Gabriel tossed a paper cup 40 times and recorded how the cup landed each time. He organized the results in the table shown. Find the experimental probability that the cup will NOT land right-side up. Express your answer as a fraction in simplest form.

Answer:

a) [tex]P(X = n) = (0.85)^{n}[/tex]

b) [tex]P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}[/tex]

c)

[tex]P(X \geq x) = P(X = x) + P(X = x+1) + ... + P(X = n)[/tex]

For each value, we use

[tex]P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}[/tex]

d) If [tex]x > E(X) + \sqrt{V(X)}[/tex], yes, otherwise no

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrived on time, or it did not. Flights are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

A measure is said to unusual if it is more than 2.5 standard deviations from the mean.

85% of recent flights have arrived on time.

This means that [tex]p = 0.85[/tex]

(a) Find the probability that all of the flights were on time.

This is [tex]P(X = n)[/tex], in which n is the size of the sample studied.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = n) = C_{n,n}.(0.85)^{n}.(0.15)^{n-n}[/tex]

[tex]P(X = n) = (0.85)^{n}[/tex]

(b) Find the probability that exactly x of the flights were on time.

Exactly x of the flights: So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}[/tex]

(c) Find the probability that x or more of the flights were on time.

This is

[tex]P(X \geq x) = P(X = x) + P(X = x+1) + ... + P(X = n)[/tex]

For each value, we use

[tex]P(X = x) = C_{n,x}.(0.85)^{x}.(0.15)^{n-x}[/tex]

(d) Would it be unusual for x or more of the flights to be on time?

If [tex]x > E(X) + \sqrt{V(X)}[/tex], yes, otherwise no

Answer:

All parents in the school

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

13 is x

144+25=169

169 is 13 squared

Answer:

$4.39 for 6 quartz

Step-by-step explanation:

if you multiply 2.89 by 2 it's more then 4.39

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

Work Shown:

a = 9, b = 12 are the two legs of the right triangle

c = unknown is the hypotenuse

Apply the pythagorean theorem to find c

a^2 + b^2 = c^2

9^2 + 12^2 = c^2

81 + 144 = c^2

225 = c^2

c^2 = 225

c = sqrt(225)

c = 15

Answer:

15

Step-by-step explanation:

Since this is a right angled triangle we can use pythagoras theorem to work out the length of the hypotenuse, or the the longest side.

pythagoras theorem says that a²+b²=c² with c² being the hypotenuse, or missing side here.

12²+9²=225

Because 225 is equal to C², or C squared, we must take the square root in order to find the actual length.

√225 = 15

Answer:

To find the answer you will have to divide 22 by 3 so 7 with 1 person left over so you round up and there will be 8 rooms needed.

Hope I helped :)

Answer:

Step-by-step explanation:

I’m assuming you meant to write

T = ⅛x + 9

T = ⅛(20) + 9 = 11.5

The required estimate of tuition for one year at the college in 2020 is $11500

Given,
The tuition T for one year at a college can be approximated by the equation.
                   T = 1/8x + 9  - - - - - - (1)
where x is the year since 2000, and T is tuition in thousands of dollars.
Tuition fee in the year 2020 to be calcuate.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The expression is given, since 2000
so the change in years
x = 2020 - 2000
x = 20
Put this x in equation 1
T = 20/8 + 9
T = 2.5 + 9
T = 11.5
SInce t is in thousand so Tuition fee = $11,500.

Thus, the required estimate of tuition for one year at the college in 2020 is $11500  

Learn more about function here:

brainly.com/question/21145944

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Answer:a²=b²+c² in a right angle triangle so answer is root 136

Step-by-step explanation:

Answer:

135 degrees.

Step-by-step explanation:

Assuming that it is a regular octagon, you can use the formula (n-2) (180) divided by n. n = sides. Therefore, (8-2) (180) divided by 8, which is 135.

Answer:

135 degrees

Step-by-step explanation:

(just took that test!!)

(Asher)

Answer:

Gallons:       Miles:

0                  0

1                   23

2                  46

3                  69

Step-by-step explanation:

First, you would figure out what the unit rate is. To do that, you would divide the 184 miles by the 8 gallons of gas. You get 23 miles per gallon of gas.

Then, to fill out the unit rate table, copy this method:

You know that 0 gallons of gas would lead you nowhere, so you would put a zero in the first row.

In the second row, you use your answer from the first row (0) and add the number of miles per gallon of gas. You would add 0 + 23 and get 23. Put 23 in the second row.

In the third row, you multiply the number of miles per gallon of gas by 2. The answer is 23 x 2 = 46.

Lastly, you multiply 23 x 3 (answer: 69) to fill out the final row.  

Answer:

6.32

Step-by-step explanation:

:|

Answer:

6.32

Step-by-step explanation:

I counted up from G to H and I got 6. Since the line is a diagonal it makes it odd as in a weird number like a decimal most times. It can't be 6 because the line wouldn't make it to H it would be just short. 5.83 is already too short. 8 is to long for the line to be as it is now as a diagonal. 8, you would have to count up 6 and 2 to the right perfect but the line doesn't do that.

Answer:

The red one

Step-by-step explanation:

Branlies plz Thank you!! :)

Answer:

65 pi, the closest one is 204.1 in^2

Step-by-step explanation:

This question is asking a surface area for a cylindrical bowl with top is empty, so you need to find one circle base and one rectangular side, as the hight is 4in, and wide is 10 inch, use the wide to find the circumference of the rectangular side, which is C = pi*d = 10 pi. Then the area for the rectangular side is A = 40 pi, and the area for the circle is A = pi*r^2 = (10/2)^2 * pi = 25 pi. Then add them together get Total area = 40 pi + 25pi = 65 pi or 65 * 3.14 = 204.1 in^2

Answer:

What is N supposed to be? Is there supposed to be some picture or something that should tell us?

Step-by-step explanation:

The answer is 3) Pythagorean.

A trigonometric identity derived from the Pythagorean theorem is called a Pythagorean identity.

Mathematically, the Pythagorean theorem states that

Hypotenuse^2 = Adjacent^2 + Opposite^2

Divide through by Hypotenuse^2

This gives

1 = cos^2(x) + sin^2(x)

Rewrite as:

cos^2(x) + sin^2(x) = 1

As a general rule, the above represents the basic Pythagorean identity.

Hence, the word that completes the blank is Pythagorean.

Read more about Pythagorean identity at:

https://brainly.com/question/1969941

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Answer:

Step-by-step explanation:

The two triangles are similar dues to the ASA therom, so we can relate the sides to one another. That means that

13x=11x-4

2x=-4

x=-0.5

Answer:

yes can i have brainliest

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I solved the question

Answer:

1 and 5= corresponding angles.

4 and 2=vertical opposite angle

3 and 6=co interior angle.

5 and 8=linear pair.

5 and 3= alternate interior angle

2 and 8=alternate exterior angle.

Answer:

Ezzzz i got u lol

Step-by-step explanation:

1 and 5 are corresponding

4 and 2 are vertical angles

3 and 6 are same side interior

5 and 8 are  Consecutive interior

5 and 3 are alt interior

2 and 8 are alt exterior

Brainliest is much apreciated Hope i helped u

Answer:

Step-by-step explanation:

have a nice day/night !

Answer:

[tex]y = 6\\\\x = 6\sqrt{2}\\x=8.485[/tex]

Step-by-step explanation:

The base-angles converse theorem states that in a triangle where two angles are congruent, the sides opposite the congruent angles are congruent. One can apply this theorem to the given triangle, and thus, y = 6, because of the base angles converse theorem.

It is also given that the given triangle is a right triangle, therefore, the isosceles triangle with a right angle theorem is applicable. This theorem states that in a right triangle (a triangle with a right angle), that is isosceles (two sides are congruent), the third side (non-congruent side) is equal to the length of the two congruent sides times the square root of (2). Hence, x = [tex]6\sqrt{2}[/tex], in the decimal form that is 8.485.

Answer:

99

Step-by-step explanation:

The formula is b x h = A

9 x 11 = A

9 x 11 = 99

A = 99

ps. PLZ give me brainliest!

Answer:

Yes, the volume of congruent figures are the same.

Step-by-step explanation:

They are the same shape and size

Answer:

the square root of 22 is 4.69

Step-by-step explanation:

Answer:

4.69041575982

Step-by-step explanation:

Answer:x = 8 Step-by-step explanation:4x + 112 = 9x + 72-112 -1124x = 9x - 40-9x -9x-5x = -40----- -------- -5 -5x = 8 

Explanation;

the answer is 5x=8

Answer:

3015

Step-by-step explanation:

Answer:

The two numbers are 8&5

Step-by-step explanation:

13 = x + y

y = x-3

13 = x+(x-3)

13=2x-3

16=2x

x=8

y=1(8)-3

y=5