Yizhang and Cheryl were waiting for Prof. Stoyanov to come for a meeting. Yizhang proposed a bet. He said that he would toss a fair coin 100 times, and if it landed tails more than 60 times, he would give Cheryl $5, otherwise Cheryl would give him $5...but Cheryl didnt want to do this. She was not sure that the coin was fair, and proposed the following test - Yizhang would toss the coin 30 times, and she would see how many times the coin landed tails, and then decide. Required:
a. How many times would you expect the coin to land tails in 30 tosses?
b. If the coin lands tails 10 times, should Cheryl play?

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

n=1.75+1.75

step-by-step explanation:

3.5/2=1.75

the answer is about 24 dollars

  b:   ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°

step-by-step explanation:

this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.

if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that

  x/sin(x) = y/sin(y) = z/sin(z)

and all of these ratios must be greater than 15, the longest side length.

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if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.

  z² = x² +y² -2xy·cos(z)

  z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°

now you can find y from the law of sines

  y = arcsin(y/z·sin(z)) = 31.242°