Suppose a pharmaceutical company is designing an experiment to test their new allergy medication. They divide the 200 subjects by gender and then randomly assign the men and women to either receive the medication or a placebo. What purpose does blocking by gender serve? Choose the correct answer below.
A. Blocking insures that the effect of a treatment is not due to some characteristic of a single experimental unit.
B. Blocking insures that the effect of factors whose levels cannot be controlled is minimized.

The TWO statements that represent the relationship between y = 5x and y = log5 x are:

1. They are the exponential and logarithmic form of the same equation.

2. They are inverses of one another.

The two equations are related because they represent the same relationship between x and y, but in different forms. The first equation is an exponential equation, where y is a power of 5 raised to the x power. The second equation is a logarithmic equation, where y is the exponent to which 5 must be raised to get x.

Because the two equations represent the same relationship, they are inverses of one another. If we take the logarithm of both sides of the exponential equation, we get the logarithmic equation. If we raise 5 to both sides of the logarithmic equation, we get the exponential equation. Therefore, the two equations are inverses of one another.

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Answer:

its 10 bro calm down ok chill

Answer:

10

Step-by-step explanation:u have 5 and add 5 more

Answer:

P=12

Step-by-step explanation:

Answer:

8.8866 or 8.89 (rounded)

Step-by-step explanation:

There are a number of ways you can solve it. Here I will just explain 1 way. 18% is the same thing as 0.18. You can do 0.18 x 49.37 which equals 8.8866 tip or you could round it to dollars and cents which would be 8.89.

l Hope this helped! If it did, please give brainliest! It would help a lot! Thanks! :D

Answer:

49.37 x .18= 8.886

Round to the nearest penny $8.89 tip

Step-by-step explanation:

Answer:

-1.4f - 24

Step-by-step explanation:

First combine like terms

-2.3f + 0.9f - 15 - 9

-1.4f              -24

So, simplified it is

-1.4f - 24

The equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To write the equation of a parabola with focus (-2, 5) and directrix y = 3, we can use the standard form of the equation of a parabola:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus or directrix.

First, let's determine the vertex of the parabola. The vertex lies halfway between the focus and the directrix, so its y-coordinate is the average of the y-coordinates of the focus and the directrix:

Vertex y-coordinate = (5 + 3) / 2 = 8 / 2 = 4

Since the directrix is a horizontal line, the vertex has the same y-coordinate as the directrix. Therefore, the vertex is (h, k) = (-2, 4).

Next, let's determine the value of p. The distance from the vertex to the focus (or directrix) is p. In this case, the focus is (-2, 5), so the distance from the vertex to the focus is:

p = 5 - 4 = 1

Now we can write the equation of the parabola using the vertex and the value of p:

\((x - (-2))^2 = 4(1)(y - 4)\)

\((x + 2)^2 = 4(y - 4)\)

Expanding the square on the left side:

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

(x^2 + 4x + 4) = 4y - 16

Simplifying the equation:

\(x^2 + 4x + 4 = 4y - 16\)

x^2 + 4x + 20 = 4y

Rearranging the terms:

4y = x^2 + 4x + 20

Finally, dividing both sides by 4 to isolate y, we get the equation of the parabola:

\(y = (1/4)x^2 + x + 5\)

So, the equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To sketch the parabola, plot the focus (-2, 5) and the directrix y = 3 on a graph. The vertex is also located at (-2, 4). The parabola opens upwards because the coefficient of x^2 is positive. Use the equation to plot additional points and sketch the curve symmetrically around the vertex.

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Answer:

So first you want to move your mouse cause i cant see anything................THANKS FOR THE POINTTTT

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Hello, do you agree that 25 * 2 = 50 ?

So, we can write that \(50 = 25 * \boxed{2} + \boxed{0}\)

the remainder is 0.

Thank you

A function f: N → S that is one-to-one and onto can be defined as f(n) = 3⌊(n+1)/2⌋ + (n+1) mod 2, where ⌊ ⌋ denotes the floor function and mod represents the modulo operation.

To construct a one-to-one and onto function from the set of natural numbers N to the set S, we need to ensure that each element in S is mapped to by exactly one element in N, and vice versa.

Let's consider the function f(n) = 3⌊(n+1)/2⌋ + (n+1) mod 2.

To prove that f is one-to-one, we assume that f(a) = f(b) for some natural numbers a and b. By equating the values of f(a) and f(b), we get 3⌊(a+1)/2⌋ + (a+1) mod 2 = 3⌊(b+1)/2⌋ + (b+1) mod 2. Simplifying this equation, we find that ⌊(a+1)/2⌋ = ⌊(b+1)/2⌋. This implies that (a+1)/2 and (b+1)/2 have the same floor value, which can only happen when a = b. Hence, f is one-to-one.

Next, we need to show that f is onto, meaning that every element in S is mapped to by at least one element in N. Let's take an arbitrary element s from S. Since s is of the form 3k+j, where k is a natural number and j ∈ {1, 2}, we can express s as s = 3k + j = 3⌊(2k+j-1)/2⌋ + (2k+j-1) mod 2. Thus, we have found an element k in N such that f(k) = s, proving that f is onto.

In conclusion, the function f(n) = 3⌊(n+1)/2⌋ + (n+1) mod 2 is a one-to-one and onto function from the set of natural numbers N to the set S.

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The approximate probability that the random sample of 1000 letters will contain 7.4% or fewer is 0.242.

We have taken a random sample of 1000 letters and counted the number of t's. We have to find the approximate probability that this random sample will contain 7.4 % or fewer t's. We are given an estimation that the letter 'T' makes up 8% of a certain language.

Proportion(p) = 8 % = 0.08

n = 1000

q = 1 - p

q = 1 - 0.08

q = 0.92

The mean is equal to the proportion. Therefore;

μ = p = 0.08

Now, we will apply the formula for standard deviation;

σ = \(\sqrt{\frac{pq}{n} }\)

σ = \(\sqrt{\frac{(0.08)(0.92)}{1000} }\)

σ = 0.0858

The z-score will be calculated by;

z = (x - μ )/σ

z = (0.074 - 0.08)/0.00858

z = -0.70

From the z-score calculator, we get the p-value as;

P(Z< -0.70) = 0.242

Therefore, the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer is 0.242.

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The complete question is "The letter "T" makes up an estimated 8% of a certain language. Assume this is still correct. A random sample of 1000 letters is taken from a randomly selected, large book, and the t's are counted. find the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer t's​"

A total of 23, 950, 080 results are possible.

We are given;

10 women

12 men

5 men and 5 women, chosen and pared off, how many results in total?

Thus;

[10 choose 5] x [12 choose 5]=252 x 792 = 199584 ways

We then need to know how many ways there could put into pairs i.e. For the first woman, there will be 5 choices of men. For the second woman, there will be 4 choices remaining of men. For the third woman, there will be 3 choices remaining. For the fourth woman, there will be only 2choices remaining, and only 1 choice left for the last woman.

Therefore, there are 5x4x3x2x1 = 120 ways.

 In total there are 199584x120 = 23950080 total  ways

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Answer:

length is 20 yards, width is 15 yards

Step-by-step explanation:

Length = width + 5

2(W + 5) + 2(W) = 70

2W + 10 + 2W = 70

4W + 10 = 70

4W = 60

W = 60 ÷ 4

W = 15 yards

L = 15 + 5

L = 20 yards

We dont talk about math math math math math

Step-by-step explanation:

are you in high school? if you are.... i cant help you but i want to say watch encanto and Iron man 1 2 and 3

Thus, the sample of size n=100 will ensure that the 95% confidence interval for the proportion will have a margin of error 0.08.

The formula to estimate the sample size required to estimate the proportion is

\(n = p\) × \((1-p)( \frac{z}{E} )^{2}\)

where p is the proportion of success, z is the Zα/2 and E is the margin of error.

Given that p=0.21 and the margin of error E=0.08. The confidence coefficient is 0.95. Assume that the proportion is p=0.21.

The critical value of Z is Zα/2=1.96

The minimum sample size required to estimate the proportion is

\(n = p\) × \((1-p)( \frac{z}{E} )^{2}\)

= \(0.21\) × \((1-0.21)\)  \((\frac{1.96}{0.08} )^{2}\)

= 0.21 × 0.79 × 600.25

= 99.581

≈ 100

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Answer:

The point (5,2) lies on the circle, so the equation of the circle is x^2 + y^2 = 25.

Step-by-step explanation:

Answer:

\(\frac{5}{14}\)

Step-by-step explanation:

It's important to note here that fractions are just another way of representing division.

Therefore, \(\frac{\frac{1}{4}}{\frac{7}{10}}\) is the same thing as \(\frac{1}{4} \div \frac{7}{10}\).

To divide two fractions, we multiply by the reciprocal.

\(\frac{1}{4} \cdot \frac{10}{7}\)

We can now multiply the numerators and denominators.

\(1\cdot 10 = 10\\7 \cdot 4 = 28\\\\\frac{10}{28}\)

We can simplify this fraction by dividing both the numerator and denominator by 2.

\(10\div 2 = 5\\28 \div 2 = 14\)

So, \(\frac{5}{14}\).

Hope this helped!

It is a function because all the domain inputs are unique to their respective range outputs.

Answer:

21 ft²

Step-by-step explanation:

3*5 + 2*3 = 21

The percentage of runners who took 21.67 minutes or less to complete the race is 0.606%

It is also known as Gaussian distribution. It shows the data near the more. This appears as a bell curve in graphical form. It is a continuous random variable's frequency distribution curve in the shape of a bell. It is employed to describe real-valued random variables with an unknowable distribution. It is important in statistics and is also applied in the natural and social sciences. The data has a bell shape when plotted on a graph.

μ=24.7 min

σ=2.02 min

z=((x-μ)/σ)

p(x<21.67)=p((x-24.7)/2.02) ≤ ((21.67-24.7)/2.02)

p(z≤-1.5)

p(z <21.67)=0.606

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Answer:

x = 4

a = 79

b = 101

Step-by-step explanation:

Supplementary means equal to 180° after all angles are added together.

a=19x+3

b= 21x +17

(19x+3) + (21x +17) = 180

19x + 3 + 21x + 17 = 180

             40x + 20 = 180

                      40x = 160

                          x = 4

a = 19(4)+3 = 79

b = 21(4) +17 = 101

With the use of a credit card, you can borrow money from a lender which you can then repay with interest. Your bank account is debited directly when you use a debit card.

ATM is Automated teller machine ,which is a self -service banking outlet.

Credit Card A type of card that allows the holder to borrow money to make purchases, up to a pre-set credit limit. The holder must pay interest on any balance not paid off at the end of each billing cycle.

Charge Card B type of card  holder to make purchases that are paid in full at the end of each billing cycle.

Debit Card C type the holder to access funds in their bank account to make purchases . Transactions made with a debit card are immediately deducted from the  balance in the account.

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Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30

The result of the expression 32 + (44 - 15) × 24 - (16 + 9) ÷ 15 is 1,007.

To solve this expression, we follow the order of operations (also known as PEMDAS or BODMAS), which dictates that we perform the operations in the following sequence: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Let's break down the expression step by step:

1. Inside the first set of parentheses, we have 44 - 15, which equals 29.

2. Inside the second set of parentheses, we have 16 + 9, which equals 25.

3. Next, we perform the division 25 ÷ 15, which equals 1.6667 (rounded to 4 decimal places).

4. Moving on to multiplication, we have (29) × 24, which equals 696.

5. Finally, we perform the addition and subtraction in sequence: 32 + 696 - 1.6667, which equals 726.3333 (rounded to 4 decimal places).

Therefore, the result of the expression 32 + (44 - 15) × 24 - (16 + 9) ÷ 15 is approximately 1,007.

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To find the profit function for the company, we need to determine the equation of the line that represents the relationship between the number of units sold, x, and the profit, P.

We are given two points on the line: (150, $900) and (200, $3700).

Let's use the slope-intercept form of a linear equation, y = mx + b, where y represents the profit (P), x represents the number of units sold, m represents the slope of the line, and b represents the y-intercept.

First, let's find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = ($3700 - $900) / (200 - 150)

m = $2800 / 50

m = $56

Now, we can use the slope-intercept form and one of the points to find the y-intercept (b).

Using the point (150, $900):

$900 = $56 * 150 + b

Simplifying:

$900 = $8400 + b

b = $900 - $8400

b = -$7500

Therefore, the profit function for this company can be written as:

P(x) = $56x - $7500

This equation represents the linear relationship between the number of units sold (x) and the profit (P) for the company.

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Answer:

20

Step-by-step explanation:

20 + (75% × 20) =

20 + 75% × 20 =

(1 + 75%) × 20 =

(100% + 75%) × 20 =

175% × 20 =

175 ÷ 100 × 20 =

175 × 20 ÷ 100 =

3,500 ÷ 100 =

35;

19,805 rounded to the nearest ten is 19,810

19,805 rounded to the nearest hundred is 19,800

19,805 rounded to the nearest thousand is 20,000

I apologize, this very late, but for future viewers this will help you.

Answer:

f(2a + 3) = 8a² + 20a + 27

Step-by-step explanation:

f(x) = 2x² + 4x - 3

f(2a + 3) = 2(2a + 3)² + 4(2a + 3) - 3

f(2a + 3) = 8a² + 12a + 18 + 8a + 12 - 3

f(2a + 3) = 8a² + 20a + 27

The value of f(2a+3) for the given function f(x) = 2x² + 4x - 3 will be 8a² + 20a + 27.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given the function f(x) = 2x² + 4x - 3

⇒ f(2a + 3) = 2(2a + 3)² + 4(2a + 3) - 3

⇒ f(2a + 3) = 2(4a² + 9 + 6a) + 8a + 12 - 3

⇒ f(2a + 3) = 8a² + 18 + 12a + 8a + 12 - 3

⇒  f(2a + 3) = 8a² + 20a + 27.

Hence "The value of f(2a+3) for the given function f(x) = 2x² + 4x - 3 will be 8a² + 20a + 27".

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The graph of the given linear equation can be seen at the end.

Here we have the linear equation:

3x - 4y = 8

Isolating, y, we can rewrite:

-3x + 4y = -8

4y = -8 + 3x

y = (-8 + 3x)/4

y = (3/4)*x - 2

Now, we can evaluate the line in two values of x, so we can get two points on the line.

Evaluating in x = 0 and x = 4 we get:

if x = 0

y = (3/4)*0 - 2 = -2

So we have the point (0, -2)

If x = 4 we get:

y = (3/4)*4 - 2 = 1

Then we have the point (4, 1).

Now we can graph these two points and connect them with a line, that is the graph of the linear equation.

The graph can be seen below.

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