write the equation 3x-2y=15 in standard form. show work.

The determinant of the given matrix using expansion by cofactors is -29640.  In expansion by cofactors, the determinant of an n x n matrix can be computed by expanding along any row or column.

Let's expand along the first row of the given matrix.

The cofactor of each element in the first row is found by taking the determinant of the submatrix formed by excluding the row and column of that element, and multiplying it by the sign \((-1)^{(i+j)\), where i and j are the row and column indices of the element.

For example, the cofactor of the element w is determined by taking the determinant of the submatrix:

10 -18 32

32 22 -35

The determinant of this 2 x 2 submatrix is (10 * (-35)) - (32 * 22) = -1050 - 704 = -1754. Multiplying this by the sign (-1)^(1+1) = 1 gives us the cofactor of w as -1754.

Repeating this process for each element in the first row, we have:

Cofactor of w = -1754

Cofactor of x = -2684

Cofactor of y = -1020

Cofactor of z = -2182

Finally, we calculate the determinant by multiplying each element in the first row by its corresponding cofactor and summing them up:

w * (-1754) + x * (-2684) + y * (-1020) + z * (-2182) = -29640

Therefore, the determinant of the given matrix using expansion by cofactors is -29640.

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The answer is:

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Answer:

the first and third option

Step-by-step explanation:

In the initial recipe, the ratio of tomato sauce to chile sauce is 1 : 3/2

To make it spicier this ratio has to be higher than the initial ratio

Ratio in the first option : 1/2 : 1 = 1 : 2

option 2 : if both recipes are double, the proportion of ingredients remain the same

oprion 3 : 1 : 3

option 4 : 1 : 1

option 5 : 1 : 5/3

Answer:

-2/7x - 6

Step-by-step explanation:

Combine Like Terms:

1/7x + 2/7x - 5/7x - 10 + 4

-2/7x - 6

(a) Yes, the sampling distribution of the sample mean is approximately normal due to the Central Limit Theorem.

(b) The sample mean is $125, and the standard deviation is $2.12 (rounded to two decimal places).

(c) The probability that the sample mean deviates from the population mean by no more than 3 is 0.9973.

(a) Yes, the sampling distribution of the sample mean is approximately normal. This is due to the Central Limit Theorem, which states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. With a sample size of 50 bills, we can assume that the sampling distribution of the sample mean is approximately normal.

(b) The sample mean is the same as the population mean, which is $125. The standard deviation of the sample mean can be calculated using the formula:

Standard deviation of the sample mean = Standard deviation of the population / Square root of the sample size

Standard deviation of the sample mean = $15 / √50 ≈ $2.12

(c) To find the probability that the sample mean deviates from the population mean by no more than 3, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.

z-score = (Sample mean - Population mean) / (Standard deviation of the sample mean)

z-score = (125 - 125) / 2.12 = 0

Using a standard normal distribution table or a calculator, we can find that the probability corresponding to a z-score of 0 is 0.5. Since we want the probability that the sample mean deviates from the population mean by no more than 3 (in either direction), we can calculate the area under the curve up to a z-score of 3 and double it:

Probability = 2 * (Area to the left of z = 3) = 2 * 0.4987 ≈ 0.9973

Therefore, the probability that the sample mean deviates from the population mean by no more than 3 is approximately 0.9973, or 99.73%.

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Answer:

square pyramids

Step-by-step explanation:

Square pyramids because they have corners and the storage box is shaped like a cube. If he gets things with rounded edges, then there will be empty space between each water tank.

Answer:

4 and -2

Step-by-step explanation:

4 + -2 = 2

4 x -2 = -8

Answer:

(-1/2, 4)

Step-by-step explanation:

Get the x intercept. The x intercept occurs at when y = 0

0 = 8x + 4

-8x = 4

x = 4/-8

x = -1/2

Get the y intercept

y intercept occurs at x = 0

y = 8(0) + 4

y = 0+4

y = 4

Hence the required solution is (-1/2, 4)

Answer:

2/3

Step-by-step explanation:

The slope is 2/3 because you can look at the x-intercept which is -2. Find another point where the blue line crosses directly into the corner of the gray lines. The formula is rise/run. A point where the blue line crosses the gray line directly is (1,2). From the point (-2,0) you go up 2 places and then you go right three places to get to the other point. Therefore, your answer is 2/3.

You could also use the formula y1-y2/x1-x2. Now, you plot in the coordinates. 2-0/1--2= 2/3. Still, the answer would be 2/3.

The ant population will double in approximately 24 weeks, or 6 months. This can be found using exponential growth formula.

To find the time it takes for the ant population to double we can use the formula for exponential growth: A = A0 * e^(rt), where A is the population at a given time t, A0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.718.

In this case, we have A0 = 4,000, r = 0.03 (since the population is increasing at a rate of 3% per week), and we want to find the value of t when A = 8,000 (since we want to know when the population has doubled). Plugging these values into the formula, we get:

8,000 = 4,000 * e^(0.03t)

Dividing both sides by 4,000 and taking the natural logarithm of both sides, we get:

ln(2) = 0.03t

Solving for t, we get:

t = ln(2) / 0.03

Using a calculator, we find that t is approximately 23.1 weeks. Rounded to the nearest week, this is 24 weeks. Therefore, it will take approximately 24 weeks, or 6 months, for the ant population to double.

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Answer:

x - 40 degree... I am sure

Answer:

Slope is 3

y - intercept is -1

Answer:

slope = 3, y- intercept is - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 1 ← is in slope- intercept form

with slope m = 3 and y- intercept c = - 1

Answer:

A

Step-by-step explanation:

The system of equations listed in answer A fits both of the criteria.

as x represents the number of 55-inch televisions and y fits the criteria of the number of 65-inch television, we can use the knowledge we have from the question that we can combine these two variables to get a total number of tv's.

As said in the question: "The first week they sold 44 TVs total" meaning that the combined total amount of TV's sold was 44, meaning x + y (which are just variables, not "known" amounts equates to 44.

x + y = 44

The second equation in the system represents the profits. Using the same knowledge from before, we don't know how many how many tv's of each were sold but we can use these variables to present that each 55-inch tv is worth $349 and each 65-inch tv is worth $469.

349x+469y = 17,516 represents this perfectly, thus making A our answer

Answer:

Step-by-step explanation:

We can use proportions to solve for the height of the monument:

Let h be the height of the monument.

Then, we have:

h/12 = 3/4

Cross-multiplying, we get:

h = (12 x 3)/4 = 9 meters

Therefore, the height of the monument is 9 meters.

The number of positive integers that can be expressed in the given form among the first 1000 positive integers is 984.

To determine the number of positive integers that can be expressed in the form $\lfloor 2x\rfloor \lfloor 4x\rfloor \lfloor 6x\rfloor \lfloor 8x\rfloor$, where $x$ is a real number, we need to analyze the conditions under which this expression takes integer values.

Let's consider the factors $\lfloor 2x\rfloor$, $\lfloor 4x\rfloor$, $\lfloor 6x\rfloor$, and $\lfloor 8x\rfloor$ separately.

For $\lfloor 2x\rfloor$ to be an integer, $x$ must be of the form $n/2$, where $n$ is an integer.

For $\lfloor 4x\rfloor$ to be an integer, $x$ must be of the form $n/4$, where $n$ is an integer.

For $\lfloor 6x\rfloor$ to be an integer, $x$ must be of the form $n/6$, where $n$ is an integer.

For $\lfloor 8x\rfloor$ to be an integer, $x$ must be of the form $n/8$, where $n$ is an integer.

To satisfy all four conditions simultaneously, $x$ must be of the form $n/24$, where $n$ is an integer.

Now, let's consider the range of positive integers up to 1000 that can be expressed in the given form.

The largest value of $n$ that gives an integer less than or equal to 1000 when divided by 24 is $24 \times 41 = 984$. So, we can express positive integers up to 984 in the form $\lfloor 2x\rfloor \lfloor 4x\rfloor \lfloor 6x\rfloor \lfloor 8x\rfloor$.

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Answer:

Step-by-step explanation:

Answer:

4  2/9π   or   4.22 (repeating)π

Step-by-step explanation:

I changed my mind. I'll attempt it.

The formula for finding the arc length: \(2\pi (r)(\frac{theta}{360} )\)

2π(4)(190/360) = 4 2/9π

82% certain the answer you're looking for is 4  2/9π (pi symbol because it asks for it in terms of pi)

Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

Answer:

The car's average speed for the entire journey = 84.315 km/h

Step-by-step explanation:

Correct Question

A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.

Solution

Average speed is given as total distance travelled divided by total time taken.

So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.

- The car travels the 50 km first part of the journey at a speed of 25 m/s.

25 m/s = 90 km/h

We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.

Speed = (Distance/Time)

Time = (Distance/Speed)

Distance = 50 km, Speed = 90 km/h

Time = (50/90) = 0.5556 hr

- The next part, the car covers 120 km at a speed of 80 km/h

Time = (Distance/Speed) = (120/80) = 1.5 hr

- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.

35 minutes = (35/60) hr = 0.5833 hr

Here, we need to calculate the distance covered for the last part.

Speed = (Distance/Time)

Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km

Total distance covered = 50 + 120 + 52.5 = 222.5 km

Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr

Average Speed = (222.5/2.6389) = 84.315 km/h

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Answer:

No solution.

Step-by-step explanation:

1. Move terms to the left side

x² - 3x = -8

x² - 3x - (-8) = 0

2. Use the quadratic formula

x = \(\frac{-b + \sqrt{b^2 - 4ac} }{2a}\)

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x² - 3x + 8 = 0

a = 1

b = -3

c = 8

x = \(\frac{-(-3) + \sqrt{(-3)^2 - 4 * 1 * 8} }{2*1}\)

3. Simplify

After simplifying:

x = \(\frac{3 + \sqrt{-23} }{2}\)

4. No real solutions because the discriminant is negative.

The square root of a negative number is not a real number.

d = -23.

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Step-by-step explanation:

1.2.4) From the above information give and calculation done, which house would you recommend to Mrs Bhengu to buy .give reason for your answer.

Answer:

11388

Step-by-step explanation:

Answer:

The answer to this question is 11,388

The bearing from north is 59.2 degrees. We can determine the length of the hypotenuse using the Pythagorean theorem.

This issue can be resolved using geometry. Let's depict a right triangle, with the airport, the aircraft, and a location immediately to its south serving as the right angle : perl

Enter the following codes: A (airport) | | | x (plane) | | | | | | | S (south)

AS is equal to 147 miles, and SX is equal to 90 miles. Give the angle between AS and the hypotenuse (the direction we are looking for) the name.

We can determine the length of the hypotenuse using the Pythagorean theorem:

AS + SX + 147 + 90 = Hypotenuse in the CSS Code code

Hypotenuse is equal to sqrt((147)^^(2) + (90)^^(2)) = 174.63 miles.

The sine and cosine values can now be used to determine:

hypotenuse = 147 / 174.63 = 0.8429 Clone code sin() = AS

SX / Hypotenuse = 90 / 174.63 = 0.5150 for cos().

We can determine using the inverse tangent function.

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The correct equation and value of x, the distance of 1 lap around the path at the park is 4.8x + 1.2 = 3.6. Then the correct option is B.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.

This is because lap will be dependent on the variable, we know that the number of them will be multiplied by the variable x we also know that 1.2 miles are constant. Now the equation will be

4.8x + 1.2 = 3.6

Thus, the correct option is B .

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The equation to find the cost of each pair of shorts is 175 = 75 + 5x where each short cost $20

Cost of jackets= $75

Number of shorts= 5

Cost of each short = x

Total amount Jim spent= $175

Total amount Jim spent = Cost of jackets + (Number of shorts × Cost of each short)

175 = 75 + 5x

subtract 75 from both sides

175 - 75 = 5x

100 = 5x

divide both sides by 5

x = 100/5

x = $20

Ultimately, each pair of shorts cost $20

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Answer:

2

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    -2*y-(-4*x+5)=0

STEP 1:

Pulling out like terms

1.1     Pull out like factors :

  -2y + 4x - 5  =   -1 • (2y - 4x + 5)

Equation at the end of step 1:

STEP 2:

Equation of a Straight Line

2.1     Solve   -2y+4x-5  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  -2y+4x-5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/-2 so this line "cuts" the y axis at y=-2.50000

 y-intercept = 5/-2  = -2.50000

Calculate the X-Intercept :

When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000

 x-intercept = 5/4  =  1.25000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = 2

Geometric figure: Straight Line

 Slope = 2

 x-intercept = 5/4 = 1.25000

 y-intercept = 5/-2 = -2.50000

Answer:

2

Step-by-step explanation:

y=mx+b where m is the slope

to get y by itself you divide both sides by -2 resulting in

y= 2x+(-5/2)

2=m

Answer:yes

Step-by-step explanation:

Answer:

1/18.

Step-by-step explanation:

2x^-2 y^-2

x= 3 and y = –2?

Answer is 2(3)^-2 * (-2)^-2

= 2/(3)^2 * 1/(-2)^2

= 2/9 *  1/4

= 2/36

= 1/18.

Answer: Less than (<), greater than (>), and not (not equal to) are examples of comparison operators.

Step-by-step explanation: They show a comparison between the two operands.

Answer:

\(a_{n}\) = 2n - 3

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

given a₁ = - 1 and a₅ = 7 , then

a₁ + 4d = 7 , that is

- 1 + 4d = 7 ( add 1 to both sides )

4d = 8 ( divide both sides by 4 )

d = 2

then

\(a_{n}\) = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

\(a_{n}\) = 2n - 3