Astronomers classify stars according to their brightness by assigning them a stellar “magnitude.” the higher the magnitude the dimmer the star. the dimmest stars visible to the naked eye have stellar magnitudes of 6. the table below shows the relative brightness of different stellar magnitudes.

(a)

(b) The relative brightness for a stellar magnitude of 9 is 0.07.

Step-by-step explanation:

Let the relative brightness be given by 'b' and stellar magnitude by 'm'.

(a)

Given:

The magnitude of relative brightness decreases as the magnitude of stellar increases.

From the table, we can conclude that the ratio for any two consecutive values of 'b' is the same and is equal to 0.4.

Now, we know that, for a common ratio 'r' of a given series, the series is called a geometric series.

The term of a geometric series is given:

Now, for the given table,

Therefore, the equation that gives the relative brightness in terms of stellar magnitude is given as:

(b)

Given:

The stellar magnitude is,

The equation to find relative brightness is:

Plug in 9 for 'm' and solve for 'b'. This gives,

Therefore, the relative brightness for a stellar magnitude of 9 is 0.07.

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

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'.