Determine the Domain and Range of each graph, then decide if the graph is exponential growth or decay.
Answers
The required,
1. figure 1, domain and range are (0, ∞) and {25000, 0}, the graph shows the exponential decay.
2. figure 2, domain and range are (-∞, ∞) and {0, ∞}, the graph shows the exponential growth.
The function which is in format f(x) =aˣ where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
As mentioned in the question, the graph of two exponential functions are given, we have to determine the domain and range of both function and justify which graph shows the exponential growth and decay.
1.
A general exponential equation is given as,
y = aˣ
Graph 1, the graph shows the exponential decay because the value of the function is getting decreasing for the domain 0 to ∞. For this domain, the value of the function starts from point A which is at 25000 and ends at point B where y = 0, so the range is {25000, 0}.
Similarly,
Graph 2 shows exponential growth,
Domain and range are (-∞, ∞) and (0, ∞).
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Related Questions
A patient recently diagnosed with Alzheimer's disease takes a cognitive abilities test and scores a 45.
The mean on this test is 52 and the standard deviation is 5. What percent of patients have his score and
below?
Answers
We can use the Z-score formula to determine what percent of patients have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
The Z-score formula is:
Z = (X - M) / SD
Where:
X = Patient's score (45)
M = Mean score (52)
SD = Standard deviation (5)
Plugging in the given values:
Z = (45 - 52) / 5
Z = -7 / 5
Z = -1.4
This Z-score of -1.4 corresponds to a percentage of approximately 9.1% of patients who have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.
It is important to note that this percentage is approximate, as it's calculated based on the standard normal distribution table which provides approximate values, and it assumes the scores of the test are normally distributed, in case this assumption is not met the result may not be accurate.
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Put 38200 in standard Form
Answers
Answer: Thirty-eight thousand two hundred.
Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:
38,000 + 200 is a good strategy to divide big numbers.
So, 38,000 = Thirty-eight thousand
And 200 = two hundred
So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)
3.82 × 10^4
Or
3.82000000 × 10^4
If a scuba diver swam from the surface at −12 1/2 feet per minute, for 4 1/2 minutes, what would be the diver’s change in elevation?
Answers
The change in elevation would be -225/4 feet
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here, Speed of scuba diver as -12¹/₂=-25/2 and time in minutes 4¹/2=9/2
Thus distance traversed -25/2 × 9/2 = -225/4
Hence, the change in elevation is -225/4 feet
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Before beginning a unit of frog anatomy, a seventh grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest). a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer.
Answers
The following method for assigning the 24 students to two equal-sized groups allows for a statistical valid comparison of the two instructional programmes.
What is instructional program?An instructional programme is a course of study that requires the completion of a specified number of course credits from a prescribed group of courses and results in a formal award.
A) Each student will be given a unique random number generated by a random number generator on a calculator, statistical software, or a random number table. The assigned numbers will be listed in ascending order. Students with the lowest 12 numbers on the ordered list will be assigned to the instructional programme that requires physically dissecting frogs.
Students with the highest 12 numbers will receive an instructional programme that simulates frog dissection using computer software.
B) By not randomizing and allowing students to self-select, there is the possibility of changes in the differences between pre test and post test scores for a specific group due to the characteristics of students who choose a particular instructional method, rather than the instructional method itself.
For example, suppose frog-loving students already know a lot about frog anatomy; these students would be less likely to show a large difference between pre and post test scores. Assume that the frog-loving students prefer the computer simulation method (perhaps because they do not like the notion of dissecting the frogs they love).
The possible low change in pre- and post-test scores for the computer simulation group could then be attributed to the students' prior knowledge of frog anatomy, rather than to the instructional method itself. Because the students entering the frog dissection group have lower pre-test scores (less prior knowledge), they are more likely to show greater improvement between pre-test and post-test scores.
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someone helpp me plsss
Answers
Answer: 2i+5
Step-by-step explanation: so (-2+14i)-(-7+12i)
Multiply (-1) to 7 and -12
Then: -2+14i+7-12i
Common numbers: (7-2) and 14i-12i
Then you get 2i+5
Use the illustration below to determine which statements are true. Select the two statements that are true statement 1: Points A, E, and C are collinear. statement 2: Lines I and m intersect at point D. statement 3: AE and DC are line segments on line I. statement 4: EA and EC are rays on the line m.
Answers
The required true statements for the given lines are 1 and 4.
What is line segments?An element or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
According to question:Statement A: E and C are co-linear.
It is true, E and C are lie in same line
statement 2: Lines I and m intersect at point D.
It is false, I and m intersect at point E.
statement 3: AE and DC are line segments on line I
It is false,because AE and DC are line segments placed in different line.
statement 4: EA and EC are rays on the line m.
It is true, as EA and EC are in same line m.
Thus, required true statements are 1 and 4.
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Answer:
1 and 4
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Answers
The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)
How to determine the correct representationsFrom the question, we have the following expression that can be used in our computation:
–3(2x – 5) < 5(2 – x)
Divide bot sides of the inequality by -1
So, we have the following representation
3(2x – 5) > -5(2 – x)
Next, we open the brackets
This gives
6x – 15 > -10 + 5x
Hence, the representation is 6x – 15 > -10 + 5x
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Complete question
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
(a) 6x – 15 > -10 + 5x
(b) 6x – 15 < -10 + 5x
(c) 3(2x – 5) > -5(2 – x)
(d) 3(2x – 5) < -5(2 – x)
What is vertically opposite angles in maths class 7?
Answers
When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles.
A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=35°, then its opposite angle is also equal to 35°. And the adjacent angle to angle X will be equal to 180 – 35 = 145°
In the given figure, ∠QOR and ∠SOP form a pair of vertically opposite angles and similarly ∠SOQ and ∠POR form such a pair. Therefore,
∠QOR = ∠SOP
∠SOQ = ∠POR
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-2(4 - 3x) - 6x = 10
Answers
Answer:
this is a problem with no solution look it up if you dont beleve me
Step-by-step explanation:
Urgent!
Use synthetic division to find the remainder
Answers
Check the picture below.
when journalizing an accounts payable account what account is debited
a. accounts payable
b. it depends on the transaction
c. cash
d. accounts receivable
Answers
How do I do this ? Because I’m having trouble with problems like this .
Answers
Answer:
[tex]\sqrt[3]{x^{9} x}[/tex]
Step-by-step explanation:
When you are multiplying powers that have the same bases (in this case x) you add the exponents. If you do not see an exponent, the exponent is 1.
9 + 1 = 10
How Do You Solve 3 linear equations with 3 variables?
Answers
The standard way to solve 3 linear equations with 3 variables is to use elimination or substitution.
-Elimination: To solve the 3 equations using elimination, add or subtract equations together to eliminate one of the variables. Keep repeating this process until you are left with one equation with one variable. Solve the equation and then use the value of the variable to substitute back into the other equations to find the values of the other variables.
-Substitution: To solve the 3 equations using substitution, pick one of the equations and solve it for one of the variables. Then substitute the value of the variable into the other equations. Keep repeating this process with the other equations and variables until you have a system of equations with one variable that you can solve. Once you have the value of the variable, substitute it back into the other equations to find the value of the other variables.
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x - (-3) + 8 - 2x - 6 =
Answers
Answer:
-x + 5
Step-by-step explanation:
x - (-3) + 8 - 2x - 6 = x - 2x + 3 + 8 - 6 = -x + 5
Answer:
[tex] \sf \: -x + 5 [/tex]
Step-by-step explanation:
Given expression,
→ x - (-3) + 8 - 2x - 6
Let's simplify the expression,
→ x - (-3) + 8 - 2x - 6
→ x + 3 + 8 - 2x - 6
→ (x - 2x) + (3 + 8 - 6)
→ (-x) + (5)
→ -x + 5
Hence, the answer is -x + 5.
Jill and beth are sisters. Jill is 1/3 of beth's age. Let b represent beth's age.Write an algebraic expression to show jill's age.
Answers
The algebraic expression to show Jill's age will be;
Jill = 1/3 x b
What is an Algebraic Expression?Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.
There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.
Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.
Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.
Coefficients - the numbers that are multiplying the variables are called coefficients.
Beth's age = b
Jill's age = 1/3 of Beth's age
Jill's age = 1/3 x b
Jill's age = 1/3b
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What is the variable in 2x 3 7?
Answers
The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms only x is the variable.
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms.
if we solve the above equation, we get
2x + 3 = 7
or, 2x = 7 - 3
or, 2x = 4
or, x = 2
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Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it. What fraction of the voters voted in favor of the measure?
Enter the fraction in simplest form.
Answers
The fraction of the voters who voted in favor of the measure will be 1/5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it.
The fraction of the voters who voted in favor of the measure will be given as,
⇒ 20%
⇒ 20 / 100
⇒ 1 / 5
The fraction of the voters who voted in favor of the measure will be 1/5.
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whats the awnser i need help
Answers
answer:10
Step-by-step explanation:
the graph show it is 1 hour and shows 10 miles and it continues
Answer:
it should be that the miles are 10 times the amount of hours
Step-by-step explanation:
Considering that to bike 10 miles it took 1 hour and to bike 20 miles it took 2 hours it will continue going like that so the miles will always be 10 times the amount of hours
Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Answers
The length of each of the four walls of the birdhouse is 5.5 inches, so the total length of all four walls is approximately 4 x 5.5 = 22 inches. Therefore, Javi's board is long enough to be cut into the four walls of the birdhouse.
What is the wall equation?Walls. Utilize the conventional equation Length x Width = Area to get the area of a wall. Next, apply the same calculation to each window and door's specific area. Subtract the area of the windows and doors from the overall size of the wall once you have recorded all of these dimensions.
The birdhouse must have four walls that are each 5.5 inches thick.
one room needs four walls because of the length of its four walls.
4*5.5=22
A board measuring 24.5 inches long is in Javi's possession. In order to cut through the birdhouse's four walls, it is sufficient.
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A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag.
Answers
In binomial distribution, the probability is .2, P(x is greater than or equal to 1)>.75, find the least possible value of n
Answers
The approximate shape of the sampling distribution of the sample will be normal.
Option E is correct.
Sampling distribution:
It is a statistic that determines the probability of an event based on data from a small group within a large population.
Given that, is greater than or equal to 15 and is greater than or equal to 15.
and
So that the new mean and standard deviation will be,
Thus, the approximate shape of the sampling distribution of the sample will be normal.
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I'm need help asap! i dont get the question, i would appreciate it if somebody could help me( giving brainilest & 20 points)!!!
Look at picture below
Answers
Answer:
215/100
Step-by-step explanation:
it is asking for improper fraction
improper fractions are just the bottom number multiplied by the number outside of the fraction so in this case it is
2*100 which is 200 then add that to the top number
which leaves you with 215/100
Does this graph represent a function?
Does this graph represent a linear rule?
Explain your answer!
PLS HELP THIS IS TEST
Answers
Answer:
it is a function because it passes a vertical line test.
Step-by-step explanation:
what is x if 2/6+x=11/18
Answers
Answer:
multiply top and bottom of 2/6 to get 6/18, then subtract the answer by 6/18 , you get 5/18
Step-by-step explanation:
Answer:
x = 5/18
Step-by-step explanation:
what is x if 2/6+x=11/18
2/6 + x = 11/18
x = 11/18 - 2/6
x = 5/18
----------------------------
check2/6 + 5/18 = 11/18
11/18 = 11/18
The answer is good
How do you solve 9x 7 =- 7?
Answers
The value of x is 0
Now, According to the question:
Let's know:
How to find the value of 'x'
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
The given equation is:
9x - 7 = -7
To solve the value of 'x'
9x - 7 = -7
Add 7 on both sides:
9x - 7 + 7 = -7 + 7
9x = 0
x = 0/9
x = 0
Hence, The value of x = 0
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The complete question is this:
How do you solve 9x - 7 = -7
2 diagonals of a regular nonagon (a 9-sided polygon) are chosen. What is the probability that their intersection lies inside the nonagon
Answers
The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answers
Answer: 5$ for 52 days
Step-by-step explanation: (5 x 52) + 90 = 350
Gabe and Bridgette are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare.
p = the number of people Gabe and Bridgette will be able to serve
m = the number of meals Gabe and Bridgette prepare
Which of the variables is independent and which is dependent?
Answers
Answer:
The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.
Step-by-step explanation:
In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.
Answer:
independent variable = m
dependent variable = p
Step-by-step explanation:
The number of people they are able to serve depends on the number of meals they prepare.
Which expression is equivalent to 12x2+x−20
Answers
If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.
What other expression is the same as 3 5?6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.
The given quadratic expression 12x^2+x-20
now, 12x^2 + 16x - 15x - 20
4x (3x+4) - 5(3x+4)
(4x-5) (3x+4)
the root of the equation is (4x-5) (3x+4)
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23
Luke invested £4000 in a savings account for 3 years.
Compound interest was paid at a rate of 1. 8% each year.
Alexa also invested £4000 in a savings account for 3 years.
Simple interest was paid at a rate of 1. 8% each year.
Luke got more interest than Alexa in total over the 3 years.
How much more?
You must show all your working.
Answers
The amount luke made more than alexa is $3.91 .
What is simple interest ?
simple interest can be defined as the ratio of product of principal amount , rate and time and 100.
Luke investment,
This is compound interest so the future value formula will be used:
= Amount * ( 1 + rate) ^ no. of years
= 4,000 * ( 1 + 1.8%)³
= $4,219.91
Alexa investment:
Simple interest is calculated with the formula:
= Amount * ( 1 + rate * time)
= 4,000 * ( 1 + 1.8% * 3)
= $4,216
Amount Luke made more than Alexa:
= 4,219.91 - 4,216
= $3.91
Hence , The amount luke made more than alexa is $3.91 .
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