You probably want the unsigned area, which means you don't compute the integral
[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]
but rather, the integral of the absolute value,
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]
[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]
Four buses carrying 198 students from the same school arrive at a football stadium. The buses carry, respectively 90, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students who were on the bus carrying the randomly selected student. One of the four bus drivers is also randomly selected. Let Y denote the number of students on her bus. a) Which of E[X] or E[Y] do you think is larger
Answer:
E[x] is larger
Step-by-step explanation:
I think E[x] is larger because the expected number of students on the bus of a randomly chosen student is larger.
This is because the higher the number of students present in a bus, the higher the probability that a randomly selected student would have been on that bus.
Whereas, for every driver to be chosen, the probability of any bus being chosen is 1/4 irrespective of the number of students in that particular bus
Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
i think its b
???
Step-by-step explanation:
im sorry if im wrong im not very confident on my answer :(
Answer:
D
Step-by-step explanation:
Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Scott is driving to visit family. After 3 hours of driving, Scott traveled 180 miles. After driving for 5 hours at the same rate, he traveled 300 miles. Which equation represents this situation
Answer:
y = 60 *x
Step-by-step explanation:
The rate is 180 miles / 3 hours = 60 miles per hour
Check by dividing 300 miles / 5 hours = 60 miles per hour
y = 60 *x where y is miles and x = time
Answer:
Step-by-step explanation:
What is the converse of r->(~q v p)
Answer:
[tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Step-by-step explanation:
In general, remember that the converse of [tex]a => b[/tex] is [tex]\neg b => \neg a[/tex] , therefore in this case [tex]a = r \ \ , b = \neg q \ \lor p[/tex]
so [tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Customers can pick their own pumpkins at the great pumpkin patch. They pay $4 to enter and $3 per pound for the pumpkins they pick. Write an equitation to model the total cost, y, for x pounds of pumpkins.
Answer:
y=3x+4
Step-by-step explanation:
4 is the y intercept and 3 is the slope which is how much per pound. The equation you can use is y=mx+b, m is the slope so you fill it in with 3 and b is the y intercept so you fill it in with 4.
What the answer fast
Answer:
HI = 13
Step-by-step explanation:
The triangle that is shown is a 45-45-90 triangle, so we know that GH = GJ = 9 and IJ = 13, we are able to solve for HI.
Technically, IJ = HI, since both triangles are congruent. Both IJ and HI will be 13.
The equation that represents the canned goods order is 24x + 64y = 384, where x = number of minutes for producing fruit cans and y = number of minutes for producing vegetable cans.
What is the meaning of the y-intercept?
Answer:
The y-intercept is the number of minutes for producing vegetable cans when no minutes are used for fruit cans
Step-by-step explanation:
The problem statement tells you y is the number of minutes for producing vegetable cans. The y-intercept is the y-value when x = 0.
The y-intercept is the number of minutes for producing vegetable cans when no minutes are used for fruit cans.
Answer:
The y-intercept, at the point (0, 6), designates the choice to compose vegetables for 6 minutes. In 6 minutes, making 64 cans of vegetables per minute, 384 cans for the order decree performed. The 0 for the x-value designs that no time spent producing cans of fruit.
Step-by-step explanation:
I got it right on edgenuity
A group of children is trying to share a pile of stickers. If every
child gets two stickers, there will be 7 stickers left over. If two
children do not get any stickers, then each of the remaining
children will get exactly 3 stickers.
How many children are in the group?
Answer:
7 children
Step-by-step explanation:
Answer:
7 children is the correct answer
and you follow me if you can't I will unfollow you
Statistics students in Oxnard College sampled 10 textbooks in the Condor bookstore, and recorded number of pages in each textbook and its cost. The bivariate data is shown below, Number of Pages ( x ) Cost( y ) 526 52.08 625 59 589 56.12 409 25.72 489 34.12 500 53 906 78.48 251 26.08 595 50.6 719 68.52 A student calculates a linear model y = x + . (Please show your answers to two decimal places) Use the model above to estimate the cost when number of pages is 563 Cost = $ (Please show your answer to 2 decimal places.)
Answer:
y = -0.85 + 0.09x; $49.82
Step-by-step explanation:
1. Calculate Σx, Σy, Σxy, and Σx²
The calculation is tedious but not difficult.
[tex]\begin{array}{rrrr}\mathbf{x} & \mathbf{y} & \mathbf{xy} & \mathbf{x^{2}}\\526 & 52.08 & 27394.08 & 276676\\625& 59.00 & 36875.00 &390625\\589 & 56.12 & 33054.68 & 346921\\409 & 25.72 & 10519.48 & 167281\\489 & 34.12& 16684.68 & 293121\\500 & 53.00 & 26500.00 &250000\\906 & 76.48 & 71102.88 & 820836\\251 &26.08 & 6546.08 & 63001\\595 & 50.60 & 30107.00 & 354025\\719 & 68.52 & 49265.88 & 516961\\\mathbf{5609} & \mathbf{503.72} &\mathbf{308049.76} & \mathbf{3425447}\\\end{array}[/tex]
2. Calculate the coefficients in the regression equation
[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{503.7 \times 3425447 - 5609 \times 308049.76}{10 \times 3425447- 5609^{2}}\\\\= \dfrac{1725466163 - 1727851103.84}{34254470 - 31460881} = -\dfrac{2384941}{2793589}= \mathbf{-0.8537}[/tex]
[tex]b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{3080498 - 2825365.48}{2793589} = \dfrac{255132}{2793589} = \mathbf{0.09133}[/tex]
To two decimal places, the regression equation is
y = -0.85 + 0.09x
3. Prediction
If x = 563,
y = -0.85 + 0.09x = -0.85 + 0.09 × 563 = -0.85 + 50.67 = $49.82
(If we don't round the regression equation to two decimal places, the predicted value is $50.56.)
The area of an Equilateral triangle is given by the formula A= 3pi squared/4(s)Squared. Which formula represents the length of equilateral triangle’s side S?
Answer:
The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .
Step-by-step explanation:
We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
So, the area of an equilateral triangle = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
where, s = side of an equilateral triangle
A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
Cross multiplying the fractions we get;
[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]
[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]
Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;
[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]
Taking square root both sides we get;
[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sequence to its appropriate recursively defined function. f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2 f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2 f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2 f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2 f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2 f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2 Sequence Recursively Defined Function -24, -96, -384, -1,536, ... 28, -112, 448, -1,792, ... 13, 39, 65, 91, ...
Answer:
sequence 3no matching sequenceno matching sequenceno matching sequencesequence 2sequence 1Step-by-step explanation:
Recursively Defined Function Sequence
f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2 13, 39, 65, 91, ...
f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2
f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2
f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2
f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2 28, -112, 448, -1,792, ...
f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2 -24, -96, -384, -1,536, ...
__
The initial values are easily seen. They match f(1). The recursive functions can be tested to see if they match the offered sequences.
sequence 1 has a common ratio of 4 (not -4)
sequence 2 has a common ratio of -4 (it is not arithmetic)
sequence 3 has a common difference of 26 (it is not geometric)
Answer:
1 is sequence 3
5 is sequence 2
6 is sequence 1
(These r not included in the test, so don't use them)
|
\ /
2 is no matching sequence
3 is no matching sequence
4 is no matching sequence
Step-by-step explanation:
PLATO
Find the unknown side length, x. Write your answer in simplest radical form.
Answer:
Correct option: D
Step-by-step explanation:
In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:
[tex]a^2 = b^2 + c^2[/tex]
Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).
So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:
[tex]x^2 = 40^2 + 42^2[/tex]
[tex]x^2 = 1600 + 1764[/tex]
[tex]x^2 = 3364[/tex]
[tex]x = 58[/tex]
So the correct option is D.
Find the slope of the line passing through the points (-5, 3) and (7,9).
Answer:
[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points
[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]
Substitute:
[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
We can use the slope formula since we have 2 points
m = ( y2-y1)/(x2-x1)
= (9-3)/( 7 - -5)
= (9-3) /( 7+5)
= 6/ 12
= 1/2
Express the following ratio in the simplest form vii) 4.5km: 450m
Answer:
4.5 ×1000 =4500m
Step-by-step explanation:
450/1000=0.45km
Answer: 10 : 1
Step-by-step explanation: Now first let’s convert this to the same units, for instance, the SI unit for length meters. 4.5 x 1000 = 4500m. Then put the ratio 4500m : 450m. You can divide 4500 by 450 as it is divisible so you get 10 as the answer.
Even if you have converted them to kilometers before, nevermind, still 4.5 divide by 0.45 is 10 and there the answer is 10 : 1 or shortly the ratio is just 10.
The charge to rent a trailer is $2525 for up to 2 hours plus $99 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.82.8 hours, 33 hours, and 8.78.7 hours. Then graph all ordered pairs, (hours, cost), for the function.
The question is not written properly! Complete question along with answer and step by step explanation is provided below.
Question:
The charge to rent a trailer is $25 for up to 2 hours plus $9 per additional hour or portion of an hour.
Find the cost to rent a trailer for 2.8 hours, 3 hours, and 8.7 hours.
Then graph all ordered pairs, (hours, cost), for the function.
Answer:
ordered pair = (2.8, 34)
ordered pair = (3, 34)
ordered pair = (8.7, 88)
Step-by-step explanation:
Charge for 2.8 hours:
$25 for 2 hours
$9 for 0.8 hour
Total = $25 + $9
Total = $34
ordered pair = (2.8, 34)
Charge for 3 hours:
$25 for 2 hours
$9 for 1 hour
Total = $25 + $9
Total = $34
ordered pair = (3, 34)
Charge for 8.7 hours:
$25 for 2 hours
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 0.7 hour
Total = $25 + $9 + $9 + $9 + $9 + $9 + $9 + $9
Total = $88
ordered pair = (8.7, 88)
The obtained ordered pairs are graphed, please refer to the attached graph.
Which of the following points is a solution of the inequality y <-Ixl
You did not give any options but i will try to answer.
y < -lxl basically means that the value of y is less than the absolute value of x time - 1.
So if x = 2, then y is any number less than -2.
And if x is -3. then y is any number less than -3.
Happy to help!
Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2
The lines of the inequalities are parallel, and the system of inequalities do not have any solution.
How to determine the solution of the inequalitiesThe system of inequalities are given as:
y ≥ 2x + 1 y ≤ 2x – 2The inequality y ≥ 2x + 1 has the following characteristics:
A slope of 2A y-intercept of 1A closed line, where the upper region is shadedThe inequality y ≤ 2x – 2 has the following characteristics:
A slope of 2A y-intercept of -2A closed line, where the lower region is shadedSee attachment for the graphs of the system of inequalities
Read more about system of inequalities at:
https://brainly.com/question/9774970
Which inequality is shown in this graph?
(0, 2) (-1,-2)
a) y>=-4x+2
b) y>=4x+2
c) y<=-4x+2
d) y<=4x+2
Answer:
B y ≥ 4x + 2
Step-by-step explanation:
1. find slope of the line: (y² - y¹) / (x² - x¹)
(0, 2) and (-1, -2)
(-2 - 2) / (-1 - 0) = -4 / -1 = 4
y = 4x + 2*
*+2 because that is the y-intercept as shown by point (0, 2)
2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >
3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥
4. final equation: y ≥ 4x + 2
Ten thousand raffle tickets are sold for $1 each. One first prize of $2000, 4 second prizes of $700 each, and 8 third prizes of $300 each are to be awarded, with all winners selected randomly. If you purchase one ticket, what are your expected winnings? 132 cents -$0.28 72 cents -$0.88
Answer:
72 cents.
Step-by-step explanation:
The expected winnings is the amount times the probability that you will get that amount.
2,000 * (1/10,000) = 2,000 / 10,000 = 2 / 10 = 0.2.
700 * (4 / 10,000) = 2,800 / 10,000 = 28 / 100 = 0.28.
300 * (8 / 10,000) = 2,400 / 10,000 = 24 / 100 = 0.24.
0.2 + 0.28 + 0.24 = 0.72.
Hope this helps!
a student took a test that had 60 questions.if he got 45 right,what percentage of the question did he get right?
Answer:
25 %
is your answer
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i will give brainliest and 50 points pls help ASP
pls can u show how to work this out thx !!! : )
its a simultaneous equation
Answer:
x = 3
y = -2
Step-by-step explanation:
Given:
8x - 3y = 30 ..................(1)
3x + y = 7 .......................(2)
Eliminate y by adding (1)+3*(2)
8x-3y + 3*( 3x+y) = 30 + 3*7
8x + 9x -3y + 3y = 51
17x = 51
x = 3 .....................(3)
substitute (3) in (2)
3(3) + y = 7
y = 7-9 = -2
y = -2 ....................(4)
Answer:
Step-by-step explanation:
[tex]8x-3y=30\\y=7-3x\\\\8x-3(7-3x)=30\\8x-21+9x=30\\17x=51\\x=3\\\\y=7-3(3)\\y=7-9\\y=-2[/tex]
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
Can someone help me with this question
Answer:
Product of given question is 6√5
Step-by-step explanation:
Given:
3√2(√10)
Find:
Product.
Computation:
⇒ 3√2(√10)
⇒ 3√20
⇒ 3√4×5
⇒ 3√2×2×5
⇒ 3×2√5
⇒ 6√5
Product of given question is 6√5
The population of Oak Forest is increasing at a rate of 4% per year. If the population is 74,145 today, what will it be in three years?
Answer:
83,403
Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.
Hope this helps!
which of the following graph represents the solution set for the inequality 3 - 1/2 x > 10
Answer:
56
Step-by-step explanation:
Solve application problems using radical equations. Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 378 square feet. How long can a side of his patio be?
Answer:
3(sqrt42) ft
Step-by-step explanation:
If l is side length of square patio, then area of patio would be l^2.
l^2 = 378
l = sqrt378 = 3(sqrt42)
Given: (in picture as I cannot type it like that.) Name the postulate or theorem you can use to prove: (also in the picture) A. HL Theorem B. AAS Theorem C. SAS Postulate D. ASA Postulate
Answer:
You need to use the AAS (angle angle side) congruency theorem
Step-by-step explanation:
youre welcome!!!
Answer:
The Angle-Angle-Side Postulate (AAS)
Step-by-step explanation:
It is given that angle 1 and 2 are equivalent so that is angle #1
It is given that angle 3 and 4 are also equivalent so that is angle #2
And finally, it is given that side TS and side TR are equivalent giving you that last side you need to prove the type of Postulate it is
If this helped, please consider giving me brainliest, it will help me a lot
Have a good day! :)
The five numbers summary for a data set is shown below. What is the range of the data set? 3, 7, 11, 14, 16
Answer:
13
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
So, in order to find the range, you first order the data from least to greatest. Which it is already.
3, 7, 11, 14, 16
Then subtract the smallest value from the largest value in the set.
16 - 3 = 13
Hope this helps you out! : )
Which of the following is an exterior angle of triangle BHE? Yes or no
Answer:
Im not 100% sure, but I think it is:
No
No
No
Yes
