Answer:
A: 244 pounds
B: 122 pounds
C: 274 pounds
Step-by-step explanation:
We have A+B+C = 640; A=2B; C=A+30. Substituting the last into the first gives ...
A + B + (A +30) = 640
2A +B = 610 . . . . . . . . . . . . subtract 30
Substituting the second into this equation gives ...
2(2B) +B = 610
B = 610/5 = 122 . . . . . divide by 5
A = 2B = 244 . . . . . . . .find A from B
C = A+30 = 274 . . . . . find C from A
Box A weighs 244 pounds; box B weighs 122 pounds; box C weighs 274 pounds.
Answer:
(-3,5)
Step-by-step explanation:
If you start at the origin (0), going up 5 spaces will leave you at 5 for your y plot. Then, 3 spaces <em>left</em> leaves you at -3 for your x. However, when writing down plots, you write x before y. So, you are left with (-3,5) as your coordinate plot for the final answer.
The sequence is geometric. Any exponential function models geometric growth. Recall the general nth term of a geometric sequence is a*(r)^(n-1) which is very similar to the form y = a*b^x. The big difference is that the x function is continuous while the function in terms of n is discrete. In this case, the common ratio is r = 1.10 to indicate we have 10% growth. Notice how 100%+10% = 1.00+0.10 = 1.10
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The first quadrant is where x and y are both positive. Since x is the time in years, it doesn't make sense to talk about negative years or negative years have passed by. We can have a negative balance in a bank account, so it makes sense to have y be negative. However, Mr Sullivan starts with some positive amount and his account grows every year. So there's no way that y can be negative in this case.
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The point (0,200) is the y intercept. It represents the starting amount he deposited into the account, which was the $200. Keep in mind that no other deposits were made, and he cannot pull money out of the account if he wants his account to grow according to the graph. Also, the interest rate must remain at 10%.
5n≥25
and if you divide 5 on both sides, n≥5 (I don't know if you are supposed to solve or simply put it in the equation form).
Product refers to multiplication. so 5 and n are being multiplied in the equation.
However, instead of using an equal sign, the sign for "greater than or equal to" must be used. "At least" is a term equivalent to "greater than or equal to".
The gas exerts a pressure of 218.75 kPa when its volume is reduced to 2.0 L, following the behavior of an ideal gas.
Ideal gas behavior:
Suppose the initial volume of carbon dioxide gas is V = 3.5l
Initial pressure is P = 125 kPa
Since the volume is reduced to 2.0l, the final volume is shown as V'= Will be done. 2L
The final pressure of the gas is P'.
We consider the behavior of gas to be ideal. From the ideal gas equation, it becomes as follows.
PV = P'V'
125 × 3.5 = P'× 2
P'= 218.75 kPa
Therefore, the final pressure is 218.5 kPa.
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