Tom has a 300-foot fence around his
rectangular yard. The width is 90 feet
less than twice the length. What is the
area of his rectangular yard?

The probability that a person who tests positive actually has the disease is 0.1046.

This problem is a classic application of Bayes' law, but let's try a more concrete approach rather than a boilerplate approach.

Suppose 1,000,000 people are being tested.

According to the incidence, 0.5 percent should be ill, so we would expect 5,000 to be ill and 995,000 not to be ill.

We are testing 5000 of him for this disease. With only a 7% false negative rate, the test is pretty good. That is, out of 5,000 or 350 people with the disease, only 7% will test negative, and the remaining 4,650 will test positive.

We are testing 995,000 people who are not sick. With only a 4% false positive rate, the test is pretty good. That means only 4% of 995,000 or 39,800 diseased people will test positive. The remaining 955,200 will be negative.

4,650 sick and tested positive

39,800 not sick but tested positive

350 sick and tested negative

955,200 not sick but tested negative

our test 955,200 + 4,650 = 959,850 people tested

4,650 + 39,800 = 44,450 people tested positive, but only 4,650 actually tested positive. This is a very small percentage, only 465044450≈0.1046.

In other words, if your doctor says you tested positive, there's only about a 10.5% chance that you actually have the disease. That's the probability we're looking for, and this low value indicates that this test isn't very good.

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To find the height of a regular tetrahedron, you can use the formula h = sqrt(2/3) * s, where h is the height of the tetrahedron and s is the length of one of its edges. In this case, the length of one of the edges is 6 inches, so plugging this value into the formula gives:

h = sqrt(2/3) * 6 inches

= sqrt(4/3) inches

= sqrt(4/3) * sqrt(1/1) inches

= 2/sqrt(3) inches

To convert this to a decimal and round to the nearest hundredth, we can use a calculator to find that the height of the tetrahedron is approximately 3.46 inches.

How many faces are there in tetrahedron?

4

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Answer:

  4.675 g

Step-by-step explanation:

You want to know the grams of fat in both of 1.5 servings and 1.25 servings of pretzels that have 1.7 grams of fat per serving.

Lara ate 1.5 +1.25 = 2.75 servings of pretzels.

Each serving has 1.7 grams of fat, so her total fat intake from the pretzels is ...

  (1.7 g/serving) × (2.75 servings) = 4.675 g

4.675 g of fat were in both servings.

Having a rectangular pasture for the animals to graze in is something a farmer wants in order to start growing cows, horses, goats, and sheep. She has decided to purchase 7500 ft of fencing. 1875 square feet is the maximum possible area that each of the four pens will enclose.

The maximum possible area of each pen is 1875 square feet. To calculate this, first calculate the total area of the large rectangle that the farmer is enclosing. To do this, multiply the total length of the fencing (7500 feet) by the width of the fence (1 foot). This gives us 7500 square feet as the area of the large rectangle.

Next, divide the area of the large rectangle by 4 to get the area of each pen. This gives us 1875 square feet as the maximum area of each pen.

Total Area of Large Rectangle = 7500 ft x 1 ft = 7500 sq ft

Area of Each Pen = 7500 sq ft / 4 = 1875 sq ft

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Answer:

1

Step-by-step explanation:

The probability that none of the patients have broken bones is  0.0352.

What is binomial distribution?

A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. By dividing the quantity of independent trials by the number of successes, one can calculate the value of a binomial.

Let X has binomial distribution with n = 15 and  p = 0.20

The PDF of the distribution can be written as:

P(X=x)  = nCx(p)x (1-p)n-x

Probability for 0 patients have broken bones can be calculated as:

P(x=0) = 15C0(0.20)0 (1-0.20)15-0

P(x=0)  = 0.035184 = 0.0352

Therefore, the probability is  0.0352

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Complete Question

Suppose 20% of all emergency room patients have broken bones. of the next fifteen patients to arrive, what is the probability that none have broken bones?

For a test concerning a mean, a sample of size is obtained from a normal population. the population variance is known in testing versus the test statistic. Therefore, The Null Hypothesis is Rejected.

In mathematics, especially statistics, there are several kinds of instruments. Each average is used to summarize a particular group of data in order to better understand the overall values ​​(magnitude and sign) of a particular data set.

For datasets, the arithmetic mean, also called the "arithmetic mean", is a measure of the central tendency of a finite set of numbers. More specifically, the sum of the values ​​divided by the number of values. The arithmetic mean of a series of numbers x₁, x₂, ..., xₙ is usually given by the overhead bar. The dataset was based on a series of observations obtained by sampling from a statistical population. The arithmetic mean is the population mean.

Sample size is a term used in market research to define the number of subjects included in the sample size. Sample size means the group of subjects selected from the general population and considered representative of the actual population for this particular study.

For example, if you want to predict how a population of a certain age group will react to a new product, you can first test with a sample representative of your target group his size. In this case, the sample size is derived from the number of people interviewed in this age group.

Population variance is a measure of variance that determines how far each data point is from the population mean. Population variance can be defined as the average squared deviation from the mean of the data. Population refers to all observations within a finite group. Population variance is calculated based on the population. However, as the number of observations increases, some data points are selected that can represent the entire population. These specific data points form the sample, and the variance calculated from these data is called the sample variance. We can use the sample variance to estimate the population variance.

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Yes, dilation affects the driving.

When you get your eyes dilated, your doctor uses special drops to open your pupils wide. This let them get a look at your whole eye, including all the nerves and blood vessels at the back, to check for signs of diseases

When dilated, the pupil is unable to get smaller, and thus block out light in bright areas. This causes glare in your vision so you can't see things clearly.

The drops also make it difficult to focus on things up close, but usually don't affect distance vision.

So, Your eyesight will be impaired, so some experts say you should play it safe and not get behind the wheel will leds to affecting your driving

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According to this equation, after 3.73 hours (3 hours, 44 minutes) of driving, Evin would run out of gas.

This equation, which is a mathematical statement showing that two or more mathematical expressions are equivalent or equal, shows the rate of change or consumption.

The rate of change that the equation demonstrates is computed as the unit of gas consumed per hour.

Gas Tank after 1 hour of driving = 7.25 gallons

Gas Tank after 4 hours of additional driving = 3.5 gallons

The quantity of gas consumed in 4 hours of driving = 3.75 gallons

The quantity of gas consumed per 1 hour of driving = 0.9375 gallons per hour (3.75/4).

The length of time that 3.5 gallons of gas can cover = 3.73 hours (3.5/0.9375)

= 3 hours 44 minutes.

Thus, Evin's car can only last for additional 3 hours 44 minutes, given the equation.

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THE GRAPH IS ATTACHED ALONG WITH THIS

The parabola has a minima, vertex and a y-intercept.

Given,

Since the equation is quadratic, the parabola has a vertex. To find it, do as follows:

x = -b/2a

Where:

a=1

b=-2

Then:

x = -(-2)/ 2 × 1 = 1

Substitute this into the equation to obtain y:

y = 1² - 2 × 1  + 3 = 2

The point of the vertex is (1,2)  

The sign of a is positive, therefore, the parabola has a minimum.

Substitute x=0 into the equation to find y-intercept:

y = 0² - 2 × 0 + 3

y = 3

You know that this point is (0,3)

Recognize that the parabola has a minimum, a vertex, and a y-intercept, and that you may graph it as shown in the accompanying image.

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The quotient would be 2.

Answer:2

Step-by-step explanation:

10/16 divided 5/16. Keep 10/16, switch division to multiplication/times turn 5/16 to 16/5 which you will get 160/80 and the answer will be 2 because 80x2 is 160 so 160/80 will be 2. You'll thank me.

The coordinates of N' will be (4.5, 5.25)

The picture is given by the product of the corresponding point on the preimage and the scale factor, with the center of dilatation at the origin.

The origin is the center of dilatation of a quadrilateral MNOP.

The picture that results from the dilatation of MNOP = M'N'O'P'

The dilation scale factor is 1.5.

N's coordinates in MNOP = N (3, 3.5)

The coordinates of a point (x', y') on the picture after dilatation with the center at the origin, of the preimage (x, y) by a scale factor are given below;

   (x', y') = Scale factor × (x, y)

Which gives;

The coordinates of N' = 1.5 × N(3, 3.5) = N'(1.5 × 3, 1.5 × 3.5) = N'(4.5, 5.25)

The coordinates of N' = (4.5, 5.25)

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The required conclusion for confidence interval for the difference of two population means contains​ 0 has no difference.

Probability dispersion help to display our reality, empowering us to get evaluations of the Probability that a specific occasion might happen, or gauge the changeability of event. They are a typical method for depicting, and perhaps anticipate, the Probability of an occasion.

In the event that your certainty stretch for a distinction between bunches incorporates zero,

it means that assuming you run your examination again you have a decent possibility tracking down no contrast between gatherings.

So, There will be no difference between both the experiments for the same.

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Step 2 of comparison shopping is to assess the purchase objectively.

Comparison shopping may be defined as a method of studying and understanding various product costs prior to making a purchase. Retailers typically use comparison shopping to determine the price at which their rivals are offering a given product on the market. Nowadays, the majority of consumers purchase their goods online, making comparison shopping a sort of trend.

As a result of this growing tendency, numerous online shopping portals have emerged. Some of the most well-known online retailers include Flipkart, Myntra, and Amazon. Because they offer many product categories in each part, these websites can be categorized as a type of online price comparison website.

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Answer:

(4,0)

Step-by-step explanation:

(x, y)

Putting these points in a graph lends on the x-intercept, the right side of the graph

The probability of getting 6 face cards (king, queen, or jack) when 6 cards are drawn from a deck without replacement is 77/1696543.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Total number of face cards in deck =12

When 6 cards are drawn = 12C6 =924

Without replacement :

P(6 face cards)=12C6 /52C6

P(6 face cards)=924/20358520

P(6 face cards)=231/5089630

P(6 face cards)=77/1696543

Or another way

P(6 face cards) =(12/52)*(11/51)*(10/50)*(9/49)*(8/48)*(7/47)

P(6 face cards)=665280/14658134400

P(6 face cards)=924/20358520

P(6 face cards)=77/1696543

Hence, the probability of getting 6 face cards (king, queen, or jack) when 6 cards are drawn from a deck without replacement is 77/1696543.

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The age of the artifact is 3523.77 years.

What is radioactive decay?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Here,

The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)

 All radioactive decay processes follow the first-order reaction.

The equation for the half-life for first-order reaction follows:

t(1/2) = 0.693/k....(1)

where,

k = rate constant of a first-order reaction

Given value:

t(1/2) = 5715 years

Put the value of t in equation (1), and we get

k = 0.693/5715

k = 1.21×10⁻⁴yr

The integrated rate law expression for first-order reaction follows:

t = 2.303/k×㏒(a/(a-x))

where,

t = time period

a = initial concentration of the reactant = 58.2 counts per minute

(a-x) = Concentration of reactant left after time t = 38.0 counts per minute

k = rate constant of a first-order reaction

Put the values in the equation and we get

t = 2.303/1.21×10⁻⁴㏒58.2/38

t = 3523.77 years.

Hence, the age of the artifact is 3523.77 years.

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Answer: 31.99$ or 32$

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 39.99 × 20/100

Discount = 39.99 x 0.2

You save = $8.00

Final Price = Original Price - Discount

Final Price = 39.99 - 7.998

Final Price = $31.99

Answer:

x/39.99 is the same as 20%/100% so you would cross multiply 39.99 x 20 then divide by 100 which is 16.8 then add 39.99 - 16.8 to get $23.19.

Answer:

25 m/s²

acceleration

Step-by-step explanation:

m = (100 - 25)/(4 - 1) = 75/3 = 25 m/s²

The slope is the rate of change in velocity as a function of time.

The rate of change of velocity is called the acceleration.

On solving the following question, the function that has domain of all real numbers is - [tex]y = -2(3X)^{\frac{1}{6} }[/tex]

All numbers that we can recall are real numbers except complex numbers. The union of the set of rational numbers and the set of irrational numbers is the set of real numbers denoted by the symbol R.

A rational number is any number that can be expressed as the ratio p/q. The fraction's denominator is denoted by "q," while the numerator is represented by "p." "q" is not zero.

Both 5 and 1/2 are actual figures. X also defines a number, but since it's negative, it's an integer because it's rational.

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The conditional probability values are 0.57 and 0.43

Missing information

              Has Eaten before   Have not           Total

Snack A     144                               108                252

Snack B      92                               228                320

Total          236                              336                572

Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.

Given a person who has eaten snack A before, the customer will want to eat snack A

Given a person who has not eaten snack A before, the customer will want to eat snack

How to determine the probabilities?

The required probabilities are conditional probabilities, and they are calculated using:

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

Using the above formula, we have:

The probability that a customer eats snack A given that the customer has eaten snack A before, to be:

P = n(Have eaten snack A)/n(Snack A)

This gives

P = 144/252

Evaluate

P = 0.57

Also, we have:

The probability that a customer eats snack A given that the customer has not eaten snack A before, to be:

P = n(Have not eaten snack A)/n(Snack A)

This gives

P = 108/252

Evaluate

P = 0.43

Hence, the probabilities are 0.57 and 0.43

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A i think maybe

:>..,.h,j.

There is no change in the figure when the scale factor is 1 .

In the question ,

it is asked what will happen when the scale factor for a figure is 1 .

we know that ,

when the scale factor is greater than 1 , then new image is enlarged .

when the scale factor is 1 , then there is no change in the size of the image .

when the scale factor is less than 1 , then the new image is smaller than the original image .

Therefore , the size of the figure of the figure will remain the same when the scale factor is 1 .

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The 12 ounce can because you get more for only two cents more.

What is cost ?

A cost is the worth of money that has been used to produce something or provide a service and is thus no longer accessible for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.

To find which tuna is a better deal, divide the cost by the number of ounces of tuna you are getting to get the cost per ounce.

$0.90/5  = $0.18 per ounce

$2.40/12 = $0.20 per ounce

Since the 5-ounce can of tuna has a cheaper unit rate price, meaning you are getting a better value, makes this the best option.

0.90/5 = 18 cents per ounce

2.40/12 = 20 cents per ounce

The 12 ounce can because you get more for only two cents more.

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Answer:

4

Step-by-step explanation:

The answer is 4.

[tex]20 / 4=5[/tex]

Answer: 1728

Step-by-step explanation:

multiples of 8 = 1,2,4,8

multiples of 12= 1,2,3,4,6,12

Answer:

the ratio would be 6:2 or 6/2. Yes, the ratio of sugar to flour change when I compare the single batch to the double batch.

Step-by-step explanation:

The probability that at least one number cube show a 2, given that the sum is even is 5/36   .

In the question ,

it is given that ,
two standard cube are rolled ,

we have to find the probability that at least one number cube show a 2, given that the sum is even ,

we know that on rolling two dice ,

the total number of outcomes is = 36 ,

the outcomes in which one cube shows 2 are ,

{ (1,2) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) , (2,1) , (3,2), (4,2) , (5,2) ,(6,2) }

and the outcomes in which the sum is even is :

{ (2,2) , (2,4) , (2,6), (4,2) , (6,2) }

So , the number of favorable outcomes is = 5 ,

So , the probability is = 5/36

Therefore , the required probability is = 5/36 .

The given question is incomplete the complete question is

You roll two standard number cube . What is the probability that at least one number cube show a 2, given that the sum is even ?

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Dalton earns more money in one week.

Dalton earns $840 and Alma earns $735 in one week.

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

The question requires us to work out the percentages of the pay each of Dalton and Alma gets.

Dalton makes;

40% of $2,100

which equals [tex]\frac{40}{100}[/tex] x 2100 = $840

While Alma makes;

20% of $3,675

which equals [tex]\frac{20}{100}[/tex] x 3,675 =  $735

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