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lions [1.4K]
3 years ago
14

PERMUTATION:

Mathematics
1 answer:
horsena [70]3 years ago
5 0

Answer:

28

Step-by-step explanation:

It can be a one digit no.

_

2C1 = 2 (only two even options available)

It can be a 2 digit no.

_ _

The last digit has to be even for the no. to be even.

2C1 × 4C1 = 8 (2C1 for the last digit, 4C1 for the first)

It can be a 3 digit no.

_ _ _

First digit has to be less than 5 to be less than 500, and the last digit has to be even.

1) 2/4 _ 4

2C1 × 3C1 = 6 (2C1 to choose between 2 and 4, 3C1 for the second digit)

2) 1/3 _ 2/4

2C1 × 3C1 × 2C1 = 12 (2C1 to choose between 1 and 3, 3C1 for the second digit, 2C1 to choose between 2 and 4)

Total = 2 + 8 + (6 + 12)

= 28

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Answer: Choice B

Shortage of corn

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Explanation:

Let's focus on each product separately, starting with the corn.

If the government sets a ceiling on the price below equilibrium, then this means the price is too low compared to what buyers and sellers would naturally agree on (through the market forces of supply and demand). The price cannot rise (legally that is) above the ceiling no matter how much it wants to.

Since the price is too low, producers aren't going to have much incentive to make as much corn. At the same time, buyers are going to demand more corn. This results in a shortage. This always happens when there are more buyers than sellers.

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Now onto the wheat.

The floor price being below the equilibrium price is a bit silly and not needed. There is no need for a floor in this location because the price will naturally gravitate toward equilibrium. If the floor was set above the equilibrium, then we'd have an oversupply of wheat. That isn't the case here.

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6 0
2 years ago
Suppose you want to build a small walkway around your garden so that there is someplace to walk around and work on your vegetabl
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Answer:

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Step-by-step explanation:

Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.

( 30 + 2x ) * ( 20 + 2x ) = 1000 - Expand "( 30 + 2x ) * ( 20 + 2x )"

600 + 100x + 4x^2 = 1000 - Subtract 1000 on either side, making on side = 0

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( Quadratic Equation is as follows ) - x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a},

x=\frac{-100+\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad \frac{5\left(\sqrt{41}-5\right)}{2},

x=\frac{-100-\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad -\frac{5\left(5+\sqrt{41}\right)}{2}

There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) \frac{5\left(\sqrt{41}-5\right)}{2}. The approximated value however is 3.5081...or approximately 3.5 feet.

4 0
3 years ago
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Volume of the prism:
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3 years ago
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Answer:

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