Crossover trial: A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time, then switch to the other. The responses of the subjects are then compared using matched-pair methods. In an experiment to compare two pain relievers, seven subjects took one pain reliever for two weeks, then switched to the other. They rated their pain level from to , with larger numbers representing higher levels of pain. The results are listed below. Can you conclude that the mean pain level is more with drug B? Let μ1 represent the mean pain level with drug A and =μd−μ1μ2. Use the =α0.10 level and the P-value method with the TI-84 Plus calculator.

Subject 1 2 3 4 5 6 7

Drug A 5 4 6 6 5 2 1

Drug B 7 4 5 6 7 5 7

1. State the appropriate null and alternate hypotheses.

2. Compute the P-value. Round the answer to at least four decimal places.

3. Determine whether to reject H0.

4. State a conclusion.

Answer:

m<DBE =50°

m<ABD=150°

Step-by-step explanation:

Because of Straight Angles, All the angles will add up to 180 degrees

Let x be m<DBE

40+x+70+20=180

x+130=180

x=50

m<DBE will be 50 degrees

To find the m<ABD, we add m<FBA, m<FBE, m<DBE.

70+50+30=150

m<ABD = 150

Answer:

angle DBE=

Step-by-step explanation:

We know that angle ABE is a right angle because 70+20=90. Therefore angle CBE is also a right angle.

Now, 90-40=50 (angle DBE's measure)

Based on this, we can know that 20+70+50=140. Angle ABD is 140 degrees.

HTH :)

Answer:

96 chocolate bars

Step-by-step explanation:

If Brian sold 25% of his chocolate bars and now he's left with 72, let's subtract 25% from 100%.

100% - 25% = 75%

Now, let's set up the equation & solve:

1. Set up Equation

2. Cross-Multiply

3. Divide both sides by 75

Therefore, Brian started with 96 chocolate bars.

Answer:

96 bars

Step-by-step explanation:

100% - 25% = 75%

\(\frac{75}{100}\) = \(\frac{72}{x}\)

x = \(\frac{100*72}{75}\) = 96 bars

Answer:

B)  73°

Step-by-step explanation:

m∠NMP = 180 -168 = 12

Sum of interior angles of ΔNMP = 180

m∠P = 180 - 95 - 12 = 73

The variability of a statistic from a random sample does not depend on the size of the population, as long as the population is at least **ten times** larger than the sample.

In statistical sampling, the size of the population relative to the sample size can affect the variability of a statistic. However, as long as the population is sufficiently larger than the sample, typically by a factor of ten or more, the impact of the population size on variability is minimal.

When the population is much larger than the sample, each unit in the sample represents a relatively small fraction of the overall population. This ensures that sampling variability is not significantly influenced by the size of the population. Therefore, the variability of a statistic, such as the mean or standard deviation, can be estimated accurately from the sample without considering the population size, as long as the population is at least ten times larger than the sample.

It's worth noting that this guideline assumes random sampling and other necessary conditions for statistical inference. Additionally, if the population size is close to or only slightly larger than the sample size, adjustments may be needed to account for the finite population correction factor.

In conclusion, as long as the population is at least ten times larger than the sample, the variability of a statistic from a random sample is not significantly influenced by the population size. This allows for valid statistical inferences to be made from the sample to the larger population.

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Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.

For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that he makes exactly 1 is P(X = 1), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{3,1}.(0.9)^{1}.(0.1)^{2} = 0.027\)

0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.

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Answer:

0.03

Step-by-step explanation:

I just did it on Khan

Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer:

Coordinates of E is (-2,7)

Step-by-step explanation:

Midpoint = ((x1+x2)/2,(y1+y2)/2)

xK = (xW + xE)/2 => xE = 2xK - xW = 2(0) - 2 = -2

yK = (yW + yE)/2 => yE = 2yK - yW = 2(3) - (-1) = 7

Answer:

y = 3/x

Step-by-step explanation:

Answer:

The distance between Mary's house and her grandmother's house is approximately 49.73 miles.

The 3 traveled the following distances:

Theo rode 50 miles, Mary drove 49.73 miles, and Nancy drove 53.299 miles.

Step-by-step explanation:

Mary's route is indeed the hypotenuse of a given triangle, that has a 13-mile adjacent hand and a 48-mile wrong side. They can solve for the length of the other side of the triangle using Pythagoras' theorem because we have two sides of the triangle.

Let us just say that triangle's ellipse is x square miles. Pythagoras's theory stated that

\(x = \sqrt{(13^2 + 48^2)} \\\\\)

  \(= \sqrt{169 + 2,304} \\\\ = \sqrt{2,473}\\\\ = 49.729\\\)

Mary's route was 49.73 square miles, to sum it up.

Nancy drove \(\sqrt{2,840} \ miles = 53.2916 \ miles\)

As a result, Mary rode the shortest distance of 49.73 miles, Theo drove 50 miles, and Nancy drove 53.299 miles.

Answer:

49.73

Mary, Theo, Nancy

Step-by-step explanation:

Approximately how many miles did Mary drive to her grandmother’s house?

✔ 49.73

Order the distances that each family member drove to their grandmother’s house from least to greatest.

✔ Mary, Theo, Nancy

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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Answer:

Option C.

Step-by-step explanation:

First, simplify the inequality. Add 2 to both sides:

4v - 2 < 10

4v - 2 + 2 < 10 + 2

4x < 12

Divide both sides by 4:

4x ÷ 4 < 12 ÷ 4

x < 3

As 3 will not satisfy the inequality, it is not a solution. The option that shows x being less than 3 but not including is option C.

Hope this helps!

There are 105 people in total. Given that there are 7 men, 7 wives, and each couple has 7 children, we can calculate the total number of people by summing the number of men, wives, and children.

In this case, there are 7 men, 7 wives, and each couple has 7 children. The number of men and wives combined is 7 + 7 = 14. Since each couple has 7 children, there are 7 children for each couple, resulting in a total of 7 x 7 = 49 children. Therefore, the total number of people is 14 (men and wives) + 49 (children) = 63. Including the original 7 men and 7 wives, the grand total is 63 + 7 + 7 = 77 people.

To break down the calculation further, we can analyze each category. There are 7 men, and each man is married to one wife. Therefore, there are 7 wives. Each couple has 7 children, so for the 7 couples, there are 7 x 7 = 49 children. Combining the men, wives, and children, we have 7 + 7 + 49 = 63 people. Adding the original 7 men and 7 wives, the grand total is 63 + 7 + 7 = 77 people.

With 7 men, 7 wives, and each couple having 7 children, there are a total of 105 people. The calculation includes the men, wives, and children, resulting in a total of 63 people. Including the original 7 men and 7 wives, the final count is 77 people.

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The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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The mathematician who lent his name to a test often mentioned in NYT crossword puzzles is Emil Post.

Emil Post was an influential mathematician who lived from 1897 to 1954. He made significant contributions to the field of mathematical logic, particularly in the area of formal systems and decision problems. One of his notable contributions is the development of the Post's Correspondence Problem, also known as the Post's Test.

The Post's Test is a problem in theoretical computer science that involves finding a solution to a sequence matching problem. It deals with determining whether there is a sequence of strings that can be concatenated in different ways to form identical sequences. This problem has important implications in the study of formal languages and computational complexity.

Due to the relevance and popularity of the Post's Test in the field of mathematical logic and computer science, Emil Post's name became associated with this problem. As a result, his name often appears in crossword puzzles, including those featured in the New York Times (NYT) crossword, which often includes clues related to various fields of knowledge, including mathematics and science.

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Without more information, it is not possible to determine the name of the mathematician who lent his name to a test in the New York Times crossword.

The question is asking for the name of a mathematician who lent his name to a test in the New York Times crossword. Unfortunately, without any specific clues or context, it is difficult to determine which mathematician is being referred to. There have been several mathematicians who have had tests or concepts named after them, such as the Pythagorean theorem named after Pythagoras or the Fibonacci sequence named after Leonardo Fibonacci. However, without more information, it is not possible to provide a specific answer.

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Rs.13680 is the answer.

Step-by-step explanation:-

Given-

•Principal (P) = Rs.57,000

•Rate (r%) = 6%

\(→ \frac{6}{100} \)

\(→ 0.06\)

•Time (n) = 4 years

Applying Interest formula,

\(→In=P \times R \times T\)

\(→57,000 \times 0.06 \times 4\)

\(→Rs.13680\)

Hence, the interest is Rs.13680

Answer:

answer is d

Step-by-step explanation:

At 8000 feet MSL in the teardrop could a descent to 3,200 feet commence.

What is aircraft?

A vehicle that can fly is known as an aircraft. It does so by getting help from the air. It does this by either employing static lift, the dynamic lift of an airfoil or, in a few rare instances, the downward push from jet engines. Aerial vehicles include, but are not limited to, planes, helicopters, airships (including blimps), gliders, paramotors, and hot air balloons.

As given, your aircraft was cleared for the ils rwy 18 at Lincoln municipal and crossed the Lincoln Vortac at 5,000 feet MSL.

Therefore, at 8000 feet MSL in the teardrop could a descent to 3,200 feet commence.

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Answer:

False 15 times 7= 105

Answer:

The two substances will have the same volume after approximately 3.453 hours.

Step-by-step explanation:

The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:

\(\displaystyle \frac{dA}{dt} = 0.3 A\)

Where t is measured in hours.

And substance B is represented by the equation:

\(\displaystyle \frac{dB}{dt} = 1\)

We are also given that at t = 0, A(0) = 3 and B(0) = 5.

And we want to find the time(s) t for which both A and B will have the same volume.  

You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:

\(\displaystyle dB = 1 dt\)

Now, we can take the integral of both sides:

\(\displaystyle \int 1 \, dB = \int 1 \, dt\)

Integrate. Remember the constant of integration!

\(\displaystyle B(t) = t + C\)

Since B(0) = 5:

\(\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5\)

Hence:

\(B(t) = t + 5\)

We can apply the same method to substance A. This yields:

\(\displaystyle dA = 0.3A \, dt\)

We will have to divide both sides by A:

\(\displaystyle \frac{1}{A}\, dA = 0.3\, dt\)

Now, we can take the integral of both sides:

\(\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt\)

Integrate:

\(\displaystyle \ln|A| = 0.3 t + C\)

Raise both sides to e:

\(\displaystyle e^{\ln |A|} = e^{0.3t + C}\)

Simplify:

\(\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}\)

Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.

By definition:

\(\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}\)

Since A(0) = 3:

\(\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3\)

Therefore, the growth model of substance A is:

\(A(t) = 3e^{0.3t}\)

To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:

\(\displaystyle A(t) = B(t)\)

Substitute:

\(\displaystyle 3e^{0.3t} = t + 5\)

Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.

Since time cannot be negative, we can ignore the first solution.

In conclusion, the two substances will have the same volume after approximately 3.453 hours.

Answer:

\(\huge\boxed{x>-2\to x\in(-2;\ \infty)}\)

Step-by-step explanation:

\(y=\log(x+2)\\\\\bold{Domain:}\\\\x+2>0\qquad|\text{subtract 2 from both sides}\\\\x+2-2>0-2\\\\x>-2\)

Step-by-step explanation:

\( \frac{642}{3} \\ \)

Answer:

\(214\)

Step-by-step explanation:

\( = 642 \div 3 \\ = 214\)

Answer:

26 units

Step-by-step explanation

The figure is divided into a total of 3 Rectangles,

The formula of are of rectangle is length x breadth.

So, area of 1st rectangle = length x breadth

                                         = 5 x 2

                                         = 10 units

Area of 2nd rectangle = 3 x 2

                                   = 6 units

Area of 3rd rectangle = 5 x 2

                                    = 10 units

Therefore, area of figure = 10 units + 6 units + 10 units

                                         = 26 units

Hope i was able to help you ; )

The solutions of the equation 2sinθ - 1 = 0 in the interval (0, 2π) are θ = π/6 and θ = 13π/6.

To find all solutions of the equation 2sinθ - 1 = 0 in the interval (0, 2π), we can solve for θ by isolating the sine term and then using inverse sine (arcsin) to find the angles.

Start with the equation: 2sinθ - 1 = 0.

Add 1 to both sides of the equation: 2sinθ = 1.

Divide both sides by 2: sinθ = 1/2.

Take the inverse sine (arcsin) of both sides: θ = arcsin(1/2).

The inverse sine (arcsin) of 1/2 is π/6, so we have one solution θ = π/6.

However, we need to find all solutions in the interval (0, 2π). Since the sine function has a periodicity of 2π, we can add 2π to the solution to find additional solutions.

Adding 2π to π/6, we get θ = π/6 + 2π = π/6, 13π/6.

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Probability of labels which are randomly selected by the company to represent that it contain a defective compact disk is equal to 0.0201 .

As given in the question,

Number of companies produced labels = 3

Percent of defective compact disk produced by company i = 5%

Percent of defective compact disk produced by company ii = 3%

Percent of defective compact disk produced by company iii = 1%

Total percent of compact disk produced

By company i = 10%

By company ii = 35%

By company iii = 55%

Probability of selecting randomly compact disk is defective

= ( 5% of 10% ) + ( 3% of 35% ) + ( 1% of 55%)

= ( 0.05 × 0.10) + (0.03 × 0.35)  + ( 0.01 × 0.55)

= 0.005 + 0.0105 + 0.0055

= 0.0210

Therefore, probability of labels which are randomly selected by the company to represent that it contain a defective compact disk is equal to 0.0201 .

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Answer:

The answer is 40cm

Step-by-step explanation:

hope this helps :)

Answer:

40

Step-by-step explanation:

Side of square = x

Long side of rectangle = x + 5

Short side of rectangle = x - 3

(x - 3)(x + 5) = 84

\(x^2+2x-15=84\)

x = 9, x = -11

X has to be 9 because x cannot be negative.

9 + 5 = 14

9 - 3 = 6

14 + 14 + 6 + 6 = 40