Problem4(10%)LetA,B∈Rn×n, and suppose that eitherAorBis non-singular. IfABis diagonalizable, show thatBAis also diagonalizable.

The coordinates of Q' after the translation is found to be Q' = (1, -1).

Whenever a figure is relocated from one place to a different one without modifying its dimension, shape, or orientation, a transition known as translation takes place.

Point Q', which has been translated by 6 units to the right and 2 units down, is the mirror counterpart of Q(-5,1).

Then,

Q' = (-5 + 6, 1 - 2)

Q' = (1, -1)

Thus, the coordinates of Q' after the translation is found to be Q' = (1, -1).

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The correct question is-

Point Q', is the image of Q(-5,1), under a translation by 6 units to the right and 2 units down.

What are the coordinates of Q'?

The percentage of  people who participated in the race finished in less than 56 minutes is 34%. This can also be written as the equivalent fraction 34/100

To find the percentage of people who finished the race in less than 56 minutes, we can use the following formula:

percentage = (part/whole) x 100%

where "part" is the number of people who finished in less than 56 minutes, and "whole" is the total number of people who participated in the race.

In this case, we know that 17 people finished in less than 56 minutes, and there were 50 people in total. So we can plug these values into the formula:

percentage = (17/50) x 100%

percentage = 34%

Therefore, 34% of the people who participated in the race finished in less than 56 minutes.

To write an equivalent fraction for this percentage, we can write:

34% = 34/100

This is an equivalent fraction because 34/100 can be simplified to 17/50

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The roots of the equation x^(2)-12x+61=0 in simplest a+bi form are 6 + 5i and 6 - 5i.

The roots of the equation x^(2)-12x+61=0 in simplest a+bi form can be found using the quadratic formula.

The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -12, and c = 61.

Plugging in the values into the quadratic formula, we get:

x = (-(-12) ± √((-12)^(2)-4(1)(61)))/(2(1))

Simplifying the equation, we get:

x = (12 ± √(144-244))/2

x = (12 ± √(-100))/2

Since the square root of a negative number is a complex number, we can write the equation as:

x = (12 ± 10i)/2

Simplifying further, we get:

x = 6 ± 5i

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Answer: B

Step-by-step explanation:

(7x^3-10x^2- 5)-(2x^3+7x^2-9)

= 5x^3 -3x^2-14

The quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

To find the quotient and remainder, use long division. First, divide the leading terms of both polynomials. 3x^4 divided by x^3 gives x.

Next, multiply the quotient by the divisor and subtract from the dividend. x(x^3-x^2+1) subtract from 3x^4-x^2 gives x+1.

Finally, divide the remainder by the divisor to get the remainder. x+1 divided by x^3-x^2+1 gives 2x^2-3. Therefore, the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

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The correct option is B an algorithm. If the wrong password is put in more than five times, Owen's computer will lock for an hour. To prevent this, he is building a programme. An illustration of a "algorithm" is this collection of instructions.

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms operate as a detailed sequence of instructions that carry out prescribed operations sequentially.

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a)0.1587 (or 15.87%)

b)0.6827 (or 68.27%)

c)0.0228 (or 2.28%)

1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).

2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).

3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).

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Even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.

No, 2 is not a zero of the polynomial p(x)=3x^(4)-14x^(3)-9x^(2)+64x-28. To determine p(k), we simply need to plug in the value of k into the polynomial and simplify.

So, p(k) = p(2) = 3(2)^(4) - 14(2)^(3) - 9(2)^(2) + 64(2) - 28

= 3(16) - 14(8) - 9(4) + 128 - 28

= 48 - 112 - 36 + 128 - 28

= 0

Therefore, p(k) = p(2) = 0.

So, even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.

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Using Algebraic expression we concluded, In practice, the angle of the pendulum may not be exactly equal to the calculated values due to factors such as air resistance, friction, and variations in the length of the pendulum.

What is Algebraic expression ?

A combination of variables and constants is an algebraic expression.

We can see that the pendulum's height drops with each swing if we make the assumption that each swing is measured from the same starting point.

Using a sequence is one technique to mathematically express this data. Assuming that n = 1, 2, 3, 4, let's define the sequence "a n" as the pendulum's height on the nth swing. Then, we could type:

a_1 = 80

a_2 = 76

a_3 = 72.2

a_4 = 68.59

Another way to represent this information is by using a formula that describes the height of the pendulum on each swing. One common formula for the height of a simple pendulum is:

[tex]h = L - L\times cos(\theta)[/tex]

where h is the height of the pendulum, L is the length of the pendulum, and θ is the angle that the pendulum swings from its resting position. Assuming that the length of the pendulum remains constant, we can use this formula to find the angle θ for each swing:

For the first swing, h = 80 cm, L = constant, so we can solve for θ:

[tex]80 = L - L\times cos(\theta)\\cos(\theta) = 1 - 80/L\\\theta = arccos(1 - 80/L)[/tex]

For the second swing, we have h = 76 cm, so we can use the same formula with h = 76 and solve for θ:

[tex]76 = L - L\times cos(\theta)\\cos(\theta) = 1 - 76/L\\\theta = arccos(1 - 76/L)[/tex]

Similarly, we can use the formula to find θ for the third and fourth swings:

For the third swing, h = 72.2 cm:

θ = arccos(1 - 72.2/L)

For the fourth swing, h = 68.59 cm:

θ = arccos(1 - 68.59/L)

Therefore, in practice, the angle of the pendulum may not be exactly equal to the calculated values due to factors such as air resistance, friction, and variations in the length of the pendulum.

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complete question -

The total decline in employment over the 5-year period is 384 employees.

In 2000, a business had 4000 employees. Each year for the next 5 years, the number of employees decreased by 2%. To find the number of employees at the end of the 5-year period, we can use the formula:

Number of employees = Initial number of employees * (1 - percentage decrease) ^ number of years

= 4000 * (1 - 0.02) ^ 5

= 4000 * 0.98 ^ 5

= 4000 * 0.9039

= 3615.6

Therefore, the number of employees at the end of the 5-year period is approximately 3616.

To find the total decline in employment over the 5-year period, we can subtract the final number of employees from the initial number of employees:

Total decline in employment = Initial number of employees - Final number of employees

= 4000 - 3616

= 384

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Answer:

There are 60 seconds in 1 minute, so in 5 1/2 minutes:

5 minutes x 60 seconds/minute = 300 seconds

1/2 minute x 60 seconds/minute = 30 seconds

Adding those together gives:

300 seconds + 30 seconds = 330 seconds

Therefore, there are 330 seconds in 5 1/2 minutes.

There are 330 seconds in 5 and 1/2 minutes. We find this by converting the minutes (both the whole and the half) into seconds and adding these amounts together.

To calculate the number of seconds in 5 and 1/2 minutes, we need to know the basic fact that 1 minute equals 60 seconds. With this, we can easily convert minutes to seconds by multiplying the number of minutes by 60.

First, let's convert the 5 whole minutes into seconds: 5 minutes x 60 seconds/minute = 300 seconds.

Next, let's convert the half minute: 1/2 minute x 60 seconds/minute = 30 seconds.

FInally, add these two amounts together: 300 seconds + 30 seconds = 330 seconds. Therefore, 5 and 1/2 minutes equals 330 seconds.

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The fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, and the maximum annual interest is given as  $2.595 million.

To solve this, we

Let x = amount invested in bonds and

y = amount invested in mutual funds.

We then can deduce the following constraints:

x + y ≤ 35 (total investment is at most $35 million)

x ≥ 5 (at least $5 million is invested in bonds)

y ≥ 20 (at least $20 million is invested in mutual funds)

100x + 200y ≤ 6000 (the total fees paid which cant exceed $6000)

Maximizing  the annual interest, which is given by:

0.06x + 0.09y

We will  use the method of Lagrange multipliers, to solve the optimization problems.

Let L(x, y, z) be the Lagrangian:

and we have that L(x, y, z) = 0.06x + 0.09y + z(x + y - 35) + μ(x - 5) + ν(y - 20) + ρ(100x + 200y - 6000)

We will have to take partial derivatives of L with respect to x, y, and z, and set them to be equals zero.

0.06 + z + μ + 100ρ = 0

0.09 + z + ν + 200ρ = 0

x + y - 35 = 0

Simplifying these equations, we have:

x = 7.5, y = 27.5, λ = -0.06, μ = 0, ν = 0, ρ = -0.02

0.06(7.5) + 0.09(27.5) = $2.595 million is the annual interest.

So then, It has been found that the fund manager should invest $7.5 million in bonds and $27.5 million in mutual funds to maximize annual interest, which is  $2.595 million.

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There are 2 quart jars can he fill.

There is 4 pint jar can he fill with any leftover sauce.

Fractions are numerical values that are a part of whole.

Julian is making barbecue sauce to the can. He uses 6 cups white vinegar, 1/2 cup honey, and 1/2 cup maple syrup.

We know that

1 quarts = 4 cups

Total number of cups is;

6 + (1/2) + (1/2) = 7

The total number of jars that he can fill is;

= total number of cups/4

=7/4

=1.75

There are 2 quart jars can he fill.

There are pint jars he can fill with any leftover sauce is;

1 quart = 2 pints

So, 2 quart = 2 × 2 = 4 pints.

There is 4 pints jar can he fill with any leftover sauce.

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The ratios 15 to 18 to 24 in their simplest forms is 5:6:8.

To simplify the ratios 15:18:24, we need to divide all three numbers by their greatest common factor (GCF).

Find the GCF of 15, 18, and 24:

The factors of 15 are 1, 3, 5, and 15.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The largest factor that all three numbers share is 3, so the GCF is 3.

Divide all three numbers by 3:

15 ÷ 3 = 5

18 ÷ 3 = 6

24 ÷ 3 = 8

Write the simplified ratio:

The simplified ratio is 5:6:8.

Therefore, the simplified ratio of 15:18:24 is 5:6:8.

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The next three terms in the sequence are 1/81, -1/243, and 1/729.

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:

a, ar, ar^2, ar^3, ...

where a is the first term, r is the common ratio

To identify the next three terms in the sequence, we need to first determine the pattern. Looking at the sequence, we can see that each term is obtained by multiplying the previous term by -1/3, which means that this is a geometric sequence with a common ratio of -1/3.

Using this common ratio, we can find the next three terms in the sequence as follows:

-1/3 * (-1/27) = 1/81

1/81 * (-1/3) = -1/243

-1/243 * (-1/3) = 1/729

Therefore, the next three terms in the sequence are 1/81, -1/243, and 1/729.

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Answer: 59.26°

Step-by-step explanation:

Use the equation 174(0.95)^21

The 174 represents the temperature difference

The 21 represents the amount of time (in minutes) that has passed

To get 0.95, because the temperature is decreasing, you subtract

1-0.05=0.95 (0.05 and not 5 because you move the decimal over two places when working with percents)

That's the standard equation that you use when solving questions like these, and when you solve this equation you should get 59.26° (you need a calculator to solve it all at once)

Answer:

33.7°

Step-by-step explanation:

the direction angle is calculated as

tanΘ = [tex]\frac{y}{x}[/tex] ( Θ is the direction angle ) , then

tanΘ = [tex]\frac{-4}{-6}[/tex] = [tex]\frac{2}{3}[/tex]

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{2}{3}[/tex] ) ≈ 33.7° ( to the nearest tenth )

Answer:

1)
Number of Seats in next three rows: 37, 41, 45

Number of seats in row 21 = 105

2)

Cost for 4, 5, 6 miles:
Miles            Cost($)
4                    14.50

5                    18.00

6                    21.50

Cost for 12 miles = $42.50

Step-by-step explanation:

1) The arithmetic sequence is
25, 29, 33 ....

Each term is 4 more than the previous term

So the next three terms starting with the 4th term area

33 + 4 = 37
37 + 4 = 41

41 + 4 = 45

In terms of the problem statement these are the number of seats in rows 4, 5, 6 respectively

The general equation for an arithmetic sequence nth term is

a(n) = a(1) + d(n - 1)

Here a(1) is the first term; here a(1) = 25

d = difference between successive terms called the common difference; here common difference = 4

n is of course the number of terms to be considered

using the values we have
a(n) = 25 + 4(n- 1)

= 25 + 4n - 4

= 21 + 4n

So the 21st term is a(21)

a(21) = 21 + 4 (21)

= 21 + 84

= 105

------------------------------------------

2. Another arithmetic sequence

The first term is the charge for the first mile = 4

The second term = 7.5 for 2 miles

The third term = 11.5 for 3 miles

So d = 11 - 7.5 = 7.5 - 4 = 3.5

The cost for 4 miles = 11 + 3.50 = $14.50

The cost for 5 miles = 14.50 + 3.50 = $18

The cost for 6 miles = 18 + 3.50 = $21.50

Using the equation for finding the nth term we get

a(n) = a(1) + d(n - 1)
a(n) = 4 + 3.5(n-1)

a(n) = 4 + 3.5n - 3.5

a(n) = 0.5 + 3.5n

We have the following table

Miles            Cost      ($)

1                     4.00

2                    7.50

3                    11.00

4                    14.50

5                    18.00

6                    21.50

For 12 miles which would correspond to the 12 term

a(12) = 0.5 + 3.5(12)

= 0.5 + 42

= $42.50

Answer:

13:00

Make a straight line from the vertex of the current Yuri line to 16:15

Step-by-step explanation:

Answer:

If sin = 1⁄2 and lies in the second quadrant, the remaining five trigonometric values are cos = √3/2, tan = 1/√3, cot = √3, sec = 2/√3, and csc = 2. These values can be derived from the basic trigonometric identities and the given value of sin. For example, the cosine of an angle in the second quadrant is the same as the sine of the same angle in the first quadrant, and vice versa. Therefore, since sin = 1⁄2 in the second quadrant, cos = √3/2 in the first quadrant. The other values can be derived in a similar manner

Step-by-step explanation:

Bob was on the top rung of his ladder (rung 30) and Roy was on the 15th rung of his ladder when they were at the same height.

Two or more expressions with an Equal sign is called as Equation.

Let's assume that Bob started at the top of his ladder and Roy started at the bottom of his ladder.

If both ladders have 30 rungs, then they have a total height of 30 - 1 = 29 rungs.

If Bob went down two rungs every second and Roy went up one rung every second, then they were changing their height at a rate of -2

Let's use "t" to represent the time they had been climbing. Then, we can write an equation to represent the heights of Bob and Roy at this moment:

Bob's height = 30 - 2t

Roy's height = t

30 - 2t = t

Solving for "t", we get:

t = 15

This means that Bob and Roy were at the same height after 15 seconds of climbing.

Bob's height = 30 - 2t = 30 - 2(15) = 0

Roy's height = t = 15

Therefore, Bob was on the top rung of his ladder (rung 30) and Roy was on the 15th rung of his ladder when they were at the same height.

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n-4m people still need to be inoculated​. As the village contains n people and a medical team insulate m people each day against yellow fever.

It is given in the question that there is n number of people in the village.

Number of people inculcated each day against yellow fever = m

Now for finding how many people have been inculcated against yellow fever we will multiply by 4 the number of people who are being inculcated against yellow fever with m

So, in four days the number of people that had been inculcated is 4m

For finding how many people are left to be inculcated against yellow fever we will subtract from the total number of people in the village the  number of people who have been inoculated against yellow fever

Therefore, People left after four days to be inculcated is = n-4m

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Another inequality that describes the solutions would be: x ∈ (4, ∞)

What is inequality ?

In mathematics, an inequality is a statement that compares two values, expressions, or quantities, and asserts that they are not equal. Inequalities are often expressed using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The inequality 3x > 12 can be solved by dividing both sides by 3:

3x/3 > 12/3

x > 4

This means that all values of x greater than 4 are solutions to the inequality 3x > 12.

This notation represents the interval of all real numbers greater than 4, including 4 itself. The symbol "(" means that 4 is not included in the interval, while "∞" indicates that the interval extends indefinitely to the right.

Therefore, Another inequality that describes the solutions would be: x ∈ (4, ∞)

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The height of the building, given the angle of elevation and the distance from the top of the building, is such that he height of the building is 95 meter.

We shall assume that the building, the distance from the foot and the angle, are in a right - angled triangle.

This means that the height of the building is the opposite side and the given distance is the adjacent side.

The relevant operation would be Tan.

The height of the building would be:

Tan ( 60 ° ) = Height / 55 m

Height = Tan ( 60 ° ) x 55

Height = 95 meters

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It is unlikely that the projected rebounds in 15 shots will actually happen.

Total shots fired equals 10.

To find that there were 15 shots total.

Consider S to be the likelihood that your team will rebound and miss a shot.

P(S) = Number of rebounds / Total Number of outcomes

P(S) = 7/15

P(S) = 0.46

Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.

Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.

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The complete question is-

During a basketball game, you record the number of rebounds from missed shots for each team.  How many rebounds should your team expect to have in 15 missed shots?

Picture for question is attached.

The probability of A and B, using conditional probability, is given as follows:

0.24 = 24%.

The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which the probabilities are listed and explained as follows:

To obtain the probability of A and B, the needed parameters are already given in the problem, and are as follows:

Hence the probability of A and B is calculated as follows:

P(A and B) = P(A) x P(B|A)

P(A and B) = 0.6 x 0.4

P(A and B) = 0.24.

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Answer:

1968 bottles of water

Step-by-step explanation:

24×82=1968

1968 bottles of water

The area of the complex figure is 178 m². Option A

The formula for calculating the area of a rectangle is expressed as;

Area = lw

Given that;

For the bigger rectangle

Area = 16(8)

Multiply

Area = 128m²

For the smaller rectangle

Area = 6(5)

Area = 30m²

For the triangle

Area = 1/ 2× base × height

Area = 1/2 × 8 × 5

Area = 20m²

Add the areas of the three figures

Total area = 128 + 20 + 30

Total area = 178 m²

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Answer: 50in^2

Remember the formula for finding the area of a rectangle is:

A = (base)(height)

In this problem you find the area like so:

A = (12[tex]\frac{1}{2}[/tex])(4)

= ([tex]\frac{25}{2}[/tex])([tex]\frac{4}{1}[/tex])

= ([tex]\frac{25}{1}[/tex])([tex]\frac{2}{1}[/tex])

= 50in^2