Natural numbers are closed under multiplication but not under subtraction and division: subtracting or dividing two natural numbers can lead to results that aren't natural numbers (negative numbers or fractions, respectively).
Explanation:The student's question pertains to the closure of natural numbers under the operations of subtraction, multiplication, and division. Natural numbers are numbers used for counting and ordering that include all positive integers from 1 onwards. Let's evaluate each of these operations with respect to closure:
Subtraction: Natural numbers are not closed under subtraction because subtracting a larger number from a smaller one results in negative numbers, which are not part of the natural numbers. For example, 3 - 5 = -2 is not a natural number.
Multiplication: Natural numbers are closed under multiplication because the product of any two natural numbers is always a natural number. For example, 2 x 3 = 6, and both the numbers and result are natural numbers.
Division: Natural numbers are not closed under division because the division of two natural numbers can result in a fraction or a decimal that is not a natural number. For example, 1 / 2 = 0.5, which is not a natural number.
When a natural number is subtracted or divided by another, the result might not always be a natural number, indicating that natural numbers are not closed under these operations.
The closure property holds for addition and multiplication of natural numbers, but not for subtraction and division.
Explanation:Addition:The closure property states that when you add two natural numbers, the result is always a natural number. For example, 2 + 3 = 5.
Subtraction:Subtraction is not closed under natural numbers. For example, if you subtract 3 from 2, you get -1, which is not a natural number.
Multiplication:The closure property holds for multiplication as well. When you multiply two natural numbers, the result is always a natural number. For example, 2 x 3 = 6.
Division:Division is not closed under natural numbers. For example, 2 ÷ 3 = 0.67, which is not a natural number.
What is 63108 divided by 72
*PLEASE HELP, BRAINLIEST* A salesman must commute 1 hour and 48 minutes from his house to the airport, fly to another city and take a bus to his destination. What is the total travel time one way?
The total travel time one way is 288 minutes.
Explanation:To find the total travel time one way, we need to add up the time spent on each part of the journey. The salesman spends 1 hour and 48 minutes commuting from his house to the airport. Let's convert this to minutes, which gives us 60 + 48 = 108 minutes.
Next, we add the flight time. The question doesn't specify the duration of the flight, so we can't determine that. We'll assume it takes 2 hours, which is 120 minutes. Finally, we add the time spent on the bus. Again, the question doesn't provide this information, so let's assume it takes 1 hour (60 minutes) by bus.
Adding up the commute time, flight time, and bus time, we get 108 + 120 + 60 = 288 minutes. Therefore, the total travel time one way is 288 minutes.
how would the expression x^3-3sqrt(3) be rewritten using difference of cubes?
Answer:
Correct option is:
C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
Step-by-step explanation:
x^3-3sqrt(3)
= [tex]x^3-3\sqrt{3} \\\\=x^3-\sqrt{3}^3[/tex]
= [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
(since, [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex])
Hence, the correct option is:
C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
A life insurance policy costs $11.61 for every $1,000 of insurance. At this rate, what is the cost of $75,000 of insurance?
When is g(x) = 0 for the function g(x) = 5⋅23x + 4?
when x = 0
when x = 1
when x = 4
never
Ronnie cuts 3/4 inch sections of wood to make a birdhouse roof. he cut 12 sections. how many inches did he cut
Ronnie cut a total of 9 inches of wood. This is determined by multiplying the number of sections he cut (12) by the length of each section (3/4 inch).
Explanation:Ronnie cut 12 sections of wood, each measuring 3/4 inch to make his birdhouse's roof. In order to find out the total length of wood he used, we need to multiply the number of sections he cut by the length of each section. This is a basic multiplication problem in fractions.
So, 12 (sections) x 3/4 (inches/section) = 9 inches.
This means Ronnie cut a total of 9 inches of wood to make the birdhouse roof.
Learn more about Fraction multiplication here:https://brainly.com/question/10252019
#SPJ12
Jack has 2,613 songs saved on his computer. Dexter has 4 times as many songs saved on his computer as Jack has. How many songs does Dexter have saved on his computer?
If y = 285 when x = 57, what is y when x = 81?
Which is the correct input-output table for the function f(x) = 7 – 4.5x?
Answer:
The function is given to be :
f(x) = 7 - 4.5x
Now, to make a correct input-output table for the given function write the given function in the form of y and x
⇒ y = 7 - 4.5x
Now, in this equation x is independent variable and y is dependent variable.
So, give the input values to the variable x and note down the output values of variable y.
The required table is :
x 0 1 2 3
y 7 2.5 -2 -6.5
The table shows the outputs, y, for different inputs, x:
Input (x) 2 5 9 12
Output (y) 20 15 12 8
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)
Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.5% loan. Frederick doesn't want to pay more than $810 in interest. How many years does Frederick have to pay back the loan?
The Earth's circumference measured at the equator is approximately 1.3148 × 108 feet. What is the number written in standard form?
Answer:
The number written in standard form is [tex]131,480,000[/tex]
Step-by-step explanation:
we have
[tex]1.3148*10^8[/tex]
we know that
[tex]10^8=100,000,000[/tex]
substitute
[tex]1.3148*10^8=1.3148(100,000,000)[/tex]
Remember that
When multiplying decimals by 10, move the decimal point one space to the right
In this case move the decimal point eight spaces to the right
[tex]1.3148(100,000,000)=131,480,000[/tex]
therefore
The number written in standard form is [tex]131,480,000[/tex]
how do you make this equation 13+5y=6x into slope-intercept form?
Approximately how many times greater is 9.75×106 than 1.25×102 ? 7.8 7800 78,000 780,000
Answer:
78,000
Step-by-step explanation:
9.75 is 7.8 times larger than 1.25.
However, we have powers of 10. In the first number, 10 is raised to the 6th power; in the second number, 10 is raised to the 2nd power. This means that the first number is 10⁴ times bigger than the second one, or 10000 times bigger.
This means in total, the first number is 7.8(10000) = 78000 times larger than the second one.
This can be confirmed by dividing the two; 9.75(10⁶)÷1.25(10²) = 78000
Answer:
78000
Step-by-step explanation:
An appointment lasted from 2:30 pm until 5:15 pm. how long was the appointment?
Final answer:
The total duration of the appointment was 2 hours and 45 minutes.
Explanation:
To determine how long the appointment lasted, we need to calculate the time difference between the start time and the end time. The appointment started at 2:30 pm and ended at 5:15 pm.
First, take note of the start time: 2:30 pm.
Then, take note of the end time: 5:15 pm.
Calculate the hours by subtracting the start hour from the end hour: 5 pm - 2 pm = 3 hours.
Next, calculate the minutes by subtracting the start minutes from the end minutes: 15 minutes - 30 minutes. Since you cannot have a negative number of minutes, you need to borrow an hour from the 3 hours calculated, making it 2 hours, and add 60 minutes to the 15 minutes. Now, 75 minutes - 30 minutes = 45 minutes.
Combine the total hours and minutes: 2 hours and 45 minutes
Tony bowled 135 and 145 in his first two games. write and solve a compound inequality to find the possible values for a third game that would give him an average between 120 and 130, inclusive.
a.) 120 <= 135 +145+n/3 <=145; 120 <= n <= 140
b.) 135 <= 120 + 140 + n/3 <= 145; 80 <= n <= 85
c.) 120 < 135 + 145 + n/3 < 130; 80 < n < 110
d.) 120 <= 135 + 145 + n/3 <= 130; 80 <= n <= 110
How to write an equation of a line in slope intercept form with two points?
someone please help me! thank you so much
Solve for N.
-n/5 = -5
N = -25
N = -1
N = 25
Identify a benefit of applying statistical forecasting methods
One benefit of applying statistical forecasting methods is the ability to make informed predictions and decisions based on historical data.
Statistical forecasting methods utilize historical data and mathematical models to make predictions about future outcomes. By analyzing patterns, trends, and relationships within the data, statistical forecasting methods can provide valuable insights and estimates for various industries and fields.
One key benefit of applying statistical forecasting methods is the ability to make informed decisions and plan for the future. By utilizing historical data and statistical models, organizations can anticipate future demand, sales, or resource needs. This enables them to optimize their operations, allocate resources efficiently, and make strategic decisions.
Statistical forecasting methods also provide a level of objectivity and reliability in the prediction process. These methods are based on rigorous mathematical techniques and statistical principles, ensuring that the forecasts are grounded in sound methodology. This allows decision-makers to have confidence in the accuracy and validity of the forecasts, reducing uncertainty and aiding in effective planning.
Overall, applying statistical forecasting methods provides a systematic and data-driven approach to predicting future outcomes. It enables organizations to anticipate and adapt to changing circumstances, optimize their resources, and make informed decisions, leading to improved efficiency, profitability, and overall performance.
To learn more about statistical forecasting methods
brainly.com/question/30652356
#SPJ11
At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12. For her party, Arpitha purchased the minimum number of hot dog packages and bun packages that she could while making sure to have the same number of hot dogs and buns. How many hot dogs can Arpitha serve at her party?
They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.
We have given that,
At a local store, hot dogs come in packages of 8, and hot dog buns come in packages of 12.
Let's first analyze the word problem we have here.
It is stating that she, Arpitha, bought the minimum packs of hotdogs and minimum packs of buns to get an equal number of buns to hotdogs.
We can find the multiples they have in common.
8, 16, 24, 32, 40
12, 24, 36, 48, 60
They both have 24 in common, She bought 3 packs of hotdogs and two packs of hotdog buns.
To learn more about the word problem visit:
https://brainly.com/question/13818690
#SPJ2
The law of cosines is used to find the measure of Q.
242 = 202 + 342 – 2(20)(34)cos(Q)
576 = 400 + 1156 – (1360)cos(Q)
576 = 1556 – (1360)cos(Q)
–980 = –(1360)cos(Q)
To the nearest whole degree, the measure of angle Q _____ is
degrees
the right answer is 44.
Answer:
44 degrees.
Step-by-step explanation:
We are asked to find the measure of angle Q using law of cosines.
Law of cosines:
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]24^2=20^2+34^2-2\times 20\times 34\times cos(Q)[/tex]
[tex]576=400+1156-1360\times cos(Q)[/tex]
[tex]576=1556-1360\times cos(Q)[/tex]
[tex]576-1556=1556-1556-1360\times cos(Q)[/tex]
[tex]-980=-1360\times cos(Q[/tex]
Upon dividing both sides of our equation by -1360 we will get,
[tex]\frac{-980}{-1360}=\frac{-1360\times cos(Q}{-1360}[/tex]
[tex]0.7205882352941176=cos(Q)[/tex]
Now we will use arccos to solve for the measure of angle Q.
[tex]cos^{-1}(0.7205882352941176)=Q[/tex]
[tex]43.896932391182=Q[/tex]
[tex]Q\approx 44[/tex]
Therefore, the measure of angle Q is 44 degrees.
Wall posters are usually sold curled up in cylindrical cardboard tubes. if the length of the tube is 84.5 cm, and the diameter of the tube is 2.40 cm, what is the area of the poster, in cm2? (assume the poster doesn't overlap itself.)
a. 637 cm2
b. 203 cm2
c. 382 cm2
d. 1529 cm2
e. 605 cm2
Which value of a would make the following expression completely factored?
x2 – a
a 12
b 36
c 49
d 81
Answer:
The correct answer is twelve.
Step-by-step explanation:
The values of a would make the expression 36, 49 and 81.
The correct options are b, c, and d.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To factor the expression x² - a completely, we need to write it as a product of two binomials.
This can be done using the difference of squares formula, which states that a² - b² = (a + b)(a - b).
If we apply this formula to x² - a, we get:
x² - a = (x + sqrt(a))(x - sqrt(a))
This is a factorization of x² - a into two binomials, where the constant term a is represented by the square root of a.
For the expression x² - a to be completely factored, both factors must be irreducible (meaning they cannot be factored any further). This requires that a be a perfect square.
Out of the given options, 36, 49, and 81 are perfect squares.
To learn more about the quadratic equation;
https://brainly.com/question/17177510
#SPj7
HEEEEEEEEEEEELP 20 POINTS FOR REAL
Shayla is baking muffins that require 1/2 cup vegetable oil. She only has 1/3 cup left. How much more does she need?
If $2500 is invested at an interest rate of 4.5% per year, compounded daily, find the value of the investment after the given number of years. (round your answers to the nearest cent.)
$2500 is invested at an interest rate of 4.5% per year, compounded daily for 2 years will amount to $5225.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, $2500 is invested at an interest rate of 4.5% per year, compounded daily, and assuming it is for 2 years.
∴ The amount compounded daily will be,
A = P(1 + (r/365)/100)ⁿˣ³⁶⁵ as compounded daily.
A = 2500(1 + (4.5/365)/100)²ˣ³⁶⁵.
A = 2500( 1 + 0.00101)⁷³⁰.
A = 2500(1.00101)⁷³⁰.
A = 2500×2.09 dollars.
A = 5225 dollars.
learn more about compound interest here :
https://brainly.com/question/14295570
#SPJ5
To calculate the future value of an investment of $2500 at a 4.5% interest rate compounded daily for 5 years, we use the compound interest formula. Assuming 5 years of growth, the future value would be approximately $3117.14.
Explanation:If $2500 is invested at an interest rate of 4.5% per year, compounded daily, we need to find the value of the investment after a certain number of years. The formula to calculate the future value of an investment with daily compounding is given by:
FV = P × (1 + r/n)^(n×t)
where:
FV is the future value of the investment,P is the principal amount ($2500),r is the annual interest rate (4.5% or 0.045),n is the number of times the interest is compounded per year (365 for daily),t is the time the money is invested for, in years.To calculate the future value, we plug in the values into the formula. However, the number of years, t, has not been specified, so we'll need that to give a final answer. For our purposes, let's assume the student asks for the value after 5 years. Using the formula:
FV = $2500 × (1 + 0.045/365)^(365×t)
FV = $2500 × (1 + 0.00012328767)^(1825)
FV = $2500 × 1.246856823
FV = $3117.14 (rounded to the nearest cent)
After 5 years, the investment would be worth approximately $3117.14.
Factor completely 4x5 − 20x4 − 36x3. (1 point)
Answer:
The factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]
Step-by-step explanation:
Given the polynomial [tex]4x^5 - 20x^4 - 36x^3[/tex]
We have to factor the above polynomial completely.
[tex]4x^5 - 20x^4 - 36x^3[/tex]
Take [tex]x^3[/tex] common from each term.
[tex]x^3(4x^2-5x-9)[/tex]
Here, the quadratic polynomial is prime i.e it cannot be factored into lower degree polynomial. It has complex roots.
Hence, the factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]
Answer: 4x^3(x^2 - 5x - 9)
Proof of validity is shown below.
To get to work, a commuter must cross train tracks. the time the train arrives varies slightly from day to day, but the commuter estimates that he'll get stopped on about 15% of work days. during a certain 5-day work week, what is the probability that he doesn't get stopped all week long?
The probability that the commuter doesn't get stopped all week long is approximately 0.44.
Explanation:To find the probability that the commuter doesn't get stopped all week long, we need to find the probability of not getting stopped on each day and then multiply those probabilities together. Since the commuter estimates that he gets stopped on about 15% of work days, the probability of not getting stopped on a single day is 1 - 15% = 85%. To find the probability of not getting stopped all week, we raise 85% to the power of 5, since there are 5 work days in a week:
Probability of not getting stopped all week = (85%)5 = 0.85 * 0.85 * 0.85 * 0.85 * 0.85 = 0.44370515625.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
The probability that the commuter doesn't get stopped by the train all week long is 44%.
Explanation:This question falls under the category of probability in mathematics. The commuter estimates he'll get stopped 15% of work days, which implies that he'll have a smooth commute 85% of the time (100% - 15%). In a 5-day work week, the probability that he doesn't get stopped at all can be computed by multiplying the probability of not getting stopped each day. Therefore, the answer is (0.85)^5 or approximately 0.44, which represents 44%.
Learn more about probability here:https://brainly.com/question/32117953
#SPJ11
The sum of three consecutive integers is 267. What is the largest integer?
There are 18 girls in the school choir. The ratio of girls to boys is 1 to 2. How many boys are in the choir?
There are 36 boys in the school choir.
What is ratio?The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
There are 18 girls in the school choir.
The ratio of girls to boys is 1 to 2.
That means,
Girls / boys = 1/2
Substituting the values,
18 / boys = 1/2
Boys = 2 x 18
Boys = 36
Therefore, there are 36 boys.
To learn more about the ratio;
https://brainly.com/question/13419413
#SPJ2