Proof: We know that angle CBA is congruent to angle FBA and
that angle CAB is congruent to angle FAB because the corresponding angles have the
same measure in degrees (as evidenced in the given equation). We see that angle
BCA is congruent to angle BFA by the reflexive property of congruence (More
accurately Third Angle Theorem). Therefore, we can conclude that triangle BCA
is congruent to triangle BFA because a pair of corresponding angles and the included side are equal, since the two triangles share a line segment (AB).
For this problem, let x be the number of children and y for adults. Formulate the equations: 1st equation, x + y = 3,200 and 2nd equation 5x + 9y = 24,000. Re-arrange 1st equation into x = 3200 - y. Then, substitute into 2nd equation, 5(3,200-y) + 9y = 24,000. Then, solve for y. The 16,000 - 5y + 9y = 24000. Final answer is, y = 2000 adults went to watch the movie.
The complete problem wants to know the more cost-effective choice is the printing company replaces its press machine every four years.
With this in mind, if they choose Company A, the total amount that needs to be paid to cover 12(4) = 48 months will be
Company A = 9 500 + 48(750) = $13 100
As for Company B, the highest probability of not having any repairs over the four years is 0.32 while there's 0.14 chance that number of repairs will be 3 over the time the contract is applied.
This means that the possible amounts to be paid to Company B are
Company B = 10 500 + 0(150) = $10 500
Company B = 10 500 + 1(150) = $10 650
Company B = 10 500 + 2(150) = $10 800
Company B = 10 500 + 3(150) = $10 950
This shows that choosing the machine from Company B would be better.
Hence, the answer is Company B<span>.</span>
So we want to know the product of 0.0000012 and 3.65*10^8 in the scientific form. First we turn 0.0000012 to scientific form: 0.0000012=1.2*10^-6. Now we multiply: (1.2*10^-6)*(3.65*10^8)=1.2*3.65*(10^-6)*(10^8)=4.38*10^(-6+8)= 4.38*10^2. So the correct product is 4.38*10^2.
