which of the following statistic measures the most frequently occuring value in a set of data A.) range B.) mean C.) mode D.) median ​

Answer: (A) 30%

Step-by-step explanation:

Given : The probability that a bird will lay an egg =0.75

The probability that the egg will hatch  =0.50

Now, the probability that the egg will lay an egg and hatch =

Also,The probability that the chick will be eaten by a snake before it fledges =0.20

Then, the probability that the chick will not  be eaten by a snake before it fledges : 1-0.20=0.80

Now, the probability that a parent will have progeny that survive to adulthood will be :-

Hence, the probability that a parent will have progeny that survive to adulthood =  30%

Answer:

1

Step-by-step explanation:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Rotate ‘r’ anticlockwise to form a 90° or 450° angle with the positive x-axis.

The sin of 450 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 450° = y = 1

Answer:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Answer:

The answer is

14 units

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(3, 5.25) and (3, –8.75)

The distance between them is

We have the final answer as

14 units

Hope this helps you

Answer:

1) x = 75°

2) x = 180° - 2×40° = 180° - 80° = 100°

3) x = 180° - 2×73° = 180° - 146° = 34°

4) x = (180° - 122°) : 2 = 58° : 2 = 29°

5) x = 90° - (180° - 80°) : 2 = 90° - 100° : 2 = 90° - 50° = 40°

Answer:

-937.5π

Step-by-step explanation:

F (r) = r = (x, y, z) the surface equation z = 3(x^2 + y^2) z_x = 6x, z_y = 6y the normal vector n = (- z_x, - z_y, 1) = (- 6x, - 6y, 1)

Thus, flux ∫∫s F · dS is given as;

∫∫ <x, y, z> · <-z_x, -z_y, 1> dA

=∫∫ <x, y, 3x² + 3y²> · <-6x, -6y, 1>dA , since z = 3x² + 3y²

Thus, flux is;

= ∫∫ -3(x² + y²) dA.

Since the region of integration is bounded by x² + y² = 25, let's convert to polar coordinates as follows:

∫(θ = 0 to 2π) ∫(r = 0 to 5) -3r² (r·dr·dθ)

= 2π ∫(r = 0 to 5) -3r³ dr

= -(6/4)πr^4 {for r = 0 to 5}

= -(6/4)5⁴π - (6/4)0⁴π

= -937.5π

Final answer:

To set up a doubleintegral for calculating the flux of the vector field through the given surface, parameterize the surface using the equation provided and the given condition. Calculate the cross product of the partial derivatives of x and y to find the normal vector. Finally, set up the double integral for the flux using the vector field and the normal vector.

Explanation:

To set up a double integral for calculating the flux of the vector field through the given surface, we first need to parameterize the surface. Given the equation of the surface z = 3(x^2 + y^2) and the condition x^2 + y^2 ≤ 25, we can parameterize the surface as follows:

x = rcosθ, y = rsinθ, z = 3r^2

We can now calculate the cross product of the partialderivatives of x and y to find the normal vector, which is: n = (3rcosθ, 3rsinθ, 1)

Finally, the double integral for calculating the flux through the surface is:

∬ F · n dA = ∬ (x, y, z) · (3rcosθ, 3rsinθ, 1) dA

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The cubic regression function of the points (1,-1), (2,-13), (3,-45), (-1,11) is y = -2x³ + 2x² - 4x + 3

How to determine the function?

The points are given as:

(x,y) = (1,-1), (2,-13), (3,-45), (-1,11)

A cubic regression function is represented as:

y = ax³ + bx² + cx + d

Next, we determine the cubic function using a graphing calculator.

From the graphing calculator, we have the following coefficients:

• a = -2
• b = 2
• c = -4
• d = 3

Recall that:

y = ax³ + bx² + cx + d

So, we have:

y = -2x³ + 2x² - 4x + 3

Hence, the cubic regression function of the points is y = -2x³ + 2x² - 4x + 3

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