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tankabanditka [31]
3 years ago
13

Kyra has a rock collection. When she puts her rocks into 2 equal plies, there are no rocks left over. When she puts her rocks in

to 3 equal piles, there are still no rocks left over. When she puts her rock into 4 equal piles, there are still no rock left over. How many rocks could kyra have?
Mathematics
1 answer:
Nat2105 [25]3 years ago
8 0

Step-by-step explanation:

According to this description we need a number that can be divided by 2,3 and 4 since the amount of rocks can be described by a natural number. However if a number is divided by 4 it is divided by 2 as well since 2*2=4.

\frac{x}{4}  =  \alpha  \\  \frac{x}{2}  = 2 \alpha

If α is a natural number then 2*α is a natural number as well as the product of two natural numbers.

Which means that we need a number devided by 3 and 4.

The smallest number that fulfills this demand is 3*4=12.

Also any product of 12 with any natural number can be devided by 3, 4 and 2.

If the exercise asks for the numbers that are divided only by 2,3 and 4 these are:

{3}^{ \alpha }  \times 12 \: and \:  {4}^{ \alpha }  \times 12 \:  \\ where \:  \alpha  \: belongs \: to \: the \: set \: of \: all \: \\ natural \: numbers

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You want to surround the perimeter of a garden with 35 stones. You need to place a certain number of large and small stones, and
murzikaleks [220]

Answer: A) x + 4x = 35;  7 large stones and 28 small stones

======================================================

Explanation:

x = number of large stones

4x = number of small stones

x+4x = total number of stones = 35

x+4x = 35 is the equation to solve

-----------

Let's isolate x

x+4x = 35

5x = 35

x = 35/5

x = 7 large stones are needed

4x = 4*7 = 28 small stones are needed

8 0
3 years ago
4. In a sample of 1000 people, 130 can wiggle their ears. Two unrelated people are
Elina [12.6K]

Using the hypergeometric distribution, it is found that there is a 0.7568 = 75.68% probability that neither can wiggle his or her ears.

The people are chosen from the sample without replacement, which is why the <u>hypergeometric distribution</u> is used to solve this question.

Hypergeometric distribution:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

In this problem:

  • 1000 people means that N = 1000
  • 130 can wiggle their ears, thus k = 130
  • Two are selected, thus n = 2.

The probability that neither can wiggle his or her ears is P(X = 0), thus:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = x) = h(0,1000,2,130) = \frac{C_{130,0}C_{870,2}}{C_{1000,2}} = 0.7568

0.7568 = 75.68% probability that neither can wiggle his or her ears.

A similar problem is given at brainly.com/question/24826394

5 0
2 years ago
The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previ
jekas [21]

Given Information:

Cost price = $4

Selling price = $10

Salvage value = $1.50

Average demand = μ = 250 boxes

Standard deviation = σ = 34 boxes

Required Information:

Number of lettuce boxes = ?

Answer:

The supermarket should purchase 268 boxes  of lettuce

Step-by-step explanation:

The required number of lettuce boxes that supermarket should purchase is given by

Number of lettuce boxes = μ + (z*σ)

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z is the z-score which is given by

p = C_us/(C_us + C_os)

The z-score corresponding to probability p will be obtained.

The cost of under stocking is given by

C_us = Selling price - Cost price

C_us = $10 - $4

C_us = $6

The cost of over stocking is given by

C_os = Cost price - Salvage value

C_os = $4 - $1.50

C_os = $2.50

p = C_us/(C_us + C_os)

p = 6/(6 + 2.50)

p = 0.7058

p  = 70.58%

The z-score corresponding to 70.58% probability is approximately 0.54

Number of lettuce boxes = μ + (z*σ)

Number of lettuce boxes = 250 + (0.54*34)

Number of lettuce boxes = 250 + (18.36)

Number of lettuce boxes = 268.36

Number of lettuce boxes ≈ 268

Therefore, the supermarket should purchase 268 boxes of lettuce.

How to use z-table?

Step 1:

In the z-table, find the probability you are looking for and note down the two-digit number of the given row. (e.g 0.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table and note down the value in the column for the remaining decimal point in the range of 0.00 to 0.09.

Step 3:

Finally, add the numbers obtained from step 1 and step 2.

8 0
3 years ago
What is the greatest common factor of 54x^3, 18x, 36x^2
Alex73 [517]
It’s 18x because 36 and 54 are both divisible by 18, and 18 can be divisible by 18 (making 1), resulting in 18 being the most common number between the numbers, whereas the ‘x’ is common between all 3 numbers and since the least amount of x is 1, the answer is just x without an exponent
4 0
3 years ago
a garden is in the shape of a square with a perimeter of 60 feet. the garden is surrounded by two fences. one fence is around th
Anon25 [30]

Answer: The total cost of the fences=$165.6

Step-by-step explanation:

Let a = the length of the side if the square.

The perimeter of the square is 60 ft

                                   4a = 60ft

divide both sides by

                                  4a = 60/4

                                    a = 15 ft

The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside

Expand to get:

                               4*a + 4(a + 2*3)

Replace a with 15 to get:

                         =  4*15 + 4(15 + 6) 60 + 4(21) 60+84

                         = 144ft

The cost of the fence is $1.15 per foot

The cost of 144 ft fence will be:

                       = 144*1.15

                       = $165.6

Learn more about event correlation here: brainly.com/question/1333555

#21165

7 0
1 year ago
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