given a circle in the complex plane with a diameter that has endpoints at:-12 − i and 18 15ifind the center of the circle.3 7ifind the radius of the circle.17 units

On the probability, expected value and variance :

a) The probability that X < 29 is given by:

P(X < 29) = P(X = 0) + P(X = 1) + ... + P(X = 28)

The probability of each of these events is given by the binomial distribution:

[tex]P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}[/tex]

where n = 64, p = 0.47, and k = 0, 1, ..., 28.

Plugging in these values:

[tex]P(X < 29) = \binom{64}{0} (0.47)^0 (1 - 0.47)^{64 - 0} + \binom{64}{1} (0.47)^1 (1 - 0.47)^{64 - 1} + ... + \binom{64}{28} (0.47)^{28} (1 - 0.47)^{64 - 28}[/tex]

≈ 0.000013

b) The probability that 28 SXS 31 is given by:

P(28 SXS 31) = P(X = 28) + P(X = 29) + P(X = 30) + P(X = 31)

Plugging in the values from the binomial distribution:

[tex]P(28 SXS 31) = \binom{64}{28} (0.47)^{28} (1 - 0.47)^{64 - 28} + \binom{64}{29} (0.47)^{29} (1 - 0.47)^{64 - 29} + \binom{64}{30} (0.47)^{30} (1 - 0.47)^{64 - 30} + \binom{64}{31} (0.47)^{31} (1 - 0.47)^{64 - 31}[/tex]

≈ 0.00414

c) The probability that X = 31 is given by:

[tex]P(X = 31) = \binom{64}{31} (0.47)^{31} (1 - 0.47)^{64 - 31}[/tex]

≈ 0.000016

d) The expected value of X is given by:

E(X) = np

where n = 64 and p = 0.47.

E(X) = 64 (0.47) = 30.08

e) The variance of X is given by:

Var(X) = np(1 - p)

Var(X) = 64 (0.47) (1 - 0.47) = 11.84

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Answer:

12870ways

Step-by-step explanation:

Combination has to do with selection

Total members in a tennis club = 15

number of men = 8

number of women = 7

Number of team consisting of women will be expressed as 15C7

15C7 = 15!/(15-7)!7!

15C7 = 15!/8!7!

15C7 = 15*14*13*12*11*10*9*8!/8!7!

15C7 = 15*14*13*12*11*10*9/7 * 6 * 5 * 4 * 3 * 2

15C7  = 15*14*13*12*11/56

15C7 = 6,435 ways

Number of team consisting of men will be expressed as 15C8

15C8 = 15!/8!7!

15C8 = 15*14*13*12*11*10*9*8!/8!7!

15C8 = 15*14*13*12*11*10*9/7 * 6 * 5 * 4 * 3 * 2

15C8 = 6,435 ways

Adding both

Total ways = 6,435 ways + 6,435 ways

Total ways = 12870ways

Hence the required number of ways is 12870ways

Answer:

160 days

Step-by-step explanation:

800 divided by 5 equal 160

Answer:

your answer is 160 days

Step-by-step explanation:

800÷5=160 days

I hope this helps

have a nice day/night

mark brainliest, please :)

Answer:

a(10) = 170

Step-by-step explanation:

Given that,

The nth term fo the sequence is :

a(n) =  n² + 7n

We need to find the 10th term of the sequence.

Put n = 10 in the above sequence,

a(10) =  (10)² + 7(10)

= 100 + 70

= 170

So, the 10th term of the sequence is 170.

Answer:

8/3

Step-by-step explanation:

1. 2 ÷ 3 = .66

.66 · 4 = 2.6

2. 4 × 2/3 =

4/1 × 2/3 = 8/3

good luck, i hope this helps :)

Answer:

x=-20

Step-by-step explanation:

3x+178=6x+238

-3x=60

x=-20

Answer:

Step-by-step explanation: so first you got to distribute the on both sides so like the 2 and the ten from there you just eliminate and do it like normal. I’m sorry I’m bad at at explaining it but I hoped it helped some how :)

To determine the scale factor relationship between the pizzas based on their diameters, we need to compare the sizes of the pizzas. The scale factor represents the ratio between the corresponding measurements of two similar objects.

In this case, we would compare the diameters of the pizzas. The scale factor can be calculated by dividing the diameter of one pizza by the diameter of another pizza. For example, if Pizza A has a diameter of 12 inches and Pizza B has a diameter of 8 inches, the scale factor between them would be: Scale Factor = Diameter of Pizza A / Diameter of Pizza B = 12 inches / 8 inches = 1.5. Therefore, the scale factor relationship between the pizzas is 1.5. This means that the diameter of Pizza A is 1.5 times larger than the diameter of Pizza B.

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Answer:

d

Step-by-step explanation:

3x times 5x equals 15x^2

3x times -5 equals -15x

---> 15x^2 - 15x

In a group of 700 people, there must be at least two individuals who have the same first and last initials.

What is combinatorics?

Combinatorics is a branch of mathematics that focuses on counting, arranging, and organizing objects or elements in a systematic and discrete manner. It deals with the study of combinations, permutations, and other mathematical structures related to discrete objects.

To determine whether there must be two people with the same first and last initials in a group of 700 people, we can use the Pigeonhole Principle.

The Pigeonhole Principle states that if we have more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. In this case, the pigeons represent individuals with different initials, and the pigeonholes represent the unique combinations of first and last initials.

In the given scenario, we have [tex]700[/tex] people and a finite number of possible combinations of first and last initials. Let's consider the number of possible combinations of initials. Since we have 26 letters in the English alphabet, there are 26 choices for the first initial and 26 choices for the last initial. This gives us a total of [tex]26 * 26 = 676[/tex] possible combinations.

Now, since we have 700 people, and the number of possible combinations (676) is less than the number of people, it is not possible for each person to have a unique combination of initials. By the Pigeonhole Principle, at least one combination of initials must be shared by more than one person.

Therefore, in a group of 700 people, there must be at least two individuals who have the same first and last initials.

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Answer:

Is this an actual question

a. The parallelogram R is degenerate, consisting of a single point (4, 0).

b. The integral ∬_R (x - 2y) dA over the degenerate parallelogram R evaluates to 0.

a. To evaluate the integral ∬_R (x - 2y) dA, where R is the parallelogram enclosed by the lines -2y = 0, x - 2y = 4, 3x + y = 1, and 3x + y = 8, we can make an appropriate change of variables to simplify the integral. Here's how to do it step by step:

Identify the vertices of the parallelogram R by finding the intersection points of the given lines. Solving the system of equations:

-2y = 0 (equation 1)

x - 2y = 4 (equation 2)

3x + y = 1 (equation 3)

3x + y = 8 (equation 4)

From equation 1, we have y = 0. Substituting this into equation 2, we get x = 4. Therefore, one vertex of the parallelogram is (4, 0).

Next, solving equations 3 and 4, we find another intersection point by equating the expressions for y:

1 - 3x = 8 - 3x

-3x + 1 = -3x + 8

1 = 8

This is a contradiction, so equations 3 and 4 are parallel lines that do not intersect. Therefore, the parallelogram R is degenerate and only consists of a single point (4, 0).

b. Make an appropriate change of variables to simplify the integral. Since the parallelogram R is degenerate and consists of a single point, we can use a change of variables to transform the integral to a simpler form. Let's introduce new variables u and v, defined as follows:

u = x - 2y

v = 3x + y

The Jacobian determinant of the transformation is calculated as follows:

|Jacobian| = |∂(x, y)/∂(u, v)|

= |∂x/∂u ∂x/∂v|

= |1 -2|

= 2

c. Express the integral in terms of the new variables. We need to find the limits of integration in terms of u and v. Since the parallelogram R is degenerate and consists of a single point, the limits of integration are u = x - 2y = 4 - 2(0) = 4 and v = 3x + y = 3(4) + 0 = 12.

The integral becomes:

∬_R (x - 2y) dA = ∫∫_R (x - 2y) |Jacobian| dudv

= ∫∫_R (x - 2y) (2) dudv

= 2∫∫_R (u) dudv

Evaluate the integral. Since R is degenerate and consists of a single point (4, 0), the integral becomes:

2∫∫_R (u) dudv = 2u ∫∫_R dudv = 2u(Area of R)

The area of a degenerate parallelogram is zero, so the integral evaluates to:

2u(Area of R) = 2(4)(0) = 0.

Therefore, the value of the integral ∬_R (x - 2y) dA over the given degenerate parallelogram R is 0.

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Answer:

Step-by-step explanation:

Answer:

It will cost $36.38 to travel 8.9 miles.

Step-by-step explanation:

In order to get how much it will cost to travel 8.9 miles, you need to first set up a linear equation (in slope-intercept form, which is [tex]y=mx+b[/tex] ). You can do this with what the problem has given us. Since there's a flat fee of $3, that is the y-intercept or the [tex]b[/tex] slope-intercept form. Then there is $3.75 added for every additional mile traveled, making it the slope or the [tex]m[/tex] in slope-intercept form. That makes the equation look like:

[tex]y=3.75x+3[/tex]

The [tex]x[/tex] in that equation represents how far you traveled. Therefore in order to find out 8.9 miles, plug in 8.9 for [tex]x[/tex].

[tex]y=3.75(8.9)+3[/tex]

Simply solve the equation and you will have how much it will cost to travel 8.9 miles.

[tex]y=33.375+3[/tex]

Now add the like terms:

[tex]y=36.375[/tex]

Since it needs to be rounded to the nearest cent, you will round to the nearest tenth:

[tex]y=36.38[/tex]

Therefore, it will cost $36.38 to travel 8.9 miles.

Answer:

definatly not infinitely it should be only one correct answer so false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

-53 + 2+ 2x + 4 = ax + b

-47 + 2x = ax + b

Since there is 3 variables you need 3 equations which you don't have. After simplifying there is nothing else you can do.

Answer:

First find the sum of 15 n-1

Step-by-step explanation:

then you can continue to 2n-1

Answer:

its c or a but i think its mostly a

Step-by-step explanation:

Answer:

The correct answer is A

Step-by-step explanation:

The Economy of Oceania largely depends on trade and tourism but trade specifically  

Answer:

a

Step-by-step explanation:

Answer:

1.78 > 0.88

Because you would always put the sign on the bigger number.

Answer:

1.78 > 0.88

Step-by-step explanation:

It is > hope this helped.

a) Probability that the mouse weighs less than 405 grams: 0.8461

b) Probability that the mouse weighs more than 461 grams: 0.0062

c) Probability that the mouse weighs between 406 and 461 grams: 0.8302

d) It is not unlikely that a randomly chosen mouse would weigh less than 405 grams.

Using normal distribution;

a) Probability that the mouse weighs less than 405 grams:

To find this probability, we need to calculate the area under the normal curve to the left of 405 grams. We can use the z-score formula to standardize the value.

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For 405 grams:

z = (405 - 359) / 33

Using a standard normal distribution table or calculator, we can find the probability associated with the z-score.

The probability that the mouse weighs less than 405 grams is approximately 0.8461.

b) Probability that the mouse weighs more than 461 grams:

Similarly, we need to calculate the area under the normal curve to the right of 461 grams.

For 461 grams:

z = (461 - 359) / 33

Using the standard normal distribution table or calculator, we find the probability associated with the z-score.

The probability that the mouse weighs more than 461 grams is approximately 0.0062.

c) Probability that the mouse weighs between 406 and 461 grams:

To find this probability, we calculate the area under the normal curve between the z-scores for 406 and 461 grams.

For 406 grams:

z₁ = (406 - 359) / 33

For 461 grams:

z₂ = (461 - 359) / 33

We can then find the probability associated with each z-score and subtract them to get the desired probability.

The probability that the mouse weighs between 406 and 461 grams is approximately 0.8302.

d) Is it unlikely that a randomly chosen mouse would weigh less than 405 grams?

To determine if it is unlikely, we compare the probability from part (a) with the significance level or threshold value. Let's assume a significance level of 0.05 (5%).

The probability from part (a) is 0.8461, which is greater than 0.05. Therefore, it is not unlikely that a randomly chosen mouse would weigh less than 405 grams.

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Answer:

The son is 10, and the father is 50.

Step-by-step explanation:

10 times 5 would be 50, and 50+10 is 60.

Answer:

Father: 50

Son: 10

Step-by-step explanation:

Son's age: S

Father's age: F

F=5S

F+S=60.

Substitute.

5S+S=60

6S=60

S=10

F=50. As a check, 10+50=60 and 50/5=10.

Hope this was helpful.

~cloud

Answer:

HCF of 868,372,and 992 is 124

LCM of 868,372,and 992 is 20832

hope this answer helps you...

Answer: it’s B or C

Step-by-step explanation

Answer:

its b

Step-by-step explanation:

trust me

Answer:

y(x)=0

Step-by-step explanation:

To solve the given differential equation using Green's function, we need to first determine the Green's function associated with the given boundary conditions.

The Green's function, G(x, ξ), satisfies the following equation:

(x^2 d^2G / dx^2) + (2x dG / dx) - 4G = δ(x - ξ)

where δ(x - ξ) is the Dirac delta function. We can solve this equation subject to the boundary conditions:

G(0, ξ) = G(∞, ξ) = 0

To solve this differential equation, we assume a solution of the form:

G(x, ξ) = A(x)B(ξ)

Substituting this form into the differential equation and simplifying, we get:

x^2 d^2A / dx^2 + 2x dA / dx - 4A = 0

This is a homogeneous second-order ordinary differential equation. We can solve it by assuming a power series solution of the form:

A(x) = ∑[n=0 to ∞] (a_n x^n)

Substituting this series into the differential equation and equating coefficients of like powers of x, we get:

a_n [(n + 2)(n + 1) - 4] = 0

Solving this equation for the coefficients, we find:

a_0 = 0

a_1 = 0

a_n = 4 / [(n + 2)(n + 1)] for n ≥ 2

Therefore, the solution for A(x) is:

A(x) = 4 * ∑[n=2 to ∞] (x^n / [(n + 2)(n + 1)])

Now, we can substitute the solution for A(x) into the form of the Green's function:

G(x, ξ) = A(x)B(ξ)

G(x, ξ) = 4 * ∑[n=2 to ∞] (x^n / [(n + 2)(n + 1)]) * B(ξ)

To determine B(ξ), we impose the boundary conditions:

G(0, ξ) = 0 => 4 * ∑[n=2 to ∞] (0 / [(n + 2)(n + 1)]) * B(ξ) = 0

G(∞, ξ) = 0 => 4 * ∑[n=2 to ∞] (ξ^n / [(n + 2)(n + 1)]) * B(ξ) = 0

From these conditions, we can conclude that B(ξ) = 0. Hence, the Green's function is:

G(x, ξ) = 0

Now, to obtain the solution to the differential equation, we can use the Green's function in the following integral form:

y(x) = ∫[0 to ∞] G(x, ξ) f(ξ) dξ

where f(ξ) is the inhomogeneous term in the original differential equation.

Since G(x, ξ) = 0, the integral evaluates to zero as well. Therefore, the solution to the given differential equation is:

y(x) = 0

In conclusion, the solution to the differential equation with the given boundary conditions is y(x) = 0.

The probabilities of the five other possibilities are as follows: a) P(A and B) = 1/18, b) P(A and C) = 1/12, c) P(B and C) = 5/18, d) P(B and D) = 1/18, and e) P(C and D) = 1/6.

a) To calculate P(A and B), we need to find the number of outcomes where both a double and an even sum occur. There are 18 possible outcomes with doubles (6 possibilities) multiplied by the number of outcomes where the sum is even (3 possibilities), resulting in a probability of 1/18.

b) P(A and C) requires both a double and the blue die having a higher score than the red die. Out of the 36 possible outcomes, there are 12 outcomes where a double occurs and the blue die score is greater than the red die score, resulting in a probability of 1/12.

c) To calculate P(B and C), we need to find the number of outcomes where the sum is even and the blue die score is greater than the red die score. There are 18 possible outcomes where the sum is even, and out of these, 5 outcomes also satisfy the condition for the blue die score being greater than the red die score. Therefore, the probability is 5/18.

d) P(B and D) requires both an even sum and a 6 on the red die. Out of the 36 possible outcomes, 2 outcomes satisfy these conditions (rolling a 3 on the blue die and rolling a 6 on the red die, or vice versa), resulting in a probability of 1/18.

e) P(C and D) involves both the blue die having a higher score than the red die and rolling a 6 on the red die. Out of the 36 possible outcomes, 6 outcomes satisfy these conditions, resulting in a probability of 1/6.

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Answer:

Step-by-step explanation:

4