Jane has $100 and Ellis has $75. Jane is saving $5 per day and Ellis is saving $7 per day. (4 points)
A. What equation represents how much money Jane will have in total after saving for d days?
B. What equation represents how much money Ellis will have in total after saving for d days?
C. What equation would be used to find out how many days it will take for Jane and Ellis to have the same amount of money saved?
D. After the amount of time found above, how much will Jane and Ellis each have saved?
$275
5d+100=7d+75
y=7d+75
y=75d+7
$325.50
7d+5d=100+75
$175
y=5d+75
100d+5=75d+7
y=5d+100
$15
$162.50
y=7d+100
y=100d+5
y=100d+75
A. Jane will have $5d + $100 in total after saving for d days.
B. Ellis will have $7d + $75 in total after saving for d days.
C. The equation that would be used to find out how many days it will take for Jane and Ellis to have the same amount of money saved is:
5d + 100 = 7d + 75
D. After the amount of time found above, they will each have $175 saved.
The closest distance between Earth and Mars is approximately 3.39×10^7 miles. The fastest rocket leaving Earth travels at an average speed of approximately 3.6×10^4 miles per hour. (8 points)
A. At that rate, which expression could be used to determine the approximate number of hours it would take the rocket to travel from Earth to Mars?
B. How many hours would it take to travel from Earth to Mars?
Expression
(3.6×10^4)÷(3.39×10^7)
(3.6×10^4)−(3.39×10^7)
(3.6×10^4)×(3.39×10^7)
(3.39×10^7)÷(3.6×10^4)
(3.39×10^7)−(3.6×10^4)
(3.39×10^7)×(3.6×10^4)
Number of hours
942
12,204
106
210
A. The expression that could be used to determine the approximate number of hours it would take the rocket to travel from Earth to Mars is:
(3.39×10^7)÷(3.6×10^4)
B. Calculating this expression gives us approximately 942 hours. This is how long it would take for the rocket to travel from Earth to Mars.
What is the value of the expression in standard form? (4.8×10^8)(2.2×10^−6)/(1.2×10^4) (2 points)
0.0058
0.00088
0.58
0.088
To find the value of the expression in standard form, we need to multiply the numbers in the numerator, divide by the number in the denominator, and simplify:
(4.8 × 10^8) * (2.2 × 10^-6) / (1.2 × 10^4)
= (4.8 * 2.2) * (10^8 * 10^-6) / 1.2 * (10^4)
= 10.56 * 10^2 / 1.2 * 10^4
= 10.56 / 1.2 * 10^-2
= 8.8 * 10^-2
= 0.088
Therefore, the value of the expression in standard form is 0.088.
Simplify the following expression to Scientific Notation: (9×10^16)^2 (1 point)
Multiply exponents to get 8.1×10^33
Multiply exponents to get 8.1×10^31
Multiply exponents to get 18×10^32
Add exponents to get 9×10^18
Add exponents to get 8.1×10^17
Add exponents to get 81×10^32
To simplify the expression to Scientific Notation, we need to multiply the exponents when raising a power to a power.
(9×10^16)^2 = 9^2 * (10^16)^2 = 81 * 10^(16*2) = 81 * 10^32
Therefore, the simplified expression in Scientific Notation is 8.1×10^32.
The option should be:
Multiply exponents to get 8.1×10^32
Fill in the blanks with the correct steps for solving: (3.71×10^5)+(4.65×10^7) (5 points)
Step 1: to get the exponents the same for adding in Scientific Notation.
Subtract 2 from the exponent 5
Subtract the exponents
Add 2 to the exponent 5
Add the exponents together
Step 2: to change the coefficient on the term that the exponent was changed.
Change 3.71 to 371
Change 3.71 to 0.0371
Change 4.65 to 0.045
Change 4.65 to 0.465
Step 3: the coefficients.
Subtract
Keep the same
Add
Divide
Multiply
Step 4: the exponents to simplify.
Subtract
Multiply
Keep the same
Add
Divide
Step 5: is the final answer in Scientific Notation.
4.6871 x 10^7
9.4 x 10^7
.94 x 10^12
8.36 x 10^2
Here are the correct steps for solving (3.71×10^5) + (4.65×10^7):
Step 1: To get the exponents the same for adding in Scientific Notation
Subtract 2 from the exponent 5
Step 2: To change the coefficient on the term that the exponent was changed
Change 3.71 to 371
Step 3: Add the coefficients
371 + 465 = 836
Step 4: The exponents to simplify
Add the exponents:
5 + 7 = 12
Step 5: The final answer in Scientific Notation
The final answer is 8.36 x 10^12.