Answer:
PQ = 34.4
Step-by-step explanation:
First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74
Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)
This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.
We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that
NO/QR = MN/PQ
Thus,
11/27 = 14/PQ
multiply both sides by PQ to remove a denominator
PQ * 11/27 = 14
multiply both sides by 27 to remove the other denominator
PQ * 11 = 14 * 27
divide both sides by 11 to isolate the PQ
PQ = 14 * 27 /11
PQ = 34.4
Answer:
2 (1/3) cups
Step-by-step explanation:
8 x 3(1/2) = 28 cups
28 / 12 = 2 (1/3) cups
Answer:
C 120
Step-by-step explanation:
120 because 60/3=20 so 20x 6=120
Hope that helped
Let x be the lengths of the steel rods and X ~ N (108.7, 0.6)
To get the probability of less than 109.1 cm, the solution is computed by:
z (109.1) = (X-mean)/standard dev
= 109.1 – 108/ 0.6
= 1.1/0.6
=1.83333, look this up in the z table.
P(x < 109.1) = P(z < 1.8333) = 0.97 or 97%
Answer:
(a) 93.19%
(b) 267.3
Step-by-step explanation:
The population mean and standard deviation are given as 502 and 116 respectively.
Consider, <em>X</em> be the random variable that shows the SAT critical reading score is normally distributed.
(a) The percent of the SAT verbal scores are less than 675 can be calculated as:
Thus, the required percentage is 93.19%
(b)
The number of SAT verbal scores that are expected to be greater than 575 can be calculated as:
So,
Out of 1000 randomly selected SAT verbal scores, 1000(0.2673) = 267.3 are expected to have greater than 575.
