In the Big 4 lottery, for a bet of $100, the payoff is $5000. What is the expected

A group of preschoolers has 16 boys and 66 girls. What is the ratio of boys to all students

GREYUIT [131]

The ratio would be 8/41 since the total number of students is 82. (16+66). then, the ratio of boys to all students is 16/82. then, just simplify the ratio and the answer is 8/41

6 0

3 years ago

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

CAN SOMEONE PLEASE HELP ME WITH THIS ITS DUE TODAY

saveliy_v [14]

1. 4 x 31 is 124

2. 7 x 49 is 658

3. 16 x 48 is 608

4. 8(5 + w) is 8w + 40

5. 11(9 + d) is 11d + 99

6. 15(p + 4 + 2) is 15p + 90

7. Let's simplify step-by-step.

2x−4+3x

=2x+−4+3x

Combine Like Terms:

=2x+−4+3x

=(2x+3x)+(−4)

=5x+−4.

8. Let's simplify step-by-step.

4y−1−3y−2

=4y+−1+−3y+−2

Combine Like Terms:

=4y+−1+−3y+−2

=(4y+−3y)+(−1+−2)

=y+−3.

9. Let's simplify step-by-step.

x+2(x−4)

Distribute:

=x+(2)(x)+(2)(−4)

=x+2x+−8

Combine Like Terms:

=x+2x+−8

=(x+2x)+(−8)

=3x+−8.

10. Part A)

The jazz band sells 31 large boxes of fruit and 74 small boxes of fruit.

For each large fruit box, the price is $20 and cost is $x.

Profit is defined as Price - Cost.

So, profit for one large fruit box = 20 - x

Profit for 31 large fruit boxes = 31(20 - x)

Price of each small fruit box is $10 and cost of each small fruit box is $y. The profit for each small fruit box is 10 - y.

Profit for 74 small fruit boxes = 74(10 - y)

The total profit for 31 large boxes and 74 small boxes will be:

Total profit = 31 (20 - x ) + 74(10 - y)

Using distributive property, we can simplify the above equation as:

Total profit = 31(20) - 31x +74(10) - 74y

Total profit = 1360 - 31x - 74y

Part B)

Cost of each large box is given to be $9. This means x = 9

Cost of each small box is given to be $4. This means y = 4

Using the values of x and y in the profit equation we can find the profit of the Jazz Band.

So, Jazz Band's Profit = 1360 - 31(9) - 74(4)

Jazz Band's Profit = $ 785

Thus the profit of Jazz Band will be $785.

Have A good day!! Hope I helped!!! ^-^

6 0

3 years ago

Find the circumference of a circle with a radius of 6 cm

inysia [295]

Answer:

C = 12π cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Circumference: C = 2πr

Step-by-step explanation:

Step 1: Define

Radius r = 6 cm

Step 2: Find C

Substitute: C = 2π(6)
Multiply: C = 12π

7 0

3 years ago

To find 27x9 I find 27x10 and remove 1 group of 27

solniwko [45]

Answer:

yes because 10 groups 27 taking 1 group of 27 is now 9 groups of 27

10*27-27=243 is equal to 9*27=243

5 0

3 years ago