HELP ME Randomthing2143! What's the mean of 2, 43, 67, 18?

Answer:

the probability that the number of heads is between 40 and 60 is 0.9535

the probability that the number of heads is between 50 and 55 is 0.3557

Step-by-step explanation:

From the given information:

A fair coin is tossed 100 times.

Let consider n to be the number of time the coin is tossed, So n = 100 times

In a fair toss of a coin; the probability of getting a head P(Head) = 1/2 = 0.5

If we assume X to be the random variable which follows a binomial distribution of n and p; therefore , the mean and the standard deviation can be  calculated as follows:

Mean μ = n × p

Mean μ = 100 × 1/2

Mean μ = 100 × 0.5

Mean μ =  50

Standard deviation σ =  [tex]\sqrt{n \times p \times (1-p)}[/tex]

Standard deviation σ =  [tex]\sqrt{100 \times 0.5 \times (1-0.5)}[/tex]

Standard deviation σ = [tex]\sqrt{50 \times (0.5)}[/tex]

Standard deviation σ = [tex]\sqrt{25}[/tex]

Standard deviation σ = 5

Now, we've made it easier now to estimate  the probability that the number of heads is between 40 and 60 and the probability that the number is between 50 and 55.

To start with the probability that the number of heads is between 40 and 60 ; we have:

P(40 < X < 60) = P(X < 60)- P(X < 40)

Applying  the central limit theorem , for X is 40 which lies around 39.5 and 40.5  and X is 60 which is around 59.5 and 60.5 but the inequality signifies less than sign ;

Then

P(40 < X < 60) = P(X < 59.5) - P(X < 39.5)

[tex]P(40 < X < 60) = P( \dfrac{X - \mu}{\sigma}< \dfrac{59.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{39.5 - 50 }{5})[/tex]

[tex]P(40 < X < 60) = P( Z < \dfrac{9.5 }{5}) - P( Z< \dfrac{-10.5 }{5})[/tex]

[tex]P(40 < X < 60) = P( Z <1.9}) - P( Z< -2.1)[/tex]

[tex]P(40 < X < 60) =0.9713 -0.0178[/tex]

[tex]P(40 < X < 60) =0.9535[/tex]

Therefore; the probability that the number of heads is between 40 and 60 is 0.9535

To estimate the probability that the number is between 50 and 55.

P(50 < X < 55) = P(X < 55)- P(X < 50)

Applying  the central limit theorem , for X is 50 which lies around 49.5 and 50.5  and X is 55 which is around 54.5 and 55.5 but the inequality signifies less than sign ;

Then

P(50 < X < 55) = P(X < 54.5) - P(X < 49.5)

[tex]P(50 < X < 55) = P( \dfrac{X - \mu}{\sigma}< \dfrac{54.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{49.5 - 50 }{5})[/tex]

[tex]P(50 < X < 55) = P( Z < \dfrac{4.5 }{5}) - P( Z< \dfrac{-0.5 }{5})[/tex]

[tex]P(50 < X < 55) = P( Z <0.9}) - P( Z< -0.1)[/tex]

[tex]P(50 < X < 55) =0.8159 -0.4602[/tex]

[tex]P(50 < X < 55) =0.3557[/tex]

Therefore; the probability that the number of heads is between 50 and 55 is 0.3557

Answer:

Step-by-step explanation:

(-2,2) (2,-4)

(-4-2)/(2+2)= -6/4= -3/2 is the slope of the graph

Answer:

The Pythagorean Triplet that has 5 is 3-4-5

Step-by-step explanation:

We can prove this using Pythagorean Theorem: a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

see if other people has already answered this question

Answer:

-1

1

1/2(1±i√3)

Step-by-step explanation:

1. x+1=0 ⇒ x= -1

2. x-1= 0 ⇒ x= 1

3. x^2-x+1=0

Answer:

Step-by-step explanation:

a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.

The principal P that must be invested at rate r for n annual withdrawals of amount A is ...

  P = A(1+r)(1 -(1 +r)^-n)/r

  P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95

__

b) 20 withdrawals of $60,000 each total ...

  20×$60,000 = $1,200,000

__

c) The excess over the amount deposited is interest:

  $1,200,000 -636,215.95 = $563,784.05

Answer: (5, 42)

Step-by-step explanation:

22 + 4x= 42

if we test the options we will see this is the only one that works

42 - 22 = 20

4x = 20

x= 5

which is equal to X the number of weeks they have gotten the allowance.

Answer:

The average revenue per passenger is about $13.85

μ = $13.85

The corresponding standard deviation is $14.51

σ = $14.51

The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Expected revenue = $1,662 ± 14.51

Step-by-step explanation:

An airline charges the following baggage fees:

$25 for the first bag and $35 for the second

Suppose 51% of passengers have no checked luggage,

P(0) = 0.51

33% have one piece of checked luggage and 16% have two pieces.

P(1) = 0.33

P(2) = 0.16

a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.

The average revenue per passenger is given by

μ = 0×P(0) + 25×P(1) + 35×P(2)

μ = 0×0.51 + 25×0.33 + 35×0.16

μ = 0 + 8.25 + 5.6

μ = $13.85

Therefore, the average revenue per passenger is about $13.85

The corresponding standard deviation is given by

σ = √σ²

Where σ² is the variance and is given by

σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16

σ² = 97.83 + 41.03 + 71.57

σ² = 210.43

So,

σ = √210.43

σ = $14.51

Therefore, the corresponding standard deviation is $14.51

b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?

For 120 passengers,

Expected revenue = 120×$13.85

Expected revenue = $1,662 ± 14.51

Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Answer:

AB=4

Step-by-step explanation:

The transitive property states if A=B and B+C than A+C  Next substitute

AB=x and x=4 so AB=4

Hope this helps, if it did, please give me brainliest, it helps me a lot. :)

Have a good day!

Answer:

Area: 7 units²

Perimeter: 14 units

Step-by-step explanation:

Area of each square:

1 unit × 1 unit = 1 unit²

There are 7 squares:

1 unit² × 7 (squares) = 7 units²

The area of the shape is 7 units².

The perimeter of the shape is the length of the outer sides.

1 + 1 + 1 + 1/2 + 1/2 + 1 + 1 + 1/2 + 1 + 1/2 + 1 + 1 + 1 + 1 + 1 + 1 =  14 units

Answer:

11n

Step-by-step explanation:

7n+4n   (factorize out n)

= n (7 + 4)

= n (11)

= 11n

Answer:

11n

Step-by-step explanation:

Combining like terms just means adding together the numbers with the same variable. 7n and 4n both have an n attached, so you would add like normal to get 7n + 4n = 11n.

Answer:

Step-by-step explanation:

(4+1)/(8-2)= 5/6

y + 1 = 5/6(x - 2)

y + 1 = 5/6x - 5/3

y + 3/3 = 5/6x - 5/3

y = 5/6x - 8/3

6(y = 5/6x - 8/3)

6y = 5x - 16

-5x + 6y = -16

Answer:

0.1048

Step-by-step explanation:

The computation of probability that they receive 10 calls in the next hours is shown below:-

Average which is given in the question 5 minutes between calls = 5/60 calls an hour so it becomes 12 calls per hour

So,

P(X = 10)

[tex]= \frac{e^{-12}12^{10}}{10!}[/tex]

= 0.1048

Therefore for computing the probability that they receive 10 calls in the next hours we simply applied the above formula.

Answer:

x=3y

Step-by-step explanation:

divide both sides by 20

20x = 60y

------   -------

20        20

x=3y

Answer:

x = 3y

Step-by-step explanation:

20x = 60y

Divide 20 into both sides.

20x/20 = 60y/20

1x = 6/2y

x = 3y

Answer:

See below for the table.

Step-by-step explanation:

The results for the thirty cases are listed below:

U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U

The table summarizing the frequency distribution of the primary causes leading to student dropout is:

[tex]\left|\begin{array}{c|c}$Cause&$Frequency\\----------&----\\\\$Unexcused absences (U)&9\\$Illness (I)&9\\$Family problems (F)&7\\$Other causes (O)&5\\-----------&---\\$Total&30\end{array}\right|[/tex]

Answer:

308.67 cm ^ 3 / week

Step-by-step explanation:

A cantaloupe is approximately a sphere, therefore its approximate volume would be:

V = (4/3) * pi * (r ^ 3)

They tell us that dr / dt 0.5 cm / week and the radius is 6.4 cm

if we derive the formula from the volume we are left with:

dV / dt = (4/3) * pi * d / dr [(r ^ 3)]

dV / dt = (4/3) * pi * 3 * (r ^ 2) * dr / dt

dV / dt = 4 * pi * (r ^ 2) * dr / dt

we replace all the values and we are left with:

dV / dt = 4 * 3.14 * (6.4 ^ 2) * 0.6

dV / dt = 308.67

Therefore the volume is changing at a rate of 308.67 cm ^ 3 / week

Answer:

x= 9 inches

Step-by-step explanation:

Hello

I can help you with this.

in this case, we have two similar triangles, let's see

Step 1

identify the rigth triangles.

1) the first triangle has these dimensions

hypotenuse( remember, the longest side)= unknown=H

adjacent side(the horizontal)=6 +x

opposite side(the vertical)=10

2) the second triangle has these dimensions

hypotenuse( remember, the longest side)= unknown=h

adjacent side(the horizontal)=6

opposite side(the vertical)=4.

As these triangles keep the same proportion and in both cases we know the length of the legs, we can establish a relationship

Step 2

establish a relationship

let's compare the opposite side and the adjacent side

triangle 1 (the bigger)

[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{10}{6+x}[/tex]

Triangle 2

[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{4}{6}\\proportion=\frac{2}{3}[/tex]

were the proportions are equal, so

[tex]\frac{10}{6+x}=\frac{2}{3}[/tex]

at this point, just isolate x to find its value

Step 3

isolate x

[tex]\frac{10}{6+x}=\frac{2}{3}\\multiply\ both\ sides\ by\ 3\\\frac{10*3}{6+x}=\frac{2*3}{3}\\\frac{30}{6+x} =2\\\\Multiply\ both\ sides\ by (6+x)\\\frac{30(6+X)}{6+x} =2(6+x)\\30=12+2x\\30-12=2x\\18=2x\\so\\x=\frac{18}{2} \\x=9[/tex]

remember the units of measure ( Inches)

x= 9 inches

I really hope it helps, have a nice day.

Answer:

4.11% probability that he has lung disease given that he does not smoke

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Does not smoke

Event B: Lung disease

Lung Disease/Nonsmoker 0.03

This means that [tex]P(A \cap B) = 0.03[/tex]

Lung Disease/Nonsmoker 0.03

No Lung Disease/Nonsmoker 0.7

This means that [tex]P(A) = 0.03 + 0.7 = 0.73[/tex]

What is the probability of the following event: He has lung disease given that he does not smoke?

[tex]P(B|A) = \frac{0.03}{0.73} = 0.0411[/tex]

4.11% probability that he has lung disease given that he does not smoke

Probabilities are used to determine the chances of an event.

The  probability that he has lung disease given that he does not smoke is 0.231

The required probability is calculated as:

[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]

From the question, we have:

[tex]\mathbf{P(Lung\ Disease\ and\ Non\ Smoker) = 0.03}[/tex]

[tex]\mathbf{P(Lung\ Disease) = P(Has Lung Disease/smoker) + P(Lung Disease/Nonsmoker)}[/tex]

[tex]\mathbf{P(Lung\ Disease) = 0.1 + 0.03}[/tex]

[tex]\mathbf{P(Lung\ Disease) = 0.13}[/tex]

So, we have:

[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]

[tex]\mathbf{P = \frac{0.03}{0.13}}[/tex]

[tex]\mathbf{P = 0.231}[/tex]

Hence, the  probability that he has lung disease given that he does not smoke is 0.231

Read more about probabilities at:

https://brainly.com/question/11234923

Answer:

B

Step-by-step explanation:

It can be figured out by using graph transformations.

When when subtracting directly next to x, it shifts the graph to the left while doing the opposite when adding. Since the graph is to the left, we know it has to be A or B since those are subtracting by 5

Outside of the absolute value, when subtracting, it makes the graph move down. That means we are looking for a -4 which is found in  B

Answer:

Options A, C and D are true.

- The average daily revenue for days when the Red Sox do not play away is $1,768.32.

- The average daily revenue for days when the Red Sox play away is $2,264.57.

- On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.

Step-by-step explanation:

The complete Question is presented in the attached image to this solution.

Analyzing the options at a time

A) The average daily revenue for days when the Red Sox do not play away is $1,768.32.

This option is true as 1768.32 is the intercept which is the average daily revenue when the Red Sox=0, that is, 0=no, when red sox do not play away.

B) The average daily revenue for days when the Red Sox play away is $1,768.32.

This is false because when the Red Sox play away, the value is 1 and the average revenue = 1768.32 + 496.25 = $2,264.57

C) The average daily revenue for days when the Red Sox play away is $2,264.57.

This is true. I just gave the explanation under option B.

D) The average daily revenue for days when the Red Sox do not play away is $1,272.07.

This is false. The explanation is under option A.

E) On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.

This is true. It is evident from the table that the 0 and 1 coefficient is 496.25. This expresses the difference in average daily revenue when the Red Sox games are played away and when they are not.

Hope this Helps!!!

Answer:

9.2

Step-by-step explanation:

The given triangle is a right angled triangle. To solve for any of the side length of such triangle, apply the trigonometry ratio formula which can easily be remembered as SOHCAHTOA.

SOH is Sin θ = opposite/hypothenuse,

CAH is Cos θ = Adjacent/hypotenuse

TOA is Tan θ = Opposite/adjacent

Thus, in the right triangle given, we have:

θ = 38°

Opposite side to the given angle = x

Hypotenuse = 15

We're going to use, sin θ = opposite/hypotenuse

Sin(38) = x/15

Multiply both sides by 15 to solve for x

15*sin(38) = x

15*0.616 = x

9.24 = x

x ≈ 9.2 (to nearest tenth)

Answer:

Product A is the cheapest unit price.

Step-by-step explanation:

Since we have given that

Weight of a Product A = 8 oz

Cost at which it is sold = $1.36

Cost per unit for Product A will be

1.38/8= $0.17

Weight of a Product B = 16 oz

Cost at which it is sold = $3.20

Cost per unit for Product B will be

So, we can see that the unit price of "Product A" is lower than the unit price of product B .

Hence, Product A has the cheapest unit price.

Answer:

It will take 1.43 hours for them to clean the car.

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/x

Tanya's rate: 1/2

Pat's rate: 1/5

Together rate = Tanya's rate + Pat's rate

[tex]\frac{1}{x} = \frac{1}{2} + \frac{1}{5}[/tex]

[tex]\frac{1}{x} = \frac{5 + 2}{10}[/tex]

[tex]\frac{1}{x} = \frac{7}{10}[/tex]

[tex]7x = 10[/tex]

[tex]x = \frac{10}{7}[/tex]

[tex]x = 1.43[/tex]

It will take 1.43 hours for them to clean the car.

Answer:

0.25

Step-by-step explanation:

Out of the 4 counters only 1 is black so the probability is 1/4 or 0.25.

Answer:

0.25

Step-by-step explanation:

Since there are four marbles 100/4 =25 in this 100 is 1 thus the answer is 0.25

Answer:

The work will be "1909212.015 J". The further explanation is given below.

Step-by-step explanation:

The given values are:

Liquid's density

= 760 kg/m³

Height

= 3 meters

Gravity

g = 3.8 m/s²

Value of y is:

y = 5 log (x-2)

y = 0

y = 4

As we know,

⇒  [tex]\Delta V=\pi r^2 \Delta y[/tex]

⇒  [tex]y =5log(x-2)[/tex]

⇒  [tex]\frac{y}{5} =log (x-2)[/tex]

⇒  [tex]e^{\frac{y}{5}}=(x-2)[/tex]

⇒  [tex]x=e^{\frac{y}{5}}+2[/tex]

Now,

[tex]\Delta F=ma[/tex]

      [tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]

So that,

⇒  [tex]\Delta W = \Delta F.distance[/tex]

            [tex]=\Delta F(4-y)[/tex]

The required work will be:

⇒  [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]

         [tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]

         [tex]=760\times 9.8 \pi[81.455][/tex]

         [tex]=1909212.015 \ J[/tex]

Answer:

Step-by-step explanation:

Answer:

-18 < -x-4 < -8

Step-by-step explanation:

We start with the initial range as:

4 < x < 14

we multiplicate the inequation by -1, as:

-4 > -x > -14

if we multiply by a negative number, we need to change the symbols < to >.

Then, we sum the number -4, as:

-4-4> -x-4 > -14-4

-8 > -x-4 > -18

Finally, the range for -x-4 is:

-18 < -x-4 < -8

Answer:

x = 465 km

y = 735 km

Step-by-step explanation:

Step 1: Write out equations

x + y = 1200

y = x + 270

Step 2: Find x using substitution

x + (x + 270) = 1200

2x + 270 = 1200

2x = 930

x = 465

Step 3: Plug in x to find y

y = 465 + 270

y = 735

Answer:

They traveled 780

Step-by-step explanation:

Got it right on the test

Answer:

A. The student scored better on the geography test.

Step-by-step explanation:

The z-score for a normal distribution, for any value X, is given by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

Where is μ the mean score, and σ is the standard deviation.

For the Geography test:

X = 74

μ = 80

σ = 5

[tex]z_g=\frac{74-80}{5}\\ z_g=-1.2[/tex]

For the Mathematics test:

X = 273

μ = 300

σ = 18

[tex]z_m=\frac{273-300}{18}\\ z_m=-1.5[/tex]

The z-score for the Geography test is higher than the score for the Mathematics test, which means that the student had a better relative score in the Geography test.

The answer is  A. The student scored better on the geography test.

Answer:

x= -14

Step-by-step explanation:

Please see attached picture for full solution.