10 waffles and 4 pancakes cost $14. Five waffles and eight pancakes cost

Mathematics

1 answer:

Stels [109]3 years ago

8 0

9514 1404 393

Answer:

pancake: $0.50
waffle: $1.20

Step-by-step explanation:

You can model the bills using w and p for the price of a waffle and pancake, respectively.

10w + 4p = 14

5w +8p = 10

Subtract half the first equation from the second:

(5w +8p) -(1/2)(10w +4p) = (10) -(1/2)(14)

6p = 3 . . . . . . . simplify

p = 0.50 . . . . . divide by 6

10w + 4(0.50) = 14 . . . . substitute into the first equation

10w = 12 . . . . . . . . . . . . subtract 2

w = 1.20 . . . . . . . . . . . . .divide by 10

A waffle costs $1.20; a pancake costs $0.50.

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A set of data items is normally distributed with a mean of 400 and a standard deviation of 60. Find the data item in this distri

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Answer:

The data item is $X = 580$

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 400 and a standard deviation of 60.

This means that $\mu = 400, \sigma = 60$