The Phillips family and the Smith family each used their sprinklers last summer. The water output rate for the Phillips family's sprinkler was 15L per hour. The water output rate for the Smith family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 70 hours, resulting in a total water output of 1850L. How long was each sprinkler used?

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Ответ:

bshreve

13.05.2020

Mathematics

$9) \$1236.27\,10)\,\$6451.07\, 11)\,\$10,152.87 \,12)\,\$907.95 \,13)\,\$4957.69$

Step-by-step explanation:

9) Since Alicia Martin's savings earns 6% quarterly for two quarters then:

$A=P(1+\frac{r}{n})^{nt}$ ⇒ Amount (A), Principle (P), rate (r) in decimal form, number of compoundings (n) a year and t, in year or its fractions.

$A=P(1+\frac{r}{n})^{nt}\Rightarrow A=1200(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A=\$1236.27$

10) Aubrey Daniel's case:

$A=P(1+\frac{r}{n})^{nt}\Rightarrow A=5725(1+\frac{0.04}{4})^{4*3}\Rightarrow A\approx \$6451.07$

11) As for Angelo, similarly to Alicia.

$A=P(1+\frac{r}{n})^{nt}\Rightarrow A=9855(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$10,152.87$

12) Simpson's. For semiannual n=2

$A=P(1+\frac{r}{n})^{nt}\Rightarrow A=860(1+\frac{0.055}{2})^{2*1}\Rightarrow A\approx \$907.95$

13) Jana Lacey amount:

$A=P(1+\frac{r}{n})^{nt}\Rightarrow A=4860(1+\frac{0.04}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$4957.69$

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