For each of the studies described, explain whether the study was an observational study or a randomized experiment.
a. A group of 100 students was randomly divided, with 50 assigned to receive vitamin C and the remaining 50 to receive a placebo, to determine whether or not vitamin C helps to prevent colds.
b. A random sample of patients who received a hip transplant operation at Stanford University Hospital during 2000 to 2010 will be followed for 10 years after their operation to determine the success (or failure) of the transplant.
c. Volunteers with high blood pressure were randomly divided into two groups. One group was taught to practice meditation and the other group was given a low-fat diet. After 8 weeks, reduction in blood pressure was compared for the two groups.

Part (a)

Refer to figure 1 in the attached image below. The a,b,c,d,e are placeholders for numbers we'll fill in later (that turns into the table for figure 2). Hopefully you agree about the placement of the numbers. If there's any confusion, then please let me know.

Along the bottom row, we can see that 39+e = 65 which solves to e = 26 after you subtract 39 from both sides. This tells us that there are 26 non-physics majors (ie their major is anything but physics).

Then along the "non-physics" column, notice how b+6 = e, which is the same as b+6 = 26 after replacing 'e' with 26. Solving that equation leads to b = 20. So we have 20 people who are seniors and non-physics majors.

Now move to the top row. We can see that a+b = 30, which is the same as a+20 = 30 because we plug in b = 20. That solves to a = 10. So we have 10 seniors who are physics majors.

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Now along the first column, we have a+c = 39, aka 10+c = 39, which solves to c = 29. There are 29 non-seniors who are physics majors.

The last variable to find is variable d.

Along the second row, we can say,

c+6 = d

29+6 = d

d = 35

Or we could say that 30+d = 65 along the last column which also solves to d = 35. This tells us we have 35 non-seniors in the class.

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

To summarize so far, we have

a = 10, b = 20, c = 29, d = 35, e = 26

These values will replace the letters as shown in figure 2.

Figure 2 will be used to answer both parts (a) and (b).

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

After that (more than) slight detour of filling in the table, we can finally tackle the question at hand. We're asked to find the probability of selecting someone who is a senior and a physics major. We have a = 10 people who fit the description out of 65 total

Divide the two values and reduce the fraction as much as possible

10/65 = (2*5)/(13*5) = 2/13

==========================================================

Part (b)

There's a lot going on with part (a). Luckily there aren't many steps here because pretty much all the work has been done already. We'll refer to figure 2 below.

We're told "given the student is a physics major", which means we focus solely on the "physics major" column only. We ignore everyone else because we know 100% that whoever we selected majored in physics.

We have a = 10 seniors who are also physics majors out of 39 physics majors total.

That constructs the fraction 10/39

Answer:

b. 11% is a statistic and is represented symbolically as p = 0.11

Step-by-step explanation:

A statistic differ from a parameter in that, statistic is a numerical property or value derived from the sample while the parameter is a numerical property of the population. The percentage given, 11% who said that they had vaped on 1 or 2 days in the last 30 days is derived from the 15000 youths which is a sample and not a population, hence, 11% is a statistic, since it is expressed as a percentage, it is a proportion ;

Hence, 11% is a statistic and can be represented symbolically as p = 0.11

27x^6 = 387420489

You want something similar but cubed.

[tex]\sqrt[3]{387420489}[/tex] = 729

YOUR ANSWER: 729x^3 = 387420489

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

Volume = 10 * 10 * 10 = 1000

Answer:

[tex]Volume = 1000[/tex]

Step-by-step explanation:

Formula to find volume of cube:

[tex]Volume=a^{3}[/tex]

[tex]Volume = 10^{3}[/tex]

[tex]Volume = 10*10*10[/tex]

[tex]Volume = 1,000[/tex]

hope this helps.....

[tex]{25x {}^{2} y}^{2} - 16[/tex]

The answer would be 18 square units

Step-by-step explanation:

When talking about surface area, just add up all the units that is listed in the question. - just a tip ;)

Anyways, Hope this helps!! If it's wrong, feel free to curse me out.. haha...

Answer:

Cost = 11 + 4*t

Step-by-step explanation:

Cost = 11 + 4*t

Part A

t = 5 hours.

Cost = 11 + 4*5

Cost = 11 + 20

Cost = 31

Part B

time = t hours.

Cost = 11 + 4*t

for 5h he would need to pay $20 ( +$11 ) $31

i dont know what T is so ya :/

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hagg

Answer:

5

Step-by-step explanation:

[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]

Answer:

Tan B = 12/5

Sin B = 12/13

Cos B = 5/13

Step-by-step explanation:

sine B =  opposite (12)/hypotenuse (13)

          = 12/13

Cosine B = adjacent/hypotenuse

               = 5/13

Tangent B = opposite/adjacent

                 = 12/5

Here is a picture that can always help you with the three trig ratios.

Answer:

The position and orientation of the new angle may vary, but it should have the same angle measure as ∠BAC

.Step-by-step explanation:

The measure of the angle is determined and the image is attached with the answer.

An angle is formed by two rays having a common end point.

The angle BAC is of certain measure.

To determine the value of the angle another angle is drawn in following steps

1. Draw a straight line XY

2. With an compass draw an arc of any length on BAC and on the new straight line XY  keeping tip of the compass on the end points A and X.

3. Measure the point at which the arc cuts the angle BAC from the point at which it intersects AC and with the same measure , keeping the point of the compass on the point where the arc intersected XY ,cut an arc on the arc.

4. The intersecting point Z of the arc is joint to X

5.The angle ZXY is measured , and this is the value of the angle BAC.

The image is attached with the answer.

To know more about Angle

https://brainly.com/question/7116550

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Step-by-step explanation:

6/5 this is the answer hopes this help

Answer:

-1/4x² + 3

Step-by-step explanation:

Given that:

Path of sprinkler is modeled by the quadratic function :

w(x) = -1/4(x^2 -12 )

w(x) = height of the water, in meters, at position x

The height of ceiling as a constant or Coefficient = w(x)

Expanding w(x)

-1/4(x^2 -12 )

-1/4 * x² + 1/4 * 12

-1/4x² + 3

The height of ceiling is -1/4x² + 3

Answer:

here is your answer

Step-by-step explanation:

here is your answer

Answer:

tubol mo mabaho kaya 1 too 5 so it means 5 days ka sa cr nag tutubol, ok i hope it helps its the grett answer do it in your solution paper or computers

Answer:

y=3^(x-2) + 1

Step-by-step explanation:

When dealing with graphs I always use a graphing calculator or Desmos to graph and double check my answers especially when doing translations!

Answer:

t=3

Step-by-step explanation:

sorry if its incorrect i got it right on edgy.

Answer:

258

Step-by-step explanation:

Answer:

The price of the house is $ 853,735.05.

Step-by-step explanation:

Since Mr. Arju wishes to purchase a house, and to buy the house he needs to make a down payment of $ 300,000 and also pay $ 15,000 every quarter for the next 8 years, if the interest charge is 9% per year compounded quarterly, to determine what is the price of the house, the following calculation must be performed:

300,000 + (15,000 x 12 x 8) = X

300,000 + (180,000 x 8) = X

300,000 + 1,440,000 = X

1,740,000 = X

X x (1 + 0.09 / 4) ^ 8x4 = 1,740,000

X x (1 + 0.0225) ^ 32 = 1,740,000

X x 1.0225 ^ 32 = 1,740,000

X x 2.0381030257737 = 1,740,000

X = 1,740,000 / 2.03810

X = 853,735.05

Therefore, the price of the house is $ 853,735.05.

Answer:

x = 12 , y = 7

Step-by-step explanation:

Let the numbers be x and y

Sum of the numbers,         x + y = 19 -------- ( 1 )

Difference of the number , x - y = 5 -------- ( 2)

( 1 ) + ( 2 ) => 2x = 24  

                    x = 12

Substitute : x in ( 2 ) => 12 - y = 5

                               => 12 - 5 = y

                              => 7 = y

Answer:

m = [tex]-\frac{8}{5}[/tex]

Step-by-step explanation:

m = slope

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{1--7}{-6--1}[/tex]

m = [tex]\frac{8}{-5}[/tex]

m = [tex]-\frac{8}{5}[/tex]

The regular price of the desk found using the discount and the selling price is $575.

What is meant by the discount rate of an item?

Discount pricing is a form of promotional pricing strategy where the original cost of a good or service is decreased in an effort to draw more customers, move inventory, and boost sales. Consumers adore feeling as though they are getting a fantastic bargain, which is why they are lured to reduced costs. The selling price is the price at which the good or commodity has actually been sold, whereas the marked price is the cost set by the seller in accordance with market norms. The buyer claims to have received a discount when the selling price is less than the marked price.

Given,

The selling price of the desk = $368

The percentage of discount = 36%

Let the regular price be x.

then we can write the following equation,

x - 36% of x = 368

x - 0.36x = 368

0.64x = 368

x = $575

Therefore the regular price of the desk found using the discount and the selling price is $575.

To learn more about the discount rate, follow the link.

https://brainly.com/question/7459025

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Answer:

there are 4 aces in the deck of 52 cards

so the probability to draw one ace is 4/52

if we draw an ace, there are 3 left in 51 cards.

so the next probability will be 3/51

we need to multiply probabilities to know how likely it is that this happens in a row.

for three in a row that's

[tex] \frac{4}{52} \times \frac{3}{51} \times \frac{2}{50} [/tex]

rewritten its:

[tex] \frac{4 \times 3 \times 2}{52 \times 51 \times 50} [/tex]

we'll see soon why this is easier to write.

we also have to account for the two cards that are no aces. it doesn't matter if the first two cards are no aces, the last two, or any rodney. just the ammount of non-aces is important.

there are 48 non-aces in the deck.

so the probability to draw one of them in the first step is 48/52.

wich each draw the number of cards left in the deck decreases by 1. and depending what we draw, that ammount also decreases.

we draw 5 cards, so we know what the denominators will be. the numerator will be the rest-ammounts of each event, like shown in the complicated fraction above.

let's write it most easily as this:

[tex] \frac{4 \times 3 \times 2 \times 48 \times 47}{52 \times 51 \times 50 \times 49 \times 48} [/tex]

this scenario looks like it only describes 3 aces, then two non-aces, but the order of multiplication isn't important. you could put the 48 and 47 to the left, same solution. so this expression represents all permutations of "3 aces when drawing 5 cards", including the two cards that are not aces.

that's why writing it as one convoluted fraction is indeed better and simpler than many fraction multiplied in row.

time to grap a calculator.

our probability for the event is

54144 possible valid outcomes out of

311875200 possible combinations.

luckily the calculator can reduce that to a simpler form of

[tex] \frac{47}{270725} [/tex]

(reduced with 2^6*3^, big number, but tried it out by hand stacking up prime factors until hittinga prime in the numerator)

written as a readable kind of number you probably know and like it's

0.0001736079047

in decimal form. now rounded as asked for:

0.00017

(as percentage: 0.017%)

hope the way how we got here is somewhat clear. feel free to ask any questions.

kind regards

Alex

Answer:

[tex] \frac{8}{?100} \times 25000[/tex]

=2000

365×10=3650

2000×3650=7300000

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$25000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=25000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=25000(1.08)^{10}\implies A\approx 53973.12[/tex]

Answer:

Step-by-step explanation:

We will design a truth table to determine the validity of the provided arguments.

As a result, we have the following presumption:

Now;

p            q             ™q             p Vs q              ™q →p

T            T              F                 T                         T

T            F              T                 T                         T

F            T              F                 T                         T

F            F              T                 F                         F

Conclusion:

The given arguments are valid.