What is the difference between independent and dependent events

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Complete question is;

The paraboloid z = 5 − x − x² − 2y² intersects the plane x = 1 in a parabola. Find parametric equations for the tangent line to this parabola at the point (1, 2, -4).

Answer:

x = 1

y = (2 + t)

z = (-4 - 8t)

Step-by-step explanation:

We are given the paraboloid z = 5 − x − x² − 2y²

That it intersects the plane x = 1 and tangent to the point (1, 2, -4).

Thus, the position of the tangent is;

r_o = (1, 2, -4).

Direction vector is; v = (x, y, z)

Let's put 1 for x into the paraboloid.

z = 5 − 1 − 1² − 2y²

z = 3 - 2y²

Now, let's use vectors to find the parametric equation, where;

x = 1

y = t

z = 3 - 2t²

Thus, the Directional vector is now;

v = (1, t, 3 - 2t²)

Derivative of this directional vector is;. v' = (0, 1, -4t)

Putting 2 for t gives;

v' = (0, 1, -4(2))

v' = (0, 1, -8)

Multiplying this derivative by T gjves;

tv' = (0, t, -8t)

The final direction vector will be;

r = r_o + tv'

r = (1, 2, -4) + (0, t, -8t)

r = (1, (2 + t), (-4 - 8t))

Thus our parametric equation is;

x = 1

y = (2 + t)

z = (-4 - 8t)

Answer:

x² - 3x + 5 - [24÷(x+3)]

Step-by-step explanation:

1. Expand (x³ + 2x - 6x - 9)

            = x³ - 4x - 9

2. Divide [x³ - 4x - 9 by x+3]

            = x² + [(-3x^2-4x-9) ÷ (x+3)]

3. Divide [(-3x^2-4x-9) by (x+3)]

            = -3x + [(5x-9) ÷ (x+3)]

x² - 3x + [(5x-9) ÷ (x+3)]

4. Divide [(5x-9) ÷ (x+3)]

            = 5 + [(-24) ÷ (x+3)]

x² - 3x + 5 + [(-24) ÷ (x+3)]

= x² - 3x + 5 - [24 ÷ (x+3)]

The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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Answer:

C

Step-by-step explanation:

10/3 = 3.33

3.3 = 3.3

pie =3.14

square root of 8 =2.8

Answer:

4years

Step-by-step explanation:

Let the present age of Mark be x

Let the present age of Max be y

Five years ago

Mark = x-5

Max = y - 5

If mark was twice as old as Max, then;

x - 5 = 2(y-5)

x-5 = 2y - 10

x-2y = -10+5

x - 2y = -5 ... 1

In three years,

mark = x+3

Max = y+3

Now if Max's age will be 2/3 that of Mark, then;

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

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

3x + 9 = 2y+6

3x-2y = -3 .... 2

Solve 1 and 2 simultaneously

x - 2y = -5 ... 1

3x-2y = -3 .... 2

From 1: x = -5 + 2y

Substitute into 2:

3(-5+2y) - 2y = -3

-15 + 6y - 2y = -3

-15 + 4y = -3

4y = -3 + 15

4y = 12

y = 3

Recall thet x = -5+2y

x = -5+2(3)

x = -5 + 6

x = 1

The sum of their ages will be x+y

x+y = 1+3

x+y = 4

Hence the sum of their ages now is 4years

Answer:

C.

Step-by-step explanation:

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer:

5 quarters

2 nickels

Step-by-step explanation:

Answer:

5 quarters and 2 nickels.

Step-by-step explanation:

One quarter is equal to 25. 25x5=125. So, it would be 5 quarters because you wouldn't be able to go any farther without going over. One nickel is 5 and if you have 2 nickels you get 10. 10+125=135. So, there will be 2 nickels and 5 quarters.

Hope this helped!

Parallelogram have two pairs of opposite sides that are parallel and congruent.

In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.

For example, let's consider a parallelogram ABCD:

These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).

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Answer:

\(f(n) = f(n- 1) * 2\); \(f(1) = 3\)

Step-by-step explanation:

Given

\(1\ minute = 3\ friends\)

Every other minute

\(Each\ friend = 2\ other\ friends\)

Required

Determine the recursive function

Let the number of minutes be represented with n.

The initial condition can be represented as:

\(n = 1\)

\(f(1) = 3\) --- i.e. 3 friends initially at the first minute

At every other minutes:

\(n \ge 2\) i.e 2 minutes upwards

This means that n follows the following sequence

\(n \to n, n -1, n -2,n -3, n - 4,.....,4,3,2\)

Note that the difference between each term is 1.

This means that recursive function has to be defined backwards i.e.

\(f(n) = f(n- 1) * k\)

Where k = 2

i.e. The number of friends that received the video from each friend

So, we have:

\(f(n) = f(n- 1) * 2\)

Hence, the recursive function is:

\(f(n) = f(n- 1) * 2\); \(f(1) = 3\)

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

Therefore, the Panthers had a better overall record for the season, with a total of 212 points earned compared to the Cowboys' total of 173 points.

Step-by-step explanation:

To compare the measures of center, we can calculate the mean and median points earned by each team:

Panthers: Mean = 212/15 = 14.13 points, Median = 14 points

Cowboys: Mean = 173/15 = 11.53 points, Median = 10 points

Based on these calculations, we can see that the Panthers have a larger mean value of about 14.13 points compared to the Cowboys' mean value of about 11.53 points. However, the median value for both teams is less useful for comparison since they are only one point apart. Therefore, we can conclude that the Panthers had the better overall record for the season based on both the total points earned and their larger mean value.

So, the answer is Panthers; they have a larger mean value of about 14.8 points (Option C is incorrect as the mean value of Panthers is approximately 14.13 and not 14.8).

Answer:

  ∠DQE = 65°

Step-by-step explanation:

You want to know the measure of Angle DQE in the given figure.

Triangle ADE is inscribed in a semicircle, so is a right triangle. That makes acute angle AED complementary to acute angle EAD. The latter is given as 50°, so ...

  ∠AED = 90° -50° = 40°

We know that tangent line QE is perpendicular to diameter AE, so angle AEQ is a right angle. Segment ED divides that right angle into complementary angles, so ...

  ∠DEA +∠DEQ = 90°

  ∠DEQ = 90° -∠DEA = 90° -40° = 50°

A.pex angle DEQ in isosceles triangle DEQ being 50° means that the base angles QDE and DQE will have measure ...

  ∠DQE = (180° -50°)/2 = 130°/2

  ∠DQE = 65°

__

Alternate solution

Let angles DQE and QDE be represented by x. Then the sum of angles in quadrilateral ADQE is 360°:

  50° +(90+x)° +x° +90° = 360°

  230° +2x = 360° . . . . . . simplify

  x = 130°/2 = 65° . . . . . solve for x

Answer:

probability of bag one 62.5% for blue marbles green- 37.5%

probability of bag 2 66.67% for yellow and for blue 33.33%

he will probably get a blue and yellow marble

:)

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

Please check attachment for graph

Step-by-step explanation:

B. With hawaii airline = -0.300

Without hawaii airline = 0.197

With hawaii airline

EX = 475.3

EY = 157.17

XY = 8042.11

X² = 26883.55

Y² = 3159.375

The correlation coefficient

= 72378.99-74702.9/7737.421

= -2323.91/7737.421

= -0.300

Without hawaii airline

EX = 396.9

EY = 152.11

EXY = 7645.406

X² = 20736.99

Y² = 3133.772

= 790.789/4021.161

= 0.197

Answer:

361 ft²

Step-by-step explanation:

Each side of the square pool,

→ 19 ft

Formula we use,

→ side²

The area of the square pool will be,

→ side²

→ (19)²

→ 361 ft²

Hence, area of the pool is 361 ft².

Answer:

Area = 361 ft²

Step-by-step explanation:

Area of a square = \(x^2\)  (where \(x\) is the side length)

Given:

\(\begin{aligned}\implies \textsf{Area of the pool}&=\sf 19^2\\& = \sf 19 \times 19\\& = \sf 361\:ft^2\end{aligned}\)

Answer:

Option D. -1 and 0

Step-by-step explanation:

Answer:

D. -1 and 0

Step-by-step explanation:

The number is not a mixed number or improper so it is going to be less than one.

Answer:

The third option

Step-by-step explanation:

Since both perimeters are equal, they are equal to each other. You would have to work out the perimeter for each shape and make them equal to each other.

Answer:

Step-by-step explanation:

(x-2)(x-2)(x-4)

Answer:

-2 | 7

0 | -1

3 | -13

-1 | 3

Step-by-step explanation:

i just did this question

Answer:

How to Write Out USD 500.2 Dollars in Words: five hundred dollars and twenty cents.

I count on the best

Answer:

2 /3 +5 = 3

5.666667≠3

False

Step-by-step explanation:

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              Hi my lil bunny!

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Lets do this step by step.

~~~~~~~~~~~~~~~~~~~~

Multiply both sides of the equation by \(\frac{3}{2}\) .

\(\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5\)

Simplify both sides of the equation.

~~~~

Simplify \(\frac{3}{2} . \frac{2}{3} . x .\)

\(x = \frac{3}{2} . 5\)

Multiply \(\frac{3}{2} . 5\)

\(x = \frac{15}{2}\)

The result can be shown in multiple forms.

Exact Form: \(x = \frac{15}{2}\)

Decimal Form: \(x = 7.5\)

Mixed Number Form: \(x = 7\frac{1}{5}\)

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

You can notice that the speed of the object remains the same as the time increases, it means that the object has a constant speed. An example of this can be a car with a cosntant speed of 60km/h.

To show an object with a decreasing speed, you can draw:

The red line indicates that the speed of the object is decreasing, for example, when a car is decreasing its speed to take a close curve.

Number 4 (43º, 62º, 75º)

26 + 42 + 106 ≠ 180 so number 1 is not a triangle.

34 + 63 + 79 ≠ 180 so number 2 is not a triangle.

62 + 34 +80 ≠ 180 so number 3 is not a triangle.

43 + 62 + 75 = 180 so number 4 is a triangle.

Because only the angles are given and not the sides, there is an infinite number of triangles. The answer is number 4 (43º, 62º, 75º).

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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