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3 years ago

7

You bought socks for all your friends. Fancy socks cost $15 a pair, and plain socks cost $8 a pair. You have 12 friends, spent e

xactly $117. How many pairs of each type of sock did you buy?

1 answer:

jonny [76]3 years ago

4 0

Answer:

9 socks for $8

3 socks at $15

Step-by-step explanation:

117 = (15 * x) + (8 * y)

8*9 = 72

15 * 3 = 45

72+ 45 = 117

9 socks at $8

3 socks at $15

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Read 2 more answers

Element X decays radioactively with a half life of 12 minutes. If there are 160

Salsk061 [2.6K]

Answer:

It would take 75.8 minutes for the element to decay to 2 grams.

Step-by-step explanation:

The number of grams of element x, after t minutes, is given by the following equation:

$X(t) = X(0)(1-r)^{t}$

In which X(0) is the initial amount and r is the decay rate.

There are 160 grams of Element X

This means that X(0) = 160.

So

$X(t) = X(0)(1-r)^{t}$

$X(t) = 160(1-r)^{t}$

Half life of 12 minutes.

This means that X(12) = 0.5*X(0) = 0.5*160 = 80. So

$X(t) = 160(1-r)^{t}$

$80 = 160(1-r)^{12}$

$(1 - r)^{12} = 0.5$

$\sqrt[12]{(1 - r)^{12}} = \sqrt[12]{0.5}$

$1 - r = 0.9438$

So

$X(t) = 160(1-r)^{t}$

$X(t) = 160(0.9438)^{t}$

How long would it take for the element to decay to 2 grams?

This is t for which X(t) = 2. So

$X(t) = 160(0.9438)^{t}$

$2 = 160(0.9438)^{t}$

$(0.9438)^{t} = \frac{2}{160}$

$\log{(0.9438)^{t}} = \log{\frac{2}{160}}$

$t\log{0.9438} = \log{\frac{2}{160}}$

$t = \frac{\log{\frac{2}{160}}}{\log{0.9438}}$

$t = 75.8$

It would take 75.8 minutes for the element to decay to 2 grams.

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The order of the pencils lengths from greatest to lowest will be converted to percentage to make it easier.

3 7/8 = 3.875

3 2/5 = 3.4

3 3/4 = 3.75

3 2/3 = 3.67

Therefore, from greatest to lowest will be:

3 ⅞, 3¾, 3⅔, 3 2/5

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The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.

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Answer:

6√2.

Step-by-step explanation:

The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90. Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.

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