Let x be the number of MP3 players TechWiz sold last week.
If TechWiz sold in total 130 MP3 and DVD players, then it sold (130-x) DVD players.
1. TechWiz Electronics makes a profit of $35 for each MP3 player sold, then it makes a profit $35x for x MP3 players sold.
2. TechWiz Electronics makes a profit of $18 for each DVD player sold , then it makes a profit $18(130-x) for (130-x) DVD players sold.
3. An expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week is
35x+18(130-x).
You can simplify it:
35x+2,340-18x=17x+2,340
Answer: 35x+18(130-x) or 17x+2,340
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
2x-438 = -438+2x= 2(x-219)
The probability, in simplest form, is 3/23.
There are 9+8+7=24 roses. The probability of drawing a white rose first is 9/24. The probability of then drawing a yellow rose is 8/23, as one of the roses is gone. The total probability is 9/24(8/23) = 72/552 which then simplifies to 3/23.
