Explain what is wrong with each of the following randomization procedures, and describe how you would do the randomization correctly.

a. Twenty students are to be used to evaluate a new treatment. Ten men are assigned to receive the treatment, and 10 women are assigned to be the controls.
b. Ten subjects are to be assigned to two treatments, 5 to each. For each subject, a coin is tossed. If the coin comes up heads, the subject is assigned to the first treatment: if the coin comes up tails, the subject is assigned to the second treatment.
c. An experiment will assign 40 rats to four different treatment conditions. The rats arrive from the supplier in batches of 10, and the treatment lasts two weeks. The first batch of 10 rats is randomly assigned to one of the four treatments, and data for these rats are collected. After a one-week break, another batch of 10 rats arrives and is assigned to one of the three remaining treatments. The process continues until the last batch of rats is given the treatment that has not been assigned to the three previous batches.

The answer is A because when you divide into 175 to find the amount discounted, then you subtract that to 175 and you get 145.25

Answer:

[tex]6x^{2} - 12xy[/tex]

Step-by-step explanation:

6x  × x = [tex]6x^{2}[/tex]

6x  ×  -2y = -12xy

[tex]6x^{2} - 12xy[/tex]

Answer:

0.0645 = 6.45% probability that exactly 10 employees will be tested in order to find 3 positives

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

40% of the employees have positive indications of asbestos in their lungs

This means that [tex]p = 0.4[/tex]

a) Find the probability that exactly 10 employees will be tested in order to find 3 positives

2 within the first 9([tex]P(X = 2)[/tex] when [tex]n = 9[/tex]), and the 10th, with 0.4 probability. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{9,2}.(0.4)^{2}.(0.6)^{7} = 0.1612[/tex]

0.4*0.1612 = 0.0645

0.0645 = 6.45% probability that exactly 10 employees will be tested in order to find 3 positives

Answer:

a) the mean percentage of defective item produced is 2.52 %

b) the standard deviation of percentage of defective item produced is 1.01%

Step-by-step explanation:

Given that;

the percentage of defective items produced was 2%, 1.4%, 4%, 3%, 2.2%.

sample size n = 5

a) Calculate the mean for these data

mean percentage of defective item produced will be;

[tex]x^{bar}[/tex] = ∑x / n

[tex]x^{bar}[/tex] = ∑x / n = ( 2% + 1.4% + 4% + 3% + 2.2% ) / 5

[tex]x^{bar}[/tex]  = 12.6 / 5

[tex]x^{bar}[/tex]  = 2.52 %

Therefore, the mean percentage of defective item produced is 2.52 %

b) Calculate the standard deviation for these data

Formula for standard deviation is;

S = √( (∑(x-[tex]x^{bar}[/tex] )²) / (n-1) )

so we make a table;

x                   ( x - [tex]x^{bar}[/tex] )%                ( x - [tex]x^{bar}[/tex] )²%

2%                 -0.52                         0.2704

1.4%               -1.12                           1.2544

4%                  1.48                          2.1904  

3%                  0.48                         0.2304

2.2%.             -0.32                         0.1024

summation                                     4.048

so (∑(x-[tex]x^{bar}[/tex] )² = 4.048%  

so we substitute the value into our equation;

S = √( (∑(x-[tex]x^{bar}[/tex] )²) / (n-1) )

S = √( (4.048%) / (5-1) )

S = √( 4.048% / 4 )

S = √( 1.0121

S =  1.00598 % ≈ 1.01%

Therefore, the standard deviation of percentage of defective item produced is 1.01%

Answer:

b i think

Step-by-step explanation:

The ratio of the corresponding sides of  MARDT and JPLSF is A. 3/4.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

By observing the given figures MARDT is similar to JPLSF.

So, the ratio of their corresponding sides must also be equal.

Given, Length of MA is 4 and the length of JP is 3.

Therefore, The ratio of sides MARDT and JPLSF is 3/4.

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Answer:

Step-by-step explanation:

y = -x²+4 and y = 2x+1

Therefore,  -x²+4 = 2x+1

x²+2x-3 = 0

x = 1,-3

There are two solutions:

(1,3) and (-3,-5)

The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).

We have,

To solve the system of equations:

Set the expressions for y equal to each other:

-x² + 4 = 2x + 1

Rearrange the equation to bring all terms to one side:

-x² - 2x + 3 = 0

Solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we will use factoring.

Factor the quadratic equation:

(-x - 3)(x - 1) = 0

Set each factor equal to zero and solve for x:

-x - 3 = 0 or x - 1 = 0

Solve the first equation:

-x = 3

x = -3

Solve the second equation:

x = 1

Substitute the values of x back into one of the original equations to find the corresponding values of y.

For x = -3:

y = 2(-3) + 1

y = -6 + 1

y = -5

For x = 1:

y = 2(1) + 1

y = 2 + 1

y = 3

Therefore,

The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).

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Answer:

0.05 kilowatts

Answer:

0. 05

Step-by-step explanation:

Answer:

B. (x+3)(2x2−7)

Step-by-step explanation:

2x3 + 6x2 - 7x- 21

(2x3+6x2)(-7x-21)

2x2(x+3)-7(x+3)

(x+3)(2x2-7)

a/b The decay can be modeled by this equation, (1 - r), the r being the rate of decay. So it would be 1-0.115. (0.115 is your answer for a) You have to convert the percent into a decimal by moving the deicmal place two places to the left. 0.885 is your answer for b.

c. For function notation, that just means write an equation. So you want your decay times your inital.  V(t)=15000(0.885)^x. We get the V(t) from the directions that they want us to put it in; it's basically y.

d. Since it's two years, plug in 2 for x. This shows the decay after two years

V(t)=15000(0.885)^2

e. As with d, plug in 10 for x. V(t)=15000(0.885)^t

Answer:

20.8

Step-by-step explanation:

so x is opposite the 60 degree angle so that means that it is half of the hypotanuese times root three

so then x would be equal

24/12=12 root three which is equal to 20.8

Answer:

6.2

Step-by-step explanation:

3.7 + 2.5 = 6.2 Therefore w = 6.2

Answer:

Step-by-step explanation:

From the given information:

Assume X represents the no. interviewed until 1 has advanced training.

X obeys a Geometric distribution with parameter 0.3.

X  [tex]\sim[/tex] Geom (0.30)

For geometric distribution, the probability density is:

[tex]P(X =x) = p(1-p) ^{x-1} \ \ \ where; x =1,2,3...[/tex]

TO calculate the required probability;

[tex]P(X =5) =0.30 (1-0.30)^{5-1}[/tex]

[tex]P(X =5) =0.30 (0.70)^{4}[/tex]

[tex]P(X=5) = 0.30 \times 0.2401[/tex]

[tex]\mathbf{P(X=5) = 0.07203}[/tex]

(b)

The expected no. of applicants that need to be interviewed are:

[tex]E(X)=\dfrac{1}{p}[/tex]

[tex]E(X)=\dfrac{1}{0.30}[/tex]

E(X) = 3.33

(c)

The mean and the variance can be computed as:

[tex]E(Y) = \dfrac{1}{p}[/tex]

[tex]E(Y) = \dfrac{1}{0.30}[/tex]

E(Y) = 3.33

[tex]V(Y)=\dfrac{1-p}{p^2}[/tex]

[tex]V(Y)=\dfrac{1-0.3}{0.3^2}[/tex]

[tex]V(Y)=\dfrac{0.7}{0.3^2}[/tex]

[tex]V(Y)=7.778[/tex]

Suppose  C represents the no. of the total cost and given that each interview costs $30.

Then C = 30Y

Recall that; C is constant for a random variable X

∴

E(C) = E(30Y)

E(C) = 30E(Y)

E(C) = 30*3.33

E(C) =99.9

E(C) [tex]\simeq[/tex] 100

V(C) = V(30Y)

V(C) = 900 V(Y)

V(C) = 900*7.778

V(C) = 7000.2

V(C) [tex]\simeq[/tex] 7000

Answer:

Right angle triangle

Step-by-step explanation:

Answer:2.10%

Step-by-step explanation:

2 is the whole number with 1/10 being also = to 10/100s

Answer:

The answer is below

Step-by-step explanation:

El número de personas que vieron solo A = n (A) = 17

El número de personas que vieron solo B = n (B) = 17

El número de personas que vieron solo C = n (C) = 23

El número de personas que vieron A y B = n (A ∩ B) = 6

El número de personas que vieron A y C = n (A ∩ C) = 8

El número de personas que vieron B y C = n (B ∩ C) = 10

El número de personas que vieron las tres películas = n (A ∩ B ∩ C) = 2

1) Número de estudiantes que han visto dos películas = n (A ∩ B) + n (A ∩ C) + n (B ∩ C) = 6 + 8 + 10 = 24

2)

n (A∩ B '∩ C') = n (A) -n (A ∩ B) -n (A ∩ C) -n (A ∩ B ∩ C) = 17-8-6-2 = 1

n (A'∩ B ∩ C ') = n (B) -n (A ∩ B) -n (B ∩ C) -n (A ∩ B ∩ C) = 17-6-10-2 = 1

n (A'∩ B '∩ C) = norte (C) -n (UNA ∩ C) -n (B ∩ C) -n (UNA ∩ B ∩ C) = 23-8-10-2 = 3

estudiantes que no han visto = 55 - n (A∩ B '∩ C') -n (A'∩ B ∩ C ') - n (A'∩ B ∩ C') - n (A ∩ B) -n ( B ∩ C) -n (UNA ∩ C) -n (A∩ B ∩ C) = 55-1-1-3-6-8-10-2 = 24

3)

número de alumnos que no han visto =

4)

número de estudiantes que vieron solo A = n (A∩ B '∩ C') = 1

Answer:

5/9

Step-by-step explanation:

Answer

The area of the shaded region under the standard normal curve is 0.4834.

Step-by-step explanation:

A random variable X is said to have a normal distribution with mean, µ and variance σ².

Then , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z  N (0, 1).

The distribution of these z-variates is known as the standard normal distribution.

Compute the area under the curve between -2.13 and 0 as follows:

Thus, the area of the shaded region under the standard normal curve is 0.4834.

Answer:

3584232 || N o- t h x—?

Step-by-step explanation:

Answer:

3584232

Step-by-step explanation:

Yes I do its Sunju #5984

Answer:

3>-3

Step-by-step explanation:

make an open dot on 3 and make a line going towards the left.

Answer:

y=-1/2x+1

Step-by-step explanation:

Answer:

1) x-2y 2) 2(13a-5)

Step-by-step explanation:

1) -1/2(-2x+4y)=2/2x-4/2y=x-2y

2) 26a-10=2(13a-5)

Answer:

30%

Step-by-step explanation:

Simply divide your final value (750) by your initial value (2500).

[tex]x = 4[/tex]

55+85=140

180-140=40

10x=40

divide by ten on each side

x=4

Answer:

B Or D

Step-by-step explanation:

The inverse function is [tex]f^{-1}(x) = \frac{1}{x + 6} + 4[/tex] and the domain is [tex]x \ne 6[/tex]

The function is given as:

[tex]f(x) = \frac{1}{x - 4} - 6[/tex]

Express f(x) as y

[tex]y = \frac{1}{x - 4} - 6[/tex]

Swap the positions of x and y

[tex]x = \frac{1}{y - 4} - 6[/tex]

Add 6 to both sides

[tex]x + 6= \frac{1}{y - 4}[/tex]

Multiply both sides by y-4

[tex](x + 6)(y -4) =1[/tex]

Divide both sides by x + 6

[tex]y - 4 = \frac{1}{x + 6}[/tex]

Add 4 to both sides

[tex]y = \frac{1}{x + 6} + 4[/tex]

Rewrite as:

[tex]f^{-1}(x) = \frac{1}{x + 6} + 4[/tex]

Hence, the inverse function is [tex]f^{-1}(x) = \frac{1}{x + 6} + 4[/tex] and the domain is [tex]x \ne 6[/tex]

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Answer:

20%

Step-by-step explanation:

The computation is shown below:

Let something be x

[tex]\frac{1}{5} = \frac{x}{10} = \frac{x}{100} = x\%[/tex]

[tex]0.2 = \frac{x}{10} = \frac{x}{100} = x\%[/tex]

So if we see that 0.2 would be equivalent to the [tex]\frac{x}{10}[/tex] and then [tex]\frac{x}{100}[/tex] after than x percentage

Therefore according to this the x percentage is 20%

Hence, the x percentage is 20%

Answer:

136.3

Step-by-step explanation:

I assume it is asking you to add both 9.3x and 8.9y together. First you would multiply 9.3 by 7 and 8.9 by 8 which gives you 65.1 + 71.2 which equals 136.3.

Answer:

The margin of error is of [tex]2.262\frac{6}{\sqrt{10}} = 4.29[/tex]

Step-by-step explanation:

We have the standard deviation for the sample. So the T-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.262

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.262\frac{6}{\sqrt{10}} = 4.29[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The equation that represents the margin of error is: [tex]E = 2.262 \times \frac{6}{\sqrt {10}}[/tex]

The given parameters are:

The margin of error is calculated using:

[tex]E = z_y \times \frac{\sigma}{\sqrt n}[/tex]

So, we have:

[tex]E = z_y \times \frac{6}{\sqrt {10}}[/tex]

The quantile at 95% confidence interval is 2.262

So, the equation becomes

[tex]E = 2.262 \times \frac{6}{\sqrt {10}}[/tex]

Hence, the equation that represents the margin of error is: [tex]E = 2.262 \times \frac{6}{\sqrt {10}}[/tex]

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Answer:

Should be $11.25

Step-by-step explanation:

Since 25% is 1/4 you can just divide 45 by 4.

45/4 = 11.25

Answer: 33.75. 25% of 45 is 11.25. So 45-11.25=33.75

Step-by-step explanation: