Step-by-step explanation:
ABC be the given isosceles right triangle such that <B = 90° , side AC is the hypotenuse; and, AB= BC
Then, (AB)^2 + (BC)^2 = (AC)^2…. Pythagoras theorem.
(AC)^2 = 98 sq. cm. ( given)
So, (AB)^2 + ((BC)^2 = 98
But, AB = BC = a ( say) …. ( given)
Therefore, a^2 + a^2 = 98
Or, 2a^2 = 98.
So, a^2 = 98 / 2 = 49
Hence, a = AB = BC = √49 = 7 cm.
The side AC ( the hypotenuse) = √98 = √(7 *7*2)
= 7 *√2 = 7* 1.414 = 9..898cm., say, 9.9 cm.
Hence, the three sides of the right isosceles triangle are 7 cm, 7cm and ~ 9.9 cm. Answer
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Since the sample standard deviation is now known, we use
the z-score test. The formula is given as:
z= (X – μ) / (s / sqrt(n))
Where,
X = sample mean = 8.6 lb to 14.6 lb
μ = population mean = 11 lb
s = population standard deviation = 6
n = sample size = 4
1st: Calculating for z when x = 8.6 lb
z = (8.6 – 11) / (6 / sqrt4)
z = - 0.8
Using the standard distribution table for z:
Probability (x = 8.6
lb) = 0.2119
2nd: Calculating for z when x = 14.6 lb
z = (14.6 – 11) / (6 / sqrt4)
z = 1.2
Using the standard distribution table for z:
Probability (x = 14.6
lb) = 0.8849
Therefore
the probability that the mean weight will be between 8.6 and 14.6 lb:
Probability (8.6 ≤ x ≤ 14.6 ) = 0.8849 - 0.2119
Probability (8.6 ≤ x <span>≤ 14.6 ) = 0.673 (ANSWER)</span>
Answer:
360 x 1/10 = 360/10 simplify is 36
36 degrees is 1/10
Step-by-step explanation:
Surface area of a triangular prism = base*height + 2length*side + length*base
Base= 24, height= 35,
length= 47, side=37
24*35 + 2*47*37 + 47*24
=840+3478+1128
=5,546cm^2
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