According to the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ⁿ
Population function:
The term population function refers 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.
Now, we need to determine the population of mosquitoes in the area at any time.
Here we have given that we have two time frames in the information given; weeks and days.
Now, we need the population after predation lets choose time in days.
And we also know that the population doubles every seven days (ignoring predation) so if P(a) is the population function we have IVP
For one week, the population function of the given situation is written as
=> dP/dt = rP
Then the value of P is P(0) = 200000
And through the given question we know that,
=> P(7) = 2P(0)
While we solving the function then we get
P = Ceⁿᵃ
When we apply the values of P(0) = 200,000 then we get the value of C = 200,000
Then, the function is rewritten as
P = 200000eⁿᵃ
Now, we have to apply the value of P(7) = 2P(0), then we get,
400000 = 200000e⁷ⁿ
When we simplify it then we get,
e⁷ⁿ = 1/2
When we apply the number of days on these function, then we can get the number of mosquitoes in the city.
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Which equations are true? Select all that apply. A. 66 ÷ 10 1 = 6 . 6 B. 660 ÷ 10 0 = 66 C. 6 , 600 ÷ 1 , 000 = 0 . 66 D. 0 . 66 ÷ 10 1 = 0 . 066 E. 6 ÷ 100 = 0 . 06
The equations 66 ÷ 10 = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true. which is the correct answer would be options (A), (B), (D), and (E).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A. 66 ÷ 10 = 6.6
66/10 = 6.6
This is the true equation.
B. 660 ÷ 10 = 66
660/10 = 66
This is the true equation.
C. 6,600 ÷ 1,000 = 0.66
This is not the true equation.
D. 0.66 ÷ 10 = 0.066
This is the true equation.
E. 6 ÷ 100 = 0.06
This is the true equation.
Thus, the equations 66 ÷ 10 = 6.6, 660 ÷ 10 = 66, 0.66 ÷ 10 = 0.066, and 6 ÷ 100 = 0.06 are true.
Hence, the correct answer would be options (A), (B), (D), and (E).
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Bro please help. Im so lost
Answer:
D: x≤-4
Step-by-step explanation:
If its not just reply to me and i will re asses
Answer:
3
Step-by-step explanation:
What value is needed to complete the square? Show all steps.
x^2 - 2x +__
In completing the square method, considering the equation X^2 - 2x + the number to be added should be 1 to make it a perfect square
How to know term that should addedThe standard quadratic equation is of the form
ax^2 + bx + c
The completing the square method is one of the methods of solving quadratic equations
The factor to be added to the equation while using the completing the square method is of the formula
(b / 2a)^2
compared to the equation in the problem X^2 - 2x +
= (b / 2a)^2
= (2 / 2)^2
= (1)^2
= 1
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a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share what is the percent loss
If a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share the percentage loss is 60%
The company's initial share price = $35 per share
The company's new share price = $14 per share
Therefore the share price decreased from $35 to $14, we have to find the percentage loss
The percentage loss = [(The company's initial share price - The company's new share price) / The company's initial share price ] × 100
Substitute the values in the equation
The percentage loss = [(35-14) / 35] × 100
= (21/35)×100
= 0.6 × 100
= 60%
Hence, if a company’s stock was selling at 35$ a share a month later it was selling at 14$ a share the percentage loss is 60%
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Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
O f(x) = x(x-a)³(x-b)³
f(x) = (x-a)²(x-b)4
f(x) = x(x-a)(x-b)²
The function that can represent the graph is the option;
f(x) = x²·(x - a)²·(x - b)⁴·(x - c)
What is Polynomial Function?A function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation is referred to as a polynomial function.
As, the graph touches the at x axis by 3 points.
So, the graph has an even multiplicity at three points as x², (x - a)², and (x - b)⁴ .
Now, The function has a single zero or factor such as (x - c) in the first equation
So, The function that could represent the graph is the function
f(x) = x²·(x - a)²·(x - b)⁴·(x - c)
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"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height by virtue of the information given is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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When a number is decreased by 53%, the result is 30
6 times a numbeer is 7 less than the square of that number. find the positive solution?
The positive solution of the given condition is 7.
What is a quadratic equation?
A second-order polynomial equation with a single variable, x, is known as a quadratic equation.
i.e. [tex]ax^{2} +bx+c=0[/tex]
Let '[tex]x[/tex]' be a number, then
The six-times a number= [tex]6x[/tex]
&, the square of a number= [tex]x^{2}[/tex]
Now, according to the question,
or, [tex]6x = x^{2} -7[/tex]
or, [tex]x^{2} -6x-7=0[/tex]
or, [tex]x^{2} -7x+x-7=0[/tex]
or, [tex]x(x -7)+1(x-7)=0[/tex]
or, [tex](x -7)(x+1)=0[/tex]
Either, [tex](x -7)=0[/tex] or, [tex](x+1)=0[/tex]
[tex]x=7[/tex] [tex]x=-1[/tex]
Therefore, the positive solution is x = 7.
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The coordinates of the vertices of a polygon are shown on the graph below.
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle
Answer:
Triangle
Step-by-step explanation:
It has three side unlike the others can't have three sides
Identify the graph of the equation of the form y=ax²+bx+c with a<0 and having two x-intercepts.
Choose the correct answer below.
E B
D A
C F
In the graphs given, only graph F has two x - intercepts and a < 0 i.e the graph is facing downwards or opens downwards
Graph of Quadratic FunctionThe graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.
In this question, we have to find the graph of a function f(x) that a < 0 and has two intercepts.
The easy features of this graph are
The graph must touch two opposite side on the x-axisThe graph must be facing downwardsIn the options given, only graph F has such features and it is the answer to the question.
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If Jeff has 1 Apple and Jessica has 2 apples how many do they have together
answer: 3
simply add 1 apple from Jeff and 2 apples from Jessica
(1+3) = ?
Thus, the answer is 3 apples all together
Between which two benchmark fractions is? How do you know?
I ready classroom mathematics grade 5 volume 1
Answer:
Their Divider
Step-by-step explanation:
1-->1/2+1/2-->1/4+1/4+1/4+1/4-->etc.
answer the questions below⬇️⬇️
The perimeter of the given figure is 19 cm and area is 20 cm².
What is perimeter?
A perimeter could be a closed path that encompasses, surrounds, or outlines either a 2 dimensional form or a one-dimensional length. The perimeter of a circle or an oval is termed its circumference.
Main body:
to find the perimeter we need the measurement of each side.
so length of DE side
DE = A F - BC
DE = 6-2
DE = 4 cm
so perimeter = 6+4+2+4+3
= 19 cm
area of figure = area of rectangle ABCG + GDEF
area = 4*3 + 4*2
area of figure = 12+8
Hence area is 20 cm².
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(12x)
D
A
E
(17x - 14)°
В
(2x + 5)°
с
The value of x for the given equation (2x+5)=(17x-14) will be 19/15.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
(2x+5)=(17x-14)
We have to rearrange the equation by applying the arithmetic operation for the like term, the terms which are similar, and we can perform arithmetic operations on it like addition and subtraction.
17x-2x=5+14
15x=19
x=19/15
Thus, the value of x for the given equation (2x+5)=(17x-14) will be 19/15.
The question is incomplete, the complete question is"solve the value of x for the given equation,
(2x+5)=(17x-14)
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Look at the table below. Which number can replace X in the table?
ratios and rates test
Group of answer choices
10
6
8
9
Answer: 9
Step-by-step explanation:
Each input is multiplied by 5. This means to get x, we need to divide 45 by 5, which is 9.
Find m and c for this line
Y+3x=1
Answer:
m = -3 ; c = 1
Step-by-step explanation:
y = -3x + 1
y = mx + c
m = -3
c = 1
Jorani buys [tex]8\frac{1}{3}[/tex] bolts of fabric. Each bolt has 24m of fabric. The fabric costs $1.65/m. Determine the total cost of the fabric.
The total cost of the fabric Jorani bought is 330 dollars.
How to find the total cost of the fabric?Jorani buys [tex]8\frac{1}{3}[/tex] bolts of fabrics. Each bolt has 24m of fabric. The fabric costs $1.65 per metres. The total cost of the fabric can be calculated as follows:
1 bolt = 24 metres
25 / 3 bolt = ?
cross multiply
length of the fabrics = 25 / 3 × 24
length of the fabrics = 600 / 3
length of the fabrics = 200 metres
Therefore,
1 metres = 1.65 dollars
200 metres = ?
cross multiply
cost of the fabric = 200 × 1.65
cost of the fabric = 330 dollars
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write the equation of a line that is parallel to y=1/2x+4 and goes thru the point(-3,4)
The standard form equation for a line passing through the point (-3, 4) and parallel to the line denoted by y = 1/2x+4 is 2y - x = 11.
The standard form equation
ax + by = c
Here a, b, and c are constants and therefore use the slope-intercept form.
y = mx + c ...... (1)
where m is the slope, b = y-intercept
y = 1/2x + 4
Slope (m) = 1/2
It passes through a line that has points (-3,4)
Let's find c by putting the value of x = -3 and y = 4 in equation (1).
4 = 1/2 (-3) + c
4 = -3/2 + c
c = 4 + 3/2
=> c = (8+3)/2
=> c = 11/2
Therefore,
y = 1/2x + 11/2
y = (x+11)/2
=> 2y - x = 11
2y - x = 11 is the standard form of the line that passes through (-3,4) and is parallel to the line represented by y = 1/2x+4.
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Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.) Auto $29,000 5 years Residual $2,000 Year Cost Accumulated Depreciation B.O.Y Book Value B.O.Y Depreciation Expense Accumulated Depreciation E.O.Y Book Value E.O.Y 1 A B C D E F 2 G H I J K L 3 M N O P Q R
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
What is the double-declining-balance method?
The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.
This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.
For each year's depreciation expense, the double rate is applied at the end of the year's balance.
For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.
Auto = $29,000
Estimated useful life = 5 years
Residual = $2,000
Depreciable amount = $27,000 ($29,000 - $2,000)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:
1st year = $11,600 ($29,000 x 40%)
2nd year = $6,960 ($17,400 x 40%)
3rd year = $4,176 ($10,440 x 40%)
4th year = $2,506 ($6,264 x 40%)
5th year = $1,758 ($3,758 - $2,000)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
4 $29,000 $22,736 $6,264 $2,506 $25,242 $3,758
5 $29,000 $25,242 $3,758 $1,758 $27,000 $2,000
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PLEASE HELP find the measure of each marked angle
Step-by-step explanation:
When dealing with transversals, most angles either add to 180 or equal to each other. These angles form a linear pair so they add to 180
[tex](x + 1) + 4x - 36 = 180[/tex]
[tex]5x - 35 = 180[/tex]
[tex]5x = 215[/tex]
[tex]x = 43[/tex]
So
[tex]x + 1 = 43+ 1 = 44[/tex]
[tex]4(43) - 36 = 136[/tex]
Answer:
x + 1 = 44 degrees
4x - 36 = 136 degrees
Step-by-step explanation:
Since the lines are parallel, the angles are same-side-interior angles, which means they are supplementary and add up to 180:
x + 1 + 4x - 36 = 180
5x - 35 = 180
5x = 180 + 35
5x = 215
x = 43
x + 1 = 43 + 1 = 44 degrees
4x - 36 = 4(43) - 36 = 136 degrees
Graphing and Solving Inequalities
m-1<-3
a
-4y <-20
5+b>1
++
-18
The last equation keeps dropping off it is -18
Solutions for the given equalities:
m < - 2
y > 5
b > -4
What is inequality in mathematics?
An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
The given inequalities are
1) m - 1 < -3
Adding 3 on both sides, we get
m - 1 + 3 < -3 + 3
m + 2 < 0
Subtracting 2 from both the side, we get
m + 2 - 2 < 0 - 2
m < - 2
The graph of this inequality is shown below
2) -4y < -20
Dividing by -4, we get
y > 5
The graph of this inequality is shown below
3) 5 + b > 1
Subtracting 1 from both the side, we get
b + 4 > 0
b > -4
The graph of this inequality is shown below
4) y = -18
This is a point on a number line, and it can be shown as
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Express x and y in terms of trigonometric ratios.
In terms of trigonometric ratios, x is 6 sin∅ and y is 6 cos∅.
Define trigonometric ratios.The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others. Circular trigonometric functions are another name for them. The ratios of an angle in a triangle are a straightforward definition of a function. This means that these trig functions provide the relationship between the angles and sides of a triangle.
Given,
Expressing x and y in terms of trigonometric ratios,
Base = 6
x = Opposite
y = Hypotenuse
x = 6 sin∅
y = 6 cos∅
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HELP ME PLS
Kevin needs to read 3 novels each month.
Let N be the number of novels Kevin needs to read in M months.
Write an equation relating N to M . Then use this equation to find the number of novels Kevin needs to read in 19 months.
Kevin needs to read 57 novels in 19 months.
Given,
The number of novels Kevin needs to read in a month = 3
N = Number of novels Kevin needs to read in M months.
Write an equation with M and N.
That is,
Kevin needs to read 3 novels in one month.
So, number of novels, N Kevin reads in M months, 3M = N
The equation is;
3M = N
Now,
The number of months Kevin needs to read the novels = 19
Then,
The number of novels Kevin reads in 19 months;
3M = N
3 × 19 = 57
That is,
Kevin needs to read 57 novels in 19 months.
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A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Answer: 240 combinations
Step-by-step explanation: So basically because you can have a possibility of 16 people being chairperson and 15 vice chairpersons, so all you have to do is multiple 16x15 which is 240.
Part A: Timothy said that AKLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy CORRECT? Explain your answer or show your work.
Yes Timothy is correct because triangle AKLM was dilated by a scale factor of 1.5 centered at the origin.
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object based on the scale factor, but not its shape.
For the given vertices of triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) or center of dilation should be calculated as follows:
Point K (-1, 3) → Point K' (-1 × 1.5, 3 × 1.5) = Point K' (-1.5, 4.5).
Point L (8, 4) → Point L' (8 × 1.5, 4 × 1.5) = Point L' (12, 6).
Point M (10, -3) → Point M' (10 × 1.5, -3 × 1.5) = Point M' (15, -4.5).
In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph, and as such Timothy is correct.
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A company that makes hair-care products had 2,000 people try a new shampoo. Of the 2,000 people, 16 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
0.08%
Step-by-step explanation:
Based on a poll, 50% of adults believe in reincarnation. Assume that 7 adults are randomly selected, and find the indicated probability. Complete parts (a) through
(d) below.
a. What is the probability that exactly 6 of the selected adults believe in reincarnation?
The probability that exactly 6 of the 7 adults believe in reincarnation is
(Round to three decimal places as needed.)
The probability that exactly 6 of the selected adults believe in reincarnation is 0.055
What is binomial distribution?The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.Here, a binomial distribution uses the two parameters n and p. The number of times the experiment is run is indicated by the variable "n," and the probability of each possible outcome is indicated by the variable "p."This will be a binomial distribution with parameters:
n = 7, p = 0.50
Hence,
a) P (Exactly 6)
= ⁷C₆(0.50)⁶ (0.50)¹
= 0.055
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f(x)=6x/5+3
Find the inverse of f(x)
f(x) can be written as y
y=6x/8
make x the subject
8y=6x
x= 8y/6
replace y with x and x with f(x)
answer:
f(x)-1 = 8x/6
A bicycle wheel has diameter 66 cm. Find how many turns the wheel makes when the bicycle travels 400 metres.
The number of turns the wheel makes is 1.93 ≈ 2.
What is Turns?
This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.
formular for calculating Turns:
Turns = Lenght
Circumference
Circumference of a circle, C= πD
Where,
Diameter=D
π =22/7
Calculating Circumference;
C= 22 * 66
7
=207.4
From the question:
D= 66cm
L =400m
Calculating Turns:
Turns = Lenght
Circumference
= 400m
207.4
Turns =1.93
Turns =1.93≈ 2
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Which set has a domain of {2,3} and a range of {5,8}?
Responses
{(2,8), (3,5), (3,0)}
{(3,5), (2,5), (3,8)}
{(8,3), (8,2), (5,2)}
{(5,8), (2,3), (3,5)}
Answer:
B
Step-by-step explanation:
The domain is the set of x-coordinates.
The range is the set of y-coordinates.
In B, x is only 2 and 3.
In B, y is only 5 and 8.
