Solved on Nov 01, 2023

A toy company checks 8-ounce bubble bottles. A bottle passes if the percent error is $\leq 2\%$ . What is the range of acceptable bottle volumes, rounded to the nearest hundredth?

STEP 1

Assumptions1. The machine is supposed to fill the bottles with8 ounces of bubbles. . A bottle passes inspection if the percent error of the amount is% or less.
3. Percent error is calculated as the absolute difference between the actual and expected value, divided by the expected value, all multiplied by100%.
4. We are looking for the range of values that a bottle could contain to pass inspection.

STEP 2

First, we need to find the amount that represents a2% error of the expected8 ounces. We can do this by multiplying the expected amount by the percent error.
$Error\, amount = Expected\, amount \\times Percent\, error$

STEP 3

Now, plug in the given values for the expected amount and percent error to calculate the error amount.
$Error\, amount =8\, ounces \\times2\%$

STEP 4

Convert the percentage to a decimal value.
$2\% =0.02$ $Error\, amount =8\, ounces \\times0.02$

STEP 5

Calculate the error amount.
$Error\, amount =8\, ounces \\times0.02 =0.16\, ounces$

STEP 6

Now that we have the error amount, we can find the range of values that a bottle could contain to pass inspection. This range is from the expected amount minus the error amount to the expected amount plus the error amount.
$Range = [Expected\, amount - Error\, amount, Expected\, amount + Error\, amount]$

STEP 7

Plug in the values for the expected amount and the error amount to calculate the range.
$Range = [\, ounces -0.16\, ounces,\, ounces +0.16\, ounces]$

STEP 8

Calculate the range of values that a bottle could contain to pass inspection.
$Range = [7.84\, ounces,8.16\, ounces]$ The bottles could contain between7.84 ounces and8.16 ounces to pass inspection.

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A toy company checks 8-ounce bubble bottles. A bottle passes if the percent error is $\leq 2\%$ . What is the range of acceptable bottle volumes, rounded to the nearest hundredth?

STEP 1

STEP 2

First, we need to find the amount that represents a2% error of the expected8 ounces. We can do this by multiplying the expected amount by the percent error.
$Error\, amount = Expected\, amount \\times Percent\, error$

STEP 3

Now, plug in the given values for the expected amount and percent error to calculate the error amount.
$Error\, amount =8\, ounces \\times2\%$

STEP 4

Convert the percentage to a decimal value.
$2\% =0.02$ $Error\, amount =8\, ounces \\times0.02$

STEP 5

Calculate the error amount.
$Error\, amount =8\, ounces \\times0.02 =0.16\, ounces$

STEP 6

STEP 7

Plug in the values for the expected amount and the error amount to calculate the range.
$Range = [\, ounces -0.16\, ounces,\, ounces +0.16\, ounces]$

STEP 8

Calculate the range of values that a bottle could contain to pass inspection.
$Range = [7.84\, ounces,8.16\, ounces]$ The bottles could contain between7.84 ounces and8.16 ounces to pass inspection.

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A toy company checks 8-ounce bubble bottles. A bottle passes if the percent error is ≤2%\leq 2\%≤2%. What is the range of acceptable bottle volumes, rounded to the nearest hundredth?

STEP 1

STEP 2

STEP 3

Now, plug in the given values for the expected amount and percent error to calculate the error amount.Error amount=8 ouncestimes2%Error\, amount =8\, ounces \\times2\%Erroramount=8ouncestimes2%

STEP 4

Convert the percentage to a decimal value.2%=0.022\% =0.022%=0.02Error amount=8 ouncestimes0.02Error\, amount =8\, ounces \\times0.02Erroramount=8ouncestimes0.02

STEP 5

Calculate the error amount.Error amount=8 ouncestimes0.02=0.16 ouncesError\, amount =8\, ounces \\times0.02 =0.16\, ouncesErroramount=8ouncestimes0.02=0.16ounces

STEP 6

STEP 7

Plug in the values for the expected amount and the error amount to calculate the range.Range=[ ounces−0.16 ounces, ounces+0.16 ounces]Range = [\, ounces -0.16\, ounces,\, ounces +0.16\, ounces]Range=[ounces−0.16ounces,ounces+0.16ounces]

STEP 8

Calculate the range of values that a bottle could contain to pass inspection.Range=[7.84 ounces,8.16 ounces]Range = [7.84\, ounces,8.16\, ounces]Range=[7.84ounces,8.16ounces]The bottles could contain between7.84 ounces and8.16 ounces to pass inspection.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

A toy company checks 8-ounce bubble bottles. A bottle passes if the percent error is $\leq 2\%$ . What is the range of acceptable bottle volumes, rounded to the nearest hundredth?

Now, plug in the given values for the expected amount and percent error to calculate the error amount.
$Error\, amount =8\, ounces \\times2\%$

Convert the percentage to a decimal value.
$2\% =0.02$ $Error\, amount =8\, ounces \\times0.02$

Calculate the error amount.
$Error\, amount =8\, ounces \\times0.02 =0.16\, ounces$

Plug in the values for the expected amount and the error amount to calculate the range.
$Range = [\, ounces -0.16\, ounces,\, ounces +0.16\, ounces]$

Calculate the range of values that a bottle could contain to pass inspection.
$Range = [7.84\, ounces,8.16\, ounces]$ The bottles could contain between7.84 ounces and8.16 ounces to pass inspection.