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kvasek [131]
3 years ago
8

Mykel is picking out some movies to rent, and he has narrowed down his selections to 66 foreign films, 33 children's movies, 66

dramas, and 44 documentaries. How many different combinations of 99 movies can he rent if he wants all 66 dramas?
Mathematics
1 answer:
uranmaximum [27]3 years ago
7 0

Answer:

Mykel can make 2.79 x 10³² different combinations

Step-by-step explanation:

We can solve this problem using combination

The formula for combination is ⁿCₐ = \frac{n!}{(n - a)!a!}

where n = total number of choices available

a = number of items being chosen

The total movies Mykel wants is 99.

Taking out the sure 66 drama movies,

Mykel is left with 99 - 66 choices = 33 choices.

The total number of choices he is left with is 66 foreign + 33 children + 44 documentaries = 143 movies

Hence, our n = 143 movies

and a = 33 choices

Hence we do, ¹⁴⁴C₃₃ = \frac{143!}{(143 - 33)!33!} = \frac{143!}{110!33!} 2.79 x 10³² combinations

∴ Mykel can make 2.79 x 10³² different combinations.

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Because you have to also think about tax of the item. Plus add them both up and it costs $2.24 without tax. Which means it's already above $2.

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Katya made another set of dolls. In the new set, the largest doll has a diameter of 8.75 cm and a height of 15.6 cm. Is this a d
Natali5045456 [20]

<em>Complete Question:</em>

<em>Katya creates handmade sets of dolls, which is sold to craft and souvenir stores. The first set of dolls has a middle diameter of 7cm and a height of 12cm.</em>

<em>Katya made another set of dolls. In the new set, the largest doll has a diameter of 8.75 cm and a height of 15.6 cm. Is this a dilation of the first set of dolls? </em>

<em></em>

Answer:

The new set is not a dilation of the first set

Step-by-step explanation:

Given

First Set:

Height = 12cm

Diameter = 7cm

New Set:

Height = 15.6cm

Diameter = 8.75cm

Required

Determine if the new set is a dilation of the second

To do this, we pass through the following steps:

1. Divide the height of the first set by the new set

2. Divide the diameter of the first set by the new set

3. Result in (1) and (2) must be equal if the new set is a dilation of the first set

Following the steps above:

(1)

Height\ Ratio = \frac{H_2}{H_1}

Height\ Ratio = \frac{15.6}{12}

Height\ Ratio = 1.3

(2)

Diameter\ Ratio = \frac{D_2}{D_1}

Diameter\ Ratio = \frac{8.75}{7}

Diameter\ Ratio = 1.25

(3) Make comparison

The ratio in (1) does not equal the ratio in (2)

i.e.

1.3 \neq 1.25

<em>Hence, the new set is not a dilation of the first set</em>

7 0
3 years ago
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