HELP ASAP unit activity: functions Task 2

Mathematics

1 answer:

GenaCL600 [577]3 years ago

4 0

Answer:

1) a)The function g is decreasing over the longest interval

b) The function g has the lowest y-intercept

2) a) The function h has the highest y-intercept

b) The function h is increasing over the longest interval

Step-by-step explanation:

The given functions are;

1) The function f has y-intercept is (0, 1)

The function increases from 0.5 < x ≤ ∞

2) The function g has y-intercept of the function occur at the point (0, -1)

The function is continuously decreasing for all the given x-values

Therefore, the function is decreasing over the longest interval

The function has the lowest y-intercept

3) The function h is the sum of 3 and four times the cube of x, which gives;

h = 3 + 4×x³

Therefore, the function has the highest y-intercept = 3

The function increases from 0 ≤ x ≤ ∞

Therefore, the function is increasing over the longest interval

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How many strings of six lowercase letters of the English alphabet contain

Marizza181 [45]

Answer:

a) 122,523,030

b) 72,930,375

c) 223,149,655

d) 100,626,625

Step-by-step explanation:

Consider that there are 5 vowels and 21 consonants in the English alphabet

a) exactly one vowel?

There a 6 possible positions for that vowel (6)

There are 5 ways to choose 1 vowel. (5)

There are 5 other positions to place one of the 21 consonants. (21^5)

$N(_{v=1})=6*5*21^5 = 122,523,030$

b) exactly two vowels?

There are C(6,2) possible positions for both vowels (C(6,2))

There are 2 positions to choose a vowel out of 5 vowels. (5^2)

There are 4 other positions to place one of the 21 consonants. (21^4)

$N(_{v=2})=C(6,2)*5^2*21^4 = \frac{6!}{(6-2)!2!}*5^2*21^4\\N(_{v=2})= 72,930,375$

c) at least one vowel?

The number of possibilities that the string contains at least one vowel is the number of total possible outcomes minus the number of outcomes with only consonants:

$N(_{v>0})=(21+5)^6-21^6 \\N(_{v>0})= 223,149,655$

d) at least two vowels?

The number of possibilities that the string contains at least two vowels is the number of possibilities that the string contains at least one vowel minus the number of possibilities that the string contains exactly one vowel:

$N(_{v>1})= 223,149,655 - 122,523,030\\N(_{v>1}) = 100,626,625$