Answer:
512
Step-by-step explanation:
Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7
.
For instance, if I divide the set into parts {1,2,4}
and {3,5}, the first part adds up to 7, and its complement adds up to 8
.
Once one makes that observation, the rest of the proof is straightforward. There are 25=32
different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.
Answer:
There are infinite vocabulary words that can be used in math, but i think these are the most commonly used.
Step-by-step explanation:
. parallel - equal- equidistant - collinear - symmetry - tangent.
. Lines- angles-circles - quadrilateral- circumference.
.Addition-subtraction-calculate- arithmetic - decimal-radius-diameter - center of gravity-centroid-equilateral- isosceles- height-median - perpendicular bisector- compass - protractor.
. Average- axis - coordinates-curve - cylinder - section - cosine- sine- multiplication - division - cube-cone- degree- divisor - dozen-ellipse - equation-numerical- even- odd - exponent- expression - corresponding - factor - factorial- factorization - fraction- geometry - algebra - graph - greater than - more - less- compare - integer- intersection - inequality - equality - identity - inverse - real - imaginary - irrational - rational- linear- mean- minus- plus- negative - positive - perimeter - parabola - parallelogram - quotient - radian- series-set- slope- sphere - solve - square root - symbol - volume-variable.
Answer:
Answer is D
Step-by-step explanation:
Answer: The constant of proportionality is 8 for the the problem on your left! The constant of proportionality for the one on you right is 6! Hope this helps!
Step-by-step explanation: Vincent earned $24 for 3 hours and so you find out how much he gets paid for 1 hour, then you divide 24 by 3 and get 8! Later he earned $72 for 9 hours, and you do the same thing which is to divide 72 by 9 which also give you 8 and so your unit rate or constant of proportionality is 8. So for the other one Justene can bike for 12 miles in 2 hours and so you find out how many miles she can bike for 1 hours and so you divide 12 by 2 which give you 6 and she can bike 6 miles in 1 hour. Then she biked 36 miles in 6 hours and you divide 36 by 6 which give you 6 and so your constant of proportionality is 6!
Answer:
Yes on one picture it says -40 and on the other one it says -4 so there is a differemce.
Step-by-step explanation:
