As per the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ˣ
Population function:
Population function means the effective population served over the course of a time
Given,
The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200000 mosquitoes in the area initially , and predators (birds, bats, and so forth) eat 20000 mosquitoes/day.
Here we need to determine the population of mosquitoes in the area at any time.
Here we have to note that we have two time frames in the information given; weeks and days.
Now, we want the population after predation lets choose time in days.
We know that the population doubles every seven days (ignoring predation) so if P(t) is the population function we have IVP
So, for one week, the population function of the given situation is,
=> dP/dt = rP
=> P(0) = 200000
And we know that,
=> P(7) = 2P(0)
While we solving the IVP for P then we get
[tex]P=Ce^{rt}[/tex]
While we apply, P(0) = 200,000 then we get the value of C = 200,000
So, the given function is rewritten as
[tex]P=200000e^{rt}[/tex]
Now we have to use P(7) = 2P(0), then we get,
400000 = 200000e⁷ˣ
Therefore, we have to use this function to find the population of mosquitoes in the area anytime.
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Identify the number line that correctly displays the solution x ≥ 3.
The Graph of x ≥ 3 is attach below
The definition of a linear inequality
The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.
What does a linear inequality in mathematics look like?
What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being used in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).
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A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $50,000 saved up for when she goes to college in 16 years, assuming the account earns a 6% return.
The person has to deposit $1948.05 per year.
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
In the given question, to find the value to be added per year we will use the formula.
[tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t} - 1}[/tex]
Here A = 50,000
r (rate of interest) = 6 % or 0.06.
n = 1
t = 16
P = value deposit per year
On substituting the values,
[tex]P= \frac{50000 \times 0.06} {(1 +0.06)^{16} - 1}[/tex]
P = 3000 / 2.54- 1
= $1948.05 .
Therefore, person has to deposit $1948.05 per year.
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An electric toothbrush costs $72, including a 20% price markup. What was the cost for the store to purchase the electric toothbrush?
$14.40
$52.00
$60.00
$64.80
Answer: c.60 is correct
Step-by-step explanation:
Combine the like terms to create an equivalent expression 5 + 2m + 3n + 6
Answer:
2m + 3n + 11
Step-by-step explanation:
You cannot combine the m and the n terms, but you can combine 5 and 6
M. |h-8| = |h+ 10|
Find the value of the variable which satisfies the equation.
Kendra earns $11.60 per hour working at the movie theater
The expression for the amount when Kendra earns $11.60 per hour working at the movie theater is 11.60h.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Based on the information illustrated, let the number of hours be h.
Since Kendra earns $11.60 per hour working at the movie theater. The expression will be:
= Amount earned per hour × Number of hours
= 11.60 × h
= 11.60h
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Kendra earns $11.60 per hour working at the movie theater. How much will she earn for h hours?
Determine the end behavior of the following polynomial function:
f(x)=−4(x−2)^12(6−x)^11
The leading term of the polynomial is ?
The degree of f(x) is ?
The leading coefficient is?
For the polynomial function,
The leading terms of the polynomial is 4
The degree of f(x) is 23
And the leading coefficient is 4x²³
Polynomial function:
Polynomial function means a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
Given,
Here we have the polynomial function
f(x) = -4(x-2)¹²(6-x)¹¹
Now, we need to find the leading term, degree and the leading coefficient of the polynomial function.
The degree of a polynomial is the highest of the degrees of the polynomial's individual terms. In our case, the degree is 23.
The leading term is the term with the highest degree. In our case, the leading term is 4x²³
The leading coefficient is the coefficient of the leading term. In our case, the leading coefficient is 4.
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Need help asap!!!!!!
Answer:
Step-by-step explanation:
The original rectangle has dimensions of 70 x 35.
Therefore, we can find its perimeter and area with the standard formulas.
A = 70 * 35
= 2450 square units
P = 2(70) + 2(35)
= 210 units
The new rectangle is dilated by a 1/5 factor, so both dimensions will be one fifth the size of the original. When you have a scale factor that is 1 over some number, you can find the new measurement by dividing by that denominator.
Therefore, new rectangle's dimensions are:
70 ÷ 5 = 14
35 ÷ 5 = 7
Now, find area and perimeter of the new rectangle.
A = 14 * 7
= 98 square units
P = 2(14) + 2(7)
= 42 units
HELP Which expression is equivalent to the given expression?
5x−2
A: 2−5x
B: 2x−2+3x
C: 3−5+2x
D: 5x−2x
What is 4(2u+9) ≥ 5u+21
Answer:
inequality form: u≥−5
Interval Notation: [−5,∞)
You can convert gallons to liters by using a factor of 3.79. That is, 1 gallon is about 3.79 liters. About how many liters are in 37 gallons? is your answers an underestimate or overestimate explain
The amount of liter in 37 gallons is 140.23 liter.
What is gallons and liter?
A gallon and liter (or US spelling liter) are units of measuring volume. There are two official symbols for liter: the Latin letter L in lower and upper case (l and L).
Given,
that 1 gallon is given as 3.79 liter
And to find the amount of liter in 37 gallon
After multiplication,
the amount of liter in gallon,
= 3.79(37)
=140.23
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Salaries for teachers in a particular elementary school district are normally distributed with a mean of $45,000 and a standard deviation of $6,200.
Find the probability that the teachers earn earn a total of over $400,000.
The probability that a randomly selected teacher earns more than $400,000 a year is 57.26.
Given that, normally distributed with a mean of $45,000 and a standard deviation of $6,200.
What is normal distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Let X be the annual salary for all U.S. teachers with a mean salary45,000 and standard deviation of 6,200.
Hence, X∼N(45000,6200²)
The standardized value is obtained by:
Z= (X-μ)/σ
Where μ and σ are the mean and standard deviation of X, respectively.
The probability that a randomly selected teacher earns between 400,000 a year can be obtained by the following expression
P(X<400,000)= (400,000-45,000)/6200
= 355000/6200
= 57.26
Therefore, the probability that a randomly selected teacher earns more than $400,000 a year is 57.26.
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Keny had 2.43 pounds of tomatoes he sold 0.4 pound to Maria and 0.25 pound to Lara for their lunches how many pounds of tomatoes does Kent have now
The pounds of tomatoes Kent have now is 1.78 pound.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that Keny had 2.43 pounds of tomatoes he sold 0.4 pound to Maria and 0.25 pound to Lara for their lunches.
The total pounds of tomatoes = 2.43
The pounds of tomatoes Kent have now;
2.43 - 0.4 - 0.25
= 1.78
Therefore, the pounds of tomatoes Kent have now is 1.78 pound.
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The equation x² - 6x = 72 has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
The equation x² - 6x = 72 has a solution between 4 and 5
Use a trial and improvement method to find this solution.
There are a number of "improvement" techniques that can be used to improve an estimate of a solution to a polynomial. Some of them use the polynomial itself to form the iterator function.
Iterator
There are a number of ways we can solve the given equation for x. Often, at least one of these will converge when used for improving the estimated value of x.
x₁ = ([tex]x^{2}[/tex] -72)/6 . . . . . . . add 6x-72, divide by 6
x₂ = 72/(x^2 -6) . . . . . . . factor out x and divide by its coefficient
x₃ = ∛(72 +6x) . . . . . . . add 6x and take the cube root
The first two of these iterators tend to diverge. For x = 4.5, they give ...
x₁ = (4.5³ -72)/6 = 3.1875
x₂ = 72/(4.5² -6) = 5.0526
Both of these stray out of the given interval of [4, 5].
However, the third one tends to converge, so can give us a useful approximation in one iteration:
x₃ = ∛(72 +6×4.5) ≈ ∛99 ≈ 4.6261
Second iteration
Applying this again, we get ...
x ≈ ∛(72 +6·4.6261) ≈ 4.6378
The approximate root to 1 decimal place is 4.6.
Additional comment
One of the quickest converging iterators is that provided by Newton's method. For finding the solution to f(x) = 0, it uses ...
x₁ = x -f(x)/f'(x) . . . . . . . where f'(x) is the first derivative
For this problem, we can define ...
f(x) = [tex]x^{2}[/tex] -6x -72 ⇒ f'(x) = 3x^2 -6
x₁ = x -([tex]x^{2}[/tex] -6x -72)/(3x^2 -6) = (3[tex]x^{2}[/tex] -6x -[tex]x^{2}[/tex] +6x +72)/(3x^2 -6)
x₁ = (2[tex]x^{2}[/tex] +72)/(3x^2 -6)
Then for x = 4.5, the "improved" solution is ...
x₁ = (2(4.5³) +72)/(3(4.5²) -6)) = 254.25/54.75 = 339/73 ≈ 4.6438
A second iteration gives ...
x ≈ 4.639026 . . . . accurate to 5 decimal places
Hence with this iterator, the number of accurate decimal places tends to double with each iteration.
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A pizza parlor offers 8 different specialty pizzas. If the Almeida family wants to order 2 specialty pizzas from the menu, which method could be used to calculate the number of possibilities?
8 factorial divided by 2 factorial
8 factorial divided by 6 factorial
8 factorial divided by the quantity 6 factorial times 2 factorial end quantity
12!
Answer:
(c) 8!/(6!·2!)
Step-by-step explanation:
You want to know how to compute the number of possible ways 2 different pizzas can be chosen from a menu of 8.
8 Choose 2The formula for computing the number of combinations of n things taken k at a time is ...
nCk = n!/(k!(n -k)!)
For 8 specialty pizzas chosen 2 at a time, this is ...
8C2 = 8!/(2!·6!)
The appropriate answer choice is ...
possibilities = 8!/(6!·2!)
__
Additional comment
That is (8·7)/(2·1) = 28 possibilities, assuming choice of different pizzas.
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How many three-letter sequences can be made from the word "COMBINATORICS" where no 2 letters can be the same?
The number of three-letter sequences that can be made from the word "COMBINATORICS" where no 2 letters can be the same is 720 ways
How to find the number of waysThe question is asking of permutation
arranging the letters without repeating a word gives
COMBINATORICS ⇒ COMBINATRS
The newly arranged word gives 10 letters and arranging 10 letters by taking 3 at a time is 10P₃
The required permutation is 10P₃
10P₃
= 10! / (10 - 3)!
= 10! / 7!
= 720
= 720 ways
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Write these fractions as percentage 2/3
Answer: 66%
Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, [tex]\frac{1}{4}[/tex] is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.
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Using your same definition, what are the zeros of this function?
The zeros of the given function are -2, and 1 in the represented graph.
What are the zeros in the function?A function's zeros are the values of x when f(x) equals 0. As a result, its name. This indicates that when f(x) = 0, x is a function zero. When the graph crosses through x = a and is considered to be the function's zero. As a result, (a, 0) is a function zero.
The graph is given in the question,
According to the shown graph, the function in the given graph has located at the x-axis of the plane, which is the location or coordinates from where the line crosses which are -2, and 1.
Therefore, the zeros of the given function are -2, and 1 in the represented graph.
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Multi-Step Problem You are choosing between two electricity providers. The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. a. Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service. Write the two equations representing the cost of each company's service for one month.
The total cost for Zap Electric Company and Bolt Electric Company are y = 0.06r + 6.55 and y = 0.12r + 2.83
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.
The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:
y = 0.06r + 6.55
The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:
y = 0.12r + 2.83
The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83
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PLEASE HELP ME
Simplify 6/7c − 5/9d − 1/2 c + 1/3d
A: 514c − 29d
B: 59c + 412d = 59c +13d
C: 59c − 412d = 59c −13d
D: 514c + 29d
The simplified form of the expression [tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex] is [tex]\frac{5}{14}c-\frac{2}{9}d[/tex]
How to simplify an expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Therefore, let's simplify the expression as follows:
To simplify an expression means to write an equivalent expression which contains no similar terms.
his means that we will rewrite the expression with the fewest terms possible.
Hence,
[tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex]
combine like terms
[tex]\frac{6}{7}c-\frac{1}{2}c-\frac{5}{9}d+\frac{1}{3}d[/tex]
Do the arithmetic
[tex]\frac{12c-7c}{14}+\frac{-5d+3d}{9}[/tex]
[tex]\frac{5}{14}c-\frac{2}{9}d[/tex]
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Convert 45 kilometers to miles. (1 kilometer = 0.62 miles)
27.9 miles
72.58 miles
13.2 miles
44.7 miles
Answer:
this is very easy, just do:
45(0.62/1)
and you get 27.9 miles
tada!
45 kilometers is equivalent to 27.9 miles.
Given that we need to convert 45 kilometers to miles.
We have given that,
1 kilometer = 0.62 miles)
To convert 45 kilometers to miles, we can use the conversion factor of 1 kilometer = 0.62 miles.
We multiply the given distance in kilometers by this conversion factor to obtain the equivalent distance in miles.
Step 1: Multiply 45 kilometers by 0.62 miles/kilometer:
45 km x 0.62 miles/kilometer = 27.9 miles
Therefore, 45 kilometers is equivalent to 27.9 miles.
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Question 7(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Three different recipes each make a different number of cookies and require a different amount of flour.
Recipe 1: 3 dozen cookies; 4.5 cups of flour
Recipe 2: 4 dozen cookies; 6 cups of flour
Recipe 3: 5 dozen cookies; 7.5 cups of flour
Determine if the three recipes use a proportional amount of flour.
Yes, it is proportional because the cookies increase by 1.5 dozen for every 1 cup of flour.
Yes, it is proportional because the ratios between the number of cookies and cups of flour are all equivalent.
No, it is not proportional because the number of cookies and cups of flour could not be zero at the same time.
No, it is not proportional because the ratios between the number of cookies and cups of flour are not all equivalent.
Answer:
Yes, All the three recipes use a proportional amount of flour.
Step-by-step explanation:
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
There are three different recipes to make cookies for different amount of flour.
Recipe 1 = 3 dozen cookies and 4.5 cups of flour
Recipe 2 = 4 dozen cookies and 6 cups of flour
Recipe 3 = 5 dozen cookies and 7.5 cups of flour
Now,
To check that all the recipes in proportion, we check the amount of flour for 1 dozen cookies.
For recipes 1;
The amount of flour = 4.5 / 3
= 1.5
For recipe 2;
The amount of flour = 6 / 4
= 1.5
For recipe 3;
The amount of flour = 7.5 / 5
= 1.5
Clearly, All are the same amount to make 1 dozen of cookies.
So, The all recipes are in proportions.
Therefore, All the three recipes use a proportional amount of flour.
PLEASE HELP
A ferris wheel is 45 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.
What is the Amplitude? _______ meters
What is the Midline? y = ________ meters
What is the Period? ______ meters
How High are you off of the ground after 3 minutes? _____ meters
The Amplitude of the Wheel is 22.5
The Midline of the wheel is 25.5;
The period of the wheel is 6;
what is amplitude?
A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.
We know that:
Amplitude = [tex]=\frac{\max -\min }{2}[/tex]
So, substituting the minimum and maximum values as:
Maximum = 48;
minimum = 3;
So, Amplitude = [tex]=\frac{48-3}{2}=22.5[/tex]
So, Amplitude = 22.5;
Now,
we know that midline is half of the sum of minimum and maximum;
So,
Midline = [tex]=\frac{\max +\min }{2}[/tex]
So,
Maximum = 48;
minimum = 3;
Midline = [tex]=\frac{48+3}{2}=25.5[/tex]
So, Midline = 25.5;
and Period is 6 minutes;
So, we can frame the function by the negative cosine function;
[tex]n=f(t)=-a \cos (b t)+c[/tex]
[tex]\begin{aligned}&b=\frac{2 \pi}{\text { period }}=\frac{2 \pi}{6}=\frac{\pi}{3} \\&\therefore \quad h=-22.5 \cos \left(\frac{\pi}{3} t\right)+25.5\end{aligned}[/tex]
Height after time t = 3 will be:
[tex]\begin{aligned}&h=-22.5 \cos \left(\frac{\kappa}{3} \times 3 .\right)+25.5 \\&h=-22.5(-1)+25.5 \\&h=48\end{aligned}[/tex]
So, The height is 48;
Hence, After 3 minutes It is 48 meters high from the ground; is 48
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Factorise 32s+40.
Write your answer as a product with a whole number greater than 1.
The expression when factored out is 8(4s + 5)
How to determine the factored expression?From the question, we have the following expression that can be used in our computation:
32s + 40
The terms of the above expression are:
32s and 40
And the factor of 32 and 40 is
Factor = 8
So, we divide 32s and 40 by 8
The results of these divisions are
32s/8 = 4s
40/8 = 5
So, we have the following results
32s + 40 = 8(4s + 5)
Hence, the factored expression is 8(4s + 5)
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Does the pentagon have the following type of symmetry? Answer yes or no in each box.
The pentagon has the following type of symmetry:
Reflection symmetry ---Yes.Point symmetry --- YesWhat is Reflection symmetry?This refers to a type of symmetry where one-half part of an object shows the other half of the object. It is also be called mirror symmetry.
Point symmetry refers to the shape of a figure or graph after begin turned about 180° and it still looks the same as its initial shape. eg Star, heart -shape, etc.
Note that When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.
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2/3n + 4 = -26 we cant figure this out pls help
Answer:
n = -45
Step-by-step explanation:
2/3n + 4 = -26
subtract 4 from both sides:
2/3n + 4 - 4 = -26 - 4
2/3n = -30
divide both sides by 2/3:
(2/3n)/(2/3) = (-30)/(2/3)
n = -45
Answer:
n=-45
Step-by-step explanation:
2/3n+4=-26
-4. -4
2/3n=-30
/2/3. /2/3
n=-30/1 *3/2
n=-90/2
n=-45
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2500 dollars is placed in an account with an annual interest rate of 9%. To the nearest year, how long will it take for the account value to reach 7500 dollars?
It will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.
According to the question,
We have the following information:
2500 dollars is placed in an account with an annual interest rate of 9%.
We know that following formula is used to find simple interest:
Simple interest = principal*rate*time/100
Now, the simple interest on any amount will be equal to the total amount after interest minus the principal amount:
7500-2500
5000
So, we have the following expression:
(2500*9*t)/100 = 5000
Now, using cross multiplication method:
t = (5000*100)/(2500*9)
t = 200/9 years
t = 22.2 years
Now, the nearest year will be 22 years.
Hence, it will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.
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How do I solve this?
-27 v-54 v²-36 v³
The equation -27v - 54v²-36v³ cannot be solved as it doesn't have a factor
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
There are 3 main types of equation
1. Slope-intercept : y = mx + c
where m is the slope and b is the y-intercept
2. Point-slope : [tex](y - y_{1} ) = m (x - x_{1} )[/tex]
Where m is the slope and [tex](x_{1},y_{1})[/tex] is a point on the line
3. Standard : Ax + By = C
where A, Band C are constants
Factorizing the equation we get
-3v(9 + 18v + 12v²)
= -9v(4v² +6v +3)
(4v² +6v +3) as this equation doesn't have a factor it is difficult to solve
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PLEASE HELP!!
Find x if it is the measure of an acute angle in a right triangle and sin x = 0.5015.
Answer:
30.1°
Step-by-step explanation:
You want the acute angle whose sine is 0.5015.
Inverse sineWhen you know the sine of an angle and want to find the angle, you use the inverse sine, or arcsine, function.
sin(x) = 0.5015
x = arcsin(0.5015) ≈ 30.1°
The value of x is about 30.1 degrees.
__
Additional comment
There are an infinite number of angles that have that sine value. Only one of them is a positive angle less than 90°. Be sure your calculator is in degrees mode, if you don't want units of radians or grads. (Spreadsheet functions will give an answer in radians.)
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