Let X be a binomial random variable with the following parameters: 1 n = 4 and р x = 0,1, ..., n 4 Find the probability distribution of the random variable Y = X2 + 1 Problem 4 (20 points) For the random variable X , probability density function is given as f(x) = { 2) 4.1, 0

Given:

Grocery store located at point (5,-4).

Park is located at point (-5,4).

Paula's house is halfway between the Grocery store and park.

School is halfway between the Paula's house and park.

To find:

Ordered pair for the school.

Solution:

Formula used:

\(\text{Midpoint}=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

Paula's house is halfway between the Grocery store and park. It means the location of Paula's house is the midpoint of (5,-4) and (-5,4).

\(\text{Paula's house}=\left(\dfrac{5+(-5)}{2},\dfrac{(-4)+4}{2}\right)\)

\(\text{Paula's house}=\left(\dfrac{0}{2},\dfrac{0}{2}\right)\)

\(\text{Paula's house}=\left(0,0\right)\)

So, the Paula's house is located at (0,0).

School is halfway between the Paula's house and park. It means the location of the school is the midpoint of (0,0) and (-5,4).

\(\text{School}=\left(\dfrac{0+(-5)}{2},\dfrac{0+4}{2}\right)\)

\(\text{School}=\left(\dfrac{-5}{2},\dfrac{4}{2}\right)\)

\(\text{School}=\left(-2.5,2\right)\)

Therefore, the correct option is B.

Answer:

13 buses are required.

Step-by-step explanation:

To find the number of minibuses required, take the total number of fans and divide by the number of fans each bus holds.

220 /18

12 2/9

We need to round up to make sure all the fans get on a bus.

13 buses are required.

Answer:

16 lbs

Step-by-step explanation:

total of apples = 1/4 + 3/8 = 2/8 + 3/8 = 5/8

then 10 x 8/5 = 16

Answer: \((x+3)^2+(y-6)^2 = 36\\\\\)

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

Explanation:

If you apply the midpoint formula to the given points, you should find the midpoint is (3,6). This point represents the center of the circle. This means (h,k) = (3,6).

The radius is r = 6 because this is the distance from the center to either given endpoint. Either count out the spaces or use subtraction of the x coordinates. This works because the y coordinates are all the same.

Use those h, k and r values to plug them into the equation below

\((x-h)^2+(y-k)^2 = r^2\\\\(x-(-3))^2+(y-6)^2 = 6^2\\\\(x+3)^2+(y-6)^2 = 36\\\\\)

which represents the equation of the circle we're after.

The graph is below.

If Judy's refund is $535, to pay for furniture worth $800, she will have to come up with $265, which is the difference.

The difference is the result of the subtraction operation.

The subtraction operation is one of the four basic mathematical operations.

Subtraction operations involve the minuend, subtrahend, the subtraction operator (-), the difference, and the equal symbol (=).

The cost of furniture = $800

Expected credit refund = $535

The difference between the cost and refund = $265 ($800 - $535)

Thus, Judy will bring $265 to make up for the purchase of the furniture.

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From the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.

From the given equations, the equation which has no solution has to be found out. When the value, does not equate for the expression, then the expression has no solution.

The first equation given in the problem is,

\(6 (x +2) > x-3\)

Solve it further,

\(6 x +12 > x-3\\6x-x > -3-12\\5x > -15\\x > -3\)

The second equation given in the problem is,

\(3+ 4x \leq 2 (1 +2x)\)

Solve it further,

\(3+ 4x \leq 2 +4x\\4x- 4x \leq 2-3\\0\leq-1\)

The value of 0 is greater than the number -1. Thus, this inequality has no solution.

The option 3 and 4 has a solution. Hence, from the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

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I think it's C I'm pretty sure u have to multiply

Billy watches tv for 7,700 minutes. Hence option c is correct.

Billy watches 7 seasons of a TV show. Each season includes 22 episodes
and each episode is 50 minutes long.

using mathematics operators it deals with numbers of operations according to the statements.

Here,
Total number of minutes bill watches tv = 7*22*50
= 7,700 minutes

Thus, Billy watches tv for 7,700 minutes.

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intersection of lines n and m is D

The equation to calculate the profit is P(x) = 100x - 800

Given that

Cost price = 350

Selling price = 450

Garage cost = 800 per month

Represent the number of chairs with x

So, we have

C(x) = 350x + 800

S(x) = 450x

So, the profit function is

P(x) = 450x - 350x - 800

P(x) = 100x - 800

For the number of pushchairs to break even, we set the profit to 0

So, we have

100x - 800 = 0

Evaluate

x = 8

If John were to sell 23 pushchairs, his profit/loss would be

P(23) = 100 * 23 - 800

P(23) = 1500

Hence, his profit would be £1500

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Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y \(+\) 6| \(=\) 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

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The approximate angle between vectors a and b is 31 degrees.

To find the angle between two vectors, you can use the dot product formula:

θ = arccos((a · b) / (|a| |b|))

Let's calculate the angle between vectors a and b:

a = 6i - 3j + k

b = 7i - k

To find the dot product (a · b), we multiply the corresponding components and sum them up:

(a · b) = (6)(7) + (-3)(0) + (1)(-1) = 42 + 0 - 1 = 41

To find the magnitudes (|a| and |b|), we calculate the square root of the sum of the squares of the components:

|a| = \(\sqrt((6^2) + (-3^2) + (1^2)) = \sqrt(36 + 9 + 1) = \sqrt(46)\)

|b| = \(\sqrt((7^2) + 0 + (-1^2)) = \sqrt(49 + 0 + 1) = \sqrt(50)\)

Now we can substitute the values into the formula to find the angle:

θ = arccos(41 / (\(\sqrt(46) * \sqrt(50)\)))

Calculating the approximate value:

θ ≈ arccos(41 / (6.782329983 * 7.071067812)) ≈ arccos(41 / 47.995) ≈ arccos(0.85425) ≈ 31.11 degrees

Therefore, the approximate angle between vectors a and b is 31 degrees.

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Answer:

700

Step-by-step explanation:

Answer:

$81.10

Step-by-step explanation:

Profit = total revenue - total cost

1 liter = 1000 mm

7 liter = 7000 mm

Number of jars needed = 7000 / 250 = 28

total revenue = number of jars sold x price per jar

28 x  $8.95 = 250.60

Total cost = $155.50 + (0.5 x 28) = 169.50

Profit = 250.60 -  169.50 = 81.10

Answer:

5/6

Step-by-step explanation:

2/3×2=4/6

1/6+4/6=5/6

Answer:

1/6 + 2/3 = 5/6

Step-by-step explanation:

When adding fractions you have to find a  common denominator(which is the bottom number of a fraction).  So 1/6 and 2/3 do not have a common denominator so you have to multiply 2/3 by 2/2 to get a 6 in the  denominator.  2/3 x 2/2 =  4/6.  The you just  add the two.  4/6 + 1/6 = 5/6

Answer:

AB || CE, so we have triangle DEO, two of whose angles are 100° and 26° (from point D, draw DE such that CD + DE = CE intersects BO). The third angle of this triangle measures 54°, so

x = 180° - 54° = 126°.

Compute the differential for both sides:

4y - 3xy + 8x = 0

→   4 dy - 3 (y dx + x dy) + 8 dx = 0

Solve for dy :

4 dy - 3y dx - 3x dy + 8 dx = 0

(4 - 3x) dy + (8 - 3y) dx = 0

When x = 0, we have

4y - 3•0y + 8•0 = 0   →   4y = 0   →   y = 0

and with dx = 0.05, we get

(4 - 3•0) dy + (8 - 3•0) • 0.05 = 0

→   4 dy + 0.4 = 0

→   4 dy = -0.4

→   dy = -0.1

The total area of both the circles as calculated from the data given is found out to be as 246.64 cm² .

The formula to calculate the area of a circle is,  (pi)r² where r = radius.

Therefore, the area of the first circle is found out to be as ,

22/ 7 x 7.8 x 7.8

=191.2 cm²

and the area of second circle will be ,

22/7 x 4.2 x 4.2

= 55.44 cm²

Therefore, the sum of the areas of the circle will be ,

191.2 + 55.44

= 246.64 cm² .

The area of a shape is known as the space occupied by it in tw dimensional space.

Every figure has a specific area and can be found by using unique formulas. The formula to calculate the area of a circle is  (pi)r².

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The chord joining the vertices of an ellipse is called the major axis, and its midpoint is the center of the ellipse.

The major axis of an ellipse is the chord that passes through the two vertices of the ellipse. It is the longest chord and its length is equal to twice the length of the semi-major axis of the ellipse. The midpoint of the major axis is the point that divides the major axis into two equal segments, and it coincides with the center of the ellipse. The center of the ellipse is the point of intersection of the major and minor axes, and it is equidistant from all points on the ellipse.

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Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

78% of the students in the sample stated they would prefer to start their own business rather than work for someone else.

The sample proportion is a statistic that measures the proportion of individuals in a sample who have a particular characteristic of interest. In this case, we are interested in the proportion of college students who stated they would prefer to start their own business rather than work for someone else.

The sample proportion can be calculated as the number of individuals in the sample who have the characteristic of interest (in this case, preferring to start their own business) divided by the total number of individuals in the sample. Using the information provided in the question, we have:

Number of individuals in the sample who prefer to start their own business: 78

Total number of individuals in the sample: 100

So the sample proportion is:

sample proportion = 78/100 = 0.78

Rounding this to two decimal places, we get:

sample proportion ≈ 0.78

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The equation of u when it is the subject is u = 9/t - 12at

From the question, the original equation is given as

9 = 12at2 + ut

Next, we rewrite the equation to show the exponents

This is represented as

9 = 12at² + ut

To solve further, we simply isolate the variable term ut

This is done by subtracting 12at²  from both sides of the equation

So, we have the following equation

9 - 12at² = 12at² - 12at² ut

Evaluate the like terms in the equation

So, we have

9 - 12at² = ut

Lastly, divide both sides of the equation by t

So, we have

(9 - 12at²)/t = ut/t

Evaluate the quotients

9/t - 12at = u

Make us the subject

u = 9/t - 12at

Hence, the solution for the equation for u is u = 9/t - 12at

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Answer:7-11

Step-by-step explanation:I am not sure but I think you just put 7 and 11 hope this helps but have a answer on the side just in case I am wrong

\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Factors.

1.) x^2-3x-10 = (x-5) (x+2)

2.)x^2-3x-18 = (x-6) (x+3)

(a) Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

(b) Where both players are indifferent between their available strategies.

(c)  The normal form representation of the game is above.

(d) No player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

(a) To derive the best response functions, we need to find the strategies that maximize the payoffs for each player given the mixed strategy of the other player.

Player Row's best response function:

If Player Column chooses L with probability q, Player Row's expected payoff for choosing U is 0q + 2(1-q) = 2 - 2q.

If Player Column chooses R with probability 1-q, Player Row's expected payoff for choosing U is 0*(1-q) + 1*q = q.

Therefore, Player Row's best response is given by:

BR_Row(q) = { U if q < 1/3, D if q > 1/3 (indifferent if q = 1/3)

Player Column's best response function:

If Player Row chooses U with probability p, Player Column's expected payoff for choosing L is 0p + 2(1-p) = 2 - 2p.

If Player Row chooses D with probability 1-p, Player Column's expected payoff for choosing L is 0*(1-p) + (-1)*p = -p.

Therefore, Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

Plotting the best response functions on a graph with p on the horizontal axis and q on the vertical axis will result in two line segments: BR_Row(q) is horizontal at U for q < 1/3 and horizontal at D for q > 1/3, while BR_Column(p) is vertical at L for p < 1/2 and vertical at R for p > 1/2.

The two segments intersect at the point (p, q) = (1/2, 1/3).

(b) To find the Nash equilibria, we look for the points where the best response functions intersect. In this case, the only Nash equilibrium is at (p, q) = (1/2, 1/3), where both players are indifferent between their available strategies.

Now let's move on to the rock-paper-scissors-lizard game:

(c) The normal form representation of the game can be written as follows:

    R    P    S    L

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

R | 0,0 -1,1 1,-1 1,-1

P | 1,-1 0,0 -1,1 1,-1

S | -1,1 1,-1 0,0 -1,1

L | -1,1 -1,1 1,-1 0,0

(d) To find the Nash equilibria, we look for any strategy profiles where no player can unilaterally deviate to improve their payoff.

In this game, there are no pure strategy Nash equilibria since each strategy can be countered by another strategy with a higher payoff.

However, there is a mixed strategy Nash equilibrium where each player chooses their actions with equal probabilities: r = p = s = l = 1/4.

In this case, no player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

In summary, the rock-paper-scissors-lizard game has a unique mixed strategy Nash equilibrium where each player randomly chooses their actions with equal probabilities.

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Answer:

Step-by-step explanation:

x + 2) = 2(x + 2)2 - 6(x + 2)

           = 2(x2 + 4x + 4) - 6(x + 2)

           = 2x2 + 8x + 8 - 6x - 12

           = 2x2 + 2x - 4

The correct statement for the given quadratic equation x² - 6x + 2 = 0 is the graph of the quadratic equation has a minimum value. Hence, correct option is C.

The graph of the quadratic equation has a maximum or minimum value depending on the sign of the leading coefficient. In this case, the leading coefficient is positive, which means the graph of the quadratic equation opens upwards and has a minimum value.

The extreme value is not at the point (7,-3) or (3,-7) because those points are not on the graph of the equation.

The solutions of the equation can be found using the quadratic formula

x = [-(-6) ± √((-6)² - 4(1)(2))] / (2(1))

x = [6 ± √(28)] / 2

x = [6 ± 2√7] / 2

x = 3 ± √7

Therefore, the correct statement is C.

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Answer:

0

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

The y is the variable.

There’s a imaginary -1 in front of the y