Answer:
The probability is 0.0069
Step-by-step explanation:
First thing to do here is to calculate the z-score
Mathematically;
z-score = (x-mean)/SD/√(n)
where x = 9.1 , mean = 8.4 , SD = 1.8 and n = 40
Plugging these values into the z-score equation, we have;
z-score = (9.1-8.4)/1.8/√(40) = 0.7/1.8/6.325 = 0.0615
Now, we check the standard normal table for P(z > 2.46) = 0.0069
Answer:
2 more quarts of oil is needed to fill
the engine to capacity
Step-by-step explanation:
Here, we want to calculate how many more quarts of oil is required to fill the engine to capacity
We have to convert the capacity to quarts
Mathematically, 1 gallon = 4 quarts
So 1 1/4 gallon will be 5/4 * 4 = 5 quarts
So the number of quarts needed to fill the engine to capacity will be 5 quarts - 3 quarts = 2 quarts
Answer:
48 - 8c
Step-by-step explanation:
let c be the number of coworkers
48 - 8c would be the expression because it starts with 48 and for every coworker 8 is subtracted.
Answer:
The end behavior of f(x)=2/3x-2 is: as x->+ infinity, f(x)->+ infinity
as x->- infinity, f(x)->- infinity
Step-by-step explanation:
When you are asked about the end behavior of a function, look to see where the function is traveling on the graph. For instance, this graph is linear, so you should look to see if the slope is positive or negative. This linear function is positive, so as x is reaching positive infinity the f(x) would also be reaching positive infinity. As x is reaching negative infinity, f(x) would also be reaching negative infinity. The end behavior of a function describes the trend of the graph on the left and right side of the x- axis. (As x approaches negative infinity and as x approaches positive infinity).
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Answer:</h2><h3>
A. Domain </h3>
The domain of a function is the x-values that the graph applies to. This means that the domain is whatever x-values the graph crosses. All vertical parabolas (like the one pictured) have a domain of all reals. This is because any x-value could be plugged into the function and provide a y-value. while it may not seem like it, that graph will cover every single x-value in existence.
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B. Range</h3>
The range is similar to the domain but is for y-values. So, the range is whatever y-values the graph applies to and crosses. As you can see from the graph, there are no y-values above 1. This means the range is y≤1.
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C. Increasing Interval</h3>
A graph is increasing when the y-values are increasing. So, on the parent function of a parabola, the graph increases to the right and decreases to the left. However, this graph is inverted and shifted to the left, so the interval will also be flipped and shifted. In this case, the graph increases from -∞ to 2.
- Increasing Interval = [-∞, 2]
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D. Decreasing Interval</h3>
The decreasing interval is very similar to the increasing interval. This interval applies when the y-values are decreasing as the x-values increase. For a parabola, the increasing and decreasing intervals always meet at the x-value of the vertex, which is 2 on this graph. The y-values decrease during the interval 2 to ∞.
- Decreasing Interval = [2, ∞]
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E. Opening</h3>
The direction of a parabola is decided by the sign (+ or -) of the leading coefficient. Positive coefficients open up and negative opens down. As you can see from the graph, the sides of the parabola point downwards. This means that the leading coefficient must be negative.
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F. Min and Max</h3>
A parabola will always only have a min or a max, never both. If a graph opens up it has a min because there is one y-value which is the minimum possible y-value. Graphs that open downwards have a maximum because there is one y-value that is the largest possible. So, this graph has a maximum of 1 because that is the largest possible y-value.
