Help with word problems and inequalities?

Mathematics

1 answer:

jeyben [28]4 years ago

8 0

Answer:

what is your question

Step-by-step explanation:

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a person invest in 9000 in a bank. the bank pays 5% interest compounded semi annually. to the nearest tenth of a year, how long

QveST [7]

Answer:

10.1 years.

Step-by-step explanation:

It is given that,

Principal = 9000

Rate of interest = 5%

No. of times interest compounded = 2 times in an year

Amount after certain time = 14800

The formula for amount:

$A=P(1+\frac{r}{n})^{nt}$

where, P is principal, r is rate of interest, n is no. of times interest compounded in an year and t is time in years.

Substitute the given values in the above formula.

$14800=9000(1+\frac{0.05}{2})^{2t}$

$\frac{14800}{9000}=(1+0.025)^{2t}$

$1.644=(1.025)^{2t}$

Taking log both sides.

$\log(1.644)=\log(1.025)^{2t}$

$\log(1.644)=2t\log(1.025)$ $[\because \log a^b=b\log a]$

$\frac{\log(1.644)}{2\log(1.025)}=t$

$t=10.066$

$t=10.1$

Therefore, the required time is 10.1 years.

3 0

3 years ago

3 3/4 divided by 12 1/2

notka56 [123]

Answer:

$\large\boxed{3\dfrac{3}{4}:12\dfrac{1}{2}=\dfrac{3}{10}}$

Step-by-step explanation:

$\text{Convert the mixed numbers to the improper fractions:}\\\\3\dfrac{3}{4}=\dfrac{(3)(4)+3}{4}=\dfrac{12+3}{4}=\dfrac{15}{4}\\\\12\dfrac{1}{2}=\dfrac{(12)(2)+1}{2}=\dfrac{24+1}{2}=\dfrac{25}{2}\\\\3\dfrac{3}{4}:12\dfrac{1}{2}=\dfrac{15}{4}:\dfrac{25}{2}\\\\\text{To divide a number by a fraction,}\\\text{multiply this number by the reciprocal of that fraction}:\\\\\dfrac{15}{4}\cdot\dfrac{2}{25}=\dfrac{30}{100}=\dfrac{3}{10}$