A holiday store is having a sale on bows and rolls of wrapping paper. One sign in the store states, “Buy 1 bow and 1 roll of wrapping paper for only $6.00.” A second sign in the store states, “5 bows and 1 roll of wrapping paper will only cost $10.00.

The solution to the original system is:x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1

The given matrix is in row echelon form, meaning that the leading entry of each non-zero row is to the right of the leading entry of the previous row. In this form, the solution to the linear system can be found by back substitution.

Starting from the bottom row, we have the equation:

-1 * x4 + 4 * x5 = -1

Solving for x4, we have:

x4 = -4 * x5 + 1

Moving up to the next row, we have:

0 * x1 + 0 * x2 + 3 * x5 = 3

Solving for x5, we have:

x5 = 1

So, x4 = -4 * 1 + 1 = -3.

Next, the third row gives us:

0 * x1 + 0 * x2 - 3 * x3 + 4 * x4 = 4

Substituting the value of x4, we have:

0 * x1 + 0 * x2 - 3 * x3 + 4 * (-3) = 4

Solving for x3, we have:

x3 = -1

Since there are no more non-zero rows in the matrix, we have found a complete solution for the linear system.

The solution set of the original system is the set of all possible values of (x1, x2, x3, x4, x5) that satisfy the system of equations represented by the matrix. Since the given matrix is in row echelon form, this solution set is unique and consists of a single point in the 5-dimensional space.

The solution to the original system is:

x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1

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To find the probability that the mean salary of a person selected at random from Acme Corporation is less than 61,000, we can use the Z-score formula.

First, we need to calculate the Z-score, which measures the number of standard deviations a value is away from the mean. The formula for the Z-score is:

Z = (X - μ) / (σ / √n)

Where:
- X is the value we are interested in (in this case, $61,000)
- μ is the population mean annual salary for Acme Corporation ($63,500)
- σ is the population standard deviation (unknown in this case)
- n is the sample size (unknown in this case)

Since we don't have the population standard deviation or sample size, we cannot calculate the exact Z-score. Therefore, we cannot find the exact probability.

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Based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

The probability of a person selected at random having a salary less than $61,000 can be determined using the z-score and the standard normal distribution.

To calculate the z-score, we need to know the population standard deviation. Since it is not provided, we cannot calculate the exact probability. However, we can use the assumption that the population standard deviation is the same as the sample standard deviation.

Let's assume the sample standard deviation is $5,000.

First, we calculate the z-score:
    \(z = (x - \mu) / (\sigma / \sqrt n)\)
=> z = (61000 - 63500) / (5000 / √1)
=> z = -2500 / 5000
=> z = -0.5

Next, we find the corresponding area under the standard normal curve using a z-table or a calculator. The area to the left of -0.5 is approximately 0.3085.

Therefore, the probability that a person selected at random will have a salary less than $61,000 is approximately 0.3085 or 30.85%.

In conclusion, based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

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Answer:

The 3rd answer

Step-by-step explanation:the

180-30\2

....

=75

30+2*75=

...

180

Answer:

30 + 2x = 180

Step-by-step explanation:

This is becuase we know this triangle is an isosceles triangle. (The two markings on the sides prove that.) An isosceles triangle is when two sides (so naturally also two angles) are the same. This means the other angle is x. We know that if we add all of the angles, we'll get 180. So, 30 + x + x = 180 or "30 + 2x = 180".

Also, x = 75.

Here:

30 + 2x = 180

30 - 30 + 2x = 180 - 30

2x = 150

2x / 2 = 150 / 2

x = 75

HOPE THIS HELPED!! HAVE AN AWESOME DAY!

Step-by-step explanation:

x2+1/x2=27

x2+1=27x2

1=26x2

x2 = 1/26

x = √(1/26)

x3+1/x3 = (√(1/26))^3 + 1 / (√(1/26))^3

x3+1/x3 = 134

Please find attached photograph for your answer

The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.

The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.

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Answer:

Distribute

Step-by-step explanation:

The first step in solving this equation is distribute (get rid of parentheses):

2x + 2 = 8x -5

Hope this helps ^^

Answer:

the third one

x=-7,0,7    

y=2,-2,-6

Step-by-step explanation:

Answer:

x = - 3 , x = 5

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

given

\(log_{2}\) (x² - 2x + 1) = 4

x² - 2x + 1 = \(2^{4}\) = 16 ( subtract 16 from both sides )

x² - 2x - 15 = 0 ← in standard form

(x - 5)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 5 = 0 ⇒ x = 5

Answer:

NO WRONG (6T)(5S)+7 IS WRONG YOU ARE SOPOSED TO ADD THAT 6+5=11      11+7=18    18 DIVIDED BY 7=2.5

Step-by-step explanation:

SORRY FO CAPLOCK THAT HOW I TYPE SIR

Find the longest side of a parallelogram.

Perimeter of parallelogram = 2 ( a + b )

We know that,

Perimeter of parallelogram = 2 ( a + b )

★ Substituting the values in the above formula,we get:

⇒ 66 = 2 ( 3x + 1 + 2x - 3 )

⇒ 66 = 2 ( 5x - 2 )

⇒ 66/2 = 5x - 2

⇒ 33 = 5x - 2

⇒ 5x - 2 = 33

⇒ 5x = 33 + 2

⇒ 5x = 35

⇒ x = 35/5

⇒ x = 7 ft

Now,

One side,a = 3x + 1

★ Putting the value of x

⇒ 3 × 7 + 1

⇒ 21 + 1

⇒ 22 ft

Other side,b = 2x - 3

★ Putting the value of x

⇒ 2 × 7 - 3

⇒ 14 - 3

⇒ 11 ft

Hence,the longest Side of given parallelogram is 22 ft ( 3x + 1 ) .

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Answer:

31

Step-by-step explanation:

C= 2πr  We will used 3.14 for pi and the radius is 5

C = 2(3.14)(5)

C =31.4 Then round to the nearest whole number which would be 31.  31.4 is closer to 31 than 32

Answer:

1.5 x cells

Step-by-step explanation:

3 cells every 2 second

1.5 cells per second

therefore

    after x seconds there ll be 1.5 *x number of cells

 =1.5x cells

The correct equation is \(P = 2.5w\) .

The average cost is the ratio of the total of cost of all the products to the total number of products.

The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

An equation says that two things are equal. It will have an equals sign "=" .

A 12-ounce box of cereal costs $4.80.

The price be 'P' and weight be 'w'.

$4.80 is the price of box with weight 12-ounce

i.e. 4.80P = 12w

Divide both side by 4.80

\(\frac{4.80P}{4.80} = \frac{12w}{4.80}\)

\(P = 2.5w\)

Therefore, the correct equation is \(P = 2.5w\) .

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The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Answer:

Your answer is -4y - 9

Step-by-step explanation:

Simplify the expression.

~Brainiliest please~

From the information provided the measure of the angles are given as,

m ∠EFH = 71; and m ∠EFG = 142°.

Angles are measured in degrees, which is why they are called "degrees". A complete circle equals 360 degrees, so it is divided into 360 parts. Each part of the revolution is a degree. Any angle, whether acute, obtuse, reflected or right, can be measured with a protractor. Although based on right angles, we are able to distinguish acute, obtuse or reflex angles. But if we have two acute angles to measure, we cannot determine the greater angle between the two. Therefore, we need to use a protractor to measure angles accurately.

According to the Question:

It is to be noted that

m ∠GFH = m ∠EFH

⇒ m ∠EFH = 71°

⇒ m ∠EFG = m ∠GFH + m EFH

Hence,

m ∠EFG = 71 + 71

              = 142°

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Answer:

20

Step-by-step explanation:

4^2 = 16

-2^2 =-4

16 -(-4) =20

The value of x that will make the expression equal is 4. Option B is correct.

Given the indices expression;

\(3^{2x+1} = 3^{x+5}\)

Since the base values are the same, they will cancel out to have:

\(2x + 1 = x + 5\)

Collect the like terms:

\(2x - x = 5 - 1\\x = 4\\\)

Hence the value of x that will make the expression equal is 4

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Answer:

the correct option is C which is 4

Step-by-step explanation:

jesus loves you!!!!!!!!!

The value of cos(8) is 0.992.

Given the equation, tan e = 35/2 and 8 is an angle in quadrant I. To find the value of cos(8), we can use the Pythagorean identity of sin²θ + cos²θ = 1.

1. Draw a right triangle in quadrant I with an angle of 8 and a hypotenuse of 150 (which is obtained by dividing the opposite and adjacent sides of the tan(e) equation by sin(e) to obtain the hypotenuse).

2. To find the adjacent side (which is equal to cos(8)), use the Pythagorean identity:

cos²8 + sin²8 = 1cos²8 + (35/150)² = 1cos²8 + 0.025 = 11.0091 - 0.025 = cos²8cos8 = ±√(0.9841)cos8 = ±0.992 (rounded to 3 decimal places)

But since angle 8 is in quadrant I, where cos is positive, the value of cos(8) is:

cos(8) = 0.992 (rounded to 3 decimal places)

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Step-by-step explanation:

\(9x + 2 + 133 = 180 \\ 9x + 135 = 180 \\ 9x = 180 - 135 \\ 9x = 45 \\ \frac{9x}{9} = \frac{45}{9} \\ x = 5\)

Ther reason is that Angles in a straight line are supplementary.

Step-by-step explanation:

The goal is to isolate that given variable. The process is the same process that you use to solve linear equations; the only difference is that you will be working with a lot more letters, you also prob will not be able to simplfy as much as linear equations

Answer:

it is more than one step so it takes longer to solve

Step-by-step explanation:

the process of isolating a variable in these literal equations is similar to solving a one-step equation because after isolating a variable you solve the rest of the equation,it is different from solving a one-step equation because it is more than one step so it takes longer to solve

Answer:

72 Grams

Step-by-step explanation:

You do 288/24 and then you would get 12 and then you would do 6 * 12 and get 72   (12 cups of tea.. darn)

Answer:

The answer is below

Step-by-step explanation:

A function shows relationship between variables usually between inputs (an independent variable) and outputs (a dependent variable).

C(F) = 5/9(F - 32) shows the relationship between C and F. C(F) is the temperature in degree Celsius for any temperature in Fahrenheit. This means that the function C(F) represents the conversion of temperature from Fahrenheit to degree Celsius.

Step-by-step explanation:

hii I wanna ask something

Answer:

2

Step-by-step explanation:

5x - 10 = 0

    +10    +10

5x = 10

/5     /5

x = 2

Answer:

x=2

you divide 10 by 5=10/5=2

Step-by-step explanation:

The only reasonable side length is x = 8 is "The solutions are -8 and 8, but only 8 is a reasonable side length."

The equation provided and evaluate the solutions in the context of the problem.

The equation mentioned in the problem is not explicitly provided, so we'll proceed with the given information.

Let's assume the side length of the square prism cake box is x.

The volume of a square prism can be calculated using the formula:

Volume = Length × Width × Height

Since the cake box is a square prism, the length and width are the same, so we can write:

Volume = x × x × 5.5

Given that the volume of each box must be 352 cubic inches, we can set up the equation:

x^2 × 5.5 = 352

Now, let's solve this equation to find the possible solutions for x:

x^2 = 352 / 5.5

x^2 ≈ 64

Taking the square root of both sides, we have:

x ≈ ±8

The solutions to the equation are -8 and 8.

Since we are dealing with a physical length, a negative side length doesn't make sense in this context.

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Answer:

All are Yes ^^^

Step-by-step explanation:

Got it right

Answer:

0.006

Step-by-step explanation:

0.6x0.005x0.02