Mathematics, 14.08.2019 08:30 AbbypiePink4942

N. creasing is starting a job with a starting annual salary of $5. each subsequent year her salary will increase $2000. what will her 10th year salary be? write an expression in sigma notation showing her cumulative salary for the decade, and then evaluate the expression.

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Answer from: sassy11111515

$68,000.

Sum of salaries in the first ten years:

$\displaystyle \sum_{n = 1}^{10}{(\$50000 + (n - 1)\times \$2000)} = \$590000$ .

Step-by-step explanation:

Start by considering the salary for the first few years:

$\begin{array}{c|c}\text{Year}&\text{Salary}\\\cline{1-2}\\[-0.5em]\text{1st}& \$50000+0\times \$2000\\\text{2nd}&\$50000 + 1\times\$2000\\\text{3rd}&\$50000 + 2\times \$2000\\\vdots&\vdots\\n\text{th}&\$50000 + (n - 1)\times \$2000\end{array}$ .

Observe the trend in annual salary. The salary on the nth year will be equal to $\$50000 + (n - 1)\times \$2000$ . The salary on the 10th year will thus be equal to

$\$50000+(10-1)\times \$2000 = \$68000$ .

The sum of the salaries for the first ten years will be:

$\displaystyle \sum_{n = 1}^{10}{(\$50000 + (n - 1)\times \$2000)}$ .

This series is arithmetic:

$\begin{aligned}&\displaystyle \sum_{n = 1}^{10}{(\$50000 + (n - 1)\times \$2000)}\\=&\$50000 + \$52000 + \cdots + \$68000\end{aligned}$ .

First term: $a_1 = \$50000$ ;Last term: $\$68000$ ;Number of terms:

Evaluate this expression using the formula for the sum of an arithmetic series:

$\begin{aligned}S_n &= \frac{1}{2} n \cdot (a_1 + a_n)\\&= \frac{1}{2} \times 10 \times (\$68000 + \$50000) \\&= \$590000\end{aligned}$

Answer from: Quest

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

Answer from: Quest

One shot. if 60% of 10 is 6, then what is 70%? we know it would be seven (since 60% is mathematically 60/100, or 6/10, then 70% is 70/100, or 7/10) but we can check anyway using ratios: 6 : 60% = x : 70%*inverse multiplicationx * 60% = 6 * 70%*divide both sides by 60%x = (6 * 70%) / 60%x = 7and since he has made 6 shots already, he would need just one more to get 7 shots or 70%. if the explanation is too confusing, comment and i will try to

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