Which ratios form a proportion? use cross products to test each pair.
a. 15/40, 35/90
b. 18/22, 45/55
c. 15/55, 33/121
d. 17/31, 32/45

B. 18/22, 45/55

C. 15/55, 33/121

Step-by-step explanation:

Cross products are ...

A. 15×90 = 1350 ≠ 1400 = 40×35 . . . . not a proportion

B. 18×55 = 990 = 22×45 . . . . ratios are a proportion

C. 15×121 = 1815 = 55×33 . . . . ratios are a proportion

D. 17×45 = 765 ≠ 992 = 31×32 . . . . not a proportion

Comment on the solution

When looking at cross products, it can work well to look at the factors of the numbers involved:

... 18×55 = 2·9·5·11 . . . . . . 22·45 = 2·11·9·5 . . . . the same list of factors

You don't actually need to multiply it out to see that the products will be equal.

In pair D, you may recognize that 31 is a prime number, so the other ratio will only be proportional if the denominator is a multiple of 31, which it is not.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.