35. A carpenter is to build a concrete ramp with an 18°

Problem 10) This is arithmetic because we subtract 6 from each term to get the next. This is the same as adding on -6. The common difference is d = -6. The first term is a = 1

Problem 11) Neither. The distance from 3 to 3/2 = 1.5 is 1.5 units, but the distance from 1.5 to 1 is 0.5 units. This implies there is no common difference value. The sequence is not arithmetic because of this. It's also not geometric either. To go from 3 to 3/2, we multiply by 1/2. But then going from 3/2 to 1, we multiply by 2/3. There is no common ratio r value.

Problem 12) This sequence is geometric. We divide each term by 3 to get the next, or put another way, we multiply each term by 1/3 to get the next term. The common ratio is r = 1/3. The first term is a = 108.

Problem 13) Neither. This is because going from term to term, we do not add the same amount each time. Example: from -2 to 4 we add 6, but then from 4 to -6 we add -10. So the sequence is not arithmetic. It's also not geometric either because we dont multiply by the same term each time. Eg: from -2 to 4, we multiply by -2; but from 4 to -6 we multiply by -1.5

Problem 14) The next three terms are: 1, 1/4, 1/16. This is found by multiplying each term by the common ratio r = 1/4, or you can think of dividing each term by 4. To get this common ratio, pick any term you want and divide it by its previous term. Example: term2/term1 = 16/64 = 1/4 = common ratio.

Problem 15) The next three terms are: -432, 2592, -15552. You multiply each term by the common ratio -6. Like with the previous problem, we divide any term over its previous one to get the common ratio, so for example, term2/term1 = -12/2 = -6 = common ratio.

3 0

3 years ago

Calvin had 30 minutes in time-out. For the first 23 1/3 minutes, Calvin counted spots on the ceiling. For the rest of the time,

scoundrel [369]

Answer: $\frac{20}{3}\ minutes$ or $6 \frac{2}{3}\ minutes$

Step-by-step explanation:

For this exercise you can convert the mixed number to an improper fraction:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained and the numerator of the fraction (This will be the new numerator).

3. The denominator does not change.

Then:

$23\frac{1}{3}= \frac{(23*3)+1}{3}= \frac{70}{3}\ minutes$

You know that he had 30 minutes in time-out, he counted spots on the ceiling for $\frac{70}{3}$ minutes and the rest of the time he made faces at his stuffed tiger.

Then, in order to calculate the time Calvin spent making faces at his stuffed tiger, you need to subract 30 minutes and $\frac{70}{3}$ minutes:

$30\ min-\frac{70}{3}=(\frac{3(30)-70}{3})=\frac{20}{3}\ minutes$ or $6 \frac{2}{3}\ minutes$

7 0

3 years ago

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