twice the sum of k and 9 is 4

The THREE true statements regarding the graph of B(w) are;

A) Based on the zeros of the function, the number of boxes of cereal sold is 0 after 0 weeks.

C) Based on the end behavior of the function, the number of boxes of cereal sold will keep falling after reaching the maximum.

E) Based on the asymptote of the function, the number of boxes of cereal sold will never reach 0 after the cereal is introduced in the store.

We are given the graph represented by the quadratic function;

B(w) = 120w/(150 + w²) for w ≥ 0 that models;

the number of boxes, B, in thousands, of the cereal sold after w weeks

From the graph, we can see that at the origin which is the coordinate (0, 0) that it remains so and as such the number of boxes of cereal sold is 0 after 0 weeks. Thus, option A is correct

Secondly, from the given graph, we see that the graph starts rising from zero to a maximum after which it keeps falling. Thus, we can say that option C is correct

Lastly, we see that the graph asymptote approaches 500 thousand boxes but never gets to zero and as such we can say that option E is correct.

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Answer:

x = 4 and y = −1

(4, -1)

Step-by-step explanation:

I going to solve this system of equations by elimination. (You could also solve by substitution too.)

Multiply the first equation by 1, and multiply the second equation by -2.

1(−2x+9y= -17)

-2(-x - 3y = -1)

Becomes:  

−2x + 9y = −17

2x + 6y = 2

Add these equations to eliminate x:

15y = −15

15y/15 = -15/15

y = -1

Now we solve for x:

-x -3(-1) = -1

-x + 3 = -1

     -3   -3

-x = -4

x = 4

Hope this helped!

Answer:

20:25

Step-by-step explanation:

it can go simpler than that if you want.

it can also be 4:5

Answer:

the ratio of cats to dogs is 20:25

Step-by-step explanation:

The ratio of cats to dogs is 20:25, 20/25, or 20 to 25 :)

Using property 8 and the midpoint rule, we have estimated the value of the integral ∫1147xdx to be approximately 14.

Property 8 of the definite integral states that if a < b and 0 < c < d, then:

∫baf(x)dx = ∫dcf(x)dx - ∫caf(x)dx

We can use this property to estimate the value of the integral ∫1147xdx. Let's choose c = 1 and d = 4, so that 0 < c < d and a < b. Then:

∫1147xdx = ∫447xdx - ∫11x dx

Next, we can use a numerical method, such as the midpoint rule or trapezoidal rule, to estimate the value of each of the integrals on the right side of the equation.

For example, using the midpoint rule with n = 4 subintervals for each integral:

∫447xdx ≈ (4 - 4/2) + (4 - 3/2) + (4 - 2/2) + (4 - 1/2) = 4 + 4 + 4 + 4 = 16

∫11x dx ≈ (1 - 1/2) + (1 - 2/2) = 1 + 1 = 2

So, our estimate of ∫1147xdx becomes:

∫1147xdx ≈ 16 - 2 = 14

Therefore, using property 8 and the midpoint rule, we have estimated the value of the integral ∫1147xdx to be approximately 14.

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The right Riemann sum for arctan(1 + xdx) is Σ[arctan(1 + iΔx)]Δx, where i ranges from 1 to n and Δx is the width of each subinterval. The correct answer among the options provided is (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx.

In a right Riemann sum, the function is evaluated at the right endpoint of each subinterval. Therefore, we add up the values of arctan(1 + iΔx) at the endpoints of the subintervals, where i ranges from 1 to n. The width of each subinterval is Δx, so we multiply the sum by Δx to get the approximate value of the integral.

The provided expression (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx satisfies the conditions of a right Riemann sum, where the function is evaluated at the right endpoint of each subinterval. Therefore, this is the correct option among the given choices.

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The equation of an exponential function is y = a(b^x)

An exponential function is a mathematical function that has a constant base raised to a variable exponent.  Exponential functions are used to model processes that exhibit exponential growth or decay, such as population growth, radioactive decay, or the spread of infectious diseases.

The general form of an exponential function is:

f(x) = ab^x

where a is the initial value, b is the base, and x is the variable exponent. If the base is greater than 1, the function will exhibit exponential growth, while if the base is between 0 and 1, the function will exhibit exponential decay.

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

Answer:

d

Step-by-step explanation:

Answer:

21.801

Good luck

Answer:

Step-by-step explanation:

\(\sqrt{x} Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\\sqrt{(5-3)^{2}+(6-k)^{2}}=2\sqrt{2}\\\\\sqrt{(2)^{2}+[(6)^{2}-(2*6*k)+(k)^{2}]}=2\sqrt{2}\\\\\sqrt{4+[36-12k+k^{2}]}=2\sqrt{2}\\\\\sqrt{40-12k+k^{2}}=2\sqrt{2}\\\)

Take square both side

\(40-12k+k^{2}=(2\sqrt{2})^{2}\\\\40-12k+k^{2}=4*2\\\\40-12k+k^{2}=8\\\\k^{2}-12k+40-8=0\\\\k^{2}-12k+32=0\\\)

Factorize,

Sum = -12

Product = 32

Factors = -8 , -4

k² - 8k - 4k + (-8)*(-4) = 0

k(k - 8) - 4(k - 8) = 0

(k - 8)(k - 4) = 0

k = 8 or 4

The points are (3,k) and (5,6).

Given, distance = 2√2 units

Applying distance formula,

Distance = √(x2-x1)^2 + (y2-y1)^2

2√2 = √(x2-x1)^2 + (y2-y1)^2

Squaring both sides,

(2√2)^2 = [√(x2-x1)^2 + (y2-y1)^2]^2

8 = (x2-x1)^2 + (y2-y1)^2

8 = (5-3)^2 + (6-k)^2

8 = 2^2 + (6^2 - 2x6xk + k^2)

8 = 4 + 36 - 12k + k^2

8 = 40 - 12k + k^2

= k^2 - 12k + 32 = 0

On factorising,

=> k^2 - 4k - 8k + 32 = 0

=> k(k-4) -8(k-4) = 0

=> (k-4)(k-8) = 0

=> k-4 = 0 , k-8 = 0

=> k = 4 , k = 8

The equation of the plane parallel to the xy-plane and passing through the point P₀(-1,0,0) is given by the equation x+y+z=0.

A plane can be represented by an equation of the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the variables x, y, and z, respectively, and D is a constant.

In this case, since the plane is parallel to the xy-plane, it means that the coefficient of z in the equation should be zero.

Therefore, we can ignore the term involving z in the equation.

Now, to find the specific equation for the plane passing through the point P₀(-1,0,0), we substitute the coordinates of the point into the equation.

We have (-1) + 0 + 0 = 0.

Thus, the equation of the plane parallel to the xy-plane and passing through the point P₀(-1,0,0) is x + y + z = 0.

This equation represents all the points in three-dimensional space that lie on the plane and have the same relationship between their x, y, and z coordinates.

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Answer:

2.75 each pack

Step-by-step explanation:

13.75 divided by 5 =2.75

Answer:

(820 ; 980)

Step-by-step explanation:

Given :

Sample size, n = 80

Number of bilingual from sample = 36

Sample proportion, phat = x / n = 36 / 80 = 0.45

Margin of Error = 4% = 0.04

Interval = sample proportion ± margin of error

0.45 ± 0.04

(0.41 ; 0.49)

(0.41 * 2000 ; 0.49 * 2000)

(820 ; 980)

Answer:

C. 6

May the 4th be with you :)

Answer:

x = 6

4(8-6)=8

4(2)=8

8=8

Answer:

-3.75 but i would guess -3

Step-by-step explanation:

A = (-10 - 5) / (4 - 0) = -15 / 4 = -3.75

Answer:

\(-\dfrac{5}{4}\)

Step-by-step explanation:

average rate of change of function f(x) between x = a and x = b

\( \dfrac{f(b) - f(a)}{b - a} \)

Here, a = 0; f(a) = f(0) = -5; b = 4; f(b) = f(4) = -10

\( \dfrac{f(b) - f(a)}{b - a} \)

\(= \dfrac{-10 - (-5)}{4 - 0}\)

\(= \dfrac{-5}{4}\)

\(= -\dfrac{5}{4}\)

Answer:

$288

Step-by-step explanation:

16+8=24

$24 per book

24 x 12 = 288

Answer:

See below

Step-by-step explanation:

a) Here,

Mode = 2

2 occurs 7 times. (frequency = 7)

b) Here,

Mode = 1 (occurring 8 times)

c) Here,

Mode = 10 (occurring 9 times)

d) Here,

Mode = 20 (occurring 5 times)

e) Here,

Mode = 3 (occurring 6 times)

f) Here,

Mode = 15 (occurring 5 times)

\(\rule[225]{225}{2}\)

The end of the plank is sliding along the ground at a rate of approximately -0.08 m/s when it is 1.4 meters from the wall of the building. The negative sign indicates that the end of the plank is sliding in the opposite direction.

To find how fast the end of the plank is sliding along the ground, we can use related rates. Let's consider the position of the end of the plank as it moves along the ground.

Let x be the distance between the end of the plank and the wall of the building, and y be the distance between the end of the plank and the ground. We are given that dx/dt = 0.26 m/s, the rate at which the worker pulls the rope.

We can use the Pythagorean theorem to relate x and y:

x² + y² = 5²

Differentiating both sides of the equation with respect to time, we get:

2x(dx/dt) + 2y(dy/dt) = 0

At the given moment when x = 1.4 m, we can substitute this value into the equation above and solve for dy/dt, which represents the rate at which the end of the plank is sliding along the ground.

2(1.4)(0.26) + 2y(dy/dt) = 0

2(0.364) + 2y(dy/dt) = 0

0.728 + 2y(dy/dt) = 0

2y(dy/dt) = -0.728

dy/dt = -0.728 / (2y)

To find y, we can use the Pythagorean theorem:

x² + y² = 5²

(1.4)² + y² = 5²

1.96 + y² = 25

y² = 23.04

y = √23.04 ≈ 4.8 m

Substituting y = 4.8 m into the equation for dy/dt, we have:

dy/dt = -0.728 / (2 * 4.8) ≈ -0.0757 m/s

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Answer:

22.287

Explanation:

This is because 15 is a whole number.

It is also 15.000

37.287

-15.000\(\\\)

22.287

After using the formula for the sum of an infinite geometric series, we conclude that the given infinite series does not converge to 1.

To prove that the infinite series ∑(i=1 to ∞) 2^(i-1) equals 1, we can use the formula for the sum of an infinite geometric series.

The sum of an infinite geometric series with a common ratio r (|r| < 1) is given by the formula:

S = a / (1 - r)

where 'a' is the first term of the series.

In this case, our series is ∑(i=1 to ∞) 2^(i-1), and the first term (a) is 2^0 = 1. The common ratio (r) is 2.

Applying the formula, we have:

S = 1 / (1 - 2)

Simplifying, we get:

S = 1 / (-1)

S = -1

However, we know that the sum of a geometric series should be a positive number when the common ratio is between -1 and 1. Therefore, our result of -1 does not make sense in this context.

Hence, we conclude that the given infinite series does not converge to 1.

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Answer:

a) The modal class for this case represent the class with the highest frequency

And for this case would be \( 24 <a<26\) with the highest frequency 8

b) \( \bar X = \frac{19*3 + 21*2 + 23*7 +25*8}{3+2+7+8} =23\)

Step-by-step explanation:

Part a

The modal class for this case represent the class with the highest frequency

And for this case would be \( 24 <a<26\) with the highest frequency 8

Part b

For this case we need to find the mid point of each interval:

Interval   Midpoint  Frequency

18-20          19                 3

20-22         21                 2

22-24         23                 7

24-26         25                 8

And we can find the sample mean with this formula:

\( \bar X = \frac{\sum_{i=1}^n f_i x_i}{n}\)

And replacing we got:

\( \bar X = \frac{19*3 + 21*2 + 23*7 +25*8}{3+2+7+8} =23\)

The class with the highest frequency  represents the modal class for this case and for this case would be (24 < a < 26) with the highest frequency of 8 and an estimate of the mean age of these employees is 23.

Given :

The table shows the age, in years, of employees in a company.

A) The class with the highest frequency  represents the modal class for this case and for this case would be (24 < a < 26) with the highest frequency 8.

B) To estimate the mean age of these employees, first, determine the midpoint.

Age              Frequency              Midpoint

18-20                    3                             19

20-22                   2                             21

22-24                    7                             23

24-26                    8                             25

The formula of the sample mean is given by:

\(\rm \bar{X} =\dfrac{\sum^{n}_{i=1}f_ix_i}{n}\)

\(\rm \bar{X} = \dfrac{19\times 3+21\times 2 +23\times 7+25\times 8}{3+2+7+8}\)

\(\rm \bar{X} = 23\)

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Answer:

The scale factor used is 0.4

Step-by-step explanation:

Given

\(R = (3,9)\)

\(R' = (1.2, 3.6)\)

Required

Determine the scale factor of RST

The question can be solved using scale factor formula

Scale factor is calculated as thus;

\(Scale\ Factor = \frac{New\ Length}{Old\ Length}\)

In this case; R' is the new length and R is the old length

\(Scale\ Factor = \frac{R'}{R}\)

Substitute the values of R and R'

\(Scale\ Factor = \frac{(1.2,3.6)}{(3,9)}\)

Factorize the denominator

\(Scale\ Factor = \frac{(1.2,3.6)}{2.5(1.2,3.6)}\)

\(Scale\ Factor = \frac{1}{2.5}\)

\(Scale\ Factor = 0.4\)

Hence, the scale factor used is 0.4

The researchers who developed predator prey models that accounted for resource limitations experienced by the prey. The correct answer is d. Rotondweig and MacArthur.

Rotondweig and MacArthur are the researchers who developed predator-prey models that considered the resource limitations experienced by the prey. Their models built upon the earlier work of Gause, Verhulst, and other researchers in population ecology. Rotondweig and MacArthur's models improved upon earlier models by incorporating the concept of limited resources and their effect on prey population dynamics.
The predator-prey models created by Rotondweig and MacArthur consider how the availability of resources influences the interactions between predators and their prey. In these models, the prey's population growth is regulated not only by the predation rate but also by the carrying capacity of their environment, which is determined by the availability of resources. As a result, their models provide a more realistic representation of natural ecosystems.
To summarize, the researchers responsible for developing predator-prey models that accounted for resource limitations experienced by the prey are Rotondweig and MacArthur. Their models improved upon earlier work by incorporating the concept of limited resources and their effect on prey population dynamics.

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Step-by-step explanation:

90 girls were at the dance

Answer:

60:90

Step-by-step explanation:

use cross multiplication :)))

Answer:

I guess 09.222....

Step-by-step explanation:

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

Luna has half a cup (1/2) (0.5) left in her cup

Step-by-step explanation:

3/4+3/8=1.125 1.125-5/8 of a cup=0.5

(a) -2.5A has an x-component of 13.225 m and a y-component of -10.857 m. (b) For A + B, the magnitude is approximately 18.098 m, and the direction is approximately 14.198° counterclockwise from the +x-axis. (c) For A - B and B - A, both have a magnitude of approximately 28.506 m, and the direction is approximately -8.080° counterclockwise from the +x-axis.

Given Magnitude of vector A: |A| = 7.5 m

Angle from the positive x-axis: θ = 145° (counterclockwise)

(a) X-component of vector A:

Ax = |A| * cos(θ)

  = 7.5 * cos(145°)

  ≈ -5.290 m

(b) Y-component of vector A:

Ay = |A| * sin(θ)

  = 7.5 * sin(145°)

  ≈ 4.343 m

Now, let's calculate the components of vector -2.5A.

(a) X-component of -2.5A:

(-2.5A)x = -2.5 * Ax

        = -2.5 * (-5.290 m)

        ≈ 13.225 m

(b) Y-component of -2.5A:

(-2.5A)y = -2.5 * Ay

        = -2.5 * (4.343 m)

        ≈ -10.857 m

Next, let's consider vector B, which has triple the magnitude of vector A and points in the +x direction.

Given:

Magnitude of vector B: |B| = 3 * |A| = 3 * 7.5 m = 22.5 m

Direction: Since vector B points in the +x direction, the angle from the positive x-axis is 0°.

Now, we can calculate the desired quantities using vector addition and subtraction.

(a) A + B: Magnitude: |A + B| = :\(\sqrt{((Ax + Bx)^2 + (Ay + By)^2)}\)

                  = \(\sqrt{((-5.290 m + 22.5 m)^2 + (4.343 m + 0)^2)}\)

                  = \(\sqrt{((17.21 m)^2 + (4.343 m)^2)\)

                  ≈ 18.098 m

Direction: Angle from the positive x-axis = atan((Ay + By) / (Ax + Bx))

                                        = atan((4.343 m + 0) / (-5.290 m + 22.5 m))

                                        = atan(4.343 m / 17.21 m)

                                        ≈ 14.198° (counterclockwise from the +x-axis)

(b) A - B: Magnitude: |A - B| = \(\sqrt{((Ax - Bx)^2 + (Ay - By)^2)}\)

                  = \(\sqrt{((-5.290 m - 22.5 m)^2 + (4.343 m - 0)^2)}\)

                  = \(\sqrt{((-27.79 m)^2 + (4.343 m)^2)}\)

                  ≈ 28.506 m

Direction: Angle from the positive x-axis = atan((Ay - By) / (Ax - Bx))

                                        = atan((4.343 m - 0) / (-5.290 m - 22.5 m))

                                        = atan(4.343 m / -27.79 m)

                                        ≈ -8.080° (counterclockwise from the +x-axis)

(c) B - A:Magnitude: |B - A| = \(\sqrt{((Bx - Ax)^2 + (By - Ay)^2)}\)

                  = \(\sqrt{((22.5 m - (-5.290 m))^2 + (0 - 4.343 m)^2)}\)

                  = \(\sqrt{((27.79 m)^2 + (-4.343 m)^2)}\)

                  ≈ 28.506 m

Direction: Angle from the positive x-axis = atan((By - Ay) / (Bx - Ax))

                                        = atan((0 - 4.343 m) / (22.5 m - (-5.290 m)))

                                        = atan((-4.343 m) / (27.79 m))

                                        ≈ -8.080° (counterclockwise from the +x-axis)

So, the complete step-by-step calculations provide the values for magnitude and direction for each vector addition and subtraction.

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The complete question is:

The magnitude of vector  A  is 7.5 m. It points in a direction which makes an angle of 145  ∘  measured counterclockwise from the positive x-axis. (a) What is the x component of the vector −2.5  A  ? m (b) What is the y component of the vector −2.5  A  ? m (c) What is the magnitude of the vector −2.5  A  ? m following vectors? Give the directions of each as an angle measured counterclockwise from the +x-direction. If a vector A has a magnitude 9 unitsand points in the -y-directionwhile vector b has triple the magnitude of A AND points in the +x direction what are te direction and magnitude of the following.

(a)  A  +  B  magnitude unit(s) direction ∘ (counterclockwise from the +x-axis) (b)  A  −  B  magnitude unit(s) direction ∘ (counterclockwise from the +x-axis) (c)  B  −  A  magnitude unit(s) direction - (counterclockwise from the +x-axis)