Let f(x) = 5 - x and g(x) = 2x - 1. Perform the following operation: (f + g)(-2).

Mathematics

1 answer:

blsea [12.9K]3 years ago

6 0

Answer:

(f + g)(-2) = 2

Step-by-step explanation:

Step 1: Define

f(x) = 5 - x

g(x) = 2x - 1

Step 2: Find (f + g)(x)

(f + g)(x) = 5 - x + 2x - 1

(f + g)(x) = x + 4

Step 3: Find (f + g)(-2)

(f + g)(-2) = -2 + 4

(f + g)(-2) = 2

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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 o

xeze [42]

Answer:

a) 95% of the widget weights lie between 29 and 57 ounces.

b) What percentage of the widget weights lie between 12 and 57 ounces? about 97.5%

c) What percentage of the widget weights lie above 30? about 97.5%

Step-by-step explanation:

The empirical rule for a mean of 43 and a standard deviation of 7 is shown below.

a) 29 represents two standard deviations below the mean, and 57 represents two standard deviations above the mean, so, 95% of the widget weights lie between 29 and 57 ounces.

b) 22 represents three standard deviations below the mean, and the percentage of the widget weights below 22 is only 0.15%. We can say that the percentage of widget weights below 12 is about 0. Equivalently we can say that the percentage of widget weights between 12 an 43 is about 50% and the percentage of widget weights between 43 and 57 is 47.5%. Therefore, the percentage of the widget weights that lie between 12 and 57 ounces is about 97.5%

c) The percentage of widget weights that lie above 29 is 47.5% + 50% = 97.5%. We can consider that the percentage of the widget weights that lie above 30 is about 97.5%