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Maru [420]
3 years ago
5

Find the value of the following expression

Mathematics
1 answer:
Misha Larkins [42]3 years ago
6 0

Looks like the expression is

(2⁸ • 5⁻⁵ • 19⁰) • (5⁻² / 2³)⁴ • 2²⁸

First, any positive number raised to 0 is 1:

(2⁸ • 5⁻⁵ • 1) • (5⁻² / 2³)⁴ • 2²⁸

(2⁸ • 5⁻⁵) • (5⁻² / 2³)⁴ • 2²⁸

Exponents in a denominator can be rewritten as negative exponents in the numerator:

(2⁸ • 5⁻⁵) • (5⁻² • 2⁻³)⁴ • 2²⁸

Distribute the 4th power across the product 5⁻² • 2⁻³ :

(5⁻² • 2⁻³)⁴ = 5⁻⁸ • 2⁻¹²

so we have

(2⁸ • 5⁻⁵) • (5⁻⁸ • 2⁻¹²) • 2²⁸

Multiplication is associative, so we can ignore the parentheses. Combine factors with equal bases and simplify the exponents:

2⁸ • 5⁻⁵ • 5⁻⁸ • 2⁻¹² • 2²⁸

2⁸⁻¹²⁺²⁸ • 5⁻⁵⁻⁸

2²⁴ • 5⁻¹³

Rewrite the negative exponent as a positive one:

2²⁴ / 5¹³

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Answer: 42

Step-by-step explanation:

Let A represents the number of freshmen participated in sports and B represents the number of  freshmen participated in clubs.

Then , we have given that

n(A)=55\\\\n(B)=68\\\\n(A\cup B)=110

Using formula

n(A\cup B)=n(A)+n(B)-n(A\cap B)

We have,

110=55+68-n(A\cap B)\\\\\Rightarrow\ n(A\cap B)=123-110=13

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n(A)-n(A\cap B)=55-13=42

Hence, 42 students are involved in just sports.

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

Methods of depreciation

In practice, several different methods for calculating depreciation are used. These methods can be either based on the passage of time or the level of usage of the asset. The following depreciation methods can be applied to different types of tangible assets:

Note that at the end of an asset lifespan, the total amount of its depreciation will be identical, no matter which method of depreciation is applied. The only thing that varies over the different methods of depreciation is the timing (the amount of money that is depreciated over the smaller periods).

In the further part of this text, we will focus on the description of the three most commonly used types of depreciation: the straight line depreciation, the declining balance depreciation, and the sum of years digits depreciation. We're going to pay attention especially to the depreciation formulas and the detailed explanation of how to calculate the value of depreciation with each of them.

Residual value and depreciation

As was already mentioned, residual value (salvage value) is an estimated amount of money that an asset will be worth after the planned number of years of use. Obviously, in real life, it is impossible to accurately predict the exact salvage value of an asset after a particular number of years.

That means that the salvage value is only an approximation. However, in accounting, this approximation is just a kind of a transition state. It is because when you sell an asset, if the cash received for it is greater than its net book value (Initial Value minus Accumulated Depreciation), you will need to record a gain on sale. On the other hand, if you sell an asset below its net book value, you will need to record a loss on sale.

Note here that, if this number of years in use is equal to the product lifetime, the residual value is zero.

Car depreciation calculator

For sure, one of the most interesting cases of depreciation is the loss of value of a motor vehicle. As you probably know, the value of a brand new car decreases sharply as soon as you drive off of the car dealership (experts say that the value of a car decreases to 91% of the initial value the minute you purchase it!). Over the next years, the value of the car decreases, until after several years (around 10 to 11), it reaches zero value. Obviously, you will still be able to sell it. However, its market value will be very low. To avoid the hassles of selling a used car, many people prefer leasing a car these days instead of buying one.

If you are interested in detailed car depreciation calculations, be sure to look at our car depreciation calculator. It uses a model more specific to automobiles.

How to use our depreciation calculator?

Our smart depreciation calculator enables you to compute the yearly depreciation and to determine the value of an asset after a certain time has passed on the basis of the three most commonly used methods. They are the straight line depreciation, the declining balance depreciation, and the sum of years digits depreciation.

To get results using our calculator, all you need to do is to fill in four fields:

Original cost - the original value of the asset (purchasing price),

Residual value - an estimated amount of money that an asset will be worth after the lifetime has elapsed (it is usually assumed that it is equal to zero, for more information see section Residual value and depreciation),

Lifetime - the estimated number of years the asset is likely to remain in service,

End book value after… - in this field, you should provide the year after which you would like to compute the book value of the asset.

And that's it! In a moment, our depreciation calculator computes three variants of depreciation. If you are curious how it works, you should get familiar with the depreciation of the formulas described in the following sections of the article. Each formula uses the same set of symbols:

OV is the original cost (value) of the asset,

RV is the residual value of the asset,

n is the lifetime of the asset,

m is the number of years that passed between when the asset was purchased and the date you want to sell it (it corresponds with the field End book value after… in the calculator).

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