Given that y = 11 cm and θ = 34°, work out x rounded to 1 DP.

In a city school, 60% of students have blue eyes, 55% have dark hair, and 35% have blue eyes and dark hair. What is the probabil

gulaghasi [49]

Answer:

58%

Step-by-step explanation:

This is a problem of conditional probability.

Let A represent the event that student has dark hair.

So P(A) = 55% = 0.55

Let B represents the event that student has blue eyes.

So, P(B) = 60% = 0.60

Probability that student has blue eyes and dark hairs = P(A and B) = 35% = 0.35

We are to find the probability that a randomly selected student will have dark hair, given that the student has blue eyes. Using the given formula and values, we get:

$P(A|B)=\frac{P(A \cap B)}{P(B)}\\\\ P(A|B)=\frac{0.35}{0.60}\\\\ P(A|B)=0.58$

Therefore, there is 0.58 or 58% probability that the student will have dark hairs, given that the student has blue eyes.

5 0

3 years ago

What does 204 and 1320 both go into NEED ANSWER ASAP!!!

Ghella [55]

Answer:

22,440

Step-by-step explanation:

204 = 2 * 2 * 3 * 17

1320 = 2 * 2 * 2 * 3 * 5 * 11

They both have 2 2's and a 3 in common, so use them once

2 * 2 * 3 * 17 * 2 * 5 * 11 = 22,440

5 0

3 years ago

Read 2 more answers

43.

aleksklad [387]

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

4 0

3 years ago

Suppose that 10% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeown

guapka [62]

Remainder of question:

Find the probability distribution of x

Answer:

The random variable x is defined as: X = {0, 1, 2, 3, 4}

The probability distribution of X:

P(X = 0) = 0.656

P(X = 1) = 0.2916

P(X= 2) = 0.0486

P(X=3) = 0.0036

P(X = 4) = 0.0001

Step-by-step explanation:

Sample size, n = 4

Random variable, X = {0, 1, 2, 3, 4}

10% (0.1) of the homeowners are insured against earthquake, p = 0.1

Proportion of homeowners who are not insured against earthquake, q = 1 - 0.1

q = 0.9

Probability distribution of x,

$P(X = r) = ^nC_r *p^r q^{n-r} \\\\P(X= 0) =(^4C_0 *p^1 q^4 )\\P(X=0) = (^4C_0 *0.1^0 0.9^4 ) = 0.656\\P(X= 1)= (^4C_1 *p^1 q^3 )\\P(X=1) = (^4C_1 *0.1^1 0.9^3 ) = 0.2916\\P(X= 2)=( ^4C_2 *p^2 q^2) \\P(X=2) = (^4C_2 *0.1^2 0.9^2 ) = 0.0486\\P(X= 3) = (^4C_3 *p^3 q^3) \\ P(X=3) = (^4C_3 *0.1^3 0.9^1 ) = 0.0036\\P(X= 4) = (^4C_4 *p^4 q^0 )\\ P(X=4) =(^4C_4 *0.1^4 0.9^0 ) = 0.0001$

5 0

3 years ago

A lot of 80 bulbs contains 45 defective and 32 non warranty bulbs. One bulb is drawn at random from the lot. What is the probabi

kenny6666 [7]

Step-by-step explanation:

Total bulbs = 80

Probability of defective bulbs = 45/80 = 9/16

Probability of non warranty bulbs = 32/80 = 4/5

5 0

3 years ago