MATHEMATICS COLLEGE

Use the data set to create a quadratic function if it applies. Use the model to predict the value of x when y = -4. (-3, 10), (0, 4), (3, -1), (6, -5), (9, -8)

Question 3 options:

A)

29.32 and 3.97

B)

32.27 and 4.57

C)

27.48 and 5.20

D)

No Solution

Answers

Answer 1

Answer:

The closest choice is ...

C) 27.48 and 5.20

Step-by-step explanation:

Using the equation ...

y = ax² + bx + c

You can substitute the first three points to get linear equations in a, b, and c.

10 = a(-3)² +b(-3) +c = 9a -3b +c

4 = a(0)² + b(0) +c = c

-1 = a(3)² + b(3) +c = 9a +3b +c

The second equation tells us c=4. Subtracting the first equation from the last, we get ...

(9a +3b +c) -(9a -3b +c) = (-1) -(10)

6b = -11

b = -11/6

Then we can find "a" from the first equation:

10 = 9a -3(-11/6) +4

1/2 = 9a . . . . subtract 19/2

1/18 = a . . . . . divide by 9

The model is ...

y = (1/18)x² -(11/6)x +4 . . . . . . . . [call this "model A"]

y = (x² -33x +72)/18

Solving this for y = -4, we have ...

-4 = (x² -33x +72)/18

x² -33x +144 = 0 . . . . . . multiply by 18, add 72

(x -16.5)² -128.25 = 0 . . . . put in vertex form

x = 16.5 ±√128.25 ≈ {5.17525, 27.8248}

___

The closest values to these among the choices offered are those of choice C. It appears that the coefficients of model A were rounded to 3 decimal places (or so) before the predicted x-values were computed.

Related Questions

The solution to 4.2x = 19.32 is x = ___. 0.28 0.45 4.6 15.12
A. 35/12B. 12/37C. 12/35D. 35/37
Find an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is divisible by 4.
Select the correct answer if g=8,what is the value of the expression g/2+3
Trick or treaters arrive to your house according to a Poisson process with a constant rate parameter of 20 per hour. Suppose you begin sitting on your front porch, observing these arrivals, at some point in time. Suppose a trick or treater arrived 30 minutes ago, but there have been none since. What is the expected value of interarrival time (in minutes) from the previous trick or treater to the next one

Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.)Center

(4, −5)

and passes through

(7, 4)

Answers

Answer:

$(x-4)^2+(y+5)^2=90$

Step-by-step explanation:

The equation of a circle of radius r, centered at the point (a,b) is

$(x-a)^2+(y-b)^2=r^2$

We already know the center is at $(4,-5)$ , we are just missing the radius. To find the radius, we can use the fact that the circle passes through the point (7,4), and so the radius is just the distance from the center to this point (see attached image). So we find the distance by using distance formula between the points (7,4) and (4,-5):

radius $=√((7-4)^2+(4-(-5))^2)=√(3^2+9^2)=√(90)$

And now that we know the radius, we can write the equation of the circle:

$(x-4)^2+(y-(-5))^2=√(90)^2$

$(x-4)^2+(y+5)^2=90$

According to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered. (In contrast, only 2% of bikes stolen in New York City are recovered.) Find the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered. Find the nearest answer.

Answers

Answer:

0.31104

Step-by-step explanation:

Given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.

If X represents the number of bicyles stolen in Sydney, X is binomial

because each cycle to be stolen is independent of the other.

Also there are two outcomes

n = 6, p = 0.40

Required probability = the probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered

==P(X=2)

= $6C2 (0.4)^2 (0.6)^4\n= 15(0.16)(0.6)^4\n=0.31104$

Answer:

Probability that exactly 2 out of 6 bikes are recovered is 0.31.

Step-by-step explanation:

We are given that according to the Sydney Morning Herald, 40% of bicycles stolen in Holland are recovered.

Also, there is a sample of 6 randomly selected cases of bicycles stolen in Holland.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 cases of bicycles

r = number of success = exactly 2

p = probability of success which in our question is % of bicycles

stolen in Holland that are being recovered, i.e; 40%

LET X = Number of bikes recovered

So, it means X ~ $Binom(n=6, p=0.40)$

Now, Probability that exactly 2 out of 6 bikes are recovered is given by = P(X = 2)

P(X = 2) = $\binom{6}{2}0.40^(2) (1-0.40)^(6-2)$

= $15 * 0.40^(2) * 0.60^(4)$

= 0.31

Therefore, Probability that, in a sample of 6 randomly selected cases of bicycles stolen in Holland, exactly 2 out of 6 bikes are recovered is 0.31.

If f(x) = 2x + 2 and g(x) = x2 - 1, find (f - g)(x).

Answers

Answer:

(f - g)(x) = - x² + 2x + 3

Step-by-step explanation:

f(x) = 2x + 2

g(x) = x² - 1

To find (f - g)(x) subtract g(x) from f(x)

That's

(f - g)(x) = 2x + 2 - [ x² - 1]

(f - g)(x) = 2x + 2 - x² + 1

Group like terms

That's

(f - g)(x) = - x² + 2x + 2 + 1

We have the final answer as

(f - g)(x) = - x² + 2x + 3

Hope this helps you

Answer:

-x2+2x+3

Step-by-step explanation:

(2x+2)- (x2-1)

2x+2-x2+1

-x2+2x+3

Find the slope of the line that contains the points:
(-6, 3) and (-4, 5).

Answers

Answer:

slope m=1

Step-by-step explanation:

m=y2-y1/x2-x1

m=5-3/-4-(-6)

m=5-3/-4+6

m=2/2

m=1

8 POINTS WILL BE GIVEN!!

Answers

24° because it says x=24° have a nice day :)

Answer:

x=39 degrees

Step-by-step explanation:

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 5%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that a) None of the LED light bulbs are defective? b) Exactly one of the LED light bulbs is defective? c) Two or fewer of the LED light bulbs are defective? d) Three or more of the LED light bulbs are not defective?

Answers

Answer:

a) There is a 59.87% probability that none of the LED light bulbs are defective.

b) There is a 31.51% probability that exactly one of the light bulbs is defective.

c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) There is a 100% probability that three or more of the LED light bulbs are not defective.

Step-by-step explanation:

For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that 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 combinatios of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

In this problem we have that:

$n = 10, p = 0.05$

a) None of the LED light bulbs are defective?

This is P(X = 0).

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

$P(X = 0) = C_(10,0)*(0.05)^(0)*(0.95)^(10) = 0.5987$

There is a 59.87% probability that none of the LED light bulbs are defective.

b) Exactly one of the LED light bulbs is defective?

This is P(X = 1).

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

$P(X = 1) = C_(10,1)*(0.05)^(1)*(0.95)^(9) = 0.3151$

There is a 31.51% probability that exactly one of the light bulbs is defective.

c) Two or fewer of the LED light bulbs are defective?

This is

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

$P(X = 2) = C_(10,2)*(0.05)^(2)*(0.95)^(8) = 0.0746$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.5987 + 0.3151 + 0.0746 0.9884$

There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) Three or more of the LED light bulbs are not defective?

Now we use p = 0.95.

Either two or fewer are not defective, or three or more are not defective. The sum of these probabilities is decimal 1.

$P(X \leq 2) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X \leq 2)$

In which

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

$P(X = 0) = C_(10,0)*(0.95)^(0)*(0.05)^(10)\cong 0$

$P(X = 1) = C_(10,1)*(0.95)^(1)*(0.05)^(9) \cong 0$

$P(X = 2) = C_(10,1)*(0.95)^(2)*(0.05)^(8) \cong 0$

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

$P(X \geq 3) = 1 - P(X \leq 2) = 1$

There is a 100% probability that three or more of the LED light bulbs are not defective.

Final answer:

The question relates to binomial distribution in probability theory. The probabilities calculated include those of none, one, two or less, and three or more LED bulbs being defective out of a random sample of 10.

Explanation:

This question relates to the binomial probability distribution. A binomial distribution is applicable because there are exactly two outcomes in each trial (either the LED bulb is defective or it's not) and the probability of a success remains consistent.

a) In this scenario, 'none of the bulbs being defective' means 10 successes. The formula for probability in a binomial distribution is p(x) = C(n, x) * [p^x] * [(1-p)^(n-x)]. Plugging in the values, we find p(10) = C(10, 10) * [0.95^10] * [0.05^0] = 0.5987 or 59.87%.

b) 'Exactly one of the bulbs being defective' implies 9 successes and 1 failure. Following the same formula, we get p(9) = C(10, 9) * [0.95^9] * [0.05^1] = 0.3151 or 31.51%.

c) 'Two or less bulbs being defective' means 8, 9 or 10 successes. We add the probabilities calculated in (a) and (b) with that of 8 successes to get this probability. Therefore, p(8 or 9 or 10) = p(8) + p(9) + p(10) = 0.95.

d) 'Three or more bulbs are not defective' means anywhere from 3 to 10 successes. As the failure rate is low, it's easier to calculate the case for 0, 1 and 2 successes and subtract it from 1 to find this probability. This gives us p(>=3) = 1 - p(2) - p(1) - p(0) = 0.98.