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2 years ago

As a children's librarian, Jodi Hassam earns $15.35 an hour

Mathematics

2 answers:

grandymaker [24]2 years ago

5 0

<h2>Answer:</h2>

Her total pay for the week is:

$ 982.40

<h2>Step-by-step explanation:</h2>

It is given that:

Jodi Hassam earns $15.35 an hour plus time and a half for weekend work.

Last week she worked her regular 40 hours plus 16 hours on the weekend.

This means that her total pay is calculated as follows:

$=40\times 15.35+16\times (1.5\times 15.35)\\\\=982.40$

( since the first term represents the pay for the regular hours and the second term represent the pay for the weekend )

Hence, her total pay for the week is: $ 982.40

mihalych1998 [28]2 years ago

3 0

Answer:

Step-by-step explanation:40X15.35+(16(15.35X1.5)= 982.4

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Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

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$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

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$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

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$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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1 year ago

Points H and F lie on circle c What is the length of line segment GH?

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Answer:

6 units

Step-by-step explanation:

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Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

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$(GH + 9)^{2} = (9)^{2} +(12)^{2}$

$(GH )^{2} + (9)^{2} + 18GH = 81 + 144$

$(GH )^{2} + 81 + 18GH = 81 + 144$

$(GH )^{2} + 18GH = 144$

Now, Let GH = <em>x</em>

$x^{2} +18x = 144$

On rearranging,

$x^{2} +18 x - 144 = 0$

$x^{2} - 6x +24x + 144 = 0$

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$(x - 6) (x + 24) = 0$

So x = 6 and x = - 24

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2 years ago

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1 year ago

0.01234567901 as a fraction

balu736 [363]

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