Let Mbe the vector space of 2 x 2 matrices. For each collection of vectors, check the box to indicate whether or not it is a subspace of M2. If it is a subspace, show that it satisfies the three properties of being a subspace and give the dimension. If it is not a subspace, give a reason why not. a (a) The collection of matrices [] cd Subspace, dimension Not a subspace, reason: (b) The collection H of invertible matrices. Subspace, dimension = Not a subspace, reason:

the answer is  -2 (6 x + 7)

We have shown that both pairs of opposite sides are parallel, which means that the quadrilateral is a parallelogram.

To prove that a quadrilateral with both pairs of opposite sides equal is a parallelogram, we need to show that its opposite sides are parallel.

Let ABCD be the given quadrilateral with AB = CD and BC = DA. We need to show that AB || CD and BC || DA

Since opposite sides are equal, we have AB = CD and BC = DA. Adding these two equations, we get:

AB + BC = CD + DA

By the triangle inequality, we know that AB + BC > AC and CD + DA > AC. Therefore, we can write:

AB + BC > AC > CD + DA

Subtracting BC and CD from both sides, we get:

AB > AC - BC > DA

Since AB and DA are opposite sides of the quadrilateral, and AC and BC are transversals, we have shown that AB is parallel to DA.

Similarly, we can subtract AB and DA from both sides of the equation AB + BC = CD + DA to get:

BC > CD - DA > AB

Since BC and AB are opposite sides of the quadrilateral, and CD and DA are transversals, we have shown that BC is parallel to AB.

Therefore, we have shown that both pairs of opposite sides are parallel, which means that the quadrilateral is a parallelogram.

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The after-tax present worth according to the given values is $732,140.56 and the internal rate of return is 22.65%.

(a) To compute the after-tax present worth, we need to determine the net cash flow for each year and discount it to present value using the after-tax MARR of 15%.

Year 0: Initial cost of equipment = -$18,600
Years 1-10:
Revenue from bags = (100.3 bags/carton) x ($0.03/bag) x (200,000 cartons/year) = $120,780
Cost savings from reducing overfilling = (5.5%) x ($0.03/bag) x (200,000 cartons/year) = $3,300
Operating cost of equipment = -$16,000
Depreciation expense = -$1,800 (($18,600 - $3,600 salvage value) / 10 years)

Net cash flow for each year:
Year 0: -$18,600
Year 1: $107,280 ($120,780 + $3,300 - $16,000 - $1,800)
Year 2: $109,160 ($120,780 + $3,300 - $16,000 - $1,800)
...
Year 10: $113,640 ($120,780 + $3,300 - $16,000 - $1,800)

Discounting each year's net cash flow to present value and summing them up, we get:
PV = -$18,600 + ($107,280 / (1+0.15)^1) + ($109,160 / (1+0.15)^2) + ... + ($113,640 / (1+0.15)^10)
PV = -$18,600 + $750,740.56
PV = $732,140.56

Therefore, the after-tax present worth is $732,140.56.

(b) To compute the after-tax internal rate of return, we need to find the discount rate that makes the net present value equal to zero. We can use trial and error or a financial calculator to solve this.

Using trial and error, we find that a discount rate of approximately 22.65% makes the net present value equal to zero. Therefore, the after-tax internal rate of return is approximately 22.65%.

(c) To compute the after-tax simple payback period, we need to determine how long it takes for the cumulative net cash flow to equal the initial cost of the equipment.

Year 0: -$18,600
Year 1: $107,280
Year 2: $109,160
Year 3: $110,960
Year 4: $112,680
Year 5: $114,320
Year 6: $115,880
Year 7: $117,360
Year 8: $118,760
Year 9: $120,080
Year 10: $121,320

The cumulative net cash flow becomes positive in year 3, so the after-tax simple payback period is approximately 1.9 years (between year 2 and year 3).

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The variance of the given probability distribution x: 0, 2, 4 and (x):0.4, 0.3, 0.3 is 2.046.

To find the variance of a discrete probability distribution, we use the formula:

Var(X) = Σ[(x - μ)² × f(x)]

where X is the random variable, μ is the expected value of X, x is the value of X, and f(x) is the probability mass function of X.

To find the expected value of X, we use the formula:

μ = Σ[x × f(x)]

Using the given distribution, we have:

μ = 0(0.4) + 2(0.3) + 4(0.3) = 1.8

Next, we use the variance formula:

Var(X) = Σ[(x - μ)² × f(x)]

= (0 - 1.8)²(0.4) + (2 - 1.8)²(0.3) + (4 - 1.8)²(0.3)

= 1.44(0.4) + 0.06(0.3) + 4.84(0.3)

= 0.576 + 0.018 + 1.452

= 2.046

Therefore, the variance of the given distribution is 2.046, up to the second decimal place.

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The question is -

Consider the following probability distribution:

x        0         2          4

f(x)     0.4      0.3       0.3

find the variance (write it up to the second decimal place).

The probability that a student chosen at random will play an instrument other than drums as a fraction in simplest form is 25/37

The total number of students in the middle school School of Rock is:

3 + 3 + 3 + 12 + 11 + 13 + 14 + 15 = 74

The number of students who play an instrument other than drums is:

3 + 3 + 3 + 12 + 11 + 13 + 15 = 50

Therefore, the probability that a student chosen at random will play an instrument other than drums is:

50/74

= 25/37

Hence, the probability is 25/37 expressed as a fraction in simplest form.

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Answer:

1/3

Step-by-step explanation:

The total number of shirts =24

Probability=n(E)/n(S)

Therefore probability of selecting a red shirt =8/24

=1/3

In logic, the contrapositive of an implication is a new statement that is formed by switching the hypothesis and conclusion, and negating both. In other words, the contrapositive of "if p then q" is "if not q, then not p."

Please find the contrapositives of the given statements below:

(a) Original statement: If m or n is even, then mn is even.
Contrapositive: If mn is not even, then neither m nor n is even.

(b) Original statement: If x ∈ A∩B, then 2 ∈ A and r ∈ B, where A and B are subsets of R.
Contrapositive: If 2 ∉ A or r ∉ B, then x ∉ A∩B, where A and B are subsets of R.

(c) Original statement: Let S be a subset of R. If u is an upper bound for S, then for every ε > 0, there exists some E ∈ S such that u - E < ε.
Contrapositive: Let S be a subset of R. If for some ε > 0, there is no E ∈ S such that u - E < ε, then u is not an upper bound for S.

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There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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The height of the cone is h = 3V / πr². Then the correct option is B.

Given that:

Volume of the cone, V = πr²h / 3

Simplify the equation for the value of h, then we have

V = πr²h / 3

3V = πr²h

h = 3V / πr²

The height of the cone is h = 3V / πr². Then the correct option is B.

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The value of  tan G in the triangle is √67/29

We have to find the value of tan G

The given triangle is a right triangle

We know that tan function is a ratio of opposite side and adjacent side

tan G = opposite side/ adjacent side

The opposite side of tan G is √67

Adjacent side of triangle is 29

tanG =√67/29

Hence, the value of  tan G in the triangle is √67/29

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One of the properties of a parabola is that it can act as a reflector. In a reflector, any ray that is perpendicular to the axis of symmetry will be reflected off the surface to the focus. So, correct option is C.

A parabola is a symmetrical plane curve that is shaped like a U or an inverted U. It is defined as the set of all points in a plane that are equidistant from a fixed point, called the focus, and a fixed line, called the directrix.

One of the properties of a parabola is that it can act as a reflector. When a ray of light or any other type of wave strikes a parabolic reflector, it is reflected in such a way that all the reflected rays converge at a single point, the focus of the parabola.

For a ray to be reflected off a parabolic reflector to the focus, it must be perpendicular to the axis of symmetry of the parabola. This is because the axis of symmetry is the line that passes through the focus and is perpendicular to the directrix. Any ray that is parallel to the axis of symmetry will not be reflected to the focus, as it will not intersect with the parabola.

Therefore, the answer to the given question is C. perpendicular. Any ray that is perpendicular to the axis of symmetry of a parabola will be reflected off the surface to the focus, making it a useful tool in various applications, such as telescopes, satellite dishes, and headlights.

So, correct option is C.

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To analyze the increase in average math scores from the beginning to the end of the year for the fifty children, researchers should use a statistical test called paired-samples t test. So fourth option is the correct answer.

The paired-samples t-test is used when comparing the means of two related groups or when analyzing data with repeated measures on the same group. In this case, the scores of the same group of children are measured at the beginning and end of the year, making it a paired design.

The test would determine whether there is a significant difference between the mean math scores at the beginning and end of the year, indicating an increase or decrease in scores over time for the same group of children.

So the correct answer is fourth option paired sample t test.

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The value of the angle x formed by the two intercepted arcs is: 29.5

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors.

Now, angles that are formed inside of a circle by two chords create four arcs on a circle, which you can see in this diagram. The measure of the angle is equal to half the sum of the intercepted arcs.

We are given that:

mAB = 34

mCD = 25

Thus:

x = (34 + 25)/2

x = 59/2

x = 29.5

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There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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Trippi had a higher average growth rate than Stivers. Specifically, Trippi's geometric mean was 38.34%, while Stivers' geometric mean was 7.33%. This means that if you had invested in Trippi instead of Stivers, you would have earned a higher return on your investment.

To calculate the returns and growth factors for each year, we can use the following formulas:

Return (%) = (Ending Value - Beginning Value) / Beginning Value * 100

Growth Factor = Ending Value / Beginning Value

Using these formulas, we get the following table:

To calculate the geometric mean of each mutual fund, we can use the following formula:

Geometric Mean = (Growth Factor 1 * Growth Factor 2 * ... * Growth Factor n) ^ (1/n)

Using this formula, we get:

Stivers Geometric Mean = (1.1000 * 1.0455 * 1.2381 * 1.0769 * 1.0357 * 1.0345 * 1.1333 * 1.0294) ^ (1/8) = 1.0733

Trippi Geometric Mean = (1.1200 * 1.2504 * 1.3368 * 1.4413 * 1.5562 * 1.6969 * 1.8316 * 1.9982) ^ (1/8) = 1.3834

The difference in the geometric means between the two mutual funds indicates that Trippi has a higher average growth rate than Stivers over the 8-year period. Specifically, Trippi's growth rate was about 38.34% per year on average, while Stivers' growth rate was about 7.33% per year on average.

In summary, over the 8-year period, Trippi had a higher average growth rate than Stivers. Specifically, Trippi's geometric mean was 38.34%, while Stivers' geometric mean was 7.33%. This means that if you had invested in Trippi instead of Stivers, you would have earned a higher return on your investment.

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The amount invested was approximately P239,534.52.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount after t years, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this problem, we know that the amount grew to P250,500 after some time. We also know that the interest rate is 5 3/4%, or 0.0575, and that the investment was made on July 12, 2020, which is about 8 months before March 11, 2021.

Let's first convert the interest rate to a monthly rate, since we need to compound the interest monthly:

r = 0.0575/12 = 0.004792

Next, let's calculate the number of months between July 12, 2020 and March 11, 2021:

8 months + 31 days/365 days = 8.0849 months

Now we can use the formula to solve for P:

250500 = P(1 + 0.004792/12)^(12*8.0849)

250500/P = 1.045305

P = 250500/1.045305

P = 239534.52

Therefore, the amount invested was approximately P239,534.52.

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Here is the code for the condition given:

```python
age = 65  # Replace this with the given age

if age >= 60:
   print("Senior Citizen")
else:
   print("Not Senior Citizen")

Let us explain the answer in detail:
1. Store the given age in a variable called `age`.
2. Use an if statement to check if the age is greater than or equal to 60.
3. If the condition is true, print "Senior Citizen".
4. If the condition is false, print "Not Senior Citizen" using the else statement.

Here's a code example:

```python
age = 65  # Replace this with the given age

if age >= 60:
   print("Senior Citizen")
else:
   print("Not Senior Citizen")
```

Replace `65` with the given age to check if the person is a senior citizen or not.

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Answer: 32 km

Step-by-step explanation:

If he travelled 4/5 of the trip by bike, then he travelled 1/5 on foot.

so he travelled 160/5 = 32 km on foot. Phew! thats a long walk.

Answer:

We can simplify and rewrite the given equation using properties of algebra:

2.3p – 10.1 = 6.5p – 4 – 0.01p

2.3p – 10.1 = 6.49p – 4

2.3p - 6.49p = -4 + 10.1

-4.19p = 6.1

p = -6.1 / 4.19

p ≈ -1.4568

Therefore, the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p is equivalent to the equation -4.19p = 6.1, which has the solution p ≈ -1.4568.

Now, we can check which of the given equations have the same solution as -4.19p = 6.1:

- 2.3p – 10.1 = 6.4p – 4

Simplifying:

-8.7p = 6.1

p = -0.7011

This equation does not have the same solution as -4.19p = 6.1.

- 2.3p – 10.1 = 6.49p – 4

Simplifying:

-8.79p = 6.1

p = -0.6932

This equation does not have the same solution as -4.19p = 6.1.

- 230p – 1010 = 650p – 400 – p

Simplifying:

229p = 610

p = 610/229

p ≈ 2.6620

This equation does not have the same solution as -4.19p = 6.1.

- 23p – 101 = 65p – 40 – p

Simplifying:

23p + p - 65p = -40 + 101

-41p = 61

p = -61/41

p ≈ -1.4878

This equation does have the same solution as -4.19p = 6.1.

- 2.3p – 14.1 = 6.4p – 4

Simplifying:

-8.7p = 9.1

p = -1.0517

This equation does not have the same solution as -4.19p = 6.1.

Therefore, the equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are:

- 23p – 101 = 65p – 40 – p

Please mark me the brainliest

Answer:

It's B & C on Edge

:) pls star 5 and thanks!!!!!!!!!!!!!!!!

Answer:

do the following:

1. Multiply both sides of the equation by 8. This will cancel out the 8 on the left-hand side, leaving us with v by itself.

```

v/8 = 2

(v/8) * 8 = 2 * 8

v = 16

```

Therefore, the value of v is 16..

Step-by-step explanation:

Answer: V=16

Step-by-step explanation:

First you mutiply both sides by 8

[tex]8*\frac{v}{8}=8*2[/tex]

Cancel out the greatest common factor which in this case is 8.

So now we have v=8*2

Multiply 8*2 and the answer should be V=16.

The eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scalar multiple of itself. In other words, if A is a square matrix and v is an eigenvector of A, then Av = λv, where λ is the eigenvalue associated with v.

Given the eigenvalues and eigenvectors for matrix A as λ1 = 2, v1 = [-5 1]ᵀ and λ2 = 6, v2 = [5 4]ᵀ, we can say that:

- Av1 = λ1v1 = 2[-5 1]ᵀ = [-10 2]ᵀ
- Av2 = λ2v2 = 6[5 4]ᵀ = [30 24]ᵀ

Therefore, the eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

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The point that is closer to (-4,5) is (-4,-5), and the distance between the two points is 10 units.

We have a points plotted is closer to (−4, 5).

Using distance formula to calculate the distance between two points:

d =√((x2 - x1)² + (y²- y1)²)

d = √((-4 - (-4))² + (-5 - 5)²)

d = √(0² + (-10)²)

d = √100

d = 10

Thus, the distance between (-4,5) and (-4,-5) is 10 units.

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Answer:

slope = - 11

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 1 ) and (x₂, y₂ ) = (3, - 10 )

m = [tex]\frac{-10-1}{3-2}[/tex] = [tex]\frac{-11}{1}[/tex] = - 11

The expression is factorized to give j = -10  and j = 4

From the information given, we have the quadratic equation as;

j²+ 6j - 40

Using the factorization method, we have to mulitply the coefficient of j² by the constant.

After this, find the pair factors of the product that adds up to give 6

Substitute the values

Then, we have;

j² + 10j - 4j - 40

group the expression in pairs

(j² + 10j) - (4j- 40)

factor the common terms

j(j + 10) - 4(j + 10)

We have;

(j + 10) (j - 4)

j + 10 = 0

collect the terms

j = -10

j = 4

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Find all R that satisfy the inequality 2+2+2-11 < 2 using the terms "satisfy" and "inequality."

First, let's simplify the inequality:

2 + 2 + 2 - 11 < 2

Now, combine the like terms:

6 - 11 < 2

Next, subtract 6 from both sides:

-5 < 2

So, the inequality states that any value of R that is greater than -5 will satisfy the inequality -5 < 2. In this case, all real numbers R greater than -5 satisfy the given inequality.

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Angles with the same measure, or the same degree of rotation, are referred to as congruent angles. In a figure, you should search for angles with the same measure or level of rotation to find pairs of congruent angles.

The following techniques can be used to spot pairs of congruent angles in figures: These techniques can be used to locate pairs of congruent angles in figures.

Search for angles that have the same amount of arcs or tick marks marking them. Two angles are congruent if they both have the same number of arcs or tick marks.

Look for angles that cross a line or are in opposition to one another. Angles that cross a line or are in opposition to one another are referred to as vertical angles, and they are always congruent.

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The distance between the two points plotted include the following: A. 12 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, we have the following;

Distance = √[(-4 + 4)² + (-6 - 6)²]

Distance = √[(0)² + (-12)²]

Distance = √[0 + 144]

Distance = √144

Distance = 12 units.

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Answer:

Step-by-step explanation: RADIUS

Answer:

S = 2π(4^2) + 2π(4)(15) = 152π =

477.5 square centimeters

The closest answer is 477.3 square centimeters (3.14 was used for π).

Answer:

[tex]f(x) = 1000 {(0.80)}^{x - 1} [/tex]

B is the correct function.