Question 10 of 10
Is APQR- AXYZ? If so, name which similarity postulate or theorem applies.
80
Q
180°
P
5
R
х
10
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
Ο Ο
D. Cannot be determined
SUBMIT

A. Similar - AA

Step-by-step explanation:

The given parameters of ΔPQR and ΔXYZ are;

In ΔPQR, we have; PQ = 3, PR = 5, and ∠PQR = 80°

In ΔXYZ, we have; XY = 6, XZ = 10, and ∠XYZ = 80°

In ΔPQR, by sine rule, we have;

3/(sin(∠PRQ)) = 5/(sin(80°))

sin(∠PRQ) = (3/5) × sin(80°)

∴ ∠PRQ = arc sin((3/5) × sin(80°))

In ΔXYZ, by sine rule, we have;

6/(sin(∠XZY)) = 10/(sin(80°))

sin(∠XZY) = (6/10) × sin(80°) = (3/5) × sin(80°)

∴ ∠XZY = arc sin((3/5) × sin(80°))

∠PRQ = ∠XZY by transitive property of equality

Therefore in ΔPQR and ΔXYZ, we have;

∠PRQ = ∠XZY and ∠PQR = ∠XYZ

Therefore, ΔPQR is similar to ΔXYZ by Angle Angle, AA, similarity postulate.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;