The answer is -21. Rule is that you follow the sign of the larger and add the opposite
You can comment below, are these supposed to be simply equations or piecewise functions?
Domain is:
x is an element of a real number, but isn't equal to -4, 7 or -7.
Answer: 212 feet
Have a look at the image shown below. On that image, I've marked key details to focus on. Namely, the bottom right triangle has the angle CAB equal to 27 degrees because of the congruent alternate interior angles. This is the reference angle we'll base everything off of.
Opposite this angle is the side BC = 108 which is the lighthouse height. Adjacent to this angle is AB = x which is unknown. The goal is to solve for x
Use the tangent rule
tan(angle) = opposite/adjacent
tan(angle CAB) = CB/AB
tan(27) = 108/x <--- substitution
x*tan(27) = 108 <--- multiply both sides by x
x = 108/tan(27) <--- divide both sides by tan(27)
x = 211.96 <-- see note below
x = 212
note: use a calculator that has the trig functions sine, cosine, etc. You'll use the tan function for tangent. Make sure your calculator is in degree mode. the result you get is approximate as shown above, which will round to 212 when rounding to the nearest whole number.
Answer:
0.6247
Step-by-step explanation:
In order to find the frequency of people who complete the test between 45 and 65 minutes, we have to find z
Z = (x – mean)/standard deviation
Le x be the time to complete the test
Z1 = (45 – 60)/10 = -1.5
Z2 = (65 – 60)/10 = 0.5
Then we use the z table to find the area under the curve.
Area for Z1 = 0.4332
Area for Z2 = 0.1915
The relative frequency is the area between the two z-scores:
0.4332 +0.1915 = 0.6247
Graphic with shaded area is attached