2) Evaluate ſa arcsin x dx by using suitable technique of integration.
Answers
To evaluate the integral ∫√(1 - \(x^{2}\)) dx, where -1 ≤ x ≤ 1, we can use the trigonometric substitution technique. We get the result (1/2) θ + (1/4) sin 2θ + C where C is the constant of integration.
By substituting x = sinθ, the integral can be transformed into ∫\(cos^2\)θ dθ. The integral of \(cos^2\)θ can then be evaluated using the half-angle formula and integration properties, resulting in the answer.
To evaluate the given integral, we can employ the trigonometric substitution technique. Let's substitute x = sinθ, where -π/2 ≤ θ ≤ π/2. This substitution helps us simplify the integral by replacing the square root term √(1 - \(x^{2}\)) with √(1 - \(sin^2\)θ), which simplifies to cosθ.
Next, we need to express the differential dx in terms of dθ. Differentiating both sides of x = sinθ with respect to θ gives us dx = cosθ dθ.
Substituting x = sinθ and dx = cosθ dθ into the integral, we obtain:
∫√(1 - \(x^2\)) dx = ∫√(1 - \(sin^2\)θ) cosθ dθ.
Simplifying the expression inside the integral gives us:
∫\(cos^2\)θ dθ.
Now, we can use the half-angle formula for cosine, which states that \(cos^2\)θ = (1 + cos 2θ)/2. Applying this formula, the integral becomes:
∫(1 + cos 2θ)/2 dθ.
Splitting the integral into two parts, we have:
(1/2) ∫dθ + (1/2) ∫cos 2θ dθ.
The first integral ∫dθ is simply θ, and the second integral ∫cos 2θ dθ can be evaluated to (1/2) sin 2θ using standard integration techniques.
Finally, substituting back θ = arcsin x, we get the result:
(1/2) θ + (1/4) sin 2θ + C,
where C is the constant of integration.
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Related Questions
When Maria started her career at the age of 24, she deposited $800 into a savings account that earns 8.75% interest compounded semiannually. If she
makes no other deposits or withdrawals, find the total amount in the
account when she retires at the age of 65.
a. $11,378.17
b. $26,791.81
c. $27,817.94
d. $209,234.59
Answers
Answer: Answer is b
Step-by-step explanation:
a) perform a linear search by hand for the array [20,−20,10,0,15], loching for 0 , and showing each iteration one line at a time b) perform a binary search by hand fo the array [20,0,10,15,20], looking for 0 , and showing each iteration one line at a time c) perform a bubble surt by hand for the array [20,−20,10,0,15], shouing each iteration one line at a time d) perform a selection sort by hand for the array [20,−20,10,0,15], showing eah iteration one line at a time
Answers
In the linear search, the array [20, -20, 10, 0, 15] is iterated sequentially until the element 0 is found, The binary search for the array [20, 0, 10, 15, 20] finds the element 0 by dividing the search space in half at each iteration, The bubble sort iteratively swaps adjacent elements until the array [20, -20, 10, 0, 15] is sorted in ascending order and The selection sort swaps the smallest unsorted element with the first unsorted element, resulting in the sorted array [20, -20, 10, 0, 15].
The array is now sorted: [-20, 0, 10, 15, 20]
a) Linear Search for 0 in the array [20, -20, 10, 0, 15]:
Iteration 1: Compare 20 with 0. Not a match.
Iteration 2: Compare -20 with 0. Not a match.
Iteration 3: Compare 10 with 0. Not a match.
Iteration 4: Compare 0 with 0. Match found! Exit the search.
b) Binary Search for 0 in the sorted array [0, 10, 15, 20, 20]:
Iteration 1: Compare middle element 15 with 0. 0 is smaller, so search the left half.
Iteration 2: Compare middle element 10 with 0. 0 is smaller, so search the left half.
Iteration 3: Compare middle element 0 with 0. Match found! Exit the search.
c) Bubble Sort for the array [20, -20, 10, 0, 15]:
Iteration 1: Compare 20 and -20. Swap them: [-20, 20, 10, 0, 15]
Iteration 2: Compare 20 and 10. No swap needed: [-20, 10, 20, 0, 15]
Iteration 3: Compare 20 and 0. Swap them: [-20, 10, 0, 20, 15]
Iteration 4: Compare 20 and 15. No swap needed: [-20, 10, 0, 15, 20]
The array is now sorted: [-20, 10, 0, 15, 20]
d) Selection Sort for the array [20, -20, 10, 0, 15]:
Iteration 1: Find the minimum element, -20, and swap it with the first element: [-20, 20, 10, 0, 15]
Iteration 2: Find the minimum element, 0, and swap it with the second element: [-20, 0, 10, 20, 15]
Iteration 3: Find the minimum element, 10, and swap it with the third element: [-20, 0, 10, 20, 15]
Iteration 4: Find the minimum element, 15, and swap it with the fourth element: [-20, 0, 10, 15, 20]
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Mrs. Johnson bought 12 pound of ham and used it to make 3 sandwiches. She uses the same amount of ham on each sandwich. What fraction of a pound of ham is on each sandwich
Answers
The fraction of a pound of ham that each sandwich has for the case when Mrs Johson used 12 pounds of ham to make 3 sandwiches is 4 pound per ham. or 4/1
How to interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, \(a \div b =\) a divided in b equal parts.
Also, we can write: \(a \div b = a \times \dfrac{1}{b}\)
(it is since a = a times 1 so \(a/b = 1 \times (a/b) = (1/b) \times a\))
For this case, we're specified that:
Total ham Mrs. Johnson bought = 12 poundsTotal sandwiches that she makes of that amount of ham = 312 pound of ham is divided in 3 parts for 3 sandwiches (assuming equally divided).
That means:
Amount of ham each sandwich gets = 12 divided by 3 = 12/3 = 4 pounds.
To find the fraction of a pound of ham that is on each sandwich, we find what part of a pound is 4 pounds.
If we take 4 times a pound, then we get 4 pounds.
Thus, 4 of a pound = 4 pound
In fraction, we have: 4 pounds = 4/1 fraction of a pound.
Thus, the fraction of a pound of ham that each sandwich has for the case when Mrs Johson used 12 pounds of ham to make 3 sandwiches is 4 pound per ham. or 4/1 fraction of a pound
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Alex has 235 candies. He wants to place the candies in five equal groups. How many candies will Alex place in each group?
A.47
B.30
C.81
D.20
(help,by the way its a math test and i need help with this question)
Answers
Answer:
A.47
Step-by-step explanation:
Step-by-step explanation:
235 / 5 = 47
Hence there are 47 candles in each group (A).
What is the value of x?
2
3
6
7
Answers
Answer:
x = 2
Step-by-step explanation:
AE is equal to the sum of AB and BE because of segment addition postulate, we can substitute to get AE = 11 + x + 1 = x + 12
DE is equal to the sum of DC and CE because of segment addition postulate, we can substitute to get DE = 1 + x + 4 = x + 5
To solve the problem, we can use power of a point, more specifically exterior secants products scenario. In this case, we can get the equation:
AE * BE = DE * CE
Now, we can substitute and solve:
(x + 12)(x + 1) = (x + 5)(x + 4)
x^2 + 13x + 12 = x^2 + 9x + 20
13x + 12 = 9x + 20
4x + 12 = 20
4x = 8
x = 2
Answer fast pleaseee, Solve the following system of equations: y= -5x +1 and y= -x-3
Answers
Answer:
x=1 y=-4
Step-by-step explanation:
Answer:
(1, - 4 )
Step-by-step explanation:
Given the 2 equations
y = - 5x + 1 → (1)
y = - x - 3 → (2)
Since both are expressed in terms of y, equate the right sides, that is
- x - 3 = - 5x + 1 ( add 5x to both sides )
4x - 3 = 1 ( add 3 to both sides )
4x = 4 ( divide both sides by 4 )
x = 1
Substitute x = 1 into either of the 2 equations and evaluate for y
Substituting into (2)
y = - 1 - 3 = - 4
Solution is (1, - 4 )
Clare follows the same workout cycle each time she goes to the gym. First, she runs for
1
3
of an hour. Then, she lifts weights for
1
6
of an hour. If Clare has 1
1
2
hours to spend at the gym, how many times can she go through her workout cycle?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answers
Answer:
3 times.
Step-by-step explanation:
She has 1 1/2 hour to spend in the gym.
1 hr = 60 minutes.
1/2 of an hour= 1/2 * 60= 30 minutes.
In total, she spends 90 minutes in the gym.
If 1/3 of an hour is meant in running, it translates into: 1/3 * 60 = 20 minutes.
If 1/6 of an hour is spent in weight-lifting, it translates into: 1/6 * 60 = 10 minutes.
In total, she spends, 20 minutes + 10 minutes = 30 minutes for both activities.
To obtain the number of times she would perform both activities, we divide the total amount of time spent in the gym by the amount of time spent for both activities.
90 minutes/30 minutes= 3 times for each cycle.
a rectangular pool is 9 meters wide and 12 meters long. if you swim diagonally across the pool, how many meters would you be swimming?
Answers
if you swim diagonally across the pool, you would be swimming for 15 meters.
Define rectangleA rectangle is a 2-dimensional shape with four straight sides and four right angles. It is a type of quadrilateral where opposite sides are parallel and congruent, and all angles are 90 degrees (right angles). The length of a rectangle is typically defined as the longer side, and the width is the shorter side.
We can use the Pythagorean theorem to find the length of the diagonal:
diagonal² = width² + length²
Substituting the given values, we get:
diagonal² = 9² + 12²
diagonal² = 81 + 144
diagonal² = 225
diagonal = √(225)
diagonal = 15 meters
Therefore, if you swim diagonally across the pool, you would be swimming for 15 meters.
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Consider the probability distribution of the random variable X
X P(X)
0 0.1
1 0.2
2 0.3
3 ?
a. Find the missing (?) probability value
b. Find E(X).
c. Find Var(X) and x.
d. If Z = 1 + 2/3X, find E(Z), Var(Z) and z.
Answers
a. The missing probability value is 0.4.
b. E(X) = 1.4.
c. Var(X) = 0.56 and σx = 0.75.
d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.
The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.
To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.
To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.
Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.
To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.
Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.
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Which of the following would not be used to describe a slope?
steepness of a line.
ratio of rise to run of a line.
ratio of the vertical change to the horizontal change of a line.
Attempted
ratio of the horizontal change to the vertical change of a line.
Answers
The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.
The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.
Slope=Vertical Change/Horizontal Change
This is also represented as the "ratio of rise to run of a line".
Slope=Rise/Run
In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".
Horizontal Change/ Vertical Change= 1/slope
This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.
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Which of the following statements are true about the figure above?
Check all that apply.
Answers
Answer:
a and c
Step-by-step explanation:
because its a 3rd demenshion sphere
You and your friends Jamal and Carla decide to make some money during summer vacation by building and selling dog houses. To get the business started, Jamal contributes $25.55, and Carla contributes $34.45 to buy equipment and materials. You all agree that each person will earn the same amount of money after Jamal and Carla get back what they invested. Your business earns a total of $450. How much money does each person get at the end of the summer?
Answers
450 - 60 = 390
390 / 3 = 130
Fill in geometry proofs. ANGLES. ( I WILL GIVE BRAINLIEST! PLS HELP!)
refer to attachment
Answers
Here are the answers
#2
Reflexive sides
#3
Already given in question
#4
Given in the question
#5
By bisector definition
#6
Third angle therom
#7
Angle-Side-Angle
.Calculate pay in the following cases- 2+4+3= 10 marks
a) Mark works at a rock concert selling programs. He is paid $20 for showing up,
plus 45 cents for each program that he sells. He sells 200 programs. How
much does he earn working at the rock concert?
b) Mary wood is an architect working for New Horizons. She makes every month a salary of 5500.
i What is her annual income?
ii What is her gross earnings per pay period.
iii How much does she earn per period if paid semi-monthly
iv How much does she earn per period if paid weekly.
c) Danny Keeper is paid $12.50 per hour. He worked 8 hours on Monday and Tuesday, 10 hours on Wednesday and 7 hours on Thursday. Friday was a public holiday and he was called in to work for 10 hours. Overtime is paid time and a half. Time over 40 hours is considered as overtime. Calculate regular salary and overtime. Show all of your work.
Answers
a) Mark earns $110 at the rock concert, b) i) Mary's annual income is $66,000, c) Danny's regular salary is $400 and his overtime salary is $75. His total salary is $475.
a) Mark sells 200 programs, so he earns an additional $0.45 for each program. Therefore, his earnings from selling programs is 200 * $0.45 = $90. In addition, he earns a fixed amount of $20 for showing up. Therefore, his total earnings at the rock concert is $20 + $90 = $110.
b) i) Mary's annual income is her monthly salary multiplied by 12 since there are 12 months in a year. Therefore, her annual income is $5,500 * 12 = $66,000.
ii) Mary's gross earnings per pay period would depend on the pay frequency. If we assume a monthly pay frequency, her gross earnings per pay period would be equal to her monthly salary of $5,500.
iii) If Mary is paid semi-monthly, her earnings per pay period would be half of her monthly salary. Therefore, her earnings per pay period would be $5,500 / 2 = $2,750.
iv) If Mary is paid weekly, we need to divide her monthly salary by the number of weeks in a month. Assuming there are approximately 4.33 weeks in a month, her earnings per pay period would be $5,500 / 4.33 = $1,270.99 (rounded to the nearest cent).
c) To calculate Danny's regular salary and overtime, we need to consider his regular working hours and overtime hours.
Regular working hours: 8 hours on Monday + 8 hours on Tuesday + 8 hours on Wednesday + 8 hours on Thursday = 32 hours.
Overtime hours: 10 hours on Wednesday (2 hours overtime) + 10 hours on Friday (2 hours overtime) = 4 hours overtime.
Regular salary: Regular working hours * hourly rate = 32 hours * $12.50/hour = $400.
Overtime salary: Overtime hours * hourly rate * overtime multiplier = 4 hours * $12.50/hour * 1.5 = $75.
Therefore, Danny's regular salary is $400 and his overtime salary is $75. His total salary would be the sum of his regular salary and overtime salary, which is $400 + $75 = $475.
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Suppose that X and Y are random variables and that X and Y are nonnegative for all points in a sample space S. Let Z be the random variable defined by Z(s) = max(X(s), Y (s)) for all elements s â S. Show that E(Z) ⤠E(X) + E(Y).
Answers
For the Random variables, X and Y where both are nonnegative for all points in a sample space S. The expected value of Z ( random variable) is, E(Z) = E(X) + E(Y).
We have X and Y are random variables and that X and Y are non-negative for all points in a sample space S. Let us consider X be another random variable defined as Z(s) = max( X(s), Y(s))
for all elements s belongs to S. We have to show that E( Z) = E(X) + E(Y)
Now, for simple way of representation let
Max ( X(s),Y(s)) = Max(X,Y)
We know that Max(X,Y) = [(X+Y) + |X-Y|]
So, Z = Max(X,Y) = [(X+Y) + |X-Y|]
Taking expectations E(Z) = E(Max(X,Y)
= E{[(X+Y) + |X-Y|]}
\(E(Z)= \frac{1}{2} [E(X+Y) + E|X-Y|] = [E(X) + E(Y) + E|X-Y|] \\ \) (Since E(X + Y) = E(X)+ E(Y))
\(E(Z) = \frac{1}{2}[E(X)+ E(Y) + E|X| + E|-Y|]\\ \)
\(= \frac{1}{2} [E(X) + E(Y) + E(X) + E(Y)]\) (Since X and Y are non negative so E|X| = E(X) and E(-Y)=E(Y) )
=> E(Z) = E(X)+ E(Y)
Hence, required results occurred.
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The angle between 0° and 360° and is coterminal with a standard position angle measuring 840° _angle is degrees. The angle between -360° and 0° and is coterminal with a standard position angle measuring 840° _angle is degrees.
Answers
The angle that is coterminal with 840° between 0° and 360° is 120°.
The angle that is coterminal with 840° between -360° and 0° is -120°.
What is the angle between 0° and 360° ?To find the angle that is coterminal with 840° between 0° and 360°, we can subtract multiples of 360° from 840° until we get a value between 0° and 360°.
840° - 360° = 480° (still greater than 360°)
480° - 360° = 120°
What is coterminal with a standard position angle measuring 840°?Therefore, the angle that is coterminal with 840° between 0° and 360° is 120°.
To find the angle that is coterminal with 840° between -360° and 0°, we can add multiples of 360° to -840° until we get a value between -360° and 0°.
-840° + 360° = -480° (still less than -360°)
-480° + 360° = -120°
Therefore, the angle that is coterminal with 840° between -360° and 0° is -120°.
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how do I do 3y - 6 = 2x
Answers
Slope: 2/3
Y-Intercept: (0,2)
Can someone please help me asap I’ll mark brainlist
Answers
Answer:
y = 54.5x
Step-by-step explanation:
i divided y by x and 54.5 was the answer for all of them
hope this helped !
What are two ways to find the area of a rectangle?
Answers
2. Or if you only know the value of one side, you can find area of a rectangle using the Pythagorean theorem.
TWO of the following formulas are correct. Select the two that are correct. Please be aware that for questions like this where there are one or more correct answers, Canvas will deduct points for incorrect selections. Z=( value − mean )/ std devn Z= (mean-value) / std devn Value =(z ∗
std devn )+ mean Value =(z− mean )/ std devn Z=( value − std devn )/ mean Value =( mean − std devn )/z
Answers
The two correct formulas are:
Z = (value - mean) / std devn
Value = (z * std devn) + mean
The first correct formula, Z = (value - mean) / std devn, represents the calculation of the Z-score. The Z-score is a measure of how many standard deviations an individual data point is from the mean of a distribution. By subtracting the mean from the value and dividing it by the standard deviation, we obtain the standardized score.
The second correct formula, Value = (z * std devn) + mean, allows us to convert a Z-score back to its corresponding original value. By multiplying the Z-score (z) by the standard deviation and adding the mean, we can recover the original value from its standardized form.
The remaining formulas in the list are incorrect. The formula Z = (mean - value) / std devn is incorrect because it reverses the order of subtraction, resulting in an incorrect calculation of the Z-score. The formulas Z = (value - std devn) / mean and Value = (mean - std devn) / z do not follow the correct structure for calculating Z-scores or converting Z-scores back to their original values.
It's essential to use the correct formulas to ensure accurate calculations and interpretations when working with Z-scores and transforming between standardized and original values in statistical analysis.
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I need help with Part c).angle of elevation. 29 degrees angle of depression. 18 degrees
Answers
From the diagram, we get that the height we are looking for is h₂*0.914. To compute h₂ we notice that it is equal to the tangent of the depression angle times 31 yds.
Therefore:
\(\begin{gathered} h_2=\tan (18^{\circ})\times31\text{yds,} \\ h_2\approx10.0725\text{ yds.} \end{gathered}\)Answer: 9.21 meters.
PLEASEEEE SOMEONE HELP I GIVE AS MUCH POINTS :’( Thank you!
Answers
The approximate area of the trapezoid is determined as 13.95 unit².
What is the approximate area of the trapezoid?The approximate area of the trapezoid is calculated as follows;
Area = ¹/₂(b₁ + b₂)h
Where;
b₁ and b₂ are the lengths of the parallel sidesh is the heightThe y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;
y(3/2) = - (3/2)²/2 + 3/2 + 5
y(3/2) = -9/8 + 3/2 + 5
y(3/2) = 5.375
y(4) = -4²/2 + 4 + 5
y(4) = -8 + 9
y(4) = 1
h = 5.375 - 1 = 4.375
The approximate area of the trapezoid is calculated as;
Area = ¹/₂(5.375 + 1) x 4.375
Area = 13.95 unit²
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Identify the graph of the inequality 2(2x – 1) + 7 < 13 or –2x + 5
Answers
Answer:
Can I help me how 2 get answers here
I am new here
Answer:
c
Step-by-step explanation:
45w + 150 > 560
PLEASE HELP Given the function \(f(x)=\sqrt{3x+3+2}\)
![PLEASE HELP Given the function [tex]f(x)=\sqrt{3x+3+2}[/tex]](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/Ad2aQsFIHOi0QE5qUc6z5ZYEYYJiGV0r.png)
Answers
Answer:
98.97
Step-by-step explanation:
I used my notes on page 34
in a party, 5 male-female couples attend. the males and females are randomly paired for a dance. what is the probability that exactly two couples are dancing together?
Answers
The probability of exactly 2 couples dancing together is 100/45 = 20/9.
To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.
The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.
So the probability of exactly 2 couples dancing together is 100/45 = 20/9.
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The probability of exactly 2 couples dancing together is 100/45 = 20/9.
To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.
The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.
So the probability of exactly 2 couples dancing together is 100/45 = 20/9.
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Expand and combine like terms.
(4m" - 5m)(4m + 5m") =
Answers
Answer:
(4m - 5m) (4m + 5m)
16m + 20m - 20m - 25m
36 m -45m
=-9m
Question 4
4 pts
You roll 2 fair 6-sided dice. What is the probability of rolling a sum of 7 or more?
18/36 or 1/2
20/36 or 5/9
19/39
21/36 or 7/12
Answers
Answer:
here we have rolled two dice. So total no. of possible outcomes will be 6^2=36. These are (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).
Now, among these cases the cases where the sum is seven for (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) i.e. there are 6 cases.
Now, it is time to calculate the probability.
The required probability is,
p = (No. of cases favorable for the event)/(Total no. of cases)
=6/36 =
Step-by-step explanation:
Two fair six-sided dice are rolled. What is the probability that the sum of the two dice is seven?
r(x)=2 square root x s(x)=square root x
(rs)(4) =
(r/s)(3)=
Answers
Answer:
rs)(4)=(2rootX)(rootX)
(rs)(4)=2x
(rs)(4)=8
(r/s)(3)=(2rootX)/(rootX)
(r/s)(3)=2
Step-by-step explanation:
PLEASE HELP ILL MARK AS BRAINLIEST IF CORRECT
Beth travels at an average speed of 30 mph for 20 miles.
Without stopping, Beth then travels 70 miles in 1.5 hours.
Find her average speed for the entire journey to 2 dp.
Answers
Answer:
41.54 mph
Step-by-step explanation:
you need to find the total distanceand total time to find the average speed
use distance/time = speed equation
time = 1.5 hours + 40 mins = 2 hours 10 mins
distance= 20 + 70 = 90 miles
90/130 mins x 60 = 41.54 mph
Given the explicit formula for an arithmetic sequence find the first five terms and the term named in theproblem.a=65- 100nFind a 39
Answers
Given:
a = 65 - 100n
Let's find the first five terms.
\(\begin{gathered} \text{First term:} \\ a_1=65-100(1)\text{ = 65-100=-35} \end{gathered}\)\(\begin{gathered} \text{Second term:} \\ a_2=65-100(2)=65-200=-135 \end{gathered}\)\(\begin{gathered} \text{Third term:} \\ a_3=65-100(3)\text{ = 65 - 300 = }-235 \end{gathered}\)\(\begin{gathered} \text{Fourth term:} \\ a_4=65-100(4)\text{ = 65-400=-335} \end{gathered}\)\(\begin{gathered} \text{Fifth term:} \\ a_5=65-100(5)=65-500=-435 \end{gathered}\)For a39, we have:
\(a_{39}=65-100(39)=65\text{ - 3900=}-3835\)ANSWER:
First term = -35
Second term = -135
Third term = -235
Fourth term = -335
Fifth term = -435
39th term = -3835