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.

Answer:

The time required is of 17.53 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.

This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]

[tex](1.0033)^{12t} = 2[/tex]

[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]

[tex]12t\log{1.0033} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]

[tex]t = 17.53[/tex]

The time required is of 17.53 years.

Answer:

Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.

Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.

Step 3: Write the answer using interval notation.

Answer: r = 3

Step-by-step explanation:

V=(4/3)πr^3 (this is the formula to identify a volume of the sphere. Since we know that V = 36π, add it into the following formula like so:

36π = (4/3)πr^3; from here we can cancel out the π

36 = (4/3)r^3; multiply both sides by 3/4

27 = r^3;

the final answer is r = 3.

Answer:

the answer is 4

Step-by-step explanation:

you subtract 13 from 17 =4

Answer:

-45 1/2

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Complementary angles add to 90

x+60 = 90

x+60-60 = 90-60

x = 30

Answer: A

Step-by-step explanation:

Complementary angles sum up to 90 degrees. Thus, we can write that:

90=angle1+angle2

90-angle1=angle2

90-60=angle2

angle2=30

Answer:

x = -1/2 , y = -5/2

x = 4, y = 29

Step-by-step explanation:

y = 2x² - 3

y = 7x + 1

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

set equal

2x² - 3 = 7x + 1

Subtract 7x + 1 from both sides

2x² - 7x - 4 = 0

Factor

(2x + 1)(x - 4) = 0

x = {-1/2, 4}

For x = -1/2

y = 7(-1/2) + 1

y = -5/2

(-1/2 , -5/2)

For x = 4

y = 7(4) + 1

y = 29

(4, 29)

Answer:

white

Step-by-step explanation:

if you cut the shape in half both ways it makes white take up a fourth.

Answer:

The answer is " The sequence converges to infinity. "

Step-by-step explanation:

Given:

[tex]\to a_n=\frac{n^3-n}{n^2+5n}[/tex]

[tex]\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}[/tex]

                   [tex]= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\[/tex]

Denominator[tex]= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1[/tex]

Numerator [tex]=\lim_{n\to \infty}n-\frac{1}{n}=\infty[/tex]

[tex]\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty[/tex]

Answer:

-6 < y < ∞

Step-by-step explanation:

The range is the values that y can take

y goes from  almost -6 to infinity ( there is an asymptote at -6)

-6 < y < ∞

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Vertices are the vertex points. there are 4 vertices at the bottom and 2 vertices at the top which makes 6.

Hope this helps

Im sorry but what I got was x=1.5 I don't know if this helps or not.

Answer:

QUALITATIVE DATA-type of data states that every value in the set is a number.

Step-by-step explanation:

QUALITATIVE DATA-type of data states that every value in the set is a number.

Answer:

QUALITATIVE DATA-type of data states that every value in the set is a number.

9514 1404 393

Answer:

  B. both a relation and a function

Step-by-step explanation:

Every linear equation with defined slope is both a relation and a function.

__

Only a vertical line of the form x=constant is linear equation that is a relation, but not a function.

Answer:

The function is as follows:

def count_bases(DNA_str):

   retDNA = {}

   for i in DNA_str:

       if i in retDNA:

           retDNA[i]+=1

       else:

           retDNA[i] = 1

   return retDNA

Step-by-step explanation:

This defines the function

def count_bases(DNA_str):

This initializes a dictionary

   retDNA = {}

This iterates through the dictionary

   for i in DNA_str:

If an item exists in the dictionary

       if i in retDNA:

The count is updated by 1

           retDNA[i]+=1

Otherwise

       else:

The count is set to 1

           retDNA[i] = 1

This returns the DAN

   return retDNA

Answer:

The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]

Step-by-step explanation:

We are given the following differential equation:

[tex]\frac{dP}{dt} = kP - h[/tex]

Solving by separation of variables:

[tex]\frac{dP}{kP-h} = dt[/tex]

Integrating both sides:

[tex]\int \frac{dP}{kP-h} = \int dt[/tex]

On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then

[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]

In which K is the constant of integration.

[tex]\ln{kP-h} = kt + K[/tex]

[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]

[tex]kP - h = Ke^{kt}[/tex]

[tex]kP = Ke^{kt} + h[/tex]

[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]

The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]

Answer:

False

Step-by-step explanation:

Take the point (2, 3)  = (x, y)

Rotated 90º clockwise (3, -2) = (y, -x)

Rotated 90º counter clockwise (-3, 2) = (-y, x)

Neither rotation becomes (-3, -2)

Answer:

-24 feet

Step-by-step explanation:

Boat is 4 feet above sea level => +4 feet

She descends 28 feet => -28 feet

Position = +4-28 = -24 feet

Therefore,

Gemma is 24 feet below the sea level

Answer:

-24 feet

Step-by-step explanation:

Because she is 4 feet above sea level, she can descend 4 feet to be at sea level. Now she only has to descend 24 feet below sea level, which is -24 feet.

Answer:

1 Its all about there favorite fruits

2 the favorite fruits of the girls are buko less than the boys.

3 the least fruit favorite fruits is pineapple among the girls boys.

4 the top choice of the fruit is the lansones both girls and boys.

5 the rambutan is the least favorite both of them

Step-by-step explanation:

Hope its help po pa brainlest

Answer:

girl

-apple

-masanas

boy

-lansones

-rambotan

sorry yan lang alam ko

Answer:

54

Step-by-step explanation:

Area of rhombus= (12×9) ÷2

Answer:

[tex]3y - 5x +11=0[/tex]

Step-by-step explanation:

Given

[tex]P(x_1,y_1) = (-1,6)[/tex]

[tex]Q(x_2,y_2) = (9,0)[/tex]

Required

The equation of l

First, calculate the slope (m) of PQ

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{0-6}{9--1}[/tex]

[tex]m = \frac{-6}{10}[/tex]

[tex]m = \frac{-3}{5}[/tex]

Since l is perpendicular to PQ, the slope of l is:

[tex]m_2 = -\frac{1}{m}[/tex]

[tex]m_2= -\frac{1}{-3/5}[/tex]

[tex]m_2 = \frac{5}{3}[/tex]

Next, calculate the midpoint of PQ

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

[tex]M = \frac{1}{2}(-1+9,6+0)[/tex]

[tex]M = \frac{1}{2}(8,6)[/tex]

[tex]M = (4,3)[/tex]

The equation of l is:

[tex]y = m(x -x_1) + y_1[/tex]

[tex]y = \frac{5}{3}(x -4) +3[/tex]

Multiply through by 3

[tex]3y = 5(x -4) +9[/tex]

Open bracket

[tex]3y = 5x -20 +9[/tex]

[tex]3y = 5x -11[/tex]

Rewrite as:

[tex]3y - 5x +11=0[/tex]

Answer:

The null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:

H[tex]_{0}[/tex]:  μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].

H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

Step-by-step explanation:

In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

The assertion made in the question can either be the null hypothesis (H[tex]_{0}[/tex]) or the alternate hypothesis (H[tex]_{1}[/tex]). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.

Therefore, the null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:

H[tex]_{0}[/tex]:  μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].

H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

Part A

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

The average rate of growth over the 4 days is .21 cm per day

Step-by-step explanation:

f(n) = 10(1.02)^n

Part A

Let f(n) = 11.04

11.04 = 10 * 1.02 ^n

Divide each side by 10

11.04/10 = 1.02^n

1.104 = 1.02^n

Taking the log of each side

log 1.104 = log 1.02^n

We know log a^b = b log a

log 1.104 = n log 1.02

log 1.104 / log 1.02 = n

4.99630=n

Rounding n to 5

The domain should be 0 ≤n≤5

Part B

f(n) = 10(1.02)^n

The function is in the form y =a b^x  where a is the y intercept

The y intercept is 10.  This is the value when n =0 days.

Part C

To find the average rate of change

f(5) - f(1)

-----------

5-1

f(5) = 11.04  

f(1) = 10 *1.02 =10.2

11.04 - 10.2

-----------

5-1

.84

-----

4

.21 cm per day

The average rate of growth over the 4 days is .21 cm per day

Answer:

A suitable estimate of all families who own their home is 42%.

Step-by-step explanation:

42% reported that they own their home.

This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.

Answer:

The correct answer is: The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.

Step-by-step explanation:

I just took the review test. The person above me is wrong

Answer:

x^1 = 1, x^2 =2

Step-by-step explanation:

its hard to explain but there's the answer

Answer:

profit

hope it is helpful to you

Step-by-step explanation:

Markup is the percentage amount by which the cost of a product is increased to arrive at the selling price.

Answer:

300 square feet

Step-by-step explanation:

Area is found by multiplying the length and width of a surface