The function h is defined, for all real numbers , answer is as follows -
h(1) = - 2
h(2) = 3
h(4) = 3.
function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable
We have been given that
h(x) = 1/4(x) - 1 if x < -2
h(x) = -(x + 1)² + 2 if -2 ≤ x < 2
h(x) = 3 if x ≥ 2
Find h (1), h (2), and h (4)
For h (1) -
Value of h(1) for h(x) = -(x + 1)² + 2 as if -2 ≤ x < 2
So put x = 1
h(x) = -(x + 1)² + 2
h(1) = -(1 + 1)² + 2
h(1) = -4 + 2
h(1) = - 2
For h (2) -
Value of h(2) for h(x) = 3 as if x ≥ 2
h(x) = 3
h(2) = 3
For h (4) -
Value of h(4) for h(x) = 3 as if x ≥ 2
h(x) = 3
h(4) = 3
Hence , the value for given functions - h(1) = - 2 , h(2) = 3 and h(4) = 3.
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We let x = pounds of alloy that is 15% tin
The problem is modeled by the equation:
0.11(30) = 0.15x + 0.09(30-x)
The equation means that the amount of tin does not change. Also, the amount of alloy (total weight - weight of 15% alloy) is (30-x).
Solving for x:
3.3 = 0.15x +2.7 - 0.09x
.06x = 0.6
x = 10 lbs
30-10 = 20 lbs
<span>10 lbs. of the 15% alloy and 20 lbs. of the 9% alloy</span>
The answer is $265 (how much did she make altogether)
The equation is x=6h+6
Using it's concept, it is found that the probability that the special ball is chosen is given by:

<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
The total number of outcomes is given by the combination of k balls from the set of n balls, given by:

One ball is special, hence the probability the special ball is chosen is given by:

More can be learned about probabilities at brainly.com/question/14398287
Answer: The expected value of the water depth is 4.5 m.
Step-by-step explanation:
Let x be a random variable which is uniformly distributed in interval [a,b] .
Then the mean of the distribution is ghiven by :-

Given : While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.
Then, the expected value of the water depth = 
Hence, the expected value of the water depth is 4.5 m.