what is the probability that abby, barry, and sylvia win the first, second, and third prizes, respectively, in a drawing if 200 people enter a contest and winning more than one prize is allowed?

The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.

Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.

The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.

In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.

To know more about angle click-
https://brainly.com/question/25716982
#SPJ1

A. The correct option for similarity is option D -  Both estimate proportions of the data contained within k standard deviations of the mean.

Both the Empirical Rule and Chebyshev's Theorem are used to estimate the proportion of data contained within a certain number of standard deviations from the mean.

Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the mean.

B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.

Another difference is that the Empirical Rule is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.

Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

To know more about empirical Rule

https://brainly.com/question/30700783

#SPJ4

The statement "Poisson distributions are useful to model any variables positive or negative as long as they are integer values" is false because Poisson distributions are specifically used for modeling the number of events occurring in a fixed interval of time or space, given a fixed average rate of occurrence (λ).

The key characteristics of a Poisson distribution are:

1. The events are independent, meaning the occurrence of one event does not influence the occurrence of another event.
2. The average rate of occurrence (λ) is constant throughout the interval.
3. The probability of more than one event occurring in an infinitesimally small interval is negligible.

Given these characteristics, Poisson distributions are not suitable for modeling any variables, positive or negative, as long as they are integer values. Instead, they are applicable for modeling non-negative integer values (0, 1, 2, ...) representing the number of events occurring in a specific context. Negative integer values are not applicable in this distribution since it would be illogical to have negative events occurring in a fixed interval.

In summary, Poisson distributions are only useful for modeling non-negative integer values representing the number of events in a fixed interval of time or space, given a fixed average rate of occurrence.

You can learn more about Poisson distribution at: brainly.com/question/17280826

#SPJ11

The diameter of the semicircle for the given area of the semicircle 1. 2717 square meters is equal to 1.8 meters.

Area of a semicircle = 1. 2717 square meters

The area of a semicircle is given by the formula,

A = πr^2 / 2

where A is the area

And r is the radius of the semicircle.

Rearrange the formula to solve for r,

r = √(2A/π)

Substituting the given value of A = 1.2717 square meters into this formula, we get,

⇒ r = √(2 × 1.2717 / π)

⇒ r = 0.9 meters

Since the diameter of a semicircle is twice the radius,

The diameter of this semicircle is equal to,

d = 2r

  = 2 × 0.9

   = 1.8 meters

Therefore, the diameter of the semicircle is equal to 1.8meters.

Learn more about diameter here

brainly.com/question/14034336

#SPJ4

The length of the rectangular prism given the volume, width and height is 19 yd.

Volume of a rectangular prism = length × width × height

Volume of the prism = 2,280 yd³

Width of the prism = 20 yd

Height of the prism = 6 yd

Length of the prism = x

So,

Volume of a rectangular prism = length × width × height

2,280 = x × 20 × 6

2,280 = 120x

divide both sides by 120

x = 2,280 / 120

x = 19 yd

Therefore, the length is 19 yd

Read more on rectangular prism:

https://brainly.com/question/8839626

#SPJ1

The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

To know more about ratio visit:

https://brainly.com/question/21575

#SPJ9

To determine if the sample fairly represents the population, we need to consider whether the sample is representative and whether there is any bias present in the sampling process.

If the principal surveyed fifty 8th graders in a way that ensures that each 8th grader in the population has an equal chance of being selected, then the sample can be considered representative. This means that the sample accurately reflects the characteristics of the population, and any conclusions drawn from the sample can be applied to the population.

However, if the sampling process was biased in some way, the sample may not be representative of the population. For example, if the principal only surveyed 8th graders in one class or in one particular group, the sample may not be representative of the entire 8th-grade population at Harding Middle School. In this case, any conclusions drawn from the sample may not accurately reflect the entire population.

Therefore, the key factor in determining whether the sample fairly represents the population is the sampling method used. If the sampling method is random and unbiased, then the sample can be considered representative of the population.

To know more about sampling process here

https://brainly.com/question/15023379

#SPJ4

Step-by-step explanation:

yes,because of SAS side angle side are equal.

The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].

Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).

Given:

[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]

Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.

We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:

The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50

Learn more about Experimental Probability here:

https://brainly.com/question/30694293

#SPJ1

The probability that the flight will leave on time when it is not raining is approximately 0.83.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).

According to the given information:

To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).

Let:

P(rain) = 0.07 (probability of rain)

P(delayed) = 0.17 (probability of delay)

P(rain and delayed) = 0.02 (probability of rain and delay)

We can use the formula for conditional probability:

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

In this case, we want to find P(on time | not raining), which can be expressed as:

P(on time | not raining) = P(on time and not raining) / P(not raining)

Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:

P(on time | not raining) = P(on time) / (1 - P(rain))

We can now substitute the given probabilities to calculate the required probability:

P(on time | not raining) = P(on time) / (1 - P(rain))

P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))

P(on time | not raining) = (1 - 0.17) / (1 - 0.07)

P(on time | not raining) = 0.83

So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).

To know more about probability visit: https://brainly.com/question/30034780

#SPJ1

If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.

The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.

In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.

We use the formula for mechanical advantage in a pulley system, which is given by:

⇒ MA = (distance moved by the effort) / (distance moved by the load),

In this case, the distance moved by the effort is 3 m, and

The distance moved by the load is 0.3 m,

Substituting the values,

We get,

⇒ MA = 3/0.3,

⇒ MA = 10,

So, mechanical advantage of "pulley-system" is 10.

Now, we use mechanical advantage to calculate the required force to lift the motorcycle.

Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:

⇒ Input force = (Output force)/(Mechanical advantage),

Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,

We get,

⇒ Input force = 7000/10,

⇒ 700 N,

Therefore, the required force to lift motorcycle is 700 N.

Learn more about Pulley System here

https://brainly.com/question/30784562

#SPJ4

The base area, the lateral area and the surface area of the prism are 124.8 cm², 288 cm² and 412.8 cm², respectively.

In this problem we need to compute three kinds of areas in a prism with a triangular base. The base area, that is, the sum of the areas of the two triangles, the lateral area, that is, the sum of the areas of the three rectangles and the surface area, that is, the sum of the base and lateral areas.

The area formulas of the triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we proceed to determine each kind of area:

Base area

A = 2 · 0.5 · (12 cm) · (10.4 cm)

A = 124.8 cm²

Lateral area

A = 3 · (8 cm) · (12 cm)

A = 288 cm²

Surface area

A = 124.8 cm² + 288 cm²

A = 412.8 cm²

To learn more on surface areas: https://brainly.com/question/29298005

#SPJ1

0.5 is used as a conservative estimate of p in determining the minimum sample size for a proportion confidence interval to account for maximum uncertainty.

In statistical hypothesis testing and estimation, we often need to make inferences about population parameters based on a sample. One of the parameters of interest is the proportion of successes in a population.

When we construct a confidence interval for a proportion, we need to specify the desired level of confidence and the desired margin of error. The margin of error depends on the sample size and the standard error of the sample proportion.

The standard error of the sample proportion is estimated using the population proportion, p, which is unknown. Since we don't know the true value of p, we typically use the sample proportion, p-hat, as an estimate. However, using p-hat alone can lead to an overly optimistic estimate of the standard error and, therefore, an overly narrow confidence interval.

To account for this uncertainty, we use a conservative estimate of the standard error that assumes a worst-case scenario for p. The worst-case scenario is when p is 0.5, which corresponds to maximum uncertainty or variability in the estimate of the proportion. This is why 0.5 is often used as a conservative estimate of p when determining the minimum sample size necessary for a proportion confidence interval. By assuming p = 0.5, we ensure that our sample size is large enough to account for the worst-case scenario and provide a reliable estimate of the proportion.

Learn more about proportion confidence interval

brainly.com/question/13686615

#SPJ11

The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

What is equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.

This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.

It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.

Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.

To know more about equations visit,

brainly.com/question/2972832

#SPJ1

We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,

To determine between which two integers 7/3 lies, we can use division and rounding.

Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:

7/3 = 2 + 1/3

Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.

This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.

Answer C, 2 and 3, is the correct answer.

To learn more about integers click on,

https://brainly.com/question/12959472

#SPJ4

Answer:

26) 1.32

27) 90

28) 0.00845

29) 2.56x10^-1

30) 9.5x10^-3

31) 7.8x10

A The histogram is the best graph showing the average scores of 5 UCI volleyball teams in UCI history. Because it allows us to divide the data into as many or as few groups as we want and clarify the comparison between them.

We would like to view the average points data of the top 5 UCI basketball players in UCI history. There are two types of charts used to present data. The first is a histogram and the second is a scatterplot. We have to decide which picture is the best. Now, as we know, scatter charts are used to plot observations based on points to show the relationship between two data sets. A histogram is a type of bar chart in which all values are divided. Divides the range of results in the data into classes or groups. It can help identify outliers or gaps in the data. After discussing the features of the two graphs, shows the average score of 5 UCI basketball players in UCI history, the histogram is the best choice here because it allows us to divide and share the difference between clearly.

For more information about Histogram, visit :

https://brainly.com/question/28164315

#SPJ4

complete question:

The above figure complete the question..

you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?

Experimental studies involve the manipulation of variables, and quasi-experimental studies involve some level of intervention but lack full control or randomization.

An observational study.

In an observational study, researchers collect data without intervening or manipulating any variables.

The study evaluated the association between exposure to anticholinergic drugs and dementia risk using existing data collected from an anonymized research database of more than 30 million individuals in over 1500 general practices. The data includes demographic information, medical diagnoses, prescriptions, referrals, laboratory results, and clinical values.
Case patients were those diagnosed with dementia during follow-up, and each case patient was matched to 5 controls by age, sex, general practice, and calendar time.

The study used information on prescriptions for 56 drugs with strong anticholinergic properties to calculate measures of cumulative anticholinergic drug exposure.

The data were analyzed from May 2016 to June 2018.
Since the researchers did not manipulate any variables or treatments and only analyzed existing data, it is considered an observational study.

The study uses data collected from a research database of routine healthcare, rather than manipulating variables in a controlled setting.

The researchers observed the exposure to anticholinergic drugs in patients and followed them over time to evaluate the association with dementia risk.

The study did not involve the manipulation of any variables, which is characteristic of experimental or quasi-experimental studies.

For similar questions on studies

https://brainly.com/question/28819016

#SPJ11

This is an observational study which we can infer from the given data in the question.

This is an observational study. In this study, the researchers evaluated the association between exposure to anticholinergic drugs and dementia risk using data collected from a large database. They identified case patients with dementia and matched them with controls based on age, sex, general practice, and calendar time. The researchers did not manipulate any variables or randomly assign participants to groups, which is characteristic of an observational study.

When conducting an observational study, researchers observe and gather data on a group of people or subjects without interfering or changing any of the factors. An observational study's objective is to identify and evaluate patterns, behaviours, or occurrences without modifying or altering them.

Observational studies can be carried out in a variety of locations, including the outdoors, businesses, homes, and communities. The social sciences, epidemiology, psychology, and medicine are just a few of the disciplines in which they might be applied.

The two subtypes of observational studies are prospective and retrospective. In a prospective observational study, a group of people is tracked over time as information is gathered on their behaviours, exposures, and results. On the other hand, a retrospective observational study looks back in time and gathers information.

Learn more about observational study here:

https://brainly.com/question/17593565

#SPJ11

The solution to the equation 4,300e^(0.07x) - 123 = 5,000 for x is 2.5.

We can solve the equation 4,300e^(0.07x) - 123 = 5,000 for x by first adding 123 to both sides and then dividing both sides by 4,300 and taking the natural logarithm of both sides:

Using the above as a guide, we have the following:

4,300e^(0.07x) - 123 = 5,000

4,300e^(0.07x) = 5,123

e^(0.07x) = 5,123/4,300

e^(0.07x) = 1.1914

0.07x = ln(1.1914)

x = ln(1.1914)/0.07

Using a calculator, we get:

x ≈ 2.50

Rounding to the nearest tenth, the solution to the equation is approximately 2.5.

Read more about equation at

https://brainly.com/question/148035

#SPJ1

a) The probability of him answering all seven questions correctly is [tex](1/4)^7[/tex]or approximately 0.000019%.

b) Therefore, the probability of him answering exactly three questions correctly is [tex]35 * (1/4)^3 * (3/4)^4[/tex]or approximately 19.7%.

c) The probability of him answering at least three questions correctly is the sum of these probabilities, which is approximately 71.5%.

Since each question has four choices and only one is correct, the probability of guessing the correct answer for any one question is 1/4.

a) To answer all seven questions correctly, Edward must guess the correct answer for each question.

Therefore, the probability of him answering all seven questions correctly is [tex](1/4)^7[/tex] or approximately 0.000019%.

b) To answer exactly three questions correctly, Edward must guess the correct answer for three questions and the incorrect answer for the remaining four questions.

The number of ways in which he can do this is given by the binomial coefficient C(7,3) = 35.

The probability of him guessing three questions correctly and four questions incorrectly is [tex](1/4)^3 * (3/4)^4.[/tex]

Therefore, the probability of him answering exactly three questions correctly is [tex]35 * (1/4)^3 * (3/4)^4[/tex]or approximately 19.7%.

c) To answer at least three questions correctly, Edward must either guess three, four, five, six, or seven questions correctly.

We have already calculated the probability of him guessing exactly three questions correctly.

The probability of him guessing exactly four questions correctly is [tex]C(7,4) * (1/4)^4 * (3/4)^3 = 35 * (1/4)^4 * (3/4)^3[/tex]or approximately 34.7%.

The probability of him guessing exactly five questions correctly is [tex]C(7,5) * (1/4)^5 * (3/4)^2 = 21 * (1/4)^5 * (3/4)^2[/tex] or approximately 16.3%.

The probability of him guessing exactly six questions correctly is[tex]C(7,6) * (1/4)^6 * (3/4)^1 = 7 * (1/4)^6 * (3/4)^1[/tex] or approximately 0.82%. Finally, the probability of him guessing all seven questions correctly is (1/4)^7 or approximately 0.000019%.

For similar question on probability.

https://brainly.com/question/28185528

#SPJ11

Answer:

gcf is 'x'

Step-by-step explanation:

the common factor to the terms 'x²' and '3x' is 'x'

We have confirmed that the sum of the series is 28/3. Therefore, the correct answer is option (b) 28/3.

A geometric series is a series of numbers where each term is a fixed multiple of the preceding term. Specifically, a geometric series has the form:

a+ar+ar²+ar³+.....

The given series is a geometric series with first term (a) = 14 and common ratio (r) = -1/2.

Consider sum of series be S, So-

S = a/(1 - r) = 14/(1 - (-1/2)) = 28/3

To see why this is the correct answer, we can also write out the first few terms of the series:

14-7+7/2-7/4+7/8-.....

It is evident that each term is produced by multiplying the one before it by -1/2.

So, the second term is obtained by multiplying the first term by -1/2, the third term is obtained by multiplying the second term by -1/2, and so on.

We can also notice that the sum of the first two terms is 7, the sum of the first three terms is 21/2, and the sum of the first four terms is 28/3. This suggests that the sum of the first n terms of the series might be given by the formula Sn = a(1 - rⁿ)/(1 - r).

We can verify that this is true by using the formula to find the sum of the first four terms:

S4 = 14(1 - (-1/2)⁴)/(1 - (-1/2)) = 28/3

To know more about common ratio visit:

https://brainly.com/question/24989238

#SPJ1

If the house value of $89,548 and two points, attorney's fees $324, title fees $105, then closing cost is option (b) $2,219.96

Closing costs are fees associated with the purchase or refinance of a property that are paid at the closing of the transaction.

To calculate the closing cost, we need to add up all the fees associated with the purchase of the house.

First, we need to calculate the cost of the points. Two points on a house value of $89,548 would be

2 x $89,548 x 0.01 = $1,790.96

Next, we need to add the attorney's fees and title fees

$1,790.96 + $324 + $105 = $2,219.96

Therefore, the correct option is (b) $2,219.96

Learn more about Closing costs here

brainly.com/question/30280701

#SPJ4

The total cups of milk orange juice Enrique has in refrigerator is equal to  18 cups.

Gallons of milk Enrique has in his refrigerator = 1 gallon

Pint of orange juice Enrique has in his refrigerator = 1 pint

Convert gallons to cups and pint to cups .

There are ,

16 cups = 1 gallon of milk

And 2 cups = 1 pint of orange juice

Enrique has 16 cups of milk

and 2 cups of orange juice.

Total cups of milk and orange juice in refrigerator

=16 cups of milk + 2 cups of orange juice

= 18 cups of milk and orange juice

Therefore, in total Enrique has  18 cups of liquid in his refrigerator.

Learn more about cups here

brainly.com/question/22334258

#SPJ4

The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.

No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.

The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.

The p value for this test is 0.788, which is greater than the alpha level of 0.01.

The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.

This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.

The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.

For similar question on population proportion:

https://brainly.com/question/29912751

#SPJ11

The guy wire must be about 55 feet long and the slope of the guy wire, expressed as a fraction is 25/11.

We can use the Pythagorean Theorem to find the length of the guy wire. Let's call the length of the guy wire "g".

g^2 = 50^2 + 22^2

g^2 = 2500 + 484

g^2 = 2984

g ≈ 54.65

So the guy wire must be about 55 feet long.

The slope of the guy wire is the ratio of the vertical distance it covers to the horizontal distance it covers. In this case, the vertical distance is 50 feet (the height of the pole) and the horizontal distance is 22 feet. So the slope is

50/22 = 25/11

Therefore, the slope of the guy wire is 25/11.

To know more about guy wire here

https://brainly.com/question/15504383

#SPJ4

Therefore, the dimensions of the crate that minimize the cost of materials are approximately:

l = 1.587 ft
w = 2.519 ft
h = 3.159 ft

To minimize the cost of materials, we need to find the dimensions of the crate that will minimize the surface area of the crate. Let's call the height, width, and length of the crate "h", "w", and "l", respectively.

We know that the volume of the crate is 16 ft3, so we can write:

lwh = 16

We want to minimize the cost of materials, which is determined by the surface area of the crate. The surface area consists of the top, bottom, front, back, left, and right sides of the crate. The cost of the materials for the base is twice the cost of the materials for the sides, and the cost of the materials for the top is half the cost of the materials for the sides. Let's call the cost of the materials for the sides "c".

The surface area of the crate can be written as:

2lw + 2lh + 2wh

We can use the volume equation to solve for one of the variables, say "h":

[tex]h = \frac{16}{(lw)}[/tex]

Now we can substitute this expression for "h" into the surface area equation:

[tex]2lw + 2l(\frac{16}{(lw))} + 2wh[/tex]

Simplifying this expression gives:

[tex]2lw + 32/l + 2wh[/tex]
To find the dimensions that minimize this expression, we need to take the partial derivatives with respect to "l" and "w" and set them equal to zero:
[tex]\frac{d}{dl} (2lw + 32/l + 2wh) = 2w - \frac{32}{l^2} = 0\\[/tex]

[tex]\frac{d}{dw} (2lw + 32/l + 2wh) = 2l + 2h = 2l + 2(16/(lw)) = 2l + 32/(lw) = 0[/tex]
Solving these equations for "l" and "w" gives:

[tex]l = 2^{(1/3)}\\w = 2^{(2/3)}[/tex]

Substituting these values into the equation for "h" gives:

[tex]h = 8/(2^{(2/3)})[/tex]

Therefore, the dimensions of the crate that minimize the cost of materials are approximately:

l = 1.587 ft
w = 2.519 ft
h = 3.159 ft

learn more about volume

https://brainly.com/question/28058531

#SPJ11

The dimensions of the box that minimize the cost of materials are approximate:

x ≈ 2.52 ft

y ≈ 3.55 ft

z ≈ 2.52 ft

Let's denote the length, width, and height of the box as x, y, and z,

respectively. We are given the volume of the box is [tex]16 ft^3[/tex], so we

have:

x × y × z = 16

We are also given that the material used to make the base costs twice as

much (per square foot) as the material in the sides.

Let's denote the cost of the material for the sides as c, so the cost of the

material for the base is 2c.

The area of the base is xy, so the cost of the material for the base is

2cxy.

Similarly, the material used to make the top costs half as much (per

square foot) as the material in the sides.

Let's denote the cost of the material for the top as 0.5c.

The area of the top is also xy, so the cost of the material for the top is 0.5cxy.

The cost of the material for the four sides is simply 4cz.

Therefore, the total cost of materials is:

C(x, y, z) = 2cxy + 4cz + 0.5cxy

Simplifying, we have:

C(x, y, z) = (2.5c)xy + 4cz

We want to minimize this function subject to the constraint that the volume of the box is [tex]16 ft^3[/tex]:

x × y × z = 16

We can use the method of Lagrange multipliers to solve this constrained optimization problem:

L(x, y, z, λ) = (2.5c)xy + 4cz - λ(xyz - 16)

Taking partial derivatives with respect to x, y, z, and λ, we get:

dL/dx = 2.5cy - λyz = 0

dL/dy = 2.5cx - λxz = 0

dL/dz = 4c - λxy = 0

dL/dλ = xyz - 16 = 0

From the first two equations, we can solve for λ:

λ = 2.5cy/yz = 2.5cx/xz

Setting these two expressions equal to each other and simplifying, we get:

y/x = z/y

This implies that x:y:z = 1:√2:1, since we know that the dimensions of the box must be in proportion to each other.

Substituting this into the constraint x × y × z = 16, we get:

x = 2∛2

y = 2∛4

z = 2∛2

for such more question on dimensions

https://brainly.com/question/28107004

#SPJ11

Answer:

14

Step-by-step explanation:

c = 2[tex]\pi r[/tex]

c = 2[tex]\pi[/tex]7

x = 14[tex]\pi[/tex]

Helping in the name of Jesus.

Answer:

Let x be width and y = length of barn wall y + 2x =20Area = xy= x(20 - 2x)=20x -2x^2dA/dx = 20 - 4xmax at dA/dx =0 so 20 - 4x = 0x=5 y=10 max area is 50 sq ft

The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.

To solve the equation (4)/(x) + (1)/(2) = (5)/(x):

Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.

Multiply the left side of the equation by 2/2 to get:

(8)/(2x) + (1)/(2) = (5)/(x)

Combine the two fractions on the left side of the equation:

(8+1)/(2x) = (9)/(2x)

Set the left side of the equation equal to the right side:

(9)/(2x) = (5)/(x)

Cross-multiply:

9x = 10x

Simplify:

x = 0

Therefore, the solution to the equation is x = 0.

Learn more about the Least Common Factor (LCM) at

https://brainly.com/question/30968751

#SPJ4