For a 6-digit zip code with no restrictions, there would be 1,000,000 possible zip codes. If the first digit could not be a '0', the number of possible zip codes would decrease to 900,000.
Explanation:We're dealing with a counting problem here. This problem involves basic principles of combinatorics.
Firstly, if there are no restrictions on the digits used, each of the six positions in the zip code can hold any digit from 0 to 9. There are 10 choices (from 0 to 9) for each of the 6 digits in the zip code which leads to 10^6 = 1,000,000 possible zip codes.
However, if the first number could not be 0, there are 9 possible choices for the first digit and 10 choices for each of the remaining 5 digits. Therefore, the number of possible zip codes would be 9 * 10^5 = 900,000.
Learn more about Combinatorics here:https://brainly.com/question/32015929
What is the probability that at least 2 students in a class of 36 have the same birthday?
Can someone please answer all these please?
a) When Lucia buys olives at the deli, the scale shows 0.325 kg at $18.88 per kg. How much should she pay?
b) John’s weekly wage is $1510.99 and he pays 2/3 of his weekly income in rent. How much rent does he pay each week?
c) A farmer owns 780 hectares of land. During a bushfire, 195 hectares are burnt. What percentage of his land was burnt?
d) Candles are $14.95 each. Estimate how much I need if I want to buy 17 of them.
Show your working.
e) Decrease 5000 by 13 %.
f) Ray bought a computer for $1600 and then a year later sold it for $1200.
Calculate his loss =
Calculate his loss as a percentage of the original price of the computer =
g) John spent $80 on dinner last Friday night. If this $80 is equal to 40% of his weekly income, calculate his weekly income.
h) Mr Jenkins invested $7500 at his local bank at 6.5% Simple Interest per annum.
What was his investment worth at the end of the first year?
Question 5
a) Express this ratio in lowest terms: 50 minutes : 2 ½ hours
b) Divide $120 in the ratio 5:7
c) Jane and Ben share in their lottery win in the ratio of 7: 3.
If Jane’s share of the money is $5600, how much does Ben receive?
hello can you please help me posted picture of question
Angela owns a set of 6-inch tall glasses. Each glass has a diameter of 3 inches. Angela has three people over for dinner. Each guest will be served a full glass of milk. How much milk will Angela need ?
What is a potential source of bias if an) if you are surveying students to find out their opinion of a new teacher with the following question: Is Mr Wilson a terrible teacher?
No source of bias.
Not specific Enough.
Implies that Mr. Wilson is a bad teacher.
Names the teacher.
Answer:
pronoun-antecedent number agreement error.
simplify this problem
An item is called "price elastic" if you drop the price and revenue goes up. Last week you sold 10 sodas for $2 each; this week you sold 30 sodas for $1 each. Is soda price elastic?
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.
Which of the following is a service that banks provide? A. Printing paychecks B. Insuring vehicles C. Access to cash D. Printing money
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.
A pair of dice are rolled. What is the probability of rolling 4 or greater?
A: 5/36
B: 1/18
C: 1/36
D: 11/12
wanda rode her bike 21/10 miles. Which mixed number shows how far Wanda rode her bike?
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.
what integer and-8 have the product of -96
A beach ball has a diameter of 12 inches.what is the volume to the nearest tenth
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.
A fluorite crystal is shaped like a regular octahedron with edges that are 2.1 inches. Which of these is the volume of the fluorite crystal in cubic inches? Round to the nearest hundredth
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).
Calculate the surface area of the portion of the surface z=x^2 + y that lies above the triangular region t wth vertices 0,0 4,0 and 4,2
A book club offers a choice of 8 books from a list of 40. In how many can a member make a collection?
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.
Explanation: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
Learn more about Combinations here:https://brainly.com/question/24703398
#SPJ2
sqrt= Square Root
A student is attempting to calculate the square root of 18. His work is shown below. Which statement below best applies to his mathematical reasoning?
Givin sqrt 18 I observe that 18 is not a perfect square. I notice the perfect squares closest to 18 are 16 and 25, so I estimate the answer to fall somewhere between those numbers. Since 18 is closer to 16, I estimate that sqrt 18= 17
A.
18 is a perfect square, and the radical could have been evaluated directly.
B.
16 and 25 are not perfect squares, and therefore the student should not have chosen those numbers to estimate sqrt 18
C.
The student did not evaluate sqrt 16 and sqrt 25 before estimating sqrt 18
D.
The student has made no error. sqrt 18= 17
Which is equivalent to sin^-1(tan(pi/4)) ? Give your answer in radians.
Answer:
the answer is b
Step-by-step explanation:
Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?
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.
You put $400 in an account. The account earns $18 simple interest in 9 months. What is the annual interest rate?
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%
Hey can you please help me posted picture of question
What are the zeroes of y = x^2 – 4x – 5?
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
A lunch counter sells two types of sandwiches, roast beef and chicken salad. The profit on the sandwiches is $2 for chicken salad and $3 for roast beef. The amount of bread available is enough for 30 sandwiches. There are 2 hours available to prepare sandwiches. If chicken salad sandwiches take 3 minutes to prepare and roast beef sandwiches take 5 minutes, how many of each type of sandwich should be prepared to maximize the profit? Assume all sandwiches get sold
Use the substitution method to determine whether the system of equations has one solution, no solution, or infinitely many solutions. 2x-y=10 x = y + 5
What are the lateral area and the surface of the cone shown below?
Assume the least squares equation is ŷ = 10 + 20x. what does the value of 10 in the equation indicate? when x = 0, y = 10. x increases by 10 for each unit increase in y. y increases by 10 for each unit increase in x. it is the error of estimation.
The value of 10 in the equation ŷ = 10 + 20x represents the y-intercept, which is the value of y when x equals zero.
Explanation:The value of 10 in the equation ŷ = 10 + 20x represents the y-intercept. In the context of the least squares equation, the y-intercept is the value of y when x equals zero. So when x = 0, y = 10, indicating that the initial value of y is 10.
Learn more about y-intercept here:https://brainly.com/question/14180189
#SPJ3
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 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]
for her bedroom Marisol is buying a rug that is 6 feet by 8 feet her room is 9 feet by 11 feet how many square feet of floor will not be covered by Rug?
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.
Explain why the ratio 3 feet / 1 yard has a value of one
How does the graph of y=1/2(x+4)^2compare to the graph of y=(x-1)^2 -3?
Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00 . The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price.
After purchasing the computer, how much does Hakim have left in his bank account? Show your work.