Answer:
x(3x+14)
Step-by-step explanation:
what do those terms share? they share the letter "x"
therefore we multiply x by 3x^2/x + 14x/x
3x^2/x = 3x and 14x/x = 14
Answer:
∠T = 135°
Step-by-step explanation:
Supplementary angles sum to 180°, thus
∠T + ∠S = 180
However, ∠T = 3∠S, hence
3∠S + ∠S = 180
4∠S = 180 ( divide both sides by 4 )
∠S = 45°, hence
∠T = 180° - 45° = 135°
(5 x 10) + (8 x 1) + (8 x 0.1)
OR
50 + 8 + .8
Fifty-eight and eight tenths
Hope this helped!
Answer:
2.33
Step-by-step explanation:
imagine a circle. its center is A, and it goes through B, so its radius is AB.
then it is important to know that the sum of all the angles in a triangle is 180 degrees.
one angle (at C) is 90. the angle at B is 25. so, the angle at A is 180 - 90 - 25 = 65 degrees.
more back to our circle.
in this circle the line CB is the sine of the angle at A multiplied by the radius.
and AC is the cosine of the angle at A multiplied by the radius.
we can ignore the orientation + and - of these functions, as we are only interested in the absolute length (and we can mirror the triangle, and all the angles and side lengths still stay the same).
=> CB = sin(A)×AB
AC = cos(A)×AB
=> 5 = sin(65)×AB
=> AB = 5 / sin(65)
=> AC = cos(65)×5/sin(65) = 5 × (cos(65)/sin(65)) =
= 5 × cot(65) = 2.33
Answer:
The 90% confidence interval using Student's t-distribution is (9.22, 11.61).
Step-by-step explanation:
Since we know the sample is not big enough to use a z-distribution, we use student's t-distribution instead.
The formula to calculate the confidence interval is given by:
Where:
is the sample's mean,
is t-score with n-1 degrees of freedom,
is the standard error,
is the sample's size.
This part of the equation is called margin of error:
We know that:
degrees of freedom 
Replacing in the formula with the corresponding values we obtain the confidence interval:
