3. you are constructing a 480 cubic feet box. the bottom of the container costs $5 per square foot to construct whereas the top and sides cost $3 per square foot to construct. use lagrange multipliers to find the minimum cost. show work.

Answer:

5 Big Airplanes

Step-by-step explanation:

16 airplanes IN TOTAL

11 airplanes ARE SMALL

so we simply subtract 11 from 16 to find how many airplanes are left besides the small ones.

The statement that defines the function's range is option a) all real numbers greater than or equal to -1.

The given function is a quadratic function, which is a parabola that opens upwards. The graph of the function has its vertex at the point (3,-1), which is the minimum point of the parabola.

The range of the function is the set of all possible output values or y-values that the function can produce.

Since the parabola opens upwards and the minimum point is at y=-1/4, the range of the function f(x)=(x-4)(x-2) is all real numbers greater than or equal to -1.

Therefore, we can say that the range is all real numbers greater than or equal to -1.

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Correct Question

The function f(x) = (x − 4)(x − 2) is shown.What is the range of the function? a) all real numbers less than or equal to 3

b) all real numbers less than or equal to −1

c) all real numbers greater than or equal to 3

d) all real numbers greater than or equal to −1

The probability that individual ii-2 exhibits the disease given a 75% penetrance is 0.75 or 75%.

Penetrance refers to the probability of an individual expressing a particular trait or disease given their genetic makeup. In this case, the penetrance of the disease is 75%, which means that there is a 75% chance that an individual with the genetic mutation for the disease will actually exhibit the disease. Therefore, the probability that individual ii-2 exhibits the disease given this penetrance is also 0.75 or 75%.

1. Penetrance is the probability that an individual with a specific genotype will express the associated phenotype or disease.
2. In this case, the penetrance of the disease is 75%, which means there is a 75% chance that an individual with the disease-associated genotype will exhibit the disease.
3. Given this penetrance, the probability that individual ii-2 exhibits the disease is 0.75 or 75%.

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There is the not sufficient evidence that the average small business loan is different that the amount stated in the  investment blog.

We have,

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Here we have given that,

Claim: To check whether the average small business loan is different that the amount stated in the  investment blog.

The hypothesis is,

H0: μ= 20 thousand dollars  Versus  H0: μ ≠ 20 thousand dollars

We have given that,

n= Number of observation = 25

x bar  = sample mean =18.5

S= sample standard deviation =5

Here, population standard deviation is unknown, we use the one sample t test.

t - statistics = (x bar - μ) / (s / √n)

                  = (18.5 - 20) / (5 / √25)

                  = -1.342

we get,

the Test statistic is -1.342

Now we find the P-value

α = level of significance = 0.05

Degrees of freedom = n - 1 = 25 - 1 = 24

This is two tailed test as our interest is to show the population mean is equal or not equal to zero.

Now, we can find the P-value

P-value = 0.1922     Using EXCEL = TDIST( | t-statistics | = 1.342 , D.F=24, tail=2)

Hence, There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.

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complete question:

Complete the steps of a one-mean hypothesis test with Population SD unknown ritical Value Approach Complete the steps of a one-mean hypothesis test with Population SD unknown - Critical Value approach Question An investment blog states the average small business loan is 20 thousand dollars. A business loan broker would like to test the claim that the average small business loan is different than the amount stated in the investment blog. To test this claim at the 5% significance level, the business loan broker collects the following data on a sample of 25 small business loans and records the amount of the loan. The following is the data from this study: Sample size=25 small business loans Sample mean= 18.5 thousand dollars Sample standard deviation = 5 thousand dollars Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=..<, or > to represent the correct hypothesis.) Provide your answer below: null hypothesis: 20 alternative hypothesis: 20

Answer: -29/15.

Step-by-step explanation:

-4/3 - 2 + 2/5 + 1

= (-20/15) - (30/15) + (6/15) + (15/15) (finding a common denominator of 15)

= (-20 - 30 + 6 + 15) / 15

= -29/15

The measure of angle x and z are 45.7° and 74° respectively.

Given that, straight line l and h are parallel.

Here, in the given figure,

(3x-31)°+z°=180° (Adjacent angles)

z°=180°-(3x-31)°

From the given figure,

z°=74° (Corresponding angles are equal)

180°-(3x-31)°=74°

180°-74°=(3x-31)°

(3x-31)°=106°

3x=106+31

3x=137

x=137/3

x=45.7°

Therefore, the measure of angle x and z are 45.7° and 74° respectively.

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The area of the regular polygon is equal to 117.99 square units

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of nonagon × (n)number of side

apothem = s/[2tan(180/n)]

6 = s/[2tan(180/9)]

s = 6 × 2tan20

s = 4.34

perimeter = 4.34 × 9 = 39.33

Area of nonagon = 1/2 × 6 × 39.33

Area of nonagon = 117.99

Therefore, the area of the regular polygon is equal to 117.99 square units

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The feedback that the runners received from their coach is called positive feedback. Positive feedback is a type of feedback that reinforces the current behavior, making it more likely to continue or increase in frequency.

In this case, the runners' average time for sprinting improved each day, so the coach provided positive feedback to encourage them to continue with their training. Positive feedback can be a powerful motivator, as it provides a sense of accomplishment and encourages individuals to continue striving for improvement. In contrast, negative feedback involves pointing out areas for improvement or mistakes, and can be demotivating if not delivered constructively.

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The mass of this rectangular object is equal to 232 grams.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular object = 5 × 4 ×  2

Volume of rectangular object = 40 cubic centimeter.

Mass of rectangular object = density × volume

Mass of rectangular object = 5.8 × 40

Mass of rectangular object = 232 grams.

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The number of paths passing from A to B if we pass through the edge at most once is 3.

Since we have that paths from A to B in the shape of triangles, we desire to find the number of paths from a to B if we travel along the edges at most once.

Now,

So, we see that there are 3 paths passing from A to B if we pass through the edge at most once.

Thus, there are 3 paths passing from A to B if we pass through the edge at most once.

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The notation P(F|E) means the probability of event F given event E.

In probability notation, P(F|E) represents the conditional probability of event F occurring given that event E has already occurred. It is read as "the probability of F given E." The vertical bar "|" indicates "given" or "conditional on." This notation allows us to calculate the probability of one event happening, taking into account the occurrence of another event. For example, P(F|E) would represent the probability of rain (event F) given that the weather forecast predicts a cloudy day (event E). The conditional probability allows us to analyze how events are related and make more accurate predictions or assessments based on the given information.

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The height of the pyramid is equal to 17 units.

In Mathematics and Geometry, the volume of a rectangular pyramid can be calculated by using the following formula:

Volume of a rectangular pyramid = 1/3 × L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular pyramid, we have the following;

765 = 1/3 × 9 × 15 ×  H

Height, H = 765/45

Height, H = 17 units.

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6y² - 13y + 6 is the product of 2y -3 and 3y - 2.

Given the following linear expression

(2y-3)(3y-2)

We need to expand the expression to get a quadratic function as shown below:

(2y-3)(3y-2) = 2y(3y) - 2(2y) - 3(3y) -3(-2)

(2y-3)(3y-2) = 6y² - 4y - 9y + 6

(2y-3)(3y-2) = 6y² - 13y + 6

Hence the product of 2y - 3 and 3y - 2 is equivalent to 6y² - 13y + 6

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The mathematical expressions or equations about the image  44%, 0.44 and 11/25

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

The fundraiser image (see attachment)

From the image, we have the following readings

Total amount to be raised = $250,000

Amount already raised = $110,000

When represented as a percentage, we have

percentage = 110,000/250,000 * 100%

Evaluate

percentage = 44%

As a fraction, we have

percentage = 44/100 = 11/25

As a decimal, we have

percentage = 0.44

Hence, the mathematical expressions about the image are 44%, 0.44 and 11/25

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Answer:

3

Step-by-step explanation:

the answer is 3, the working is in the image

Answer:

  264 cm²

Step-by-step explanation:

You want the area of a polygon composed of a 12 cm square with triangles of height 5 cm attached to each side.

The area of the square is the square of its side lenght:

  A = s²

  A = (12 cm)² = 144 cm²

The area of the four triangles is ...

  A = 4 × (1/2bh)

  A = 4 × 1/2(12 cm)(5 cm) = 120 cm²

The total area of the composite figure is ...

  A = square area + triangle area

  A = 144 cm² +120 cm² = 264 cm²

The area of the polygon is 264 cm².

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The value of x in the parallel line is 11.

When parallel lines are cut with a transversal line, angle relationship are formed such as corresponding angles, alternate interior angles, alternate exterior angles, corresponding angles, vertically opposite angles etc.

Therefore, let's use the angle relationship to find the value of x .

Hence,

6x + 14 = 80(corresponding angles and vertically opposite angles)

6x + 14 = 80

subtract 14 from both sides of the equation

6x + 14 - 14 = 80 - 14

6x = 66

divide both sides of the equation by 6

x = 66 / 6

x = 11

Therefore,

x = 11

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In this case, the inflection point occurs at 2 years with a population level of 333. Since the inflection point represents half of the carrying capacity, you can calculate the carrying capacity by multiplying the population level at the inflection point by 2: Therefore, the carrying capacity of this population is 666.

To answer this question, we first need to understand what is meant by carrying capacity. Carrying capacity refers to the maximum number of individuals that can be supported by an ecosystem or environment without causing negative impacts on that ecosystem. It is the point at which the resources available in the environment can no longer support any additional growth in the population.
Given that the population is growing logistically, we can assume that it is following the logistic growth model, which takes into account the carrying capacity of the environment. The inflection point in the graph occurs when the population growth rate starts to slow down, indicating that the carrying capacity has been reached.
At the inflection point, the population level is 333, and we know that this is happening at 2 years. However, without more information about the growth rate or carrying capacity, it is not possible to calculate the carrying capacity. We would need additional data points from the graph or information about the growth rate to determine the carrying capacity.
In summary, we need more information about the growth rate or additional data points from the graph to determine the carrying capacity. Answering this question with more than 100 words, we can also emphasize the importance of understanding carrying capacity in population growth and how it is critical for sustainable growth and conservation efforts.
A population growing logistically experiences an S-shaped curve on its graph, where the carrying capacity is the maximum population size that the environment can sustain. In a logistic growth model, the inflection point is the point at which the population's growth rate is at its maximum, which usually occurs when the population reaches half of the carrying capacity.
In this case, the inflection point occurs at 2 years with a population level of 333. Since the inflection point represents half of the carrying capacity, you can calculate the carrying capacity by multiplying the population level at the inflection point by 2:
Carrying Capacity = 333 * 2 = 666
Therefore, the carrying capacity of this population is 666.

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The expected profit of one roll in this game is $0.

To determine the expected profit of one roll in the die game, we need to calculate the weighted average of the possible outcomes.

The probability of rolling a 2 is 1/6 since there is one favorable outcome out of six possible outcomes. In this case, you win $25.

The probability of rolling any other number (1, 3, 4, 5, or 6) is 5/6 since there are five unfavorable outcomes out of six possible outcomes. In this case, you lose $5.

Now, we can calculate the expected profit:

Expected Profit = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)

= (1/6 * $25) + (5/6 * -$5)

= $4.17 - $4.17

= $0

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Answer:

25350 cm²

Step-by-step explanation:

A Cube has a length of 65cm. find its surface area.

65 × 65 × 6 =

4225 × 6 =

25350 cm²

Answer:

[tex]4 {a}^{3} - {a}^{2} b - 36a + 9b[/tex]

[tex] = {a}^{2} (4a - b) - 9(4a - b)[/tex]

[tex] = ( {a}^{2} - 9)(4a - b)[/tex]

[tex] = (a + 3)(a - 3)(4a - b)[/tex]

To make inferences about the average length of stay, an assumption must be made regarding the population's distribution. The assumption is that the population follows a normal distribution or is approximately normally distributed.

In order to make accurate inferences about the average length of stay, it is important to assume that the population from which the sample is drawn follows a normal distribution or is approximately normally distributed. The normal distribution assumption allows for the use of statistical techniques that rely on the properties of the normal distribution, such as calculating confidence intervals and conducting hypothesis tests.

When the population distribution is approximately normal, the Central Limit Theorem comes into play. According to this theorem, the sampling distribution of the sample means will be approximately normally distributed, regardless of the population distribution shape, as long as the sample size is sufficiently large. This allows for the use of inferential statistics to make inferences about the population parameter, such as the average length of stay.

Therefore, assuming a normal distribution or an approximately normal distribution within the population is crucial when making inferences about the average length of stay. It provides the foundation for applying statistical techniques and drawing meaningful conclusions based on the sample data.

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The step in showing that[tex]n^3+2n[/tex] is divisible by 3 by mathematical induction is: Prove that the statement is true when n = k. Option B

This step involves substituting k for n in the expression [tex]n^3+2n[/tex] and showing that the result is divisible by 3. In other words, we need to show that:

[tex]k^3 + 2k[/tex] is divisible by 3.

If we assume that the statement is true for n = k, then we can substitute k+1 for n in the expression [tex]n^3+2n[/tex] and simplify:

=[tex](k+1)^3 + 2(k+1) = k^3 + 3k^2 + 3k + 1 + 2k + 2[/tex]

= [tex]k^3 + 3k^2 + 5k + 3[/tex]

= [tex](k^3 + 2k) + (3k^2 + 3k)[/tex]

Since we assumed that the statement is true for n = k, we know that [tex]k^3 + 2k[/tex] is divisible by 3. Also, [tex]3k^2 + 3k[/tex] is divisible by 3 because it has a factor of 3. Therefore, the entire expression [tex](k+1)^3 + 2(k+1)[/tex]is also divisible by 3.

This completes the inductive step, and we can now conclude by mathematical induction that the statement [tex]n^3+2n[/tex] is divisible by 3 is true for all positive integers n.

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Answer:

2 students

Step-by-step explanation:

First, you have to find how many made a level 5, so we do 36•1/9=4. So, 4 students made a level five. That leaves us with 36-4=32 students left. Next, you find the students that made a level 4. 36•5/6=30 students made a level 4, so that leaves us with 32-30=2 students that got a level 3.

[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =2\\ s=6 \end{cases}\implies 6=r2\implies \cfrac{6}{2}=r\implies 3=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(3)^2}{2}\implies A=9~in^2[/tex]

Answer:

Mean: 20

Median: 16

Mode: No mode

Step-by-step explanation:

For the mean:

44 + 4 + 27 + 5 = 80

80/4 = 20

For the median:

5 + 27 = 32

32/2 = 16

For the mode:
None of the numbers are repeated.

Therefore, the total surface area of the pyramid is 312 square inches.

To find the surface area of a pyramid, we need to find the area of the base and the area of each triangular face and then add them together.

The area of the base is 1 square foot = 12 inches x 12 inches = 144 square inches.

To find the area of each face, we need to find the area of the corresponding triangle. We know that the height of each face is 14 inches and the base of each triangle is half the base of the pyramid, which is 6 inches. Therefore, the area of each face is:

(1/2) x base x height = (1/2) x 6 inches x 14 inches = 42 square inches.

Since there are four triangular faces, the total area of the faces is 4 x 42 square inches = 168 square inches.

Therefore, the total surface area of the pyramid is:

144 square inches (base) + 168 square inches (faces) = 312 square inches.

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Since these values are not equal, Lin and Noah would obtain different volume measurements when using their small cubes to find the volume of the 1 1/2 inch cube.

No, Lin and Noah would not get the same value for the volume of the 1 1/2 inch cube using their small cubes.

The volume of a cube is determined by multiplying the length of its edges three times. Lin's cube has an edge length of 1/2 inch, and Noah's cube has an edge length of 1/4 inch.

For Lin's cube, the volume would be (1/2) * (1/2) * (1/2) = 1/8 cubic inches.

For Noah's cube, the volume would be (1/4) * (1/4) * (1/4) = 1/64 cubic inches.

Lin's cube would yield a volume of 1/8 cubic inches, while Noah's cube would result in a volume of 1/64 cubic inches.

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