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ki77a [65]
3 years ago
9

Wich of the following is an example of a Proper fraction? A.4/17 B.15/2 C.6/6 D.11/10/

Mathematics
1 answer:
ycow [4]3 years ago
3 0
A. 4/17

- Because 4 is smaller than 17
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Evaluate -3x 3 - 4x for x = -1. 1 7 -1
7nadin3 [17]
-3x^{3}-4x
=-3(-1)^{3} -4(-1)
=-3*(-1)+4
=3+4
=7
5 0
3 years ago
Use rounding or compatible number to estimate the difference 287- 162
Nookie1986 [14]
Okay so i subtract and then i got my number 125 as the total answer
5 0
3 years ago
The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08
kvv77 [185]

Answer:

a) 44.93% probability that there are no surface flaws in an auto's interior

b) 0.03% probability that none of the 10 cars has any surface flaws

c) 0.44% probability that at most 1 car has any surface flaws

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the binomial probability distributions.

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:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Binomial 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.

Poisson distribution with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So \mu = 10*0.08 = 0.8

(a) What is the probability that there are no surface flaws in an auto's interior?

Single car, so Poisson distribution. This is P(X = 0).

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

P(X = 0) = \frac{e^{-0.8}*(0.8)^{0}}{(0)!} = 0.4493

44.93% probability that there are no surface flaws in an auto's interior

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

For each car, there is a p = 0.4493 probability of having no surface flaws. 10 cars, so n = 10. This is P(X = 10), binomial, since there are multiple cars and each of them has the same probability of not having a surface defect.

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

P(X = 10) = C_{10,10}.(0.4493)^{10}.(0.5507)^{0} = 0.0003

0.03% probability that none of the 10 cars has any surface flaws

(c) If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?

At least 9 cars without surface flaws. So

P(X \geq 9) = P(X = 9) + P(X = 10)

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

P(X = 9) = C_{10,9}.(0.4493)^{9}.(0.5507)^{1} = 0.0041

P(X = 10) = C_{10,10}.(0.4493)^{10}.(0.5507)^{0} = 0.0003

P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0041 + 0.0003 = 0.0044

0.44% probability that at most 1 car has any surface flaws

5 0
3 years ago
The sum of two numbers is 15. The difference of he same two numbers is 3. What are the two numbers?
Angelina_Jolie [31]

x+y =15

x-y = 3

add the two equations

2x = 18

divide by 2

x = 9

x + y = 15

9 + y =15

subtract 9

y = 9

The two numbers are 6 and 9

7 0
3 years ago
What is the slope of the line through (6,9) and (7,1)
suter [353]
Slope of (6, 9) & (7, 1)

To find the slope, we use the equation : m = y₂-y₁ / x₂-x₁

**Remember : m = slope**

Let's say that (6, 9) is our first set of points, and (7, 1) is our second.

If those are our first and second points, then we now know this :

x₁ = 6, x₂ = 7, y₁ = 9, y₂ = 1

Now that we know that, we can simply plug those points into our slope equation.

m = y₂ - y₁ / x₂ - x₁

m = (1 - 9) / (7 - 6 )

Simplify.

m = -8 / 1

Simplify.

m = -8

So, our slope is -8. 

~Hope I helped!~ 
6 0
3 years ago
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