Answer:
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given random sample of size 'n' =17
Given mean of the sample 'x⁻' = 56
Given standard deviation of sample 's' = 10
95% confidence intervals about the population mean is determined by

Degrees of freedom
ν = n-1 = 17-1 =16
t₀.₀₅ = 1.7459 (from t-table)
<u><em>Step(ii):-</em></u>
95% confidence intervals about the population mean is determined by


( 56 - 4.2344 , 56 + 4.2344)
<em>(51.7656 , 60.2344)</em>
<u>Conclusion:</u>-
<em>95% confidence intervals about the population mean is </em>
<em>(51.7656 , 60.2344)</em>
Answer:
Angle θ would be about 17.1 degrees.
Step-by-step explanation:
To figure out what Angle θ is, first we have to find the hypotenuse. You can easily do that by find the square root of BC² + AC².
c = √4² + 13²
Square 4 and 13 to get 16 and 169 respectively.
c = √16 + 169
Add 16 and 169 to get 185.
c = √185
Find the square root of 185 (I'll round to the nearest tenth.)
c = 13.60147 ≈ 13.6 units
To find angle β, divide AC by AB and find the inverse sine of that.
β = arcsin(13/13.6)
Divide 13 by 13.6. Round to the nearest thousandth.
β = arcsin(0.955)
β ≈ 1.2723 rad
To convert radians to degrees, multiply the radians by 57.2957795 for an approximate amount.
β ≈ (1.2723 * 57.2957795)°
β ≈ 72.8974203 ≈ 72.9 degrees
Now subtract 72.9 from 90 to get angle θ's measure of 17.1 degrees.
Answer:
25x² - 16
Step-by-step explanation:
Given
(5x + 4)(5x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
5x(5x - 4) + 4(5x - 4) ← distribute parenthesis
= 25x² - 20x + 20x - 16 ← collect like terms
= 25x² - 16
Answer:
y=1/2x-10
Step-by-step explanation:
y=1/2x+b
-8=1/2(4)+b
-8=2+b
-10=b
y=1/2x-10