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2 months ago

What is 72.1 repeating as a fraction

Mathematics

2 answers:

Leona [12.6K]2 months ago

6 0

Assume

$x=72.111...$

Scale x by an appropriate power of 10 so the non-integer portion lines up:

$10x=721.111..$

Now subtract $x$ from $\\10x$

$10x-x=721.111-72.111=649$

This removes the repeating decimal bits

$\\9x=649$

Isolate x

Divide both sides by $9$

$9x/9=649/9$

$x=649/9$

Hence

So the result is

The fraction is $\frac{649}{9}$

tester [12.3K]2 months ago

4 0

$x=72.\overline{1}\\
10x=721.\overline{1}\\
10x-x=721.\overline{1}-72.\overline{1}\\
9x=649\\
x=\dfrac{649}{9}$

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One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples

babunello [11817]

Answer:

Step-by-step explanation:

Hello!

To determine whether boys excel in math classes compared to girls, two random samples were collected:

Sample 1

X₁: score achieved by a boy in calculus

n₁= 15

X[bar]₁= 82.3%

S₁= 5.6%

Sample 2

X₂: score obtained by a girl in calculus

n₂= 12

X[bar]₂= 81.2%

S₂= 6.7%

To estimate a confidence interval for the difference between the average percentages of boys and girls in calculus, it's essential that both variables come from normally distributed populations.

For utilizing a pooled variance t-test, it is also required that the population variances, though unknown, are assumed to be equal.

The confidence interval can then be calculated with:

[(X[bar]_1 - X[bar]₂) ± $t_{n_1+n_2-2;1-\alpha /2}$ * $Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }$ ]

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*(5.6^2)+11*(6.7^2)}{15+12-2} }= 6.108= 6.11$

$t_{n_1+n_2-2;1-\alpha /2}= t_{15+12-2;1-0.05}= t_{25;0.95}= 1.708$

[(82.3 - 81.2) ± 1.708 * (6.11 * $\sqrt{\frac{1}{15}+\frac{1}{12} }$ ]

[-2.94; 5.14]

Using a 90% confidence level, the interval [-2.94; 5.14] is expected to encompass the true difference between the average percentages achieved by boys and girls in calculus.

I hope this is of assistance!

3 0

2 months ago