How many times can 5 go into 78
2 answers:
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Answer:
Probability that a randomly selected can will have less than 15.5 ounces is 0.1587.
Step-by-step explanation:
We are given that the amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of 0.5 ounce.
<em>Let X = amount of soda</em>
So, X ~ N()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean amount = 16 ounces
= standard deviation = 0.5 ounce
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, the probability that a randomly selected can will have less than 15.5 ounces is given by = P(X < 15.5 ounces)
P(X < 15.5 ounces) = P( <
) = P(Z < -1) = 1 - P(Z
1)
= 1 - 0.8413 = 0.1587
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.</em>
Hence, the probability that a randomly selected can will have less than 15.5 ounces is 0.1587.
Answer:
Step-by-step explanation:
This is a right triangle (the small square in the corner signifies a 90 degree angle), so Pythagorean Theorem can be used.
where a and b are the legs of the triangle and c is the hypotenuse. In this triangle, 17 and x are the legs because they form the right angle. 29 in the hypotenuse because it is opposite the right angle.
Solve the exponents.
- 17²=17*17=289
- 29²= 29*29=841
289 is being added to x and the inverse is subtraction. Subtract 289 from both sides to isolate the variable.
x is being squared and the inverse is a square root. Take the square root of both sides of the equation.
Let's round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 9.
x is approximately 23.49 centimeters.