To find the length of the table, multiply the area by the reciprocal of the width. Convert the mixed number to an improper fraction and then solve the equation. Simplify the resulting fraction, if possible.
To find the length of the table, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, we are given the area of the table as 27 1/8 square feet and the width as 3 1/2 feet. So, we can set up the equation: 27 1/8 = length × 3 1/2.
First, we need to convert the mixed number 27 1/8 to an improper fraction. Multiply the whole number (27) by the denominator (8) and add the numerator (1), then write the result over the denominator: 27 × 8 + 1 = 217/8.
Now we can solve the equation: 217/8 = length × 3 1/2. To isolate the variable, we can multiply both sides of the equation by the reciprocal of 3 1/2, which is 2/7. This cancels out the fraction on the right side, giving us: length = (217/8) × (2/7).
To multiply fractions, we multiply the numerators together and the denominators together: length = (217 × 2) / (8 × 7) = 434/56. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2: length = 217/28.
So, the length of the table is 217/28 feet.
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Find average rate of change for the first 10 minutes
how many students will be in the auditorium after 15 minutes of filling
To find the rate of change, we must find the amount of people that have changed over a given time period, and then find the unit rate. As 473-23=450 (we can subtract because we have the end number minus the starting number to find the amount changed) students enter over 10 minutes, and we want to find the rate of change for 1 minute, we can divide 450 10 times. As we move the decimal point of a number 1 to the left when dividing by 10, we have 450.00 -> 45.000 after dividing by 10. Therefore, the average rate of change is 45 students per minute. To find how many students will be in the auditorium after 15 minutes of filling, we can use this average rate of change to figure out approximately how many students will enter in 5 minutes. Therefore, as 45 students come in every minute, after 1 minute, 45 more students will come in. After 2, 45+45=45*2=90 students will come in, and so on. Thus, 45*5=225 students will come in after 5 minutes. Since we know that 473 students are in the auditorium after 10 minutes, we can add 225 to 473 to get 698 students after 15 minutes.
Feel free to ask further questions, and Happy Holidays!
A 50
B 45
C 24
D 60
-5
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2
3
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5
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This looks confusing. Can you try reposting this to make it look clear?