Evaluate 2A - 3B for A = 6 and B = -3.
2 answers:
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Using the normal distribution, it is found that 58.97% of students would be expected to score between 400 and 590.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The proportion of students between 400 and 590 is the <u>p-value of Z when X = 590 subtracted by the p-value of Z when X = 400</u>, hence:
X = 590:
Z = 0.76
Z = 0.76 has a p-value of 0.7764.
X = 400:
Z = -0.89
Z = -0.89 has a p-value of 0.1867.
0.7764 - 0.1867 = 0.5897 = 58.97%.
58.97% of students would be expected to score between 400 and 590.
More can be learned about the normal distribution at brainly.com/question/27643290
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(a) The projectile remains in the air for 10 seconds
(b) It travels a horizontal distance of 600 meters
Step-by-step explanation:
A projectile is fired at such an angle that
1. The vertical component of its velocity is 49 m/sec
2. The horizontal component of its velocity is 60 m/sec
We need to find:
(a) How long the projectile remains in the air
(b) The horizontal distance it travels
∵ The vertical distance y = t -
g t², where
is the vertical component of its velocity, g is the acceleration
of gravity and t is the time
∵ y = 0 ⇒ it return to the same initial height
∵ = 49 m/s
∵ g = 9.8 m/s²
- Substitute these values in the rule above
∴ 0 = 49 t - (9.8) t²
∴ 0 = 49 t - 4.9 t²
- Take t as a common factor
∴ 0 = t (49 - 4.9 t)
- Equate each term by 0
∴ t = 0 ⇒ at initial position
∴ 49 - 4.9 t = 0
- Add 4.9 t to both side
∴ 49 = 4.9 t
- Divide both sides by 4.9
∴ t = 10 seconds
(a) The projectile remains in the air for 10 seconds
∵ The horizontal distance = t, where
is the
horizontal component of its velocity
∵ = 60 m/sec
∵ t = 10 seconds
∴ x = 60 × 10 = 600 meters
(b) It travels a horizontal distance of 600 meters
Learn more:
You can learn more about the component of velocity in brainly.com/question/4464845
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