A denotes an m x n matrix. Determine whether the statement is true or false Justify your answer. The row space of A^T is the same as the column space of A
Choose the correct answer below
A. The statement is false because the rows of A^T are also the rows of (A^T)^T=A
B. The statement is true because the number of pivot columns of AT is the same as the nu
C. The statement is false because the number of free variables in the equation A^Tx= 0 is
D. The statement is true because the rows of A^T are the columns of (A^T)^T=A

Answer:

d

Step-by-step explanation:

To construct an angle bisector with a compass  D. Place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.

An angle bisector is a line segment that divides angle into two equal parts.

According to the given statements to construct an angle bisector using a compass span any width of radius in a compass pace in onto the vertex of the angle cut the two arc on the two lines then without changing the radius draw two arcs where the previous arcs have intersected the two lines.

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Explanation:

The given equation y = -3x+1/2 is in slope intercept form y = mx+b

We match the terms to find that m = -3 is the slope and b = 1/2 is the y intercept.

The y intercept is where the graph crosses the vertical y axis.

Answer:x=1/y+5

Step-by-step explanation:This equals x =

Answer:

5

Step-by-step explanation:

Answer:

The correct answer is 10.63

Step-by-step explanation

I just took the test

Answer:

y=-3x+2

Step-by-step explanation:

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:y=124

x=67

Step-by-step explanation:

y=180-56

y=124

x=67

Answer:

4

Step-by-step explanation:

\( \sqrt[5]{32^2} = (\sqrt[5]{32})^2 = 2^2 = 4 \)

To simplify the given polynomial expression, we can start by combining like terms.

First, let's simplify the first part of the expression: (3x^2 - x - 7) - (5x^2 - 4x - 2).

Combining like terms, we have: (3x^2 - 5x^2) + (-x + 4x) + (-7 - 2).

This simplifies to: -2x^2 + 3x - 9.

Next, let's simplify the second part of the expression: (x + 3)(x + 2).

Using the distributive property, we expand this expression: x(x + 2) + 3(x + 2).

Multiplying, we get: x^2 + 2x + 3x + 6.

Combining like terms, this simplifies to: x^2 + 5x + 6.

Now, we can combine the simplified parts of the expression:

(-2x^2 + 3x - 9) + (x^2 + 5x + 6).

Combining like terms, we get: -x^2 + 8x - 3.

Therefore, the simplified polynomial expression is: -x^2 + 8x - 3.

The degree of the polynomial is determined by the highest power of x in the expression. In this case, the highest power is 2 (x^2), so the degree of the polynomial is 2.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer: her increase is 1.245 dollars an hour

Step-by-step explanation:

If A and B are independent, then the correct statements are P(A and B) = 0.12 and P(A or B) = 0.58.

Let's evaluate each statement:

P(B/A) = 0.4:

This statement is incorrect. If events A and B are independent, the occurrence of event A does not affect the probability of event B.

Therefore, P(B/A) would still be equal to the probability of B, which is 0.4 in this case.

P(A and B) = 0.12:

This statement is correct. The probability of the intersection of independent events A and B is calculated by multiplying their individual probabilities. In this case, P(A and B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.

P(A/B) = 0.3:

This statement is incorrect. If events A and B are independent, the occurrence of event B does not affect the probability of event A. Therefore, P(A/B) would still be equal to the probability of A, which is 0.3 in this case.

P(A or B) = 0.58:

This statement is incorrect. To calculate the probability of the union of two events, we need to consider whether the events are mutually exclusive or not.

If events A and B are independent, but not mutually exclusive, we can calculate P(A or B) as P(A) + P(B) - P(A and B). In this case, P(A or B) = 0.3 + 0.4 - 0.12 = 0.58.

Therefore, the correct statements are:

The statements regarding P(B/A) = 0.4 and P(A/B) = 0.3 are incorrect in the context of independent events A and B.

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Answer:

11.4

Step-by-step explanation:

Answer:

11.4

Step-by-step explanation:

Answer:

a)25%

b)5%

Step-by-step explanation:

hope it will help goodbye

The sum of degrees is not equal to twice the number of edges, there is no graph that satisfies the given conditions with 7 vertices and degrees 1, 1, 2, 3, 3, 3, and 6.

There exists a graph with 7 vertices and degrees 1, 1, 2, 3, 3, 3, and 6, we can use the Handshaking Lemma.

The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges in the graph. In other words:

Sum of degrees = 2 × Number of edges

Let's calculate the sum of degrees using the given degrees:

Sum of degrees = 1 + 1 + 2 + 3 + 3 + 3 + 6 = 19

Now, let's calculate the maximum number of edges possible in a graph with 7 vertices

Max number of edges = (n × (n - 1)) / 2

where n is the number of vertices.

For n = 7, the maximum number of edges is:

Max number of edges = (7 × (7-1)) / 2

Max number of edges = 7 × 6/2

Max number of edges = 21

According to the Handshaking Lemma, the sum of degrees is equal to twice the number of edges.

Sum of degrees = 2 × Number of edges

19 = 2 × 21

19 ≠ 42

Since the sum of degrees is not equal to twice the number of edges, there is no graph that satisfies the given conditions with 7 vertices and degrees 1, 1, 2, 3, 3, 3, and 6.

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Prediction for some count is usually expressible as expectation of some random variable. The reasonable prediction for the number of times a white or red marble will be drawn is 54

A  random variable is usually taking some numerical information of each elementary event of the sample space . (map from sample space to real numbers). Its expected value is the best prediction value in most of the cases.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

\(X \sim B(n,p)\)

The probability that out of n trials, there'd be x successes is given by

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

For the given case, as the ball being drawn is being replaced too, so we can take all 180 experiments to be independent from each other.

If we call

Success = Event of drawing white or  red marble

Failure = Event of drawing any other marble instead of white or red

Then, each marble drawing event is having two outcomes: success or failure. This makes each drawing a Bernoulli  experiment.

Modelling this situation with binomial distribution would be good.

Let X = number of successes in those 180 experiments.

Thus, we get

\(X \sim B(n = 180, p= 0.3)\)

The expectation of random variable X is the best prediction of count of times we will get in those 180 trials.

The expectation of a  random variable is: \(E(X) = np\)

Thus, we get:

\(E(X) = 180 \times 0.3 = 54\)

Thus, the reasonable prediction for the number of times a white or red marble will be drawn is 54

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The value of k is 2, so correct option is B.

Integration is a fundamental concept in calculus that involves finding the area under a curve or the accumulation of a quantity over a continuous range. It is the inverse operation of differentiation, and together, they form the basis of calculus.

The process of integration involves finding an antiderivative (or indefinite integral) of a function f(x), which is another function F(x) whose derivative is equal to f(x). The antiderivative is denoted by ∫f(x)dx and is read as "the integral of f(x) with respect to x". The symbol ∫ is called the integral sign, and dx represents the variable of integration.

We have:

(6kx-2k) dx = k^3

Integrating the given expression with limits k and 0, we get:

[3kx² - 2kx]k⁰

= 3k(0)² - 2k(0) - [3k(k)² - 2k(k)]

= 0 + 0 - (3k³ - 2k²)

= -3k³ + 2k²

So, we have:

-3k³ + 2k² = k³

4k³ = 2k²

2k = 4

k = 2

Therefore, the correct option is B 2.

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If you can show that the following two items are true

then you have shown that triangle A'B'C' is a translated or shifted copy of triangle ABC. In other words, they are the same triangle.

Answer:

1

Step-by-step explanation:

An equilateral triangle is a triangle with all three sides of equal length, so there's only one option, a triangle with all three sides 7 centimeters.

The square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500 square mils.

To find the square mil area for a 2 inch wide by 1/4 inch thick copper busbar, we need to multiply the width and thickness of the busbar in mils.

1 inch = 1000 mils

So, the width of the busbar in mils = 2 inches x 1000 mils/inch = 2000 mils

And, the thickness of the busbar in mils = 1/4 inch x 1000 mils/inch = 250 mils

Therefore, the square mil area of the copper busbar = width x thickness = 2000 mils x 250 mils = 500,000 square mils.

Hence, the square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500,000 square mils.

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Answer:

middle

Step-by-step explanation:

Irs a little hard to see.  But Dilation means the size of the object changed ( increase or decrease) but the shape stays exactly same

The graph that shows a dilation among the given graphs is; Graph B.

Dilation in graphs simply means each side is multiplied by the same scale factor. What this means is that the ratio of each dilated side to their respective old sides before dilation must be the same scale factor.

Here, we have,

We can see that the pre-dilated image has 2 units along the y - axis and 3 units across the x-axis.

After dilation, it now has 4 units along the y - axis and 6 units across the x-axis.

This means the scale factor in both axis are; 4/2 = 2 and 6/3 = 2.

They are both the same scale factors and as such this graph shows a dilation.

Hence, The graph that shows a dilation among the given graphs is; Graph B.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer: 30%

15/50=.3

30%

I hope this is good enough:

Answer:

14

Step-by-step explanation:

The diameter is always the same as 2*the radius, so if the radius is 7, the diameter is 14.  Most of the information presented is unrelated.

Answer:

31 does not belong because it isn't dividable by 3 xx

Step-by-step explanation:

vat of a cap=13/100*452

=58.76

price after vat=58.76+452=510.76

price after vat of 5 cap = 510.76*5=2553.8

Answer:

D, 6500 increased by 1.4% is 6591 plus another 1.4% which is 6683 and for the last year you add another 1.4% to get the final answer which is D 6,776.84

Answer:

P- 6500

R-1.4%

T- 3yrs

I-?

I first find simple interest,

I=P×R×T÷100

=273

then you add your answer to the price(6500)

273+6500=6773

Answer:

542

Step-by-step explanation:

divide it I hope it helps

Answer:

241.20 dollars

Step-by-step explanation:

Use the equation I=prt, where I is the interest and p is the percentage of simple interest, which is 6% or 0.06. T is the rate of time in years. R is the amount Felix deposited. Our equation would be:

I=(0.06)(1340)(3)

I=(0.18)(1340)

I=$241.20