Laura and Philip each fire one shot at a target. Laura has probability 0.4 of hitting the target, and Philip has probability 0.1. The shots are independent. (i). Find the probability that the target is hit.(3 points) (ii). Find the probability that the target is hit by exactly one shot.(3 points) (iii). Given that the target was hit by exactly one shot, find the probability that Philip hit the target.(4 points)

(i) 0.46, (ii)0.42, and (iii)0.143

Step-by-step explanation:

Let be the probability of hitting the target and be the probability of missing the target by Laura.

Given that

As Laura either hit or miss the target, so .

Again, let be the probability of hitting the target and be the probability of missing the target by Philip.

Here,

Similarly,

(i)The probability that the target is hit means that the target is not missed by both, either of one or both hit the target.

=1-(probability of missing the target by both)

=1- [from equation (2) and (4) ]

=

=

=0.46

(ii) The probability that the target is hit by exactly one shot means either of one hit the target.

=Hit by Laura and missed by Philip or hit by Philip and missed by Laura

[from equations (1),(4) and (3),(2)]

=0.42

(iii)Given that the target was hit by exactly one shot, so, the given probability is 0.42 [from (ii) part]

No, the probability that the target was hit by Philip = probability of hitting the target by Philip and missing the target by Laura

[from equations (3) and (2)]

=0.06

So, the probability of hitting the target by Philip

(approx)

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'.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)