The population is growing at an annual rate of 16.2%
Here, we want to calculate the exponential growth rate
Mathematically, we can write the exponential equation of growth as follows;
[tex]\begin{gathered} P=I(1+r)^t \\ \\ \end{gathered}[/tex]Where P is the population after a certain number of years ( 270 after 3 years
I is the initial popultaion which is 200
r is the percentage we want to calculate
t is the number of yeats to reach P which is 3 in this case
[tex]\begin{gathered} 270=200(1+r)^3 \\ (1+r)^{3\text{ }}\text{ = }\frac{270}{200} \\ \\ (1+r)^3\text{ = 1.35} \\ \\ 1\text{ + r = }\sqrt[3]{1.35} \\ \\ 1\text{ + r = 1.162} \\ \\ r\text{ = 1.162 - 1} \\ \\ r\text{ = 0.162} \end{gathered}[/tex]To the nearest tenth of a percentage, this is 16.2%
please help I've been trying to solve this for over an hour
24x +8y ≥ 20
3x - 6y > 24
First, express both equations in slope-intercept form
y= mx+b
Where:
m= slope ( rise (y) / run (x))
b= y-intercept (where the line crosses the y axis)
Solve for y:
24x +8y ≥ 20
8y ≥ -24x +20
y ≥ (-24x +20 ) / 8
y ≥ -3x + 2.5
3x - 6y > 24
-6y > 24- 3x
y < (24 -3x) / -6
y < 1/2x -4
System:
y ≥ -3x + 2.5
y < 1/2x -4
Solution = the area where the 2 solutions overlap (blue+ red)
maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day. Create a table of values to represent the relationship between the number of days and the number of puzzles she has completed determine if it is proportional and show your reasoning Brainliest will possibly be a prize :)
The table of values to represent the relationship between the number of days and the number of puzzles she has completed will be:
Days Puzzle completed
1. 4
2. 8
3. 12
4. 16
5. 20
How to illustrate the information?From the information, Maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day.
Therefore, the first day, she will do 4 puzzles. The second day will be:
= 2 × 4 = 8 puzzles
Third day = 3 × 4 = 12 puzzles.
In this case, the method that was used is simply to multiply the number of days by 4 since he does 4 puzzles everyday.
It should be noted that this illustrates a proportional relationship
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Solve the inequality for x
(x+8)(x-3)^2(x-7)^3<0
The solution for the given inequality is −8<x<3 or 3<x<7.
The given inequality is (x+8)(x-3)²(x-7)³<0.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality can be solved as follows
Solve for x by simplifying both sides of the inequality, then isolating the variable.
Inequality Form: x+8<0
x<-8 (Subtract 8 on both the sides of the inequality)
(x-3)²<0
⇒ x-3<0
⇒ x<3 (Add 3 on both the sides of the inequality)
(x-7)³<0
⇒ x-7<0
⇒ x<7 (Add 7 on both the sides of the inequality)
Solution is −8<x<3 or 3<x<7
Therefore, the solution for the given inequality is −8<x<3 or 3<x<7.
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find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: let (x,y) be the unknown endpoint. apply the midpoint formula, and solve the two equations for x and y.) midpoint (-15, -6), end point (-16,-3)
The coordinates of the other endpoint of the segment, given its midpoint and one endpoint are (-14, -9)
How to find the midpoint coordinate of a Line?The Midpoint Formula for a line with endpoints as (x₁, y₁) and (x₂, y₂) is;
((x₁ + x₂)/2, (y₁ + y₂)/2)
We are given the following;
Midpoint (-15,-6)
End point (-16,-3)
Let x₁ = -16, the x coordinate of the endpoint
Let x₂ = the x coordinate of the unknown endpoint
Let y₁ = -3, the y coordinate of the endpoint
Let y₂ = the y coordinate of the unknown endpoint
Thus, for the x coordinate of the unknown endpoint;
(x1 + x2)/2
(-16 + x₂)/2 = -15
-16 + x₂ = -30
x₂ = -14
For the y coordinate of the unknown endpoint;
(y1 + y2)/2
(-3 + y₂)/2 = -6
-3 + y₂ = -12
y₂ = -12 + 3
y₂ = -9
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Write a quadratic function in standard form whose graph has the given characteristics.
The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
The standard form of a quadratic equation in vertex form is given as,
y = a(x-h)² + 8
Where (h,k) is the coordinate of the vertex and a is constant.
Given the vertex (h,k) = (-1,8)
Substitute, vertex, and (0,2)
2 = a(0 + 1)² + 8
a = -6
Therefore, the equation converts as,
y = -6(x+1)²+8
Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".
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what number is 90% of 20
Let's begin by listing out the given information:
[tex]\begin{gathered} 90\text{\%}\cdot20\Rightarrow\frac{90}{100}\cdot20 \\ \Rightarrow0.9\cdot20=18 \\ \Rightarrow18 \end{gathered}[/tex]Therefore, 90% of 20 is equal to 18
Order from least to greatest5/6 4/50.82
Okay, here we have this:
Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:
Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:
Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.
Math
-2-(-7) = ?
Bookmark
Answer:
5
Step-by-step explanation:
We know that - (-7) = +7, so
-2 - (-7) = -2 + 7 = 5
A poll showed that 62.4% of Americans say they believe that some people see the future in their dreams. What is the probability (in percent form) of randomly selecting someone who does not believe that some people see the future in their dreams.Probability = % (Please round your answer to one decimal place.)
Let
A
be the event of selecting an American that believes that some people see the future in their dreams. From the problem,
P(A)=62.4%=0.624
Let
A' be the event of selecting an American who does not believe that some people see the future in their dreams
Remember that
P(A')=1-P(A)
substitute given value
P(A')=1-0.624=0.376=37.6%
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 37.6%
write in standard form the equation of the line through each pair of points
9. (0,1) and (3,0)
10. (1/2,2/3) and (-3/2,5/3)
11. (-3,-2) and (1,6)
The equation of the line 3y + x = 3 through pair of points (0,1) and (3,0), the equation of the line 6y = 2x +3 through pair of points (1/2,2/3) and (-3/2,5/3) and the equation of the line y = 2x + 4 through pair of points (-3,-2) and (1,6)
The equation of the line through pair of points (0,1) and (3,0)
⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )
Here x₁ = 0 and y₁ = 1
x₂ = 3 and y₂ = 0
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 1 = [(0-1)/(3-0)](x -0)
⇒ y - 1 = (-1/3)x
⇒ 3y - 3 = x
⇒ 3y + x = 3
The equation of the line through pair of points (1/2,2/3) and (-3/2,5/3)
⇒ y - 2/3 = [(5/3 -2/3)/(-3/2-1/2)](x -1/2)
⇒ y - 2/3 = [(3/3)/(-4/2)](x -1/2)
⇒ y - 2/3 = (1/3)(x -1/2)
Multiply by 6 both sides of the equation,
⇒ 6y - 4 = 2(x -1/2)
⇒ 6y = 2x -1 + 4
⇒ 6y = 2x +3
The equation of the line through pair of points (-3,-2) and (1,6)
⇒ y - (-2) = [(6-(-2))/(1-(-3))](x -(-3))
⇒ y + 2= (8/4)(x + 3)
⇒ y = 2x + 6 -2
⇒ y = 2x + 4
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The part 1 picture of the same question the part 2Because is a little long.
The answer would be B.
The relationship is proportional. The constant of proportionality is 5.
Leonard Desmond founded his traveling circus many years ago, and since that time he has featured 32 high-wire unicyclists and 24 ball-balancing seals. What is the ratio of high-wire unicyclists to ball-balancing seals?
Answer:
The ratio of the high-wire unicyclists to ball-balancing seals is;
[tex]4\colon3[/tex]Explanation:
Given that;
He has featured 32 high-wire unicyclists and 24 ball-balancing seals.
The ratio of the high-wire unicyclists to ball-balancing seals can be written as;
[tex]32\colon24[/tex]Reducing toits lowest form, we have;
divide both sides by 8;
[tex]\begin{gathered} \frac{32}{8}\colon\frac{24}{8} \\ 4\colon3 \end{gathered}[/tex]Therefore, the ratio of the high-wire unicyclists to ball-balancing seals is;
[tex]4\colon3[/tex]Which statement allows the line q and p are parallel ?
According to the converse of corresponding angles theorem, the statement that allows Carmen to conclude that lines p and q are parallel is: ∠2 ≅ ∠6.
What is a Transversal?A transversal is a line that crosses two straight lines. For example, line t is a transversal that crosses the lines p and q in the given diagram above.
What are Parallel Lines?Parallel lines are lines that do not meet each other at any point and are of equal distant to each other.
When a transversal intersects two parallel lines, they form angle pairs. One of such angle pairs is, corresponding angles, which are always congruent to each other.
Thus, if corresponding angles are formed and are equal to each other, then the lines they lie on must be parallel lines based on the corresponding angles converse theorem.
Angles 2 and 6 are corresponding angles that are formed by the transversal that intersects lines q and p. If they are congruent angles, then the lines are parallel.
Therefore, Carmen can use the statement, ∠2 ≅ ∠6 to show that lines q and p are parallel.
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Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Shirley, and Matthew are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that you, Shirley, and Matthew are chosen is 0.0001
Probability:
Probability refers the measure of the likelihood of an event to occur.
The formula of Probability is
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Given,
Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat.
Here we need to find the probability that you, Shirley, and Matthew are chosen.
Here we have assuming that the selection process is fair;
We know that, the total number of employees is 28
Therefore, the probability of selecting each employee is,
=> 1/28
So, the probability of selecting yourself, Shirley, and Matthew is calculated as,
=> 1/28 x 1/27 x 1/26
=> 1/19656
=> 0.00005
When we round off it into four decimal place then we get,
=> 0.0001
Therefore, the probability that you, Shirley, and Matthew are chosen 0.0001.
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What happens to the surface area of a sphere if the radius is doubled?b. What happens to the surface area of a sphere if the radius is tripled?
Given:
a) The radius is doubled.
b) The radius is tripled.
To find:
The changes to the surface area of a sphere
Explanation:
Let us take the original radius as r.
The surface area of the original sphere is,
[tex]A=4\pi r^2[/tex]a) The new radius will be,
[tex]R=2r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(2r)^2 \\ =4\pi(4r^2) \\ A=4(4\pi r^2) \\ A=4\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes four times the original surface area if the radius is doubled.
b) The new radius will be,
[tex]R=3r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(3r)^2 \\ =4\pi(9r^2) \\ A=9(4\pi r^2) \\ A=9\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is tripled.
Please help I am stuck
Compute the given function
[tex]f(x)=- 3x^{2}-7x-3[/tex]
How the given function is computed?
Let us consider f (-3)
f(-3)= -3(9)- 7(-3) -3
=-27+21-3
= -9
Let us consider f (4)
f(4) = -3(16)-7(4)-3
=-48-28-3
= - 79
A) f(-3) * f (4)
= (-9) * (-79)
= 711
B) f(-3) / f (4)
= (-9) / (-79)
= 9/79 (or 0.11)
What are functions?
The core of calculus in mathematics is the concept of functions. The unique types of relations are the ones with functions. Mathematical functions are represented as a rule that, for each input x, produces a distinct result.Mathematicians refer to a function as being mapped or transformed.To learn more about functions, refer:
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Alice is saving to buy a house and currently has$2,000 in her savings account. She's planning tocontribute $150 to the account each month,Identify the function that describes therelationship between the number of monthsthat pass (n) and the balance of her savingsaccount,f(n).
Alice plans to buy a house. She has $2,000 in her savings account.
She plans to contribute $150 to the account each month.
We know that with each month, n, she deposits $150 and so, each month, her savings account balance increases by $150.
This simply means that after n months, her savings account balance would have increased by:
150 * n = 150n
Her initial balance was $2000, therefore, her balance after n months will be the sum of 150n and the amount that was initially there.
That is:
f(n) = 2000 + 150n
This is the function that describes the relationship between the number of months and her balance.
Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score
Problem
Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score
Solution
Let x the score for Steve and y the score for Denia.
We know that the score of Denia is the opposite of Steve
So then the scores needs to be:
Steve =-5
Denia =5
And with this we satisfy all the requirements
74/5+1 9/10 what is the the lowest denominata to use to solve?
A lowest denominator to solve the given equation is 10.
What are fractions?
Fraction are ratios in which numerator and denominator are both integers and denominator is not zero.
We are given a equation
[tex]\frac{74}{5}+1\frac{9}{10}[/tex]
Upon solving we get the following
[tex]\frac{74}{5}+\frac{19}{10}[/tex]
If we multiply both numerator and denominator of the first term by 2 we get
[tex]\frac{148}{10}+\frac{19}{10}[/tex]
Hence after this we can add
Hence A lowest denominator to solve the given equation is 10
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Melissa bought 10 party subs and 3 cases of water for a party she's hosting. The subs cost $47 each, and each case of water cost $7 How much did Melissa
spend on subs and water?
Answer:
melissa spent approximately $491 in total
Solve 3x - 2y = - 6 if the domain is {-2, -1, 0, 2, 3).
Write your answer as ordered pairs.
The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.
Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,
At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.
These are the values of outputs, and the ordered pair will be expressed as
{0, 3/2, 3, 6, 15/2}.
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Introduction to the probability of an eventA spinner with 8 equally sized slices has 8 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellowslice?write your answer as a fraction in simplest form.
Step 1:
[tex]Probability\text{ of any event = }\frac{Number\text{ of required outcomes}}{\text{Number of possible outcomes}}[/tex]Step 2:
There are 8 slices, hence the possible outcomes = 8
All the slices are color yellow. hence the required outcomes = 8
Step 3:
[tex]\text{The probability that the dial stops on yellow slice = }\frac{8}{8}\text{ = 1}[/tex]The probability that the dial stops on yellow slice = 1
Final answer
Marcus has an aquarium with three different types of fish. 1/9 of the fish are goldfish. 5/9of the fish are angelfish. • The rest of the fish are guppies. What fraction of the fish are guppies?
The fraction of fishes which are guppies in Marcus's aquarium is 2/3
Number of gold fishes in the aquarium = 1/9
Number of angelfish in the aquarium = 5/9
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Let x be the total number of fishes in Marcus's aquarium:
Number of guppies = Total fishes - Number of gold fishes - Number of angelfishes
= x - 1/9 - 5/9
= x - 6/9
x = 6/9 or 2/3
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The linear function
M= 10- 1.44p represents the amount m (in dollars)
of money that you have after printing p photographs.
(See Example 5.)
a. Interpret the terms and coefficient in the equation.
b. Find the domain of the function. Is the domain
discrete or continuous? Explain.
c. Graph the function using its domain.
Considering the given linear function, it is found that:
a)
The intercept is of 10, meaning that initially you have $10.The slope is of -1.44, meaning that the cost of printing each photo is of 1.44.b) The discrete domain of the function is: {0, 1, 2, 3, 4, 5, 6, 7}.
c) The graph of the function is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule given below:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).The amount of money you have remaining after printing p photographs is modeled by the following function:
M(p) = 10 - 1.44p.
Hence the coefficients are as follows:
The intercept is of b = 10, meaning that initially you have $10 to spend on printing photos.The slope is of -1.44, meaning that the cost of printing each photo is of 1.44, that is, for each photo you print, you are going to lose $1.44 from your amount.The number of photos printed is a discrete number, as this number cannot assume decimal values, hence the domain is also discrete.
You cannot print a negative value of numbers, neither can M(p) be negative, hence the domain, which is the number of photos you can print, is:
{0, 1, 2, 3, 4, 5, 6, 7}.
Considering the above domain, the graph of the function is given by the image at the end of the answer.
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Which is a better value for money, $5.99 for a package of 8 cold remedy
capsules or $2.85 for 2 capsules?
Answer:
the 8 pack
Step-by-step explanation:
So to start we should find how much an individual capsule in each is
Well start off by 5.99/8 which will give us 0.74875 per capsule and well round in to 0.75 each to put it in terms of money.
Now we will do 2.85/2 which then gives you 1.425 and well say that's about 1.43 per capsule
4n+1=25Please help with an explanation as well
Question:
Solve
4n + 1 = 25
Solution:
Consider the following formula:
[tex]4n+1\text{ = 25}[/tex]this is equivalent to:
[tex]4n\text{ = 25 -1}[/tex]this is equivalent to:
[tex]4n\text{ = 24}[/tex]solving for n, we get
[tex]n\text{ = }\frac{24}{4}=\text{ 6}[/tex]Then, we can conclude that the correct answer is:
[tex]n\text{ = 6}[/tex]A company prints designs on T-shirts. They charge $40 for set-up costs plus $12 per shirt. Write the equation for the situation.
The equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.
According to the situation,
We have the following information:
The company charges $40 for set-up costs plus $12 per shirt.
So, the basic charge is added to every t-shirt.
Now, let's take the number of T-shirts on which the company prints designs on shirts to be x.
So, we have the charge for x number of t-shirts is:
$(40+12x)
Hence, the equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.
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What is the number of terms in the polynomial -y4 + 7y³
The sum of three consecutive even integers
is –78. What are the integers?
Describe how you would use the strategy of writing an equation to solve the given problem.
Answer:
- 28, - 26 and - 24Step-by-step explanation:
The difference between two consecutive even integers is 2.
Let the first of the three integers is x, then the following ones are:
x + 2 and x + 4.
The sum of the three is - 78. Express it as equation and solve for x:
x + x + 2 + x + 4 = - 783x + 6 = - 783x = - 84x = - 84/3x = - 28The integers are - 28, - 26 and - 24
If x
2 = 25 , where x ε z then x =
After thoroughly calculation, we have come to find that, If equation x² = 25, where x ε z then x = √25 = 5, thus x is 5.
What is equation?Equation, also known as a statement of equality between two expressions with variable- and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics.
From straightforward algebraic equations that only require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them.
Simultaneously occurring equations, or system of equations Algebra requires the simultaneous solution of two or more equations (i.e., the solution must satisfy all the equations in the system). The quantity of equations must match the quantity of unknowns for a system to have a distinct solution.
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