rove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = a b and s = c d for some ---Select--- a, b, c, and d with ---Select--- . Write r − s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r − s = Both the numerator and the denominator are integers because ---Select--- . In addition, bd ≠ 0 by the ---Select--- . Hence r − s is a ---Select--- of two integers with a nonzero denominator, and so by definition of rational, r − s is rational.
Answers
Answer:
Step-by-step explanation:
Question:
Prove the following statement directly from the definitions.
The difference of any two rational numbers is a rational number.
Answer, see attachment for proof.
Related Questions
A pancake recipe require 1 2/3 cups of flour to make 20 pancakes and you have 9 cups of flour.
a. How many pancakes can you make with 1 cup of flour?
b. How many pancakes can you make with 9 cups of flour?
C. Do you have enough to make 100 pancakes? Explain
Answers
Quantity of flour needed to make 20 pancakes =
[tex] = 1 \frac{2}{3} \: [/tex]
[tex] = \frac{3 \times 1 + 2}{3} [/tex]
[tex] = \frac{5}{3} \: cups \: of \: flour[/tex]
Then , number of pancakes that can be made from 1 cup of floor :-
[tex]20 \div \frac{5}{3} [/tex]
[tex]20 \times \frac{3}{5} [/tex]
[tex] \frac{60}{5} [/tex]
[tex] = 12 \: pancakes[/tex] .
Therefore , 12 pancakes can be made from 1 cup of floor .
Solution (b) :-Number of pancakes that can be made with 1 cup of flour = 12 pancakes
Number of pancakes that can be made with 9 cups of flour :-
= 9 × 12
= 108 pancakes
Therefore , I can make 108 pancakes with 9 cups of flour .
Solution (c) :-Yes , I have enough flour to make 100 pancakes . I say this because :-
With one cup of flour I can make = 12 pancakes
With 9 cups of flour I can make =
= 9 × 12
= 108 pancakes
As I can make 108 pancakes with 9 cups of flour , I can conclude that I have enough flour to make 100 pancakes .
What is the solution to 2x-8 <12?
o x<2
O x<3
Ox<10
0x<40
Answers
Answer:
x<10
Step-by-step explanation:
i think this is the answer
x<10 is the solution of the inequality 2x-8 <12
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 2x-8<12
Two times of x minus eight less than twelve
x is the variable
We have to find the solution of the inequality
2x<20
Divide both sides by 2
x<10
Hence, x<10 is the solution of the inequality 2x-8 <12
To learn more on Inequalities click:
https://brainly.com/question/28823603
#SPJ7
Please help with this
Answers
a. r + (-s) = r - s
b. r - (-s) = r + s
c. -r + (-s) = -r - s
d. -r - (-s) = -r + s
Jason is only able to work 28 hours a week this month (at $12 an hour) so he is worried that he will be in a bind paying his bills. He has to pay
his rent ($875) and his car payment ($330) with insurance ($130). How miuch will Jason have left over at the end of the month?
Answers
Answer:
9
Step-by-step explanation:
28 x 4=112
112 x 12= 1344
1344-875-330-130=9
Answer:
he will have $9 left over
The total amount of time University students in the United States spend sleeping,grooming,eating and drinking and traveling is about?
Answers
Answer:
11.7 hours
Step-by-step explanation:
According to data gathered between the years of 2015-2020 from full-time University Students at various Universities throughout the US, it was discovered that they spend roughly 11.7 hours completing these tasks (sleeping, grooming, eating/drinking, and traveling) per day. This applies strictly to full-time University Students that have the responsibilities associated with that life such as studying, attending class, group projects, etc. and does not include extra activities such as cooking.
Find constants a , b, and c such that the function
y = ax2 + bx + c satisfies the differential equation y′′ + y′ − 2y = 4x2.
Answers
Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
2+2 answer this and get 85 points
Answers
Answer:
4
Step-by-step explanation:
Thank you so much!! really appreciate it, I just need a few more points to become so thank you so much again!!:)
Answer:
4
Step-by-step explanation:
2+2=4
3/4x-2=2/5
Rewrite so there is no fractions
Answers
Answer:
15x - 40 = 8
Step-by-step explanation:
3/4x-2=2/5
Multiply each side by 4*5 or 20
20 (3/4x-2=2/5)
15x - 40 = 8
3x - 5 = 2x + 10
What’s the value of x
Answers
Answer:
x = 3
Step-by-step explanation:
braniest pls
Answer:
x=3
Step-by-step explanation:
-5 +10
+5=15
+5=0
3x, 2x
+2 -2
5x=15
_ _
x=3
anybody wanna answer for me ?????
Answers
Answer:
y=11x
Step-by-step explanation:
EX:
11(2)=22
Simplify and write answer in terms of i as appropriate. *. i^25
Answers
Answer:
i
Step-by-step explanation:
Given the complex value i^25, we are to write in terms of i. In complex number:
i² = -1
i^25 =( i²)¹² × i
= (-1)¹² × i
Note that -1 to a negative number will give a positive number hence (-1)¹² = 1
(-1)¹² × i = 1×i
= i
Hence i^25 = i
Kalvin sells bottles of water at baseball games he pays 0.75 per bottle and 3.78 for the ice to keep cold let b represent the number of bottles of water he buys c represent his total cost
Answers
Answer:
3.78+.75b=c
Step-by-step explanation:
find the measures of angles 1, 2, and 3
Answers
x = 33°
Then :-
m∠1 = 33° ( angle x and angle 1 are corresponding angles on a transversal )
Which means :-m∠1 + m∠2 = 90° ( angle 1 and angle 2 are complementary angles )
33 + ∠2 = 90
∠2 = 90 - 33
m∠2 = 57°
Then :-m∠1 + m∠3 = 180° ( angle 1 and angle 3 are a linear pair )
33 + ∠3 = 180°
∠3 = 180 - 32
m∠3 = 147°
Therefore , m∠1 = 33°m∠2 = 57° m∠3 = 147°Chase rode his roller skates around the block 5 times for a total of 1 mile yesterday. Today he wants to ride his roller skates 3/5 of a mile. How many times will he need to ride his roller skates around the block?
Answers
A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution
Answers
Answer:
The number of standard deviation above the mean is [tex] z_o = 1.4607 [/tex]
Step-by-step explanation:
From the question we are told that
The mean weight of ears of corn from each farm is [tex]\mu=1.26[/tex]
The standard deviation of ears of corn from Iowa is [tex]\sigma_1[/tex]
The standard deviation of ears of corn from Ohio is
[tex] \sigma_2= 0.01 + \sigma_1 [/tex]
The weight of a random selected ear of corn from Iowa is x = 1.39 pound
The standardized score is z =1.645
The weight of a random selected ear of corn from Ohio is [tex]x_1 = 1.39\ pound[/tex]
Generally the standardized score of weight of corn from Iowa is mathematically represented as
[tex]z = \frac{ 1.39 - 1.26 }{\sigma_1 }[/tex]
=> [tex] 1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }[/tex]
=> [tex] \sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}[/tex]
=> [tex] \sigma_1 = 0.0790 [/tex]
Generally the standardized score of weight of corn from Ohio is mathematically represented as
[tex]z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }[/tex]
=> [tex] z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }[/tex]
=> [tex] z_o = \frac{ 1.39 - 1.26 }{ 0.089}[/tex]
=> [tex] z_o = 1.4607 [/tex]
Because the value is positive it means that this value represent the number of standard deviation above the mean.
Using the normal distribution, it is found that the weight with respect to the Ohio distribution is 1.46 standard deviations from the mean.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For the Iowa farm:
The mean is of 1.26 pounds, hence [tex]\mu = 1.26[/tex].The weight is of 1.39 pounds, hence [tex]X = 1.39[/tex]The standardized score is of 1.645, hence [tex]Z = 1.645[/tex].Then, the standard deviation can be found as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{1.39 - 1.26}{\sigma}[/tex]
[tex]1.645\sigma = 0.13[/tex]
[tex]\sigma = \frac{0.13}{1.645}[/tex]
[tex]\sigma = 0.079[/tex]
In Ohio:
Same mean.Standard deviation 0.01 pound greater, hence [tex]\sigma = 0.079 + 0.01 = 0.089[/tex]Same weight.Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.39 - 1.26}{0.089}[/tex]
[tex]Z = 1.46[/tex]
The weight with respect to the Ohio distribution is 1.46 standard deviations from the mean.
To learn more about the normal distribution, you can check https://brainly.com/question/24663213
In which number is the digit 7 ten times larger than it is in the number 175?
A) 379
B) 607
C) 730
D) 7,513
Answers
Answer:
c 730
Step-by-step explanation:
because the 7 in 730 is one digit to the left
Answer:
C. 730
Step-by-step explanation:
The 7 in the original number is in the tens place. So if you multiply that by 10, the seven moves into the hundreds place.
3 over 5 =nothing over 20
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ion even know yet
gyfujkl;kjbhvgfcdxsrtuiokl;, nbvghjkjhbgyu
can you help
thank you
Answers
Answer:
In first box: top left __7, in top right __4, on left top __9, left bottom __6.
In second box: top left __7, in top right __3, on left top __3, left bottom __5.
Step-by-step explanation:
Answer:
Here you go! I believe this is correct.
Use a number line to show the sum of 6+(-7) ?
Answers
Answer:
-1
Step-by-step explanation:
When you make the number line, go to the middle then move left once. Then mark that " -1 " and you put the dot over that.
It's hard to explain how to write number lines.
Anyways, the problem equals -1 because 6-7 is negative 1. The + is there to confuse you.
Mark brainliest if possible please :)
5. At the beginning of an experiment, there are ten bacterial cells in Petri Dish A and five bacterial cells in Petri Dish B. The number of bacterial cells
o in Dish A after h hours can be modeled with the equation a - 10(125)". The number of bacterial cells bin Dish B after h hours can be modeled
with the equation b - 5(25)" Based on this information, which of the following statements is true?
After one hour, the number of bacterial cells in Dish Ais equal to the number in Dish B
After one hour, the number of bacterial cells in Dish A is greater than the number in Dish B
After one hour the number of bacterial cells in Dish A is less than the number in Dish B.
After ten hours, there are approximately 125 bacterial cells in Dish A
After ten hours, there are approximately 50,000 bacterial cells in Dish B.
Answers
After 5.5 hours, Allie had traveled 264 miles. If she travels at a constant speed, how far will she have traveled in 6 hours?
Answers
Answer:
288 Miles
Step-by-step explanation:
Solve for x (speed)
5.5x = 264
Divide by 5.5
x = 48
y = 48x
Subsitute 6 hours in for x
y = 48(6)
y = 288
Answer: Allie went 288 miles in 6 hours.
Step-by-step explanation:
First, you must find out how many miles Allie travled in one hour
= 264/5.5
= 48
Next, multiply the quotient by the number of hours to get the answer.
= 48 x 6
= 288
The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what pattern would you expect in a normal quantile plot of these data?
a. The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be bell-shaped.
b. The histogram would by non-symmetric, and the normal quantile plot would have data points that would be non- linear.
c. The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be non-linear.
d. The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern.
Answers
Answer:
d. The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern.
Step-by-step explanation:
Since the variable is normally distributed, the histogram of women's height should be approximately bell shaped (if the data was obtained form a random sample).
Again, the variable is normally distributed, therefore, the quantile plot should follow a straight line pattern (a diagonal line to be more precise).
Which property justifies the statement if y = 7, then 7 = y?
Answers
Given m||n, find the value of x.
t
>m
(x+14)
(9x-8)"
Answers
Answer:
1st one
Step-by-step explanation:
Answer:
1st one
Step-by-step explanation:
uestion 1:
Damon wants to sell his motorcycle that he paid $4,000 for 3 years ago. The motorcycle depreciated (decreased in value) at a constant rate each month over a 3-year period. If x represents the monthly depreciation amount, write an expression that shows how much Damon can sell his motorcycle for today.
Answers
Answer:
4,000 -x3
Step-by-step explanation:
x times 3 is equal to the decrease so therefore you take the decrease away form 4/oo
Answer:
3y-x=4,000
Step-by-step explanation:
The perimeter of a playing field for a certain sport is 214 ft. The field is a rectangle, and the length is 41 ft longer than the width. Find the dimensions
The width of the playing field is
(Type an integer or a decimal)
Answers
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
L is the length of the rectangle:
W is the width of the rectangle.
Given
Perimeter = 214feet
If the length is 41 ft longer than the width, then L = 41+W
Substitute L = 41+W into the formula:
P = 2(L+W)
214 = 2(41+W+W)
214 = 2(41+2W)
214 = 82+4W
4W = 214-82
4W = 132
W = 132/4
W = 33 feet
Since L = 41+W
L = 41+33
L = 74 feet
Hence the dimension of the field is 74ft by 33ft
The width of the playing field is 33feet
Which is true 0.45>0.5
0.45<0.5
4.05=0.45
4.05 <0.45
Answers
Answer:
4.05 is greater than 0.45
6th grade math i mark as brainliest
Answers
Answer:
16
Step-by-step explanation:
Plz help i only need c im confused lol 6th grade history
Answers
Answer:
War
Step-by-step explanation:
Criminals
Solve the following: - 8h = -0.36
Answers
Answer:
h=0.045
Step-by-step explanation:
