Answers
we have the function
[tex]P(t)=\frac{60(1+0.4t)}{0.01t+3}[/tex]Part A
For t=0
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(0))}{0.01(0)+3} \\ \\ P(t)=\frac{60(1)}{3} \\ \\ P(t)=20 \end{gathered}[/tex]The initial population was 20 insectsPart B
For t=5 years -------> Convert to months
t=60 months
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(60))}{0.01(60)+3} \\ \\ P(t)=\frac{60(1+24)}{0.6+3} \\ \\ P(t)=\frac{1500}{3.6} \\ \\ P(t)=416.67 \end{gathered}[/tex]The answer is 417 insectsPart C
Determine horizontal asymptote
[tex]\begin{gathered} P(t)=\frac{60\left(1+0.4t\right)}{0.01t+3} \\ \\ rewrite \\ P(t)=\frac{60+24t}{0.01t+3} \end{gathered}[/tex]The horizontal asymptote is given by the ratio of
[tex]\frac{24}{0.01}=2,400[/tex]P(t)=2,400 ---------> horizontal asymptote
that means
as the value of time t increases ------> the value of the population tends to 2,400 insects
the population cannot be greater than 2400 insects
The range for the function P(t) is the interval [20, 2400)
All real numbers greater than or equal to 20 insects and less than 2400 insects
Part D
Using a graphing tool
Related Questions
An electric current that alternates sinusoidally with a frequency of 60
cycles per second and is at maximum at t = 0.1 seconds can be described by
the equation
I(t) = 10cos(120πt - 12π) + 5,
where I is current in Amperes and t is time in seconds. What is the
approximate range of the current?
Answers
The current is defined as rate of flow of charge I = dq/dt.
The approximate range of the current is 299.5.
How to estimate the approximate range of the current?The current is defined as rate of flow of charge I = dq/dt
Let the equation be [tex]$q=\int i d t$[/tex]
Given: I(t) = 10 cos(120πt - 12π) + 5
We will substitute it in the above equation
q = [tex]$$\int[/tex] 10 cos(120πt - 12π) + 5 dt
now here limits of time is from t = 0.1 to t = 60 s
so here it will be given as
[tex]$\int 10 cos(120\pi t - 12\pi ) + 5 dt[/tex]
Rewrite using trig identities
[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t)+5 d t$$[/tex]
Apply the Sum Rule:
[tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]
substitute the values in the above equation, we get
[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t) d t+\int_{0.1}^{60} 5 d t$[/tex]
simplifying the equation,
[tex]$\int_{0.1}^{60} 10 \cos (120 \pi t) d t=0[/tex]
[tex]$\int_{0.1}^{60} 5 d t=299.5$[/tex]
= 0 + 299.5
= 299.5
Therefore, the approximate range of the current is 299.5.
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Solve for u.u^2-u-12=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution."
Answers
we have the quadratic equation
[tex]u^2-u-12=0[/tex]we have that
a=1
b=-1
c=-12
Applying the formula to solve a quadratic equation
[tex]u=\frac{-(-1)\pm\sqrt{-1^2-4(1)(-12)}}{2(1)}[/tex][tex]u=\frac{1\pm7}{2}[/tex]The values of u are
u=4 and u=-3
therefore
The answer is
u=-3,4The graph of function f is shown. An exponential function on a coordinate plane passes through (minus 1, 7), (1, 2), (10, minus 1) and also intercepts the x-axis at 3 units and the y-axis at 4 units. Function g is represented by the table. x -1 0 1 2 3 g(x) 24 4 0 Which statement correctly compares the two functions? A. They have the same x- and y-intercepts. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same x-intercept and the same end behavior as x approaches ∞. D. They have the same y-intercept and the same end behavior as x approaches ∞.
Answers
Can you help me find the x and y of this triangle I don’t understand it
Answers
Answer: [tex]x=5\sqrt{3}, y=15[/tex]
Step-by-step explanation:
[tex]\sin 60^{\circ}=\frac{x}{10}\\\\x=10 \sin 60^{\circ}\\\\x=5\sqrt{3}\\\\\\\tan 30^{\circ}=\frac{5\sqrt{3}}{y}\\\\\sqrt{3}=\frac{y}{5\sqrt{3}}\\\\y=15[/tex]
Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards. The line of fit is given by ŷ = 3.98 + 53.59s. If the ball travels for a duration of 5 seconds, what is the predicted distance of the ball?
Answers
The predicted distance of the ball would be 27.1.93 yards when the ball travels for a duration of 5 seconds.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
The distance, y, is measured in yards and the speed, s, is measured in miles per hour.
The regression line is defined as ŷ = 3.98 + 53.59s ... (i)
The slope and y-intercept of the regression line must be determined.
The general equation for a linear regression line is y = a + bx...(ii), where x is a variable. The variable is indicated by s in the above equation.
When I and (ii) are compared, we obtain a = 3.98 and b = 53.59.
It indicates that the slope is 53.59 and the y-intercept is 3.98.
The slope, b = 53.59, implies that for every mile per hour of speed, the distance rises by 53.59 yards.
The ball travels for a duration of 5 seconds
Substitute the value of s = 5 in equation (i) to get
ŷ = 3.98 + 53.59(5)
ŷ = 271.93
Thus, the predicted distance of the ball would be 27.1.93 yards.
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Answer:
271.93
Step-by-step explanation:
You have 8 times as many dimes as nickels. You have 18 dimes and nickels altogether how much money do you have in all?
Answers
For the given condition of dimes is 8 times of nickel and there are 18 dimes and nickels altogether, then total money is equal to $1.
As given in the question,
Let x be the number of dimes
Then number of nickels are 8x.
As per given condition,
Total number of dimes and nickels = 18
⇒ x + 8x = 18
⇒ 9x = 18
⇒ x= 2
Number of dimes =2
Number of nickels = 8(2)
= 16
Conversion:
1 dime = 0.10$
1 nickel = 0.05$
Total amount of money in dollars
= 2 ×(0.10) + 16× (0.05)
= 0.20 + 0.80
= 1.00
Therefore, for the given condition of dimes is 8 times of nickel and there are 18 dimes and nickels altogether, then total money is equal to $1.
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Use the long division method to find the result when 9x³ +30x² + 10x - 24 is
divided by 3x + 8. If there is a remainder, express the result in the form
q(x)+7(2).
Answers
Answer:
8
3x² + 2x - 2 - ----------
3x + 8
Step-by-step explanation:
3x² + 2x - 2
--------------------------------
3x + 8 | 9x³ + 30x² + 10x - 24
-9x³ - 24x² ↓
--------------------------------
6x² + 10x
-6x² - 16x ↓
-------------------------
-6x - 24
+6x + 16
----------------
-8
I hope this helps!
We can desribe 15x-10 as an expression.
We would describe 6x-2<35 as an
Answers
We can describe 15x-10 as an expression.
We would describe 6x-2<35 as an inequality.
What is an inequality?In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.
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can someone help me i will give brainlest :) 5, 6, 7, 8 only do those one's
Answers
Answer:
5. -2 > x
6. 4 [tex]\leq[/tex] x
7. 0 [tex]\geq[/tex] x
8. -3 < x
Step-by-step explanation:
f(x)=2x^3+ax^2-24x+1 has a local maximum at x=-4. find a
Answers
Step-by-step explanation:
ax2+2x3−24x+1=y
Step 2: Add -2x^3 to both sides.
ax2+2x3−24x+1+−2x3=y+−2x3
ax2−24x+1=−2x3+y
Step 3: Add 24x to both sides.
ax2−24x+1+24x=−2x3+y+24x
ax2+1=−2x3+24x+y
Step 4: Add -1 to both sides.
ax2+1+−1=−2x3+24x+y+−1
ax2=−2x3+24x+y−1
Step 5: Divide both sides by x^2.
ax2
x2
=
−2x3+24x+y−1
x2
a=
−2x3+24x+y−1
x2
Answer:
a=
−2x3+24x+y−1
x2
please help me ! please
Answers
Answer:
[tex] \sf {\large{4\pi }}[/tex]
Step-by-step explanation:
Circumference of a circle ⭕ = [tex] 2 \pi r [/tex]
Where,
r = d/2
d means diameter
r = 4/2 = 2
So, substitute to equation C = 2πr
C = 2πr
C = (2r)π
C = (2•2)π
C = 4π
find the area of this question.
30pts.
Answers
Answer:
A=40, formula for area of a rectangle is a=L×W
Step-by-step explanation:
A=L×W = 10×4
The diagram shows a quadrilateral ABCD with each of its sides extended.
AB = AD
Show that ABCD is a kite. Give a reason for each stage of your working
(The diagram is attached)
Thanks, by neve124
Answers
It is to be noted that by the proof given below, the attached shape ABCD is a kite.
What is a kite in Euclidean Geometry?A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equivalent angles and two pairs of adjacent equal-length sides as a result of its symmetry.
The proof is as follows:
AB = AD [Given]
∠ADC = 115° [Angles on a Straight line]
That is 180 - 65 = 115°
∠BCD = 20° [Vertical Angles are equal]
∠ABC = (360 - (20+115+110))
= 115° [Angles in a quadrilateral]
Hence,
ABCD = Kite [Definition of a Geometric Kit]
That is
It two equivalent angles (∠ABC and ∠ADC)It also has two pairs of adjacent equal-length sides (that is |AD| ≈ |AB|.QED
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PLS HELP WITH 15. (GIVING EXTRA POINTS)
Answers
Answer:
[tex]4^{6}[/tex] or 4096
Step-by-step explanation:
When the bases are the same, you add the exponents.
Answer:
Step-by-step explanation:
[tex]\boxed{\bf\\a^n*a^m=a^{n+m}}[/tex]
[tex]\displaystyle(4)^2\cdot(4)^4\cdot(4)^0=(4)^{2+4+0}=4^6=4096[/tex]
For Problems 3–6, find the opposite of the number.4.5
Answers
ANSWER
-4.5
EXPLANATION
We want to find the opposite of the number 4.5
The opposite of a number is the number that is the same distance from 0 on the number line but on the other side.
So, if the number is on the right hand side, its opposite is on the left hand side.
In simpler terms, the opposite of a number is the negative of a number.
So, the opposite of 4.5 is -4.5.
WILL GIVE BRAINLIEST
Answers
Answer:
1. Hyperbole
2. Center: (0,0)
3. Vertices: (-3, 0), (3, 0)
4. Foci: (-6, 0), (6, 0)
5. Asymptotes: y = [tex]\frac{\sqrt{18}}{3} }[/tex]x and y = [tex]-\frac{\sqrt{18}}{3} }[/tex]x
Step-by-step explanation:
A salesperson works 40 hours per week at a job where he has two options for being paid option a is an early wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option
Answers
The salesperson needs to make weekly sales of $9,500 to earn the same amount with each option.
The amount he earns by option A can be calculated as follows;
As he works 40 hours per week and the hourly wage is $19; therefore the amount he will earn can be determined by multiplication as follows;
Option A earning: 40 × 19 = $760
Thus, the salesperson earns $760 through option A.
Consider x to be the amount of weekly sales;
As the commission rate is 8% of sales therefore 8% of x should be equal to $760 for the salesman to earn the same amount with both options.
(8/100)x = 760
0.08x = 760
x = 760 / 0.08
x = 9,500
Hence the salesman needs to make weekly sales of $9,500 to earn the same amount with both options.
Although there is a mistake in your question, you might be referring to this question;
A salesperson works 40 hours per week at a job where he has two options for being paid option a is an hourly wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option
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At the start of a trip, a car's gas tank contains 12 gallons of gasoline. During the trip, the car consumes 10 gallons of gasoline. How much gasoline is left in the tank? Should you represent this amount with a positive or negative value? Why?
Answers
If the tank contains 12 gallons and then the car consumes 10, we can know how much gasoline is left by substracting 12 with 10:
12 - 10 = 2
Then, 2 gallons of gasoline is left in the tank
Since there is still gasoline because 12 is higher than 10, then we represent this amount with a positive value.
The equation of the line that is perpendicular to the line 5x + 6y = 18 and passes through the point (10,7)
Answers
Answer:
y = ( 6 / 5 )x - 5;
Step-by-step explanation:
Perpendicular Line Theoryy = - ( 1 / m )x + c;
AlgebraConvert dual intercept to standard form.
5x + 6y = 18;
Subtract 5x from both sides.
6y = - 5x + 18;
Divide both sides by 6.
y = ( - 5x + 18 ) / 6;
y = ( - 5x / 6 ) + ( 18 / 6 );
y = ( - 5 / 6 )x + 3;
Get the perpendicular line.
y = ( 6 / 5 )x + c;
Substitute the point.
7 = ( 6 / 5 )( 10 ) + c;
7 = 12 + c;
Subtract 12 from both sides.
- 5 = c;
c = - 5;
y = ( 6 / 5 )x - 5;
what is 16 divided by 3,482
Answers
Answer:217.625
Step-by-step explanation:
Let S be any sample space, and E, F and G be any three events. Describe the event that E and G occur, but not the event F.
Answers
In the sample space, the annotation for the event where both E and G but not F occurs is given as:( E ∩ G ) ∩ Fc (Option B).
What are events in Math?An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.
Colloquially, the sample space for a given set of events is the collection of all potential values for the events. Technically, a sigma-algebra is formed by the set of probable occurrences for a given random variate, and sample space is defined as the biggest set in the sigma algebra.
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Full Question:
Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.
a) ( Ec ∪ G ) ∩ Fc
b) ( E ∩ G ) ∩ Fc
c) ( E ∪ G ) ∪ Fc
d) ( Ec ∪ Gc ) ∩ F
e) ( E ∩ G ) ∩ F
f) None of the above.
The annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc which is the correct answer would be an option (B).
What are events in probability?In probability theory, an event is a predetermined group of outcomes from a random experiment. Another definition of an event is any subset of a sample space, which is the collection of all possible results of a random experiment.
We are allowed to use here for the necessary notation, though one way to indicate this is the complement of E U F U G. This would be the area in the sample space S that lies outside E, F, and G in a Venn diagram.
Thus, the annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc
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The question seems to be incomplete the correct question would be
Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.
a) ( Ec ∪ G ) ∩ Fc
b) ( E ∩ G ) ∩ Fc
c) ( E ∪ G ) ∪ Fc
d) ( Ec ∪ Gc ) ∩ F
e) ( E ∩ G ) ∩ F
f) None of the above.
The difference between two-fifth of a number and 9 is 7. Find the number.
Answers
Answer:
The number is 40.
Step-by-step explanation:
Step 1: Assume your variables
Consider the 'number' to be [tex]x[/tex].
Step 2: Create an equation(s)
The information in the question states that the difference between [tex]\frac{2}{5}[/tex] of [tex]x[/tex] and [tex]9[/tex], is [tex]7[/tex].
Representing this mathematically gives us:
[tex](\frac{2}{5}\times x) -9=7[/tex]
Step 3: Solve the equation
The equation we have is:
[tex](\frac{2}{5}\times x) -9=7[/tex]
So, let's solve it:
[tex](\frac{2}{5}\times x) -9=7\\\\\text{Add 9 to both sides:}\\(\frac{2}{5}\times x) -9+9=7+9\\\\\text{Simplify:}\\(\frac{2}{5}\times x)=16\\\\\text{Multiply by}~\frac{5}{2}~\text{on both sides:}\\\frac{5}{2}\times\frac{2}{5}\times x=16\times \frac{5}{2}\\\\\text{Simplify:}\\1\times x=\frac{80}{2}\\\\\text{Calculate:}\\x=40[/tex]
A bag contains 2 white balls, 6 orange balls and 2 red balls. If a ball is drawn, find the probability that it is a white or red ball.
Answers
First, let's calculate the total amount of balls:
[tex]2+6+2=10[/tex]Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.
So the probability is:
[tex]p=\frac{red\text{ or }white}{total}=\frac{4}{10}=\frac{2}{5}[/tex]Correct option: A
Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculatorlog5 (15x + 20y)
Answers
The given expression is
[tex]\log _5(15x+20y)[/tex]Factor out the greatest common factor between 15x and 20y.
[tex]\log _5(5(3x+4y))[/tex]Then, use the product property to expand the logarithm.
[tex]\log _55+\log _5(3x+4y)[/tex]At last, simplify the first logarithm because its base is equal to its argument.
[tex]1+\log _5(3x+4y)[/tex]Therefore, the simplest form of the logarithm is
[tex]1+\log _5(3x+4y)[/tex]Which function is shown in the graph?
Answers
Answer:
1st option
Step-by-step explanation:
A painter has three partially filled paint cans.1 7/8 gallonsthe second contains 1 1/5 gallonsand the third contains 1 3/4which anwer is closet to the total amount of paint?A.2B.3C.4D.5
Answers
A painter has three partially filled paint cans.
The first contains 1 7/8 gallons
The second contains 1 1/5 gallons
The third contains 1 3/4 gallons
The total amount of paint is the sum of these paint cans.
[tex]total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4}[/tex]Now let us add these mixed fraction numbers
[tex]\begin{gathered} total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4} \\ total=(1+1+1)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(1.825) \\ total=4.825 \end{gathered}[/tex]As you can see, 4.825 is closest to 5.
Therefore, the correct option would be D
What is a correct congruence statement for the triangles shown?
Enter your answer in the box.
Answers
Answer:
ASA
Step-by-step explanation:
there are two congruent angles with an included side in between
Answer: Triangle RHS and NKW are congruent through the Congruence Theorem Angle-Side-Angle.
Step-by-step explanation:
The side HS is congruent to the side KW.
The angle H is congruent to angle K.
The angle S is congruent to angle S.
what proportion of american households has at least one television? group of answer choices virtually all american households have at least one tv. except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of american households have at least one tv. more than 50% of american households have at least one tv. virtually all middle-class and upper-class households have at least one tv; however, about 50% of lower-income families have a tv.
Answers
About 50% of Americans households have a tv except who live in low-income, single-parent, or disadvantaged homes
What is meant by Proportion?Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole
Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.
however, about 50% of Americans households have a tv
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A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?
Answers
With the width and length being held constant, the height of the box decreases at rate 5 cm/s
Let:
l = length
w = wide
h = height
Then, the volume of the box is given by:
V = l . w. h
The length and the width are assumed to be constant. Hence, the derivative with respect to time is:
dV/dt = l . w dh/dt
Parameters given:
dV/dt = - 541 cm³/dt
l = 9 cm
w = 12 cm
Plug these parameters into the formula:
-541 = 12 . 9 . dh/dt
dh/dt = 5 cm/s
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Write an equation of a parabola with a vertex at the origin and a directrix at y=5
Answers
SOLUTION
The equation of the parabola is defined using
[tex]y=\frac{1}{4(f-k)}(x-h)^2+k[/tex]Since the vertex is at the origin the equation becomes
[tex]\begin{gathered} y=\frac{1}{4(f-0)}(x-0)^2+0 \\ y=\frac{1}{4f}x^2 \end{gathered}[/tex]Since the directrix is y=5
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix
It follows
[tex]\begin{gathered} f-k=k-5 \\ f=-5 \end{gathered}[/tex]Thus the equation becomes
[tex]\begin{gathered} y=\frac{1}{4\times-5}x^2 \\ y=-\frac{x^2}{20} \end{gathered}[/tex]Therefore the equation of the required parabola is
[tex]y=-\frac{x^2}{20}[/tex]Answer: Y=-1/20x^2
Step-by-step explanation: