Prove that the matrices H and I - H are idempotent, that is, HH = H and (I - H)(I-H) = I-H.

Complete question is;

Determine whether the experiment is blind or double blind.

Is the aspirin produced by the World’s Best Pharmaceutical Company better than that of a competitor at relieving headaches? 200 headache sufferers are chosen at random. Migrained Testing Service administers the experiment and provides the results evaluation. Three levels are made: participants receive contents from Bottle A, Bottle B, or Bottle C. Other than the fact that one bottle contains placebo aspirin, no other information is given to the testing service regarding the bottles’ contents.

a) blind study

b) double blind study

C) Neither

Answer:

Double blind study.

Step-by-step explanation:

We are told that participants receive contents from Bottle A, Bottle B, or Bottle C.

However, the testing service only knows that one bottle contains placebo aspirin but they don't know the other contents nor which of the participants is taking the one with placebo aspirin.

Thus, this is a double blind experiment because neither the participants nor the testing service have knowledge of who is taking the bottle that contains placebo aspirin unlike a blind experiment where the testing service will know which participants got the bottle containing aspirin.

Answer:

3.2

Step-by-step explanation:

32x6=192

192/60=3.2

Answer:

D

Step-by-step explanation:

We are given:

\(\displaystyle \sqrt{\sqrt[3]{2}}\)

Recall the property:

\(\displaystyle \sqrt[b]{x}=x^{1/b}\)

Hence:

\(\displaystyle \sqrt{\sqrt[3]{2}}=\sqrt{2^{1/3}}\)

Using the same property:

\(\sqrt{2^{1/3}}=(2^{1/3})^{1/2}\)

Recall the property:

\((x^a)^b=x^{ab}\)

Hence, multiply:

\((2^{1/3})^{1/2}=2^{1/6}\)

Therefore:

\(\displaystyle \sqrt{\sqrt[3]{2}}=2^{1/6}\)

Our answer is D.

Answer:

The answer is \(2^{\frac{1}{6} }\).

Step-by-step explanation:

To find which answer is equal to \(\sqrt{} \sqrt[3]{2}\), start by simplifying \(\sqrt{} \sqrt[3]{2}\). The radical will simplify to \(\sqrt[6]{2}\).

An easy way to determine which answer is correct, convert each of the numbers to decimal form.

For \(\sqrt[6]{2}\), it will look like 1.122 in decimal form.

For \(2^{\frac{2}{3} }\), it will look like 1.587 in decimal form.

For \(2^{\frac{3}{2} }\), it will look like 2.828 in decimal form.

For \(2^{\frac{1}{3} }\), it will look like 1.260 in decimal form.

For \(2^{\frac{1}{6} }\), it will look like 1.122 in decimal form.

Then, by seeing which two decimal forms are the same, it causes the answer to be \(2^{\frac{1}{6} }\).

Answer: B, 53

53 is the only prime number between 50 and 60

The positive solution to the equation \(-x^{2} +2x+1=0\) is \(x=1+\sqrt{2}\).

Given quadratic equation is:

\(-x^{2} +2x+1=0\)

The general form of a quadratic equation is \(ax^{2} +bx+c=0\) and \(a\neq 0\).

On comparing with general form of quadratic equation

a = -1

b = 2

c = 1

So, from the Shreedharacharya formula,

\(x = \frac{-b+-\sqrt{b^{2} -4ac} }{2a}\)

\(x = \frac{-2+-\sqrt{2^{2} -4(-1)(1)} }{2*(-1)}\)

\(x = 1-\sqrt{2} \\x=1+\sqrt{2}\)

as \(x = 1-\sqrt{2}\) is negative

So, the positive solution is \(x=1+\sqrt{2}\)

Therefore, the positive solution to the equation \(-x^{2} +2x+1=0\) is \(x=1+\sqrt{2}\).

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Answer:  x = 2 + √2. x = 2 - √2 ·

Step-by-step explanation:

- x² + 2x + 1 = 0. x² - 2x - 1 = 0. Here,. a = 1. b = - 2. c = - 1

Answer:7032

Step-by-step explanation:

The population of the town in 2016 will be 7032

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

Given that, A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year.

We know that, Decrease rate =

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = rate

n = years or time

Therefore,

A = 12000(1-0.035)¹⁵

A = 12000(0.965)¹⁵

A = 7032.19

A ≈ 7032

Hence, the population of the town in 2016 will be 7032

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The radius of convergence of the power series is scaled down by a factor of 6, when raising the variable to the power of 6.

To find the radius of convergence of the power series ∑cnx6n, we can use the ratio test. Let an = cnx6n, then we have:

lim┬(n→∞)⁡|a_(n+1)/a_n| = lim┬(n→∞)⁡|c_(n+1)x^(6(n+1))/c_nx^(6n)|

= |x|^6 lim┬(n→∞)⁡|c_(n+1)/c_n|

Since the radius of convergence of the power series ∑cnxn is R, we know that the series converges absolutely for |x| < R and diverges for |x| > R. Therefore, the ratio test for ∑cnxn tells us that:

lim┬(n→∞)⁡|c_(n+1)/c_n| = L

exists, where L is a real number.

Thus, the radius of convergence of the power series ∑cnx6n is:

R' = (R)^(1/6)

This means that the series ∑cnx6n converges absolutely for |x| < (R)^(1/6) and diverges for |x| > (R)^(1/6).

In other words, the radius of convergence of the power series is scaled down by a factor of 6, when raising the variable to the power of 6.

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For the given data the monthly charges for Jim’s mobile phone will be £31.31.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Monthly charge of £20,100 for free minutes then 9p per minute for 200 free texts, then 11p per text. During one month, Jim makes 140 minutes of calls and sends 261 texts.

If there are 100 free minutes then it cost 9p per minute as a result, The charge is applied for calls,

40x9=£3.60

If there are 200 free texts, then it cost  11p per text as a result, The charge is applied for text,

61x11=£6.71

The total charge for the text and call is,

£6.71+£3.60=£10.31

If the monthly charge is £20. The total charge for the month,

£20+£10.31=£31.31

Thus, for the given data the monthly charges for Jim’s mobile phone will be £31.31.

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Answer:

hehe

Step-by-step explanation:

The equation of the function is y = 12(3.7)^n

We have to note that if we have an exponential function, it then follows that we have to look at the arrangement of the graph so that we can be able to use the points that are on the graph to be able to read off the function that we want to work on.

In this case, the function that we want to work on is the function that has been graphed here and we can be able to read off the initial value and the rate of growth from the values of the graph that have been shown in the image.

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The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer:

1: b

2: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

1-D

2-B

The boundary and initial conditions provided, we can fill in the constants in the solution: u(x,0) = 1 sin(πx) + 6 sin(27πx) + 7 sin(31πx) + 11 sin(41πx)

To match the  solution format, let's fill in the constants:
u(x, t) = (1)e^(-π^2t)sin(πx) + (6)e^(-27^2π^2t)sin(27πx) + (7)e^(-31^2π^2t)sin(31πx) + (11)e^(-41^2π^2t)sin(41πx)
Here, the constants are: 1, 6, 7, and 11 for the amplitudes of each sine term
π, 27π, 31π, and 41π for the sine argument multipliers
-π^2, -27^2π^2, -31^2π^2, and -41^2π^2 for the exponents of e in the time-dependent coefficients.

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Answer:

13#

Step-by-step explanation:

5 cakes equal to 65$

1 cake equals ?

1/5×65

13$

Answer:

Each cake is $13

Step-by-step explanation:

If each cake costs the same and you bought 5, spending a total of $65, you would simply divide the $ you spent by the amt. of cakes to find how much each cake is. Let's assume x is how much each cake is, and 5 is the number of cakes you buy, so 5 (The amount of cakes) multiplied by x (how much each cake costs) must give you 65.

Equation:

5x=65

x=65/5

x=13

Answer: Each cake is $13.

It's important to note that this calculation assumes that the interest rate remains constant and that no additional charges are added to the balance. In reality, the time it takes to pay off the balance could be longer due to these factors.

Assuming the minimum payment is calculated as a percentage of the balance, we can use the following formula to determine the time it would take to pay off the balance:

t = (-1/12) * log(1 - (r/12) * b/p) / log(1 + r/12)

where t is the time in years, r is the annual percentage rate (APR), b is the balance, and p is the minimum payment.

Substituting the given values, we get:

t = (-1/12) * log(1 - (0.14/12) * 1000/20) / log(1 + 0.14/12) = 94.5 months

It would take approximately 94.5 months or 7.9 years to pay off the balance with only minimum payments.

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Answer: Answer is 0.52

Step-by-step explanation:

So we have the fraction 13 Out of 25.

step 1: here we divide numerator(which is 13) by denominator(which is 25).

step 2: first we make denominator 100 by multiplying by 25 with 4 and also 13 with 4.

ie. \(\frac{13 * 4}{25 * 4}\)

step 3: we get \(\frac{52}{100}\)

step 4: now we can easily write the decimal fraction. ie. 0.52

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Answer:

2334

Step-by-step explanation:

The length of the arc will be 22 cm.

Length of the radius 'r'= 28 cm

central angle 'a' in degrees = 45

The formula for length of arc is 2πra÷360

The standard value of pie that we take is 22÷7

so after putting all the given values, we get,

2×22/7×28×45 = 22cm.

Radius is any line that we draw from the centre of the circle to its outside edge.

Arc is the part of the circle's circumference.

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The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.

To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.

In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.

The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.

To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.

Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.

The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.

To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).

P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
           = P(X1 + X2 + ... + X511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)

Since each value of X is 2.4, we can rewrite the probabilities as:

P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
           = P(2.4 * 511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)

Now, we can calculate the probabilities:

P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)

Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:

P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
                 = 1 - 1
                 = 0

Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.

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\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer:

h = 9

Step-by-step explanation:

\(volume = \pi \: {r}^{2} h \\ 1,386 = \frac{22}{7} \times 7 \times 7 \times h \\ 1,386 = 154 \times h \\ h = \frac{1,386}{154} \\ h = 9\)

Answer: A =350 (1.05)^t

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form; 5/100=0.05)

t= years

A = population after t years

Replacing with the values given:

A = 350 (1+0.05)^t

A =350 (1.05)^t

Feel free to ask for more if needed or if you did not understand something.

Answer:

Sure, here's the solution to the word problem:

Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.

```

$10 / $2 = 5 weeks

```

Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.

Here's another way to solve the problem:

We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:

```

$10 - $2x = 0

```

Solving for x, we get:

```

x = 5

```

Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.

Answer:

in 5 weeks he will have 0$ in his account

Step-by-step explanation:

10 meters away is the bus from the bus stop after 10 seconds.

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.

In this way bus forms an arithmetic sequence

10, 20, 30, 40........up to 10 terms.

nth term of an arithmetic sequence is represented by

\(T_{n}\) = a+ (n - 1)d

Here a = 10 and d = common difference = 10

Therefore 10th term = 10 + (10-1)10

                                  = 10 + 90

                                  = 100

Therefore after 10 seconds bus will be 10 meters away from the bus stop.

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Answer:I think it’s 75

Step-by-step explanation:

Answer:

Step-by-step explanation: a=4, b=2.

Answer:

b = 39

Step-by-step explanation:

\(a-6=b\)

if a = 45:

\(45-6=b\\39=b\)

Hope this helps

Answer:

16

Step-by-step explanation:

i got it right on the test

Answer:

16...

hope, it helps! x

The points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on graph.

Table is a way to represent the data of the two or more variable. To read the data from the table, look for the value of one variable, and get the resultant value of other variable from the corresponding block.

Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005.

The table gives the number of tickets sold for each concert. Select the points that represent this data.

The graph which represent the data in the data is attached below year wise.

For the first point, select the value 10 on graph vertically at year 2000. Similarly, select all the points on the graph for the table.

Thus, the points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on the graph.

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