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seropon [69]
3 years ago
8

Tom worked 48 hours last week and gets time-and-a-half pay for overtime. His regular pay is $32 per hour. a) How much does he ma

ke for an hour of overtime?
Mathematics
1 answer:
torisob [31]3 years ago
8 0

Answer:

$48

Step-by-step explanation:

From the question we know that;

His regular pay is $32 per hour.

Tom worked 48 hours last week and gets time-and-a-half pay for overtime.

Time and a half pay = 1.5

Hence, if Tom works for an hour of overtime, his pay for his overtime is calculated as:

= 1.5 × $32 × 1

= $48

Therefore, he was paid $48 for one hour of overtime.

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A rectangular sheet of tin measures 20 inches by 12 inches. suppose you cut a square out of each corner and fold up the sides to
stich3 [128]

The volume of the box is maximized when a 6 x 6 inch or 10 x 10 inch square is cut from the corners of the rectangular sheet.

Volume of rectangle:

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units.

The formula for Volume of the rectangle is

V = l x b x h

where

l represents the length

b represents the breadth

h represents the height.

Given,

A rectangular sheet of tin measures 20 inches by 12 inches. suppose you cut a square out of each corner and fold up the sides to make an open-topped box.

Here we need to find the volume of the box is maximized when a square is cut from the corners of the rectangular sheet.

Here we have the following values:

h = x

l = 20 - 2x

b = 12 - 2x.

Here we have to subtract two times of x value because in the question they said that we have to cut a square from it.

Apply the values on the volume formula then we get,

=> V = (20 - 2x) x (12 - 2x) x (x)

=> V = [240 - 40x - 24x + 4x²] x (x)

=> V = [240x - 64x² + 4x³]

Now differentiate:

=> V' =  240 - 64x + 4x²

Simplify and order the equation,

Then we get,

=> V' = x² - 16x + 60

When we factorize the equation then we get,

=> V' = x² - 6x - 10x + 60

Take the common term out of it,

=> V' = x (x-6) -10(x -6)

Therefore, the value of x is, either 6 or 10.

Now you need to look at your solutions.

At x=6, the volume is,

=> V = (20 - 2(6)) x (12 - 2(6)) x (6)

=> V = (20 - 12) x (12 - 12) x 6

=> V = 8  x 0 x 6

=> V = 0

our corner squares devour the entire piece of cardboard and you are left with zero volume; so that solution is a minimum.

Now at the value of x = 10,

The volume is

=> V = (20 - 2(10) x (12 - 2(10)) x (10)

=> V = (20 - 20) x (12 - 20) x 10

=> V = 0 x (-8) x 10

=> V = 0

So, in both cases we have 0 as minimum volume. So, we can take any one of the value to get the maximum out of it.

To know more about Volume of the Rectangle here.

brainly.com/question/13798973

#SPJ4

8 0
1 year ago
Multiply and simplify. 2x4yx⋅6xy2z3
OLEGan [10]

Answer:

The given expression 2x^4yx \times 6xy^2z^3   on multiplying  is 12x^6y^3z^3

Step-by-step explanation:

Consider the given two expressions 2x^4yx and 6xy^2z^3

We have multiply both expressions,

2x^4yx \times 6xy^2z^3

To multiply two terms first multiply constant numbers that is 6 × 2 = 12

For x , y and z apply property of exponent,

x^a\cdot x^b=x^{a+b}

Then power of x together will be,

x^4\cdot x\cdot x=x^{4+1+1}=x^6

Similarly for y powers,

y \cdot y^2=y^{1+2}=y^3

Since first term do not have any expression for z so it will remain same.

Thus, the given expression  on multiplying become,

2x^4yx \times 6xy^2z^3 is 12x^6y^3z^3




7 0
3 years ago
Read 2 more answers
A shopkeeper bought a television for Rs. 10000 and he sold it at profit of 25%. What was the selling price of the television? Pl
-Dominant- [34]

Answer:

12,500

Step-by-step explanation:

125%/100% x 10000

12,500

6 0
2 years ago
A man and his three children spent $40 to attend a show. A second family of three children and their two parents spent $53 for t
wariber [46]
The cost for the children tickets is $9
5 0
3 years ago
Which of the following are mutually exclusive events?
Alexandra [31]

Answer: A

Step-by-step explanation: Ape x

6 0
2 years ago
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