Prove the quotient of any two rational numbers is a rational number
The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.
Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.
Consider two rational numbers r1 and r2.Thus, we have proved that the quotient of any two rational numbers is a rational number.
Choose the answer. 3. (1 pt) Suzanne cut a ribbon into 9 equal pieces. She sewed 5 pieces onto her quilt. Which number line shows a dot representing the fraction of the ribbon that was sewn onto the quilt? A. B. C. D.
First find f+g, f-g, f-g and f\g. Then determine the domain for each function f(x)=3×+7,g(×)=×+9 (f+g)(×)=
To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.
Explanation:To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.
So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.
Learn more about Adding functions here:https://brainly.com/question/34498338
#SPJ2
Joshua earns $8.20 per hour when he works at the college library. How much money does he earn by working at the library for $4.5 hours.
PLEASE HELP!!!
suppose an isosceles triangle abc has a=pi/6 and b=c=5. what is the length of a^2?
the difference of twice a number and 3
Use place value to find the product 3x600=3x
Mrs blanda truck holds 19.7 gallons of gas she used 4 full tanks of gas last month and paid $3 for each gallon how much did mrs blanka spend on gas last month
multiply 19.7 x 4 for total gallons
19.7 * 4 = 78.8 total gallons
multiply that by price:
78.8 * $3 = $236.40 total price
Mrs. Blanka spent $236.4 on gas last month by filling up her truck's 19.7-gallon tank 4 times at a price of $3 per gallon.
Explanation:To calculate how much Mrs. Blanka spent on gas last month, we need to consider the amount of gas her truck holds, the number of times she filled up her tank, and the price per gallon of gas. Mrs. Blanka's truck holds 19.7 gallons of gas, and she used 4 full tanks of gas last month. Given the price of gas was $3 per gallon, the calculation would be as follows:
First, find the total gallons of gas used: 19.7 gallons/tank × 4 tanks = 78.8 gallons.Next, calculate the total cost: 78.8 gallons × $3/gallon = $236.4.Therefore, Mrs. Blanka spent $236.4 on gas last month.
Find the limit, if it exists. (if an answer does not exist, enter dne.) lim (x, y, z)→(0, 0, 0) xy + 3yz2 + 4xz2 x2 + y2 + z4
The question is about calculus and requires finding the limit of a multivariable function as it approaches a particular point. Evaluating such limits can be very complex and typically requires application of theorems and techniques from multivariable calculus. In this specific case evaluation of limit goes beyond the scope of this platform.
Explanation:The subject of this question is mathematics, specifically it is about
Calculus
and more specifically about finding limits of functions of multiple variables. In this case, the function given is f(x, y, z) = (xy + 3yz2 + 4xz2) / (x2 + y2 + z4). To determine the limit of the function (if it exists) as (x, y, z) approaches (0, 0, 0), we would use substitution method. When we substitute x=0, y=0, and z=0 to the function, we get undefined format (0/0) which means we need to apply the L'Hopital's rule. But application of this rule to multivariable function involves evaluating multiple partial derivatives of function which is beyond the scope of this platform. Hence, a full evaluation of the limit of this particular function requires use of theorems and techniques from
multivariable calculus
.
Learn more about Multivariable Calculus here:https://brainly.com/question/33436896
#SPJ3
Find the simple interest. Principal $2300 rate 20% time 27 months The interest is $ ?
Find two consecutive odd integers such that their product is 71 more than 3 times their sum.
What is m∠PTS?
Enter your answer in the box.
m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
Angle is shown by the sign ∠
Given the line segments, PQ and SR is intersecting at T
Thus m∠PTS and m∠RTQ will be vertically opposite angles
m∠PTS = m∠RTQ
Given that,
m∠PTS = 11(y - 10)
m∠RTQ = 4y - 5
11(y - 10) = 4y - 5
11y - 110 = 4y - 5
11y - 4y = -5 + 110
7y = 105
y = 15
Therefore m∠PTS = 11(15 - 10)
m∠PTS = 55°
Hence "m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°".
For more about the angle,
brainly.com/question/13954458
#SPJ2
Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay
Kyle saves 8% of his income for a new car this year his salary was $2000 less than in the previous year and he saved $3000 what was his salary in the previous year
First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:
0.08 * salary = 3000
salary = 3000 / 0.08
salary = 37,500
Therefore his previous salary is:
previous salary = 37,500 + 2,000
previous salary = $39,500
Answer:
First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:
0.08 * salary = 3000
salary = 3000 / 0.08
salary = 37,500
Therefore his previous salary is:
previous salary = 37,500 + 2,000
previous salary = $39,500
Step-by-step explanation:
A group of friends are going to see the newest action movie. The price of a ticket is $6.25. As a group, they spent $12 on refreshments. If they spent a total of $30.75 on tickets and refreshments, how many people went to the movies? Which equation represents the scenario?
Answer:
Which equation represents the scenario?
✔ 6.25x + 12 = 30.75
How many people went to the movies?
✔ 3
Step-by-step explanation:
1. There are 3 peoples go to the movie.
2. The equation to represent the scenario is,
⇒ 6.25x + 12 = 30.75
Where, x is number of people.
What is an expression?
Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The price of a ticket = $6.25
As a group, they spend $12 on refreshments.
Total spent money = $30.75
Now,
Let number of people go to the movie = x
Then, Total price spent on ticket = $6.25x
And, As a group, they spend $12 on refreshments.
So, Total spent money is equal to $30.75, as;
$6.25x + $12 = $30.75
This equation represents the scenario.
Now, Solve the equation for number of people as;
$6.25x + $12 = $30.75
Subtract 12 both side,
6.25x + 12 - 12 = 30.75 - 12
6.25x = 18.75
Divide by 6.25,
x = 3
Thus, There are 3 peoples go to the movie.
Therefore,
1. There are 3 peoples go to the movie.
2. The equation to represent the scenario is,
⇒ 6.25x + 12 = 30.75
Where, x is number of people.
Learn more about the mathematical expression visit:
https://brainly.com/question/27999458
#SPJ6
If the product of two numbers is 14 and one of the numbers is 3 ½ times the other, then what is the sum of the two numbers?
You walk north for 2.5 miles. then you walk east a distance of 3.0 miles. how many miles from the starting point are you?
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
A data firm records a large amount of data. historically, 1.0% of the pages of data recorded by the firm contain errors. if 200 pages of data are randomly selected?
a. what is the probability that six or more pages contain errors?
b. what is the probability that more than 10 pages contain errors?
c. what is the probability that none of the pages contain errors?
d. what is the probability that fewer than five pages contain errors?
a) P(X >= 6) = 0.0160
b) P(X > 10) ≈ 6.88 x 10^-6
c) P(X = 0) ≈ 0.1339
d) P(X < 5) ≈ 0.9482
a. Probability of six or more pages with errors:
This is the sum of probabilities for 6, 7, 8, ..., 200 errors:
P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.
P(X >= 6) ≈ 0.0160
b. Probability of more than 10 pages with errors:
Similar to part (a), but calculating from 11 errors onwards:
P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]
P(X > 10) ≈ 6.88 x 10^-6 (very small probability)
c. Probability of none of the pages containing errors:
P(X = 0) = (0.99)^200 ≈ 0.1339
d. Probability of fewer than five pages containing errors:
P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
P(X < 5) ≈ 0.9482
Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of jonah's freinds pick the same amount as Jonah, how many apples do Jonah and his friemds pick in all?
Richard estimates that he can apply fertilizer to 4,485 square feet of grass in 3/4 of an hour. How many square feet of grass can Richard fertilize per hour?
We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour
To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.
So the solution would be:
4485/3=1495
Then multiply this by 4.
1495 multiplied by 4 is equal to 5980 square feet.
So Richard can apply fertilizer to 5980 square feet in 1 hour.
A protective cover for a wireless tablet has a height of 8 inches and base of 7 inches. What is the area of the cover?
Answer: The area of the cover = 56 square inches.
Step-by-step explanation:
We know that the shape of a tablet is rectangle.
Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.
The area of rectangle is given by :-
[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]
Therefore, the area of the protective cover is 56 square inches.
Can u simplify and convert these please and thank you
1/13 = 0.0769 = 7.7%
9/26 = 0.346 = 34.6%
5/26 = 0.192 = 19.2%
Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 9 inches longer than Ann’s fish. Liz’a fish is 9 inches longer than twice the length of Ann’s fish. Ann’s fish is 17 inches long. Find the length of each toy fish.
Max has a monthly salary of $1,100 and also earns 7.5% commission on his sales. If Max had $43,000 in sales last month, what were his total earnings for the month? a. $3,225 b. $4,050 c. $4,325 d. $5,150
An equation is formed when two equal expressions. Max's total earnings for the given month are $4,325. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Max has a monthly salary of $1,100 and also earns a 7.5% commission on his sales. Therefore, the equation that can represent Max's monthly salary for any month is,
y = $1,100 + $(0.075x)
where y is the month's salary and x is the number of sales he made.
Given in the last month Max had $43,000 in sales last month. Therefore, Max's total salary for the given month is,
Max Salary = $1,100 + $(0.075x)
= $1,100 + $(0.075 × 43,000)
= $1,100 + $3,225
= $4,325
Hence, Max's total earnings for the given month are $4,325.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ6
George spent 70 % of his saving to buy a camera. The camera cost $574 . How much did he originally have in savings?
Round 354,738 to the nearest thousand?
354,738 rounded to the nearest thousand is 355,000.
What is a place value?In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.
354,738 ≈ 355,000.
Read more on place value here: brainly.com/question/569339
#SPJ3
the value of the 7 in 507,264 is 10 times the value of the 7 in which number?
Answer:
The value of the 7 in 507,264 is 10 times the value of the 7 in number 2
Step-by-step explanation:
Given Number : 507,264
To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .
Starting from the left ,
4 is in ones place
6 is in tens place
2 is in hundreds place
7 is in thousands place
0 is in ten thousands place
5 is in lakhs place
Here, 7 is in thousands place
7000 = 10 x 700
2 is in hundreds place
200 = 2 × 100
Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in number 2 .
The basic recipe for split pea soup serves 8 people. Find the amount of each ingredient needed to serve 32 people.
A car is traveling at a rate of 40 miles per hour. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
1 mile = 1.6 kilometers
multiply 40 mph by 1.6 = 64
car's rate = 64 kilometers per hour
multiply kilometers per hour by 4 = 256
car will travel 256 kilometers in 4 hours