a mail truck picks up two boxes of mail from the post office. the total weight of the boxes is 32 pounds . one box is 8 pounds heavier than the other box. how much does each box weight
Answers
Final answer:
The boxes weigh 12 pounds and 20 pounds respectfully. We found this by setting up and solving an equation based on the problem's parameters.
Explanation:
Let's assume the lighter box weighs 'x' pounds, this makes the heavier box weigh 'x+8' pounds. According to the problem, the total weight of both boxes that the mail truck picks up from the post office is 32 pounds. So, we can set up the following equation: x + (x+8) = 32. Solving this equation we get 2x = 24, which means x = 12. So, one box weighs 12 pounds and the other box, which is 8 pounds heavier, weighs 20 pounds.
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A. y=-2
B. y=-1
C. y=1
D. y=2
Answers
.
Answers
since (x-3) is a factor. if you put x=3 in the equation, it must be equal to zero. So the equation becomes (9k2 - 3k -2 = 0). if you solve this you will get k=(-1/3) and k=(2/3). You can substitute this k in the original equation and check, (x-3) is a factor.
Answers
(68/100) * y = 119
0.68*y = 119
y = 119 / 0.68 Use your calculator
y = 175
The number y is = 175
b. the account pays 2.25% annual interest compounded monthly
c. the account pays 2% annual interest compounded daily
(SHOW YOUR WORK)
Answers
.03 ÷ 4 = .0075. Add 1 to include your principal. 1.0075 and raise it to the 12th power since you will be doing this 4 times a year for 3 years (4 x 3 =12).
Since you want 3000 at the end of this period you should do:
3000 ÷ (1.0075¹²) and you get $2742.71 which is how much you should put in.
B) .001875 is the monthly rate of 2.25% (.0225 divided by 12)
This time we have to do it to the 36th power since there are 36 months in 3 years.
Don't forget to add the 1 to include your money.
3000 ÷ (1.001875¹²) = $2804.36
C) 2% compounded daily means .02 ÷ 365 = (about) .00005479
Once again we add our principal by putting a 1 in front 1.00005479
3000 ÷ (1.00005479¹⁰⁹⁵) (1095 because 365 x 3 years = 1095 days)
= $2825.31
Just to emphasize why I always added 1. Since I am dividing, dividing by 1 givesyou the same as you start with (3000 ÷1 is still 3000) The small numbers after the 1 reduce the amount (3000) to the amount you will have to put in to realize $3000 at the end of each time period.
Final answer:
To have $3000 in the savings account after 3 years, you should deposit $2688.97 for situation a, $2669.29 for situation b, and $2667.99 for situation c.
Explanation:
To find the amount you should deposit for each situation, we can use the formula for compound interest:
A = P(1 + (r/n))^(nt)
where A is the final amount, P is the principal amount (the initial deposit), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.
Using the given information, we can calculate:
- For situation a (3% annual interest compounded quarterly), we have A = $3000, r = 3% = 0.03, n = 4 (since interest is compounded quarterly), and t = 3. Rearranging the formula, we get:
P = A / (1 + (r/n))^(nt) = $3000 / (1 + (0.03/4))^(4*3) = $2688.97 (rounded to two decimal places). - For situation b (2.25% annual interest compounded monthly), we have A = $3000, r = 2.25% = 0.0225, n = 12 (since interest is compounded monthly), and t = 3. Substituting these values into the formula, we get:
P = A / (1 + (r/n))^(nt) = $3000 / (1 + (0.0225/12))^(12*3) = $2669.29 (rounded to two decimal places). - For situation c (2% annual interest compounded daily), we have A = $3000, r = 2% = 0.02, n = 365 (since interest is compounded daily), and t = 3. Plugging these values into the formula, we get:
P = A / (1 + (r/n))^(nt) = $3000 / (1 + (0.02/365))^(365*3) = $2667.99 (rounded to two decimal places).
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Mass (g)
Soccer ball
400
Small can of oranges
312
Baseball
142
Science textbook
1,900
Walnut in the shell
20
Comparing it to the items in the table, what is a reasonable mass for an orange to have?
A.
1,000 g
B.
250 g
C.
500 g
D.
50 g
Answers
Answer:
B.
Step-by-step explanation:
500 g is a little more than 1 pound.
3 walnuts = 60 g, but 3 walnuts weigh much less than 1 orange.
Answers
The expression is 3x.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
We can write an expression as,
(1/3) x (9x)
= (9/3)x
= 3x
Thus,
The expression is 3x.
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