Yet because we can compare the set of positive rational numbers exactly to the collection of natural numerals, we may infer that the set of positive rational must have a number of clusters of 0, or n(Q+)=0. Due to the fact that these two numbers must equal one another, 02 = 0.
Since they may be arranged in a one-to-one correspondence with the natural numbers (the integers, such as 1, 2, and 3), Cantor showed in 1873 that the rational numbers, although being infinite, are countable (or denumerable).
How are the rational numbers counted as a group?
To achieve this, we take into account the this double integers grid upon that positive orthogonal. If p and q are positive natural numbers, then p/q may be used to represent any positive valid value.
Simply put, we establish the following values: h(0) = 0, h(2n) = f(n), for all natural numbers n > 0, and h(2n-1) = g(n) = -f(n), for all natural numbers n > 0.
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the perimeter of a rectangle is 175 feet. the short sides are each feet long, but the lengths of the long sides are . a) which equation represents this situation? correct b) write in terms of . incorrect
this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.
a) The equation that represents this situation is:
2x + 2y = 175
where x is the length of the short sides (in feet) and y is the length of the long sides (in feet).
b) The equation in terms of y is:
2(6) + 2y = 175
which simplifies to:
12 + 2y = 175
2y = 163
y = 81.5
However, this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.
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PLS I HAVE TO TURN ALL OF THIS IN BY LIKE TONIGHT
Answer:
1. irrational
2. irrational
3. rational
4. rational
5. irrational
6. rational
Step-by-step explanation:
A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.
1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL
2.) the line above the 46 means that it is repeating, making it IRRATIONAL
3.) the square root of 100 is 10, making it RATIONAL
4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL
5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL
6.) 10 is a whole number, making it RATIONAL
For what real numbers x is the value of x2
– 6x + 9 negative?
Answer:
Step-by-step explanation:
EZ
its 21
ou and i each have a fair coin. i flip n times, and you flip n 1 times. you win if i get fewer heads than you. what is the probability that you win the game?
Answer: 3
Step-by-ste3p explanation:
10. 4 out of 5 students are going on the field trip tomorrow. If there are 400 students, how many
are going on the field trip?
The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.
Define Fraction?A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).
If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.
To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:
Number of students going on the field trip = (4/5) x 400
Number of students going on the field trip = 320
Therefore, 320 students are going on the field trip.
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Help em fin the answer
Answer:
1 ft per 4 seconds
120 seconds
72 seconds
Step-by-step explanation:
Help needed LIKE RN!! URGENT!!
The surface area of the cylinder is approximately 127.17 cm².
What is the surface area of the cylinder?Surface area of cylinder is the total space covered by the flat surfaces of the bases of the cylinder and its curved surface. The formula for the surface area of a cylinder is: 2πr² + 2πrh.
To solve this problem, we first need to find the radius of the cylinder. The diameter of the cylinder is 3 cm, so the radius is half of that:
r = 3/2
= 1.5 cm
We need to substitute the values we know into the formula for surface area:
= 2π(1.5)² + 2π(1.5)(12)
= 2π(2.25) + 2π(18)
= 4.5π + 36π
= 40.5π
We will now approximate the value of π to get the numerical answer, so, our Surface Area will be:
= 40.5π
= 40.5 * π
= 40.5 * 3.14
≈ 127.17 cm²
Answered question "A cylinder is 12 cm tall and has a diameter of 3 cm. What is the surface area?"
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The figure shows intersecting lines k and m. What is the measure of angle a?
Type the number in the box.
86°
a
degrees
According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.
The angles add up to 180 degrees.
Then we receive,
[tex]a + 86 =180[/tex]
Or, a = 180 -86
Or, a = 94°.
As a result, an is 94°.
The angle an is 94 degrees.
Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.
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The graphs below have the same shape. What is the equation of the red
graph?
f(x) = 4 – x²
g(x) = ?
O A. g(x) = (7 - x)2
O B. g(x) = 1 - x2
O C. g(x) = 7 - x2
D. g(x) = (1 - x)2
Answer:
C
Step-by-step explanation:
The red graph is obtained by shifting the graph of f(x) = 4 - x² upwards by some amount. We can see that the highest point on the red graph occurs at x = 0, where the value is 4.
To shift the graph of f(x) upwards by 3 units, we can add 3 to the entire function:
f(x) + 3 = 4 - x² + 3
= 7 - x²
So the equation of the red graph is:
g(x) = 7 - x²
Therefore, the correct answer is option C: g(x) = 7 - x².
in exercise physiology, a person's maximum heart rate, in beats per minute, is found by subtracting his age in years from 220. so, if a represents your age in years, then your maximum heart rate is:
Step-by-step explanation:
If your age is ' a ' then your max heart rate = 220 - a
A gamer is observing her score, y, as she plays a video game. She currently has 3,200 points and is gaining 200 points for every minute, x, she plays.
Which of the following equations can be used to describe this linear relationship?
A. y = 3,200x − 200
B.y = 3,200x + 200
C. y = 200x − 3,200
D. y = 200x + 3,200
Answer: d
Step-by-step explanation:
the slope is positive 200 because she is gaining 200 points for every minute which is x. 200x or 200 multiplied by x is her slope and her y intercept is 3200
Aron needs 5/7 of a yard of fabric to cover a chair ad 2/3 of a yard of the fabric to cover a footstool. How much more fabric is required for the chair than the footstool?
Answer:
Step-by-step explanation:
To find out how much more fabric is required for the chair than the footstool, we need to subtract the amount of fabric required for the footstool from the amount of fabric required for the chair.
The amount of fabric required for the chair is 5/7 of a yard.
The amount of fabric required for the footstool is 2/3 of a yard.
So to find the difference, we need to subtract:
5/7 - 2/3
To do this, we need to find a common denominator, which is 21 in this case. We get:
(15/21) - (14/21) = 1/21
Therefore, Aron needs 1/21 more yard of fabric to cover the chair than the footstool.
how do you solve this to get the answer
Answer:
The answer is
-7/8 + 3/10
Step-by-step explanation:
See the picture
Hope you understand :)
Describe and correct the error a student made in identifying the growth or decay factor for the
function y = 2.55(0.7)
Step 1 The base of the function
is 0.7, so it represents
exponential decay.
Step 2 The function in the form
y = a(1-r)* is
y = 2.55(1-0,7)*
Step 3 The decay factor is 0.3.
X
The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.
Explain function?
A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.
The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]
To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]
So, the corrected version of the solution is:
Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.
Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]
Step 3: The decay factor is [tex]0.3.[/tex]
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Please help :( I don't quite understand...
Step-by-step explanation:
For Part A, use the function f(x) to find the average of tests taken.
X is number of test taken
f(x) is the average score given said num of tests taken,x,
We want after test number 3 so using the function,
[tex]f(x) = 0.2x + 79[/tex]
Plug in. 3 for x, and we will get our answer.
[tex]f(3) = 0.2(3) + 79 = 79.6[/tex]
Part B: Use the table for the answer.
When 2 test are taken, the average test score is
84
So part B is 84.
Part C:
[tex]f(2) = 0.2(2) + 79 = 79.4[/tex]
[tex]g(2) = 84[/tex]
Since
[tex]g(2) > f(2)[/tex]
The science class had a higher average after 2 tests
Answer:
you shoulda payed attention in class
Step-by-step explanation:
also u know it's bad when the test is so hard you can't even cheat on it
2. The function f gives the dollar value of a bond t years after the
bond was purchased. The graph of Jis shown.
What is f(0)? What does it mean in this situation?
b. What is f(4.5)? What does it mean in this situation?
c. When is f(t) = 1500? What does this mean in this
situation?
The function f a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year. b. f(4.5) represents the value of the bond 4.5 years later.
What does a mathematical function mean?A function in mathematics is a rule that designates a certain output value for each input value. Each input from the domain has precisely one output in the range, forming a relationship between two sets known as the domain and the range. The letter f(x), where x is the input variable and f(x) is the output variable, is a common way to represent a function. The output variable is specified by the function's rule, but the input variable can accept any value from the function's domain.
For the given graph of the function:
a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year.
b. f(4.5) represents the value of the bond 4.5 years later.
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The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced three times. What is the voltage in exponential form?
Answer: x 3= 27/125
Step-by-step explanation:
Whether the economy is in a recession is illustrated in the AD/AS model by how close the _____ is to the potential GDP line.
a. AD curve
b. AS curve
c. AS and AD curve
d. equilibrium
When the equilibrium point is above the potential GDP line, the economy is experiencing inflationary pressure.
In the AD/AS model, whether the economy is in a recession is illustrated by how close the equilibrium is to the potential GDP line. The potential GDP line represents the maximum level of output that an economy can produce with its existing resources and technology.What is the AD/AS model?The AD/AS model is a graphical representation of the macroeconomic relationship between aggregate demand (AD) and aggregate supply (AS). This model is used to explain the behavior of the economy by demonstrating how changes in the level of aggregate demand and aggregate supply can impact the economy's level of output and prices.
The model's AD curve represents the total demand for all goods and services in an economy at different price levels. The AS curve represents the total supply of all goods and services in the economy at different price levels.
The intersection of the AD and AS curves represents the equilibrium point where the economy's output level and price level are determined. The economy is in a recession when the equilibrium point is below the potential GDP line.
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A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. What is the mean salary paid to the office assistants in this company?
A. $22,500
B. $23,700
C. $25,500
D. $27,300
E. $28,500
Therefore, the mean salary paid to the office assistants in this company is $24,000.Answer: B. $24,000
A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. The mean salary paid to the office assistants in this company can be calculated by taking the weighted average of the mean salaries of the two offices.
Here's the formula to calculate the weighted average:
Weighted average = (weight1 × value1 + weight2 × value2) / (weight1 + weight2)
Where weight represents the number of data points, and value represents the mean salary of office assistants.
In this question, the weight of the New Jersey office is 128, and the weight of the Utah office is 32. The value of the New Jersey office is $28,500, and the value of the Utah office is $22,500.
Now let's plug in the values:
Weighted average = (128 × 28,500 + 32 × 22,500) / (128 + 32)
= (3,648,000 + 720,000) / 160
= 24,000
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A grocer can buy oranges for $1.65 per pound.
1. Write an equation relating c, the cost; and p, the pounds of oranges.
2. An orange order cost $260.10. How many pounds did the grocer order? (Round to the nearest whole number)
Answer:
157 pounds I'm pretty sure the equation would be 1.65c=p
Step-by-step explanation:
p is 1 because no given varible since p=1 pound 1.65 would equal p they 157 pounds bc 260.10/1.65 gives you 157 rounded
Question 11
Aiguo rode his bike twice as many miles as Xavier. Together, they rode a total of 22.5 miles. How many miles did
Xavier ride?
Part A
Write a system of equations that represents the situation.
y =
x + y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
Done and
I’m literally so confused
Xavier rode 7.5 miles and Aiguo rode twice as much, or 15 miles.
How many miles did Xavier ride?Let x be the number of miles Xavier rode. Since Aiguo rode twice as many miles as Xavier, let 2x be the number of miles Aiguo rode.
Together, they rode a total of 22.5 miles, so we have the equation:
x + 2x = 22.5
Simplifying, we will get:
3x = 22.5
x = 22.5/3
x = 7.5
We can check our answer by verifying that the sum of their distances is indeed 22.5 miles:
= 7.5 + 15
= 22.5
Therefore, the solution is x = 7.5 and y = 15.
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A city has a population of 370,000 people. Suppose that each year the population grows by 4. 75%. What will the population be after 11
years?
The population of the city will be approximately 597,543 people after 11 years.
We can solve this problem using the formula for exponential growth:
[tex]N = P(1 + r)^t[/tex]
where:
N = final population
P = initial population
r = annual growth rate (as a decimal)
t = number of years
In this case, we have:
P = 370,000
r = 0.0475 (since the annual growth rate is 4.75%)
t = 11
Substituting these values into the formula, we get:
[tex]N = 370,000(1 + 0.0475)^{11}[/tex]
Using a calculator, we can simplify this expression to:
N = 597,542.64
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a rectangular container 12 cm long, 8 cm wide, and 36 cm high was one - third full. when some syrup from a bottle was poured into the container, it got half full. find the volume of the syrup poured from the bottle into the container in millimeters
when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.
Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and 36 cm.Now the volume of the container is:
V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now we convert the above result into millimeters by multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm
Now to find the volume of the syrup that was poured into the container, we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:
1/3(V) + x = 1/2(V), where v is the volume of the container in millimeters, so we substitute the calculated value of the volume we get :
=>1/3(V) + x = 1/2(V)
=>x = 1/2(V) - 1/3(V)
=> x = 1/6(V) = 1/6(3,456,000) = 576,000 cubic mm
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Aria puts 0. 75 liters of apple juice and 0. 5 liter of cranberry juice in a pitcher that holds 2 liters of liquid. She fills the rest of the pitcher with orange juice. What fraction of the mixture is orange juice?
Answer:
Step-by-step explanation:
Your equation is 0.75L + 0.5L + x = 2L
x = Orange juice
0.75L + 0.5L = 1.25L
2L - 1.25L = 0.75L
[tex]\frac{0.75L}{2L}[/tex] is your fraction
[tex]\frac{75}{200}[/tex] simplified is [tex]\frac{3}{8}[/tex]
I hope this helped,
S.
5.
You may be surprised to learn that prime
numbers are used for sending information
securely over the internet. The internet uses
computers, so they do this by multiplying two
huge prime numbers. It is hard work. Here is
a challenge for you. The number 51 is the
product of two prime numbers. What are the
two prime numbers?
The prime factors or the prime numbers whose product is 51 are 3 and 17.
What is the operation of prime numbers?
The operation of prime numbers refers to the various mathematical operations that can be performed using prime numbers. Prime numbers are positive integers that have exactly two divisors, 1 and the number itself. Some of the important operations involving prime numbers include:
Prime factorizationGCD and LCMModular arithmeticPrimality testingCryptographyNow,
If you meant to ask for the prime factors of 51, then they are 3 and 17.
because 51 is divisible by 3 because 5+1=6
and after dividing 51/3=17 which is also a prime number.
Hence,
the prime factors of 51 are 3 and 17.
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if the dental director wanted to analyze the data collected from the cpi, which type of descriptive statistics should be used to measure central tendencies?
To measure central tendencies in the data collected from the Consumer Price Index (CPI), the dental director should use measures of central tendency, such as the mean, median, and mode.
The mean is the average of a set of numbers and is calculated by adding all the numbers together and then dividing by the total number of numbers. The median is the middle number when the numbers are placed in order from least to greatest. The mode is the number that appears most often in a set of numbers.
Using these measures of central tendency will allow the dental director to gain a better understanding of the CPI data, as they will be able to identify the center point of the data and also see how frequently particular values appear. This can help in making informed decisions about policies and other changes.
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130.25.122.63mario's pizzeria bakes olive pieces in the outer crust of its 20-inch (diameter) pizza. there is at least one olive piece per inch of crust. how many olive pieces will you get in one slice of pizza? assume the pizza is cut into eight slices.
By using circumference of circle, we find that In one slice of pizza you will get about 8 olive pieces from Mario's Pizzeria.
The circumference of circle of a 20-inch diameter pizza can be calculated as follows:
Circumference = π × diameter
Circumference = 3.14 × 20
Circumference = 62.8 inches
If there is at least one olive piece per inch of crust, then there will be 62.8 olive pieces on the outer crust of the entire pizza.
If the pizza is cut into eight slices, each slice will have 1/8th of the total circumference of the pizza. Therefore, each slice will have:
62.8 inches ÷ 8 slices = 7.85 inches of outer crust
Since there is at least one olive piece per inch of crust, each slice will have approximately 8 olive pieces on the outer crust.
Therefore, you can expect to get about 8 olive pieces in one slice of pizza from Mario's Pizzeria.
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What is the equation of this graph?
A.) y=-x²-2x-8
B.) y=x²-2x-8
C.) y=3x²-12x-8
D.) y=-3x²-12x-8
The equation of the quadratic function that passes through these points is:
[tex]y = -3x^2 - 12x - 8.[/tex]
What is quadratic equation?
A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be [tex]y = ax^2 + bx + c[/tex].
Using the point (0, -8), we get:
[tex]-8 = a(0)^2 + b(0) + c[/tex]
c = -8
Using the point (-1, 1), we get:
[tex]1 = a(-1)^2 + b(-1) - 8[/tex]
a - b = 9
Using the point (-3, 1), we get:
[tex]1 = a(-3)^2 + b(-3) - 8[/tex]
9a - 3b = 27
Using the point (-4, -8), we get:
[tex]-8 = a(-4)^2 + b(-4) - 8[/tex]
16a - 4b = 0
Using the point (-2, 4), we get:
[tex]4 = a(-2)^2 + b(-2) - 8[/tex]
4a - 2b = 12
Solving this system of equations, we get:
a = -3
b = -12
c = -8
Therefore, the equation of the quadratic function that passes through these points is:
[tex]y = -3x^2 - 12x - 8.[/tex]
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write the equation of a circle with center at (-1/2,1/4) and r= [3]
The equation of the circle is 16 x^2 + 16x +16 y^2- 4y -45 =0
Here the center of circle is at (1/2, 1/4 ) and radius is √ 3
The equation of a circle with center (h , k) and radius r is given by
(x - h)^2 + ( y - k)^2 = r^2
Here it is given that the center of circle (-1/2 , 1/4) = (h, k) and radius r= √ 3
Therefore the equation of required circle is
(x - (-1/2) )^2 + (y-1/4)^2= √ 3^2
=> x^2 + 1/4 + x + y^2 +1/16 - 4y= 3
=> 16x^2 + 4 +16x+ 16 y^2 -4y +1= 48
=>16 x^2 + 16x +16 y^2- 4y -45 =0
therefore the required equation of circle is
16 x^2 + 16x +16 y^2- 4y -45 =0
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we know the sample size is 90. for what sample proportion would the p-value be equal to 0.05? assume that all conditions necessary for inference are satisfied.
The sample proportion would be 0.5.we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.
To determine what sample proportion would yield a p-value of 0.05, we must first understand the formula for calculating a p-value. The formula for a p-value is p-value = 1 - [tex](1 - proportion)^n[/tex], where n is the sample size. By manipulating this equation, we can solve for the proportion when the p-value is equal to 0.05. We can isolate the proportion by taking the inverse of both sides of the equation, which yields: proportion = 1 - [tex](1 - 0.05)^(1/n)[/tex]. Since the sample size is 90, we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.
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