Answer:
Holly's score is an outlier because the mean of the data is 83, and 30 is very far then 83.
The mean is 83
The median is 87
Removing the outlier change the mean because the mean became higher.
The mean was most affected by the outlier because the mean changed to 86. 31
This problem can be solve by graphing (technology), as suggested.
The answer is posted as an attached image. We see that after about 14.75 years, the invading species will surpass the indigenous population.
If it needs to be solved mathematically and accurately, the math is a little more advanced, using the bisection method, or Newton's method.
However, we can also do that by trial and error, starting from 14.75. It is easier than you might think.
Post if you would like to have more information on one or the other methods.
Note: the scale of y has been shrunk by 1000, so each unit on the y-axis represents 1000 frogs.
Answer:
8z+15
Step-by-step explanation:
a^2 + b^2 = c^2
Let c = hypotenuse = 2x
One of the legs = x. Let a or b = x.
I will let a = x. We can then say that b = 3.
3^2 + x^2 = (2x)^2
9 + x^2 = 4x^2
9 = 4x^2 - x^2
9 = 2x^2
9/2 = x^2
sqrt{9/2} = sqrt{x^2}
3/sqrt{2} = x
Rational denominator.
[3•sqrt{2}]/2 = x = a
Side 3 is given to be 3 feet. So, b = 3.
Hypotenuse = 2x
Hypotenuse = 2([3•sqrt{2}]/2)
Hypotenuse = 3•sqrt{2}
Understand?
The three sides are 3, [3•sqrt{2}]/2 and
3•sqrt{2}.
Answer: x = 3, y = 1, z = 2
<u>Step-by-step explanation:</u>
EQ 1: x - y - z = 0
EQ 3:<u> -x + 2y + z = 1 </u>
y = 1
EQ 2: 2x - 3y + 2z = 7 → 1(2x - 3y + 2z = 7) → 2x - 3y + 2z = 7
EQ 3: -x + 2y + z = 1 → -2( -x + 2y + z = 1) → <u>-2x + 4y + 2z = 2</u>
y + 4z = 9
y = 1 ⇒ 1 + 4z = 9
4z = 8
z = 2
Input y = 1 and z = 2 into one of the equations to solve for x:
EQ 1: x - y - z = 0
x - (1) - (2) = 0
x - 3 = 0
x = 3
Check:
EQ 2: 2x - 3y + 2z = 7
2(3) - 3(1) + 2(2) = 7
6 - 3 + 4 = 7
3 + 4 = 7
7 = 7