Answer: 38°
Using cosine rule,
a² = b² + c² -2bc cos(A)
Insert values from diagram
14² = 18² + 22.8² - 2(18)(22.8) cos(A)
196 = 324 + 519.84 - 820.8 cos(A)
-820.8 cos(A) = 196 - 324 - 519.84
-820.8 cos(A) = -647.84
cos(A) = -647.84/-820.8
A = cos^{-1} (-647.84/-820.8)
A = 37.88°
A ≈ 38°
Answer: 7.6, 22/7, 1.01
Step-by-step explanation:
Answer:
D. -1.75°C
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Assume that the mean reading is 0degrees°C and the standard deviation of the readings is 1.00degrees°C. This means that .
Find the temperature reading that separates the bottom 4% from the others.
The bottom 4% if the 4th percentile.
This is the value of X when Z has a pvalue of 0.04. This is .
The correct answer is:
D. -1.75°C
RX is + XS is the hypotenuse of the right triangle RTS, then:
(RX + XS)^2 = (RT)^2 + (ST)^2
=> (4+9)^2 = (RT)^2 + (ST)^2
=> 13^2 = (RT)^2 + (ST)^2 .....equation (1)
Triangle RTX and XST are also right triangles.
RT is the hypotenuse of RTX and ST is the hypotenuse os SXT.
Then, (RT)^2 - (RX)2 = (TX)^2 and (ST)^2 - (SX)^2 = (TX)^2
=> (RT)^2 - (RX)^2 = (ST)^2 - (SX)^2
=> (RT)^2 - (ST)^2 = (RX)^2 -(SX)^2
=> (RT)^2 - (ST)^2 = 4^2 - 9^2 = 16 - 81 = - 65
=> (ST)^2 - (RT)^2 = 65 ..........equation (2)
Now use equations (1) and (2)
13^2 = (RT)^2 + (ST)^2
65 = (ST)^2 - (RT)^2
Add the two equations:
13^2 + 65 = 2(ST)^2
2(ST)^2 =178
(ST)^2 = 234/2 = 117
Now use (ST)^2 - (SX)^2 = (TX)^2
=> (TX)^2 = 117 - 81 = 36
=> (TX) = √36 = 6
Answer: 6