Answer:
P(X < 80) = 0.89435.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean 
and standard deviation 
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
P(X < 80)
This is the pvalue of Z when X = 80. So
has a pvalue of 0.89435.
So
P(X < 80) = 0.89435.
We know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
where (h,k,l) is the center and r is the radius
we have
x²+y²+z²<span>−2x−4y+8z+17=0
</span>
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²+2x)+(y²-4y)+(z²+8z)=-17
<span>Complete
the square. Remember to balance the equation by adding the same constants
to each side
</span>(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=-17+1+4+16
(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=4
Rewrite as perfect squares
(x+1)²+(y-2²)+(z+4)²=4
(x+1)²+(y-2²)+(z+4)²=2²
the center is the point (-1,2,-4) and the radius is 2 units
The first thing we must do in this case is to define variables:
t = time to write the words
v = write speed.
w = number of words.
The correct expression is:
t = w / v
By substituting we have:
t = 1000/6
t = 166.6666667
Rounding:
t = 167 minutes
Answer:
The correct expression is:
t = w / v
The time is:
t = 167 minutes
Answer:
Step-by-step explanation:
t1 = a1
t2 = a1 + d
t3 = a1 + 2d
The sum is t1 + t2 + t3 = a1 + a1 + d + a1 + 2d = 3a1 + 3d
Second question
t1 = a1
t2 = a1 + d
t3 = a1 + 2d
t4 = a1 + 3d
...
tn = a1 + (n - 1)*d
Sum = (a1 + a1 + (n- 1)*d) * n / 2
Sum = (2a1 + nd - d) * n / 2
Sum = (2a1*n + n^2*d - nd) / 2
