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3 years ago

Find the circumference of a circle with the diameter of 10 inches. Leave your answers in form of pi

Mathematics

1 answer:

MrRa [10]3 years ago

4 0

Answer:

Circumference = 10π

Step-by-step explanation:

First identify the circumference formula as such:

2πr (where r ⇒ radius, π ⇒ pi)

Knowing 2 times the radius (2r) in the formula can be rewritten as the diameter, the formula itself can be rewritten as:

πd (where d ⇒ diameter, π ⇒ pi)

If we know the diameter = 10 inches, substitute in the circumference formula πd to get:

π * 10 inches = 10 * π inches = 10π inches

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20 points Return to questionItem 4Item 4 20 points Police records in the town of Saratoga show that 13 percent of the drivers st

Sladkaya [172]

Answer:

a) 0.1423

b) 0.2977

c) 0.56

Step-by-step explanation:

For each driver stopped for speeding, there are only two possible outcomes. Either they have invalid licenses, or they do not. The probability of a driver having an invalid license is independent from other drivers. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

13 percent of the drivers stopped for speeding have invalid licenses.

This means that $p = 0.13$

14 drivers are stopped

This means that $n = 14$

(a) None will have an invalid license.

This is $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{14,0}.(0.13)^{0}.(0.87)^{14} = 0.1423$

(b) Exactly one will have an invalid license.

This is $P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{14,1}.(0.13)^{1}.(0.87)^{13} = 0.2977$

(c) At least 2 will have invalid licenses.

Either less than 2 have invalid licenses, or at least 2 does. The sum of the probabilities of these events is decimal 1. Mathematically, this is

$P(X < 2) + P(X \geq 2) = 1$

We want $P(X \geq 2)$

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1) = 0.1423 + 0.2977 = 0.44$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.44 = 0.56$

8 0

2 years ago

Clear selection

elena-s [515]

Answer: Velveeta

Step-by-step explanation:

Unit rate is basically the price for a single slice. This being said you would divide 2.50 by 10 and you would get .25, then you would do 4.00 by 20 which would be .20. So the better deal would be Velveeta.

6 0

3 years ago

I need help on 10,11,12, and 13 plz help me

Mila [183]

10. 14
2 * 7 <==

11. 12
6 * 2
2 * 3 * 2 = 2^2 * 3 <==

12. 15
3 * 5 <==

13. ur gonna have 3 tables that each have 4 chairs

7 0

3 years ago

a foreman must order enough sod to cover a dirt area 36 feet wide by 28 feet long. each piece of sod is 3 feet long and 12 inche

Andrews [41]

If we divide the area we have to cover by the area of a piece, we will get the number of pieces needed:

$n=\dfrac{\text{dirt area}}{\text{piece area}}=\dfrac{36\times 28}{3\times 12} = \dfrac{36\times 28}{36}=28$