population whose mean is 45 and standard deviation is 9. Calculate the probability that a sample mean is less than 42. (round to 4 decimal places)
HINT: When you randomly select a group (n > 1) then you need to re-calculate the standard deviation using the formula:
σ n
Answer:
Using z table
= 0.0013
The probability = 0.0013
Step-by-step explanation:
Given that,
mean = μ = 45
standard deviation = σ = 9
n=81
μT = μ =45
[tex]\sigma T = \sigma / \sqrt n = 9 / \sqrt81 =1[/tex]
[tex]P(T <42 )\\= P[(T - \mu T ) / \sigma T < (42-45) /1 ]\\\\= P(z <-3 )[/tex]
Using z table
= 0.0013
probability= 0.0013
The coordinates of three points are A(- 1, - 3) , B(2, 3) and C(6, k) . If AB is perpendicular to BC find (i) the value of k, (ii) the gradient of AC (iii) the acute angle that AC makes with the x-axis.
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Answer:
(i) k = 1
(ii) 4/7
(iii) arctan(4/7) ≈ 29.7°
Step-by-step explanation:
(i) A graph of the given points is helpful. It shows us the slope of AB is ...
mAB = rise/run = 2/1 = 2
so the slope of BC must be the opposite reciprocal, -1/2.
Point C is 6-2 = 4 units to the right of point B, so will be (-1/2)(4) = -2 units from point B in the vertical direction. That is, ...
k = 3 -2
k = 1
__
(ii) The gradient of AC is found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(6 -(-1))
mAC = 4/7
__
(iii) The angle that line AC makes with the +x axis is the arctangent of the slope:
arctan(4/7) ≈ 29.7° . . . angle between AC and +x axis
Which statement is true about the parts of this expression?
StartFraction 5 over 6 EndFraction + one-fourth x minus y
The constant is StartFraction 5 over 6 EndFraction.
The only coefficient is One-fourth.
The only variable is y.
The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
Answer:
The constant is StartFraction 5 over 6 EndFraction
Step-by-step explanation:
StartFraction 5 over 6 EndFraction + one-fourth x minus y
5/6 + 1/4x - y
A. The constant is StartFraction 5 over 6 EndFraction.
True
B. The only coefficient is One-fourth.
False
There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1
C. The only variable is y
False
There are 2 variables: variable x and variable y
D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
False
5/6 and 1/4x are not like terms
The only true statement is: The constant is StartFraction 5 over 6 EndFraction
Answer:
It's A if you don't want to read. A). The constant is 5/6
Step-by-step explanation:
Find the number of distinguishable arrangements of the letters of the word SEPTILLION
Answer:
10!
Step-by-step explanation:
Septillion-10 letters
1-s-10 places to be in
2-e-9
3-p-8
4-t-7
5-i-6
6-l-5
7-l-4
8-i-3
9-o-2
10-n-1
So, then
10×9×8×7×6×5×4×3×2×1=10!
or 3628800
The arrangement of the number will be equal to 3628800.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
The given word is SEPTILLION. The word has 10 characters. The different ways of the arrangement will be calculated as,
Arrangement = 10!
Arrangement = 10×9×8×7×6×5×4×3×2×1
Arrangement = 3628800
Therefore, the arrangement of the number will be equal to 3628800.
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Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?
Answer: -3/8
Step-by-step explanation:
Expanding z we get
z = 4x^2 - 4xy + y^2 - 2y^2 - 3y
= -y^2 - (4x + 3) y + 4x^2.
After Archimedes chooses x, Brahmagupta will choose
y=-(4x+3/2) in order to maximize z
Then
z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2
z=8x^2+6x+9/4
To minimize this expression, Archimedes should choose x=-3/8
You throw two four-sided dice. Let the random variable X represent the maximum value of the two dice. Compute E(X). Round your answer to three decimal places.
Answer:
E(X)=3.125
Step-by-step explanation:
We are given that two four sided dice.
Then , the sample space
{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
Total number of outcomes=16
Let the random variable X represent the maximum value of the two dice
Outcomes X P(X)
(1,1) 1 1/16
(1,2),(2,1),(2,2) 2 3/16
(1,3),(2,3),(3,1),(3,2),(3,3) 3 5/16
(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4) 4 7/16
Using the probability formula
[tex]P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}[/tex]
Now,
[tex]E(X)=\sum_{i=1}^{n}x_iP(x_i)[/tex]
[tex]E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)[/tex]
[tex]E(x)=\frac{1+6+15+28}{16}[/tex]
[tex]E(x)=\frac{50}{16}=3.125[/tex]
Which of the following statements is false?
A 3 5x
= 1
5x 3
B. 6xy + (-6xy) = 0
C. 5xy+ 2zx = 2zx + 5xºy
D. 8x? = 9xy = 9xy = 8x?
