Answer:
-499,485.
Step-by-step explanation:
We can transform this to an arithmetic series by working it out in pairs:
6^2 - 7^2 = (6-7)(6+7) = -13
8^2 - 9^2 = (8-9)*8+9) = -17
10^2 - 11^2 = -1 * 21 = -21 and so on
The common difference is -4.
The number of terms in this series is (998 - 6) / 2 + 1
= 992/2 + 1 = 497.
Sum of n terms of an A.S:
= n/2 [2a1 + (n - 1)d
Here a1 = -13, n = 497, d = -4:
Sum = (497/2)[-26 - 4(497-1)]
= 497/2 * -2010
= -499,485.
Answer:
Line y = –x + 4 intersects the line y = 3x + 3
Step-by-step explanation:
The solution is described as the point of intersection of the two lines. The description above is the only one that says anything about that.
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<em>Comments on other answer choices</em>
Any line with finite non-zero slope intersects both the x- and y-axes. That fact does not describe the solution to a system of equations.
Any linear equation with an added (non-zero) constant will not intersect the origin. These two equations have +4 and +3 added, so neither line intersects the origin.
Answer:
C
Step-by-step explanation:
(x+3)/3 =(y+2)/2
x/3 +3/3 = y/2 +2/2
x/3 +1 = y/2 +1
x/3 = y/2
Answer:
Marian can order 1,771 combinations
Step-by-step explanation:
In this question, we are interested in calculating the number of combinations Marian can order given that there are 23 flavors that can be served in three ways.
Mathematically, the number of combinations that can be ordered is simply 23C3
This is equal to 23!/(23-3)!3! = 23!/20!3! = 1,771
The number of combinations she can order is thus 1,771 combinations
Answer:
There is no evidence that the doors are too long and need to be trimmed (H₀ is accepted)
Step-by-step explanation:
The null hypothesis, 
Alternative hypothesis, 
Test statistic is calculated as follows:
Find the P-value
P(z > 1.27) = 1 - P(z < 1.27)
P(z > 1.27) = 1 - 0.898
P(z > 1.27) = 0.102
Significance level, α = 0.01
Since P - value(0.102) is greater than α (0.01), the null hypothesis will be accepted.
