(6 × 10^-6) × (7 × 10^5) × (6 × 10^6)
To multiply numbers in scientific notation, you multiply their coefficients and add their exponents. So:
(6 × 10^-6) × (7 × 10^5) × (6 × 10^6) = 6 × 7 × 6 × 10^-6 × 10^5 × 10^6 = 252 × 10^-1 × 10^5 × 10^6
To add the exponents together, you can add or subtract them depending on whether it's a multiplication or division. In this case, we have multiplication, so we add:
= 252 × 10^-1+5+6 × 10^6 = 252 × 10^10 × 10^6
Now, we can add the exponents again:
= 252 × 10^10+6 = 252 × 10^16
Therefore, (6 × 10^-6) × (7 × 10^5) × (6 × 10^6) equals 252 × 10^16.
possible answers:
Question 1 options:
A)
2,520,000
B)
252 × 10^-180
C)
252 × 10^5
D)
25,200,000
The correct answer is:
D) 25,200,000
Find the simple interest. Round your answer to the nearest cent.
Principal = $850
Rate = 8%
Time in years = 2 1/2
Question 2 options:
A) $265.63
B) $17.00
C) $170.00
D) $27.20
To calculate simple interest, you can use the formula:
Interest = Principal × Rate × Time
Given:
Principal = $850
Rate = 8% (converted to decimal form, which is 0.08)
Time in years = 2 1/2 (2.5 years)
Plugging these values into the formula:
Interest = $850 × 0.08 × 2.5
Calculating the expression:
Interest = $850 × 0.08 × 2.5 = $170
Rounding to the nearest cent, the simple interest is $170.00.
Therefore, the answer is C) $170.00.
Find the mode or modes.
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mode(s).
54, 64, 61, 50, 55, 59, 65, 58, 56
Question 5 options:
A) 54, 64, 61, 50, 55, 59, 65, 58, 56
B) 58
C) No mode
D) 58.0
To find the mode(s), you need to determine the value(s) that appear most frequently in the given data set.
The ages at retirement are: 54, 64, 61, 50, 55, 59, 65, 58, 56.
In this data set, the number 58 appears twice, which is more than any other number. Therefore, the mode is 58.
So, the answer is B) 58.
Solve the problem.
A building 240 feet tall casts a 100 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.)
Question 6 options:
A) 67°
B) 25°
C) 65°
D) 23°
To solve this problem, we can use trigonometry. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the tangent of the angle we want to find is the height of the building divided by the length of the shadow.
Tangent(angle) = (height of building) / (length of shadow)
Tangent(angle) = 240 / 100
Tangent(angle) = 2.4
Now, we can use the inverse tangent function (arctan or tan^(-1)) to find the angle.
Angle = tan^(-1)(2.4)
Using a calculator, we find that the angle is approximately 67 degrees.
Therefore, the answer is A) 67°.
Matthew has $2600 invested in the stock market. This amounts to 20% of his total savings. How much has Matthew saved?
Question 7 options:
A)
$13,100
B)
$13,010
C)
$13,000
D)
$130,000