$(\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}$

Step-by-step explanation:

Given

$(\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})$

Required

Simplify

For clarity, group the expression in threes

$((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Evaluate the first group [Divide 8 by 4]

$((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 9 by 3]

$((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 15 by 3]

$((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 16 by 2]

$((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Evaluate the second group [Divide 35 and 25 by 5]

$(\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 49 by 7]

$(\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 24 by 3]

$(\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Merge the first and second group

$((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Evaluate the last group [Divide 99 by 9]

$(\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))$

[Divide 63 by 9]

$(\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))$

[Divide 64 and 80 by 8]

$(\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))$

[Divide 10 and 4 by 2]

$(\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))$

[Divide 100 by 5]

$(\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))$

$(\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))$

$(\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})$

$1*(\frac{11}{20})$

$\frac{11}{20}$

Hence;

$(\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}$

4 0

3 years ago

Over the last 80 years, the average annual U.S. inflation rate was about

aliina [53]

Answer:

a answer is correct

Step-by-step explanation:

A. 3.6 percent , implying that prices have increased 16-fold.

may be this is helpful answer!

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3 years ago

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iVinArrow [24]

Answer:

x = 20 degrees.

Step-by-step explanation:

cos40∘=sin(x+30∘)

sin (x + 30) = 0.766

x + 30 = arcsin 0.766 = 50

x = 50 - 30 = 20.

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Step-by-step explanation:

I hope this helps :)

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