Answer:
For a height of 66 inches, Z = 0.65.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average height was about 64.3 inches; the SD was about 2.6 inches.
This means that
66 inches:
The z-score for a height of 66 inches is:
For a height of 66 inches, Z = 0.65.
Answer:
g(x) is flipped across the x-axis and translated -3 units
Step-by-step explanation:
BACKGROUND:
The rules of functions of the type you're asking for follow this structure (note that terms I use may not abide by the textbook definition):
f(x) = <em>a</em>(x - <em>b</em>)^<em>n</em> + <em>c</em>
<em>a</em> - vertical stretch or compression. If negative it will also flip the function across the x-axis.
<em>b</em> - horizontal translation. Note that if the number representing <em>b</em> is positive, there will be a negative translation and if negative there will be a positive translation.
- ex: (x + 3) will move the function 3 units to the <em>left </em>or in the <em>negative </em>direction on the graph
<em>c </em>- vertical translation of the function. Does not abide by the same rule as the horizontal in terms of having the opposite effect on the graph compared to what's implied.
- ex: (x + 3) - 4 will move 4 units down just like what's implied by the negative sign
<em>n </em>- there are a few special rules you can use to figure out the end behavior (EB) of functions like this one. If the exponent is positive, no matter how big the number it will have the same end behavior as a quadratic function. A function with an odd exponent will have the same end behavior as a linear function. (not useful in this case but still noteworthy)
- ex: f(x) = x^2 has the same end behavior as g(x) = x^6
WORK:
In this case, if abiding by these rules, g(x) = -(x + 3)^4 is:
- flipped across the x axis because of the negative value for <em>a</em>.
- translated 3 units to the left because of the value of <em>b</em>.
- has the same end behavior as the function f(x) = -x^2 (EB isn't useful in this case but may be in the future.)
Note: please comment with questions because the explanation I'm giving is highly visual and based on what I was taught, so I'm not a master at this type of math either. I'd recommend the free app Desmos to check out how changing a function impacts its graph.
Answer:
76
Step-by-step explanation:
recall that for a quadratic equation in the form
ax² + bx + c = 0, the discriminant is given by
discriminant, D = b²- 4ac
we are given the following:
-6x² + 2x + 3 = 0,
comparing this with the general equation above, it is clear that,
a = -6, b = 2 and c = 3,
substituting these into our equation for discriminant:
D = b²- 4ac
= 2² - 4(-6)(3)
= 4 + 72
= 76
Answer:
Slope = -4
Step-by-step explanation:
Given points are :
(-1,30) and (4, 10)
We need to find the slope of the line that passes through these points.
We know that, the formula for the slope of line is given by :
We have, x₁ = -1, y₁ = 30, x₂ = 4 and y₂ = 10
Put values in the above formula.
So, the slope of the line is -4.
Answer:
117
Step-by-step explanation:
The average of all 7 people is the total weight of the original 6 people, plus the weight of the 7th person, all divided by 7.
For problems like this involving an average of numbers that are "close" together, here is a different strategy for solving the problem that you might like to try.
The original 6 people have an average weight of 173, which is 8 pounds more than the average of all 7 people. So all together, the weight of those 6 people is 6*8=48 pounds over the 165 average. That means the 7th person's weight must be 48 pounds below the 165 average.
So the weight of the 7th person is 165-48 = 117 pounds.