Which of the following equations could represent the line of best fit for this scatter plot?


A. y = ‒10x + 2
B. y = 2x ‒ 10
C. y = 10x ‒2
D. y = ‒2x + 10

The UCLR (Upper Control Limit) and LCLR(Lower Control Limit) are 2.22 and 0 respectively.

Given that,

At five soups that were chosen at random, average temperatures were recorded. X-bar and r-bar positions were 45.25 degree and 1.05 degree, respectively.

To find : UCLR (Upper Control Limit) and LCLR (Lower Control Limit)

R-bar = 1.05 Degrees

X-bar = 45.25 Degrees

Sample Size , n=5

D3=0

D4=2.114

3 Sigma control limits of Range Chart

LCLR = D3*R-bar = 0*1.05 =0

UCLR =D4*R-bar = 2.114*1.05 = 2.22

The UCLR (Upper Control Limit) and LCLR (Lower Control Limit) are therefore 2.22 and 0, respectively.

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Answer:

negative or undefined

Step-by-step explanation:

Answer:

Negative

Step-by-step explanation:

Read it left to right if going up it's positive going down negative

Simplifying

f(x) = 6x5 + 5x4 + 4x

Multiply f * x

fx = 6x5 + 5x4 + 4x

Reorder the terms:

fx = 4x + 5x4 + 6x5

Solving

fx = 4x + 5x4 + 6x5

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.

f = 4 + 5x3 + 6x4

Simplifying

f = 4 + 5x3 + 6x4

The correct conversion of 4.532×10^4 square feet to m^2 is 4.210×10^3 m^2. The allowed operations when dealing with quantities of different units are A+B, A-B, A*B, A/B, and A^2.

To convert square feet to square meters, we need to know the conversion factor. The conversion factor for area units between square feet and square meters is 1 square meter = 10.764 square feet.

Therefore, to convert 4.532×10^4 square feet to square meters, we divide the given value by the conversion factor:

4.532×10^4 square feet / 10.764 = 4.210×10^3 square meters.

Hence, the correct conversion is 4.210×10^3 m^2.

Regarding the operations with quantities of different units, the following operations are allowed:

Addition (A + B) when both A and B have the same units.

Subtraction (A - B) when both A and B have the same units.

Multiplication (A * B) to combine different units (e.g., m * s).

Division (A / B) to divide different units (e.g., m / s).

Squaring (A^2) to calculate the square of a quantity with units.

Thus, A + B, A - B, A * B, A / B, and A^2 are all allowed operations.

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The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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Answer:

Option (D)

Step-by-step explanation:

Let the equation of the line be,

y = mx + b

where m = slope of the line

b = y-intercept

Slope of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

Since, line 'l' is passing through two points (0, 1) and (-1, 0),

Therefore, slope 'm' = \(\frac{1-0}{0+1}\) = 1

y-intercept 'b' = 1

Therefore, equation of the line will be,

y = 1(x) + 1

y = x + 1

Option (D). will be the answer.

The coordinates of point D 0.25 x-axis for the points A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10) are (-2, -2.5) when point D is reflected across the x-axis. This is obtained by negating the y-coordinate of point D and keeping the x-coordinate the same.

To find the coordinates of point D 0.25 x-axis, we need to reflect point D across the x-axis. This will result in the y-coordinate of point D being negated while the x-coordinate remains the same.

The coordinates of point D are (-2, 10), so when we reflect it across the x-axis, we get the new coordinates:

D 0.25 x-axis = (-2, -10/4) = (-2, -2.5)

Therefore, the coordinates of point D0.25∘rx-axis for the given points A, B, C, and D are (-2, -2.5).

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The coordinate plane that shows the graph of the function is the first graph in the second attachment

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

x y

0 1

1 2

2 3

3 4

From the above, we can see that

The x value is added to 1 to get the y value

This means that

The input value is added to 1 to get the output value

So, we have

y = x + 1

From the list of options, the graph that represent the relation is the second graph (first in the second attachment)

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Answer:

Step-by-step explanation:

Answer:

Please refer to the attachment

Hope it helps

Pls mark me as the brainliest

Thank you

The linear function for this problem is defined as follows:

y = x + 50.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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Answer:

6 3/10

Step-by-step explanation:

3 1/2 = 7/2

1 4/5 = 9/5

7/2 x 9/5 = 7x9/2x5 = 63/10 = 6 3/10

Answer:

the blue one <3

Step-by-step explanation:

the black one has slope of 1

the blue one has slope of 4/2 which is also 2

Answer:

Perform an experiment

Step-by-step explanation:

The experiments state that it is the test which is to be carried to confirm or refute the hypotheses they had about a specific subject. Therefore, the study findings will be based on the outcome of these experiments.

Now, according to the given situation, an analysis of the impact of potato chips on the human digestive system with fat replacement is refer to perform an experiment.

So, the right answer is to perform an experiment.

The correct equations are 4x²+10x = 2x(2x+5) and 30x⁴−12x³ = 6x³(5x−2).

For the equation 4x²+10x = 2x(2x+5)

A common factor between 4 and 10 is 2x. if we should divide each number by 2x, we would be left with 2x and 5 and if we multiple 2x and 5 by 2x, we get the original equation.

To ascertain that 30x⁴−12x³ = 6x³(5x−2), we look for a common factor between bot numbers and that is 6x³. If we divide 30x⁴ by 6x³, we should be left with 5, and if we divide 12x³  by 6x³, we simply get 2. If we multiply these lowest form by 6x³ we get the original equation.

for 8x³ − 6x = 2x³(4−3x³), we can see that it does not add up. The common denominator for 8x³  and  6x is 2x. If we divide it, we are left with 4x² and 3 whereas we have just 4 in parenthesis.

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The probability that less than or equal to 5 of the 10 independent customers will take more than 3 minutes to check out their groceries is approximately 0.9245.

To calculate this probability, we can use the binomial probability formula. Let's denote X as the number of customers taking more than 3 minutes to check out. We want to find P(X ≤ 5) when n = 10 (number of trials) and p (probability of success) is not given explicitly.

Step 1: Determine the probability of success (p).

Since the probability of each customer taking more than 3 minutes is not provided, we need to make an assumption or use historical data. Let's assume that the probability of a customer taking more than 3 minutes is 0.2.

Step 2: Calculate the probability of X ≤ 5.

Using the binomial probability formula, we can calculate the cumulative probability:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = C(10, 0) * p^0 * (1 - p)^(10 - 0) + C(10, 1) * p^1 * (1 - p)^(10 - 1) + C(10, 2) * p^2 * (1 - p)^(10 - 2) + C(10, 3) * p^3 * (1 - p)^(10 - 3) + C(10, 4) * p^4 * (1 - p)^(10 - 4) + C(10, 5) * p^5 * (1 - p)^(10 - 5)

Substituting p = 0.2 into the formula and performing the calculations:

P(X ≤ 5) ≈ 0.1074 + 0.2686 + 0.3020 + 0.2013 + 0.0889 + 0.0246

P(X ≤ 5) ≈ 0.9928

Rounding this probability to the nearest hundredth/second decimal place, we get approximately 0.99. However, the question asks for the probability that less than or equal to 5 customers take more than 3 minutes, so we subtract the probability of all 10 customers taking more than 3 minutes from 1:

P(X ≤ 5) = 1 - P(X = 10)

P(X ≤ 5) ≈ 1 - 0.9928

P(X ≤ 5) ≈ 0.0072

Therefore, the probability that less than or equal to 5 customers out of 10 will take more than 3 minutes to check out their groceries is approximately 0.0072 or 0.72%.

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Answer: 4 i think

Step-by-step explanation:

(a) The inverse z-transform of X(2) is r[n] = 8δ[n-2] + 3δ[n-2].

(b) The inverse z-transform of X(2) is r[n] = 7δ[n-2] + 3δ[n-2] + 2δ[n-2].

(c) The inverse z-transform of X(2) is r[n] = 22(-0.75)^n + 0.125(-2)^n.

(a) The inverse z-transform of X(2) is obtained by replacing z with the unit delay operator δ[n-2], which represents a shift of the signal by 2 units to the right. Since X(2) has two terms, we multiply each term by the corresponding δ[n-2] to obtain the inverse z-transform r[n] = 8δ[n-2] + 3δ[n-2].

(b) Similar to (a), we replace z with δ[n-2] and multiply each term in X(2) by the corresponding δ[n-2]. This yields the inverse z-transform r[n] = 7δ[n-2] + 3δ[n-2] + 2δ[n-2].

(c) For X(2), we have a geometric series with a common ratio of -0.75 or -2, depending on the absolute value of the term. By applying the inverse z-transform, we obtain r[n] = 22(-0.75)^n + 0.125(-2)^n.

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Answer:

54 degrees

Step-by-step explanation:

Full angle is 131 degrees

131-77=54

The rate of change of the radius is -9/(2π*99) inches/second.

The volume of a cylinder can be found with the equation V = πr^2h, where V is the volume, r is the radius, h is the height and π is a constant. We know that the volume is constant at 1318 cubic inches and we know that the height of the cylinder is increasing at a constant rate of 9 inches per second.

V = πr^2h

1318 = π * 99^2 * h

Now we can differentiate this equation with respect to time.

dV/dt = 2πr*dr/dt * h + πr^2 * dh/dt

where dV/dt is the rate of change of the volume, dr/dt is the rate of change of the radius and dh/dt is the rate of change of the height.

Now we know that dV/dt = 0, dh/dt = 9 and we know the value of r, we can substitute these values in the above equation and solve for dr/dt

0 = 2π * 99 * dr/dt * h + π * 99^2 * 9

dr/dt = -9/(2π*99) inches/second

The rate of change of the radius is -9/(2π*99) inches/second at the instant when the radius of the cylinder is 99 inches.

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The volume of oil exiting the pipe is approximately 100 cu in/hr, 2,400 cu in/day, and 1.39 cu ft/day when converting cu in/day to cubic feet per day.



To calculate the volume of oil exiting the pipe every hour, you would need to know the flow rate of the oil in cubic inches per hour. Let's assume the flow rate is 100 cubic inches per hour.To find the volume of oil exiting the pipe every day, you would multiply the flow rate by the number of hours in a day. There are 24 hours in a day, so the volume of oil exiting the pipe every day would be 100 cubic inches per hour multiplied by 24 hours, which equals 2,400 cubic inches per day.

To convert the volume from cubic inches per day to cubic feet per day, you would need to divide the volume in cubic inches by the number of cubic inches in a cubic foot. There are 1,728 cubic inches in a cubic foot. So, dividing 2,400 cubic inches per day by 1,728 cubic inches per cubic foot, we get approximately 1.39 cubic feet per day.

Therefore, the volume of oil exiting the pipe is approximately 100 cubic inches per hour, 2,400 cubic inches per day, and 1.39 cubic feet per day.

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The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

152.60 square units

Step-by-step explanation:

Area of the sector is expressed as;

A = theta/360 * Area of the circle

A =54/360 * 3.14*18²

A = 54/360 * 1,017.36

A = 54,937.44/360

A = 152.604

Hence the area of the sector to the nearest hundredth is 152.60 square units

Answer:

152.68

Step-by-step explanation:

Answer:

Yaa!!! you are right option A is your answer

Answer:

\(\frac{12}{35}\)

Step-by-step explanation:

We need to multiply the numerators, or the numbers on top of the bar (4 and 3) and the denominators, or the numbers below the bar (7 and 5) separately. This is shown below:

\(\frac{4}{7} *\frac{3}{5} =\frac{4 * 3}{7 * 5}\)

4 * 3 is equal to 12, and 7 * 5 is equal to 35. So our final answer is \(\frac{12}{35}\).

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Answer:

x=(k-14)/5

Step-by-step explanation:

subtract 14 to get

5x=k-14

Then divide by 5 to get

x=(k-14)/5

:D

Answer:

x = (k-14)/5

Step-by-step explanation:

5x + 14 = k

Subtract 14 from each side

5x + 14-14 = k-14

5x = k-14

Divide by 5

5x/5 = (k-14)/5

x = (k-14)/5