what is the are in square feet of a 100 yard by 60 yard football field

The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.

When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.

In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.

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The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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The set of points on this graph is a relation but not a function

We know that every function can be a relation but every relation cannot be a function.

A relation means the connection between the input and the output.

A function means that for every input there should only be one output.

Here, we have the data as:

(2,5), (1,2), (3,4), (3, 1), (6,5) and  (5,3)

We can say that it is a relation as for every input, there is an output.

But, it is not a function.

This is because the input 3 has 2 outputs as 1 and 4 which is not possible in a function.

Therefore, the set of points on this graph is a relation but not a function.

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The amount of cheese which will be required for the dilated bagel as for the original is half and hence is 0.5.

According to the question;

Assume the required cream cheese for the original is 1 unit.

Hence, upon Dilation, the amount of cream cheese required is; 0.5 times the amount used for the original.

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The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

Results

Step-by-step explanation:

Where are the results I cant help u

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The equation is given in "slope-intercept" form.

  y = mx + b

where m is the slope, and b is the y-intercept.

__

For graphing, it is usually convenient to start with the y-intercept. The value of 'b' in your equation is +1, so the graph will go through the point y=1 on the y-axis. That point's coordinates are (0, 1).

The value of m represents the slope, or "rise"/"run" of the line. A slope of -2/3 means the line "rises" -2 units for each "run" of 3 units to the right. Then another point on the graph will be 3 units to the right of the y-axis, and 2 units down from y = 1. That point is (3, -1).

The line is drawn through these points you found on the graph.

Answer: 1200 cherries.

Step-by-step explanation:

If 240 cherries are need for 3 pies, multiply 240 by 5 to get the answer.

Your answer is 1200 cherries.

Greg needs 1200 cherries to make 15 perfect cherry pies.

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

The pattern is multiplying by 2.

Next three terms: 64,128,256

Step-by-step explanation:

4,8,16,32

To get from 4 to 8 we can multiply by 2.

To get from 8 to 16 we can multiply by 2.

To get from 16 to 32 we can multiply by 2.

So the pattern is multiplying by 2.

To find the next three terms:

32*2=64

64*2=128

128*2=256

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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The diameter of circle A is 4.8. The correct option is the second option- 4.8

From the question, we are to determine the diameter of circle A

From the given information,

Circle A is dilated by a scale factor of 2.5 to form circle B

That is,

If the diameter of circle A is d, then the diameter of circle B will be 2.5d

Also, from the given information,

Diameter of circle B = 12

Then, we can write that

2.5d = 12

∴ d = 12/2.5

d = 4.8

Hence, the diameter of circle A is 4.8. The correct option is the second option- 4.8

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Answer:

0.225

Step-by-step explanation:

5 + 7 + 8 = 20 crayons.

we want 4 blue crayons from 15 draws. p(blue) = 5/20.

p(4 from 15 draws) = 0.225

Answer:

−4 1/4 = −4 +1/4

= −4/1+1/4

=(−4/1×4/4)+1/4

=−16/4 + 1/4= −17/4

So, -17 divided by 4 equals

-4.25

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

35 cm

Step-by-step explanation:

Answer:

0.35 meters^2 or 35 cm^2

Step-by-step explanation:

we break up the shape and the problem into two parts.

we will begin by finding the area of the triangle first (or you could find the square's area first) and we know the area formula for a triangle is

Area (triangle) = (1/2) base x height

height = 0.04 meters or 4cm

base = 0.05 meters or 5 cm

therefore the area is:

(1/2) (5cm)(4cm) = 10 cm^2

now we find the area of the square which is very easy. it is simply base times the height (b x h)

Area (square) = 5cm x 5cm = 25cm^2

finally, we add the total area

Area (total) = Area (square) + Area (triangle) = 10 cm^2 + 25 cm^2

= 35 cm^2

Answer:

$34

Step-by-step explanation:

50% is half of 100%

(Because 50% x 2 = 100%)

Thus, half the money ($68) to find 50%.

So, 68÷2 = 34

Final answer is $34

Or

50/100 x $68 =$34

Hope this helps!

You have two events:

A: pick an ace

B: pick a club

A suffled standard has: 52 cards.

4 aces

13 clubs

As the events A and B are not mutually exclusive (can happen at the same time) the probability is:

Probability of A: #aces/#cards = 4/52

Probability of B: #clubs/#cards = 13/52

Probability of A and B: #ace clubs/#cards = 1/52

Then the probability of pick an ace or a club is:

Then, the probability is 4/13

The height of the plane above the ocean is approximately 15,000 meters to the nearest meter.

The angle of depression is an angle formed between a horizontal line (such as the ground, ocean surface, or any other reference plane) and a line of sight from an observer looking downward towards an object or point of interest that is located below the observer's line of sight.

According to the given information:

The angle of depression is the angle formed between the horizontal line (such as the ocean's surface) and the line of sight from an observer looking downward to an object (such as the island). In this case, the angle of depression is given as 45 degrees.

Given:

Angle of depression = 45 degrees.

Distance from airplane to island = 15,000 meters.

To find the height of the plane, we can use trigonometry. The tangent function is commonly used to relate angles of depression to the height of an object above the horizontal.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle of depression is the height of the plane, and the side adjacent to the angle is the distance from the airplane to the island.

Using the tangent function:

tan(angle of depression) = height of plane/distance to the island

Plugging in the given values:

tan(45 degrees) = height of plane / 15,000 meters

We can now solve for the height of the plane:

height of plane = tan(45 degrees) * 15,000 meters

Using a calculator, we find:

height of plane = 15000 * tan(45 degrees) ≈ 15000 meters (rounded to the nearest meter)

So, the height of the plane above the ocean is approximately 15,000 meters to the nearest meter.

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Using supplementary angle theorem

As BD bisects AC

So ∆AEC\(\cong \)∆DEC(SAS)

Also similarly

Hence it's a parallelogram

Given: BD bisects AC and ∠CBE≅∠ADE.  ABCD is a proved to be a parallelogram by proving that opposite sides are parallel to each other.

A parallelogram is a quadrilateral with opposite sides parallel.

Given in the question,

AE = EC

∠CBE = ∠ADE

result 1:

∠CBE = ∠ADE : alternate interior angles

Thus, BC is parallel to AD.

In triangles BCE and ADE,

∠CBE = ∠ADE (given)

AE = EC (given)

∠BEC = ∠DEA (opposite angles)

triangles BCE and ADE are congruent by AAS congruence.

Implying, BE = ED (cpct)

In triangles BEA and CED,

AE = EC (given)

BE = ED (cpct)

∠BEC = ∠DEA (opposite angles)

triangles BEA and CED are congruent by SAS congruence.

∠ECD = ∠EAB (cpct)

Result 2:

∠ECD = ∠EAB : alternate interior angles

Thus, BA is parallel to CD.

Since, both opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

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Answer:

After 121 passes, there will be 11 cups facing up

Step-by-step explanation:

Given that:

Peter initially  lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.

We can have an inequality ; i.e 1 ≤ n ≤  121; if n represents the divisor including n itself for which n  = odd number. Thus at the end of this claim, the cup will be facing up.

On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)

For each divisor on the ith pass of n;

\(i \ th \ pass \ = \ n \ \to \ p |n\)  since we are dealing with possibility of having an odds number:

Thus; \(p =i\) and \(i^2 = n\)  where ; n = perfect square.

Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes

Answer:

B y ≥ 4x + 2

Step-by-step explanation:

1. find slope of the line: (y² - y¹) / (x² - x¹)

(0, 2) and (-1, -2)

(-2 - 2) / (-1 - 0) = -4 / -1 = 4

y = 4x + 2*

*+2 because that is the y-intercept as shown by point (0, 2)

2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >

3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥

4. final equation: y ≥ 4x + 2

\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 2x² + x - 3

The rate of change of the function for the interval between 0 to 2 is calculated as,

Average rate = [f(2) - f(0)] / [2 - 0]

Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2

Average rate = 10 / 2

Average rate = 5

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

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Answer:

Answer 4

Step-by-step explanation:

Rise 9, Run 8

Answer: 2 is the answer

Step-by-step explanation:

Answer:

B.64 in.³

Step-by-step explanation:

the formula for the volume of cube is a³

Separate the variables.

\((x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx\)

Integrate both sides. On the right, substitute \(u=x^2+11\) and \(du=2x\,dx\).

\(\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u\)

\(\ln|y| = \frac12 \ln|u| + C\)

\(\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C\)

\(e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}\)

\(\boxed{y = C\sqrt{x^2+11}}\)

Using separation of variables, the solution to the differential equation is:

y = ksqrt(x² + 11)

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is:

(x² + 11)y' = xy

Applying separation of variables, we have that:

y'/y = x/(x² + 11)

\(\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}\)

\(\ln{y} = \frac{\ln{x^2 + 11}}{2} + K\)

\(\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K\)

\(\ln{y} = \ln{\sqrt{x^2 + 11}} + K\)

Hence the solution is:

y = ksqrt(x² + 11)

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