Answer:
the scale factor is 6
Step-by-step explanation:
X and Y are independent random variables, and a and b are constants. Which one of the following statements is true?
X and Y are independent random variables, and a and b are constants is
Var(X-Y) = Var(X) + Var(Y)
Now, According to the question:
Let's Know:
Independent random variable:
Two random variables X and Y are independent if
E(XY) = E(X)E(Y).In case of n random variables the formula is extended as
\(E(X_1,X_2,X_3....X_n)=E(X_1)E(X_2)E(X_3)...E(X_n)\)
Are the random variables X and Y independent?
If X and Y are two random variables and the distribution of X is not influenced by the values taken by Y, and vice versa, the two random variables are said to be independent.
Hence, X and Y are independent random variables, and a and b are constants is
Var(X-Y) = Var(X) + Var(Y).
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What is the largest interval containing x = 2n on which sin x is one-to-one?
Select one:
a. [n, зn]
b. [π/2, 5π/2]
c. [3π/2, 7π/2]
d. [3π/2, 5π/2]
The largest interval containing x = 2n on which sin x is one-to-one is [3π/2, 5π/2].
The sine function, sin x, is periodic with a period of 2π. This means that for any value of x, sin x = sin(x + 2π). To determine the interval on which sin x is one-to-one, we need to find the range of x values where sin x does not repeat.
Considering x = 2n, where n is an integer, we can see that for n = 0, x = 0, and sin x = 0. As we increase n, x increases by 2π, and sin x continues to repeat. However, when we reach n = 2, x = 4π, and sin x = 0 again.
So, the largest interval containing x = 2n on which sin x is one-to-one is [3π/2, 5π/2]. In this interval, sin x takes on all values between -1 and 1 exactly once, without repeating. Therefore, option d) [3π/2, 5π/2] is the correct answer.
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In rectangle FGHI, diagonals FH and GI intersect at E. G F E H I • IE = 3x + 4 • EG = 5x - 6 What is the length of FH ?
Answer:
FH = 38
Step-by-step explanation:
Here, given the point of intersection of the two diagonals at E, we want to calculate the length of FH
The point of intersection of the diagonals is the midpoint of each as the diagonals bisect each other
thus,
3x + 4 = 5x - 6
5x-3x = 6+ 4
2x = 10
x= 10/2
x = 5
but Eg is 5x-6
and FH = 2EG
FH = 2(5x-6)
FH = 10x - 12
Substitute x = 5
FH = 10(5) -12
FH = 50-12
FH = 38
The length of FH is 38.
The calculation is as follows:
3x + 4 = 5x - 6
5x-3x = 6+ 4
2x = 10
x = 5
Here EG is 5x-6
and FH = 2EG
So,
FH = 2(5x-6)
= 10x - 12
Substitute x = 5
= 10(5) -12
= 50-12
= 38
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factories:
x(x+1)-y(y+1)
Answer:
\((x - y)(x + y + 1)\)
Step-by-step explanation:
\(x(x + 1) - y(y + 1)\)
Lets expand it.
\( = > {x}^{2} + x - {y}^{2} - y\)
Lets re-arrange it.
\( = > {x}^{2} - {y}^{2} + x - y\)
\( = > (x + y)(x - y) + 1(x - y)\)
Lets take (x - y) common.
\( = > (x - y)[(x + y) + 1] \)
\( = > (x - y)(x + y + 1)\)
(x-y)(x+y+1)
Step-by-step explanation:
x2+x-y2-y
(x+y)(x-y)+(x-y)
(x-y)(x+y+1)
Find P(A) given that P(A) = 0.75
Answer:
P(A)=0.75
Step-by-step explanation:
I think you already have your answer. If this is all the information given in the problem, there is nothing more to do.
can you guys please help me?
Answer: The mean, which is needed to be rounded to the nearest tenth, would be 10.6.
Step-by-step explanation:
Since this question is asking for the mean weight for eight cats, I will simply tell you what is the mean.
A mean of a data set is when you add the total of all of the numbers in the data plot and divide that number by how many numbers you added up. It is painfully a lot of math to do, so that's why it's really MEAN!
In this case, you will need to add "6, 13, 6, 14, 8, 13, 11, & 14" up together to find the total number which is 85.
Now, since there is eight numbers in this data plot, you divide 85 by 8 and you would get 10.625. To the nearest tenth, it would round to 10.6.
Therefore, the pet store's eight cats have an average weight of 10.6 pounds per cat. Hope this helps! :)
-From A Fifth Grade Honors Student
A scuba diver descends in the water at a rate of 23 1/2 feet per minute for 2.6 minutes. He immediately changes course when he sees a large fish and ascends at a rate of 28 feet per minute for 2 minutes.
What is the scuba diver's position relative to sea level after the 4.6 minutes?
Enter your answer as a decimal in the box.
Answer:
-5.1
Step-by-step explanation:
I took the K12 test
answer is -5.1 is the answer i got
two ferries simultaneously depart from opposite banks of a river and cross perpendicular to the banks. their speeds are constant, but not equal. the ferries meet 220 yards from the riverbank, and continue along their routes. on their return trips, the ferries meet 100 yards from the other bank. what is the width of the river?
The width of the river is 1700m
What is the time, distance & speed relation?
Speed is calculated by dividing the distance traveled by the amount of time it took to get there. Divide the distance by the speed to find the passing time. To get the distance, multiply the speed by time.
Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank
boat one has travelled 700 (rate = 700/unit time) boat two has travelled x rate = x / unit time
boat one then travels x + 400 more and boat two travels 700 + (700+x -400) more when they meet
The time is the same:
rate x time = distance
distance/rate = time
equate the distances divided by the respective rates
(700 + x + 400)/700 = ( x + 700 + (700+x-400) )/x
1100x + x^2 = 1400x + 700000
x^2 - 300x - 700000 = 0
quadratic formula yields x = 1000
One boat travels 700 the other 1000 when they first meet.....width of the river = 700+ 1000 = 1700 m
Hence, the width of the river is 1700m
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You ride the metro train 16 times a month to work for $5.25 a day. A monthly pass is $70. Which
would cost less?
Answer:
Yes it would be Cheaper to get the pass becuse without it your spending 84 dollars and with it your spending 70
Step-by-step explanation:
Answer:
A monthly pass that is $70
Step-by-step explanation:
16*5.25= 84
$84 is greater than $70
let r1,r2 both be the usual order ≤on n. let t = {(1,3),(2,2),(4,1)}. identify any greatest and maximal elements in t, in the lex order on n ×n.
The greatest element in t is (4, 1) and there are no maximal elements in t.
In the lex order on n × n, (a, b) is less than (c, d) if a < c or if a = c and b < d. The greatest element in t is the element that is greater than or equal to all other elements in t. In this case, (4, 1) is the greatest element in t because it has the largest first component and the smallest second component among all the elements in t.
A maximal element in t would be an element that is not less than any other element in t. However, in the lex order on n × n, there are no maximal elements in t because, for every element (a, b) in t, there exists another element in t that is greater than (a, b) by having a larger first component or a larger second component.
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find the perimeter of triangle ABC in which ab is equals to 10 .2 cm, BC is equals to 17.5 cm and AC is equals to 15.3 CM
Answer:
43 cmStep-by-step explanation:
Given,
Sides of triangle ABC = 10.2cm, 17.5cm and 15.3cm
As we know,
Perimeter of a triangle = a + b + c
[Where, a, b and c are the three sides of the triangle]Therefore,
Perimeter of triangle ABC
= 10.2 cm + 17.5 cm + 15.3 cm
[On adding]= 43
Hence,
The reqiured perimeter of triangle ABC is 43cm (Ans)
You put $200 into an account earning 6% interest compounded yearly.
Write a rule to model the situation. Your answer should not include spaces and be formatted like: y=3(4)^x
Based on your equation, when will the account be worth $2500? Round your answer to the nearest hundredths place and do not include labels. Ex. 3.14
Answer:
43.35 years
Step-by-step explanation:
From the above question, we are to find Time t for compound interest
The formula is given as :
t = ln(A/P) / n[ln(1 + r/n)]
A = $2500
P = Principal = $200
R = 6%
n = Compounding frequency = 1
First, convert R as a percent to r as a decimal
r = R/100
r = 6/100
r = 0.06 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(2,500.00/200.00) / ( 1 × [ln(1 + 0.06/1)] )
t = ln(2,500.00/200.00) / ( 1 × [ln(1 + 0.06)] )
t = 43.346 years
Approximately = 43.35 years
Johannes Kepler thought that the Platonic solids were related to the orbits of the planets. He made models of each of the Platonic solids. He made a frame of each of the Platonic solids by fashioning together wooden edges. How many edges did Kepler have to make for the cube?
In order to construct frames for each of the platonic solids, Kepler has to construct nine wooden edges for the cube. These edges will then be pieced together to make the frames.
The Edges of Kepler:He created models of each of the platonic solids since it is shown in the data that they are connected to the planets' orbits. Kepler fashioned wooden edges to form each of the platonic solids into a frame.
Two of the six planets identified at the time were regarded to be platonic solid cubes. The three-dimensional shape of a cube has 12 edges and 8 corners.
Thus, there are 4 x 2 + 1 edges.
= 9
Kepler must create nine wooden edges for the cube in order to piece together wooden edges to form frames for each of the platonic solids.
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The hypotenuse of a right triangle is 6 feet long. One leg is 2 feet longer than the other. Find the length of each leg to the nearest hundredth of a foot.
please help me I'm confused
Answer:
B
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = \(\frac{1}{2}\) bh ( b is the base and h the height )
Here b = 26 and h = 5 , then
A = \(\frac{1}{2}\) × 26 × 5 = 13 × 5 = 65 ft² → B
find four consecutive multiples of 4 such that twice he sum of the least and greatest exceeds three times the least by 32.
According to the question, the four consecutive numbers can be written as :
First = \(x\); Second = \(x+2\); Third = \(x+4\); Fourth = \(x+6\)
As per the question, the final expression is :
\(2((x+2)+(x+4)) = 3(x)+32\)
\(4x+12 = 3x+32\)
\(x = 20\)
Therefore, the four values can be calculated by substituting the above value:
\(x=20; x+2=22; x+4=24; x+6=26\)
The four consecutive numbers are: \(20,22,24,26\)
Substitute the calculated values in the final expression, to check whether the answer is correct or not.
\(2(22+24) = 3(20)+32\)
\(92=92\)
Therefore, the calculated values are correct.
What are consecutive terms?
Consecutive terms are those terms which follow one sequential order.
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I need help with question b
Answer:
A triangular pyramid, otherwise known as a tetrahedron.
Step-by-step explanation:
I learned this in math class a long time ago. My major in college revolves around math and I tutor in geometry, so I memorized this type of stuff.
Glad to see that my hard work is paying off.
solve for w: x=7w-8z-4
Answer:
W=x/7+ 8z/7 + 4/7
Step-by-step explanation:
Solving Equations by Adding or Subtracting Fractions
Show all working
n + 23 = 19
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn's estimate?
A: 2.14%
B. 2.18%
C.12%
D.46.83%
Check if the following items approximate the qolden ratio. Up to 3 decimal places (89)/(55)
The given fraction, (89)/(55), does not approximate the golden ratio up to 3 decimal places.
The golden ratio, represented by the value φ, is an irrational number that has been of great interest in mathematics, art, and nature. It is approximately equal to 1.6180339887, but is often rounded to 1.618 for simplicity.
To check if a given fraction approximates the golden ratio, we can calculate its decimal value and compare it to the decimal representation of the golden ratio. If the values match up to a certain number of decimal places, then the fraction is considered to be an approximation of the golden ratio.
In this case, we are given the fraction (89)/(55) and asked to check if it approximates the golden ratio up to 3 decimal places. When we divide 89 by 55, we obtain the decimal value 1.61818, which is larger than the golden ratio. Since it exceeds the desired precision of 3 decimal places, we can conclude that (89)/(55) is not a close approximation of the golden ratio.
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Someone help me pls thanks :)
Answer:
I think you need to add them.
Answer:
0.24
Step-by-step explanation:
Miles he drives: x
55.96+0.12x=49.96+0.16x
0.04x=6
x=0.24mi
Suppose you are producing an outdoor festival. You estimate that you will make $200000 if it does not rain! and make $45000 if it does rain. The weather bureau predicts that the chance of rain is 46% for the day of the concert. What are your expected earnings for the festival?
The expected earnings for the festival is $128,700.
What is the expected earnings?
Probability is used to determine the chance that a random event would happen. The chance that the random event occurs lie between 0 and 1 or between 0% and 100%. The more likely it is that an event would happen, the more closer to one or hundred percent, the probability value is.
The chance it does not rain = 100% - chance it rains
100% - 46% = 54%
The expected earnings is a function of the chance that it rains, chance it does not rain and the amount that it would earn if it rains or it does not rain.
Expected earnings = (chance it would rain x amount you would earn if it rains) + chance it does rain x amount you would earn if does not rain)
($200,000 x 0.54) + ($45,000 x 0.46)
108,000 + 20,700 = $128,700
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let a and b be n × n matrices such that ab = in . prove that the rank of a is n
The rank of matrix A is n.
To prove that the rank of matrix A is n, we'll use the facts that AB = I_n (the n x n identity matrix) and that the rank of a product of matrices is less than or equal to the minimum of the ranks of the individual matrices. Here's a step-by-step explanation:
1. Given: A and B are n x n matrices such that AB = I_n.
2. Let's denote the rank of A as rank(A) and the rank of B as rank(B).
3. Since AB = I_n, it's clear that the product of matrices A and B results in the identity matrix, which has a rank of n (rank(I_n) = n).
4. According to the properties of matrix ranks, rank(AB) ≤ min(rank(A), rank(B)).
5. As AB = I_n, we have rank(I_n) ≤ min(rank(A), rank(B)).
6. Since the rank of the identity matrix is n, we have n ≤ min(rank(A), rank(B)).
7. As A and B are n x n matrices, their maximum possible rank is n, so rank(A) ≤ n and rank(B) ≤ n.
8. From step 6, we know that n ≤ rank(A). Combining this with rank(A) ≤ n, we conclude that rank(A) = n.
Therefore, the rank of matrix A is n.
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Consider the following hypothesis test: H0: p ? .75 Ha: p < .75 A sample of 300 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use ? = .05. Round your answers to four decimal places.
a. p = .68 p-value? Conclusion: p-value H0?
b. p = .72 p-value? Conclusion: p-value H0 ?
c. p = .70 p-value? Conclusion: p-value H0 ?
d. p = .77 p-value? Conclusion: p-value H0?
For each given sample result, the p-value and conclusion are as follows:
a. p-value = 0.0067, Conclusion: Reject H0, b. p-value = 0.0830, Conclusion: Fail to reject H0, c. p-value = 0.0322, Conclusion: Reject H0
d. p-value = 0.6221, Conclusion: Fail to reject H0
The p-value is a measure of the evidence against the null hypothesis (H0). It represents the probability of obtaining a sample result as extreme as or more extreme than the observed result, assuming the null hypothesis is true. A p-value less than the significance level (α) indicates strong evidence against the null hypothesis and suggests that the alternative hypothesis (Ha) may be true.
a. For p = .68, we need to determine the probability of observing a sample proportion as extreme as or less than .68, assuming the null hypothesis is true. By conducting the appropriate statistical test (e.g., using the normal approximation to the binomial distribution), we find the p-value to be 0.0067. Since the p-value is less than α = .05, we reject the null hypothesis and conclude that there is evidence to support the claim that the proportion is less than .75.
b. For p = .72, the p-value represents the probability of observing a sample proportion as extreme as or less than .72. Calculating the p-value using the appropriate statistical test yields 0.0830. Since the p-value is greater than α = .05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion is less than .75.
c. With p = .70, the p-value indicates the probability of observing a sample proportion as extreme as or less than .70. The calculated p-value is 0.0322. As the p-value is less than α = .05, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion is less than .75.
d. For p = .77, the p-value represents the probability of observing a sample proportion as extreme as or greater than .77. After performing the necessary calculations, we find the p-value to be 0.6221. Since the p-value is much greater than α = .05, we fail to reject the null hypothesis. Consequently, we do not have sufficient evidence to conclude that the proportion is less than .75.
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What is the median of following scores 3 5 4 9 8?
The median for the next batch of observations is 5.
What is median?The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.
Here,
given set of observation,
=3,4,5,8,9
n=5
median=(5+1)/2
=3rd term
=5
The median for following set of observation is 5.
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Someone answer quick and right.
13points
Answer:
no
Step-by-step explanation:
A particle is moving along a spiral path defined by the equation r = a * e^(b * θ), where a and b are constants. Determine the velocity of the particle at a given value of θ.
Step-by-step explanation:
The velocity of the particle at a given value of θ can be found by taking the derivative of the position vector with respect to time:
v(θ) = dr/dt = dr/dθ * dθ/dt = dr/dθ * ω
where ω is the angular velocity and dr/dθ is the derivative of the position vector with respect to θ.
The position vector r = a * e^(b * θ) * i + a * b * e^(b * θ) * j
Taking the derivative with respect to θ:
dr/dθ = a * b * e^(b * θ) * i + a * b^2 * e^(b * θ) * j
So the velocity of the particle is given by:
v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * j
Answer:
Step-by-step explanation:
v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * jj
the tendency of group members to exert less effort when they work in groups than they would exert if they were acting alone is known as
The tendency of group members to exert less effort when they work in groups than they would exert if they were acting alone is known as social loafing.
Social loafing is a common phenomenon that occurs when individuals feel that their individual effort will not significantly affect the group's overall performance or when they believe that other group members will compensate for their lack of effort.
This phenomenon can be observed in various group settings, such as in work teams, sports teams, and even in classroom group projects. The lack of accountability and the diffusion of responsibility that occur in groups can contribute to social loafing.
Social loafing can have negative consequences on group performance, as it can decrease the overall quality of the group's output and reduce motivation among group members.
To mitigate social loafing, it is important to establish clear roles and responsibilities for each group member and to provide regular feedback and recognition for individual contributions.
Additionally, creating a sense of collective identity and establishing group goals can also help to combat social loafing by promoting a sense of shared responsibility and commitment to the group's success.
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Which of the following statements is not true about chi-square distributions? The mean decreases as the degrees of freedom increase. OPG? < 0) = 0 O PU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1 There are an infinite number of chi-square distributions, depending on degrees of freedom. They are always skewed to the right Previous Only saved at 4:44pm
The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.
Is it true that the mean of a chi-square distribution decreases as the degrees of freedom increase?In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.
The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.
Regarding the other statements:
The statement "OPG? < 0) = 0" is true. The probability of a chi-square random variable being less than zero is always zero, as chi-square values are non-negative.The statement "OPU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1" is true. As the degrees of freedom increase, the right-tail probability of a chi-square distribution also increases.The statement "There are an infinite number of chi-square distributions, depending on degrees of freedom" is true. The number of chi-square distributions is infinite because the degrees of freedom can take any positive integer value.The statement "They are always skewed to the right" is generally true. Chi-square distributions tend to be skewed to the right, especially when the degrees of freedom are small.In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.
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