There is a bag filled with 4 blue and 5 red marbles.

A blimp travels 255 feet in 1/2minute, 510 feet in 1/6 minute, and 3,060 feet in 1 minute.

borishaifa [10]

Answer:

We conclude that there is NOT a proportional relationship between the distance the blimp travels and the time it travels.

Step-by-step explanation:

We know if y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where k is called the constant of variation.

In our case we are given:

A blimp travels 255 feet in 1/2 minute

A blimp travels 255 feet in 1/2minute.

here:

y = 255, and x = 1/2 = 0.5

so substituting y = 255 and x = 0.5 in the equation

k = y/x

k = 255 / 0.5

k = 510

A blimp travels 510 feet in 1/6 minute

here:

y = 510 , and x = 1/6

so substituting y = 510 and x = 1/6 in the equation

k = y/x

k = [510] / [1/6]

k = 3060

A blimp travels 3,060 feet in 1 minute

here

y = 3,060, and x = 1

so substituting y = 3,060 and x = 1 in the equation

k = y/x

k = 3,060 / 1

k = 3060

HERE IS THE VARIATION OF THE CONSTANT OF VARIATION:

A blimp travels 255 feet in 1/2 minute

k = 510

A blimp travels 255 feet in 1/2 minute

k = 3060

A blimp travels 3,060 feet in 1 minute

k = 3060

It is clear that the constant of variation does not remain constant.

Therefore, we conclude that there is NOT a proportional relationship between the distance the blimp travels and the time it travels.

6 0

3 years ago

A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective

andriy [413]

Answer:

(a) P(X $\leq$ 20) = 0.9319

(b) Expected number of defective light bulbs = 15

(c) Standard deviation of defective light bulbs = 3.67

Step-by-step explanation:

We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.

Firstly, the above situation can be represented through binomial distribution, i.e.;

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

where, n = number of samples taken = 150

r = number of success

p = probability of success which in our question is % of bulbs that

are defective, i.e. 10%

Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.

So, Let X = No. of defective bulbs in a box

Mean of X, $\mu$ = $n \times p$ = $150 \times 0.10$ = 15

Standard deviation of X, $\sigma$ = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.7

So, X ~ N( $\mu = 15, \sigma^{2} = 3.7^{2})$

Now, the z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X $\leq$ 20) = P(X < 20.5) ---- using continuity correction

P(X < 20.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{20.5-15}{3.7}$ ) = P(Z < 1.49) = 0.9319

(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = $n \times p$ = $150 \times 0.10$ = 15.

Standard deviation of defective light bulbs is given by = S.D. = $\sqrt{np(1-p)}$ = $\sqrt{150 \times 0.10 \times (1-0.10)}$ = 3.67

8 0

3 years ago

A) Work out the value of 213 + (29)2

Alina [70]

a) 2^13 / 2^18

b) 216

6 0

3 years ago

What is time-and-a-half for $7.51?

padilas [110]

Answer:

$15.2

Step-by-step explanation:

3 0

3 years ago

“Bishon needs to sell at least 0.3 of his Collin sports card to make room for new cards.is 3/20 of his collection enough? Explai

Darya [45]

Answer:

I dont know But maybe the answer is No

Step-by-step explanation:

0.3 is 30% and if 1/10 is 10% then 2/20 must be 10% because 5% is 1/20

so maybe 3/20 is only 15%

I hope this helps :)

Sorry if it dosent i suck at explaining things ; - ;

3 0

3 years ago