Asurvey of a group’s viewing habits over the last year revealed the following information: (i) 28% watched gymnastics (ii) 29% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and baseball (v) 12% watched baseball and soccer (vi) 10% watched gymnastics and soccer (vii) 8% watched all three sports. calculate the percentage of the group that watched none of the three sports during the last year. (a) 24% (b) 36% (c) 41% (d) 52% (e) 60%

D) 52%

Step-by-step explanation:

G = gymnastics

B = baseball

S = soccer

G = 28%

BA = 29%

S = 19%

G and BA = 14%

BA and S = 12%

G and S = 10%

GBS = 8%

So, as we can see at the Venn diagram attached (consider every number in %)

GBS = 8

A = G and S - GBS = 10 - 8 = 2

B = G and BA - GBS = 14 - 8 = 6

C = BA and S - GBS = 12 - 8 = 4

Only G = G - A - B - GBS = 28 - 2 - 6 - 8 = 12

Only BA = BA - B - C - GBS = 29 - 6 - 4 - 8 = 11

Only S = S - A - C - GBS = 19 - 2 - 4 - 8 = 5

So, 2+6+4+12+11+5+8 = 48

100 - 48 = 52%

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus

true

step-by-step explanation:

intersecting chords are just lines that intersect. so a line is equal to 180 degrees, so when it is intersected by another chord, then it create supplementary angles, and because the lines cross, vertical angels are also formed.