A company makes three purchases on July 5, one for $550, another for $250 and a third for $75. It returns merchandise costing $35. If the Company is given a discount 2/10 and pays the total amount due on July 20, how much was due?

To convert the improper fraction 21/10 to a mixed number, divide 21 by 10 to get 2 with a remainder of 1. The mixed number is 2 1/10.

The student is asking for help converting an improper fraction to a mixed number. An improper fraction is one where the numerator is greater than the denominator. To convert 21/10 to a mixed number, we divide the numerator by the denominator.

Divide 21 by 10, which equals 2 with a remainder of 1.

The whole number part of the mixed number is the quotient, which is 2.

The remainder becomes the new numerator, and the original denominator stays the same, making it 1/10.

Therefore, the mixed number is 2 1/10.

Answer:

[tex]x=28[/tex]

Step-by-step explanation:

[tex]-10+\sqrt{x+8}=-4[/tex]

⭆ Add 10 to both sides:-

[tex]-10+\sqrt{x+8}+10=-4+10[/tex]

[tex]\sqrt{x+8}=6[/tex]

⭆ Square both sides:-

[tex]x+8=36[/tex]

⭆ Subtract 8 from both sides:-

[tex]x+8-8=36-8[/tex]

[tex]x=28[/tex]

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Answer:

x=5 or x=-1

Step-by-step explanation:

The zeroes of the equation is when the x values when y=0.

We can determine this using a method that when we times out the brackets of our simplification we arrive at the original equation. We know that we must get -5 and -4x and x^2:

We can write:

[tex]y=x^2-4*x-5=0[/tex]

[tex](x-5)*(x+1)=0[/tex]

If we use the rules of algebra and multiply each term with each other:

[tex]x*x+x*1-5*x-5*1=0[/tex]

We can simplify:

[tex]x^2-4*x-5=0[/tex]

We end up with the original equation:

Therefore the zeros of the equation is when:

[tex](x-5)*(x+1)=0[/tex]

[tex]x-5=0[/tex] and [tex]x+1=0[/tex]

[tex]x=5[/tex]

[tex]x=-1[/tex[

x=5 or x=-1

This is a math combination problem. The number of ways a member can choose 8 books from a list of 40 is 76,904,685 ways.

This is a combinatorics problem, specifically a combination problem. A combination is a selection of items from a larger set where the order does not matter. In this case, we have a set of 40 books and want to know how many ways one can select 8 books from those 40. The formula for calculating combinations is nCr = n! / [(n - r)! * r!] where 'n' represents the total number of items, 'r' represents the number of items to choose, 'nCr' represents the number of combinations of n items taken r at a time, and '!' denotes factorial, the product of all positive integers up to that number.

Applying the combination formula, a member can make the choice of 8 books from a list of 40 in:

40C8 = 40! / [(40 - 8)! * 8!] = 76,904,685 ways

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Final answer:

Marisol's bedroom is 99 square feet, and the rug area is 48 square feet. By subtracting the rug area from the total room area, we find that 51 square feet of floor will not be covered by the rug.

Explanation:

To find out how many square feet of Marisol's bedroom floor will not be covered by the rug, we must first calculate the area of her entire room and then the area of the rug. The area of a rectangle is found by multiplying the length by the width. The area of Marisol's room is 9 feet × 11 feet = 99 square feet. The area of the rug is 6 feet × 8 feet = 48 square feet.

Next, we subtract the area of the rug from the area of the entire room to find the uncovered floor area.

Uncovered floor area = Total room area – Rug area
= 99 square feet – 48 square feet
= 51 square feet

Therefore, 51 square feet of Marisol's bedroom floor will not be covered by the rug.

Answer:

6%

Step-by-step explanation:

Let's start by finding the amount earned per month:

[tex]\frac{18}{9}[/tex]=2

Now let's find the % per month

[tex]\frac{2}{400} =.005[/tex], or .5%

Now let's multiply by 12 months to get the annual interest rate

[tex].005 * 12 = .06[/tex] or 6%

Answer:

the answer is b

Step-by-step explanation:

Final answer:

Soda is price elastic because lowering the price from $2 to $1 resulted in an increase in total revenue from $20 to $30, indicating that a decrease in price caused a larger increase in quantity sold.

Explanation:

When determining whether an item is price elastic or not, we look at the effect that changing the price has on the total revenue. If a decrease in price leads to an increase in total revenue, the demand for the product is considered price elastic. In the example given, soda was sold at different prices and quantities: 10 sodas at $2 each last week, and 30 sodas at $1 this week. We use these numbers to calculate the total revenue for each week:

Last week: 10 sodas × $2/soda = $20

This week: 30 sodas × $1/soda = $30

Since the total revenue increased from $20 to $30 when the price was lowered from $2 to $1, we can see that the revenue increased as a result of the price drop, indicating that the demand for soda is indeed price elastic.

The volume of a beach ball with a diameter of 12 inches is approximately 904.3 cubic inches.

To find the volume of a beach ball with a diameter of 12 inches, we first need to find the radius. The radius is half of the diameter, so the radius is 6 inches.

The formula for the volume of a sphere is:

V = (4/3)πr³

Where V is the volume and r is the radius. Plugging in our radius:

V = (4/3)π(6)³

V ≈ (4/3)π(216)

V ≈ (4/3)(678.24)

V ≈ 904.32 cubic inches

To the nearest tenth, the volume of the beach ball is approximately 904.3 cubic inches.

To find the volume of the fluorite crystal, you can use the formula for the volume of an octahedron with the given edge length of 2.1 inches, rounded to the nearest hundredth to be approximately 7.69 cubic inches.

The volume of the fluorite crystal can be calculated as follows:

Identify the formula for the volume of an octahedron: V = (1/3) × [tex]\sqrt{2}[/tex] × a³, where 'a' is the edge length.

Substitute the given edge length: V = (1/3) × [tex]\sqrt{2}[/tex] × 2.1³.

Calculate the volume: V = 7.69 cubic inches (rounded to the nearest hundredth).

Answer:

C. Access to cash

Step-by-step explanation:

Bank provides access to cash in multiple manners, you can debit the money from your savings account, apply for different type of loans, draft your DD etc.

While for the other options like printing paychecks are done by any company in order to  provided paychecks to its employees, Insurance companies provides vehicle insurance services to anyone will to get their vehicle insured and printing money is provided only by central bank of any country, not every bank is allowed to print money.

Answer:

Lower value: 14

Highest value: 41

Lower quartile: 24.5

Upper quartile: 34.5

Median: 28

Step-by-step explanation:

The expression for the total number of bacteria at t = 3 hours, given an initial 1000 bacteria at t = 0, is:  [tex]\[ 1000 + \int_0^3 R(x) \, dx \][/tex]

To find the number of bacteria in the container at time t = 3 hours, given that the rate of increase is [tex]\( R(t) \)[/tex] bacteria per hour and there are 1000 bacteria at time t = 0, you can use the following steps:

Start with the initial condition :

  You are given that there are 1000 bacteria at t = 0.

So, the initial condition is [tex]\( N(0) = 1000 \),[/tex]  where N(t) represents the total number of bacteria at time t.

Integrate to find the change in number of bacteria over time :

  Since the rate of increase is R(t), the total increase in bacteria from time t = 0 to t = t is given by integrating R(t) with respect to time.

This integral provides the cumulative increase in bacteria:

[tex]\[ \int_0^t R(x) \, dx. \][/tex]

Add the initial bacteria to the increase :

  Since there are already 1000 bacteria at t = 0, the total number of bacteria at time t is given by:

  [tex]\[ N(t) = 1000 + \int_0^t R(x) \, dx. \][/tex]

Find the expression for t = 3 hours :

  To find the total number of bacteria at t = 3 hours, you substitute t = 3 into the expression derived in step 3:

  [tex]\[ N(3) = 1000 + \int_0^3 R(x) \, dx. \][/tex]

Thus, the expression [tex]\( 1000 + \int_0^3 R(x) \, dx \)[/tex] gives the number of bacteria in the container at time t = 3 hours.

Question :

the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

The correct expression that gives the number of bacteria in the container at time t = 3 hours is D.  [tex]1000 + \int_0^3 R(t) \, dt[/tex]

The problem asks us to find the number of bacteria in a container at t = 3 hours, given that the number of bacteria increases at a rate of R(t) bacteria per hour and there are 1000 bacteria at time t = 0.

To solve this, we need to integrate the rate function R(t) to find the total change in the number of bacteria over the interval from t = 0 to t = 3.

1. Initial number of bacteria:

At t = 0, the number of bacteria is 1000.

2. Change in number of bacteria:

The rate of change of the number of bacteria is given by R(t) bacteria per hour.

To find the total number of bacteria added over the time interval from t = 0 to t = 3, we need to integrate R(t) from 0 to 3.

Total change in number of bacteria = [tex]\int_0^3 R(t) \, dt[/tex]

3. Total number of bacteria at t = 3 hours:

This is the sum of the initial number of bacteria and the total change in the number of bacteria over the 3 hours.

Number of bacteria at t = 3 hours = [tex]1000 + \int_0^3 R(t) \, dt[/tex]

Complete Question:

The number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0, which of the following expressions gives the number of bacteria in the container at time t=3 hours?

(A) R(3)

(B) 1000+R(3)

(C) [tex]$\int_0^3 R(t) d t$[/tex]

(D) [tex]$1000+\int_0^3 R(t) d t$[/tex]

Jason wants to form a team of 9 players out of total 12 players.

Here the order of selection does not matter because there is no particular post for any player. So we need to use Combinations and choose 9 players out of 12 players.

We know the formula for Combinations is given as follows :-

[tex]nCr=\frac{n!}{r!*(n-r)!} \\\\ Choosing \;9 \;out \;of \;12 \\\\ 12C9 = \frac{12!}{9!*(12-9)!} =\frac{12!}{9!*3!} =\frac{12*11*10*9*8*7*6*5*4*3*2*1}{(9*8*7*6*5*4*3*2*1)*(3*2*1)} \\\\ 12C9 = \frac{12*11*10}{3*2*1} =\frac{1320}{6} =220 \;combinations[/tex]

Hence, all the possible number of different teams = 220 combinations.