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2 years ago

Lucy buys 7kg of nuts to sell.

Mathematics

1 answer:

Nikitich [7]2 years ago

3 0

Answer:

Lucy's percentage profit = 33.33% based on Sales Value

and 50% based on Cost.

Step-by-step explanation:

a) Calculations:

7kg = 7,000g of nuts

Cost of 7,000g = £10

350g = 20 bags (7,000/350)

Sales value = £15 (20 x 75p)

Profit = Sales value minus Cost

Profit = £5 (£15 - £10)

Profit percentage based on sales = Profit/Sales x 100 = 5/15 x 100 = 33.33%

Profit percentage based on cost = Profit/Cost x 100 = 5/10 x 100 = 50%

b) Profit is the excess of sales over cost. There are two ways to express it in percentages. Profit can be expressed as a percentage of the cost (Markup). It can also be expressed as the percentage of the sales value (Margin).

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6 is a quarter of her walk ... there are 4 quarters in a whole (6x4) = 24

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3 years ago

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Round 8.54951607694 to 6 decimal places.

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Answer:

8·549516

Step-by-step explanation:

To round the number given to 6 decimal place, we will follow the steps below;

First count six digits after the decimal point

Then after the six digit number take the next number and see if it below 5 then this means you will be rounding down, so you will leave your six digit after the decimal points the way they are and discard the other digits after the the six digits, but if the digit number right after the sixth digit is 5 and above, then you will be rounding up, you will add one to your sixth digit and then discard the digits after the sixth digits.

That is;

In the number given: 8.54951607694

The sixth digit after the decimal point is 6, the number that comes after it is zero, so we will leave the 6 the way it is and discard the other digits after 6

8.54951607694 ≈ 8·549516 to 6 decimal place

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3 years ago

Find the base of a parallelogram with the area of 60 in.² and height of 4 inches use the formula for the area of the parallelogr

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Hope this helped!

7 0

2 years ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

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3 years ago

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Morgarella [4.7K]

Answer:

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Step-by-step explanation:

We have given the expression $(e^3)^4$

We have to simplify this expression with the help of property of exponent

According to property of exponent when there is exponent to exponenet then both the exponent are multiplied with each other

So $(e^3)^4=e^{3\times 4}=e^{12}$

Here 4 and 3 are exponent to exponent so these are multiplied with each other

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2 years ago