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2 years ago

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Angela uses 2/3 cups of strawberries to make 5/6 of a liter of smoothie. What is the unit rate in cups of strawberries per liter

of smoothie?
1. 5/9 cups per liter
2. 3/4 cups per liter
3. 4/5 cups per liter
4. 5/4 cups per liter

1 answer:

Leviafan [203]2 years ago

6 0

5/6 litre of Smoothie = 2/3 cups of smoothie

Divide both sides by 5/6

So 1 litre of smoothie = 2/3 ÷ 5/6 cup of smoothies

= 2/3 × 6/5 cup of smoothies

= 4/5 cup of smoothies

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Answer:

Sophie will get <u>$56</u> in exchange.

Step-by-step explanation:

Given:

TravelEz sells dollars at a rate of ($1.40)/(1 euro).

And dollars they buy at a rate of ($1.80)/(1 euro).

Sophie exchanged $540 to get 300 euros, at the beginning of trip.

And, she is left with 40 euros at the end of trip.

So exchanges the euros back to dollars.

Now, to find the dollars Sophie will get in exchange.

Let the dollars Sophie will get in exchange be $x.$

The rate at which TravelEz sells dollars = $\frac{\$1.40}{1\ euro}$

Number of euros Sophie is left with = $40.$

Now, to get the dollars she will get we set proportion:

<em>As, </em> $\$1.40$ <em> is equivalent </em> $1\ euro$ <em>.</em>

<em>So, </em> $x$ <em> is equivalent to </em> $40\ euros$ <em>.</em>

Thus,

$\frac{1.40}{1} =\frac{x}{40}$

By cross multiplying we get:

$56=x$

$x=\$56.$

Therefore, Sophie will get $56 in exchange.

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2 years ago

The triangle DEF is shown in the diagram.<br>Find the exact value of x.<br>

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Answer:

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Step-by-step explanation:

Using cosine triangle formula, we know that;

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2 years ago

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2 years ago

Debra and Ian shared in $1,000,000 estate. If Ian received $125,000 and debra the rest, what fraction of the estate did Debra re

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

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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:

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

Substitute $\frac{128}{y}$ for x

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

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.

Different A with respect to y

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

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

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:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

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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2 years ago