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Zigmanuir [339]

3 years ago

11

Twenty-four distinguishable balls are to be placed in six boxes.(DIFFERENT BOXES) (a) In how many different ways can this be don

e? (b) In how many different ways can this be done if box 1 must get 12 balls, box 2 must get 7 balls, box 3 must get 5 balls, and boxes 4, 5, and 6 must be empty?

1 answer:

zvonat [6]3 years ago

3 0

Answer: a) 124,596, b) 2142691552.

Step-by-step explanation:

Since we have given that

Number of distinguishable balls = 24

Number of boxes = 6

(a) In how many different ways can this be done?

$^{24}C_6\\\\=134,596$

(b) In how many different ways can this be done if box 1 must get 12 balls, box 2 must get 7 balls, box 3 must get 5 balls, and boxes 4, 5, and 6 must be empty?

Number of ways would be

$\dfrac{24!}{12!7!5!}=2142691552$

Hence, a) 124,596, b) 2142691552.

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18.96 x 2.03 correct to 2 significant figures equals what?

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3 years ago

Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/22 , 2 1/4 ) and (−2

Nana76 [90]

Answer: $k=18\dfrac{8}{11}$ .

Step-by-step explanation:

If a line passing through two points, then

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

Endpoints of segment MN have coordinates (0, 0) and (5, 1).

Slope of MN $=\dfrac{1-0}{5-0}=\dfrac{1}{5}$

The endpoints of segment AB have coordinates $\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)$ and $\left(-2\dfrac{1}{4} , k\right)$ .

$A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)$

$B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)$ .

Slope of AB $=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}$

$=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}$

$=\dfrac{4k-9}{4}\times \dfrac{44}{-145}$

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$=\dfrac{44k-99}{-145}$

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Slope of MN × Slope of AB = -1

$\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1$

$\dfrac{44k-99}{-725}=-1$

$44k-99=725$

$44k=725+99$

$k=\dfrac{824}{44}$

$k=\dfrac{206}{11}$

$k=18\dfrac{8}{11}$

Therefore, the value of k is $k=18\dfrac{8}{11}$ .

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4 years ago

Read 2 more answers

For consumers making purchases online, 60% have devices made by Apple, 85% own a smartphone, and 75% use Venmo. Also, out of the

kompoz [17]

Answer:

The probability that a customer selected at random has an Apple device or own a smartphone or both is 0.94

Step-by-step explanation:

The percentage of costumers that have a device made by Apple = 60%

The percentage of customers that own a smartphone = 85%

The percentage of customers that use Venmo = 80%

The percentage out of the smartphone users that use Venmo = 80%

The probability both independent events A and B occurring = P(A) × P(B)

The exclusive probability of A or B occurring P(A XOR B) = P(A) + P(B) - 2 × P(A ∩ B)

Therefore, the probability of A or B or both occurring is given as follows;

P(A or B or Both) = P(A) + P(B) - 2 × P(A ∩ B) + P(A) × P(B)

Where A represent the percentage of costumers that have a device made by Apple and let B represent the percentage of users that have a smartphone, we have;

P(A or B or Both) = 0.6 + 0.85 - 2×0.6×0.85 + 0.6 × 0.85 = 0.94

Therefore, the probability that a customer selected at random has an Apple device or own a smartphone (or both), P(A or B or Both) = 0.94

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3 years ago