The number of frogs in a certain lake is inversely related to the number of snakes in the lake. If x represents the number of snakes in the lake, then y = 100/x represents the number of frogs in the lake. Describe the reasonable domain and range values. Graph the function.
Answers
1. Domain: The set of natural numbers / Range: The set of natural numbers
2. Shown below
Step-by-step explanation:1. Domain and Range.In this problem, we have that the number of frogs in a certain lake is inversely related to the number of snakes in the lake. Hence we are facing an Inverse Variation, so this means that if the number of snakes in the lake increases then the number of frogs in the lake decreases, because snakes eat frogs! The function that describes this is a rational function defined as:
[tex]y=\frac{100}{x}[/tex]
Where:
[tex]x: \ represents \ the \ number \ of \ snakes \ in \ the \ lake \\ \\ y: \ represents \ the \ number \ of \ frogs \ in \ the \ lake[/tex]
As you can see, [tex]x[/tex] is in the denominator, therefore [tex]x\neq 0[/tex]. Since we need to provide a reasonable domain, we say that the domain is the set of natural numbers and this doesn't include the number 0. Why aren't negative values included in the domain as well? Well, although negative values are included in the function, they aren't reasonable because [tex]x[/tex] represents the number of snakes and you always get positive numbers when counting things.
To get the range, let's take the inverse of this function, so:
[tex]y=f(x)=\frac{100}{x} \\ \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{100}{y} \\ \\ \\ Isolate \ y: \\ \\ y=\frac{100}{x} \\ \\ f^{-1}(x)=\frac{100}{x}[/tex]
So the domain of [tex]f^{-1}(x)[/tex] is the range of our given function [tex]y=f(x)[/tex]. As you can see the inverse function is the same as our given function, then the range is the set of natural numbers as well.
2. Graph.First of all, we can define the pattern of the rational function as:
[tex]y=g(x)=\frac{1}{x}[/tex]
So our function will be:
[tex]f(x)=100g(x)=100\frac{1}{x}=\frac{100}{x}[/tex]
So the graph of [tex]f(x)[/tex] will be the same graph of [tex]g(x)[/tex] but it's been stretched vertically by a constant of 100, that is, each y-value is multiplied by 100. Also, since [tex]x \neq 0[/tex] and [tex]y \neq 0[/tex] then at [tex]x=0[/tex] there is a vertical asymptote and at [tex]y=0[/tex] there is an horizontal asymptote. Finally, the graph is shown below for [tex]x>0 \ and \ y>0[/tex], but remember: Whenever [tex]x \ and \ y[/tex] are natural numbers.
Answer:
Both the number of snakes and the number of frogs will be positive, so positive values are reasonable for the domain and range.
Step-by-step explanation:
Related Questions
If a cup of coffee is at 90°C and a person with a body temperature of 36°C touches it, how will heat flow between them?
from the hand to the cup
from the cup to the hand
from the cup to the surrounding air
from the hand to surrounding air
Answers
Answer:
b
Step-by-step explanation:
Answer: From the cup to the hand
Given that the cup of coffee is at 90°C and the person has a body temperature of 36°C.
We know that 36 < 90.
So the temperature of the person is less.
The heat will flow from the higher temperature towards the lower temperature.
So the heat should flow from the cup to the hand.
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Evaluate (x + y)0 for x = -3 and y = 5.
Answers
Answer:
0
Step-by-step explanation:
you substitute:
(x+y)= (-3+5)= (5-3)= 2(0)= 0
For the polygon, use Euler's Formula to find the missing number. Faces:? edges:13 vertices:8
Answers
Answer:
F = 7
Step-by-step explanation:
Euler's formula relating faces, edges, vertices is
V - E + F = 2
8 - 13 + F = 2
- 5 + F = 2
F = 5 + 2
F = 7
Shelley drove from New Haven, Connecticut, to New York City in 90 minutes. Which equation relates the distance she traveled to her speed?
A.
distance = speed + 90
B.
distance = speed × 90
C.
distance − speed = 90
D.
distance × 90 = speed
Answers
The correct answer is B.
Distance = speed x 90
Answer:
It’s b
Step-by-step explanation:
Divide the following complex numbers (2 + i ) ÷ ( 1 - 4i )
Answers
-2/17 + 9i/17 fractions
Answer:
- [tex]\frac{2}{17}[/tex] + [tex]\frac{9}{17}[/tex] i
Step-by-step explanation:
Multiply the numerator/denominator by the complex conjugate of the denominator.
The conjugate of 1 - 4i is 1 + 4i
[tex]\frac{(2+i)(1+4i)}{(1-4i)(1+4i)}[/tex] ← expand factors
= [tex]\frac{2+9i+4i^2}{1-16i^2}[/tex] → i² = - 1
= [tex]\frac{2+9i-4}{1+16}[/tex]
= [tex]\frac{-2+9i}{17}[/tex]
= - [tex]\frac{2}{17}[/tex] + [tex]\frac{9}{17}[/tex] i
Spencer is carrying out a survey of the bear population at Yellowstone National Park. He spots 2 bears - one has a light colored coat and the other has a dark coat.
1- Assume that there are equal numbers of male and female bears in the park. What is the probability that both bears are male?
2- If the lighter colored bear is a male, what are the odds that both are male?
Answers
Answer:
1. 1/4
2. 1/2
Step-by-step explanation:
If there are equal numbers of males and females, we can simplify that by saying there's one male and one female for each coat color.
1. What's the probability that both are males?
Well, there's a 1/2 chances the light-colored coat bear is a male and there's also a 1/2 chances the dark-colored coat bear is a male. So, we can make this reference table:
Light Dark
Male Male
Male Female
Female Male
Female Female
As you can see, the probability that both of the spotted bears are males is 1/4 (1/2 * 1/2).
2. If the light-colored bear, what are the odds both are males?
If we know for sure the light-one is male, then there's 1/2 chances the other is too, refer to the table above to verify.
The graphs of y = x2 and y = x2 + c are shown below.
Answers
Where’s the question though :/
Which expression is equivalent to 4/9(2n-3)
Answers
Answer:
[tex]\large\boxed{\dfrac{8}{9}n-\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{9}(2n-3)\qquad\text{use the distributive property}\\\\=\left(\dfrac{4}{9}\right)(2n)+\left(\dfrac{4}{9}\right)(-3)=\dfrac{8}{9}n-\dfrac{4}{3}[/tex]
Equivalent expression are the equation which have the same identical solution for the variable but the way of representation is different. The given expression in the problem is equivalent to the,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Thus the option 4 is the correct option.
Given Information-The given expression [tex]f(n)[/tex] is,
[tex]f(n)=\dfrac{4}{9} (2n-3)[/tex]
Equivalent expression-Equivalent expression are the equation which have the same identical solution for the variable but the way of representation is different.
Open the bracket of above equation by multiplying the fraction with the numbers inside the bracket.
[tex]f(n)=\dfrac{4\times 2n}{9} -\dfrac{4\times 3}{9}[/tex]
[tex]f(n)=\dfrac{8n}{9} -\dfrac{12}{9}[/tex]
[tex]f(n)=\dfrac{8n}{9} -\dfrac{4}{3}[/tex]
Fraction 4/c can be written as the mixed number. Thus,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Hence the given expression in the problem is equivalent to the,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Thus the option 4 is the correct option.
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[tex]10 {x}^{2} - 6 = 144 [/tex]
Answers
Answer:
[tex]\large\boxed{x=\pm\sqrt{13}}[/tex]
Step-by-step explanation:
[tex]10x^2-6=144\qquad\text{add 6 to both sides}\\\\10x^2=130\qquad\text{divide both sides by 10}\\\\x^2=13\to x=\pm\sqrt{13}[/tex]
What is the radius of a circle whose equation is x^2+y^2+8x-6y+21=0
Answers
Answer:
2
Step-by-step explanation:
If m<13=m<15=m<7, what conclusions can you make about lines a, b, c, and d?
Answers
Answer:
option D
Lines a and b are parallel and lines c and d are parallel.
Step-by-step explanation:
Given in the question four lines a , b, c, d.
Prove oneIf two parallel lines (a,b) are cut by a transversal(d), then corresponding angles m<7 and m<15 are congruent.
They are know as corresponding angles.
Hence lines a and b are parallel.
Prove twoIf two parallel lines (c,d) are cut by a transversal(d), then corresponding angles m<13 and m<13 are congruent.
They are know as corresponding angles
Hence lines c and d are parallel
Answer:
it has to be a is parallel to b
Step-by-step explanation:
what is the slope of a line paralle to a line with a slope of -5 /6
Answers
Answer:
-5/6
Step-by-step explanation:
in order for a line to be parallel to the other it must have the same slope (angle)
The slope of a line parallel to a line with a slope of -[tex]\frac{5}{6}[/tex] is also −[tex]\frac{5}{6}[/tex], as parallel lines have identical slopes to demonstrate a consistent rate of change.
The question concerns the concept of parallel lines in coordinate geometry. When two lines are parallel, they have the same slope. Therefore, a line parallel to another line with a slope of −[tex]\frac{5}{6}[/tex] will also have a slope of −[tex]\frac{5}{6}[/tex]. This value reflects the consistent rate of change in the y-value per unit of change in the x-value along the line.
It's important to remember that this slope is unchanging for a given straight line, as it represents the regression line: a summary of the average relationship between two variables in a scatter diagram.
Someone please help me with this problem
Answers
Answer:
corresponding
Step-by-step explanation:
ANSWER
corresponding.
EXPLANATION
We can trace an F-pattern for <5 and <7.
These two angles are on corresponding sides of the F-pattern.
The two lines l and m are parallel lines.
F-pattern angles form on parallel lines are called corresponding angles.
The correct choice is the last option.
Four points from a line are shown in the table below.
INPUT OUTPUT
lol 3
| 1 | 2
12 . 1
3 .
Use the table to determine the slope-intercept form of the equation of the line.
CA. y = 3x-1
B.
y = x + 3
c. y = 3x + 1
D.
y = -x + 3
Answers
Answer:
Correct choice is D. [tex]y=-x+3[/tex].
Step-by-step explanation:
pick any two points from the table say (0,3) and (1,2)
Now we we can use both points to find the equation of line.
slope [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-3}{1-0}=\frac{-1}{1}=-1[/tex]
now plug slope m=-1 and any point say (0,3) into point slope formula
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-3=-1\left(x-0\right)[/tex]
[tex]y-3=-1\left(x\right)[/tex]
[tex]y-3=-x[/tex]
[tex]y=-x+3[/tex]
Hence correct choice is D. [tex]y=-x+3[/tex].
Suppose the population mean of a sample of the nest counts is 28 examples of 6 - 9 nestlings with a standard deviation of 3. Which of the following would be a reasonable inference to make about the sample?
The population and the sample statistics should be the same.
The population statistics over-counted the number of nestlings.
The sample represents the population.
The sample undercounts the population of nestlings.
Answers
Answer:
The sample undercuts the population of nestings
Step-by-step explanation:
The sample undercounts the population of nestlings would be a reasonable inference to make about the sample option, fourth is correct.
What are population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
We have:
The population mean of a sample of the nest counts is 28 examples of 6 – 9 nestlings, with a standard deviation of 3.
We have given reasonable inference to make about the sample:
The population and the sample statistics should be the same.The population statistics over-counted the number of nestlings.The sample represents the population.The sample undercounts the population of nestlings.As per the data given, we can say that The sample undercounts the nestling population.
Thus, the sample undercounts the population of nestlings would be a reasonable inference to make about the sample option fourth is correct.
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Sketch the quadratic function f(x) = -2x2 + 4x + 6. Which key feature of the graph is not true?
A) maximum (1, 8)
B) y-intercept (0, 6)
C) x-intercept (3, 0)
D) x-intercept (-2, 0)
Answers
Answer:
D is false
Step-by-step explanation:
f(x) = -2x2 + 4x + 6 should be written with a " ^ " to indicate exponentiation:
f(x) = -2x^2 + 4x + 6.
Because of the - sign, we know that the graph of this function opens down, so there is a maximum at the vertex. We can determine the x-value at the vertex by using the formula x = -b/(2a), which here is x = -4/(2*-2), or 1.
Evaluating f(x) = -2x^2 + 4x + 6 at x = 1, we get -2 + 4 + 6, or 8. So statement A is true: there's a max at (1, 8). This is also the vertex of the graph.
Let's now look at C and D. We evaluate f(x) at x = 3 and x - 2. If the output (y) value is 0, we know we have an x - intercept:
f(3) = -2(9) + 4(3) + 6 = 0. Yes, C is true, (3, 0) is an x-intercept.
f(-2) = -2(4) - 8 + 6 is not 0. Therefore D is false; (-2, 0) is not an x-intercept.
Look at B: Let x = 0 and find y: it's 6. Thus, (0, 6) is the y-intercept. B is true.
Answer:
B) x + 12 < 8 − 3x
Step-by-step explanation:
PLEASE HELP ASAP!! WILL MARK BRAINLIEST
Answers
Answer:
the answer is b
Step-by-step explanation:
because the angle of 45 with the x and the answer once the graph have the number we can find the expressopm
which of the following graphs could represent a quadratic function
Answers
Option: A is the correct answer.
A. Graph A
Step-by-step explanation:A quartic function is a function whose degree is 4 i.e. even.We know that for any even degree function the end behavior of the graph is in the same direction i.e. when x tends to infinity and minus infinity then the function goes in the same direction.And for any odd degree function the end behavior of the graph goes in the opposite direction.Among the given graphs Graph A is such that both the ends of the graph goes in the same direction while in other they goes in opposite direction.
Hence, the correct answer is:
Graph A
Sharon wants to start a savings account with the money she earns selling scented candles. She already has $50 and would like to save at least $90. She earns $2 for each candle she sells. How many candles should Sharon sell in order to meet her goal?
Answers
Answer:
She must sell as least 20 candles
Step-by-step explanation:
Sharon has 50 dollars
She makes 2 dollars per candle
Money in 50+2c
She needs at least 90
90≤ 50+2c
We need to solve this inequality
Subtract 50 from each side
90-50≤ 50-50+2c
40 ≤ 2c
Divide by 2
40/2 ≤ 2c/2
20 ≤ c
She must sell as least 20 candles
90-50=40 40 divided by 2 = 20. sharon needs to sell 20 candles
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Answers
Answer:
Therefore, the plant that grew at a faster rate would be Megan’s at 2.5 inches per week.
Step-by-step explanation:
Megan's rate = 12 - 4.5 / 4 -1 = 2.5 inches per week
Suzanne's rate = 11 - 5 / 4-1 = 0.5 inches per week
Without the actual growth measurements, we cannot make a comparison or identify which plant grew faster.
Using the examples:
Suzanne's plant grew at a faster rate (1.5 inches/week) compared to Megan's plant (1 inch/week).
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To determine whose plant grew at a faster rate and what was the rate, we need information about the growth of their plants over the four-week period.
Without this information, we cannot determine the rate of growth or compare the rates of growth of their plants.
Assuming that we have the required information about their plant growth, we can compare the rates of growth of their plants by calculating the average weekly growth rate of each plant.
The plant with a higher average weekly growth rate grew at a faster rate.
For example:
If Megan's plant grew by 4 inches over four weeks, its average weekly growth rate would be:
The average weekly growth rate of Megan's plant = (Total growth in 4 weeks) / (Number of weeks)
= 4 inches / 4 weeks
= 1 inch/week
Similarly,
If Suzanne's plant grew by 6 inches over four weeks, its average weekly growth rate would be:
The average weekly growth rate of Suzanne's plant = (Total growth in 4 weeks) / (Number of weeks)
= 6 inches / 4 weeks
= 1.5 inches/week
In this example:
Suzanne's plant grew at a faster rate (1.5 inches/week) compared to Megan's plant (1 inch/week).
Thus,
Without the actual growth measurements, we cannot make a comparison or identify which plant grew faster.
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The price of a computer was decreased by 30% to £336. What was the price before the decrease?
Answers
Answer:
£480
Step-By-Step Explanation:
x = the original price of a computer
£x = 100% of the original price
The price of a computer was decreased by 30% to £336.
This means:
£336 = 100% - 30%
£336 = 70% of the original price
From this, we will find 1% of the original price.
£336 ÷ 70 = 1%
£4.8 = 1%
Since the original price ( x ) = 100% of the original price, we will find 100% of the original price.
£4.8 × 100 = 100%
£480 = 100%
Therefore, the original price of a computer = £480
Am I right???help asap!
Answers
Answer:
yes you are
Step-by-step explanation:
24 quarts equals how many pints
Answers
Answer: 48 Pints
Step-by-step explanation: Quarts are always half the number of pints so say if we had 48 pints, half of 48 is 24 so that is our answer..
The population of bobcats in northern Anzona since 2008 can be modeled using the function (t) = -0.32+ 2.7t +
253
Answers
Answer:
t=-148+1/1.5740740740741
Step-by-step explanation:
(t)=-0.32+2.7t+253
We move all terms to the left:
(t)-(-0.32+2.7t+253)=0
We add all the numbers together, and all the variables
t-(2.7t+252.68)=0
We get rid of parentheses
t-2.7t-252.68=0
We add all the numbers together, and all the variables
-1.7t-252.68=0
We move all terms containing t to the left, all other terms to the right
-1.7t=252.68
t=252.68/-1.7
t=-148+1/1.5740740740741
Answer: t=-148+1/1.5740740740741
Step-by-step explanation: (t)-(-0.32+2.7t+253)=0
t-(2.7t+252.68)=0
t-2.7t-252.68=0
-1.7t-252.68=0
-1.7t=252.68
t=252.68/-1.7
t=-148+1/1.5740740740741
Which statement is true about credit cards? A) money is directly withdrawn from bank account B) interest is charged if balance is not paid each month C) you must have enough money in your account to cover your purchases D) if you don’t record your purchases, you may overdraw and have to pay a fine
Answers
Answer:its c
Step-by-step explanation:
becuase you cant have a overdrawn bank becuase if you do you have to pay that and the fine.
The true statement about credit cards is that interest is charged if the balance is not paid each month (Option B). Credit cards provide a short-term loan, unlike debit cards, which draw directly from your bank account.
Credit cards work by providing a short-term loan from the credit card company to the user. If the balance is not paid each month, interest is charged on the remaining amount. This is different from debit cards, where money is immediately withdrawn from the user's bank account when making a purchase.
Therefore, option B is correct
total sales 12500 commission rate 3.25
Answers
Answer:
multiply.0325 and 12,500 to get commission
Alex belongs to a music club. Club membership entitles him to buy a discount card for 19.95. the card allows him to buy CDs for 3.95 each. After one year, Alex has spent 63.40. How many CDs did he buy?
Answers
Answer:
11
Step-by-step explanation:
63.40 - 19.95 = 43.45
43.45/3.95 = 11
Answer:
11 CDs
Step-by-step explanation:
took it on progress learning got it right :)
A system of equations consists of a line s of the equation y = x - 5 that is graphed in orange, and a line t that passes through the points (0, 2) and (8, -4). The equation of line t is y = −3 4 x + 2. What is the solution to this system of linear equations?
Answers
ANSWER
[tex]x = 4[/tex]
and
[tex]y = - 1[/tex]
EXPLANATION
Line s has equation:
y=x-5
And line t has equation:
[tex]y = - \frac{3}{4}x + 2[/tex]
We equate the two equations to get:
[tex]x - 5 = - \frac{3}{4} x + 2[/tex]
Multiply through by 4
[tex]4x - 20 = - \frac{3}{4} x \times 4 + 2 \times 4[/tex]
[tex]4x - 20 = - 3 x + 8[/tex]
[tex]4x + 3x = 8 + 20[/tex]
7x=28
[tex]x = \frac{28}{7} = 4[/tex]
[tex]y = 4 - 5 = - 1[/tex]
Answer:
(4, -1) is the solution of the system of equations.
Step-by-step explanation:
A system of equations consists of a line y = x - 5 and a line passing through two points (0, 2) and (8, -4)
And the equation of that passes through these points will be [tex]y=-\frac{3}{4}x+2[/tex]
Now we have to find the solution of the system of linear equations.
By equating both the equations
x - 5 = [tex]-\frac{3}{4}x+2[/tex]
Now we multiply this equation by 4
4(x - 5) = -3x + 4×2
4x - 20 = -3x + 8
4x + 3x = 8 + 20
7x = 28
x = 4
Now we put x = 4 in the equation y = x - 5
y = 4 -5
y = -1
Therefore, (4, -1) is the solution of the system of equations.
Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. Kevin determines about how many times the spinner will land on red or green, and his work is shown below.
What mistake did Kevin make, if any?
Kevin has the formula reversed; it should be the total number of sections over the number of red or green sections.
Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.
Kevin should multiply by the number of sections in the spinner rather than the total number of spins.
Kevin calculated the prediction correctly and did not make any mistakes.
Answers
Answer: 2nd answer
Step-by-step explanation:
Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.
The mistake that kevin make is:
Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.Step-by-step explanation:It was given that there are 10 sections in the spinners 2 of each color.
Hence, in order to find the probability that the spinner lands on green or red is:
He need to find the total sections which are red or green,.
There are 4 sections which are red or green
( Since 2 are green and 2 are red)
and the probability that it will land on green or red is:
[tex]=\dfrac{4}{10}\times 180\\\\\\=72[/tex]
Hence, she should have taken 4 in the numerator to calculate the probability.
how many solutions does the linear system 3×+5y=8 and 3×+5y=1have
Answers
Answer:
No solution
Step-by-step explanation:
When put in a graphing calculator, the lines are parallel and will never intersect, therefore there is no solution.