Answers
Answer:
1. n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}
2. n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}
3. D. I, II and III.
Step-by-step explanation:
U = {21, 22, 23, ..., 64}
A prime number is a number that can be divided only by 1 and itself.
A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
B = {24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}
C = {6, 10, 12, 15, 20, 30, 60}
1. Find n[(A U B) - C]
n(A U B) = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63}
n[(A U B) - C] = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63} - {6, 10, 12, 15, 20, 30, 60}
Since only 30 and 60 are common to n(A U B) and C, we therefore remove them it and have:
n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}
2. Find n[(A - B) U C]
To get n(A - B) we remove all the elements of B in A. Since there are no common elements between A and B, we therefore have:
A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
C = {6, 10, 12, 15, 20, 30, 60}
Therefore, we have:
n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}
3. Which of the following is/are true?
I. A ∩ B = A ∩ C
A ∩ B = ∅
A ∩ C = ∅
Therefore, A ∩ B = A ∩ C is true.
II. A - B = A - C
A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
A - C = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
Therefore, A - B = A - C is true.
III. A ∩ (B ∪ C) = ∅
A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
B U C = {6, 10, 12, 15, 20, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}
Therefore, A ∩ (B ∪ C) = ∅ is true.
Therefore, the correct option is D i.e. I, II and III are true.
Related Questions
Plsss answer plsss
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The number of unique letter arrangements that can be created using all the
letters in the word QUIZLET if the vowels and consonants must alternate is
Answers
Answer:
Quiz
Let
It
Step-by-step explanation:
I believe that is it. Hope this helps ^^
Have a great day! :p
x^2 + 6x +15=0 solve the equation using the quadratic formula
Answers
Help me with this. I am really stuck.
Answers
By Side-Angle-Side congruence theorem and the assumption that ΔABC is an equilateral triangle and ∠ 1 ≅ ∠ 2 , we conclude that the angles ADB and CDB are congruent.
How to prove a feature of a geometric system
In this problem we find a geometric system formed by two triangles that form an equilateral triangle, whose proof must be done by using definitions of definitions and theorems from Euclidean geometry. The complete procedure is shown below:
AB ≅ AC ≅ BC Definition of equilateral triangle∠ 1 ≅ ∠ 2 GivenDB is a side of ΔABD and ΔBCD GivenDB is a bisector of ∠B Definition of bisectorΔABD ≅ ΔBCD SAS Theorem of congruence of triangles∠ADB ≅ ∠CDB Step 3 / ResultHence, the angles ADB and CDB of the geometric system formed by the triangles ABD and BCD shown in the picture are congruent.
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plssssssssssss help!
Answers
Answer: D
Explaination: Because they are equal but different at the same time
Calculate -0.4 as a percentage of 1.8
Answers
Answer:
-22.2222222222%
Step-by-step explanation:
-0.4/1.8×100
Please help! Easy question, answer pls, 15 pts.
Answers
Answer:
360 in
Step-by-step explanation:
To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:
\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)
So, the dressmaker has 360 in of ribbon.
Which equation of an exponential function has a graph that passes through the points
(1,5) and (2,15)?
Answers
Answer:
\(y = \frac{5}{3} (3^{x} )\)
Step-by-step explanation:
In general, \(y = k(b^{x})\)
Substitute x = 2, y = 15
(1) \(15 = kb^{2}\)
Substitute x = 1, y = 5
(2) \(5 = kb^{1} = kb\)
Divide equation (1) by equation (2)
\(\frac{15 = kb^{2} }{5= kb }\)
3 = b
Now substitute b = 3 in equation (2) to find k
5 = k(3)
\(k = \frac{5}{3}\)
Since we know the values for k and b, we now have the exponential function that passes thru (1, 5) and (2, 15)
\(y = \frac{5}{3} (3^{x} )\)
Evaluate the expression when b= -4 and x=2. b - 2x
Answers
-4 - 2 * 2
-4 - 4 = -8
The answer is
-8
A bookstore owner has 15 different books to arrange on the shelves in a display case. Each shelf can display 3 books.In how many different ways can the owner arrange 3 books on the top shelf of the display case
Answers
There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.
How many different ways can you arrange3 books on a shelf?different bundles of novels, and we have to put this bundle and other 3 books onto the shelf. So the total number of ways is 3! × (3 + 1)! = 144.How many ways can you arrange 3 books on a shelf from a group of 7?= 5040 arrangements. Three books that we want together have 3!Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways.A trilogy is a set of three distinct works that are connected and can be seen either as a single work or as three individual works. They are commonly found in literature, film, and video games.When using three shelves, place the middle shelf higher or lower than the one on either side. Five shelves can be staggered with two or three higher than the others, alternating every other shelf for a horizontal groupingTo learn more about arrange3 books on a shelf refers to:
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A rug like a rectangle has a width of 3 m . The length of the rug is 2 m greater than its widith . What is the perimeter of the rug in meters
Answers
Answer:
16m
Step-by-step explanation:
Given data
Width = 3m
Lenght = 2+3= 5m
We know that the expression for perimeter is
P= 2L+2W
Substitute
P= 2*5+ 2*3
P= 10+6
P= 16 m
Hence the perimeter is 16m
find the length and width of a rectangle that has the given perimeter and a maximum area.perimeter: p units
Answers
Question: Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: p unitsMain Answer:The maximum area of a rectangle with a given perimeter occurs when the rectangle is a square.
Thus, to find the length and width of a rectangle that has the given perimeter and a maximum area, we must solve for the dimensions of a square using the given perimeter.The formula for the perimeter (P) of a rectangle is given as: P = 2l + 2w, where l represents the length of the rectangle and w represents the width.To solve for the length and width of a rectangle that has a given perimeter (p) and a maximum area,
we must first solve for the length and width of the corresponding square using the given perimeter (p). We can do this by dividing the perimeter by 4 (since a square has four equal sides).Length of one side of the square is `p/4`.As the square is the rectangle with maximum area, we can say that l = w= `p/4` units.Explanation:Thus, the length and width of the rectangle are both equal to `p/4` units, and the rectangle with these dimensions has the given perimeter and maximum area.
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Suppose that X is a random variable with mean 20 and standard deviation 4. Also suppose that Y is a random variable with mean 40 and standard deviation 7. Find the mean and the variance of the random variable Z for each of the following cases. Be sure to show your work.
(a) Z = 40 - 5X
(b) Z = 15X - 20
(c) Z = X + Y
(d) Z = X - Y
(e) Z = -2X + 3Y
Answers
(a) The mean of Z in case (a) is -60 and the variance is 400.
(b) The mean of Z in case (b) is 280 and the variance is 3600.
(c) The mean of Z in case (c) is 60 and the variance is 65.
(d) The mean of Z in case (d) is -20 and the variance is 65.
(e) The mean of Z in case (e) is 80 and the variance is 505.
To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.
(a) Z = 40 - 5X
Mean of Z:
E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60
Variance of Z:
Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400
Therefore, the mean of Z in case (a) is -60 and the variance is 400.
(b) Z = 15X - 20
Mean of Z:
E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280
Variance of Z:
Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600
Therefore, the mean of Z in case (b) is 280 and the variance is 3600.
(c) Z = X + Y
Mean of Z:
E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60
Variance of Z:
Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65
Therefore, the mean of Z in case (c) is 60 and the variance is 65.
(d) Z = X - Y
Mean of Z:
E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20
Variance of Z:
Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65
Therefore, the mean of Z in case (d) is -20 and the variance is 65.
(e) Z = -2X + 3Y
Mean of Z:
E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80
Variance of Z:
Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505
Therefore, the mean of Z in case (e) is 80 and the variance is 505.
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On a print-out of these slope fields, sketch for each three solution curves to the differential equations that generated them. Then complete the following statements: For the slope field in figure 1. a solution passing through the point (0.-1) has slope. For the slope field in figure 1. a solution passing through the point (-2.2) has slope. For the slope field in figure 2. a solution passing through the point (1.-3) has slope For the slope field in figure 2. a solution passing through the point (0.4) has a slope.
Answers
Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.
What is slope field?A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.
Here,
For figure 1 slope field=
\(\frac{dy}{dx}=\frac{-17x-2y}{y}\)
For figure 2 slope field=
\(\frac{dy}{dx} = xy-3\\\)
For figure 1 a solution passing through the point (0,-1)
therefore,
slope=
\(\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2\)
so slope comes out to be negative
For figure 1 a solution passing through the point (-2,2)
\(\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30\)
so slope comes out to be negative
For the slope field in figure 2. a solution passing through the point (1.-3)
\(\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6\)
so slope comes out to be negative
\(\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3\)
so slope comes out to be negative.
Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.
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When two consecutive whole numbers are randomly selected, what is the probability that one of them is a multiple of 4
Answers
The total number of possibilities in this case is 24 + 25 = 49. Hence, the probability of selecting two consecutive whole numbers where one of them is a multiple of 4 is: P = (25 + 49) / (100 × 99) = 0.74.
Probability is defined as the measure of the likelihood of an event occurring. It can be determined by dividing the number of ways an event can occur by the total number of possible outcomes. The probability of randomly selecting two consecutive whole numbers where one of them is a multiple of 4 can be found
There are two scenarios to consider:Either the first number is a multiple of 4 or the second number is a multiple of 4.Case 1: The first number is a multiple of 4There are 25 such multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, and 100. Therefore, the number of possibilities in this case is 25.Case 2: The second number is a multiple of 4If the first number is a multiple of 4.
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Find the distance.
1. (-2,2) (4, -1)
2. (-3,-5) (2, 5)
3. (-4,0). (2, 3)
Answers
Answer:
1)3√5
2)5√5
3)3√5
A bicycle costs $240 and loses 35 of its value each year. What is the value of the bike after 3 years?
Answers
Answer:
135 In the 3rd year
Step-by-step explanation:
240-35= 205
205-35=170
170-35=135 (Or just use a calculator)
The time spent (in days) waiting for a kidney transplant for people with ages 35-49 can be approximated by the normal distribution with a mean of 1667 and a standard deviation of 207.4. What waiting time represents the first quartile?
Answers
The waiting time represents the first quartile is approximately 1530.4 days. Given that the time spent (in days) waiting for a kidney transplant for people with ages 35-49 can be approximated by the normal distribution with a mean of 1667 and a standard deviation of 207.4.
The formula for the normal distribution is:z = (x - μ) / σWhere,z is the standard score,μ is the mean,σ is the standard deviation,x is the observation whose standard score, z, is to be found. First quartile (Q1) is the 25th percentile and it divides the distribution into 25% and 75%
So,We have,μ = 1667σ = 207.4Q1 = 25th percentile = 0.25
From the Z- table, the value corresponding to 0.25 is -0.67z = -0.67
Let the waiting time be x days.So,-0.67 = (x - 1667) / 207.4
Multiplying by 207.4 on both sides of the equation,-0.67 × 207.4 = x - 1667-136.6 = x - 1667x = 1530.4
Therefore, the waiting time represents the first quartile is approximately 1530.4 days.
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solve this equation using synthetic division x³+2x²+4x+8=0
Answers
Answer:
Your answer is.......
x^3 + 2x^2 + 4x + 8=0 Note.. if x=-2 then whole equation is 0
So, (x+2) is one factor.
x^3 + 2x^2 + 4x + 8
=x^2(x+2)+4(x+2)
(x+2)(x^2+4)
Mark my answer as brainlist. pls pls pls
open parentheses fraction numerator f cubed to the power of -2 end exponent over denominator h to the power of negative 1 end exponent end fraction close parentheses to the power of 4.I need this in exponential form, please.
Answers
First part
numerator f cubed g to the power of negative 2
The numerator can be written as
\(f^3g^{-2}\)Second part
denorminator h raised to the power of negative 1
The numerator can be written as
\(h^{-1}\)combining part one and two
Open parentheses fraction - fraction - close parentheses to the power of 4
This gives
\((\frac{f^3g^{-2}}{h^{-1}})^4\)simplifying the expression to remove negative exponent
Simplifying the numerator
\(\begin{gathered} f^3g^{-2}=f^3\times g^{-2} \\ f^3g^{-2}=f^3\times\frac{1}{g^2} \\ f^3g^{-2}\text{ = }\frac{f^3}{g^2} \end{gathered}\)simplfying the denorminator
\(h^{-1}\text{ = }\frac{1}{h}\)combining simplfied values for numerator and denorminator in the general form we have
\(\begin{gathered} (\frac{f^3g^{-2}}{h^{-1}})^4\text{ = }(\frac{\frac{f^3}{g^2}}{\frac{1}{h}})^4 \\ (\frac{f^3g^{-2}}{h^{-1}})^4=\text{ (}\frac{f^3}{g^2}\times h)^4\text{ } \\ (\frac{f^3g^{-2}}{h^{-1}})^4\text{ = (}\frac{f^3h}{g^2})^4 \end{gathered}\)Hence, the simplified form of the expression is
\((\frac{f^3h}{g^2})^4\)Write 3.1415×106 in standard notation
Answers
Answer:
332.999
Step-by-step explanation:
juice wrld
compute the cost of filling a hole 5.50 meters long, 5.50 meters wide, and 5.50 meters deep. the cost of the fill soil is $4.75 per cubic meter. round the answer to the nearest dollar.
Answers
Answer:
$790
Step-by-step explanation:
volume = LWH
volume = 5.50 m * 5.50 m * 5.50 m
volume = 166.375 m^3
cost = volume * unit cost
cost = 166.375 m^3 * $4.75/m^3
cost = $790.28125
Answer: $790
The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section. Suppose the strength of an oak beam is 69 , when the beam is 7 inches wide and 3 inches deep. Determine the strength, S, of the largest rectangular beam that can be cut from a 28 -inch-diameter oak tree, given that the beam must be 14 inches wide. Remember y is proportional to x if there is a constant k such that y=kx. The constant k is known as the constant of proportionality. a) S=9016 b) S=2231 c) S=8232 d) S=392
Answers
The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.
Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.
For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.
The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.
Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.
Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.
This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.
Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.
The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.
Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.
Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the answer is (b) S = 2231.
The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.
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0.21212121... as a fraction
Answers
Adding 3 to some number, then multiplying the result by 7 gives 28 .
What was the original number ?
Answers
Answer:
1
Step-by-step explanation:
1+3 = 4 4*7 = 28
it's 1 because 28/7 = 4 and you add 3 to the number so 1 + 3 = 4 * 7 = 28 is correct.
how many terms are in the following expression?
Answers
The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.
How to find the number of terms ?In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:
62 x- 4 y 5 zEach term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.
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The full question is:
How many terms are in the following expression 6 + 2 x - 4 y + 5 z
the seller of a loaded die claims that it will favor the outcome 6. we don't believe that claim, and roll the die 200 times to test an appropriate hypothesis. our p-value turns out to be 0.03. which conclusion is appropriate? explain. a) there's a 3% chance that the die is fair. b) there's a 970/0 chance that the die is fair. c) there's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair.
Answers
It is plausible to assume that the die is fair because there is a 3% possibility that a loaded die might randomly yield the outcomes that we saw.
The appropriate conclusion is that there is a 3% chance that a loaded die could randomly produce the results we observed. We tested this hypothesis by rolling the die 200 times and our p-value turned out to be 0.03. This means that there is only a 3% chance that the results we observed could have been produced randomly by a loaded die, so it is reasonable to conclude that the die is fair. This is because a p-value of 0.03 is considered to be statistically significant, which indicates that the results we observed are unlikely to have been due to chance. Therefore, we can conclude that the seller's claim that the die will favor the outcome 6 is likely false.
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809,000 s in scientific notation
Answers
Answer:
8.09 x 10^5 s
Step-by-step explanation:
2
Write the fraction when:
30 is the numerator and 57 is the denominator.
29 is the numerator and 54 is the denominator.
Answers
Answer:
30/57 29/54
Step-by-step explanation:
The numerator is the number on top of the fraction
the denominator is the number on the bottom
\(\frac{30}{57}\) 30 is the numerator
57 is the denominator
Answer:
\(\frac{30}{57}\)
\(\frac{29}{54}\)
Step-by-step explanation:
The numerator of a fraction is the number that is above the line and the denominator of a fraction is the number that is below the line. We can use this to help find fractions with only the numerator and denominator.
When 30 is the numerator and 57 is the denominator.
\(\frac{30}{57}\)
When 29 is the numerator and 54 is the denominator.
\(\frac{29}{54}\)
What is the length of segment AC?
Answers
The y difference of the 2 lines are 6(you can just count these)
The x difference of the 2 lines are 8(again you can count this)
Now calculate distance using distance formula (the pythag theorem)
sqrt(6^2+8^2)=sqrt 100= 10
Therefore the distance of AC is 10.
45. Find sin 2 θ if cos θ=\frac{\sqrt{3}}{5} and sin θ>0 .
Answers
Given that cos θ = √3/5 and sin θ > 0, we can find sin 2θ using trigonometric identities, which gives us sin 2θ = 2sin θ cos θ.
To explain further, we can use the double-angle identity for sine. The double-angle identity states that sin 2θ = 2sin θ cos θ. By substituting the given value of cos θ into the equation, we get sin 2θ = 2sin θ (√3/5).
However, we still need to determine the value of sin θ. Since sin θ > 0, and we know that cos θ = √3/5, we can use the Pythagorean identity to find sin θ.
The Pythagorean identity is sin^2 θ + cos^2 θ = 1. By substituting the value of cos θ, we get sin^2 θ + (√3/5)^2 = 1. Simplifying the equation, we have sin^2 θ + 3/5 = 1. Subtracting 3/5 from both sides, we get sin^2 θ = 2/5.
Taking the square root of both sides, we find sin θ = √(2/5).
Substituting this value into the equation sin 2θ = 2sin θ (√3/5), we can calculate the final result for sin 2θ, which comes out to be 2sin θ cos θ.
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