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ANTONII [103]
3 years ago
7

Help binomial distributions

Mathematics
1 answer:
Ymorist [56]3 years ago
3 0

We have the formula to compute the probability of having exactly k successed over n trials, given a probability p of success (and implicitly a probability 1-p of failure), which is


P(\text{k successed on n trials}) = \binom{n}{k}p^k(1-p)^{n-k}


Now, the probability of at least 3 successes is the union of the following event: exactly three successes,exactly four successes and exactly five successes.


We can compute their probability and sum them:\binom{5}{3}\left(\frac{3}{7}\right)^3\left(\frac{4}{7}\right)^2 + \binom{5}{4}\left(\frac{3}{7}\right)^4\left(\frac{4}{7}\right)^1 + \binom{5}{5}\left(\frac{3}{7}\right)^5 \approx 0.36788


So, the answer is about 36.79%

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Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. Which statements are true? Check all that apply. To begin conver
umka21 [38]

Answer:

1) False, to begin converting the equation to standard form, each side must be added by 36. 2) True, to complete the square for the x terms, add 4 to both sides, 3) True, the center of the circle is at (-2, 3), 4) False, the center of the circle is at (-2, 3), 5) False, the radius of the circle is 7 units, 6) False, the radius of the circle is 7 units.

Step-by-step explanation:

Let prove the validity of each choice:

1) To begin converting the equation to standard form, subtract 36 from both sides:

Let consider the following formula and perform the following algebraic operations:

(i) x^{2} + y^{2} + 4\cdot x - 6\cdot y  - 36 = 0 Given

(ii) x^{2} + 4\cdot x + y^{2} - 6\cdot y - 36 = 0 Commutative Property

(iii) (x^{2} + 4\cdot x + 4) - 4 + (y^{2} - 6\cdot y + 9) - 9 -36 = 0 Modulative/Associative Property/Additive Inverse Existence

(iv) (x+ 2)^{2} - 4 + (y - 3)^{2} - 9 - 36 = 0  Perfect Trinomial Square

(v) (x+2)^{2} +(y-3)^{2} = 4 + 9 + 36 Commutative Property/Compatibility with Addition/Additive Inverse Existence/Modulative Property

(vi) (x+2)^{2} + (y-3)^{2} = 49 Definition of Addition/Result

False, to begin converting the equation to standard form, each side must be added by 36.

2) True, step (iii) on exercise 1) indicates that both side must be added by 4.

3) The general equation for a circle centered at (h, k) is of the form:

(x-h)^{2}+ (y-k)^{2} = r^{2}

Where r is the radius of the circle.

By direct comparison, it is evident that circle is centered at (-2,3).

True, step (vi) on exercise 1) indicates that center of the circle is at (-2, 3).

4) False, step (vi) on exercise 1) indicates that the center of the circle is at (-2, 3), not in (4, -6).

5) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

6) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

5 0
3 years ago
Read 2 more answers
4 1/2 cups of salad dressing fill 3 3/4 identical jars. How many cups fill each jar
matrenka [14]

Answer:gbvvvyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuyhuuyyyybyby8bybybyyyyyyyyyyyyyyyyyyyyyyyyyyyyybybyubyubyubbubhbubuhbybbbbbbbbbbbbbbbbbbbbbbbbbhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh                                 hbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjoioioioioioioioioioioioioioioioioioioioioioioioioioioibv

Step-by-step explanation:

5 0
2 years ago
Please help me with this!!
Naddik [55]

Step-by-step explanation:

To find the y-coordinate points we need to evaluate the function for all the x values in the table. In other words, we need to replace x with each value in our given function and simplify.

- For x = 0

f(x)=(x-2)^2-5

f(0)=(0-2)^2-5

f(0)=(-2)^2-5

f(0)=4-5

f(x)=-1

Since x=0 and y=-1, our first point is (0, -1)

- For x = 1

f(x)=(x-2)^2-5

f(1)=(1-2)^2-5

f(1)=(-1)^2-5

f(1)=1-5

f(x)=-4

Our second point is (1, -4)

- For x = 2

f(x)=(x-2)^2-5

f(2)=(2-2)^2-5

f(2)=(0)^2-5

f(x)=-5

Our third point is (2, -5)

- For x = 3

f(x)=(x-2)^2-5

f(3)=(3-2)^2-5

f(3)=(1)^2-5

f(3)=1-5

f(x)=-4

Our fourth point is (3, -4)

- For x = 4

f(x)=(x-2)^2-5

f(4)=(4-2)^2-5

f(4)=(2)^2-5

f(4)=4-5

f(x)=-1

Our fifth point is (4, -1)

Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.

3 0
3 years ago
______________ is how much an individual makes before taxes or deductions are taken out of their paycheck.
xenn [34]

the answer is: b. gross income

can you please mark me brainliest

7 0
3 years ago
A store had 913 sodas, both diet and regular. The ratio of diet sodas to regular sodas was 8:3. How many diet sodas were there?
Elodia [21]

Answer:

<h2>There are 664 diet soda</h2>

Step-by-step explanation:

Step one:

given data

total soda= 913

we are told that the ratio of diet sodas to regular sodas is 8:3

this means that for every 8 diet soda there is 3 regular soda

the total ratio is 8+3=11

Step two:

we are going to use part to all principle

let the diet soda be x

8/11=x/913

cross multiply

11x=913*8

divide both sides by 11

x=913*8/11

x=7304/11

x=664

There are 664 diet soda

5 0
2 years ago
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