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Complete the algebraic proof by identifying the reason for each statement.

The matrix equations are solved as

a) The value of matrix X is   [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

b) The value of matrix X is  [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the value of the matrix be X

Now , the equation is

[tex]2X = \begin{pmatrix}-4&0&8\end{pmatrix}[/tex]

Now , on simplifying the equation , we get

Divide by 2 on both sides of the equation , we get

[tex]X = \begin{pmatrix}-4&0&8\end{pmatrix} / 2[/tex]

Now , the value of matrix X is

[tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

Therefore , the value of matrix X is   [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

b)

Let the value of the matrix be X

Now , the equation is

[tex]3X\:-\:\begin{pmatrix}1&7\end{pmatrix}=\begin{pmatrix}-16&-4\end{pmatrix}[/tex]

On simplifying the equation , we get

Adding  [tex]\begin{pmatrix}1&7\end{pmatrix}[/tex]  on both sides of the equation , we get

[tex]3X=\begin{pmatrix}-16&-4\end{pmatrix}+\begin{pmatrix}1&7\end{pmatrix}[/tex]

Now , the value for 3X can be calculated as adding the 2 matrices

[tex]3X=\begin{pmatrix}-15&3\end{pmatrix}[/tex]

Divide by 3 on both sides of the equation , we get

[tex]X=\frac{1}{3}\begin{pmatrix}-15&3\end{pmatrix}[/tex]

So , [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

Therefore , the value of matrix X is  [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

Hence , the matrix equations are solved as

a) The value of matrix X is   [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]

b) The value of matrix X is  [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]

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Answer:

(24x-18)-9x

hope this helps, tell me if you need to simplify it further

Answer:

-4 = -6(r+3)

r+3 = 2/3

r = -1/2/3

Answer:

[tex]\sf P(B|A)=0.60[/tex]

Step-by-step explanation:

Given:

If events A and B are independent then:

[tex]\boxed{\begin{aligned} \sf P(A \cap B)&=\sf P(A)P(B)\\\sf P(A|B)&=\sf P(A)\\\sf P(B|A)&=\sf P(B)\end{aligned}}[/tex]

Therefore:

[tex]\implies \sf P(B|A)=P(B)=0.60[/tex]

Answer:

S , P , T

Step-by-step explanation:

collinear points are points that lie on the same line.

S , P , T lie on the same line and are therefore collinear

Answer:

SPT

Step-by-step explanation:

You also have XPY but that isn't a choice in your list. SPT goes in a straight line making it collinear

Ashley's hair grew at a rate of approximately 0.545 inches per month.

What is the rate of change?

Rate of change problems can generally be approached using the formula R = D/T, or rate of change equals the distance traveled divided by the time it takes to do so.

To find the rate at which Ashley's hair grew per month, we need to divide the total amount of hair growth by the number of months.

First, let's convert the units to a common denominator. 1 and 1/2 inches is the same as 3/2 inches, and 2 and 3/4 months is the same as 11/4 months.

Now we can divide the total amount of hair growth (3/2 inches) by the number of months (11/4 months) to get the rate at which Ashley's hair grew per month:

(3/2 inches) / (11/4 months) = (3/2) * (4/11) inches/month

= 6/11 inches/month

= approximately 0.545 inches/month

Therefore, Ashley's hair grew at a rate of approximately 0.545 inches per month.

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Answer:

Step-by-step explanation:

Can You Please Send Me A Clearer Picture I Can Help

Answer:

The shoes are on sale for $28.79

Step-by-step explanation:

First, you find the 20% of 35.99 which is 7.198.

Then, i rounded that number to 7.20.

Then do $35.99 - 7.20.

Your final answer is $28.79!

Hope this helps and good luck!

The answer for the equation is  x = 1 , y = 3.

Solve the following system: using elimination:

x + 5 y = 17 | (equation 1)

6 x - 5 y = -3 | (equation 2)

Swap equation 1 with equation 2:

6 x - 5 y = -3  (equation 1)

x + 5 y = 17  (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

6 x - 5 y = -3 (equation 1)

0 x+(20 y)/3 = 20 (equation 2)

Multiply equation 2 by 3/20:

{6 x - 5 y = -9 | (equation 1)

{0 x+y = 3 | (equation 2)

Add 5 × (equation 2) to equation 1:

6 x+0 y = 6 (equation 1)

0 x+y = 3 | (equation 2)

Divide equation 1 by 6:

x+0 y = 1 | (equation 1)

0 x+y = 3 | (equation 2)

Collect results:

Answer: x = 1 , y = 3

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Answer:

Step-by-step explanation:

To find which one is faster, it would be distance/speed.

40m/3 = 13.33 repeating

50m/4 = 12.5

You would be traveling faster at 40 miles in 3 hours since you are going at 13.33 miles per hour

Answer:

The largest possible product of two positive integers whose sum is 9 is achieved when the two integers are as far apart as possible, which occurs when one integer is the largest possible integer and the other is the smallest possible integer. The largest possible integer is the one that is closest to but less than 9, which is 8, and the smallest possible integer is 1. The product of 8 and 1 is 8, so the largest possible product of two positive integers whose sum is 9 is 8.

Lets Recall the formula of Probability, where we know that;

P = Favourable outcomes / possible outcome

Given that , after rolling a die once we get the chances of probability

So , the total possible outcomes are 6 because are only 6 highest outcome possible

The factors of 4 are the numbers 1 , 2 and 4 which means its 3 outcomes

And the multiple of 3 are the numbers 3 and 6 which means it has 2 outcome

So, the chances of the outcome on the dice are = 1,2,3,4,6

Thus,

Probability = (1,2,4,3,6) / 6

There are 5 favourable outcomes on the numerator , 

Thus,

P=5/6

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To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.

Given,

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except _____.

Now, According to the question:

Let's know:

The Degrees of Freedom:

Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.

Hence, To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.

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Answer: y=1/5x + b

Step-by-step explanation:

The slope intercept for the equation is y=mx +b

Your equation is already in the slope-intercept form!

The correct option for the given linear equation condition is D. i.e. Liza will pass Ralph after 5 hours, and they each will have travelled 325 miles.

What is a linear equation?

When the parameter in the equation has a degree of 1, the system is said to be linear. One, two, or even more variables could be present.

The collection of two or more linear equations involving the same variables is known as a system of linear equations.

From the question,

The situation is given as:

y = 60x + 25

y = 65x

The time after Liza leaves, she passes Ralph will be

or, 65x = 60x + 25

or, 5x = 25

or, x = 5 hours

Then the distance covered by both of them, then after 5 hours will be

y = 65 (5)

y = 325 miles

Hence, the correct option is D.

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The 200th term in the sequence is 2,396.

To find the 200th term in the sequence we have the formula:

an=a1+(n-1)d    --------(1)

Given that values of a1 and d are 8,12

"a1" is called the first value of the sequence.

"d" is called the difference between two numbers.

Assume that n is 200 because we have to find the 200th term.

Now, we will substitute all the values in the above equation(1)

an=a1+(n-1)d

a200=8+(200-1)12

a200=8+(199)12

a200=8+2,388

a200=2,398.

So, the 200th term in the sequence is:2,398

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Answer: It will be 4.433333333 as a decimal and 4 13/30 as a mixed number in simplest form

The probability that at least one die is a 5, given that the sum of the numbers on the dice is at least 8 = 2/5

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The outcomes when the sum dice is 8 are

S = { (2,6), (3,5), (4,4), (5,3) , (6,2)}

Total outcomes = 5

Number of outcomes when there is at least one die is a 5,

given that the sum of the numbers on the dice is at least 8 = 2

Probability = (Number of possible outcomes)/(Total number of outcomes)

So, the probability that at least one die is a 5, given that the sum of the numbers on the dice is at least 8 = 2/5

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Answer: Fries = $1.50 Hamburger = $2

Step-by-step explanation:

   so since the first person payed 11 for 4 burgers and 2 fries and the second person got 2 more fries than the first person and spent 14 and there is a 3 dollar difference which 3 divided by 2 is 1.5 which means that the fires a 1 dollar and 50 cents. so 3 dollars subtracted from 11 equals 8 and 8 divided by 4 is 2 dollars leaving you with hamburgers being 2 dollars and fries being 1 dollar and 50 cents

Answer:

(2,0)

Step-by-step explanation:

5x + 9y = 10

4x -3y = 8  If I multiple this second equation all the way through by 3, then the y's would cancel out when I add the equations together.

12x -9y = 24  multiplied the second equation through by 3

5x + 9y = 10  Add the 2 equations together

17x         = 34  Divide both sides by 14

x = 2

Plug 2 in for x for either of the two original equations and solve for y

5x + 9y = 10

5(2) + 9y = 10

10 + 9y = 10  Subtract 10 from both sides

9y = 0  Divide both sides by 0

y = 0

(2,0)

Answer:

150 miles

Step-by-step explanation:

60*2.5=150

Answer:

f(x) = x^3 - 7x + 1

Step-by-step explanation:

ƒ”(x)=6x ==> ƒ”(x)=6 * (x^1)

f'(x)=6/(1+1) * x^(1+1) + C  ==> C is a constant that doesn't affect the derivative

f'(x)=6/2 * x^2 + C ==> simplify the first derivative

f'(x)=3 * x^2 + C ==> f'(x)=3(x^2) + C

f'(-3)=3((-3)^2) + C  ==> plug in -3 into the derivative equation

f'(-3)=3(9) + C ==> simplify

20=3(9) + C  ==> plug in 20 for f'(-3)

20=27+C

20-27=27-27+C ==> solve for C

C=-7

f'(x)=3(x^2) + (-7)  ==> plug in -7 for C

f'(x)=3(x^2) - 7  ==> simplify

f(x) = 3/(2+1) * x^(2+1) - 7x + C

f(x) = 3/3 * x^3 - 7x + C

f(x) = x^3 - 7x + C

f(-3) = (-3)^3 - 7(-3) + C ==> plug in -3 into f(x)

f(-3) = -27 - (-21) + C

f(-3) = -27 + 21 + C ==> simplify

f(-3) = -6 + C

-5 = -6 + C  ==> plug in -5 for f(-3)

-5 + 6 = -6 + 6 + C ==> solve for C

C = 1 ==> simplify

f(x) = x^3 - 7x + 1

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Answer:

D

Step-by-step explanation:

Use a calculator to approximate [tex]\ln 28[/tex] to the nearest thousandth.

Answer: 22

Step-by-step explanation:

f(x) = -5x + 2

Substitute the x for -4

f(-4) = -5(-4) + 2

f(-4) = 20+2

f(-4) = 22

Answer:

-6x²-x-6

Step-by-step explanation:

-7x²-1+x²-x-5

-6x²-1-x-5

-6x²-x-6

Applying the Pythagorean theorem, the missing side of each of the right triangle are:

i. c = 15.8 m

ii. s = 24.1 cm

iii. a = 12.8 feet

iv. t = 4.6 inches

Pythagorean theorem is one that can be used to determine the third unknown side of a right angled triangle. It is given by:

/Hyp/^2 = /Adj/^2 + /Opp/^2

The missing side of each of the right triangle can be determined as:

1. Let the value of unknown hypotenuse side by represented by c, so that:

/Hyp/^2 = /Adj/^2 + /Opp/^2

c^2  = /13/^2 + /9/^2

             = 169 + 81

             = 250

c = [tex]\sqrt{250}[/tex]

  = 15.8

c = 15.8 m

2. Let the value of unknown hypotenuse side be represented by s, so that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

 s^2 = /16/^2 + /18/^2

        = 256 + 324

        = 580

s = [tex]\sqrt{580}[/tex]

  = 24.1

s = 24.1 cm

3. Let the value of unknown adjacent side be represented by a,

/Hyp/^2 = /Adj/^2 + /Opp/^2

19^2 = a^2 + /14/^2

361 = a^2 + 196

a^2 = 361 - 196

      = 165

a = [tex]\sqrt{165}[/tex]

  = 12.8

a = 12.8 ft

4. Let the unknown adjacent side be represented by a,

/Hyp/^2 = /Adj/^2 + /Opp/^2

/11/^2 = t^2 + /10/^2

121 = t^2 + 100

t^2 = 121 - 100  

      = 21

t = [tex]\sqrt{21}[/tex]

  = 4.6

t = 4.6 in

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39 is 0.3​% of 13,000.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the number be x

So, 0.3% of x= 39

0.3/ 100 x= 39

0.3 x = 3900

x= 3900/ 0.3

x= 13000

Hence, 39 is 0.3​% of 13,000.

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The 12th term of the geometric sequence is a₁₂ = -244140625.

Define Geometric Progression

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is,

aₙ = a₁ · rⁿ⁻¹.

The geometric sequence,

5, -25, 125 ....

from here,we know

a₁ = 5

Calculate the ratios of all the adjacent terms ,

r = aₙ₊₁ / aₙ

r = -25/5 = -5

r = 125/-25 = -5

We know, the formula for geometric sequence is

aₙ = a₁ · rⁿ⁻¹

Where, a₁ = initial term

r = common ratio

Now, we need to find 12th term so for that n = 12

Now, plug in the values

aₙ = a₁ · rⁿ⁻¹

a₁₂ = 5 * (-5) ¹²⁻¹

     = 5 * -5¹¹

After calculation we get,

a₁₂ = -244140625

Hence, the 12th term of the geometric sequence is a₁₂ = -244140625.

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