The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result  in a profit of $20 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? Use the graphical LP approach.

Answer:

x = 11

Step-by-step explanation:

180 - (82+50)

180 - 132

48

5x-7 = 48

5x = 55

x = 11

The expression for the amount received for the second donor will be d² + 8d.

From the information, Aditi is participating in a walkathon fundraiser. two anonymous donors agree to donate money according to the distance she walks. the money, a, in dollars, that she receives from the first donor for walking d kilometers is given by the formula a(d)=12d.

The total money, t, in dollars, that she receives from both donors for walking d kilometers is given by the formula t(d)=d^2+20d.

The amount received for the second donor will be:

d² + 20d - 12d

= d² + 8d

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Complete question

Aditi is participating in a walkathon fundraiser. two anonymous donors agree to donate money according to the distance she walks. the money, a, in dollars, that she receives from the first donor for walking d kilometers is given by the formula a(d)=12d. the total money, t, in dollars, that she receives from both donors for walking d kilometers is given by the formula t(d)=d^2+20d. Find the amount received for the second donor.

Answer:

30

Step-by-step explanation:

Ah okay, so this is a simple proportion.

If 1 rose = 6 tulips, then you just multiply however many roses you have by 6. So in your case, 5 x 6 = 30. So in short, for every 5 roses Genny uses, she will use 30 tulips.

Answer:

30 tulips

Step-by-step explanation:

This question gives us the amount of tulips for one rose.

Let us make 1 rose as r and a tulip is t. Now write an equation for the tulips.

Tulip = 6r

If we have 5r:

5r = 6t x 5

Solve!

5r = 30t

5 roses = 30 tulips

Hope this helps :)

There are 120 different combinations when selecting Christmas presents.

There are 10 available presents in all under a Christmas tree, and

The number of presents chosen to be placed beneath a Christmas tree is 3.

We must determine how many possible combinations there are.

There are a total of three methods by which the 10 gifts can be chosen \(10C_{3}\).

that is

\(nC_{r}=\frac{n!}{r!(n-r)!}\)

\(10C_{r} =\frac{10!}{3!(10-3)!}\)

=120

In order to choose three gifts from a total of ten, there are 120 possible different combinations.

The term "probability" is most commonly used to refer to the likelihood that a specific event (or group of events) will occur, either as a linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.

5rdx

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Answer:

54 Degrees

Step-by-step explanation:

We know that the interior angles of a triangle add up to 180 degrees.

we also know that angle KLM = 48 degrees

and angle JKM = 78 degrees

since these triangles are on parallel lines we know that their angles must be equal (just inverted)

and thus:

180 - (48+78) = 54

Answer:

Step-by-step explanation:

The change over 6 week period is -24 degrees Celcius.

A.  -24/6

B . So in average every week  the temperature change is -24/6 = -4 degrees Celcius

for the square root you must look for a number that multiplied with itself gives you the indicated value

for this case a number that multiplied by itself gives you 100

sothe square root of 100 is:

Answer:

Step-by-step explanation:

For obects already in motion, the distance travelled, s, is:

s = vi*t + (1/2)at^2

where vi is the initial velocity, a is the acceleration, and t is the time in seconds.

We want the time, t, to reach 1000 meters.

1000 m = (3 m/s)*t + (1/2)*(0.1m/s^2)*(t^2)

(1/2)*(0.1m/s^2)*(t^2) = 0.05t^2

0.05t^2 + 3t -1000 = 0

Solve quadratic equation:

t = 114.6 seconds

The number of points on the curve is (a) None

From the question, we have the following parameters that can be used in our computation:

x^2/5 y^2/5 = 1

For the equation x^2/5 - y^2/5 = 1, the slope of the curve at any point is the derivative of y with respect to x,

However, the derivative of y with respect to x will never be equal to 0, which means that the curve will never have a tangent line that is horizontal.

Hence, the answer is A. None.

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Answer: x= -3

Hope this helps :)

Answer:x=-9

Step-by-step explanation: Simplify both sides of the equation 3/4x = 27/4

Multiply both sides by 4/3

4/3 • 3/4x = 4/3 • -27/4

Using Euler's method with step size h = 0.2, the approximate solution to the initial value problem at x = 4.2, 4.4, 4.6, and 4.8 is 4.8, 10.344, 21.719650882754717, and 65.86222981762188, respectively.

To approximate the solution to the initial value problem using Euler's method with a step size of h = 0.2, we can follow these steps:

Step 1: Define the differential equation:

Given initial value problem:

dy/dx = 3/x(y^2 + y), y(4) = 3

Step 2: Define the step size:

h = 0.2

Step 3: Define the points at which we want to approximate the solution:

x = 4.2, 4.4, 4.6, and 4.8

Step 4: Implement Euler's method:

We'll use the iterative formula:

y[i+1] = y[i] + h * f(x[i], y[i])

where x[i+1] = x[i] + h, and f(x[i], y[i]) represents the value of dy/dx at x[i] and y[i].

Using the given initial value y(4) = 3, we'll start with x = 4 and y = 3.

For x = 4.2:

x[1] = 4 + 0.2 = 4.2

y[1] = y[0] + h * f(x[0], y[0])

= 3 + 0.2 * (3/4 * (3^2 + 3))

= 3 + 0.2 * (3/4 * 12)

= 3 + 0.2 * 9

= 3 + 1.8

= 4.8

For x = 4.4:

x[2] = 4.2 + 0.2 = 4.4

y[2] = y[1] + h * f(x[1], y[1])

= 4.8 + 0.2 * (4.2/4.8 * (4.8^2 + 4.8))

= 4.8 + 0.2 * (4.2/4.8 * 31.68)

= 4.8 + 0.2 * 27.72

= 4.8 + 5.544

= 10.344

For x = 4.6:

x[3] = 4.4 + 0.2 = 4.6

y[3] = y[2] + h * f(x[2], y[2])

= 10.344 + 0.2 * (4.6/10.344 * (10.344^2 + 10.344))

= 10.344 + 0.2 * (4.6/10.344 * 127.051344)

= 10.344 + 0.2 * 56.87825441377359

= 10.344 + 11.375650882754718

= 21.719650882754717

For x = 4.8:

x[4] = 4.6 + 0.2 = 4.8

y[4] = y[3] + h * f(x[3], y[3])

= 21.719650882754717 + 0.2 * (4.8/21.719650882754717 * (21.719650882754717^2 + 21.719650882754717))

= 21.719650882754717 + 0.2 * (4.8/21.719650882754717 * 1007.8317707837554)

= 21.719650882754717 + 0.2 * 220.7128946743358

= 21.719650882754717 + 44.14257893486716

= 65.86222981762188

Therefore, the approximate solution to the initial value problem at the points x = 4.2, 4.4, 4.6, and 4.8 is:

For x = 4.2, y ≈ 4.8

For x = 4.4, y ≈ 10.344

For x = 4.6, y ≈ 21.719650882754717

For x = 4.8, y ≈ 65.86222981762188

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The probability that a person truly does not have the disease if they test negative is 0.9510.

If a person tests negative for the disease, the probability that the person does not have the disease can be found using the Bayes theorem.

Bayes Theorem:

It is a formula used to find the probability of an event given the probability of another event.

Bayes Theorem formula is as follows:

P(A|B) = (P(B|A) * P(A)) / P(B)

Where, P(A) and P(B) are the probabilities of events A and B respectively.

P(B|A) is the probability of event B occurring given that event A has already occurred.

P(A|B) is the probability of event A occurring given that event B has already occurred.

Given,

P(D) = 0.03 [prior probability of disease]

P(D') = 0.97 [prior probability of no disease]

P(+) = 0.94 [probability of test is positive given that the person has a disease]

P(-|D') = 0.98 [probability of test is negative given that the person doesn't have a disease]

We have to calculate the probability that a person does not have the disease if he tests negative.

Using Bayes Theorem, we can find the probability of the person truly not having the disease given that he tested negative.

P(D'|-) = (P(-|D') * P(D')) / P(-)

Where,

P(-) = P(-|D') * P(D') + P(-|D)*P(D) [total probability of negative test results]

P(-) = (0.98 * 0.97) + (0.02 * 0.03)

P(-) = 0.9991P(D'|-)

     = (0.98 * 0.97) / 0.9991= 0.9510ans

     = 0.9510 (approximately)

Therefore, the probability that a person truly does not have the disease if they test negative is 0.9510.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

100 Miles

Step-by-step explanation:

If 1 inch = 25 Miles

Take 1*4 = 4 Inches

Then take 25 * 4 = 100 Miles

Using the z-distribution, supposing a population standard deviation of 5, the minimum number of snapdragons you need for the new study is of 267.

The bounds of the confidence interval are presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which the parameters are described as follows:

The margin of error of the interval is:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value of the interval is of z = 1.96.

The population standard deviation is given as follows:

\(\sigma = 5\)

The minimum number of dragons needed is n when M = 0.6, hence:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.6 = 1.96\frac{5}{\sqrt{n}}\)

\(0.6\sqrt{n} = 1.96 \times 5\)

\(\sqrt{n} = \frac{1.96 \times 5}{0.6}\)

\((\sqrt{n})^2 = \left(\frac{1.96 \times 5}{0.6}\right)^2\)

n = 266.8 = 267 (rounded up, as 266 would have a margin of error slightly above the desired).

The population standard deviation is missing, and we suppose that it is of 5.

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The divergence theorem states that the surface integral of the divergence of a vector field over a closed surface is equal to the triple integral of the divergence of the vector field over the volume enclosed by the surface

we are given the vector field F = (11x, 2y, \(z^{2}\)) and the surface S defined by the equation \(x^2 + y^2 + z^2\)= 1, which represents a unit sphere.

To evaluate the surface integral ∬S F · ds using the divergence theorem, we first need to calculate the divergence of the vector field F. The divergence of F, denoted as ∇ · F, is given by the sum of the partial derivatives of the components of F with respect to their corresponding variables. Therefore, ∇ · F = ∂(11x)/∂x + ∂(2y)/∂y + ∂(z^2)/∂z = 11 + 2 + 2z.

Applying the divergence theorem, the surface integral ∬S F · ds is equal to the triple integral ∭V (∇ · F) dV, where V represents the volume enclosed by the surface S.

Since the surface S is a unit sphere centered at the origin, the triple integral ∭V (∇ · F) dV can be evaluated by integrating over the volume of the sphere.

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Answer:

-3y^4+7y^3-11y^2+9y-2

After analysing the given data we conclude that the height of the streetlight is 29.4 feet, under the condition that a six-foot man places a 15 foot shadow. At the same time a streetlight casts an 80-foot shadow.

Now Let us consider the height of the streetlight "h".
The given angle of elevation is 52.5 degrees. This projects that the angle between the horizontal line and the line of sight to the top of the streetlight is 52.5 degrees.
We can apply the tangent function to evaluate h. tan(52.5) = h/20.
Evaluating  for h, we get h = 20 × tan(52.5) = 29.4 feet (rounded to one decimal place).
Therefore, the height of the streetlight is approximately 29.4 feet.
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The complete question is
A six-foot man casts a 15 foot shadow. At the same time a streetlight casts an 80-foot shadow.
The same six-foot tall man wants to indirectly measure the streetlight in screen 3. But it is a cloudy day and there are no shadows. So holding his phone by his eye, he uses the "level" feature on the Measure app to sight the top of the streetlight. Standing 20 feet away he finds an angle of elevation of 52.5 degrees.
Write and solve an equation to determine the height of the streetlight.

Answer:

ur welcoem

Step-by-step explanation:

The 28th term in the sequence of positive rationals produced by the counting process described in Theorem 5.3.1 is 3/2.

Theorem 5.3.1 describes a counting process in which positive rationals are listed in increasing order. The process starts with 1/1, followed by all rationals of the form m/1, 1/m, where m is a positive integer.

Next, all rationals of the form m/(m+1), (m+1)/m are listed, where m is a positive integer. This process continues, with all remaining rationals listed in increasing order.

To find the 28th term in this sequence, we need to determine which rational number is listed in the 28th position. Following the described counting process, we can list out the first few rationals in the sequence:

1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, 2/5, 5/2, 3/5, 5/3, 4/5, 5/4, ...

Counting through this list, we see that the 28th term is 3/2.

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The natural breaks, quantile, and equal interval classification schemes are methods used to categorize data for the purpose of creating thematic maps. Each scheme has its own approach and considerations: Natural Breaks, Quantile, Equal Interval.

Natural Breaks (Jenks): This classification scheme aims to identify natural groupings or breakpoints in the data. It seeks to minimize the variance within each group while maximizing the variance between groups. Natural breaks are determined by analyzing the distribution of the data and identifying points where significant gaps or changes occur. This method is useful for data that exhibits distinct clusters or patterns.

Quantile (Equal Count): The quantile classification scheme divides the data into equal-sized classes based on the number of data values. It ensures that an equal number of observations fall into each class. This approach is beneficial when the goal is to have an equal representation of data points in each category. Quantiles are useful for data that is evenly distributed and when maintaining an equal sample size in each class is important.

Equal Interval: In the equal interval classification scheme, the range of the data is divided into equal intervals, and data values are assigned to the corresponding interval. This method is straightforward and creates classes of equal width. It is useful when the range of values is important to represent accurately. However, it may not account for data distribution or variations in density.

In summary, the natural breaks scheme focuses on identifying natural groupings, the quantile scheme ensures an equal representation of data in each class, and the equal interval scheme creates classes of equal width based on the range of values. The choice of classification scheme depends on the nature of the data and the desired representation in the thematic map.

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Answers:

====================================

Explanation:

Answer: A. 9

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

We begin with the given function \(f(x)=x^2\)

To find \(g(x)\), we can plug \(3x\) into the function \(f(x)=x^2\)

\(f(x)=x^2\\\\f(3x)=(3x)^2\\\\f(3x)=9x^2\\\\g(x)=9x^2\)

Now that we know the equation of  \(g(x)\), we can find the graph that is equivalent to it.

The only graph that is even close to the function \(g(x)=9x^2\) is B, so that is our answer.

Answer:

i really dont know to be honest