Consider a clinical trial where we would like perform inference concerning π, the probability that the treatment is successful. We observed y=8 successes among n=12 trials. Here is the display of the pmf for the B(n=12,π=0.5) distribution. round (dbinom (0:12,12,0.5),3) (a) Using the values of for the above pmf, compute the p-value to test H 0
​
:π=0.5 against H a
​
:π

=0.5 with the Binomial test using the min likelihood method. (b) Using the values of for the above pmf, compute the p-value to test H 0
​
:π=0.5 against H a
​
:π

=0.5 with the Binomial test using the central method. (c) Give the Clopper-Pearson 95% confidence interval for π by using quantiles of an appropriate beta distribution. (Hint: use qbeta.) (d) Use the Score Test to test H 0
​
:π=0.5 against H a
​
:π

=0.5. Give the observed value of the test statistic, the p-value and the conclusion.

If the volume of a tank is 4,750 cubic centimeters, the volume of the tank in cubic meters is 0.00475 m³.

To convert the volume of the tank from cubic centimeters to cubic meters, follow these steps:

Step 1: Understand the conversion factor between cubic centimeters and cubic meters.

There are 1,000,000 cubic centimeters in 1 cubic meter

(1 cm³ = 0.000001 m³ or 1 m³ = 1,000,000 cm³).

Step 2: Divide the volume of the tank in cubic centimeters by the conversion factor.

In this case, divide 4,750 cm³ by 1,000,000.

Step 3: Perform the calculation:

4,750 cm³ ÷ 1,000,000 = 0.00475 m³.

So, the volume of the tank in cubic meters is 0.00475 m³.

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Answer:

The answer that you're looking for is x = 3

Step-by-step explanation:

You start with the equation:

76x-11=72x+1

You then want to separate the variables and constants so you do the inverse of positive 72 which is to subtract 72x from each side.

(76x-72x)-11=(72x-72x)+1
4x-11=1

After that, you add the inverse of -11 which is adding 11 to both sides to leave 4x by itself.

4x(-11+11)=(1+11)
4x=12

You then finally divide 4 by both sides giving you x = 3 as the final answer.

4x/4=12/4
x = 3

Answer: D

Step-by-step explanation:

I don’t know how to explain this to you step by step but when it comes to questions like this try to think more “logically” (if that makes sense) especially if you’re not familiar with the topic, like me. Think about it, if it was the first one the line on the graph would be above the middle line (its addition plus its greater than y so that wouldn’t be correct). Now the second one is subtraction but its less than y and everything thats coloured goes up not down so it has to be greater than y. C is not the correct answer because its a regular equation and thats not what the question wants plus its the only question out of the the 4 answers which is completely the odd one out so you can just cancel that out. Mow we come to the last answer which is the correct answer because it follows all the right “points” I mentioned earlier. I hope this makes sense to you, sorry I couldn’t explain it better!

Answer:

The answer is D because outliers are data far away from the main data set.

Answer:

d

Step-by-step explanation:

Answer:

A picture provided would be better, but here's a picture to help you find an answer to your question.

Step-by-step explanation:

The two angles marked in red are corresponding angles on a pair of parallel lines. Corresponding angles are ALWAYS congruent to each other.

After factorizing the expression 72a⁹b³-18a⁷b⁵completely we get the value of a and b will be ±1 and ±2.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

⇒72a⁹b³-18a⁷b⁵=0  ------(1)

We have to factor in the expression,

⇒72a⁹b³-18a⁷b⁵=0

Take 18a⁷b³ as common,

⇒18a⁷b³(4a²-a²b²)=0

⇒18a⁷b³=0

⇒(4a²-a²b²)=0

⇒4a² = a²b²

⇒b²=4

⇒b=±2

Substitute the value of b in equation 1 we get,

72a⁹b³-18a⁷b⁵=0  

72a⁹(2)³-18a⁷(2)⁵=0

576a⁹-576a⁷=0

a²=1

a=±1

Thus, after factorizing the expression 72a⁹b³-18a⁷b⁵completely we get the value of a and b will be ±1 and ±2.

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the dimensions of the lot is 100 yards by 400 yards. In this problem, a parking lot has a rectangular area of 40,000 square yards, and the length is 200 yards more than twice the width.

Determining the dimensions of a rectangular area, such as a parking lot, can be a useful task for many purposes, such as planning and designing a new lot or estimating the amount of space available for parking.

Let's call the width of the parking lot "w". Then, the length of the parking lot can be represented as 2w + 200.

The total area of the parking lot is 40,000 square yards, so we can set up an equation to solve for w: w * (2w + 200) = 40,000.

Solving for w, we get w = 100. This means that the width of the parking lot is 100 yards and the length is 2 * 100 + 200 = 400 yards.

The dimensions of the parking lot are 100 yards by 400 yards.

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Answer:

15.8

Step-by-step explanation:

First off, I think you mean area. You can't find the perimeter of a triangle with only two sides listed, neither can you find that side unless you have the perimeter.

1. Area of the triangle formula is axb/2= (9.9x3.2)/2, which when put in a calculator is 15.84.

2. Rounded to 1DP makes it 15.8

Answer:

they are called constants. they don't have a variable on them, so their value throughout the problem will remain the same or constant.

Step-by-step explanation:

Answer:

75 percent

Step-by-step explanation:

To find percent increase, do (final-initial/initial) * 100.

This would be 133-76/76 * 100, meaning you get a 75 percent increase.

The percent increase is 75 %.

The ratio of the increased value to the original value, multiplied by 100, is the percentage increase formula. It is outlined as a percentage. Anything's value will increase if it is valued more, so will its proportion.

Given:

Sonya's heart rate was 76 beats per minute.

After running, heart beat rate= 133  beats per minute.

So, percent increase

= (133- 76)/ 76 x 100

= 0.75 x 100

= 75%

Hence, the percent increase is 75 %.

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Answer:

26.93 gallons were used

Step-by-step explanation:

Subtract the amount left from the amount started with

28.03

-  1.1

----------------

26.93 gallons were used

Answer:

The answer is B. \(\frac{2x+1}{x^{2}-7} ,x\neq \sqrt{7}\)

Step-by-step explanation:

\(f(x)=2x+1\\g(x)=x^{2} -7\)

Focusing on the denominator makes it equal to = 0

\(x^{2} -7=0\\x^{2} =7\\x=+\sqrt{7},-\sqrt{7}\)

If the denominator equals zero then the equation ends up undefined. A number over zero, zero can not go divided into a number.

Answer:

30 parts of red paint

Step-by-step explanation:

9 white-5red

54white-x

(54×5)/9=30

Given the probabilities P(A) = 0.7, P(Ac) = 0.3, P(B|A) = 0.4, and P(B|Ac) = 0.8, the joint probabilities can be calculated as follows: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.12, and P(Ac and Bc) = 0.18.

The joint probability P(A and B) represents the probability of events A and B occurring simultaneously. It can be calculated using the formula P(A and B) = P(A) * P(B|A). Given that P(A) = 0.7 and P(B|A) = 0.4, we can multiply these probabilities to obtain P(A and B) = 0.7 * 0.4 = 0.28.

It can be calculated as P(A and Bc) = P(A) * P(Bc|A). Since the complement of event B is denoted as Bc, and P(Bc|A) = 1 - P(B|A), we can calculate P(A and Bc) as P(A) * (1 - P(B|A)) = 0.7 * (1 - 0.4) = 0.42.

Finally, P(Ac and Bc) represents the probability of both event A and event B not occurring. It can be calculated as P(Ac and Bc) = P(Ac) * P(Bc|Ac). Using P(Ac) = 0.3 and P(Bc|Ac) = 1 - P(B|Ac), we can calculate P(Ac and Bc) as P(Ac) * (1 - P(B|Ac)) = 0.3 * (1 - 0.8) = 0.18.

Therefore, the joint probabilities are: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.24, and P(Ac and Bc) = 0.18.

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The  measure of arc XZ is 45.

The correct option is D.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

We have,

<EYX = 45

The arc is the portion of the circle's circumference that lies between two of its points. The arc is measured twice:

Using the second point the measure of arc XZ is 45.

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The dependent variable can be defined as a variable that depends on other variables. In other words, it is the variable being measured or tested in an experiment and is therefore the outcome of interest.

From the given answer options, the dependent variable is "time to complete the maze."What is the dependent variable?The dependent variable is the outcome variable that is influenced by the independent variable or experimental variable.

The dependent variable can be defined as a variable that depends on other variables. It is the variable being measured or tested in an experiment and is therefore the outcome of interest.In the given options, "time to complete the maze" is the dependent variable since it depends on the independent variable (receiving a food award or not) and will be affected by it. Therefore, it is the variable being measured in the experiment.

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No, f is not continuous at x=-3. To show this, let's take the limit from both sides.

From the left side, the limit of f(x) as x approaches -3 is 5. From the right side, the limit of f(x) as x approaches -3 is 3. Since the two limits are not equal (5≠3), then f is not continuous at x=-3.No, f is not continuous at x=-3. This is because the limit of f(x) as x approaches -3 does not equal f(-3). The limit of f(x) can be calculated using the formula lim x->-3 f(x) = lim x->-3 (x^2 + 9). Calculating this limit, we get lim x->-3 f(x) = lim x->-3 (x^2 + 9) = 9. However, f(-3) = (-3)^2 + 9 = 0, which does not match the limit.

Mathematically, this can be shown using the following:

limx→−3 f(x) = 5 ≠ 3 = limx→−3+ f(x)

Since the two limits are not equal, then f is not continuous at x=-3.

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Answer:

25%

Step-by-step explanation:

As the given situation the parameters are below:-

Cost of each box = 3 pounds

Amount of cereal in each box = 160 g

now,

160 g of cereal = 100%

and

25% of 1 box of cereal = 25% of 160 g which is

\(= \frac{25}{100} \times 160 g= 40 g\)

As per the question,  it is mention that Jane need her idea to give the equal value of amount as Tim's idea, provided

160 g of cereal costs 3 pounds

and

1 g of cereal will cost

=  \(\frac{3}{60}\ pounds\)

40 g of cereal will cost \(40\times \frac{3}{160} = \frac{3}{4}\ pounds\)

So, the percentage of \(\frac{3}{4}\) the pound is of 3 pounds is 3 ÷ 4 ÷ 3 × 100

= 25%

Therefore as the situation, Jane need to decline the amount by 25% for the same amount as Tim's idea.

Answer:

\( {8}^{3n} = {8}^{6} \\ 3n = 6 \\ n = 2\)

Answer:

\(n = 2\)

Step-by-step explanation:

\(( {8}^{n} )^{3} = {8}^{6} \)

\( {8}^{n \times 3} = {8}^{6} \)

\(n \times 3 = 6\)

\(n = \frac{6}{3} \)

\(n = 2\)

Using the given information, the mean number of books read is 3.41

From the question, we are to calculate the mean number of books read

From the given information, we have the table

Number of students             Number of books

        2                                               1

        11                                              3

        16                                             4

Then,

Mean number of books read = [(2×1) +(11×3) + (16×4)]/(2+ 11+ 16)

Mean number of books read = (2 + 33+ 64)/29

Mean number of books read = 99/29

Mean number of books read = 3.41

Hence, the mean number of books read is 3.41

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Answer:

Step-by-step explanation:

The graph covers the interval

Inequality to reflect this

Answer:

-3 < x ≤ 2

Step-by-step explanation:

Answer:

The answer will be 8

Step-by-step explanation:

SInce you notice there is movies with an 8 difference....

Answer:

4 horror movies

Step-by-step explanation:

This seems to be a problem related to ratios. We are given that, for every 24 kids' movies, there are 32 horror movies. We need to figure out how many horror movies there would be if there were just 3 kids' movies. We can set up an equation using proportions:

\(\frac{24}{32}=\frac{3}{x}\)

We don't know how many horror movies there would be so we can let this quantity equal x. Now, we can cross multiply and solve for our unknown:

\(24x = 3*32\\24x = 96\\x = 4\)

This means that there are 4 horror movies

Answer:

18.33%.

Step-by-step explanation:

The total number of cars is 60

what you want is the red number (11)

You set up what you want over what you have and end up with:

11/60

turn this into decimal and you get 0.183

to turn into percent multiply by a 100

You end up with 18.33%

Answer:

18.3%

Explanation:

Red = 11, silver = 24, gray = 16 black = 9

\(\sf probability = \dfrac{favorable \ outcomes}{total \ possible \ outcomes}\)

\(\rightarrow \sf \dfrac{11}{60} \ x \ 100\)

\(\rightarrow \sf 18.3 \%\)

Answer:

a

Step-by-step explanation:

the plots are going up from the origin which means its positive and linear

Answer:

No, I don't think so.

Step-by-step explanation:

The correct 98% confidence interval for the true proportion of graduates working in the field of study in which they obtained their degree is (0.811, 0.892).

To calculate the confidence interval, we need to use the formula for estimating proportions and the standard error of the proportion. The formula is:

Confidence interval = sample proportion ± z * standard error

Calculate the sample proportion

In this case, the sample proportion is the number of graduates working in their field of study (361) divided by the total number of graduates surveyed (424):

Sample proportion = 361/424 ≈ 0.852

Calculate the standard error

The standard error of the proportion is calculated using the formula:

Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size)

Using the given values, we have:

Standard error = sqrt((0.852 * (1 - 0.852)) / 424) ≈ 0.014

Determine the confidence interval

To find the z-value for a 98% confidence level, we look up the corresponding value in the z-table. The z-value for a 98% confidence level is approximately 2.33.

Substituting the values into the confidence interval formula, we have:

Confidence interval = 0.852 ± 2.33 * 0.014

Confidence interval ≈ (0.811, 0.892)

Therefore, the correct 98% confidence interval for the true proportion of graduates working in their field of study is (0.811, 0.892).

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When training a classifier, the training set is used to learn the conditional probabilities.

The training set is used to learn the conditional probabilities because the training set is used to train the classifier on the patterns and features in the data, which in turn helps the classifier to learn the conditional probabilities of the different classes in the data.

The hold-out set and test set are used to evaluate the performance of the classifier and ensure that it is not overfitting to the training set.

By evaluating the classifier on data that it has not seen before, we can get a more accurate estimate of its true performance and the probability of correctly classifying new data.

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Step-by-step explanation:

so you have to make an equation where you let x=the number, so it would be

x+(2/3)x+(1/4)x=5 3/4

you combine the like terms to get

(23/12)x = 5 3/4

multiply both sides by the reciprocal of 23/12 to isolate x, and you're left with

x=36/92, which simplifies to 9/23.

Scatter plot

Box plot

Dot plot

To compare bite strength to weight for different carnivores, scatter plot, box plot, and dot plot are appropriate representations.

Scatter plot: A scatter plot can show the relationship between bite strength and weight by plotting each carnivore as a data point. The x-axis can represent weight, the y-axis can represent bite strength, and each point on the plot represents a different carnivore. This allows for visualizing the overall trend or pattern between the two variables.

Box plot: A box plot can display the distribution of bite strength and weight for different carnivores. It provides information about the median, quartiles, and any outliers in the data. By comparing the box plots for different carnivores, we can assess the variations in bite strength relative to weight.

Histogram: A histogram is not appropriate in this case because it represents the distribution of a single variable, such as bite strength or weight, and does not directly compare the two variables.

Table: A table can present the bite strength and weight data for different carnivores, but it does not provide a visual comparison or representation of the relationship between the two variables.

Dot plot: A dot plot can show the individual data points of bite strength and weight for each carnivore. Each dot represents a carnivore, and by comparing the position and density of dots, we can observe the relationship between bite strength and weight.

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