Answer:
The price where the manufacture sells the maximum number of toys is $20
Step-by-step explanation:
The given equation for that represents the number of toys the manufacturer can sell is given as follows;
T = -4·p² + 160·p - 305
Where;
p = The price of the toys in dollars
At the point where the manufacture sells the maxim number of toys on the graph of the equation T = -4·p² + 160·p - 305, which is the top of the graph, the slope = 0
Therefore, at the maximum point;
The slope = 0 = dT/dp = d(-4·p² + 160·p - 305)/dp = -8·p + 160
∴ -8·p + 160 = 0
160 = 8·p
8·p = 160
p = 160/8 = 20
The price where the manufacture sells the maximum number of toys is = p = 20 dollars
Answer:
Lina's solution is correct because it expresses 126 as a product of prime factors.
Step-by-step explanation:
Prime factorization can be defined as a methodology of breaking down an original number down into the set of prime numbers which when multiplied together give us the original number.
Prime factorization makes use of a factor tree
The number we are to carry out prime factorization on is 126
126
/\
3 42
/\
6 7
/\
2 3
The Prime Factorization is:
2 x 3 x 3 x 7
Hence, Lina's factor tree of 126. 126 branches to 3 and 42. 42 branches to 6 and 7. 6 branches to 2 and 3. The equation is 126
= 2 times 3 squared times 7.
Is correct.
Answer:
1. 258
2. 452
3. 626
4. 645
Step-by-step explanation:
multiply all the numbers by 0.97 because the family has to decrease the clothing budget by 3%