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1 year ago

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Indicate whether the statement below is true or false. A store is offering a 15% discount. Tom wants to know how much he will ha

ve to pay after the discount. He can determine this in a single step by multiplying the original price by .85.

1 answer:

eduard1 year ago

3 0

Answer:

false

Step-by-step explanation:

I think it is backwards to figure a fifteen percent discount, you would make 15% into .15 and then multiply .15 times the original prioce to see the amount off.

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A certain type of aluminum screen has, an average, one flaw in a 100-foot roll. Assume the flaw distribution approximately follo

julsineya [31]

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:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Binomial 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.

(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 $\mu = 1$ . Only one roll means that the Poisson distribution is used.

This is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

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

$P(X = 0) = \frac{e^{-1}*1^{0}}{(0)!} = 0.3679$

$P(X = 1) = \frac{e^{-1}*1^{1}}{(1)!} = 0.3679$

$P(X = 2) = \frac{e^{-1}*1^{2}}{(2)!} = 0.1839$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3679 + 0.3679 + 0.1839 = 0.9197$

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 $P(X = 0)$ , Poisson(single 200-foot roll) when $\mu = \frac{200*1}{100} = 2$ . So

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

$P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353$

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 $p = 0.1353$

10 200-foot rolls means that $n = 10$

We want $P(X = 3)$ . So

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

$P(X = 3) = C_{10,3}.(0.1353)^{3}.(0.8647)^{7} = 0.1074$

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 $p = 0.1353$

2 with flaws in the first 14, which is $P(X = 2)$ when $n = 14$

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

$P = 0.1353*P(X = 2) = 0.1353*(C_{14,2}.(0.1353)^{2}.(0.8647)^{12}) = 0.1353*0.2911 = 0.0394$

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

3 0

2 years ago

PLEASE HELP!!!!!!!!!!!!

Ratling [72]

Answer:

see explanation

Step-by-step explanation:

PQRS is a cyclic quadrilateral.

the opposite angles in a cyclic quadrilateral sum to 180° then

∠ Q + ∠ S = 180 ( substitute values )

3x - 8 + 3x + 8 = 180

6x = 180 ( divide both sides by 6 )

x = 30

Then

∠ Q = 3x - 8 = 3(30) - 8 = 90 - 8 = 82°

∠ S = 3x + 8 = 3(30) + 8 = 90 + 8 = 98°

∠ P = x + 15 = 30 + 15 = 45°

∠ R = 180° - ∠ P = 180° - 45° = 135°

5 0

1 year ago

A line passes through the point (4, -6) and has a slope of -3/4. Which is the

soldi70 [24.7K]

Answer:

I have not dealt with slope for a while but if its in the form y=mx+b then the x is the slope so it would be -3/4x and b is the y intercept. the y in the cords is -6

Step-by-step explanation:

y= -3/4x -6

7 0

2 years ago

Which is different? Find "both" answers.

Sloan [31]

Answer:

Step-by-step explanation:

Question 1

BC - AC and AB will provide different answers when compared to AC + CB and CA + BC. This is because AC means A multiplied by C (AC) or C multiplied by A (CA); thus means AC and CA are the same. Also, CB means C multiplied by B (CB) or B multiplied by C (BC); thus means CB and BC are the same.

Hence, Finding AC + CB will provide the same answer as finding CA + BC

However, finding BC - AC will provide different answer to finding AB because BC - AC means the multiplication of A and C is subtracted from the multiplication of B and C - the answer thereof will most likely be different from the multiplication of just A and B.

Question 2

From the explanation above,

The "different" answer is

Find BC - AC and Find AB

The "same" answer is

Find AC + CB and Find CA + BC

7 0

2 years ago

A model predicts the profit, p of a company as p(x) = x3 – 3x2 – 16x + 48, where p is in thousands of dollars and x is number of

zavuch27 [327]

The first step is to determine the zeros of p(x).
From the Remainder Theorem,
p(a) = 0 => (x-a) is a factor of p(x), and x=a is a zero of p(x).

Try x=3:
p(3) = 3^3 - 3*3^2 - 16*3 + 48 = 27 - 27 - 48 + 48 = 0
Therefore x=3 is a zero, and (x-3) is a factor of p(x).

Perform long division.
x² - 16
-------------------------------------
x-3 | x³ - 3x² - 16x + 48
x³ - 3x²
-----------------------------------
- 16x + 48
- 16x + 48

Note that x² - 6 = (x+4)(x-4).

Therefore the complete factorization of p(x) is
p(x) = (x-3)(x+4)(x-4)

To determine when p(x) is negative, we shall test between the zeros of p(x)
x p(x) Sign
---- --------- ---------
-4 0
0 48 +
3 0
3.5 -1.875 -
4 0

p(x) is negative in the interval x = (3, 4).

Answer
The time interval is Jan. 1, 2014 to Jan. 1, 2015.

3 0

2 years ago