Steven deposits $200 in a savings account, and decides to increase the amount by $5 every month. Identify the function that describes the arithmetic sequence, and the amount he should deposit after 8 months.
possible answer: D = 8n + 200; $240
possible answer: D = −5n + 200; $160
possible answer: D = 5n + 200; $240
possible answer: D = −8n + 200; $160

Answers

Answer 1

The required equation is D = 5n + 200 and the amount deposited after 8 months is $240

Given the amount that steven deposited every month as $200

Let n be the number of months

If he decides to increase the amount by $5 every month, then the amount added after n months will be $5n

The function that describes the arithmetic sequence will be expressed as sum of the amount deposited and increment:

D = 200 + 5n = 5n + 200

In order to get the amount deposited after 8 months, we will replace n by 8 to have:

D = 200 + 5(n)

D = 200 + 5(8)

D = 200 + 40

D = 240

Hence the required equation is D = 5n + 200 and the amount deposited after 8 months is $240

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28.375 (rounded to 29 grams)

Step-by-step explanation:

there are about 454 grams in a pound and 16 ounces in a pound, so to find the relationship we divide 454 by 16 to get 28.375 or about 29 grams

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[tex]\\ \sf\longmapsto 1\dfrac{2}{3}+2\dfrac{3}{4}+3\dfrac{5}{6}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{3}+\dfrac{11}{4}+\dfrac{23}{6}[/tex]

[tex]\\ \sf\longmapsto \dfrac{20+33+46}{12}[/tex]

[tex]\\ \sf\longmapsto \dfrac{99}{12}[/tex]

[tex]\\ \sf\longmapsto 8.2ft[/tex]

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Answer:

1¾ ft ≈ 1,75 ft

Step-by-step explanation:

[tex] \sf 1\frac{2}{3} + 2 \frac{3}{4} + 3\frac{5}{6} [/tex]

[tex] \sf = \frac{3 + 2}{3} + \frac{4 \times 2 + 3}{4} + \frac{6 \times 3 + 5}{6} [/tex]

[tex] = \sf \frac{5}{3} + \frac{11}{4} + \frac{23}{6} [/tex]

[tex] \sf = \frac{5 \times 4 + 11 \times 3}{3 \times 4} + \frac{23}{6} [/tex]

[tex] = \sf \frac{20 +33 }{12} + \frac{23}{6} [/tex]

[tex] \sf = \frac{53}{12} + \frac{23}{6} [/tex]

[tex] = \sf \frac{53}{12} + \frac{23 \times 2}{6 \times 2} [/tex]

[tex] \sf = \frac{53}{12} + \frac{46}{12} [/tex]

[tex] \sf = \frac{99}{12} [/tex]

[tex] \sf = \frac{10}{1} - \frac{99}{12} [/tex]

[tex] \sf = \frac{10 \times 12 - 99}{12} [/tex]

[tex] = \sf \frac{120 - 99}{12} [/tex]

[tex] \sf = \frac{21}{12} [/tex]

= 1¾ ft ≈ 1,75 ft

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#CarryOnLearning

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