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.
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%
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.
George spent 70 % of his saving to buy a camera. The camera cost $574 . How much did he originally have in savings?
Which is the image of Triangle ABC for a 180° counterclockwise rotation about P?
Answer:
Triangle GHI is rotating 180° counterclockwise .
Step-by-step explanation:
Given : Triangles.
To find : Which is the image of Triangle ABC for a 180° counterclockwise rotation about P.
Solution : We have triangle ABC .
If we Rotate GHI triangle in counterclockwise 180 degree we get triangle ABC.
We can prove it by rotating triangle ABC in clockwise direction 180° We get triangle GHI.
Therefore, Triangle GHI is rotating 180° counterclockwise .
Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay
what is the estimate of 8.354
Find two consecutive odd integers such that their product is 71 more than 3 times their sum.
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.
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Write a real-life situation that can be modeled by the expression .
5 x 3/4
Answer:
On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?
Solutions 5 x3/4 = 3.75 inches of cake
Step-by-step explanation:
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?
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°".
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A plumber charges a flat fee of $79 to visit a home and examine a clogged drain. The plumber charges an additional $21 per hour spent fixing the drain. The total cost, c (in dollars), for fixing a drain that takes, h hours is given by the following function.
C(h)=79+21h
(a) What is the total cost for fixing a drain that takes 7 hours?
(b) If the plumber charges a total of $310, how many hours did he spend fixing the drain?
Final answer:
The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.
Explanation:
The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.
To find the total cost of fixing a drain that takes 7 hours, we substitute h with 7 in the given equation: C(7) = 79 + 21(7). Calculating this, we get C(7) = 79 + 147, which equals $226. Therefore, the total cost for fixing a drain that takes 7 hours is $226.To find out how many hours the plumber spent fixing the drain when the total charge is $310, we set C(h) equal to 310 and solve for h: 310 = 79 + 21h. Subtracting 79 from both sides gives us 231 = 21h. Dividing both sides by 21 yields h = 11 hours. Thus, the plumber spent 11 hours fixing the drain.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:
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?
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.
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
.
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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
Use place value to find the product 3x600=3x
Part b what is the value of the smallest bond angle in xef4?
Answer:
90 degrees
Step-by-step explanation:
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.
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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.
The basic recipe for split pea soup serves 8 people. Find the amount of each ingredient needed to serve 32 people.
Central City High School's robotics team is at a competition. In the last round, the team earned 80 points for their robot climbing over an obstacle and an additional 12 points for each ball the robot shot through a hoop. They won the round with 344 total points. Write an equation in the form a = bx + c that can be used to find the number of balls, x, their robot shot through the hoop. Fill in a, b, and c to complete the equation for this situation. Big fraction Parentheses Vertical bars Square root Root Superscript (Ctrl+Up) Subscript (Ctrl+Down) Plus sign Minus sign Middle dot Multiplication sign Equals sign Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Pi Alpha Beta Epsilon Theta Lambda Mu Rho Phi Sine Cosine Tangent Arcsine Arccosine Arctangent Cosecant Secant Cotangent Logarithm Logarithm to base n Natural logarithm Bar accent Right left arrow with under script Right arrow with under script Angle Triangle Parallel to Perpendicular Approximately equal to Tilde operator Degree sign Intersection Union Summation with under and over scripts Matrix with square brackets
Answer:
[tex]344=12x+80[/tex]
[tex]a=344[/tex]
[tex]b=12[/tex]
[tex]c=80[/tex]
Step-by-step explanation:
Let x be number of balls shot through the hoop by Central City High School's robot.
We have been given an equation [tex]a=bx+c[/tex] and we are asked to find the values of a, b and c.
We are told that Central City High School's team earned an additional 12 points for each ball the robot shot through a hoop. So the points earned by shooting x balls through the hoop will be 12x.
The team also earned 80 points for their robot climbing over an obstacle. So total number of points earned by team will be equal to [tex]12x+80[/tex].
We are also told that the team won the round with 344 total points. We can represent this information in an equation as: [tex]344=12x+80[/tex]
Upon comparing this equation with our given equation we will get,
[tex]a=344[/tex]
[tex]b=12[/tex]
[tex]c=80[/tex]
Therefore, the equation [tex]344=12x+80[/tex] can be used to find the number of balls, x, team's robot shot through the hoop.
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.
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.
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a receipe calls for 3 1/3 cup of heavy cream, If i double the receipe and want to make 2 1/2 times the amount how much heavy cream do I have to use?
For 2 1/2 times the doubled recipe, starting with an initial amount of 3 1/3 cups of heavy cream, the total amount needed would be 16 2/3 cups of heavy cream.
To calculate how much heavy cream is needed, we must first understand the initial amount required and then apply the necessary adjustments to upscale the recipe.
If the original recipe calls for 3 1/3 cups of heavy cream and we want to double the recipe, we would need 2 x 3 1/3 cups which is 2 x (10/3) cups = 20/3 cups or 6 2/3 cups.
Now, if we want to make 2 1/2 times the amount of the doubled recipe, we multiply 6 2/3 cups by 2 1/2 (5/2), resulting in (20/3) x (5/2) cups. Simplifying this, we get:
(20/3) x (5/2) = (100/6) cups = 16 2/3 cups.
Therefore, for 2 1/2 times the doubled recipe, you would need 16 2/3 cups of heavy cream.
suppose an isosceles triangle abc has a=pi/6 and b=c=5. what is the length of a^2?
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.
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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?