Consider the sets X = 4 and Y = {4}. (a) True or False: X = Y .
(b) True or False: X ⊆ Y (c) True or False: X ∈ Y . (d) True or
False: X ∈ {4, r}. (e) True or False: Y ∈ {4, r}.
Answers
In this question, we are given two sets X = {4} and Y = {4}, and asked to determine the truth value of various statements. The solution is that (a) is false, (b) is true, (c) is false, (d) is true, and (e) is false.
(a) False: X and Y are sets with the same element, which is 4. However, sets are equal only if they have the exact same elements. In this case, X contains only the element 4, while Y also contains only the element 4. Therefore, X and Y are not equal.
(b) True: X is a subset of Y if every element of X is also an element of Y. In this case, X has only one element, which is 4, and that element is also present in Y. Therefore, X is a subset of Y.
(c) False: The notation X ∈ Y is used to check if X is an element of Y. In this case, X is not an element of Y because X is a set containing the element 4, while Y is a set containing the element 4 itself. Sets are not elements of other sets.
(d) True: The statement X ∈ {4, r} is true if X is an element of the set {4, r}. In this case, X is indeed an element of the set {4, r} because X contains the element 4, which is present in the set.
(e) False: The statement Y ∈ {4, r} is false because Y is not an element of the set {4, r}. Y is a set itself, containing element 4, but sets are not elements of other sets.
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Related Questions
Last year, wind turbines along a hilly ridge had an average output of 340 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more. What is the new average yearly output
Answers
The required new average is 646-kilowatt hours per year,
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Last year, wind turbines along a hilly ridge had an average output of 340-kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more.
So,
new average = 340 + 90% of 340
new average = 340 + 0.90 × 340
new average = 340 + 306 = 646 kilowatt hours per year,
Thus, the required new average is 646-kilowatt hours per year,
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what is the slope if the line that passes through the points (10,8) and (7,14)? write your answer in simplest form
Answers
Answer:
-2
Step-by-step explanation:
we use the y2-y1/x2-x1 fomrula to find slope
14-8/7-10
6/-3
-2 is the slope
hopes this helps
lori took a trip during her recent trip to NYC. They charged a flat rate of $2.50, plus an additional $3.00 per mile. Lori only has $20
Answers
Explanation
We know we can use slope intercept form
y = mx + b
m = 3.00 per mile, this is the rate or slope
b= 2.50, the y intercept or flat fee that doesn’t change
y = $20, the total she has to spen
≤ is less than or equal to sign because the amount has to be less than or equal to $20
We are looking for “x” the amount of miles
3.00x + 2.50 ≤ $20
Subtract 2.50 from each side to isolate the variable
3.00x + 2.50 - 2.50 ≤ $20 - 2.50
Simplify
3.00x ≤ $17.50
Divide both sides by 3.00 to solve x
3.00/3.00x ≤ 17.50 / 3.00
x ≤ 5.83 miles
What is the answer to my question? No links please. Urgent.
Answers
Answer:
57cm^3
i belive this is right.
In space, how many planes can be perpendicular to a given line at a given point on that line in space?
A. 1
B.0
C. 3
D. infinitely many
Answers
In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.
The correct answer is Option D.
The key concept here is that a plane is defined by having at least three non-collinear points.
When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.
Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.
Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.
The correct answer is Option D.
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What is the probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, i = 2, 3,. , 12?.
Answers
Answer:
0, 1/18, and 1/36
Step-by-step explanation:
For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.
For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.
For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.
The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.
We have,
The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."
Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.
Let's go through the cases:
i = 2 (only possible sum with two dice):
In this case, both dice must show a 1.
The probability of this happening on a fair 6-sided die is
(1/6) * (1/6) = 1/36.
i = 3: The combinations are (1, 2) and (2, 1).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 4:
The combinations are (1, 3), (2, 2), and (3, 1).
The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.
i = 5:
The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).
The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.
i = 6:
The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).
The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.
i = 7:
The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.
i = 8:
The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).
The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.
i = 9:
The combinations are (3, 6), (4, 5), and (5, 4).
The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.
i = 10:
The combinations are (4, 6) and (6, 4).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 11:
The combinations are (5, 6) and (6, 5).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 12:
The combination is (6, 6).
The probability of this happening is (1/6) * (1/6) = 1/36.
Now, sum up the probabilities for each case:
(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)
This simplifies to:
69/36 = 23/12
Thus,
The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.
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find the hypotenuse: c =
Answers
Which is another way to represent
five hundred six and ninety-two
thousandths?
Select all that apply.
(5 x 100) + (6 × 1)
+ X
(9 × 10) + (2x 100)
(5 x 100) + (6 × 1)
+(9 × 100) + (2.× 1,000)
506.092
506.902
506.92
Answers
Which of the following factors does NOT control the stability of a slope?
the angle of repose for intact bedrock
whether the slope is rock or soil
the amount of water in the soil
the orientation of fractures, cleavage, and bedding
Answers
The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.
Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.
The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.
To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.
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Solve for the value of x 3x - 9 + 12 - 6x = -18
Answers
Answer:
x=7
Step-by-step explanation:
\(3x-9+12-6x=-18\)
now let’s put together the like terms
\(3-3x=-18\)
\(-3x=-21\)
now we divide \(-21\) By \(-3\)
the result is
\(x=7\)
Answer:
X=7
Step-by-step explanation:
Verification
\(3(7)-9+12-6(7)=-18\\21-9+12-42=-18\\12+12-42=-18\\24-42=-18\)
\(-18=-18\)
I hope this help.Please give me the brainliest
What’s 7 1/2 - 1 2/7
Answers
87/14 or 6 3/4. That's an improper fraction and then a mixed fraction. Same answer though
You find a common denominator which would be 14.
7 1/2 becomes 7 7/14.
1 2/7 becomes 1 4/14
When you subtract 7 1/2 - 1 4/14 it equals 6 3/14
if mating is at random and red-green colorblindness does not affect survival or fertility, what should be the proportion of color-blind women in a population when they are at hwe in which 8% of the men are color-blind? colorblind women? (you may also answer in %) show your work.
Answers
The proportion of color-blind women would be 4% as each individual has two alleles.
In a population where mating is random and red-green colorblindness does not affect survival or fertility, the proportion of color-blind women can be calculated based on the Hardy-Weinberg equilibrium (HWE) equation.
If 8% of the men are color-blind, the proportion of color-blind women in the population would be 1.6% (or 0.016).
According to the Hardy-Weinberg equilibrium, in a population with random mating, the frequencies of alleles and genotypes remain constant from generation to generation in the absence of evolutionary forces.
The equation for the HWE is p² + 2pq + q² = 1, where p represents the frequency of the dominant allele (non-colorblind) and q represents the frequency of the recessive allele (colorblind).
In this case, if 8% of the men are color-blind, it means q² = 0.08. Solving for q, we take the square root of 0.08, which is approximately 0.2828.
Since q represents the frequency of colorblind individuals (men and women combined), and women have two alleles, the frequency of color-blind women (q²) would be (0.2828)² = 0.08 (or 8%).
Converting this to proportion, the proportion of color-blind women would be 0.08/2 = 0.04 (or 4%), as each individual has two alleles.
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1 poin
A catering assistant mixes 4 parts of cordial to 12 parts of water. Express
this as a ratio in its simplest form.*
1:1/3
O 1:2
O 1:3
O 14
Answers
4 goes into 12 three times.
4/12 = 1/3 = 1:3
a student answered 44 questions correctly on a test with 55 questions. what percent of the test was answered correctly?
(plz tell me how to figure it out)
Answers
Answer:
80%
Step-by-step explanation:
The basic idea of this problem is to convert \(\frac{44}{55}\) into a percentage. \(\frac{44}{55}\) can be simplified to \(\frac{4}{5}\) which is also 80%.
Answer:
Step-by-step explanation:
44 out of 55
divide :44/55=0.8
to convert it to decimal you multiply by 100 and put percentage next to it
0.8*100=80
%80
Evaluate the expression for d=-17.5, f = -3
Write your answer as a decimal or whole number.
Answers
Answer:
d=-17.5
f = -3
Step-by-step explanation:
These are expressions, not equations. Therefore they are already "expressed."
Construct the discreet probability distribution for the random variable described express the probabilities as simple fractionsThe number of heads in four toss of a coin
Answers
Explanation
In four tosses of a coin
The sample space is
There are 16 possible outcomes
The probability for the number of heads is given below
when x = 0
P(x) will be
\(P(0)=\frac{1}{16}=0.0625\)when x =1 means when we have 1 head
\(P(1)=\frac{4}{16}=\frac{1}{4}=0.25\)when x =2
\(P(2)=\frac{6}{16}=0.375\)when x = 3
\(P(3)=\frac{4}{16}=\frac{1}{4}=0.25\)When x =4
\(P(4)=\frac{1}{16}=0.0625\)
I need this done today whoever gets this correct gets brainliest!!! PLZZ HELPP MEE!!!
hurryy
Answers
Answer:
A
Step-by-step explanation:
This is a really easy algebra question tho
1. Step 1 -> Step 2 is wrong
2. Step 1:
3. But Step 2:
4. She added 0.2 to each term instead of multiplying by 0.2
Answer:
A (I carefully did it)
Step-by-step explanation:
This is a really easy algebra question tho
1. Step 1 -> Step 2 is wrong
2. Step 1:
\(0.2(4+1.4y-2.1)=0.8+0.28y-0.42\)
3. But Step 2:
\(0.2(4+1.4y-2.1)\neq 4.2+1.6y-1.9\)
4. She added 0.2 to each term instead of multiplying by 0.2
a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) how fast is the radius of the balloon changing at the instant the radius is 50 centimeters?
Answers
0.015 the radius of the balloon changing at the instant the radius is 50cm
given that
a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute
radius = 50 centimeters
now we need to find the volume of the balloon
Let V = volume of the balloon at time t
r = radius of the balloon at time t
V = (4/3)πr3
Given: dV/dt = 500
Find: dr/dt when r = 50
dV/dt = (4/3)(3πr^2)(dr/dt)
500 = 4π(50)^2(dr/dt)
dr/dt = 1/(20π)
dr/dt = 0.015 cm/min
0.015 the radius of the balloon changing at the instant the radius is 50cm
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solve for X
somebody help me out
Answers
Answer:
2x=20 and x=10
Step-by-step explanation:
Answer:x =10
Step-by-step explanation:
2x -7=13
2x =13 +7
2x = 20
X= 20/2
X= 10
2.1Simplifying Expressions: Problem 1 (1 point) Simplify the following expression. 6- 4(x - 5)-
Answers
The simplified expression is 26 - 4x.
To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.
6 - 4(x - 5)
First, distribute -4 to the terms inside the parentheses:
6 - 4x + 20
Now, combine like terms:
(6 + 20) - 4x
Simplifying further:
26 - 4x
Therefore, the simplified expression is 26 - 4x.
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Sketch a graph of
y=3(x − 2)(x + 1) (x – 4)
ASAPP!
Answers
Answer:
Use the distributive property to multiply 3 by x−2.
y=(3x−6)(x+1)(x−4)
Use the distributive property to multiply 3x−6 by x+1 and combine like terms. y=(3x 2 −3x−6)(x−4)
Use the distributive property to multiply 3x 2 −3x−6 by x−4 and combine like terms. y =3x 3 −15x 2 +6x+24
Step-by-step explanation:
I also up a link there of a graph. Please tell me if you can open it. Hope this helps! :P
hey do anybody know 14+18÷2×18-7
Answers
Answer:
169
Step-by-step explanation:
14 + 162 - 7 = 169
hoped this helped:)
perform the necessary questions -5 -(-3) + (-8)
Answers
the answer is 0 because -5 -(-3) equals 8 which cancels out when u add negative 8 :)
Find the area of the figure 14mm 29mm?
Answers
Total Area = Area of circle + Area of Cylinder Side
= pi*14^2 + 2pi*14*29
= 3166.73 mm^2
The surface area of the cylinder is S = 3,780.56 mm²
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the surface area of cylinder be S
where the radius r = 14 mm
And , the height of cylinder h = 29 mm
Now , Surface area of cylinder = 2πr ( r + h )
On simplifying , we get
S = 2 ( 3.14 ) ( 14 ) ( 14 + 29 )
S = 87.92 ( 43 )
S = 3,780.56 mm²
Hence , the surface area is S = 3,780.56 mm²
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Which of the following fractions is closest to 1?
a. 10/11 b. 2/3 c. 5/12 d. 7/8
Answers
Answer:
A. 10/11
Step-by-step explanation:
(I just know) Have a Beautiful day.
Answer:the answer is A
To get the answer, just divide the answers to see if you will get a number closer to one
Step-by-step explanation:
112 is 70% of _______
Answers
Answer:
160
Step-by-step explanation:
70% of 160=112.
A handy trick is to divide the number by the percentage.
Brainliest please I need those points.
112 is 70% of 160
test the series for convergence or divergence. 4 5 − 4 7 + 4 9 − 4 11 + 4 13 −
Answers
Therefore, the series 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ... is convergence in nature.
To test the convergence or divergence of the given series: 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ..., we can use the alternating series test. The alternating series test states that if a series has the form (-1)^n b_n, where b_n is a positive sequence that is decreasing and approaches zero as n approaches infinity, then the series converges.
In the given series, we have b_n = 4/(2n+3), which is a positive sequence that approaches zero as n approaches infinity. To see that b_n is decreasing, we can note that b_{n+1}/b_n = 2(2n+3)/(2n+5) < 1 for all n, since the numerator is always less than the denominator. Therefore, b_n is a positive, decreasing sequence that approaches zero as n approaches infinity.
Furthermore, the series has the form (-1)^n b_n, where the sign alternates between positive and negative. Therefore, we can apply the alternating series test, which tells us that the series converges.
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20 POINTS FOR AN EXPLANATION!!!
Answers
Answer:
Graph using a table of values.
x y−2║−7/3
−1║−5/3
0║ −1
1║−1/3
2║1/3
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (32,0)
y-intercept(s): (0,−1)
Step-by-step explanation:
F(x)=2/3x-1
Answer:
Graph using a table of values.
x y
−2║−7/3
−1║−5/3
0║ −1
1║−1/3
2║1/3
Step-by-step explanation:
Determine the range of the following graph:
Please help. Desperate!!:(
Answers
Answer:
[-6, 3]
Step-by-step explanation:
The range refers to the interval between the minimum and maximum possible y-values.
Solving :
Minimum = -6Maximum = 3Range is : [-6, 3] (closed square bracket is necessary as indicated by the solid dots on the graph)The range of the graph is given by R [ -6 , 3 ]
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the graph be represented as A
Now , the value of A is given in the figure where
The maximum value of graph A = 3
The minimum value of graph A = -6
So , the range of the function is R = maximum value to minimum value
The domain is all the values of the graph from left to right. The range is all the values of the graph from down to up
Hence , the range of the function is [ -6 , 3 ]
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-5x <2
true false
x=-2 x=-2
x=1 x=1
x=2 x=2
x=-1 x= -1
Answers
The inputs that are solutions for the inequality are:
x = 2
x= 1
For which inputs is the inequality true?Here we have the following inequality:
-5x < 2
We want to see which of the given inputs is a solution for this.
First we can isolate the variable in our inequality, so we get:
-5x < 2
-2 < 5x
-2/5 < x
-0.4 < x
So any value larger than -0.4 is a solution, from the given options, the two that are solutions are:
x = 1
x = 2.
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