The national debt of a small country is $635 billion and the population is 2,426,000.
What is the amount of debt per person?
Express the answer in scientific notation.
Question 10 options:
A)
$2.62 × 106
B)
$2.62
C)
$26.20
D)
$2.62 × 105
The amount of debt per person can be calculated by dividing the national debt by the population.
Debt per person = National debt / Population
= $635 billion / 2,426,000
To express the answer in scientific notation, we divide the debt by 10^9 (since 1 billion = 1 x 10^9) and multiply by 10^6 to account for the 6 digits in the population.
Debt per person = ($635 billion / 2,426,000) x (1 x 10^6 / 1 x 10^9)
= $2.62 x 10^6
Therefore, the amount of debt per person is $2.62 x 10^6, or option A) $2.62 x 10^6.
39.5% of the students at a certain college are men.
If the total number of students at the college is 1400, how many female students are there?
To find the number of female students, we need to subtract the percentage of male students from 100% and then multiply that value by the total number of students.
Percentage of female students = 100% - 39.5% = 60.5%
Number of female students = Percentage of female students x Total number of students
= 60.5% x 1400
To calculate this, we multiply 1400 by 0.605 (60.5% expressed as a decimal).
Number of female students = 1400 x 0.605
= 847
Therefore, there are 847 female students.
Bicycles are often on sale in September. The regular price of one bicycle is $140.95.
With a 20% discount, what is the sale price of the bicycle?
Round to the nearest cent.
To calculate the sale price of the bicycle with a 20% discount, we need to subtract 20% of the regular price from the regular price.
Discount amount = 20% x $140.95
To calculate this, we multiply $140.95 by 0.20 (20% expressed as a decimal).
Discount amount = $140.95 x 0.20
= $28.19
To find the sale price, we subtract the discount amount from the regular price.
Sale price = Regular price - Discount amount
= $140.95 - $28.19
= $112.76
Rounding to the nearest cent, the sale price of the bicycle is $112.76.
To determine the number of fish in a lake, a park ranger catches 220 fish, tags them, and returns them to the lake.
Later, 144 fish are caught, and it is found that 40 of them are tagged.
Estimate the number of fish in the lake.
To estimate the number of fish in the lake, we can use a proportion to compare the ratio of tagged fish to the total number of fish caught in both instances.
Let's assume the total number of fish in the lake is x.
In the first instance:
Number of tagged fish = 220
Total number of fish caught = 220
So the proportion of tagged fish to the total number of fish is:
220/x = 40/144
To solve for x, we can cross-multiply and solve the resulting equation:
40x = 220 * 144
x = (220 * 144) / 40
x ≈ 792
Therefore, the estimate for the number of fish in the lake is approximately 792 fish.
A computer printer costs $630. If the sales tax rate is 3(1/2)%, how much tax is charged and what is the total price?
Round your answers to the nearest cent.
To calculate the tax charged on the computer printer, we need to multiply the cost of the printer by the sales tax rate.
Tax charged = $630 * 3.5%
To calculate this, we multiply $630 by 0.035 (3.5% expressed as a decimal).
Tax charged = $630 * 0.035
= $22.05
Therefore, the tax charged on the computer printer is $22.05.
To calculate the total price including tax, we add the tax charged to the cost of the printer.
Total price = Cost of printer + Tax charged
= $630 + $22.05
= $652.05
Therefore, the total price of the computer printer, including tax, is $652.05.
An experiment calls for cooling a mixture to -18°F, then increasing the temperature 80 degrees. What is the final temperature the experiment is to obtain?
To find the final temperature, we need to add the change in temperature to the initial temperature.
Initial temperature = -18°F
Change in temperature = 80°F
Final temperature = Initial temperature + Change in temperature
= -18°F + 80°F
= 62°F
Therefore, the final temperature the experiment is to obtain is 62°F.
Perform the indicated operation by first expressing each number in scientific notation.
Write answer in scientific notation.
(270,000,000)(2,000,000,000)
To perform this multiplication operation, we can express each number in scientific notation and then multiply the coefficients and add the exponents.
The first number, 270,000,000, can be expressed in scientific notation as 2.7 x 10^8.
The second number, 2,000,000,000, can be expressed in scientific notation as 2 x 10^9.
Now, let's multiply the coefficients:
2.7 x 2 = 5.4
And add the exponents:
10^8 x 10^9 = 10^(8+9) = 10^17
Therefore, the result of the multiplication, in scientific notation, is 5.4 x 10^17.
\frac{43}{20000}\times \:10^7 decimal notation
To express \(\frac{43}{20000}\) in decimal notation, we divide 43 by 20,000.
\(\frac{43}{20000} = 0.00215\)
To multiply this by \(10^7\), we move the decimal point 7 places to the right:
\(0.00215 \times 10^7 = 21,500\)
Therefore, the decimal notation of \(\frac{43}{20000} \times 10^7\) is 21,500.
The First Nations Bank pays 7 % interest per year on non-checking accounts.
What is the annual income on a non-checking account of $86,800?
Round to the nearest dollar.
To calculate the annual income on a non-checking account, we need to multiply the account balance by the interest rate.
Annual income = Account balance x Interest rate
Interest rate = 7% = 7/100 = 0.07
Account balance = $86,800
Annual income = $86,800 x 0.07
To calculate this, we multiply $86,800 by 0.07.
Annual income = $6,076
Therefore, the annual income on a non-checking account with a balance of $86,800 is $6,076.
Left out part of the question.
The First Nations Bank pays 7 3/4% interest per year on non-checking accounts.
What is the annual income on a non-checking account of $86,800?
Round to the nearest dollar.
To calculate the annual income on a non-checking account with an interest rate of 7 3/4%, we first need to convert the mixed fraction into a decimal.
To convert 7 3/4% to a decimal, we can add the whole number part (7) to the fraction part (3/4) and divide it by 100.
Interest rate = 7 + 3/4 = 7.75%
Account balance = $86,800
Annual income = Account balance x Interest rate
Annual income = $86,800 x 7.75%
To calculate this, we multiply $86,800 by 0.0775 (7.75% expressed as a decimal).
Annual income = $86,800 x 0.0775
Annual income = $6,721
Therefore, the annual income on a non-checking account with a balance of $86,800 and an interest rate of 7 3/4% is $6,721 when rounded to the nearest dollar.
b/10 - 4 = -3
To solve the equation \(b/10 - 4 = -3\), we will go through the steps one by one:
1. First, let's isolate the term containing \(b\). Add 4 to both sides of the equation:
\(b/10 - 4 + 4 = -3 + 4\)
Simplifying, we have:
\(b/10 = 1\)
2. To solve for \(b\), we multiply both sides of the equation by 10:
\(10 \cdot \left(\dfrac{b}{10}\right) = 10 \cdot 1\)
This simplifies to:
\(b = 10\)
Therefore, the solution to the equation \(b/10 - 4 = -3\) is \(b = 10\).
-7x + 1 - 5(x + 1) = 4x - 5
Let's simplify and solve the equation step by step:
-7x + 1 - 5(x + 1) = 4x - 5
-7x + 1 - 5x - 5 = 4x - 5 (distribute the -5 to both terms inside the parentheses)
-12x - 4 = 4x - 5 (combine like terms)
To isolate the variable terms, we want to bring all the x terms to one side of the equation and the constant terms to the other side.
-12x - 4 - 4x = 4x - 5 - 4 (subtract 4x from both sides)
-16x - 4 = 0x - 9 (subtract 5 from both sides)
Now, simplify the equation further:
-16x - 4 = -9
To solve for x, we'll continue isolating the variable by adding 4 to both sides:
-16x - 4 + 4 = -9 + 4
-16x = -5
Finally, divide by -16 to solve for x:
x = -5 / -16
Simplifying:
x = 5/16
So, the solution to the equation -7x + 1 - 5(x + 1) = 4x - 5 is x = 5/16.
round to the nearest hundredth, if necessary
-3(t - 2) = |-6-21| - 10t
Let's simplify and solve the equation step by step:
-3(t - 2) = |-6-21| - 10t
First, simplify the absolute value expression on the right side:
-3(t - 2) = |-27| - 10t
|-27| = 27
-3(t - 2) = 27 - 10t
Now, distribute the -3:
-3t + 6 = 27 - 10t
Next, combine like terms:
-3t + 10t = 27 - 6
7t = 21
Finally, solve for t by dividing both sides by 7:
t = 21 / 7
t = 3
So, the solution to the equation -3(t - 2) = |-6-21| - 10t is t = 3.