What are the roots of the equation 2x^2+85=7

Of all the registered automobiles in a city, 12% fail the emissions test. Fourteen automobiles are selected at random to undergo

postnew [5]

Answer:

a) 0.1542

b) 0.7685

c) 0.2315

d) No, it is not unusual

Explanation:

The procedure to make the test meets the requirements of binomial experiments because:

there are two possible mutually exclusive outputs: fail the test, or pass the test.
the probability of each event remains constant during all the test (p=12% = 0.12, for failing the test, and 1-p = 88% = 0.88, for passing the test)
each trial (test) is independent of other trial.

Solution

(a) Find the probability that exactly three of them fail the test.

You want P(X=3)

Using the equation for discrete binomial experiments, the probability of exactly x successes is:

$P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}$

Substituting C(n,x) with its developed form, that is:

$P(X=x)=\dfrac{n!}{x!\cdot (n-x)!}\cdot p^x\cdot (1-p)^{(n-x)}$

Thus, you must use:

x = 3 (number of automobiles that fail the emissions test)
n = 14 (the number of automobiles selected to undergo the emissions test),
p = 0.12 (probability of failing the test; this is the success of the variable on our binomial experiment)
1 - p = 0.88 (probability of passing the test; this is the fail of the variable on our binomial experiment)

$P(X=3)=\dfrac{14!}{3!\cdot (14-3)!}\cdot 0.12^3\cdot 0.88^{11}=0.1542$

(b) Find the probability that fewer than three of them fail the test.

The probability that fewer than three of them fail the test is the probability that exactly 0, or exactly 1, or exactly 2 fail the test.

That is: P(X=0) + P(X=1) + P(X=2)

Using the same formula:

$P(X=0)=\dfrac{14!}{0!\cdot 14!}\times 0.12^0\cdot 0.88^{14}$

$P(X=0)=0.1670$

$P(X=1)=\dfrac{14!}{1!\cdot 13!}\cdot 0.12^1\cdot 0.88^{13}$

$P(X=1)=0.3188$

$P(X=2)=\dfrac{14!}{2!\cdot 12!}\codt0.12^2\cdot 0.88^{12}$

$P(X=2)=0.2826$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.7685

(c) Find the probability that more than two of them fail the test.

The probability that more than two of them fail the test is equal to 1 less the probability that exactly 0, or exactly 1, or exactly 2 fail the test:

P( X > 2) = 1 - P( X = 0) - P(X = 1) - P(X = 2)

P X > 2) = 1 - [P(X=0) + P(X = 1) + P(X = 2)]

P (X > 2) = 1 - [0.7685]

P (X > 2) = 0.2315

(d) Would it be unusual for none of them to fail the test?

Remember that not failing the test is the fail of the binomial distribution. Thus, none of them failing the test is the same as all of them passing the test.

You can find the probability that all the automibles pass the emission tests by multiplying the probability of passing the test (0.88) 14 times.

Then, the probability that none of them to fail the test is equal to:

$(1-p)^{14}\\\\(0.88)^{14}=0.1671$

That means that the probability than none of the automobiles of the sample fail the test is 16.71%.

Unusual events are usually taken as events with a probability less than 5%. Thus, this event should not be considered as unusual.

5 0

3 years ago

A salesman receives a commission of $4 for every pair of dress shoes he sells. He is paid $3 for every pair of athletic shoes he

Crank

Answer: he sold 9 pairs of dress shoes.

he sold 4 pairs of athletic shoes.

Step-by-step explanation:

Let x represent the number of pairs of dress shoes that he sells.

Let y represent the number of pairs of athletic shoes that he sells.

The total number of pairs of shoes that he sold in a day is 13. It means that

x + y = 13

The salesman receives a commission of $4 for every pair of dress shoes he sells. He is paid $3 for every pair of athletic shoes he sells. The commission that he got on that day was $48. It means that

4x + 3y = 48- - - - - - - - - - 1

Substituting x = 13 - y into equation 1, it becomes

4(13 - y) + 3y = 48

52 - 4y + 3y = 48

- 4y + 3y = 48 - 52

- y = - 4

y = 4

x = 13 - y = 13 - 4

x = 9

4 0

3 years ago

Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection. y + 5 = 2 x y = 7 − 2

Butoxors [25]

Answer:

The point of intersection is (3,1)

Step-by-step explanation:

Manipulate these equations to achieve the form of y = mx + c

1) y + 5 = 2x

Y = 2x - 5

2) y = 7 - 2x

Y = -2x + 7

Point of intersection is (3,1) on the graph attached

To check algebraically:

2x - 5 = -2x + 7

4x = 12

X = 3

Substitute to get y

Y = 2x - 5

Y = 2 x 3 - 5

Y = 1

Therefore (3,1)

5 0

2 years ago

What are the slope and y-intercept of the graph of the given equation?

inn [45]

The equation given is in slope-intercept form. This is the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -4 and the y-intercept is 2. The answer is A.

5 0

4 years ago

Read 2 more answers

Divide the following fractions and reduce to lowest terms 2/3 divided by 4/5

pshichka [43]

Well to divide 2 fraction you first have to find a least common number between the 2 bottom numbers in the fractions, we know automaticall that 15 fits in both the 3 and the 5. now u have to find out what to multiply by each number to get 15, for example what number do you multiply by 3 to get 15?? well it will be 5, so go ahead and multiply it by the fraction (note that what you do in the bottom you have to do in the top) this will give you 10/15, because I multiplied the top and bottom number by 5... lets try the other one what number do you multiply by 5 to get 15?? well it will be 3 so go ahead and multiply that to get 12/15.. now add the top numbers (note that the bottoms always stay the same, you never add or subtract them) when you do you will get 22/15, now you have to see if you can simplify it any further in this case you can't so your final answer is 22/15

Hope this helps

5 0

3 years ago