1. Instant Meals sent out free samples to introduce its new product, Sesame soup. Each

1 answer:

5 0

Hello there! For this word problem we first have to identify the numbers and variables if there are any. Our numbers are 36 cents per 23 ounces, each sample weighs 69 ouches, and how much it costs to mail out one hundred eighty-eight.

Next, let's see how many 23 ounces are in 69 ounces. To solve for that, we can divide 69 by 23. 63 divided by 23 is 3, so there is 3 sets of 23 ounces per 69 ounce samples. Then, we can multiply 3 by 36 cents in order to see how much each sample costs. 3 times .36 is 1.08 or 1 dollar and 8 cents. Lastly, we need to multiply 188 by 1.08 to figure out how much it costs to mail out 188 samples.

188 times 1.08 equals to 203.04 or 203 dollars and 4 cents. Therefore, it would cost $203.04 to mail out 188 samples. Hope this helps! Have a great day!

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The diameter of cold virus cell is about 3x10-9 meter,and the diameter of a streptoccus bacterium cell is about 9x10-7 meter. Wh

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Here we need to compare the orders of magnitude of two measures.

We will see that the bacteria is 300 times larger than the virus.

We know that:

The diameter of the virus-cell is:

$D_v = 3 \cdot 10^{-9} m$

The diameter of the bacteria cell is:

$D_b = 9 \cdot 10^{-7} m$

So, to compare them, first notice that both are in the same units, meters, so we only need to compare the numbers.

Is common sense to identify the one with the largest exponent as the largest number, and the largest exponent is -7, thus the bacteria should be the larger one.

But let's prove this with math, remember the property:

$\frac{a^n}{a^m} = a^{n - m}$

Let's take the quotient between the diameters and see what we get, I will use the diameter of the bacteria in the numerator, thus if the quotient is larger than 1, it would mean that the bacteria is greater and by how much.

$quotient = \frac{ 9 \cdot 10^{-7} m}{ 3 \cdot 10^{-9} m} = \frac{9}{3} \cdot 10^{-7 + 9}\\\\= 3*10^2$