Answer:
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Answer:
4.75% probability that the line pressure will exceed 1000 kPa during any measurement
Step-by-step explanation:
Problems of normally distributed samples are 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:
What is the probability that the line pressure will exceed 1000 kPa during any measurement
This is 1 subtracted by the pvalue of Z when X = 1000. So
has a pvalue of 0.9525
1 - 0.9525 = 0.0475
4.75% probability that the line pressure will exceed 1000 kPa during any measurement
Answer:
A) 151 in³ or 151 cubic inches
Step-by-step explanation:
Volume of rocket = Volume of Cylinder + Volume of Cone
Step 1
Find the volume of the cylinder
Volume of a cylinder = πr²h
r = Diameter/2
= 5/2 = 2.5 inches
h = 6 inches
Hence,
π × 2.5² × 6
= 117.81 cubic inches
Step 2
Find the volume of the cone
Volume of a cone =1/3 πr²h
h = 11 inches - 6 inches
= 5 inches
r = 2.5 inches
Hence,
1/3 × π × 2.5² × 5
= 32.72 cubic inches
Therefore:
Volume of rocket = Volume of Cylinder + Volume of Cone
= 117.81 cubic inches + 32.72 cubic inches
= 150.53 cubic inches
Approximately to the nearest inch = 151 in³ or 151 cubic inches
Option A is correct
Since it's a right triangle you can use the Pythagorean theorem or Trig (Soh Cah Toa).
I'll just use the Pythagorean theorem : a² + b² = c²
a = 9
b = x
c = 18
9² + x² = 18²
81 + x² = 324
x² = 324 - 81
x² = 243
x = √(243)
factor 243 to find a perfect square
x = √(3*81)
x = 9√(3)<u />
Answer:
rectangles are similar figures, thus if scaled copies of each other then the ratios of corresponding sides must be equal
compare ratios of lengths and widths
rectangles A and B
k = = ← ratio of lengths
k = = ← ratio of widths
scale factors are equivalent, hence rectangle A is a scaled copy of B
rectangles C and B
k = = ← ratio of lengths
k = = ← ratio of width
scale factors (k ) are not equal, hence C is not a scaled copy of B
rectangles A and C
k = = ← ratio of lengths
k = ← ratio of widths
the scale factors are not equal hence A is not a scaled copy of C
Step-by-step explanation:
