Since in this case we are
only using the variance of the sample and not the variance of the real population,
therefore we use the t statistic. The formula for the confidence interval is:
<span>CI = X ± t * s / sqrt(n) ---> 1</span>
Where,
X = the sample mean = 84
t = the t score which is
obtained in the standard distribution tables at 95% confidence level
s = sample variance = 12.25
n = number of samples = 49
From the table at 95%
confidence interval and degrees of freedom of 48 (DOF = n -1), the value of t
is around:
t = 1.68
Therefore substituting the
given values to equation 1:
CI = 84 ± 1.68 * 12.25 /
sqrt(49)
CI = 84 ± 2.94
CI = 81.06, 86.94
<span>Therefore at 95% confidence
level, the scores is from 81 to 87.</span>
Answer:

Step-by-step explanation:

Multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.



Or, You can simply reduce the fraction with 2, which results to 1.
Hope I helped!
Best regards! :D
Answer:
<em><u>3</u></em><em><u>(</u></em><em><u> </u></em><em><u>x </u></em><em><u>+</u></em><em><u> </u></em><em><u>2</u></em><em><u> </u></em><em><u>)</u></em><em><u>. </u></em><em><u>=</u></em><em><u> </u></em><em><u>5</u></em><em><u>(</u></em><em><u> </u></em><em><u>x </u></em><em><u>-</u></em><em><u> </u></em><em><u>2</u></em><em><u>)</u></em>
<em><u>3</u></em><em><u>x</u></em><em><u> </u></em><em><u>+</u></em><em><u> </u></em><em><u>6</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>5</u></em><em><u>x</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>1</u></em><em><u>0</u></em>
<em><u>-2x </u></em><em><u>=</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>1</u></em><em><u>6</u></em><em><u> </u></em>
<em><u>minus,</u></em><em><u>minus </u></em><em><u>cancel</u></em>
<em><u>x </u></em><em><u>=</u></em><em><u> </u></em><em><u>1</u></em><em><u>6</u></em><em><u>/</u></em><em><u>2</u></em><em><u> </u></em>
<em><u>x </u></em><em><u>=</u></em><em><u> </u></em><em><u>8</u></em><em><u> </u></em>
1) we calculate the area of the circular piece of metal.
area=πr²
area=π(3.5 m)²=12.25π m² ≈ 38.48 m²
2)we calculate the total cost of the circular piece of meta by the rule of three.
$3.25-------------------1 m²
x--------------------------38.48 m²
x=($3.25 * 38.48m²) / 1 m²=125.06$
Answer: 125.06$
We can also calcultate the total cost of the ciucular piece of metal by the ratius.
Ratius=$3.25/1m²
Total cost=ratius * area of the circular piece of metal.
total cost=($3.25/ m²)*(38.48 m²)=$125.06
Answer: $125.06
Rearrange the equation so that x = 11 divided by 1/8
Solve for x (11 divided by 1/8 = 88)