Answer:
0.81859
Step-by-step explanation:
We solve using z score method
The formula for calculating a z-score is is z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
Mean 0.8 pound
Standard deviation 0.25 pound
For x = 0.55 pound
z = 0.55 - 0.8/0.25
= -1
Probability -value from Z-Table:
P(x = 0.55) = 0.15866
For x = 1.3 pounds
Z = 1.3 = 0.8/0.25
= 2
Probability value from Z-Table:
P(x = 1.3) = 0.97725
The probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds is
P(x = 1.3) - P(x = 0.8)
0.97725 - 0.15866
0.81859.
Your triangle has acute angles X and Y, and right angle Z.
For an acute angle A in a right triangle:
The sine is the ratio of the opposite leg to the hypotenuse.
sin A = opp/hyp
The cosine is the ratio of the adjacent leg to the hypotenuse.
cos A = adj/opp
The hypotenuse of a right triangle is the side opposite the right angle. It is the longest side of a right triangle. There is only one hypotenuse in a triangle, so there is no confusion with the hypotenuse.
The two sides that form the right angle are called the legs. Each leg is opposite an acute angle. The legs may or may not be congruent to each other, but each leg is always shorter than the hypotenuse. Since there are two legs, we need to be able to distinguish them. If you take an acute angle as your angle of interest, the leg that is part of the angle is called the adjacent leg. The other leg is the opposite leg. Adjacent leg and opposite leg are relative terms. They depend on the acute angle you are considering.
For your triangle, if you look at angle X, then the adjacent leg is side XZ. The opposite leg for angle X is side YZ.
Using the ratios mentioned above for sine and cosine, you get:
sin X = opp/hyp = sqrt(119)/12
cos X = adj/hyp = 5/12
Answer:
The probability that the first marvel will be red and the second will be green is 7.14%.
Step-by-step explanation:
Since a bag contains 2 red marbles, 2 green marbles and 4 blue marbles, if we choose a marble and then other marble without putting the first one back in the bag, to determine what is the probability that the first marvel will be red and the second will be green, the following calculation must be performed:
2 + 2 + 4 = 8
2/8 x 2/7 = X
0.25 x 0.2857 = X
0.0714 = X
Therefore, the probability that the first marvel will be red and the second will be green is 7.14%.
Answer: 0.038
Step-by-step explanation:
Given: Total games : n= 375
Number of games won by the team that was winning the game at the end of the third quarter. = 300
The proportion (p) of the team that was winning the game at the end of the third quarter: 
Critical z-value for 90% confidence: z* = 1.645
Margin of error =
The margin of error in a 90% confidence interval estimate of p 
Hence, the required margin of error = 0.038
