Answer:
The speed of 65 mph is an outlier in the distribution of the player's serve speeds
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100 mph
Standard Deviation, σ = 10 mph
Formula:
Outlier on basis of z-score:
- Any z-score greater than 3 or less than -3 is considered to be an outlier.
- This rule of thumb is based on the empirical rule.
Calculation of z-score:
![x = 65\Rightarrow z = \dfrac{65-100}{10} = -3.5\\\\x = 110\Rightarrow z = \dfrac{110-100}{10} = 1\\\\x = 120\Rightarrow z = \dfrac{120-100}{10} = 2](https://tex.z-dn.net/?f=x%20%3D%2065%5CRightarrow%20z%20%3D%20%5Cdfrac%7B65-100%7D%7B10%7D%20%3D%20-3.5%5C%5C%5C%5Cx%20%3D%20110%5CRightarrow%20z%20%3D%20%5Cdfrac%7B110-100%7D%7B10%7D%20%3D%201%5C%5C%5C%5Cx%20%3D%20120%5CRightarrow%20z%20%3D%20%5Cdfrac%7B120-100%7D%7B10%7D%20%3D%202)
Thus, the speed of 65 mph is an outlier in the distribution of the player's serve speeds as the corresponding z-score is less than -3.
Answer: D. 4
Step-by-step explanation:
In the given picture , we have given a triangle ΔMLN in which
ML= 4x and MN= x+3
∠L=∠N=50°
⇒ MN=ML [∵ Basically by Isosceles triangle property :sides opposite to equal angles of a triangle area equal.]
![\Rightarrow\ x+3=4x](https://tex.z-dn.net/?f=%5CRightarrow%5C%20x%2B3%3D4x)
Subtract x from both sides , we get
![3=3x](https://tex.z-dn.net/?f=3%3D3x)
Divide bothe sides by x , we get
1= x or x =1
Then, the length of MN
= x+3=1+3=4 units
Answer: x = -7 or x = -4
Step-by-step explanation: When an equation has a squared term in it
such as x² + 11x + 28 = 0, it's called a polynomial equation.
The rule for solving a polynomial equation
is to first set it equal to zero, then factor.
Since this equation is already set equal to zero,
our first step is to factor the left side of the equation.
To factor x² + 11x + 28, we need the factors
of 28 that add to 11 which are 7 and 4.
So we have (x + 7)(x + 4) = 0.
Whenever two terms are multiplied together to equal zero,
this means that either one or the other must equal zero.
So if (x + 7)(x + 4) = 0, then either x + 7 = 0 or x + 4 = 0.
Solving each equation from here, we get x = -7 or x = -4.
So our solution is {-7, -4}.
Answer: The answer is 1,037. You did good with the first three steps but you need to do the same for the last step, because you have 21 you have to find how many times 3 goes into it, which would be 7, and that gives you your full answer of 1,037.
Simplify numbers to layman terms.
will be a little more than
, since
is 3.14.
will be a little less than -4, since
.
will be a little more than 4, since ![\sqrt{18}>\sqrt{16}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D%3E%5Csqrt%7B16%7D)
will be a little less than -2, since ![-\sqrt{7}](https://tex.z-dn.net/?f=-%5Csqrt%7B7%7D%3C-%5Csqrt%7B4%7D)
Now we can order them.
![-\sqrt{18},-\sqrt{7},\frac{\pi}{2},\sqrt{18}](https://tex.z-dn.net/?f=-%5Csqrt%7B18%7D%2C-%5Csqrt%7B7%7D%2C%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5Csqrt%7B18%7D)
Hope this helps.
頑張って!