All categories

2 years ago

Cellus

Mathematics

1 answer:

mote1985 [20]2 years ago

4 0

Answer:

y = 6 when x = 18

Step-by-step explanation:

The appropriate formula for this direct proportion is y = kx, where k is the constant of proportionality.

We know y = 3 when x = 9: 3 = k(9)

This yields k = 3/9, or k = 1/3

Then the formula is y = (1/3)x

and when x = 18, y = (1/3)(18) = 6

y = 6 when x = 18

You might be interested in

The Springfield School band has 300 sweatshirts to sell at the fund-raiser.A survey shows that 2 out of 7 students in the school

nydimaria [60]

260 students is the prediction for how many sweatshirts will be sold so no they will not sell all of them

5 0

3 years ago

An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. (a) Use a bin

Advocard [28]

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial 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.

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.

To use the Poisson approximation for the binomial, we have that:

$\mu = np$

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that $p = \frac{1}{2500} = 0.0004$

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is $P(X = 4)$ when $n = 7000$ . So

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

$P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558$

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

$\mu = np = 7000*0.0004 = 2.8$ . So

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

$P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557$

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

6 0

3 years ago

A jar contains 12 red marbles numbered 1 to 12 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. F

klasskru [66]

Answer:

Step-by-step explanation:

Step one:

given data

sample space

red marbles= 12

blue marbles= 10

sample size= 12+10

sample size= 22

Step two:

Required

Find the probability of the given event. (a) The marble is red

Let the probabiilty be P(R)

P(R)= 12/22

P(R)= 6/11

8 0

3 years ago

3. A number increased by 5 and divided by 2 is equal to 75. What is the number?

frez [133]

Answer:

633

Step-by-step explanation:

3 0

3 years ago

Simplify (3x + 2)(4x - 4)

NISA [10]

Answer:

12x² - 4x - 8

Step-by-step explanation:

Use FOIL method

(3x + 2)(4x - 4) = 3x*4x + 3x*(-4) + 2 *4x + 2*(-4)

= 12x² - 12x + 8x - 8 {add like terms}

= 12x² - 4x - 8

Hint: 3x * 4x -----> Multiply the coefficients = 3 *4 = 12 and then multiply the variables and for multiplying the two variable, add the powers

x*x = $x^{1+1)=x^{2}$

3x * 4x = 12x²

4 0

3 years ago