drag and drop the numbers into the table to complete the table of values for the equation y=4x+9

Plugging the values into a table on desmos, it clearly follows an exponential equation as shown by the equation of best fit. Therefore, the relationship is exponential.

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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\(\textbf{ Heya !}\)

Your Answer Is:-

\(\sf{9x\div6}\)

because,

               it has a coefficient of 9 (a number that comes before a variable)

`hope that was helpful to u ~

For two vectors to be orthogonal, their dot product must be zero:

u · v = 4k + 5(1) + k(k-1) = 0

Simplifying this quadratic equation, we get:

k^2 + 3k + 5 = 0

Using the quadratic formula, we find that the solutions are:

k = (-3 ± sqrt(3^2 - 4(1)(5))) / (2(1)) = (-3 ± i√7) / 2

Therefore, the two vectors are orthogonal if and only if k is equal to one of these values:

k = (-3 + i√7) / 2, (-3 - i√7) / 2

So the answer is:

k = (-3 + i√7) / 2, (-3 - i√7) / 2

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The Volume generated when the region between the curves is rotated around the y - axis is 1216500335.46

Volume of the curves:

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫dc [f(y)]2dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).

Given,

y = x³

Here we have to find the volume along to the y axis.

With limit as y = 0 and y = 27.

When we apply the values it can be written as,

=>\(V=\pi \int\limits^0_{27} {(x^3)^2} \, dx\)

\(\implies V=\pi \int\limits^0_{27} {(x^6)} \, dx\)

Apply the limits then we get,

\(\implies V = \pi [0^6 - (27)^6]\)

=> V = π [0 - 387420489]

=> V =   π x 387420489

=> V = 1216500335.46

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The statement is true. Simple random sampling is a method of selecting a sample from a larger population in which every member of the population has an equal chance of being selected for the sample.

This method is associated with a high degree of generalizability because it ensures that the sample is representative of the population. When a sample is representative of the population, the findings from the sample can be generalized to the entire population with a high level of confidence.

Simple random sampling is considered to be one of the most reliable and unbiased methods of sampling, making it a popular choice in many research studies.

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If the bag contains a total of n blocks and m of them are blue, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws, assuming the selection process is random and the probabilities remain constant.

Let's assume that the bag contains a total of n blocks, and m of them are blue blocks. The probability of selecting a blue block on each draw, P(blue), would be m/n.

Since we are replacing the block after each selection, the total number of blocks in the bag remains the same throughout the process. Therefore, the probability of selecting a blue block on each draw remains constant at m/n.

To find the expected number of times we would select a blue block, we can multiply the probability of selecting a blue block on each draw (m/n) by the total number of draws (12):

Expected number of blue blocks = (m/n) * 12

The reasoning behind this is that in each individual draw, the probability of selecting a blue block is m/n. By performing 12 independent draws, we can expect to encounter this probability m/n a total of 12 times on average.

Therefore, if the bag contains n blocks with m blue blocks, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws.

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The height of the image formed by the concave mirror is approximately 12.44 cm.

To determine the height of the image formed by a spherical concave mirror, we can use the mirror formula:

1/f = 1/v - 1/u

Where:

f = focal length of the mirror

v = image distance from the mirror (positive for real images)

u = object distance from the mirror (positive for objects in front of the mirror)

Given:

f = -20 cm (since it's a concave mirror with a positive radius of curvature)

u = -15 cm (since the object is placed in front of the mirror)

h = 4.0 cm (height of the object)

Let's calculate the image distance (v) using the mirror formula:

1/(-20 cm) = 1/v - 1/(-15 cm)

Simplifying the equation:

-1/20 = 1/v + 1/15

Combining the fractions:

-3/60 = (15 + 20)/(15v)

-3/60 = 35/(15v)

Cross-multiplying:

-3 * 15v = 35 * 60

-45v = 2100

Dividing both sides by -45:

v = -2100 / -45

v ≈ 46.67 cm

The image distance (v) is approximately 46.67 cm. Since the magnitude of v is positive, the image formed is a real image.

To find the height of the image (h'), we can use the magnification formula:

h'/h = -v/u

Substituting the values:

h'/4.0 cm = -46.67 cm / -15 cm

Simplifying:

h'/4.0 cm = 46.67 cm / 15 cm

Cross-multiplying:

h' = (46.67 cm * 4.0 cm) / 15 cm

h' ≈ 12.44 cm

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9x + 6 - 4x - 2x + 1 - 15

9x - 4 x- 2x = (9-4-4)x = 3x

6 +1 -15 = -8

____________

Answer

3x -8

______________

Please tell me if you can see the updates

ok

________________

In this case, I will consider the relationship between a person's age and their income. I believe that income is more likely to have a higher standard deviation compared to age.

1. Economic Factors: Income is influenced by economic factors such as job market conditions, economic growth, and industry trends. These factors can fluctuate over time, leading to variations in income levels. On the other hand, age progresses in a more predictable manner.

2. Career Development: Income is strongly influenced by career development, including promotions, job changes, and salary negotiations. These factors introduce a level of unpredictability, as individuals may experience significant income changes at different stages of their careers. Age, although related to career progression, follows a relatively more predictable pattern.

3. Individual Choices: Income can also be influenced by individual choices such as entrepreneurship, investment decisions, and career changes. These choices introduce a higher level of variability as they depend on personal circumstances, risk appetite, and market conditions. Age, in contrast, progresses in a more linear and predictable manner.

Considering these reasons, it is reasonable to expect that income would have a higher standard deviation compared to age. Income is influenced by various external and personal factors that can result in significant fluctuations, making it less predictable compared to the relatively more stable progression of age.

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A better method to determine the more popular sport is by conducting a comprehensive, unbiased survey with a random sample

a. Concluding that baseball is more popular than soccer based on a poll at a championship event is not valid due to potential sample bias, self-selection bias, limited sample size, and question phrasing.

b. A better method to determine the more popular sport is by conducting a comprehensive, unbiased survey with a random sample of students in a neutral setting, using clear and unbiased questions that allow for all preferences

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The value of x= 4 and y= 1.

We can use the following steps to find x and y:

1. Multiply the matrices on the equation's left and right sides. This results in the equation shown below:

[4 3 L1 01] * [3 −1 4 -5 -1 7 -31] = [x + y] * [21 L6 -5 5]

2. Increase the matrix product. This results in the equation shown below:

[12 9 1 0] = [21x + 6y L 6x - 5y]

3. Put the matching terms on both sides of the equation into an equation. This results in the equations that follow:

12 = 21x + 6y 9 = 6x - 5y 1 = y

4. Resolve the equations in the system. The following steps can be used to accomplish this:

* Find y in the first equation. This results in y = 1. * Replace this

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Answer:

Step-by-step explanation:

−4−(−7)=

The opposite of −7 is 7.

−4+7

Add −4 and 7 to get 3.

3

Answer:

3

Step-by-step explanation:

Think of -4-(-7) as -4+7

just remove the negative and add instead

your answer is 3

Answer:

look at the picture i sent......

Answer:

400

Step-by-step explanation:

Ok so if 60% of the total is 240 than create an expression:

60% of x=240

Now divide both sides by 3:

20% of x=80

Multiply both sides by 5 ( because 5 times 30 is 100):

100% of x=400

Thats the answer hope this helped! :)

400 cards were in her collection.

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:

Total hockey cards sold= 240

So, Kaitlan sold 60% of her hockey card

let the total number of Hockey cards be x.

So, 60% of x= 240

60 x /100 = 240

x= 24000/ 60

x= 400

Hence, 400 cards were in her collection.

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To determine if the value 5π/4 is a solution for the equation 3√(sin θ) + 2 = -1, we need to substitute the value of θ and verify if the equation holds true.

Let's substitute θ = 5π/4 into the equation:

3√(sin(5π/4)) + 2 = -1

Now, let's simplify the equation step by step:

First, let's evaluate sin(5π/4). In the unit circle, 5π/4 is in the third quadrant, where sin is negative. Additionally, sin(5π/4) is equal to sin(π/4) due to the periodic nature of the sine function.

sin(π/4) = 1/√2

Now, substitute the value of sin(π/4) back into the equation:

3√(1/√2) + 2 = -1

Simplifying further:

3√(1/√2) = 3 * (√(1)/√(√2)) = 3 * (1/√(2)) = 3/√2 = 3√2/2

Now the equation becomes:

3√2/2 + 2 = -1

To add fractions, we need a common denominator:

(3√2 + 4)/2 = -1

Since the left side of the equation is positive and the right side is negative, they can never be equal. Therefore, the equation is not satisfied, and 5π/4 is not a solution to the equation 3√(sin θ) + 2 = -1.

Thus, the statement "The value 5π/4 is a solution for the equation 3√(sin θ) + 2 = -1" is false.

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Answer:

3 and 5

Step-by-step explanation:

order of operation

step 1

look at problem and see if there is a number that occurs like 2-3+x=4-3+x

step 2 your done

==========================================================

Work Shown:

x = first number

x+1 = second number

x+2 = third number

x+3 = fourth number

x+4 = fifth number

Note how the numbers are one after another. Consecutive numbers follow this pattern. For example: 6,7,8,9,10 are consecutive numbers. One number follows right after the other.

---------------

Add up those five expressions. Set the sum equal to 70 and solve for x

(x)+(x+1)+(x+2)+(x+3)+(x+4) = 70

(x+x+x+x+x)+(1+2+3+4) = 70

5x+10 = 70

5x = 70-10

5x = 60

x = 60/5

x = 12 is the first number and the smallest number

x+1 = 12+1 = 13 is the second number

x+2 = 12+2 = 14 is the third number

x+3 = 12+3 = 15 is the fourth number

x+4 = 12+4 = 16 is the fifth number

Check:

12+13+14+15+16 = 70

which confirms our answer

-----------------

You could use a guess and check method, but the algebraic approach is much more efficient.

The value of the contour surface passing through the point (1, 0, 2) is ψ(1, 0, 2) = 1^2 + 2e^0 = 1 + 2 = 3.

To find the points on the curve where the tangent is horizontal, we need to determine the values of t that satisfy the condition for a horizontal tangent, which is when the derivative of y with respect to t is equal to 0.

Given the parametric equations:

x = 2t^3 + 3t^2 - 12t

y = 2t^3 + 3t^2 + 1

Taking the derivative of y with respect to t:

dy/dt = 6t^2 + 6t

Setting dy/dt equal to 0 and solving for t:

6t^2 + 6t = 0

t(6t + 6) = 0

From this equation, we have two possible solutions:

t = 0

6t + 6 = 0, which gives t = -1.

Therefore, the points on the curve where the tangent is horizontal are (0, y(0)) and (-1, y(-1)). To find the corresponding y-values, substitute the values of t into the equation for y:

For t = 0:

y(0) = 2(0)^3 + 3(0)^2 + 1 = 1

For t = -1:

y(-1) = 2(-1)^3 + 3(-1)^2 + 1 = -2 + 3 + 1 = 2

Hence, the points on the curve where the tangent is horizontal are (0, 1) and (-1, 2).

To find the points on the curve where the tangent is vertical, we need to determine the values of t that satisfy the condition for a vertical tangent, which is when the derivative of x with respect to t is equal to 0.

Taking the derivative of x with respect to t:

dx/dt = 6t^2 + 6t - 12

Setting dx/dt equal to 0 and solving for t:

6t^2 + 6t - 12 = 0

t^2 + t - 2 = 0

(t + 2)(t - 1) = 0

From this equation, we have two possible solutions:

t + 2 = 0, which gives t = -2

t - 1 = 0, which gives t = 1.

Therefore, the points on the curve where the tangent is vertical are (x(-2), y(-2)) and (x(1), y(1)). To find the corresponding x-values and y-values, substitute the values of t into the equations for x and y:

For t = -2:

x(-2) = 2(-2)^3 + 3(-2)^2 - 12(-2) = -16 + 12 + 24 = 20

y(-2) = 2(-2)^3 + 3(-2)^2 + 1 = -16 + 12 + 1 = -3

For t = 1:

x(1) = 2(1)^3 + 3(1)^2 - 12(1) = 2 + 3 - 12 = -7

y(1) = 2(1)^3 + 3(1)^2 + 1 = 2 + 3 + 1 = 6

Hence, the points on the curve where the tangent is vertical are (20, -3) and (-7, 6).

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Using quadratic function concepts, it is found that the statement is false.

\(f(x) = ax^2 + bx + c\)

The discriminant is:

\(\Delta = b^2 - 4ac\).

Additionally, it will have two solutions that are negatives of one another when coefficient b is 0, as:

\(ax^2 + c = 0\)

\(ax^2 = -c\)

\(x^2 = -\frac{c}{a}\)

\(x = \pm \sqrt{-\frac{c}{a}}\)

Hence it is not related to the discriminant, and the statement is false.

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Answer:

height is 32 ft

Step-by-step explanation:

384 = LWH?

(3W) (W) (H) = (3 x 2) (2) (16 x 2) = (6) (2) (32) = (12) (32) = 384 cubic ft

The value of x can be determined by using the z-score formula and substituting the given z-score into it. For a z-score of -2.25, when x=50 and x=3, the calculated value of x will be around 18.5.

Explanation: A z-score represents the number of standard deviations an x-value is away from the mean of a distribution. To find the corresponding x-value for a given z-score, we can use the formula: x = z * σ + μ, where z is the z-score, σ is the standard deviation, and μ is the mean.

In this case, the z-score is -2.25, but the mean (μ) and standard deviation (σ) are not provided. Therefore, we cannot calculate the exact value of x. However, we can estimate it by comparing the z-scores of the given x-values (50 and 3) with the given z-score (-2.25).

If x=50, the z-score would be (x - μ) / σ. Since the z-score for x=50 is -2.25, we have (-2.25) = (50 - μ) / σ.

Similarly, for x=3, the z-score would be (-2.25) = (3 - μ) / σ.

By comparing these two equations, we can observe that the change in x from 50 to 3 should be approximately equal to the change in z-score from -2.25. Therefore, we can estimate that the value of x, when x=3, would be around 18.5.

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Answer:

4712.4ft^3 :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

I believe the triangle adds up to 180 degrees. Each sides are equal angles so:

180/3=60 degrees each angle

The triangle has a same side in the value for X and the line is straight.

SO x= 60 degrees.

Answer:

Step-by-step explanation:

6c + 18-4c + 16

Solving like terms

2c + 34

Answer: 2c + 2

6(c + 3) - 4(c + 4)

= 6c + 18 - (4c + 16)

= 6c + 18 - 4c - 16

= 2c + 2

Step-by-step explanation:

Answer: \((x-7)^2+(y+2)^2=11^2\) ; \(A=121\pi\)

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

\((x-a)^2+(y-b)^2=r^2\)

Begin by grouping the 'x' terms and 'y' terms:

\((x^2-14x)+(y^2+4y-68)=0\)

Complete the square for the second polynomial:

\((\frac{b}{2} )^2=(\frac{4}{2} )^2=4\)

\((x^2-14x)+(y^2+4y+4-4-68)=0\)

\((x^2-14x)+(y^2+4y+4)-4-68=0\)

\((x^2-14x)+(y^2+4y+4)-72=0\)

\((x^2-14x)+(y+2)^2-72=0\)

Do the exact same process with the other polynomial:

\((x^2-14x-72)+(y+2)^2=0\)

Complete the square:

\((\frac{14}{2} )^2=49\)

\((x^2-14x+49-49-72)+(y+2)^2=0\)

\((x^2-14x+49)-49-72+(y+2)^2=0\)

\((x^2-14x+49)-121+(y+2)^2=0\)

\((x-7)^2-121+(y+2)^2=0\)

Bring the 121 to the other side to get:

\((x-7)^2+(y+2)^2=121\)

\((x-7)^2+(y+2)^2=11^2\)

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

\(A=\pi r^2=121\pi\)

Answer:

11

Step-by-step explanation

  sorry