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.
(6 × 10^-6) × (7 × 10^5) × (6 × 10^6)
37 answers
possible answers:
Question 1 options:
A)
2,520,000
B)
252 × 10^-180
C)
252 × 10^5
D)
25,200,000
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
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
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.
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
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.
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°
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°.
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
Question 7 options:
A)
$13,100
B)
$13,010
C)
$13,000
D)
$130,000
To find out how much Matthew has saved in total, we need to find the total amount that corresponds to 100% if $2600 represents 20%.
Let X be the total savings.
We can set up the following equation to solve for X:
(20/100) * X = $2600
To solve for X, we multiply both sides of the equation by 100/20:
(100/20) * (20/100) * X = (100/20) * $2600
X = $13,000
Therefore, Matthew has saved $13,000.
Hence, the answer is C) $13,000.
Let X be the total savings.
We can set up the following equation to solve for X:
(20/100) * X = $2600
To solve for X, we multiply both sides of the equation by 100/20:
(100/20) * (20/100) * X = (100/20) * $2600
X = $13,000
Therefore, Matthew has saved $13,000.
Hence, the answer is C) $13,000.
Solve the problem.
When Maria finished medical school she owed $48,000 in student loans. She repaid (2/5) of the total amount within two years of graduating. How much did she repay within two years of graduating?
Question 8 options:
A)
$17,280
B)
$21,120
C)
$1920
D)
$19,200
When Maria finished medical school she owed $48,000 in student loans. She repaid (2/5) of the total amount within two years of graduating. How much did she repay within two years of graduating?
Question 8 options:
A)
$17,280
B)
$21,120
C)
$1920
D)
$19,200
To find out how much Maria repaid within two years of graduating, we need to find (2/5) of the total amount she owed.
The total amount she owed is $48,000.
To find (2/5) of $48,000, we can multiply the total amount by the fraction (2/5):
Amount repaid = (2/5) * $48,000
Calculating the expression:
Amount repaid = (2/5) * $48,000 = $19,200
Therefore, Maria repaid $19,200 within two years of graduating.
Hence, the answer is D) $19,200.
The total amount she owed is $48,000.
To find (2/5) of $48,000, we can multiply the total amount by the fraction (2/5):
Amount repaid = (2/5) * $48,000
Calculating the expression:
Amount repaid = (2/5) * $48,000 = $19,200
Therefore, Maria repaid $19,200 within two years of graduating.
Hence, the answer is D) $19,200.
Fill in the missing value.
786,300 m^2 = km^2
Question 9 options:
A)
78.63
B)
7.863
C)
7863
D)
0.7863
786,300 m^2 = km^2
Question 9 options:
A)
78.63
B)
7.863
C)
7863
D)
0.7863
To convert from square meters to square kilometers, we need to divide the given value by 1,000,000.
786,300 m^2 ÷ 1,000,000 = 0.7863 km^2
Therefore, the missing value is D) 0.7863.
786,300 m^2 ÷ 1,000,000 = 0.7863 km^2
Therefore, the missing value is D) 0.7863.
Use the order of operations to simplify the expression.
(2/3) ∙ ((1/6) + (1/3)) ∙ 6
Question 10 options:
A)
2
B)
1(1/3)
C)
4
D)
1
(2/3) ∙ ((1/6) + (1/3)) ∙ 6
Question 10 options:
A)
2
B)
1(1/3)
C)
4
D)
1
To simplify the expression using the order of operations (also known as PEMDAS), we'll follow the steps:
Step 1: Solve within the parentheses: (1/6) + (1/3) = 1/6 + 2/6 = 3/6
Step 2: Simplify: 3/6 = 1/2
Now we have: (2/3) × (1/2) × 6
Step 3: Multiply the fractions: (2/3) × (1/2) = (2 × 1) / (3 × 2) = 2 / 6
Step 4: Simplify: 2/6 = 1/3
Now we have: (1/3) × 6
Step 5: Multiply: (1/3) × 6 = 6/3 = 2
Therefore, the simplified expression is 2.
Hence, the answer is A) 2.
Step 1: Solve within the parentheses: (1/6) + (1/3) = 1/6 + 2/6 = 3/6
Step 2: Simplify: 3/6 = 1/2
Now we have: (2/3) × (1/2) × 6
Step 3: Multiply the fractions: (2/3) × (1/2) = (2 × 1) / (3 × 2) = 2 / 6
Step 4: Simplify: 2/6 = 1/3
Now we have: (1/3) × 6
Step 5: Multiply: (1/3) × 6 = 6/3 = 2
Therefore, the simplified expression is 2.
Hence, the answer is A) 2.
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
(-0.7, -3.2) and (0.4, -2.4)
Question 11 options:
A)
(8/11); rises
B)
- (8/11); falls
C)
(11/8); rises
D)
- (11/8) falls
(-0.7, -3.2) and (0.4, -2.4)
Question 11 options:
A)
(8/11); rises
B)
- (8/11); falls
C)
(11/8); rises
D)
- (11/8) falls
To find the slope of the line through the given pair of points, we can use the formula:
Slope = (change in y) / (change in x)
The coordinates of the two points are (-0.7, -3.2) and (0.4, -2.4).
Change in x = (0.4 - (-0.7)) = 1.1
Change in y = (-2.4 - (-3.2)) = 0.8
Plugging these values into the slope formula:
Slope = (0.8) / (1.1)
Calculating this expression gives us approximately:
Slope ≈ 0.7272
Since the slope is positive (0.7272 > 0), the line rises from left to right.
Therefore, the answer is C) (11/8); rises.
Slope = (change in y) / (change in x)
The coordinates of the two points are (-0.7, -3.2) and (0.4, -2.4).
Change in x = (0.4 - (-0.7)) = 1.1
Change in y = (-2.4 - (-3.2)) = 0.8
Plugging these values into the slope formula:
Slope = (0.8) / (1.1)
Calculating this expression gives us approximately:
Slope ≈ 0.7272
Since the slope is positive (0.7272 > 0), the line rises from left to right.
Therefore, the answer is C) (11/8); rises.
Solve the problem.
A radio transmission tower is 110 feet tall. How long should a guy wire be if it is to be attached 12 feet from the top and is to make an angle of 30° with the ground? Give your answer to the nearest tenth of a foot.
Question 13 options:
A)
220.0 ft
B)
127.0 ft
C)
113.2 ft
D)
196.0 ft
A radio transmission tower is 110 feet tall. How long should a guy wire be if it is to be attached 12 feet from the top and is to make an angle of 30° with the ground? Give your answer to the nearest tenth of a foot.
Question 13 options:
A)
220.0 ft
B)
127.0 ft
C)
113.2 ft
D)
196.0 ft
To solve this problem, we can use trigonometry. The guy wire, the tower, and the ground form a right triangle. The length of the guy wire is the hypotenuse of the triangle.
Given:
Height of tower = 110 feet
Distance from attachment point to the top = 12 feet
Angle with the ground = 30°
To find the length of the guy wire, we can use the sine function:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the tower minus the distance from the attachment point to the top.
sin(30°) = (110 - 12)/hypotenuse
Rearranging the equation, we get:
hypotenuse = (110 - 12)/sin(30°)
Using a calculator, we find:
hypotenuse ≈ 113.1820791
Rounding to the nearest tenth of a foot, the length of the guy wire should be approximately 113.2 feet.
Therefore, the answer is C) 113.2 ft.
Given:
Height of tower = 110 feet
Distance from attachment point to the top = 12 feet
Angle with the ground = 30°
To find the length of the guy wire, we can use the sine function:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the tower minus the distance from the attachment point to the top.
sin(30°) = (110 - 12)/hypotenuse
Rearranging the equation, we get:
hypotenuse = (110 - 12)/sin(30°)
Using a calculator, we find:
hypotenuse ≈ 113.1820791
Rounding to the nearest tenth of a foot, the length of the guy wire should be approximately 113.2 feet.
Therefore, the answer is C) 113.2 ft.
Solve the problem.
The man weighed 132 lb. How many kilograms is this?
Question 14 options:
A)
290.4 kg
B)
139.9 kg
C)
335.3 kg
D)
59.4 kg
The man weighed 132 lb. How many kilograms is this?
Question 14 options:
A)
290.4 kg
B)
139.9 kg
C)
335.3 kg
D)
59.4 kg
To convert pounds (lb) to kilograms (kg), we need to use the conversion factor:
1 lb = 0.453592 kg
Given:
Weight in pounds = 132 lb
To find the weight in kilograms, we can multiply the weight in pounds by the conversion factor:
Weight in kg = 132 lb * 0.453592 kg/lb
Calculating the expression:
Weight in kg ≈ 59.874864 kg
Rounding to the nearest tenth, the weight is approximately 59.9 kg.
Therefore, the answer is B) 59.9 kg.
1 lb = 0.453592 kg
Given:
Weight in pounds = 132 lb
To find the weight in kilograms, we can multiply the weight in pounds by the conversion factor:
Weight in kg = 132 lb * 0.453592 kg/lb
Calculating the expression:
Weight in kg ≈ 59.874864 kg
Rounding to the nearest tenth, the weight is approximately 59.9 kg.
Therefore, the answer is B) 59.9 kg.
Find the median.
18, 30, 35, 46, 68, 71, 90
Question 15 options:
A)
51
B)
35
C)
68
D)
46
18, 30, 35, 46, 68, 71, 90
Question 15 options:
A)
51
B)
35
C)
68
D)
46
To find the median, we first need to arrange the numbers in ascending order:
18, 30, 35, 46, 68, 71, 90
The median is defined as the middle value in a set of numbers when they are arranged in order. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In this case, we have an odd number of values (7), so the median is the middle number, which is:
Median = 46
Therefore, the answer is D) 46.
18, 30, 35, 46, 68, 71, 90
The median is defined as the middle value in a set of numbers when they are arranged in order. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In this case, we have an odd number of values (7), so the median is the middle number, which is:
Median = 46
Therefore, the answer is D) 46.
Indicate the metric unit of measurement that you would use to measure the object.
The diameter of a bolt.
Question 16 options:
A)
millimeters
B)
decimeters
C)
meters
D)
kilometers
The diameter of a bolt.
Question 16 options:
A)
millimeters
B)
decimeters
C)
meters
D)
kilometers
The metric unit of measurement that you would use to measure the diameter of a bolt is:
A) millimeters
A) millimeters
Solve the equation.
3m + 7 + 2(4m - 4) = 4(m + 4)
Question 17 options:
A)
{(17/7)}
B)
{(17/15)}
C)
{(15/7)}
D)
{(31/7)}
3m + 7 + 2(4m - 4) = 4(m + 4)
Question 17 options:
A)
{(17/7)}
B)
{(17/15)}
C)
{(15/7)}
D)
{(31/7)}
YAEY!!!!!!!!!!!!!!!! BOT is so wrong
Apologies for the confusion. Let's solve the given equation step by step:
3m + 7 + 2(4m - 4) = 4(m + 4)
First, apply the distributive property:
3m + 7 + 8m - 8 = 4m + 16
Combine like terms:
11m - 1 = 4m + 16
Next, subtract 4m from both sides:
11m - 4m - 1 = 4m - 4m + 16
Simplifying:
7m - 1 = 16
Add 1 to both sides:
7m - 1 + 1 = 16 + 1
Simplifying further:
7m = 17
Finally, divide by 7:
m = 17/7
Thus, the correct answer is A) {(17/7)}.
3m + 7 + 2(4m - 4) = 4(m + 4)
First, apply the distributive property:
3m + 7 + 8m - 8 = 4m + 16
Combine like terms:
11m - 1 = 4m + 16
Next, subtract 4m from both sides:
11m - 4m - 1 = 4m - 4m + 16
Simplifying:
7m - 1 = 16
Add 1 to both sides:
7m - 1 + 1 = 16 + 1
Simplifying further:
7m = 17
Finally, divide by 7:
m = 17/7
Thus, the correct answer is A) {(17/7)}.
To solve the equation, we'll start by simplifying both sides:
3m + 7 + 2(4m - 4) = 4(m + 4)
First, we distribute the 2 on the left side:
3m + 7 + 8m - 8 = 4(m + 4)
Combine like terms on the left side:
11m - 1 = 4(m + 4)
Next, distribute the 4 on the right side:
11m - 1 = 4m + 16
Now, we'll isolate the m term on one side by subtracting 4m from both sides:
11m - 4m - 1 = 4m - 4m + 16
Simplifying further:
7m - 1 = 16
To solve for m, we'll isolate the m term by adding 1 to both sides:
7m - 1 + 1 = 16 + 1
Simplifying once more:
7m = 17
Finally, to solve for m, we divide both sides by 7:
7m / 7 = 17 / 7
The answer is:
m = 17/7
Therefore, the solution to the equation is:
A) {(17/7)}.
3m + 7 + 2(4m - 4) = 4(m + 4)
First, we distribute the 2 on the left side:
3m + 7 + 8m - 8 = 4(m + 4)
Combine like terms on the left side:
11m - 1 = 4(m + 4)
Next, distribute the 4 on the right side:
11m - 1 = 4m + 16
Now, we'll isolate the m term on one side by subtracting 4m from both sides:
11m - 4m - 1 = 4m - 4m + 16
Simplifying further:
7m - 1 = 16
To solve for m, we'll isolate the m term by adding 1 to both sides:
7m - 1 + 1 = 16 + 1
Simplifying once more:
7m = 17
Finally, to solve for m, we divide both sides by 7:
7m / 7 = 17 / 7
The answer is:
m = 17/7
Therefore, the solution to the equation is:
A) {(17/7)}.
Solve the problem. Round to the nearest tenth if necessary.
Last year, Maria earned $362 per week. This year, her salary increased to $398 per week. What is the percent of increase?
Question 18 options:
A)
91%
B)
9.9%
C)
9%
D)
90.1%
Last year, Maria earned $362 per week. This year, her salary increased to $398 per week. What is the percent of increase?
Question 18 options:
A)
91%
B)
9.9%
C)
9%
D)
90.1%
To find the percent increase, we can use the formula:
Percent Increase = (New Value - Old Value) / Old Value * 100
Given:
Old Value (last year) = $362 per week
New Value (this year) = $398 per week
Plugging these values into the formula:
Percent Increase = (398 - 362) / 362 * 100
Calculating the expression:
Percent Increase = 36 / 362 * 100 ≈ 9.944751381%
Rounding to the nearest tenth, the percent increase is approximately 9.9%.
Therefore, the answer is B) 9.9%.
Percent Increase = (New Value - Old Value) / Old Value * 100
Given:
Old Value (last year) = $362 per week
New Value (this year) = $398 per week
Plugging these values into the formula:
Percent Increase = (398 - 362) / 362 * 100
Calculating the expression:
Percent Increase = 36 / 362 * 100 ≈ 9.944751381%
Rounding to the nearest tenth, the percent increase is approximately 9.9%.
Therefore, the answer is B) 9.9%.
Evaluate the arithmetic expression by performing the operations in the appropriate order.
24 ÷ 4 ∙ (12 - 3)
Question 19 options:
A)
75
B)
54
C)
69
D)
90
24 ÷ 4 ∙ (12 - 3)
Question 19 options:
A)
75
B)
54
C)
69
D)
90
To evaluate the arithmetic expression, we need to follow the order of operations (PEMDAS), which states that we should perform any calculations inside parentheses first, then perform any multiplication or division from left to right, and finally perform any addition or subtraction from left to right.
The expression is:
24 ÷ 4 ∙ (12 - 3)
First, we simplify the expression inside the parentheses:
12 - 3 = 9
Now the expression becomes:
24 ÷ 4 ∙ 9
Next, we perform the division:
24 ÷ 4 = 6
Now the expression becomes:
6 ∙ 9
Finally, we perform the multiplication:
6 ∙ 9 = 54
Therefore, the answer is B) 54.
The expression is:
24 ÷ 4 ∙ (12 - 3)
First, we simplify the expression inside the parentheses:
12 - 3 = 9
Now the expression becomes:
24 ÷ 4 ∙ 9
Next, we perform the division:
24 ÷ 4 = 6
Now the expression becomes:
6 ∙ 9
Finally, we perform the multiplication:
6 ∙ 9 = 54
Therefore, the answer is B) 54.
Use the present value formula to determine the amount to be invested now, or the present value needed.
The desired accumulated amount is $34,000 after 11 years invested in an account with 7% interest compounded semiannually
Question 20 options:
A)
$16,153.16
B)
$18,048.88
C)
$15,951.12
D)
$72,471.39
The desired accumulated amount is $34,000 after 11 years invested in an account with 7% interest compounded semiannually
Question 20 options:
A)
$16,153.16
B)
$18,048.88
C)
$15,951.12
D)
$72,471.39
To determine the present value needed, we can use the present value formula for compound interest:
Present Value = Accumulated Amount / (1 + (r/n))^(n*t)
Given:
Accumulated Amount = $34,000
Interest rate = 7% (converted to decimal form, which is 0.07)
Number of compounding periods per year (
Present Value = Accumulated Amount / (1 + (r/n))^(n*t)
Given:
Accumulated Amount = $34,000
Interest rate = 7% (converted to decimal form, which is 0.07)
Number of compounding periods per year (