Select all the true sentences!!!

Two linearly independent eigenvectors corresponding to the eigenvalue λ = 2 are v₁ = [-1, 0, 3] and v₂ = [0, 1, 1].

Given the matrix A = [−1 1 −1], one of the eigenvalues is λ = 2. We need to find two linearly independent eigenvectors corresponding to this eigenvalue.

To find the eigenvectors, we solve the equation (A - λI)v = 0, where A is the matrix, λ is the eigenvalue, I is the identity matrix, and v is the eigenvector.

In this case, the equation becomes:

(A - 2I)v = 0

Substituting the values, we have:

[−1 1 −1] - 2[1 0 0] [x] [0]

[y] = [0]

[z] [0]

Simplifying further:

[−3 1 −1] [x] [0]

[y] = [0]

[z] [0]

This gives us the following system of equations:

-3x + y - z = 0

y = 0

z = 0

From the second equation, we get y = 0. Plugging this into the first equation, we have -3x - z = 0, which simplifies to -3x = z.

Choosing a value for z, let's set z = 3. Then, -3x = 3, and solving for x gives x = -1.

Therefore, one eigenvector corresponding to the eigenvalue λ = 2 is v₁ = [-1, 0, 3].

To find the second linearly independent eigenvector, we can choose a different value for z. Let's set z = 1.

Again, from the equation -3x + y - z = 0, we have -3x + y - 1 = 0. By choosing x = 0, we get y = 1.

Thus, another eigenvector corresponding to λ = 2 is v₂ = [0, 1, 1].

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Answer:

(-5, -4)

Step-by-step explanation:

A dilation at the origin would just result with you multiplying the coordinates by the scale factor.

-10 * 1/2 and -8 * 1/2

Answer:

Step-by-step explanation:

Answer:

46.08

Step-by-step explanation:

the formula for finding the volume of the cone is: V = π r^2 h/3

Insert the information provided (2 because half the diameter is the radius)

and solve. Hope this helps!

Answer:

C) 88

Step-by-step explanation:

so we are given a circle, and m<ACB is 44°. We need to find the measure of arc AB

<ACB is an inscribed angle (it is inside the circle), and it intercepts the arc AB

Inscribed angle theorem is a theorem that states the measure of an inscribed angle is half of the measure of the arc it intercepts

which also means that the measure of the intercepted arc is twice the measure of the inscribed angle (this is because of how algebra works)

which means mAB=2m<ACB (inscribed angle theorem)

mAB=2*44° (substitution)

mAB=88° (algebra)

therefore, your answer is C

Hope this helps!

From Shamma's study, there are 14 people in her sample. How many people were in Shamma's sample? Shamma's sample consists of 14 people.

Explanation: We can find the answer in the given text, which is the number of people in Shamma's sample.

The sentence that holds the answer is: "We conducted a one-tailed, one-sample t-test comparing the sample mean BDI score (28.4) against a population mean of 24, t(14) = 2.25, p = 0.021." We see that the value of t is in brackets with a value of 14.

Therefore, there are 14 people in Shamma's sample. Now, let's write the null hypothesis and an alternative hypothesis.

Null Hypothesis, H0: H0: μ = 24, There is no significant difference between the sample mean BDI score and population mean. Alternative Hypothesis, Ha: Ha: μ > 24, There is a significant difference between the sample mean BDI score and population mean.

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The sample mean is greater than the population mean i.e., μ > 24.

There were 15 people in Shamma's sample.

Shamma randomly gives the Beck's Depression Inventory (BDI) to a group of her patients.

After analyzing the One Sample T-test from her study she writes:

We conducted a one-tailed, one-sample t-test comparing the sample mean BDI score (28.4) against a population mean of 24, t(14) = 2.25, p = 0.021.

The value given in the bracket is 14.

As we know that N-1 is used as the degrees of freedom, so the number of people in Shamma's sample is:

[tex]N-1 = 14N = 14 + 1 = 15[/tex]

Thus, the number of people in Shamma's sample is 15.

The null hypothesis for Shamma's study would be:

H0: The sample mean is equal to the population mean i.e., μ = 24.

The alternative hypothesis for Shamma's study would be:

HA: The sample mean is greater than the population mean i.e., μ > 24.

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Answer:

Step-by-step explanation:

The correct choice is:

B. The derivative is the vector-valued function i + Di + k

The given function is u(t) = 2t³i + (t²-1)j - 8k, which represents a vector-valued function.

To compute the derivative of (19 + 21)u(t), we need to differentiate each component of the vector function with respect to t.

The scalar function (19 + 21) is a constant multiple, and when we differentiate a constant multiple of a vector function, we can simply differentiate each component of the vector function.

Taking the derivative of each component separately, we get:

d/dt (2t³i) = 6t²i

d/dt ((t²-1)j) = 2tj

d/dt (-8k) = 0

Putting the derivatives of each component together, we have:

(6t²i + 2tj + 0k) = 6t²i + 2tj

Hence, the derivative of the function (19 + 21)u(t) is the vector-valued function 6t²i + 2tj.

Therefore, the correct choice is:

B. The derivative is the vector-valued function i + Di + k

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Answer:

3

Step-by-step explanation:

Answer:

3,500

plz mark me as brainliest

Answer:

G

Step-by-step explanation:

The number of total bottles sold on that day is 40

11 + 7 + 18 + 4 = 40

On Tuesday, theoretically, this is what will be sold:

22 bottles of apple juice

14 bottles of cranberry juice

36 bottles of orange juice

8 bottles of pineapple juice

We need to find out what doesn't fit the data.

F: 14 - 8 = 6, not correct answer

G: the number of cranberry juice will be 6 times the number of pineapple juice sold? It's not even twice the amount!

H: 36 + 14 = 50, not correct answer

J: 22 - 8 = 14, not correct.

From this, G is the correct answer as it is not even close to matching the data.

Answer:

The ratio should be 2:3

Step-by-step explanation:

Hope this helped!

Answer:

2:3 or 2/3 depending on which form they want the answer in.

Step-by-step explanation:

There are 2 squares and 3 circles.

The data set is bimodal with modes at 4 and 14.

To determine the mode(s) and the modality of a data set, we need to identify the values that occur most frequently.

The given data set is: 4, 14, 14, 14, 4

To find the mode(s), we can count the frequency of each value:

4 appears 2 times14 appears 3 times

The mode(s) are the value(s) that appear with the highest frequency. In this case, both 4 and 14 have the same frequency of occurrence, so this data set is bimodal, with modes at 4 and 14.

Therefore, the data set is bimodal with modes at 4 and 14.

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Answer:

30x

Step-by-step explanation:

missing must be 2×3x×5=30x

9x²+30x+25=(3x+5)²

Answer:

1. 2:5

2. 5:2

3. 2,5

Step-by-step explanation:

Hope you have a great day

The perimeter of triangle is the sum of the lengths of its three sides. In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, we can determine the perimeter in terms of x.

Let's consider the sides of the triangle:

The side opposite the 30° angle is x/2, which can be derived using the properties of a 30-60-90 triangle.

The side opposite the 60° angle is x√3/2, which can also be derived using the properties of a 30-60-90 triangle.

The hypotenuse, which is opposite the 90° angle, has a length of x.

To find the perimeter, we add up the lengths of these three sides:

Perimeter = x/2 + x√3/2 + x

Combining like terms, we can simplify the expression:

Perimeter = (x + x√3 + 2x)/2

Perimeter = (3x + x√3)/2

Perimeter = x(3 + √3)/2

Therefore, the perimeter of the triangle in terms of x is 2x + x√3.

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(a) The range has a significant difference between Set A and Set B.

(b) The interquartile range is a more appropriate measure for the data of Set B, considering the presence of outliers.

For Set A:

Range = 7 - 1 = 6

Interquartile Range = Q3 - Q1 = 5 - 2 = 3

Variance = 4.67

Standard Deviation = 2.16

For Set B:

Range = 50 - 1 = 49

Interquartile Range = Q3 - Q1 = 6 - 2 = 4

Variance = 205.14

Standard Deviation = 14.33

(a) The measure of dispersion that has a significant difference between Set A and Set B is the range.

(b) The most appropriate measure of dispersion to be used to measure the distribution of the data of Set B depends on the specific characteristics of the data. However, considering the presence of outliers (such as the value 50), a robust measure like the interquartile range may be more suitable for Set B.

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Answer:

I'm pretty sure the answer is A.

Step-by-step explanation:

Since 90 plus 9 = 99 and 99 is the tens and ones place.

So, the answer should be A.

Hope this helps! :)

90 / 9 = 10 compares the tens place and one's place in 9,999. Option A is correct.

Given that,
To determine the equation correctly compare the tens place and one's place in 9,999.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
In the number 9999,
let the number on the ten places be x times the number on unit place,
90 = x * 9
x = 90 / 9
x = 10

Now,
90 / 9 = 10

Thus, 90 / 9 = 10 compares the tens place and one's place in 9,999. Option A is correct.

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R₄,₄ gives an approximation of order h⁸ when approximating ∫(a to b)f(x)dx using Romberg integration. Therefore second option is the correct answer.

When approximating the integral ∫(a to b) f(x) dx using Romberg integration, the term "R₄,₄" refers to the fourth row and fourth column of the Romberg matrix.

This specific entry represents the approximation obtained using the Romberg method with four iterations. The order of approximation is determined by the highest power of h in the error term of the approximation.

Since R₄,₄ has a subscript of 4, it indicates that the approximation is of order h⁸. This means that the error decreases at a rate of h⁸ as the step size h decreases, providing a more accurate estimation of the integral.

Therefore the correct answer is second option.

The question should be:

When approximating ∫(a to b)f(x)dx using Romberg integration, R₄,₄ gives an approximation of order:

h10  

h8

h4

h6

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Answer:

3

Step-by-step explanation:

5/2 ÷ 5/6 = 5/2 × 6/5

5/2 × 6/5 = 30/10 or 3

The interest on the loan of $35,000 at a 6% interest rate for 9 months is $1,575.

To calculate the interest on a loan, you can use the formula:

Simple Interest = Principal x Rate x Time.

In this case, the principal is $35,000, the interest rate is 6%, and the time is 9 months.

First, convert the interest rate to a decimal by dividing it by 100: 6% = 0.06. Next, calculate the interest by multiplying the principal, rate, and time: Interest = $35,000 x 0.06 x 9/12.

Simplifying the calculation, we get: Interest = $35,000 x 0.06 x 0.75 = $1,575.

Therefore, the correct answer is option B: $1,575.

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The graph should pass through the points (-5, -2), (6, 8), (12, 10), and (-12, -12), forming a diagonal line from the bottom left to the top right of the graph.

To graph the function f(x) = x + 2 + 1, we will plot four points on the graph.

Given the points: (-5, -2), (6, 8), (12, 10), and (-12, -12).

Plotting the points on a graph:

(-5, -2):

Starting from the origin (0,0), move 5 units to the left along the x-axis and 2 units downward along the y-axis. Plot the point (-5, -2).

(6, 8):

From the origin, move 6 units to the right along the x-axis and 8 units upward along the y-axis. Plot the point (6, 8).

(12, 10):

Move 12 units to the right along the x-axis and 10 units upward along the y-axis from the origin. Plot the point (12, 10).

(-12, -12):

Move 12 units to the left along the x-axis and 12 units downward along the y-axis from the origin. Plot the point (-12, -12).

Connecting the plotted points, we get a straight line. This line represents the graph of the function f(x) = x + 2 + 1.

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Answer:

2/5!

Step-by-step explanation:

Your expected profit from one ticket, after accounting for the ticket cost, is $2. This means that, on average, you can expect to make a profit of $2 per ticket if you were to play the lottery multiple times.

To find the expected cash prize, we multiply each cash prize by its corresponding probability and sum up the results.

Expected cash prize = (0.00000000821 * $16,000,000) + (0.00000014 * $1,000,000) + (0.000001746 * $200,000) + (0.000153924 * $10,000) + (0.005426433 * $100) + (0.006847638 * $7) + (0.01791359 * $4) + (0.96965652079 * $3) + (0.01791359 * $0)

Calculating this, we get an expected cash prize of $3.00025908719.

Interpreting the result, we can say that, on average, the expected cash prize for one ticket is approximately $3. This means that if you were to play the lottery multiple times, the average amount you could expect to win per ticket would be around $3.

To calculate the expected profit from one ticket, we subtract the cost of the ticket ($1) from the expected cash prize:

Expected profit = $3 - $1 = $2.

Therefore, your expected profit from one ticket, after accounting for the ticket cost, is $2. This means that, on average, you can expect to make a profit of $2 per ticket if you were to play the lottery multiple times.

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The given relation is P (|Xn - μ| / σ < 0.25) ≥ 0.99. We need to determine the smallest value of n that satisfies the given relation using the central limit theorem.

Step 1: We know that the standard normal distribution is used in the central limit theorem to approximate the distribution of the sample means. The standard normal distribution has a mean of zero and a standard deviation of one. We need to standardize the given relation so that we can use the standard normal distribution.

Step 2: We substitute the values from the given relation and simplify as follows: P(|Xn - μ| / σ < 0.25) ≥ 0.99P(|Xn - μ| / (o/√n) < 0.25) ≥ 0.99P((Xn - μ) / (o/√n) < 0.25) ≥ 0.99P(-0.25 < (Xn - μ) / (o/√n) < 0.25) ≥ 0.99P(Z < 0.25√n) - P(Z < -0.25√n) ≥ 0.99where Z is the standard normal random variable.

Step 3: We look up the values of -0.25√n and 0.25√n from the standard normal distribution table and find their difference. We use the absolute value of the difference since we are dealing with probabilities. We get: |P (Z < 0.25√n) - P (Z < -0.25√n) | = 0.99. Since the standard normal distribution is symmetric, we have P (Z < 0.25√n) - P (Z > 0.25√n) = 0.99We can rearrange this as: P (Z < 0.25√n) = 0.995P(Z > 0.25√n) = 0.005

Step 4: We look up the value of 0.995 from the standard normal distribution table and find its corresponding z-score. We get: z = 2.58. Using the z-score formula, we can solve for the value of 0.25√n. We get:2.58 = 0.25√nn = (2.58 / 0.25) ²n ≈ 107.58We round up to the nearest integer to get n = 108. Therefore, the smallest number of items n that must be taken in order to satisfy the given relation is 108.

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The probability is approximately 0.0079, or 0.79%.

To find the probability that all three heads of lettuce in the sample are spoiled, we need to calculate the ratio of favorable outcomes to the total number of possible outcomes.

The total number of possible outcomes is the number of ways to choose 3 heads of lettuce from the 41 available in the basket without replacement. This can be calculated using the combination formula (nCr):

Total possible outcomes = 41 C 3 = (41!)/(3!(41-3)!) = (414039)/(321) = 412013 = 10,660.

The number of favorable outcomes is the number of ways to choose 3 spoiled heads of lettuce from the 9 spoiled ones in the basket:

Favorable outcomes = 9 C 3 = (9!)/(3!(9-3)!) = (987)/(321) = 84.

Therefore, the probability that all three heads of lettuce in the sample are spoiled is:

Probability = Favorable outcomes / Total possible outcomes = 84 / 10,660 ≈ 0.0079 (rounded to four decimal places).

So, the probability is approximately 0.0079, or 0.79%.

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