find a 2×2 matrix such that [−4−2] and [−54] are eigenvectors of the matrix with eigenvalues 4 and −10, respectively. [

His/her lowered score was most likely due to statistical regression.

The missing options in the question are:

A. compensation rivalry  B. Demoralization C.  Differential selection

D.  Testing E.  Statistical regression

From the question, we have:

A change (whether higher or lower) in the score is caused by statistical regression.

This is so because several variables could attribute to the change in the score.

The relationship between these variables is referred to as statistical regression

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let's recall that two tangent lines to the same circle meeting outside it, will have the same length, so all those pair of tangent lines are equal in length.

Check the picture below.

Explanation:

If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.

If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.

Choices A, C and D are true for any parallelogram (rectangle or not).

The number which best completes the sequence is option c) 72.

The sequence seems to be alternating between multiplying by 3 and dividing by 2.
Starting with 10, we have:
10 x 3 = 30
30 ÷ 2 = 15
15 + 1 = 16
16 x 3 = 48
48 ÷ 2 = 24
24 + 1 = 25

So, the next number in the sequence should be:
25 x 3 = 75
75 ÷ 2 = 37.5

However, none of the answer options match 37.5. Therefore, we need to look for a pattern that matches one of the answer options.

If we multiply 25 by 3 and then divide by 2, we get 37.5. However, if we continue with this pattern, we get:
37.5 x 3 = 112.5
112.5 ÷ 2 = 56.25

Again, none of the answer options match 56.25.

Let's try multiplying 24 by 3 and then dividing by 2:
24 x 3 = 72
72 ÷ 2 = 36

Since 36 is not in the sequence, we can eliminate option b) 75.

Therefore, the number which best completes the sequence is option c) 72.
The number which best completes the sequence 10, 30, 15, 16, 48, 24, 25 is:

c) 72

The sequence can be described as alternating between multiplying by 3 and dividing by 2, then adding 1.

10 x 3 = 30
30 / 2 = 15
15 + 1 = 16
16 x 3 = 48
48 / 2 = 24
24 + 1 = 25
25 x 3 = 75

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To make layla's favorite shade of purple, she needs 8 ounces of blue for every 14 ounces of red, and she need for 63 ounces of red, then the blue would be 36 ounces.

To make layla's favorite shade of purple, she needs 8 ounces of blue for every 14 ounces of red.

Based on the given conditions,

She needs ounces of blue = 8

For every ounces of red = 14

She need for 63 ounces of red = 63

Let us assume,

She need for ounces of blue = x

So,

We can write,

Need for 63 ounces of red ⇒ Every 14 ounces of red

she needs 8 ounces of blue ⇒ She need for X ounces of blue

Then,

\(\frac{8}{14}\) = \(\frac{x}{63}\)

We can solve the equation of \(\frac{8}{14}\) = \(\frac{x}{63}\)

Swap the sides,

\(\frac{x}{63}\) = \(\frac{8}{14}\)

Divide both sides of the equation by the coefficient of variable,

\(x\) = \(\frac{8}{14} *63\)

Simplify fractions,

x = 4*9

Calculate the product or quotient,

x = 36

Therefore,

To make layla's favorite shade of purple, she needs 8 ounces of blue for every 14 ounces of red, and she need for 63 ounces of red, then the blue would be 36 ounces.

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Problem 2: Using the law of sines with α=74°, γ=36°, and c=6.8, we find that a≈10.67. Problem 4: With α=46°, β=88°, and c=10.5, b≈6.77. Problem 6: Given β=16°30', γ=84°40', and a=15, c≈4.27.



Problem 2:

Using the law of sines, we can set up the following equation:

sin(α) / a = sin(γ) / c

Plugging in the given values, we have:

sin(74°) / a = sin(36°) / 6.8

Now we can solve for a:

a = (sin(74°) / sin(36°)) * 6.8

a ≈ 10.67

Problem 4:

Using the law of sines, we can set up the following equation:

sin(α) / a = sin(β) / b

Plugging in the given values, we have:

sin(46°) / a = sin(88°) / 10.5

Now we can solve for b:

b = (sin(46°) / sin(88°)) * 10.5

b ≈ 6.77

Problem 6:

Using the law of sines, we can set up the following equation:

sin(β) / b = sin(γ) / c

Plugging in the given values, we have:

sin(16°30') / b = sin(84°40') / 15

Now we can solve for c:

c = (sin(16°30') / sin(84°40')) * 15

c ≈ 4.27

In all the problems, we used the law of sines to relate the angles and sides of the triangle, and then solved for the required side lengths using the given values and trigonometric ratios.

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Answer:

11/9 or 1 2/9

Step-by-step explanation:

3 5/9=32/9

2 1/3=7/3

LCM is 9

7/3=21/9

32/9-21/9

=11/9

=1 2/9

Answer:

x=<_26/3

OR

x=>_14/3

Add them together and divide

The Number of ways that four people can be seated on the bench so that john is not next to paul is 12

In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.

The arrangement of n items in r ways is given by

Here we have

4 people (John, Paul, George, and Ringo) are seated in a row on a bench

Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24

The number of ways of seating the four people so that john is next to paul is 12

Then the number of ways the four people on the bench so that john is not next to paul can find as given below

= Total No of ways, 4 can be seated - No of ways that john next to paul  

= 24 - 12 = 12        

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Sample size required is 333, 42, 97 and 33,285, respectively using  confidence level and different parameters of standard deviation.

To estimate a population mean to within 40 units with 99% confidence and a population standard deviation of 200, the sample size required can be calculated using the formula

n = (Zα/2)² * (σ²) / (E²)

where Zα/2 is the z-score corresponding to the desired level of confidence (99% in this case), σ is the population standard deviation, and E is the desired margin of error (40 units).

Plugging in the values, we get

n = (2.576)² * (200)²/ (40)²

n = 332.84

Therefore, a sample size of at least 333 should be used.

If the population standard deviation is changed to 50, the same formula can be used with the new value of σ:

n = (2.576)² * (50)²/ (40)²

n = 41.68

Therefore, a sample size of at least 42 should be used.

If using a 95% confidence level, the z-score changes to 1.96

n = (1.96)² * (200)²/ (40)²

n = 96.04

Therefore, a sample size of at least 97 should be used.

To estimate the population mean to within 10 units, the margin of error (E) is changed to 10 in the formula, and the sample size is recalculated

n = (2.576)² * (200)² / (10)²

n = 33,284

Therefore, a sample size of at least 33,285 should be used.

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The required sample size should be 166 to estimate the population mean within 40 units with 99% confidence, given a population standard deviation of 200.

To determine the required sample size for estimating a population mean with a given level of confidence and margin of error, we can use the formula:

n = (Z * σ / E)^2

Where:

n = Sample size

Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence corresponds to a Z-score of 2.576)

σ = Population standard deviation

E = Margin of error (in this case, 40 units)

Substituting the given values into the formula, we have:

n = (2.576 * 200 / 40)^2

Simplifying further:

n = (12.88)^2

n ≈ 165.6544

Since the sample size must be a whole number, we round up the value to the nearest integer:

n = 166

Therefore, the required sample size should be 166 to estimate the population mean within 40 units with 99% confidence, given a population standard deviation of 200.

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Answer:

I don't see what the question is

Answer:

\(a^{\frac{15}{2} }\)

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\((a^m)^{n}\) = \(a^{mn}\)

(\(a^{\frac{1}{2} }\) × a)^5

= \((a^{\frac{1}{2}+1) }\)^5

= \((a^{\frac{3}{2}) } ^{5}\)

= \(a^{\frac{15}{2} }\)

1, 5, 25,  125

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

5 gives the next term. In other words,  an=a1⋅rn−1. Geometric Sequence: r=5

This is the form of a geometric sequence.an=a1rn−1 Substitute in the values of a1=1 and r=5.an=(1)⋅(5)n−1 Multiply (5)n−1 by 1. an=5n−1

Answer:

w = -11/6

Step-by-step explanation:

-8 5/9 = 4 2/3w

-8 5/9  = -77/9

4 2/3 = 14/3

So, our equation is

-77/9 = 14/3w

Divided  both sides by 14/3

w = -11/6

Answer:

D

Step-by-step explanation:

Firstly let's see definition of Rational numbers ,

Rational numbers :-

From the options , look at option D ,its

→ √400

→ √{20²}

→ 20

When the diameter of the sphere is 60 mm, its radius is 30 mm. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius.

To find how fast the volume is increasing, we need to take the derivative of V with respect to time, which gives dV/dt = 4πr^2 (dr/dt). Substituting the given values, we get dV/dt = 4π(30)^2 (2) = 7200π mm^3/s. Therefore, the volume of the sphere is increasing at a rate of 7200π mm^3/s when the diameter is 60 mm. The radius of a sphere is increasing at a rate of 2 mm/s. When the diameter is 60 mm, the radius is 30 mm. The volume of a sphere is given by the formula V = (4/3)πr³. Using the chain rule, dV/dt = (4/3)π(3)r²(dr/dt), where dV/dt is the rate of volume increase and dr/dt is the rate of radius increase. Plugging in r = 30 mm and dr/dt = 2 mm/s, we get dV/dt = 4π(30)²(2) = 7200π mm³/s. So, the volume is increasing at a rate of 7200π mm³/s when the diameter is 60 mm.

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A two-sided confidence interval is appropriate because the research question is about whether the average mileage is significantly different from 300 miles.

(a) To determine if a one-sided or two-sided confidence interval is appropriate for this situation, we need to consider the research question and the nature of the hypothesis being tested. If the research question is specifically focused on whether the average mileage is less than or greater than 300 miles, then a one-sided confidence interval would be appropriate. On the other hand, if the research question is broader and seeks to determine whether the average mileage is significantly different from 300 miles (i.e., it could be less or greater), then a two-sided confidence interval would be appropriate.

(b) To compute a 95% confidence interval, we can use the formula:

CI =X ± (Z * (σ/√n))

Where X is the sample mean, Z is the z-value corresponding to the desired confidence level (in this case, 95% corresponds to Z = 1.96 for a large enough sample), σ is the population standard deviation (unknown, so we use the sample standard deviation), and n is the sample size.

Plugging in the given values:

CI = 285 ± (1.96 * (50/√226))

Simplifying the expression:

CI = 285 ± (1.96 * 3.322)

CI = [278.15, 291.85]

Interpretation: The 95% confidence interval for the average mileage from Pullman to home is [278.15, 291.85]. This means that we are 95% confident that the true average mileage of all Washington State University students falls within this interval. It suggests that based on the sample data, the average mileage is likely to be between 278.15 and 291.85 miles.

(c) If the confidence level is decreased to 90%, the new confidence interval will be narrower since a smaller confidence level requires less certainty, resulting in a narrower interval. Conversely, if the confidence level is increased to 99%, the new confidence interval will be wider as a higher confidence level demands greater certainty, leading to a wider interval to capture a larger range of potential values. Therefore, the answer is D. narrower for a confidence level of 90% and A. wider for a confidence level of 99%.

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Answer:

You look to see if one of the angles has a box around it and you add up the other angle with 90 and then subtract the whole thing by 180 because there are 180 degrees in a triangle.

Step-by-step explanation:

See above.

Answer:

draw another segment I think. __________

Step-by-step explanation:

The probability from the odds is 3/7

The value of the odds is given as

Odds = 3 to 4

Represent the odds as a fraction

So, we have the following representation

Odds = 3/4

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

Probability = (3/4)/(3/4 + 1)

Evaluate the sum

Probability = (3/4)/(7/4)

Evaluate the quotient

Probability = 3/7

Hence, the probability is 3/7

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Answer:

-6

Step-by-step explanation:when there is a negative you whuld do 6+-12

Answer: overindulgence in or dependence on an addictive substance, especially alcohol or drugs.

overindulgence in or dependence on an addictive substance, especially alcohol or drugs

Answer: Distance she ran on Thursday = 2.38 miles

Step-by-step explanation:

Given, Amille ran on Monday = 2.36 miles

On Tuesday, she ran 4.88 miles.

On Wednesday, she ran 3.19 miles.

Total distance she ran till Thursday = 12.81 miles.

Now, Distance she ran on Thursday = (Total distance) - (Distance ran on Monday to Wednesday)

= 12.81-(2.36+4.88+3.19)

= 12.81-10.43

= 2.38 miles

Hence, Distance she ran on Thursday = 2.38 miles

Answer:

The measure of the angle is 15 degree.

Step-by-step explanation:

The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle.

Supplementary angles are those that add up to 180, and complementary angles add up to 90.

Let \(x\) represent the angle.

\((180^{\circ} - x)\) is the supplementary angle and \((90^{\circ}-x)\) is the complementary angle.

\(180^{\circ}-x=3(90^{\circ}-x)-60^{\circ}\\180^{\circ}-x=270^{\circ}-3x-60^{\circ}\\180^{\circ}-x+3x=210^{\circ}\\2x=30^{\circ}\\x=15^{\circ}\)

\((90-15)^{\circ}=75^{\circ}\) is the complementary

\((180-15)^{\circ}=165^{\circ}\) is the supplementary angle

Since ab > 0, it is clear that the discriminant D > 0. Therefore, the equation ax^2 + bx + c = 0 has two distinct real roots.

Since 4a + 2b + c = 0, we can rewrite c as c = -4a - 2b. Substituting this into the quadratic equation ax^2 + bx + c = 0 gives ax^2 + bx - 4a - 2b = 0. Factoring out an 'a' gives a(x^2 + (b/a)x - 4) - 2b = 0.

Since ab > 0, we know that a and b must have the same sign. This means that either both a and b are positive or both a and b are negative. In either case, (b/a) is negative. So we can rewrite the equation as a(x^2 - |(b/a)|x - 4) - 2b = 0.

To solve for the roots of the equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the coefficients, we get x = (-b ± √(b^2 - 4a(-4a-2b))) / 2a, which simplifies to x = (-b ± √(b^2 + 16ab)) / 2a.

Since ab > 0, we know that b^2 + 16ab > 0. Therefore, the quadratic equation ax^2 + bx + c = 0 has two real roots.

Based on the information provided, let's consider the equation ax^2 + bx + c = 0, where a, b, and c are real numbers and 4a + 2b + c = 0. Since ab > 0, both a and b have the same sign (either both positive or both negative).

The given equation can be rewritten as a quadratic equation in the standard form:

ax^2 + bx + c = 0

Using the discriminant formula, D = b^2 - 4ac, we can analyze the nature of the roots of the quadratic equation. Given that 4a + 2b + c = 0, we can express c as:

c = -4a - 2b

Now, let's plug this value of c into the discriminant formula:

D = b^2 - 4a(-4a - 2b)

D = b^2 + 16a^2 + 8ab

Since ab > 0, it is clear that the discriminant D > 0. Therefore, the equation ax^2 + bx + c = 0 has two distinct real roots.

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Answer:

1. 82 2. 82 3. 82 4. 98 5. 123 6. 122 7. 119 8. 60 9. 60 10. 125 11. 35 12. 105

The initial amount is worth $ 1538.46

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that may be added over time.

Simple interest is calculated as a percentage of the principal amount and is usually expressed as an annual rate.

The formula to calculate simple interest is:

Simple Interest = Principal x Rate x Time/ 100

Here we have

You are going to receive $2,000 in 6 years from now

The annual simple interest rate is 5%

Let 'P' be the initial or principal amount

Using the formula, I = PTR/100

Simple interest will gain on 'P' at 5% for 6 years

=> I = P(6)(5)/100  

=> I = 0.3P

And total amount = P + 0.3P = 1.3P

It is given that after 6 years we get $ 2000

=> 1.3P = 2000

=> P = 1538.46

Therefore,

The initial amount is worth $ 1538.46

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