i need help on math

We have

As we can see in order to find the shaded area of the figure, we only need to calculate the area of a square.

the shaded area is 400 mm^2

If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

Answer:

A and B

Step-by-step explanation:

54 , 89

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

a) The system of linear equations representing the situation is:

r + l + i = 15 (total flowers in one centerpiece)

r = 2(l + i) (twice as many roses as irises and lilies combined)

10(2.50r + 4l + 2i) = 370 (total budget)'

Matrix equation: AX = B, where

A = [[1, 1, 1], [2, -1, -1], [25, 40, 20]],

X = [[r], [l], [i]], and

B = [[15], [0], [370]]

b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

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The Complete Question:

A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $370 allocated for the centerpieces and wants each centerpiece to contain 15 flowers, with twice as many roses as the number of irises and lilies combined. (Let r represent the number of roses, l represent the number of lilies, and i represent the number of irises.)

a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.

b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

The surface area of a sphere with a radius of 10 feet is approximately 1,256 ft².

The surface area of a sphere refers to the total area that covers the surface of the sphere. It is the sum of all the areas of the small flat faces that make up the sphere.

To find the surface area of a sphere with a radius of 10 feet, we need to use the formula:

Surface Area = 4πr²

Where r is the radius of the sphere.

Plugging in the value of r=10 into the formula, we get:

Surface Area = 4π(10) = 400π

Since π is an irrational number, we cannot calculate its exact value. However, we can approximate it to 3.14. Therefore,

=> Surface Area = 400 * 3.14 = 1256

Rounding to the nearest whole number, we get the surface area of the sphere with a radius of 10 feet as 1,256 ft², which is option (a).

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Answer:

first one is 42/7 = 6

11*6 = 66

second one

1/2 inch = 3/2 feet

17/2 inches = 17*3 = 51/2 = 25.5

Answer:

Question 4

You have actual length of the stage is 42 feet and the scale drawing is 11cm: 7ft. Divide the 42 by 7 and the answer is 6. You would need 6 of the 7 ft increments to equal the total of the 42 ft stage. If you multiply one side of a ratio, then you have to multiply both sides. 11 x 6= 66!

Step-by-step explanation:

42/7 = 6

11cm x 6: 7ft x 6

66cm: 42ft

Question 5

You have an actual length of the garage is 8 1/2 inches, or 8.5 inches on the blueprint. It take 2 of the 1/2 inch segments to get 1 inch. You need 8 1/2 or 8.5 total inches. You have to multiply 8.5 by 2 to get the total number of 1/2 inch increments that you need. 8.5 x 2 = 17. This tells you that you would need 17 of the 1/2 increments to get your total blueprint length. If you multiply one side of a ratio, then you have to multiply the other side. 17 x 1 1/2 or 1.5 = 25.5

Step-by-step explanation:

1/2 inch or 0.5 inch x 2 = 1 inch

8 1/2 inches or 8.5 inches x 2 increments = 17 increments

1 1/2 ft or 1.5 ft x 17 = 25.5 ft

Answer:

B

Step-by-step explanation:

The formula for finding the volume of a pyramid with a triangular base is:

V = (1/3) * A * h

Where:

V represents the volume of the pyramid,

A represents the area of the triangular base, and

h represents the height of the pyramid.

To find the volume, we multiply the area of the triangular base by the height and then divide the result by 3.

To calculate the area of the triangular base (A), you can use different formulas depending on the available information about the triangle. Here are a few common scenarios:

1. If you know the base and height of the triangular base:

  A = (1/2) * base * height

2. If you know the lengths of all three sides (a, b, c) of the triangular base:

  You can use Heron's formula to find the area:

\(A = \sqrt{(s * (s - a) * (s - b) * (s - c))\)

  where s represents the semiperimeter of the triangle, given by s = (a + b + c)/2.

Once you have determined the area of the triangular base, you can substitute it into the volume formula along with the height of the pyramid to calculate the volume.

It's important to ensure that the base and height measurements are in the same unit of measurement for accurate calculations. Remember that the resulting volume will be expressed in cubic units, corresponding to the unit of length used for the base and height.

By using the formula V = (1/3) * A * h, you can calculate the volume of a pyramid with a triangular base, provided you have the necessary measurements.

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The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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Answer:

a^2+b^2=c^2

Step-by-step explanation:

the distance formula is used to find the distance between two points in the plane.

is based on a right triangle

Answer:

-7ss

------

rr

Step-by-step explanation:

First, you rewrite the problem as shown in the image.

After this, you may reduce the fraction and simplify.

Once you do this, the answer will be -7ss/rr.

(I used rr and ss but it would have the numbers).

Systematic random sampling is sometimes used in place of simple random sampling due to its efficiency, representativeness, ease of implementation, and cost-effectiveness.

Systematic random sampling is sometimes used in place of simple random sampling for several reasons, including:
Efficiency:

Systematic random sampling can be more efficient than simple random sampling, as it involves selecting elements at regular intervals from the population.

This often reduces the time and effort needed to collect data compared to simple random sampling.
Representativeness:

Systematic random sampling may provide a more representative sample of the population.

By selecting elements at regular intervals, it ensures that different segments of the population are included, reducing the potential for sampling bias.
Ease of implementation:

Systematic random sampling is relatively easy to implement, as it involves fewer random selections compared to simple random sampling.

This makes it more practical for large populations or when a sampling frame is not readily available.
Cost-effectiveness:

Systematic random sampling can be more cost-effective than simple random sampling.

Since the process is more efficient, it may require fewer resources, such as time and personnel, to collect data.

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Answer:

Growth rate = 4.08%

Step-by-step explanation:

Rate of interest 'i' for the growth in the cost of the house,

i = \((\frac{\text{Final amount}}{\text{Initial amount}})^{\frac{1}{n}}-1\)

Here 'n' = Duration or time (in years)

i = \((\frac{560000}{320000})^{\frac{1}{14}}-1\)

i = \((\frac{7}{4})^{\frac{1}{14}}-1\)

i = 1.0408 - 1

i = 0.0408

i = 4.08%

Therefore, growth rate for this period is 4.08%.

Answer:

Step-by-step explanation:

Algebraic, exponential and trigonometric are three different types of derivatives.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Power rule, product, quotient, chain, are the rules for derivatives.

Algebraic, exponential and trigonometric are three different types of derivatives.

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(1/2)²-6(2-2/3)

(1/2)²-6(2-2/3)

LCM=6

1/2²-6(2/1-2/3)

12-4

______

6

1/2²-6(8/6)

1-(48/36)

1-(4/3)

= -4/3

Given:

The edge length of a cube = 6 inches

To find:

The volume of the cube.

Solution:

We know that, the volume of a cube is

\(V=a^3\)            ...(i)

Where, a is the edge length.

Substituting a=6 in (i), we get

\(V=(6)^3\)

\(V=216\)

Therefore, the total volume of the cube is 216 cubic inches.

a. The expected holding-period return of Business Adventures is 1.17 with a standard deviation of 0.40. b. The expected return of a portfolio invested half in Business Adventures and half in Treasury bills is 0.605 with a standard deviation of 0.20.

a. The expected holding-period return can be calculated by taking the weighted average of the returns in each scenario, where each scenario has an equal probability of occurring:

Expected Return = (Return in Boom * Probability of Boom) + (Return in Normal Economy * Probability of Normal Economy) + (Return in Recession * Probability of Recession)

Expected Return = (2.00 * 1/3) + (1.00 * 1/3) + (0.50 * 1/3)

Expected Return = 1.17

To calculate the standard deviation of the holding-period return, we need to calculate the variance first. The variance is the average of the squared deviations from the expected return:

Variance = [(Return in Boom - Expected Return)² * Probability of Boom] + [(Return in Normal Economy - Expected Return)² * Probability of Normal Economy] + [(Return in Recession - Expected Return)² * Probability of Recession]

Variance =\([(2.00 - 1.17)^2 * 1/3] + [(1.00 - 1.17)^2 * 1/3] + [(0.50 - 1.17)^2 * 1/3]\)

Variance = 0.1611

Finally, the standard deviation is the square root of the variance:

Standard Deviation = √Variance

Standard Deviation = √0.1611

Standard Deviation ≈ 0.40

b. To calculate the expected return of the portfolio, we need to find the weighted average of the returns of Business Adventures and Treasury bills:

Expected Return of Portfolio = (Weight of Business Adventures * Expected Return of Business Adventures) + (Weight of Treasury bills * Expected Return of Treasury bills)

Expected Return of Portfolio = (0.5 * 1.17) + (0.5 * 4%)

Expected Return of Portfolio = 0.585 + 0.02

Expected Return of Portfolio ≈ 0.605

The standard deviation of the portfolio can be calculated using the formula for a two-asset portfolio:

Standard Deviation of Portfolio = √[(Weight of Business Adventures^2 * Variance of Business Adventures) + (Weight of Treasury bills^2 * Variance of Treasury bills) + (2 * Weight of Business Adventures * Weight of Treasury bills * Covariance)]

Since Treasury bills have no variance and covariance with Business Adventures, the equation simplifies to:

Standard Deviation of Portfolio = Weight of Business Adventures * Standard Deviation of Business Adventures

Standard Deviation of Portfolio = 0.5 * 0.40

Standard Deviation of Portfolio = 0.20

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The year in which the number of deaths were 80,000 is A = 1997

Given data,

To estimate the year when there were 80,000 deaths, we need to find the value of x that corresponds to D(x) = 80,000.

Given the function D(x) = 2144x^2 + 5224x + 5244, we can set it equal to 80,000:

2144x² + 5224x + 5244 = 80,000

Rearranging the quadratic equation, we get:

2144x² + 5224x + 5244 - 80,000 = 0

2144x² + 5224x - 75456 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 2144, b = 5224, and c = -75456.

Substituting the values into the quadratic formula:

x = (-5224 ± √(5224² - 4 * 2144 * -75456)) / (2 * 2144)

After performing the calculations, we find two values for x:

x ≈ -3.048 and x ≈ 13.664.

Since x represents the number of years after 1984, a negative value does not make sense in this context.

Therefore, we consider the positive value of x.

x ≈ 13.664

To estimate the year when there were 80,000 deaths, we add x to 1984:

1984 + 13.664 ≈ 1997.664

Hence , the estimate for the year when there were 80,000 deaths is approximately 1997.

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Answer:

100

Step-by-step explanation:

If the directions say to Evaluate or Simplify, then we're going to work it out and get a number answer.

4(5)²

= 4•25

= 100

Without any extra parenthesis, the second power does not reach over to the 4. It is only on the 5. You have to square the 5 first (you get 25). Then multiply by 4. That's the proper order to evaluate or simplify.

If your question is about exponential functions or logarithms, please comment or edit in some directions. Hope this helps!

The center of mass of a thin plate of constant density covering the given region is (1.8, 3.6).

To find the center of mass, we must calculate the weighted average of all the points in the region. The region is bounded by the parabola y = 3x - x² and the line y = -3x.

We must calculate the integral of the region and divide by the total mass. The mass is equal to the area times the density, .

The integral of the region is calculated using the limits of the two curves, yielding a final integral of 32/15. Dividing this integral by the density gives the total mass, and multiplying by the density gives us the center of mass, (1.8, 3.6).

We can also find the center of mass by calculating the moments of the plate about the x-axis and y-axis.

The moment about the x-axis is calculated by finding the integral of the parabola and line using the x-coordinate, and the moment about the y-axis is calculated by finding the integral of the parabola and line using the y-coordinate. Once the moments are found, we can divide each moment by the total mass to get the center of mass.

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Answer: 22.79

Step-by-step explanation:

A=length x width

4.3x5.3=22.79

Answer: C.) Inverse.

Step-by-step explanation: To write the inverse of a conditional statement, you use the "opposite" of the hypothesis and the conclusion in a conditional statement.

Given a linear system of equations in unknowns x, y, and z with the following augmented matrix:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}Use Gauss-Jordan elimination to solve the system for x, y, and z.Solution:Step 1. The first step in solving this linear system of equations is to write the matrix in the form of an augmented matrix. In the following, we list the system of equations associated with the augmented matrix: 1x−1y=−72x+3y=24z−y=1  We begin by focusing on the first equation, which is:1x−1y=−7.

To get rid of the x-coefficient, we add one time the first equation to the second equation. This operation is written as follows:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}We add row1 to row2. -2r1 + r2 = r2{-2, 2, 0, 0, 14}r3 = r3This gives us the new augmented matrix.{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}Step 2Next, we focus on the second equation:0x+1y=−5.

The y-variable is isolated, and we now look at the third equation.4z−2y=1We can isolate the variable z by dividing the entire equation by 4 as follows:z−0.5y=0.25In order to eliminate y in the third row, we add 0.5 times the second row to the third row. This operation is written as follows:{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}We add 0.5 r2 to r3. r3 + 0.5r2 = r3{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -1, -1]}Step 3We can now solve for z using the third equation:4z−1y=−1z = (-1 + y) / 4.

Substituting this into the second equation gives:-2((1 - y) / 4) + 3y = 2y - 1 = 2y - 1Thus, y = 1/2.Substituting the value of y = 1/2 into the first equation gives:x - (1/2) = -7, so x = -13/2.Finally, we can substitute the values of x and y into the third equation to get the value of z: 4z - 1(1/2) = -1, so z = -3/2.The solution to the system of linear equations is: x = -13/2, y = 1/2, and z = -3/2.

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Answer:

5 batches

Step-by-step explanation:

15/4 divided by 3/4= ^^^

when you flatten a spherical meatball into a hamburger, you increase its surface area while keeping the volume constant.

A sphere is a three-dimensional shape that has a curved surface. When you flatten a spherical meatball into a hamburger, you are essentially reshaping it into a flat, disk-like form. By doing so, you increase the area that is in contact with the cooking surface, such as a pan or grill. This larger surface area allows for more even cooking and browning.

However, the total amount of meat remains the same when you flatten the meatball. The volume of an object refers to the amount of space it occupies, and since the meatball is being flattened without adding or removing any meat, the volume remains constant. In other words, the flattened hamburger will have a larger surface area but the same amount of meat as the original spherical meatball.

So, when you flatten a spherical meatball into a hamburger, you increase its surface area while keeping the volume constant.

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When you flatten a spherical meatball into a hamburger, you decrease its volume and increase its surface area.

When a spherical meatball is flattened into a hamburger, its shape changes from a sphere to a flat disk. This transformation affects both the volume and surface area of the meatball.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. The surface area of a sphere is given by the formula A = 4πr^2.

On the other hand, the volume of a disk (or a circle) is given by the formula V = πr^2, where r is the radius of the disk. The surface area of a disk is given by the formula A = 2πr.

When the meatball is flattened, its radius decreases, resulting in a smaller volume. The volume of the flattened meatball is less than the volume of the original spherical meatball.

However, the surface area of the flattened meatball increases. The surface area of the flattened meatball is greater than the surface area of the original spherical meatball.

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