Except than x = 1, all real numbers fall within the function's domain.
Why can't a domain consist entirely of real numbers?Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.
The rational function r(x) = 2x/(x-1) is defined as follows.
So, we set the denominator to zero and solve for x in order to determine the domain of r(x):
x - 1 = 0
x = 1
Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.
We can express the domain as follows in interval notation:
(-∞, 1) U (1, ∞)
Except than x = 1, all real numbers fall within the function's domain.
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Question:
Which of the following correctly describes the domain of the function shown below?
r(x) = 2x x-1
A. {x:x0}
B. {x: x = 1}
c. x all .real .numbers}
D. xx1}
Which of the contexts below represents exponential growth?
A town's population shrinks at a rate of 8.1% every year.
A taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile.
A town's population grows at a rate of 4% every year.
A radioactive compound decays at a rate of 5% per hour.
The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The context that represents exponential growth is "A town's population grows at a rate of 4% every year."
Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.
As the population grows, the growth rate also increases, resulting in an exponential increase over time.
Let P(t) be the population of the town after t years, where t is a positive integer.
The exponential function that models the population growth is -
[tex]P(t) = P0 \times (1 + r)^t[/tex]
where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.
In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.
Therefore, the exponential function for the town's population growth is -
[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]
Simplifying the expression, we get -
[tex]P(t) = P0 \times 1.04^t[/tex]
This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.
In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).
Therefore, the exponential growth is displayed by town's population growing 4% every year.
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assume that 50 million households in the u.s. watched a particular show at 9:00 pm, and 90 million households had their television sets turned on at 9:00 p.m. calculate the share of audience.
The share of audience for the particular show at 9:00 pm is 55.56% for 50 million households.
We need to know the number of households that watched the programme and the total number of households with televisions on at 9:00 p.m. in order to determine the proportion of audience for that programme.
In this instance, it is stated that 90 million homes had their televisions on at 9:00 p.m. in addition to 50 million households watching the programme. Consequently, the following formula can be used to determine the show's viewership share:
Share of audience is calculated as follows: (Number of households that watched the programme / Total number of households with TVs on) x 100%
= 100% x (50 million / 90 million)
= 55.56%
As a result, 55.56% of the audience watched the specific show at 9:00 p.m. This indicates that the programme was viewed by more than half of the homes with on-air televisions at the time.
The share of audience is a crucial measurement in television ratings since it aids networks and advertisers in understanding how popular a show is and how far it might be able to reach the intended audience.
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which answer refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time? group of answer choices
The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.
Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.
Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.
Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.
Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.
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two positive whole numbers greater than 1 multiply to 576 and have no common factors other than 1. what is the sum of those two numbers?
Thus, the two positive whole numbers that are greater than one multiply to 576 and share only the number one in common is 5.
Explain about the positive whole numbers?One of the categories that mathematicians have created for numbers is titled whole numbers, and it contains all of the numbers from 0 to infinity.
The specific class or collection of numbers known as whole numbers includes:
Are all positive numbers with no fractional or decimal parts, including zero.Positive numbers with no decimal or fractional portions are referred to as whole numbers, including zero. They are numerical representations of whole, unbroken things. The set of whole numbers is mathematically represented by the numbers 0 through 9.Two positive whole numbers greater than 1 are 2 and 3.
2 and 3 does not have any common factor except 1.
sum of 2 and 3 = 5
Thus, the two positive whole integers that are greater than one multiply to 576 and share only the number one in common is 5.
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What function is represented by the graph
The function [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.
What is graph?
A graph is a visual representation of data or a mathematical function, usually plotted on a coordinate plane. It is a way to display information in a clear and concise manner, making it easier to analyze and interpret.
From the graph, it can be observed that the function intersects the x-axis at three points, namely x=-1, 2, and 5. Therefore, these values are considered to be the zeros of the function.
According to the definition, if c is a zero of a function f(x), then (x-c) is a factor of f(x). Applying this definition, we can infer that (x+1), (x-2), and (x-5) are the factors of the given function.
In summary, the zeros of the function are -1, 2, and 5, and the corresponding factors of the function are (x+1), (x-2), and (x-5).
Therefore the function [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.
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It takes Rosita 32 hours to drywall a basement by herself and 18 hours if Paola helps her. How long would it take Paola to drywall the basement by herself? Round your answer to the nearest hour.
Clark and bruce went to taco hut for lunch. Clark bought 4 burriots and 5 tacos. Which cost him $13. Bruce bought 5 burritos and 3 tacos, which cost him $13. Determine how much a burriot cost at taco hut
A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.
From the problem, we know that:
4b + 5t = 13 (for Clark)
5b + 3t = 13 (for Bruce)
We want to determine the cost of a burrito, so we can solve for "b" using the second equation:
[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]
Now we can substitute this expression for "b" into the first equation:
[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]
So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":
[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]
Therefore, a burrito costs $2 at Taco Hut.
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The radius of a circle is 3 miles. What is the circle's area?
Answer:
A≈28.27mi²
Step-by-step explanation:
[tex]A=\pi r^2[/tex]
[tex]\pi \times 3^2[/tex]
≈ 28.27433mi²
A≈28.27mi²
The table shows the ratios of black and white keys on pianos of various size
The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.
The ratio of black to white keys of Piano of different sizes are as follow,
Black A 36 63 90
White 13 B 91 C
From the table of black and white keys relation of proportionality is equal to,
( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )
This implies ,
( A / 13 ) = ( 63 / 91 )
⇒ A = ( 63 / 91 ) × 13
⇒ A = ( 9 / 13 ) × 13
⇒ A = 9
Similarly,
( 36 / B ) = ( 63 / 91 )
⇒ B = 36 × ( 91 / 63 )
⇒ B = 36 × ( 13 / 9 )
⇒ B = 52
And
( 63 / 91 ) = ( 90 / C )
⇒ C = 90 × ( 91 / 63 )
⇒ B = 90 × ( 13 / 9 )
⇒ B = 130
Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.
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The above question is incomplete, the complete question is:
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
where is the water table in a swamp? group of answer choices well below the surface. at the surface. well above the surface. generally, 2 miles below the surface.
Generally, the water table in a swamp is located 2 miles below the surface.
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the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is:
The probability that the number of calls between 2:00 pm and 2:10 pm is exactly 200 is 0.000002204.
This can be calculated using the Poisson distribution. The Poisson distribution is used to model the probability of a given number of events occurring in a given time interval.
The Poisson equation is P(x) = (λ^x e^-λ)/x!
where λ is the expected number of occurrences per interval.
For this question, λ = 3/min, since the rate of calls to the computer software help desk is 3 per minute.
Plugging λ = 3/min into the Poisson equation, we get
P(x) = ((3/min)^200 e^-(3/min))/200!.
This simplifies to
P(x) = 0.000002204.
The probability of having exactly 200 phone calls to a computer software help desk in the 10-minute period from 2:00 pm to 2:10 pm is 0.000002204.
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5.
Ka'mya is planning a zoo which will be built on the Oregon coast. Each carnivore (a meat eating animal) will
cost $30 each week to feed, and each herbivore (a plant eating animal) will cost $10 each week to feed.
Her starting budget for feeding all of the animals is $360 per week. The location for the zoo will have
room for 24 animals. How many carnivores and how many herbivores should she plan on having in her zoo?
Answer:
6 carnivore's and 18 herbivore's
Step-by-step explanation:
How to elimination 18x-6y=-20 -9x+3y=15
The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.
What is an elimination?
To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.
Let's start with the given equations:
18x - 6y = -20
-9x + 3y = 15
We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:
18x - 6y = -20
-18x + 6y = 30
Now we can add the two equations together:
0x + 0y = 10
This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.
Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.
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Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.
24÷4=6
24
÷
4
=
6
can be thought of as 24
24
broken into 4
4
groups of 6
6
each
The equation 24÷4=6 can be thought of as 24 broken into 4 groups of 6 each. This can be shown mathematically as follows: 24/4 = 6.
The division 24 ÷ 4 = 6 can be represented as 24 divided into 4 groups of 6 each. Therefore, each group contains 6 elements.
Another way to represent this division is by using a division box. In this case, 24 is the dividend, 4 is the divisor, and 6 is the quotient. Here's how to write it in the division box format:``` 6|24----4```The divisor is outside the division box, while the dividend is inside the division box. Then, we divide 24 by 4 to obtain 6. Therefore, 24 ÷ 4 = 6.
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Kira is choosing between two exercise routines.
In Routine #1, she burns 24 calories walking. She then runs at a rate that burns 15.5 calories per minute.
In Routine #2, she burns 52 calories walking. She then runs at a rate that burns 9.9 calories per minute.
For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2?
Use t for the number of minutes spent running, and solve your inequality for t.
For any value of inequality for t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.
What is inequality?
In mathematics, an inequality is a statement that compares two quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Let's start by calculating the total number of calories burned in each routine as a function of the number of minutes spent running:
Routine #1:
Total calories burned = 24 + 15.5t
Routine #2:
Total calories burned = 52 + 9.9t
To find the point where Routine #1 burns at most as many calories as Routine #2, we need to solve the inequality:
24 + 15.5t ≤ 52 + 9.9t
Simplifying this inequality, we get:
5.6t ≤ 28
Dividing both sides by 5.6, we get:
t ≤ 5
Therefore, for any value of t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.
So the answer is: t ≤ 5.
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John's parents deposited $1000 into a savings account as a collage fund when he was born. How much will john have in this account after 18 years at a yearly simple interest rate of 3. 25%?
John's parents deposited 1000 into a savings account as a college fund when he was born. We need to find out how much John will have in this account after 18 years at a yearly simple interest rate of 3.25%.
We can use the formula for simple interest to solve this problem.
The formula for simple interest is:
I = PRT
Where,I = interest
P = principal (the initial amount of money)
R = rate of interest (as a decimal)
T = time (in years)
We are given that John's parents deposited 1000 when he was born. So, P = 1000. The interest rate is 3.25% per year, which is 0.0325 as a decimal. And we are given that the time is 18 years, so T = 18 years.Using the formula for simple interest, we can find the amount of interest earned:
I = PRTI = (1000)(0.0325)(18)I = 585
We can then add the interest earned to the principal to find the total amount of money in the account after 18 years:
A = P + IA = 1000 + 585A = 1585
Therefore, John will have 1585 in this account after 18 years at a yearly simple interest rate of 3.25%.
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Pls help answer with good detailed explanation
Juan spent 10 minutes on his history homework and 3 minutes per question on his math homework. Which graph shows the total homework time, t, related to the number of math questions, q?
Discrete graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 5 to 40, on the vertical axis. Solid circles appear at points (0, 10), (1, 13), (2, 15), (3, 19), (4, 22), (5, 25), (6, 29), (7, 32), (8, 34).
Continuous graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 5 to 40, on the vertical axis. Solid circles appear at points (0, 10), (1, 13), (2, 15), (3, 19), (4, 22), (5, 25), (6, 29), (7, 32), (8, 34).
Discrete graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 3 to 24, on the vertical axis. Solid circles appear at points (0, 0), (1, 3), (2, 6), (3, 9), (4, 12), (5, 15), (6, 18), (7, 21), (8, 24).
Answer:Graph attached below. : Given : Juan spent 10 minutes on his history homework and 3 minutes per question on his math homeworkWe have to plot the graph that shows the total homework time, t, related to the number of math questions, q.Since, t denotes the total homework time taken by Juanand q denotes the number of math questions done by JuanThen we can represent the situation using a linear equation.Since he spent 10 minutes on his history homework and 3 minutes per question on his math homework.Then q questions take 3q timeand 10 minutes are fixed so, Total time is given by equation t = 10 + 3qAnd graph for the equation is attached below.
Step-by-step explanation:
Answer: Its A (the one all the way to the left)
explanation: Just guessed
Choose the statements that describe characteristics of a probability distribution? Select all that apply.
A. Half of the possible outcomes have associated probabilities grater than 0. 5.
B. The probability of an outcome is between 0 and 1.
C. The sum of the probabilities of all possible outcomes is 1.
D. The distribution is symmetrical.
E. The outcomes are mutually exclusive
B. The probability of an outcome is between 0 and 1. C. The sum of the probabilities of all possible outcomes is 1.
Option B is correct because probability values must be between 0 and 1.
Option C is correct because the sum of the probabilities of all possible outcomes must equal 1.
Option A is incorrect because it is not necessary for half of the possible outcomes to have probabilities greater than 0.5.
Option D is incorrect because the distribution does not have to be symmetrical.
Option E is incorrect because the outcomes can have common events and can be dependent.
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F(x)=l3xl+3
g(x)=-x+8x-5
Represent the interval where both functions are increasing on the number line provided
the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:
To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.
The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:
F'(x) = 3x/|x|
Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.
Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:
g'(x) = -1 + 8
Simplifying the expression, we get:
g'(x) = 7
Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.
To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.
Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:
<=====o------------------------>
x<0 x>0
In this interval, both functions are increasing as x becomes more negative.
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Of the following, which is NOT an immediate goal of treatment for individuals with anorexia nervosa?
helping them recover from malnourishment
helping them eat normally again
helping to make family changes within the dysfunctional system
helping them regain their lost weight
The answer is: "helping to make family changes within the dysfunctional system."
Step-by-step explanation:
While family-based therapies can be effective for treating anorexia nervosa, helping to make family changes within the dysfunctional system is not an immediate goal of treatment for individuals with anorexia nervosa.
The immediate goal of treatment for individuals with anorexia nervosa is to restore their physical health, which includes helping them recover from malnourishment, helping them eat normally again, and helping them regain their lost weight.
Once their physical health is stabilized, additional therapies may be recommended to address the psychological, emotional, and social factors that contribute to their eating disorder, which may include family-based therapies.
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PLEASE HURRY !! I NEED HELP!!!
Answer:$10
Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?
He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.
what is the probability of obtaining at least one tail when a coin is flipped six times? (enter the probability as a fraction.)
PLEASE HELP ME
A pizza shop surveyed a random group of customers to determine their favorite pizza topping. Out of 400 people, how many would you expect to say their favorite topping is sausage?
The percent that reported mushroom as their favorite from the pizza shop survey would be 10 %.
The percent that instead reported cheese or pepperoni as their favorite is 62.5 %.
Out of 400 people, the number that would say their favorite was sausage is 50 people .
How to find the number of people in the survey ?The percent that prefer mushroom would be:
= Number of those who chose mushroom / Number surveyed
= 8 ( 35 + 8 + 15 + 12 + 10 )
= 8 / 80
= 10 %
The percentage that instead chose cheese or pepperoni:
= ( 15 + 35 ) / ( 35 + 8 + 15 + 12 + 10 )
= 50 / 80
= 62.5 %
The number out of 400 that would be expected to choose sausage :
= 10 / ( 35 + 8 + 15 + 12 + 10 ) x 400
= 50 people
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suppose 58% of recent college graduates plan on pursuing a graduate degree. thirteen recent college graduates are randomly selected. a. what is the probability that no more than four of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) b. what is the probability that exactly seven of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) c. what is the probability that at least six but no more than ten of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.)
The probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437. b. X= 7 = 0.2004.
What is binomial distribution?With a set number of independent trials, each of which has just two potential outcomes—success or failure—a binomial distribution defines the number of successes. The chance of success, represented by p, and the number of trials, denoted by n, are the two factors that define the distribution.
Given that, 58% of recent college graduates plan on pursuing a graduate degree.
Using the binomial probability formula we have:
[tex]P(X \leq 4) = \sum (i = 0 \to 4) (n C i) * p^i * (1 - p)^{(n-i)}\\\\[/tex]
Here, n = 13, p = 0.58.
[tex]P(X \leq 4) = Σ(i = 0 \to 4) (13 C i) * 0.58^i * (1 - 0.58)^{(13-i)}= 0.1437[/tex]
Hence, the probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437.
b. For X = 7:
[tex]P(X = 7) = (13 C 7) * 0.58^7 * (1 - 0.58)^{(13-7)}= 0.2004[/tex]
Hence, the probability that exactly seven of the college graduates plan to pursue a graduate degree is approximately 0.2004.
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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
Identify the two choices that best completes the statement below.
What is the sum of the first 10 terms of the series 1 + 2 + 4 + 8...?
The sum of the first 10 terms of the geometric progression that is given in the question is 1023.
What is geometric progression ?
Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.
The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.
The sum of the first n terms of a geometric progression is given by the formula:
[tex]S_n = a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Using this formula, we can find the sum of the first 10 terms of the given series as:
[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]
[tex]= 1(1 - 1024) / (-1)[/tex]
[tex]= 1023[/tex]
Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.
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What is the product of (3x+2) and (x - 7) ?
I have a square piece of card. I cut a triangle from each corner so that the remaining card is in the shape of a regular octagon. The perimeter of the regular octagon is 32cm. Work out length y
The required length of y representing the length of the cut piece from each corner of triangle to form regular octagon is equal to 2√2cm.
Let us consider the length of the side of the square card be x
Cut the corners of the triangle of length y cm.
Then as triangles at the corner are right angled triangle.
Using Pythagoras theorem we have,
Each side of the regular octagon is same as hypotenuse .
Hypotenuse = √y² + y²
⇒Hypotenuse = y√2
Length of each of regular octagon = y√2
Perimeter of the octagon = 8y√2
⇒8y√2 = 32
⇒ y = 4/√2
⇒ y = 2√2cm.
Therefore, the length of y with the given perimeter of the regular octagon is equal to 2√2cm.
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the angle below has a measure of 5.8 radians. determine the exact coordinates of the terminal point ( x , y ) .
Exact coordinates of the terminal point (x, y) are (-3.40, 4.71).
Let's dive deeper into the details below.
The angle below has a measure of 5.8 radians. The exact coordinates of the terminal point (x, y) can be determined by using trigonometry.
First, we must remember that the formula for the x-coordinate is x = r cos θ, where r is the length of the radius and θ is the measure of the angle. Therefore, we can calculate the x-coordinate by plugging in the radius (which is given) and the measure of the angle (5.8 radians) into the formula:
x = 5.8 cos (5.8) = 5.8 × -0.5806 = -3.40
Now, we must use the formula for the y-coordinate which is y = r sin θ. Plugging in the radius and the measure of the angle, we can calculate the y-coordinate:
y = 5.8 sin (5.8) = 5.8 × 0.8139 = 4.
Therefore, the exact coordinates of the terminal point (x, y) are (-3.40, 4.71).
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