To show that the relation T defined on the set of integers Z is an equivalence relation, we need to prove three properties: reflexivity, symmetry, and transitivity.
1. Reflexivity: For any integer a, we need to show that aTa (mod). In modular arithmetic, a is congruent to itself modulo any integer, so this property holds.
2. Symmetry: For any integers a and b, if aTb (mod), then we need to show that bTa (mod). In modular arithmetic, if a is congruent to b modulo some integer, then b is also congruent to a modulo the same integer. Therefore, the symmetry property holds.
3. Transitivity: For any integers a, b, and c, if aTb (mod) and bTc (mod), then we need to show that aTc (mod). In modular arithmetic, if a is congruent to b modulo some integer and b is congruent to c modulo the same integer, then a is also congruent to c modulo that integer. Therefore, the transitivity property holds.
Since the relation T satisfies all three properties (reflexivity, symmetry, and transitivity), we can conclude that T is an equivalence relation.
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3x+4y=-12 x-y=10 using elimination no links or download
Answer:
x = 4, y = -6
Step-by-step explanation:
Elimination Method
3x + 4y = -12 ---- (1)
x-y = 10 ---- (2)
(2) x 4:
4(x) 4(-y) = 4(10)
4x - 4y = 40 ---- (3)
(1) + (3):
3x + 4y + (4x - 4y) = -12 + 40
3x + 4y + 4x - 4y = 28
7x = 28
x = 28/7
x = 4
Sub x = 4 into (2):
(4) - y = 10
-y = 10 - 4
-y = 6
y = -6
What does the y-intercept of the graph represent?
PLEASE HELP ME WILL MARK BRAINLIEST !!! :)
Answer:
lateral area = side area = (10 x 6 x 2) + (14 x 10 x 2) = 400 in²
total surface area = lateral area + top & bottom area = 400 + (14 x 6 x 2) = 568 in²
A shipment of 5 boxes of toys weighed
34.53 pounds. Each box measures the same
weight, so what's the weight of 1 box?
Answer:
Each box weighs 6.906 pounds.
Step-by-step explanation:
We know the total weight of the boxes. We also know how many boxes we have. To find the weight of one box, we want to divide the total weight by the total number of boxes.
34.53 / 5
= 6.906
Each box weighs 6.906 pounds.
Hope this helps!
Let X be a continuous random variable with probability density function f. We say that X is symmetric about a if for all x,
P(X ≥ a+x)=P(X ≤ a-x).
(a) Prove that X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
(b) Show that X is symmetric about a if and only if f(x) = f(2a - x) for all x.
(c) Let X be a continuous random variable with probability density function
f(x) = [1 / √(2phi)] e^-(x-3)²/2, x E R,
and Y be a continuous random variable with probability density function
g(x) = 1 / phi [1 + (x-1)²], x E R.
Find the points about which X and Y are symmetric.
Let X be a continuous random variable with probability density function f. We say that X is symmetric about a if for all x,
P(X ≥ a+x)=P(X ≤ a-x).
(a) f(a - x) = f(a + x) if and only if X is symmetric about a.
(b) X is symmetric about a if and only if f(x) = f(2a - x) for all x.
(c) X and Y are symmetric about 3.
(a) To prove that X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
Proof: P(X ≥ a+x) = P(X ≤ a-x) ...(1)
Given X is a continuous random variable with probability density function f.
Let F denote the cumulative distribution function of X.
Then, F(x) = P(X ≤ x).
We can now re-write equation (1) as follows: 1-F(a+x) = F(a-x) ... (2).
Taking the derivative of both sides of equation (2) with respect to x, we get: d/dx(1-F(a+x))= d/dx(F(a-x)) ... (3).
Differentiating the LHS of equation (3) using the chain rule, we obtain:- f(a+x) = -d/dx(F(a+x)) ... (4).
Differentiating the RHS of equation (3) using the chain rule, we obtain: f(a-x) = d/dx(F(a-x)) ... (5).
Combining equations (4) and (5), we get: f(a+x) = f(a-x).
Hence, we can conclude that X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
Answer: (a) f(a - x) = f(a + x) if and only if X is symmetric about a.
(b) To show that X is symmetric about a if and only if f(x) = f(2a - x) for all x.
Proof: X is symmetric about a if and only if for all x, we have f(a - x) = f(a + x).
Hence, it follows that: f(a + (2a - x)) = f(a - (2a - x)) ... (6).
Simplifying equation (6), we obtain: f(2a - x) = f(x).
Therefore, X is symmetric about a if and only if f(x) = f(2a - x) for all x.
Answer: (b) X is symmetric about a if and only if f(x) = f(2a - x) for all x.
(c) Let X be a continuous random variable with probability density function f(x) = [1 / √(2phi)] e^-(x-3)²/2, x E R, and Y be a continuous random variable with probability density function g(x) = 1 / phi [1 + (x-1)²], x E R.
Find the points about which X and Y are symmetric.
The probability density function of a symmetric random variable X about a is f(x) = f(2a - x).
Therefore, if X is symmetric about a, then we have: f(x) = f(2a - x) ...(7).
Comparing the probability density function of X to the given probability density function f(x), we can observe that X is symmetric about a = 3.
Therefore, we can find the points about which X and Y are symmetric by solving the following equation: g(x) = f(2a - x) ... (8).
Substituting the value of a in equation (8), we get:
f(2a - x) = [1 / √(2phi)] e^-(2a-x-3)²/2
= [1 / √(2phi)] e^-(x-3)²/2
= f(x)
Therefore, X and Y are symmetric about 3.
Answer: (c) X and Y are symmetric about 3.
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) The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store w How many customers were older than 45? Ages of Store Customer
1 0 2 3 3 69 8
2 1 1 3 4 5 6 6 8 9
3 2 2 4 4 4 5 7
4 1 2 3 3 5 8
5 0 0 1 5 6
6 2 4 5 5
7 3
The correct answer is there are 12 customers who are older than 45.
To determine how many customers were older than 45, we need to examine the values in the stem-and-leaf plot that are greater than 45.
Looking at the plot, we can see that the stem values range from 1 to 7. However, the stem values 8 and 9 are missing, so there are no customers with ages starting from 80 to 99.
For the stem values 1, 2, 3, 4, 5, 6, and 7, we can count the number of leaf values that are greater than 5.
Stem 1: There are no leaf values greater than 5.
Stem 2: There are 3 leaf values greater than 5 (6, 6, 8).
Stem 3: There are 4 leaf values greater than 5 (6, 7).
Stem 4: There are 3 leaf values greater than 5 (8).
Stem 5: There are 2 leaf values greater than 5 (6).
Stem 6: There are 0 leaf values greater than 5.
Stem 7: There are 0 leaf values greater than 5.
Adding up the counts for each stem, we get:
0 + 3 + 4 + 3 + 2 + 0 + 0 = 12
Therefore, there are 12 customers who are older than 45.
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A person draws balls twice, with replacement, from a urn which contains only one red ball and one black ball. (a) (5 pt) Using the notations R and B to denote the red balls and black balls, respectively, list all the elements of the sample space S. (b) (5 pt) Which elements are in the event A that the person draws one red ball and one black? (c) (5 pt) What is P(A)?
(a) All the elements of S are : S = {RR, RB, BR, BB},
(b) Elements in event A are {RB and BR},
(c) The probability of "event-A", which is the person drawing one "red-ball" and one "black-ball", is 1/2.
Part (a) : The "sample-space" (S) consists of all possible outcomes when drawing two balls with replacement. In this case, there are four possible outcomes : S = {RR, RB, BR, BB},
Part (b) : The "event-A" represents the person drawing one red-ball and one black-ball. The elements in event A are {RB and BR},
Part (c) : To calculate the probability P(A), we need to determine the ratio of favorable outcomes (elements in A) to the total number of possible outcomes (elements in S).
P(A) can be written as : (Number of favorable outcomes)/(Total number of possible outcomes),
Substituting the values from part(a) and part(b),
We get,
P(A) = 2/4
P(A) = 1/2
Therefore, the required probability is 1/2.
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Please help 6th grade math please please help i will give brainliest
A researcher did not reject her null hypothesis, but wrote that, because she had a small sample, she thought she had made a Type 1 error. What is the correct assessment of what the researcher wrote? O She definitely made a Type 1 error. O She could not have made a Type 1 error. O She could be right about making the Type 1 error, but there is no way of knowing for sure. O There's a slight chance that she made a Type 1 error. Question 34 1 pts A study was conducted that compared the mean motor competence of a random sample of 41 left- handed preschool children with the motor competence of a random sample of 41 right-handed preschool children relationship between handedness (left or right) and motor competence in preschool children. How many degrees of freedom should there be for an appropriate t test for this study? O 82 O 40 80 O 41 Question 26 1 pts If we take a sample from a population with a standard deviation equal to sigma, how will the standard error of the mean be affected if we decide to increase the sample size? O It changes unpredicatably. O It stays the same. It decreases. O It increases. Question 25 1 pts A researcher plans to compute a confidence interval for the population mean body mass index. What will make the confidence interval narrower? O studying a population with larger variance in body mass index O increasing the confidence level O being careless in measuring body mass index O increasing the sample size 1 pts Question 24 When statistical power for hypothesis testing is lower than it should be, what does that mean for estimation with confidence intervals? O The confidence interval will be narrower. O The lower confidence limit and upper confidence limit will be raised. O The lower confidence limit will be raised and the upper confidence limit will be lowered. O The confidence interval will be narrower. Question 1 1 pts Dr. Smith draws a random sample of size 50 from a known population. Dr. Jones draws another random sample of size 50 from the same population. They both measure, among other things, serum cholesterol levels for their studies. Which of the following descriptions of their sample means for serum cholesterol is consistent with central limit theorem? O It's more probable that the means will be far apart than close together. OSmith and Jones will probably come up with the same mean. O It's more probable that the means will be close together than far apart. O It is equally probable for the two means to be far apart as it is for them to be close together. 1 pts Question 2 For two-tailed t tests, as the computed value of the test statistic (for example, Student's t) gets closer to the rare zone of the sampling distribution, what happens to the p value? O It increases toward the left tail and decreases toward the right tail. O It remains unchanged. O It decreases. O It increases. 1 pts Question 3 If the alternate hypothesis is justifiably directional (rather than non-directional), what should the researcher do when conducting a t test? O a one-tailed test a two-tailed test set the power to equal B O set ß to be less than the significance level Question 6 What is the term for rejecting a null hypothesis that is actually true? O Type 1 error O precision Type 2 error O correct decision
The researcher wrote that, because she had a small sample, she thought she had made a Type 1 error.
The correct assessment of what the researcher wrote is: She could be right about making the Type 1 error, but there is no way of knowing for sure. Here's why:In statistics, a Type I error occurs when a null hypothesis that is true is incorrectly rejected. The probability of a Type I error occurring is referred to as the level of significance.
If a researcher states that she did not reject her null hypothesis but believes she may have made a Type I error due to a small sample size, it is possible that she is correct. However, since she did not reject the null hypothesis, it is impossible to know for sure whether a Type I error occurred. Hence, the correct assessment of what the researcher wrote is: She could be right about making the Type 1 error, but there is no way of knowing for sure.
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A study of students taking a 20 question exam ranked their progress from one testing period to the next Students scoring 0 to 5 form group 1, those scoring 6 to 10 form group 2, those scoring 11 to 15 form group 3 and those scoring 15 to 20 form group 4 The transition matrix to the right shows the result Use the transition matrix to complete parts (a) and (b) below 0.325 0.05 021 0 415 0311 0.351 0.194 0.144 0 0.327 0.485 0 188 (a) Find the long-range prediction for the proportion of the students in each group The proportion of students will be ]% in group 1, 3% in group 2. % in group 3 and % in group 4. (Type integers or decimals rounded to two decimal places as needed) (b) Suppose all students are initially in group 1 When a student reaches group 4 the student is said to have mastered the ma student stays in that group forever. Find the number of testing periods you would expect for at least 70% of the students to haw increasing values of nin xoP") The number of testing periods is__.
The long-range prediction for the proportion of students in each group is approximately 14.2% in Group 1, 20.6% in Group 2, 34.5% in Group 3, and 30.7% in Group 4. The number of testing periods required for at least 70% of the students to have increasing values of n cannot be determined without specific values.
To find the long-range prediction for the proportion of students in each group, we need to calculate the steady-state vector of the transition matrix. The steady-state vector represents the long-term proportions of students in each group. We can find this vector by solving the equation:
π * P = π
where π is the steady-state vector and P is the transition matrix.
The given transition matrix is:
Copy code
0.325 0.05 0.021 0
0.415 0.311 0.351 0.194
0.144 0 0.327 0.485
0 0.188 0 0.812
Let's solve for the steady-state vector using matrix calculations. We can represent the steady-state vector as π = [π1, π2, π3, π4]. Therefore, the equation can be rewritten as:
[π1, π2, π3, π4] * P = [π1, π2, π3, π4]
This gives us the following system of equations:
π1 * 0.325 + π2 * 0.415 + π3 * 0.144 = π1
π1 * 0.05 + π2 * 0.311 + π3 * 0.188 + π4 * 0.188 = π2
π1 * 0.021 + π2 * 0.351 + π3 * 0.327 = π3
π2 * 0.194 + π3 * 0.485 + π4 * 0.812 = π4
We also know that the sum of the probabilities in the steady-state vector must be 1:
π1 + π2 + π3 + π4 = 1
Now we can solve this system of equations to find the steady-state vector.
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0.325π1 + 0.415π2 + 0.144π3 = π1
0.05π1 + 0.311π2 + 0.188π3 + 0.188π4 = π2
0.021π1 + 0.351π2 + 0.327π3 = π3
0.194π2 + 0.485π3 + 0.812π4 = π4
π1 + π2 + π3 + π4 = 1
Solving this system of equations, we find:
π1 ≈ 0.142
π2 ≈ 0.206
π3 ≈ 0.345
π4 ≈ 0.307
Therefore, the long-range prediction for the proportion of students in each group is approximately:
Group 1: 14.2%
Group 2: 20.6%
Group 3: 34.5%
Group 4: 30.7%
Now, let's move to part (b) of the question.
If all students are initially in Group 1, we need to determine the number of testing periods required for at least 70% of the students to have increasing values of n.
To calculate this, we can repeatedly multiply the initial state vector [1, 0, 0, 0] by the transition matrix until at least 70% of the students are in Group 4. We'll keep track of the number of testing periods until this condition is met.
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Initial state vector: [1, 0, 0, 0]
Transition matrix:
[0.325, 0.05, 0.021, 0]
[0.415, 0.311, 0.351, 0.194]
[0.144, 0, 0.327, 0.485]
[0, 0.188, 0, 0.812]
Starting with the initial state vector, we can calculate the new state vector as follows:
State vector after 1 period: [1, 0, 0, 0] * Transition matrix
State vector after 2 periods: [1, 0, 0, 0] * Transition matrix * Transition matrix
State vector after 3 periods: [1, 0, 0, 0] * Transition matrix * Transition matrix * Transition matrix
and so on...
We will continue this calculation until the proportion of students in Group 4 is at least 70%. The number of periods it takes to reach this point will be the answer.
Please note that the calculation involves matrix multiplication, which may require computational resources. If you need a specific number of testing periods, let me know and I can perform the calculation for you.
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what is the axis of symmetry for the graph shown?
Answer:
x=2
Step-by-step explanation:
The axis of symmetry goes through the vertex and is the line that makes the image the same on one side as the other
Since this is a vertical parabola, the axis is symmetry is of the form x=
The vertex is at x=2 so the axis of symmetry is x=2
Which of the following expressions are equivalent to -9.7. -0.8. -7.8. -3.8? Choose all answers that apply:
A. 9.7.-0.8.-7.8.-3.8.
B. -9.7.0.8. 7.8.-3.8
C. None of the above
Answer:
A.
it’s a because i just got it right on the test
Answer:
its A cause i got it right
Step-by-step explanation:
for the boys
liam is making chocolate chip cookies. The recipe calls for 1 cup of sugar for every 3 cups of flour. Liam only has 2 cups of flour. How much sugar does liam use?
1/5 cups of sugar.
have a nice day
Sales by Quarter A company made sales of $1,254,000 last year. Quarter 1 Quarter 2 Produced 13 more sales than in quarter 1 Quartor 3 Quarter 4 Produced 17% of total sales for the year Sales increased 100% ovor tho provious quarter. Question: Adjust the ple chart to represent the sales each quarter.
Quarter 1: $300,000Quarter 2: $300,013Quarter 3: $250,000Quarter 4: $500,000 the adjusted chart representing the Sales .
The given chart to represent the sales each quarter, we need to find out the sales of each quarter first and then represent them in the chart. Let's calculate the sales of each quarter one by one:
Sales of Quarter 1Let the sales of Quarter 1 be xSales of Quarter 2As per the given data, Quarter 2 produced 13 more sales than Quarter 1Therefore, sales of Quarter 2 = x + 13Sales of Quarter 3Let the sales of Quarter 3 be sales of Quarter 4As per the given data, Quarter 4 produced 17% of total sales for the year
therefore, 17% of $1,254,000 = (17/100) x 1,254,000= 213,180Sales of Quarter 4 = 213,180Sales increased 100% over the previous quarter
Therefore, sales of Quarter 4 = 2 x sales of Quarter 3= 2yNow, we can form the equation as follows: Total Sales = Sales of Quarter 1 + Sales of Quarter 2 + Sales of Quarter 3 + Sales of Quarter 4$1,254,000 = x + (x + 13) + y + 2y + 213,180$1,254,000 = 4x + 3y + 213,193or 4x + 3y = $1,040,807
Now, we can assume some values of x and y and then calculate the values of other variables. Let's assume x = $300,000 and y = $250,000Therefore, sales of Quarter 1 = $300,000Sales of Quarter 2 = $300,000 + $13 = $300,013Sales of Quarter 3 = $250,000Sales of Quarter 4 = 2 x $250,000 = $500,000Now, we can represent these sales in the chart as follows:
Quarter 1: $300,000Quarter 2: $300,013Quarter 3: $250,000Quarter 4: $500,000
Therefore, the adjusted chart representing the sales each quarter is shown above.
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Solve for x. (log510 - log52) (log61296) = log₂(x - 5)²
The solution to the equation (log510 - log52) (log61296) = log₂(x - 5)² is x = 9. To solve the given equation, let's break it down step by step.
First, we simplify the left side of the equation using logarithmic properties. Using the property log(a) - log(b) = log(a/b), we can rewrite (log510 - log52) as log5(10/2), which simplifies to log5(5) or 1.
Next, we simplify the right side of the equation. Using the property logₐ(b²) = 2logₐ(b), we can rewrite log₂(x - 5)² as 2log₂(x - 5).
Now our equation becomes 1 * log61296 = 2log₂(x - 5).
Since log61296 is the logarithm base 6 of 1296, which is 4, we can simplify the equation further to 4 = 2log₂(x - 5).
Dividing both sides by 2, we have 2 = log₂(x - 5).
Now we can rewrite this equation in exponential form: 2² = x - 5.
Simplifying, we get 4 = x - 5.
Adding 5 to both sides, we find x = 9.
Therefore, the solution to the equation (log510 - log52) (log61296) = log₂(x - 5)² is x = 9.
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A worker at a computer factory can assemble 8 computers per hour. How long would it take this worker to assemble 200 computers?
A.8 h
B.20 h
C.25 h
D.200 h
To determine how long it would take for the worker to assemble 200 computers, we need to consider the rate at which the worker assembles computers and the total number of computers to be assembled.
Given that the worker can assemble 8 computers per hour, we can set up a proportion to find the time required:
8 computers / 1 hour = 200 computers / x hours
Cross-multiplying and solving for x, we get:
8x = 200
x = 200 / 8
x = 25
Therefore, it would take the worker 25 hours to assemble 200 computers. The correct answer is option (C) 25 h.
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6. Consider the trigonometric equation sin x + 2 = 0. Explain why this equation would have no solutions. [C-2]
The given trigonometric equation is sin x + 2 = 0.
It is important to note that sine values range from -1 to 1 and never exceed those bounds. Thus, it can be determined that sin x + 2 will never equal zero.This is because the lowest possible value of sine is -1, which is not equal to zero. When 2 is added to that value, the sum is still negative. Therefore, the equation sin x + 2 = 0 has no solutions.
A trigonometric equation is one that has a variable and a trigonometric function. For instance, sin x + 2 = 1 is an illustration of a mathematical condition. The equations can be as straightforward as this or more complicated than that, such as sin2 x – 2 cos x – 2 = 0.
The six mathematical capabilities are sine, secant, cosine, cosecant, digression, and cotangent. The trigonometric functions and identities are derived by referencing a right-angled triangle as a reference: Sin is the opposite side or the hypotenuse.
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The point (1, -5) is an ordered pair for which function?
ƒ( x ) = 2 x - 7
ƒ( x ) = - x + 9
ƒ( x ) = 3 x - 11
Answer:
The first one.
Step-by-step explanation:
so 1 stands for x and -5 stands for y. When you plug in 1 into the equation the answer is -5. So that order pair works with that equation.
A simple random sample of 36 men from a normally distributed population results in a standard deviation of 64 beats per minute. The normal range of pulse rates of adults is typically given an 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the cam that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below a. Identify the null and attemative hypotheses. Choose the correct answer below OA H₂ 2 10 beats per minute He<10 beats per minute OB. He 10 beats per minute H: 10 beats per minute OC. He 10 beats per minute OD H10 beats per minute He 10 beats per minute H₁ #10 beats per minute b. Compute the test statistic. (Round to three decimal places as needed) c. Find the P-value P-value- (Round to four decimal places as needed.) d. State the conclusion. evidence to warrant rejection of the claim that the standard deviation of men's puise alas H. because the P-value is is equal to 10 beats per minute. the level of significance.
The conclusion is that there is evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
a. Null and alternative hypotheses Null hypothesis (H0): The standard deviation of men’s pulse rates is equal to 10 beats per minute.H0: σ = 10Alternative hypothesis (Ha): The standard deviation of men’s pulse rates is not equal to 10 beats per minute.
Ha: σ ≠ 10b. Calculation of test statistic The test statistic for the standard deviation is calculated as: \[χ^2 = \frac{(n-1)S^2}{σ^2}\]Where n = sample size, S = sample standard deviation, and σ = hypothesized standard deviation. Substituting the values, \[χ^2 = \frac{(36-1)(64)^2}{(10)^2}\] \[χ^2 = 1322.56\]
c. Calculation of P-value We can use the chi-square distribution table to find the P-value. At a significance level of 0.10 and 35 degrees of freedom (36-1), the critical values are 19.337 and 52.018.
Since the test statistic value (χ2) of 1322.56 is greater than 52.018, the P-value is less than 0.10. Therefore, we reject the null hypothesis and conclude that the standard deviation of men’s pulse rates is not equal to 10 beats per minute.
Since it is a two-tailed test, we divide the significance level by 2. The P-value for the test is P = 0.000. Therefore, the P-value is less than the level of significance (0.10).
d. Conclusion Since the P-value is less than the level of significance, we reject the null hypothesis. Hence, there is evidence to support the claim that the standard deviation of men's pulse rates is not equal to 10 beats per minute.
Therefore, the conclusion is that there is evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
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can someone please help me with this question?? (no links!!!)
Answer:
960
Step-by-step explanation:
it says use 3 for pi, so you plug the values into given equation
V = 3·(4)²·20
r is 4 because it is half of 8.
Then multiply
3·16·20 = 48·20 = 960
Answer:
960 cm
Step-by-step explanation:
8/2 = 4 (radius)
3 (since we're using 3 for pi) * 4^2 * 20
3 * 16 * 20
48 * 20
= 960 cm
I hope this helps heh :)
let a be a square matrix. prove an alternate form of the polar decomposition for a: there exists a unitary matrix w and a positive semidefinite matrix p such that a = pw.
The alternate form of the polar decomposition of `A` is given by `A = PW`, where `W` is a positive semidefinite Hermitian matrix and `P` is a positive semidefinite Hermitian matrix.
Let `A` be a square matrix. Prove an alternate form of the polar decomposition for `A`.For a given square matrix `A`, the polar decomposition of `A` is a factorization of `A` into the product of a unitary matrix `U` and a positive semi-definite Hermitian matrix `P`. This polar decomposition of `A` can be given by `A = UP` or `A = PU*`, where `U` is the unitary matrix and `P` is a positive semidefinite matrix such that `P = (AA*)^(1/2)` or `P = (A*A)^(1/2)`.
The alternate form of the polar decomposition of `A` is given by `A = PW`, where `W = P^(1/2)U P^(1/2)` and `P` is a positive semidefinite matrix.Let `A = UP` be the polar decomposition of `A`, where `U` is unitary and `P` is positive semi-definite Hermitian. Then `P = A(A*)^(1/2)` and `U = P^(-1)A`. Let `W = P^(1/2)U P^(1/2)` and `W* = P^(1/2)U* P^(1/2)`. Since `U` is unitary, we have `U* = U^(-1)`. Hence `W* = P^(1/2)U^(-1) P^(1/2)`.Multiplying `UP` by `P^(1/2)`, we get `UP^(1/2) = P^(1/2)U P`. Multiplying both sides of the equation by `P^(1/2)` on the right, we get `UP^(1/2)P^(1/2) = P^(1/2)U P P^(1/2)` or `UP = P^(1/2)U P^(1/2)P^(1/2)` or `UP = P^(1/2)U P^(1/2)` or `U = P^(-1/2)W P^(1/2)`.
Substituting the value of `U` in `A = UP`, we get `A = P^(-1/2)W P^(1/2)P`. Since `P` is positive semi-definite, `P = (P^(1/2))^2` is a Hermitian matrix. Therefore, `W = P^(1/2)U P^(1/2)` is a Hermitian matrix and is positive semi-definite. Thus, we have `A = PW` where `W = P^(1/2)U P^(1/2)` is a positive semidefinite Hermitian matrix. Hence, the alternate form of the polar decomposition of `A` is given by `A = PW`, where `W` is a positive semidefinite Hermitian matrix and `P` is a positive semidefinite Hermitian matrix.
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Use a net to find the surface area of the cone to the nearest square centimeter. Use 3.14 for pie The numbers are 19cm and 8cm
Answer:
678.672cm^2
Step-by-step explanation:
Given data
A cone is described by the length and radius
l=19cm
r=8cm
The formula for the surface area of the cone is
T.S.A=πrl+πr^2
Substitute
T.S.A=3.142*8*19+3.142*8^2
T.S.A=477.584+201.088
T.S.A=678.672
Hence the surface area is
678.672cm^2
As sales manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development.
You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts.
Montevideo signs per month, is 15 contracts. This is down 5 contracts from the figure last year, when your company charged only $2,000.
Construct a linear demand equation in the form q= ap + b where the number of contracts q is given as a function of the hourly fee p Montevideo charges for development.
Give a formula for the total revenue obtained by charging $p per hour.
The costs to Montevideo Productions are estimated as follows:
Fixed costs: $120,000 per month and Variable costs: $80,000 per contract
Express Montevideo Productions’ monthly cost as a function of the hourly production charge p.
Express Montevideo Productions’ monthly profit as a function of the
hourly development fee p and hence the price it should charge to maximize the profit.
The XYZ Clothing Company manufactures football boots for sale to
College/University bookstores, in Trinidad. Football boots are in runs of up to 500. It cost (in dollars) for a run of x football boots is:
(x) = 3,000 + 8x + 0.1x2 0 ≤ x ≤ 500
XYZ Clothing sells the football boots at $ 120 each.
(a) How many football boots does XYZ have to sell to breakeven?
(b) How many football boots does XZY have to sell to make maximum profit?
(c) On a labelled pair of axes, sketch the XYZ’s profit function. Label all important points.
(a) The number of football boots XYZ Clothing needs to sell to break even can be found by solving the quadratic equation.
(b) To maximize profit, XYZ Clothing needs to sell 1120 football boots.
(c) Plotting relevant points on a graph, we can sketch XYZ Clothing's profit function, indicating important points.
(a) To find the number of football boots XYZ Clothing needs to sell to break even, we set the profit function equal to zero:
Profit = Revenue - Cost
Since the revenue is given as $120 per football boot and the cost function is provided as C(x) = 3,000 + 8x + 0.1x^2, the profit function is:
Profit = 120x - (3,000 + 8x + 0.1x^2)
Setting the profit function equal to zero, we have:
0 = 120x - (3,000 + 8x + 0.1x^2)
Simplifying the equation, we get:
0 = 112x - 0.1x^2 - 3,000
To find the number of football boots needed to break even, we solve the quadratic equation:
0.1x^2 - 112x + 3,000 = 0
Solving this equation will give us the value of x, which represents the number of football boots XYZ Clothing needs to sell to break even.
(b) To find the number of football boots XYZ Clothing needs to sell to maximize profit, we need to determine the vertex of the profit function. The profit function is the same as in part (a):
Profit = 120x - (3,000 + 8x + 0.1x^2)
To find the vertex, we can use the formula x = -b/2a, where a = 0.1 and b = 112.
x = -(-112) / (2 * 0.1)
x = 1120
So, XYZ Clothing needs to sell 1120 football boots to maximize profit.
(c) To sketch the profit function on a pair of axes, we can plot the points that are relevant to the problem. We know that the profit function is given by:
Profit = 120x - (3,000 + 8x + 0.1x^2)
We can plot the following points:
Breakeven point: (x, 0) where x is the number of football boots needed to break even.
Maximum profit point: (1120, Profit(1120)) where Profit(1120) is the maximum profit obtained when 1120 football boots are sold.
Additionally, we can plot a few more points to get an idea of the shape of the profit function.
By connecting these points, we can sketch the profit function on the axes, indicating the relevant points and labeling them accordingly.
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I’ll give brainless to who ever respond correctly and fast
Answer:
34cm squared
Step-by-step explanation:
Formula: 2(WL+HL+HW)
(2*5) + (1*5) + (1*2) = 10 + 5 + 2 = 17 17*2 = 34
Answer:
34
Step-by-step explanation:
2(wl+ hl+hw)
2(10+5+2)
= 34
Find inverse of f(x) = 2 + 3x / x - 2
Know answer is 2x + 2 / x - 3 I just want someone to explain the steps for my revision!
Thank you.
Which number represents the probability of an event that is impossible to
occur?
Answer:
An impossible event has a probability of 0. A certain event has a probability of 1.
Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interval for a sample of size 176 with 118 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. 99.9% C.1. =
The 99.9% confidence interval for a sample of size 176 with 118 successes is (0.558, 0.778).
The formula for finding the confidence interval for a sample proportion is given as follows:
Confidence interval = sample proportion ± zα/2 * √(sample proportion * (1 - sample proportion) / n)
Where,
zα/2 is the z-value for the level of confidence α/2,
n is the sample size,
sample proportion = successes / n
Here, level of confidence, α = 99.9%, so α/2 = 0.4995. The value of zα/2 for 0.4995 can be found from the z-table or calculator and it comes out to be 3.291.
Putting all the values in the formula, we get:
Confidence interval = 0.670 ± 3.291 * √(0.670 * 0.330 / 176)
= (0.558, 0.778) (rounded to three decimal places and put in parentheses)
Thus, the 99.9% confidence interval for a sample of size 176 with 118 successes is (0.558, 0.778).
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There are 25 people competing in a race. In how many ways can they finish in first and second
place?
49
400
600
625
Answer:
C) 600-----------------------
The number of ways to choose the first place finisher is 25, since any of the 25 people can win.
After the first place finisher is determined, there are 24 people left who can finish in second place.
Therefore, the total number of ways is:
25 × 24 = 600Correct choice is C.
The algebra question is in the image
Answer:
B
Step-by-step explanation:
A or constant is the answer
Aerin's friend Fritz gives her a riddle to solve about the ages of the people in his family. There are 5 people in Fritz's family: Mom, Dad, his sisters Adele and Erika, and Fritz. Here are the clues to the puzzle. 1) Mom is 8 years younger than Dad. 2) Dad is 2 times as old as Fritz. 3) Adele is 4 years old. 4) Fritz's age plus Adele's age equals Erika's age. 5) Mom was 24 when Erika was born. 6) In 9 years, Mom will be twice as old as Erika will be. All the ages are whole numbers. Aerin decides to use variable for the unknown ages and write equations to express the information. M
Answer:
Dad = 47, Mom = 39, Fritz = 11, Erika = 15 and Adele = 4
Step-by-step explanation:
Let M = Mom's age, D = Dad's age, F = Fritz's age, A = Adele's age and E = Erika's age.
Given that
1) Mom is 8 years younger than Dad, we have D = M + 8 (1)
2) Dad is 2 times as old as Fritz. D = 2F (2)
3) Adele is 4 years old. A = 4 (3)
4) Fritz's age plus Adele's age equals Erika's age. F + A = E (4)
5) Mom was 24 when Erika was born. M = E + 24 (5)
6) In 9 years, Mom will be twice as old as Erika will be. M + 9 = 2(E + 9) (6)
Substituting (5) into (6), we have
E + 24 + 9 = 2(E + 9)
E + 33 = 2E + 18
subtracting E from both sides, we have
2E - E + 18 = 33 + E - E
E + 18 = 33
subtracting 18 from both sides, we have
E + 18 - 18 = 33 - 18
E = 15
M = 15 + 24 = 15 + 24 = 39
From (4) F = E - A = 15 - 4 = 11
From (1) D = M + 8 = 39 + 8 = 47
So, their ages are Dad = 47, Mom = 39, Fritz = 11, Erika = 15 and Adele = 4