The equivalence

means that n-5 is a multiple of 12.
that is
n-5=12k, for some integer k
and so
n=12k+5
for k=-1, n=-12+5=-7
for k= 0, n=0+5=5 (the first positive integer n, is for k=0)
we solve 5000=12k+5 to find the last k
12k=5000-5=4995
k=4995/12=416.25
so check k = 415, 416, 417 to be sure we have the right k:
n=12k+5=12*415+5=4985
n=12k+5=12*416+5=4997
n=12k+5=12*417+5=5009
The last k which produces n<5000 is 416
For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,
thus there are 417 integers n satisfying the congruence.
Answer: 417
Answer:
From the above we can roughly for an equation which is:
58.50 = Bill - (10% x Bill)
58.5 = Bill - (1/10 x Bill)
58.5 = 9/10 x Bill (Divide both sides by 9/10)
We get:
Bill = 58.5 / (9/10)
Bill = 65
Original bill is $65.
Answer:
True. See explanation below
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
If we assume that we have
groups and on each group from
we have
individuals on each group we can define the following formulas of variation:
And we have this property
The degrees of freedom for the numerator on this case is given by
where k represent the number of groups.
The degrees of freedom for the denominator on this case is given by
.
And the total degrees of freedom would be
And the we can find the F statistic
Answer:
$2.50 per movie and $6.50 per video game.
Step-by-step explanation:
The correct answer is $6.50 for each video game and $2.50 for each movie. My work:
3 x 2.50 = $7.50 and 5 x 6.50 = $32.50
32.50 + 7.50 = $40.00
12 x 2.50 = $30.00 and 2 x 6.50 = $13.00
30.00 + 13.00 = $43.00
Hope i helped you
Answer:
120 trees
Step-by-step explanation:
4x10=40
40x3=120
120 trees will be planted