Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research.


Which insect population is growing at a faster rate?
The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week.
The bee hive is growing at a faster rate. It will multiply by 3.8 each week while the ant colony will add 3.8 each week.
The ant colony is growing at a faster rate. It will add 3.8 each week while the bee hive will subtract 3.8 each week.
The bee hive is growing at a faster rate. It will add 3.8 each week while the ant colony will divide by 3.8 each week.

Answer:

need more info, can't solve if it's very hard to read.

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

Both should be in same measurement. so convert 4 kg to gram

1 Kg = 1000 g

4 kg = 4 * 1000 = 4000 g

\(\frac{200}{4000}*100=\frac{2}{40}*100\\\\=\frac{1}{20}*100 = 1 * 5\\\)

= 5%

Answer:

and

Step-by-step explanation:

The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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Answer:

\(y = 4x - 3\\Slope \ m_1 = 4\)

EQUATION OF LINE PERPENDICULAR

\(Lines \ are \ perpendicular => m_1 \cdot m_2 = -1\\\)

\(slope, m_2 = \frac{-1}{4}\)

\(equation \ of \ the\ line \ passing \ through \ (-2, 2) \ slope ,m_2 :\\(y - y_2) =m_2(x - x_2)\\ (y - 2) = \frac{-1}{4} (x -(-2))\\\\y - 2 = \frac{-1}{4} (x +2)\\\\y = \frac{-1}{4}x - \frac{1}{2} + 2\\\\y = \frac{-1}{4}x + \frac{3}{2}\)

EQUATION OF LINE PARALLEL

\(Lines \ are \ parallel => m_1 \cdot m_3 = 1\\slope, m_3 = \frac{1}{4}\)\(Equation \ of \ the \ line \ through \ (-2, 2) \ and \ slope, m_3:\\(y - y_3) =m_3(x - x_3)\\\\(y-2) = \frac{1}{4} (x - (-2))\\\\y-2 = \frac{1}{4}(x+2)\\\\y = \frac{1}{4}x + \frac{1}{2} +2\\\\y = \frac{1}{4}x + \frac{5}{2}\)

The down payment you need to purchase the house for 185,000 with a 20% down payment is 37,000.

a : a part of a whole expressed in hundredths a high percentage of students attended

b : the result obtained by multiplying a number by a percent the percentage equals the rate times the base 2 a : a

share of winnings or profits

To calculate the down payment needed to purchase a house for 185,000 with a 20% down payment, follow these steps:

Determine the percentage required for the down payment:

20%

Convert the percentage to a decimal by dividing by 100:

20% ÷ 100 = 0.20

Multiply the house price by the decimal:

185,000 x 0.20 = 37,000

The down payment you need to purchase the house for 185,000 with a 20% down payment is 37,000.

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Answer:

The second and third option are both functions!!

Glad to help!!

Step-by-step explanation:

Answer:

3 1/2

Step-by-step explanation:

Quarter bag plus three quarter bag=1 bag

2 half bags is one bag

2 three quarters full is 1 1/2 bag :)

3 1/2 (three and a half)

Step-by-step explanation:

if u mean full bags, then add them

all together and simplify:

1/4+1/2+1/2+3/4+3/4+3/4=

=1/4+1+9/4=

=14/4=

=7/2=

=3 1/2 bags.

so 3 full bags and 1 half bag.

Answer: Choose A my smart self just knew

First, we have to find the percent that went to social issue on saturday

So, with this we can calculate the Sunday amount

399 people are expected to go to Social Issues

Answer:

hello the figure related to your question is missing attached below is the missing figure

answer : 157.08 m^2

Step-by-step explanation:

Calculate the area of the shaded area

= Area of the large circle - Areas of the small circles

= (( \(\frac{\pi }{4}\) ) * D^2) - 2(  ( \(\frac{\pi }{4}\) ) * d^2 )     given that the small circles are congruent

= (( \(\frac{\pi }{4}\) ) * 20^2 ) - 2 ( ( \(\frac{\pi }{4}\) ) * 10^2 )

= 314.16 - 157.08

= 157.08 m^2

Therefore, the correct option is b. 0.317.

We are given that a bag contains 8 purple marbles and 12 green marbles.

A marble is drawn and then replaced.

This is done 40 times.

We need to find the probability that a purple marble is drawn at most 15 times.

Let X be the number of purple marbles drawn in 40 draws.

Then, X is a binomial random variable with n = 40 and p = 8/20 = 0.4

We are to find the probability that X ≤ 15.

Using the binomial probability formula, we have:P(X ≤ 15)

= ∑P(X = r),

where the summation is taken over all possible values of r from 0 to 15.

P(X = r) = nCr p^r (1-p)^(n-r),

where nCr = n!/[r!(n-r)!]

Hence,P(X ≤ 15) = ∑P(X = r) (for r = 0, 1, 2, ..., 15)

= P(X = 0) + P(X = 1) + P(X = 2) + ....... + P(X = 15)

We can use binomial probability tables or a calculator to find the above probabilities and sum them up.

After rounding to three decimal places, we get :P(X ≤ 15) = 0.317

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An object moving horizontally will always have a negative acceleration ax if it is slowing down or decelerating.

An object moving horizontally will always have a negative acceleration ax if it is slowing down or decelerating. Acceleration is a measure of the change in velocity of an object and is typically defined as the second derivative of the position with respect to time.

If an object is slowing down or decelerating, its velocity will be decreasing, and its acceleration will be negative. This means that the direction of the acceleration will be opposite to the direction of motion, resulting in a negative value for ax. In physics, acceleration is a vector quantity, meaning it has both magnitude and direction.

If an object is moving horizontally and slowing down, the direction of the change in velocity will be perpendicular to the direction of motion, resulting in a negative acceleration ax.

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Answer:

The answer is 1,102

Step-by-step explanation:

First, we need to figure out how much per hour.

406 divided by 7 = 58

Now we multiply by the hours

58 x 19 = 1,102

Answer:

1,102 miles

Step-by-step explanation:

406=7

406/7= 58

1 hour = 58 miles

19 times 58 = 1,102

Two steps that will complete the list correctly are:

4. The original measurement should be multiplied by the conversion factors.

5. Verify that it makes sense.

A conversion factor can be used to switch from one set of units to another by multiplying or dividing a number. When a conversion is necessary, the appropriate conversion factor to an equivalent value must be applied.

Let's use an example of converting from inches to centimeters to address this query.

10 inches should be converted to cm.

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Coplanar points are those that are all in the same PLANE. The other point that lies on line AC is B.

Collinear Points: Points are collinear if they are all in the same straight line.

Coplanar points: Coplanar points are those that are all in the same PLANE.

A.) Another way to label KF is F K.

B.) The other point that lies on line AC is B.

C.) Yes, Any two points can form a line, thus, A and D are colinear.

D.) Coplanar points are those points that lie in the same place. Although D and K lie on the same plane,j; the point E does not lie on the same plane. Thus, points E, D, and K are not coplanar points.

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Answer:

here

2/3 / 1/7

2/3 * 7/1

14/3

In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

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The system of equation 2x + y = 2 y = –2x – 1 has infinitely many solutions because the coefficient of the x and y in the equations are same.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations:

2x + y = 2  …(1)

y = –2x – 1  or

2x + y = -1 ...(2)

As we can see the coefficient of the x and y in the equation (1) and (2) are same which means they infinitely many solutions.

Thus, the system of equation 2x + y = 2 y = –2x – 1 has infinitely many solutions because the coefficient of the x and y in the equations are same.

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The salary of the teacher who is 45 year old according to the best fit line is $50000.

A straight line that minimizes the gap between it and some data is called a line of best fit.

In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

It is a result of regression analysis and a tool for forecasting indicators and price changes.

The line of best fit is a tool used in finance to find patterns or correlations in market returns across assets or across time.

From the graph the two coordinates of the best fit line are:

(30, 40000) and (70, 70000)

The equation of the line is given as:

y = mx + c

The slope of the equation is given as:

m = (y2 - y1) / (x2 - x1)

m = (70000 - 40000)/ 70 - 30

m = 30000/4

m = 750

Substituting the value of slope and coordinate in the point slope form we have:

y - y1 = m (x - x1)

y - 40000 = 750 (x- 30)

y = 750x + 17500

Here, x is the age and y is the salary.

Substituting x = 45 we have:

y = 750(45) + 17500

y = 50000

Hence, the salary of the teacher who is 45 year old according to the best fit line is $50000.

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The correct question is:

The number of square centimeters in the area of rectangle $A_3$ is 105.

The area of the rectangle is the region enclosed by the perimeter of the rectangle and is equal to product of length and width. We have two squares $A_1$ and $A_2$ with areas of 25 and 49 square centimeters, respectively. Let's find the side lengths of the squares by taking the square root of their areas:\(A1s=25=s2=25−−√=5 cm$$A2s=49=s2=49−−√=7\)cm.

We know that the area of a rectangle is equal to the product of its length and width. Therefore, the area of rectangle  A3$is:$A3=7⋅15=105 cm2. Therefore, the number of square centimeters in the area of rectangle $A_3$ is 105.

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Answer:

9

-5 - 7(-2)

-5 - (-14)

+9

Answer:

39 minutes (rounded to nearest minute from 39.2699)

Step-by-step explanation:

π(50)^2*30= 235619.449/6000=39.2699

round to nearest minute: 39 minutes

Answer:

3rd table

Step-by-step explanation:

explain attached

Answer:

The measure of the angle is 15 degree.

Step-by-step explanation:

The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle.

Supplementary angles are those that add up to 180, and complementary angles add up to 90.

Let \(x\) represent the angle.

\((180^{\circ} - x)\) is the supplementary angle and \((90^{\circ}-x)\) is the complementary angle.

\(180^{\circ}-x=3(90^{\circ}-x)-60^{\circ}\\180^{\circ}-x=270^{\circ}-3x-60^{\circ}\\180^{\circ}-x+3x=210^{\circ}\\2x=30^{\circ}\\x=15^{\circ}\)

\((90-15)^{\circ}=75^{\circ}\) is the complementary

\((180-15)^{\circ}=165^{\circ}\) is the supplementary angle

The correct answer is option C. The after-tax rates of return on the municipal and corporate bonds would be 6% and 6%, respectively.

Municipal bonds are issued by state and local governments and are generally exempt from federal income taxes. In most cases, they are also exempt from state and local taxes if the investor resides in the same state as the issuer. Therefore, the interest income from the municipal bond is not subject to federal income tax or state and local taxes.

On the other hand, corporate bonds are issued by corporations and their interest income is taxable at both the federal and state levels. The investor's marginal tax bracket of 25% indicates that 25% of the interest income from the corporate bond will be paid in taxes.

To calculate the after-tax rate of return for each bond, we need to deduct the tax liability from the pre-tax rate of return.

For the municipal bond, since the interest income is tax-free, the after-tax rate of return remains the same as the pre-tax rate of return, which is 6%.

For the corporate bond, the tax liability is calculated by multiplying the pre-tax rate of return (8%) by the marginal tax rate (25%). Thus, the tax liability on the corporate bond is 0.25 * 8% = 2%.

Subtracting the tax liability of 2% from the pre-tax rate of return of 8%, we get an after-tax rate of return of 8% - 2% = 6% for the corporate bond.

Therefore, the after-tax rates of return on the municipal and corporate bonds are 6% and 6%, respectively. Hence, the correct answer is C. 6%; 6%.

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The solutions to the given system of equations are given as follows:

1. x = 3, y = -3.

2. No solution.

3. x = 2, y = 1.

4. x = -1, y = 10.

5. No solution.

6. (x,y) = (x, 8 - 2x).

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

There are multiple ways to solve a system, and in this problem the substitution method is used, in which we write a variable as a function of another variable, replace in the other equation, then we find each variable.

From the first equation, we have that:

y = 2x - 9.

Replacing in the second:

x + 3(2x - 9) = -6

7x - 27 = -6

7x = 21

x = 3.

Then:

y = 2(3) - 9 = -3.

Then the solution is:

x = 3, y = -3.

From the first equation, we have that:

y = 2x - 7.

Replacing in the second:

6x - 3(2x - 7) = 14

6x - 6x + 21 = 14

0x = -7.

x = -7/0.

Hence no solution due to division by 0.

From the first equation, we have that:

y = 5 - 2x.

Replacing in the second:

3x - 3y = 3.

x - y = 1 (simplifying by 3)

x - 5 + 2x = 1.

3x = 6.

x = 2.

Then:

y = 5 - 2(2) = 5 - 4 = 1.

Then the solution is:

x = 2, y = 1.

From the first equation, we have that:

y = 7 - 3x

Replacing in the second:

4x + 2y = 16

4x + 2(7 - 3x) = 16

4x + 14 - 6x = 16

-2x = 2

2x = -2

x = -2/2

x = -1

Then:

y = 7 - 3(-1) = 7 + 3 = 10.

Then the solution is:

x = -1, y = 10.

From the first equation, we have that:

y = 4x - 6

Replacing in the second:

2x - 0.5y = 4

2x - 0.5(4x - 6) = 4

2x - 2x + 3 = 4

0x = 1.

Hence no solution due to division by 0.

From the first equation, we have that:

y = 8 - 2x

Replacing in the second:

3x + 1.5y = 12.

3x + 1.5(8 - 2x) = 12.

3x + 12 - 3x = 12

0x = 0.

There are infinite solutions in the following format:

(x,y) = (x, 8 - 2x).

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The Coordinates after dilation of 1.5 about the origin is

F'(1.5, -1.5)

G'(0, 3)

H'(1.5, 3)

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

Given:

We have the Coordinates F(1, -1), G(0, 2), H(1, 2).

As, the Dilation Rule for point (x, y) about origin with scale factor h

h(x, y)------>(hx, hy)

Applying the Dilation Rule we get

F(1, -1)-----> 1.5 F'(1, -1)-----> F'(1.5, -1.5)

G(0, 2)-----> 1.5 G'(0, 2)-----> G'(0, 3)

H(1, 2) -----> 1.5 H'(1, 2)-----> H'(1.5, 3)

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