What do you need to know to describe the velocity of an object?--Three things total

Answer:

a) 0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.

b) 0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.

c) 0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it.

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the Binomial distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

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.

(a) Find the probability that a 100-foor roll has at most 2 flaws.

A certain type of aluminum screen has, an average, one flaw in a 100-foot roll, which means that [tex]\mu = 1[/tex]. Only one roll means that the Poisson distribution is used.

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1}*1^{0}}{(0)!} = 0.3679[/tex]

[tex]P(X = 1) = \frac{e^{-1}*1^{1}}{(1)!} = 0.3679[/tex]

[tex]P(X = 2) = \frac{e^{-1}*1^{2}}{(2)!} = 0.1839[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3679 + 0.3679 + 0.1839 = 0.9197[/tex]

0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.

(b) Suppose that I bought 10 200-foot rolls, find the probability that there are exactly 3 rolls that have no flaws in them.

Two parts.

Probability that a single 200-foot roll has no flaw.

This is [tex]P(X = 0)[/tex], Poisson(single 200-foot roll) when [tex]\mu = \frac{200*1}{100} = 2[/tex]. So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]

0.1353 probability that a single 200-foot roll has no flaw.

Probability that on 10 200-foot rolls, 3 have no flaws.

Multiple 200-foot rolls means that we use the binomial distribution.

0.1353 probability that a single 200-foot roll has no flaw means that [tex]p = 0.1353[/tex]

10 200-foot rolls means that [tex]n = 10[/tex]

We want [tex]P(X = 3)[/tex]. So

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

[tex]P(X = 3) = C_{10,3}.(0.1353)^{3}.(0.8647)^{7} = 0.1074[/tex]

0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.

(c) What is the probability that the 15th roll he inspected was the 3rd one that have no flaws in it.

0.1353 probability that a single 200-foot roll has no flaw means that [tex]p = 0.1353[/tex]

2 with flaws in the first 14, which is [tex]P(X = 2)[/tex] when [tex]n = 14[/tex]

The 15th has no flaw, with probability of 0.1353. So

[tex]P = 0.1353*P(X = 2) = 0.1353*(C_{14,2}.(0.1353)^{2}.(0.8647)^{12}) = 0.1353*0.2911 = 0.0394[/tex]

0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it

Answer:

y = 1/5x + 3

Step-by-step explanation:

To have a parralel line to another line, have the slopes of the lines be the same, just change the y- intecept. HOPE THIS HELPS!

Answer:

width of rectangle is 9m

deduct one whole number from the other number

Answer:

(x - 3)^2 + (y + 2)^2 = 16

Step-by-step explanation:

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

r = radius

(h, k ) is center of circle.

The center of the circle is (3, 2) and r is 4.

(x - 3)^2 + (y + 2)^2

16

Best of luck :3

Answer:

117.2

Step-by-step explanation:

I hope this helps a little bit.

Answer:

119

Step-by-step explanation:

common different: 7-3=4

initial value =3

so x-3=(n-1)d

only 119-3=116 is divisible by 4

It's the ans cuz n-1 has to be integer

Answer:

the answer is 1 over 12

Answer:

honestly I don't know 5

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

14 + 8 + 15

Answer: 1680³

Step-by-step explanation:

length x width x height

14 x 15 x 8

Answer:

i dont know what you are asking but 3/10-8/10

Step-by-step explanation:

Answer:

48 packages

Step-by-step explanation:

Hello There!

The first step is to find out how many uniforms they need to do so we multiply 127 and 3

3x127=381

Then we divide it by 8 ( because that's how many uniforms are sold in one package.)

381/8=47.625

you cannot have a 6th of a package so we just round to the nearest whole

so we can conclude that they will need 48 packages

~TheMathWiz

Answer:

-4

Step-by-step explanation:

by finding the exact value.

Answer:

Step-by-step explanation:

Area of a circle=πr²

Radius = 16/2=8 Area of a circle=3.14×8×8

= 3.14×64

= 200.96cm²

= 201 cm² to the nearest unit.

Answer: D and E I'm sure

Answer:

The surface area of this cylinder is 3545 cm²

∵ π =

∴ The lateral area = 24 × × 35.

∴ The area of the base = × (12)² = (144) = 452 cm²

∴ The surface area = 2640 + 2(452 ) = 3545 cm²

∴ The surface area of this cylinder is 3545 cm²

Step-by-step explanation:

Hope it is helpful.....

Answer:

no answer choices i cant help

Step-by-step explanation:

moan

Step-by-step explanation:

2.

- the volume of initial prism is 3*3*6=54 cm³;

- the number of cubics of the requested 72 cm³ is 72;

- 'Chelsea wants to add eight layers' means 72=3*3*8 cubics, then one layer in this case consists of 3x3 cubics;

- 'Stephen says they only need to add four layers' means 72=4*3*6 cubics, then one layer in this case consists of 3x6 cubics.

3.

- the volume of initial prism is 4*4*1=16 in³; it means one layer is 16 inches³;

- according to the requirement 3 layers is 16*3=48 in³; three times 16.

- according to the requirement 5 layers is 16*5=80 in³; five times 16.

- according to the requirement 7 layers is 16*7=112 in³; seven times 16.

Answer:

Step-by-step explanation: Determine the radius of a circle. ...

Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm .

You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² .

The circumference of the given circle is approximately 43.96 inches.

Given that a circle with radius of 7 inches, we need to find the circumference of the circle,

We know that,

In the case of a circle, the circumference is the distance around the circle.

It is the total length of the curve that forms the boundary of the shape.

To find the circumference of a circle, you can use the formula:

Circumference = 2π × radius

The radius of the circle is 7 inches, and using the approximation of π as 3.14, we can substitute these values into the formula:

Circumference = 2 × 3.14 × 7

Circumference = 43.96 inches

Therefore, the circumference of the given circle is approximately 43.96 inches.

Learn more about Circumference click;

https://brainly.com/question/28757341

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Answer:

-3x-8=16

-3x = 16+8

-3x = 24

x = 24/-3

x = -8

= -2(x-7)

= -2(-8-7)

= 30

Hope this helps you. Do mark me as brainliest.

Answer:

y=8x+1

Step-by-step explanation:

The slope is a positive 8 because the line is going upwards. Slope equals rise over run. The rise is 8 units, and the run is 1 positive unit since it is going to the right. So 8/1 is 1. There's a +1 in the equation because the y-intercept is at positive 1. The y-intercept is where the line crosses the y-axis (vertical line). Here, the line crosses it at 1.

Answer:

Step-by-step explanation:

The surface area of a rectangular prism is

A=2(xy+xz+yz). where x,y,z are its dimensions, in this case

A=2(12(11)+12(10)+11(10))

A=2(132+120+110)

A=2(362)

A=724 cm^2

Answer: 724cm²

Step-by-step explanation:

The formula is: 2(lw + hl + hw). Our units are 12, 11, and 10. So, the Length, Width, and Height are,

12 is the Length.

11 is the Width

10 is the Height.

Let's solve now. Our problem will be written like this,

2 · (11 × 12) + (10 × 12) + (10 × 11)

Let's solve.

1. Multiply 11 by 12.

11 × 12 = 132

2. Multiply 10 by 12.

10 × 12 = 120

3. Multiply 10 by 11.

10 × 11 = 110

4. Add up all the products.

132 + 120 + 110 = 362

5. Multiply 362 by 2.

362 × 2 = 724

Hence, 724 is the answer.

Answer:

a) According to probability theory, the following are possible:

(1) The probability that a customer will buy 5 items in a single purchase is 30%.  This represents a 0.30 chance of the customer buying 5 items.

(3) The probability that a customer will buy 3 items in a single purchase is 99%  This means that there a 0.99 chance that the customer will buy 3 items.

b) According to probability theory, the following are not possible:

2) The probability that a customer will buy 3 items in a single purchase is 101%.  Probability is always equal to 1 or 100%.  It cannot exceed 100%.

(4) The probability that a customer will buy 8 item.  This part lacks the necessary information to solve the problem.

Step-by-step explanation:

Probability describes the likelihood or chance of an event happening out of the many possible events that can take place.  The sum of all probabilities for a particular event is always equal to 1.  This shows that probability does not exceed 100%.

Answer:

The inequality 3x-(x-1)>5 represents this situation. Since Diana can run more than 1 mile on tuesday and more than 6 miles on sunday.

Step-by-step explanation:

Answer:

A (i think)

Step-by-step explanation:

If i'm right please mark me branliest