As a researcher for a pharmaceutical company, you are designing a study to test the effectiveness of a new treatment for migraine headaches in comparison with the current leading medicine used to treat migraines. You have been given a list of 126 people willing to participate in the trial. The first 70 people are female; the remaining 56 are male. Preliminary research suggests that men and women respond differently to this new treatment.

d) Design an appropriate experiment to determine the effectiveness of the migraine medicine. Scan or take a picture of your design and upload it.

The unit segments from 3 to 7 are infinite.

The number from 3 to 7 is given.

We have to find out the no. of segments between the two numbers.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

Consider any number x such that 3 < x < 6

Then ;

The segment from x to x+1 is a unit segment and, by definition, it will lie within the interval to 7.

As, there are infinitely many possible choices for x, then there are infinitely many unit segments.

i.e.,

from 3 to 4

from 3.1 to 4.1

from 3.01 to 4.01

from 3.00002 to 4.00001

and you can keep adding decimal digits forever.

Thus , there are infinite unit segments from 3 to 7.

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Answer: x = -7

Step-by-step explanation:

7(x + 4) = -21

x + 4 = -3

x = -7

Answer:

-7 because -7 + 4 is -3 and 7 x -3 is -21

Step-by-step explanation:

Answer:

a is 17 1/2 i dont know b sorry

Answer:

A.7/2

alternate form: 3 1/2

B.36/7

alternate form: 5 1/7

i hope it help

The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5

To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:

A) x1 = 5, x2 = 4.63, Z = 52.78

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)

B) x1 = 5, x2 = 5.25, Z = 56.5

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)

C) x1 = 5, x2 = 5, Z = 55

Checking the constraints:

17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)

D) x1 = 4, x2 = 6, Z = 56

Checking the constraints:

17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)

3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)

From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.

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The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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a) The probability that a randomly chosen student completes the activity in less than 29.9 seconds is approximately 0.1292.

b) The probability that a randomly chosen student completes the activity in more than 40 seconds is approximately 0.3085.

c) The proportion of students who take between 29.4 and 39.1 seconds to complete the activity is approximately 0.3839.

d) 95% of all students finish the activity in less than approximately 49.816 seconds.

a) To calculate the probability of completing the activity in less than 29.9 seconds, we need to find the z-score using the formula z = (x - μ) / σ, where x is the given time, μ is the mean, and σ is the standard deviation. By looking up the z-score in the standard normal distribution table, we find the corresponding probability.

b) Similar to part (a), we calculate the z-score for completing the activity in more than 40 seconds and find the corresponding probability from the standard normal distribution table.

c) To determine the proportion of students taking between 29.4 and 39.1 seconds, we calculate the z-scores for both values and find the corresponding probabilities. Then, we subtract the smaller probability from the larger probability.

d) To find the time at which 95% of students finish the activity, we use the z-score corresponding to the 95th percentile (1.645) and calculate the time using the formula x = μ + z * σ.

Understanding the probabilities and proportions in relation to the normal distribution helps in analyzing the performance and characteristics of students in physical activities.

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Complete question is in the image attached below

Answer: $10.20

Step-by-step explanation:

convert the percentage to a decimal: 0.15

multiply the decimal 0.15 by the original price, $12, to find the amount that it will be discounted by: $1.80

subtract the discount from the original price: $10.20

Answer:

$9

Step-by-step explanation:

reduced price=15%*$12

= 15/100*$12

= $3

Sale price=original price - reduced Price

=$12-$3

=$9

Answer:

C = 28.26 in

Step-by-step explanation:

the circumference (C) is calculated as

C = πd ( d is the diameter ) , then

C = 3.14 × 9 = 28.26 in

\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

                 What's the circumference of a circle with a diameter of 9 inches?

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

  We are asked to find the circumference of a circle, which we can find using the following formula:-

\(\bold{Circumference{(circle)}=\pi d}\)

\(\hookrightarrow\sf{C=3.14\times9}\)

\(\bigstar\) On simplification,

\(\hookrightarrow\sf{C=28.26\:inches}\)

Notice that we are not asked to round our answer, so we leave it like that - C=28.26.

                  \(\rule{200}{2}\)

Answer:

20%

$18.84

Step-by-step explanation:

3.14 is what percent of 15.70?

Use the percent-to-dollar conversion (100: 15.70) :

3.14 * 100% / 15.70 =

3.14 / 15.70 * 100% =

1/5 * 100% =

100% / 5 = 20% ==> percent tip

$15.70 + $3.14 = $18.84  ==> Total cost

Answer:

15.2 cm

Step-by-step explanation:

Inch to centimeter conversion is multiplying the number of inches by 2.54

6 * 2.54 = 15.24

the 2 is in the tenths place

4 is less than and not equal to 5, therefore the 2 stays the same

6 inches = 15.2 centimeters

hope this helps:)

Answer:

0.3232323232... is an irrational number

Step-by-step explanation:

An irrational number is any number that cannot be written as a fraction of whole numbers.

Therefore, a 1.5 amp current would result in 60 volts across a similar resistance.

Electrical resistance is implemented as a circuit element by a resistor, a passive two-terminal component. By adding a regulated amount of resistance to an electrical circuit, it is used to restrict or regulate the flow of electric current in electrical circuits .The main job of a resistor is to lower the voltage and lessen current flow in a particular region of the circuit.

Ohm's law states that a resistor's voltage V and current I are precisely proportional to one another1. Therefore, we can get the resistance R as follows if a current of 12 amps results in 480 volts across a resistor:

R = V/I = 480/12 = 40 ohms.

Now that we are aware of the resistor's resistance, we can apply Ohm's law once more to determine how many volts a 1.5 amp current would produce across a similar resistor:

V = IR = 1.5 x 40 x 60 = 60 volts.

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Answer:

2 dinner roll 12 dozen roll and 15 flour

We need to construct a rational graph with the data in the picture. So, the drawing is some like this:

In the picture above, the vertical asymptotes are yellow, the horizontal asymptote is in green, and a possible rational function is in red.

The points (0, -5) and (-5/3, 0) belong to the function.

When the function approach to x=0.5 from the right goes to -infinity, that is the limit.

When the function approach to x=0.5 from the left goes to infinity, that is the limit.

When the function approach to x=1 from the right goes to infinity, that is the limit.

When the function approach to x=1 from the left goes to infinity, that is the limit.

And when the function goes to x = -infinity or x=infinity the functions approach to the horizontal asymptote y=3/2.

You can see in the picture this behaviour of the red line.

The value of the quotient when 30.94 is divided by 0.7 will be 44.2

Dividing two numbers involves obtaining the number of times the denominator value can be obtained from the numerator.

Here, the numerator is 30.94 and the denominator is 0.7

To make things easier, we can convert the values to whole numbers by multiplying the values by 100

30.94 × 100 = 3094

0.7 × 100 = 70

Hence, Using a calculator ;

3094 / 70 = 44.2

The quotient value would be 44.2

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The maximum possible outcome for the given situation is 36.

The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.

Given, Ruby is designing a new board game and is trying to figure out all the possible outcomes. she flips a coin, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.

Since there are three things happening simultaneously and favorable moments will be chosen by all three.

Thus Maximum possible outcome = 2 * 6 * 3 = 36

Therefore, For the given situation, 36 outcomes are available in total.

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Answer: C

Step-by-step explanation:

- 5/8k -8 + 2 + 1/3k

-5/8 = -15/24

1/3 = 8/24

-15/24k -8 + 2 + 8/24

-7/24k -6

The unit rate of the water being pumped is 18  gal/min and in 13.5 minutes water pumped into the pool is about 243 gallons

From the table we can see that for 35 gallons it takes the pump only 2 minutes, and for 90 gallon it takes 5 minutes.

Hence unit rate of the pump  = 36 / 2 = 90 / 5 = 18 gal/min .

To calculate the water filled after a given amount of time we simply multiply the unit rate with the time elapsed.

Amount of water filled after 12 minutes = 12 × 18 = 216 gallons.

Amount of water filled after 13.5 minutes = 13.5 × 18 = 243 gallons.

A unit rate is a ratio between two separate units that uses one as the numerator. Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc.

The area of mathematics that we utilize in daily life the most is arithmetic, which also has a lengthy historical basis.

The unit rate of the water being pumped is 18gal/min and in 13.5 minutes water pumped into the pool is about 243 gallons  .

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The  probability of the union of being either a freshman or senior is 0.16.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

In the question, we are said that students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

∴ Probability(A student is a junior) = 1/4 = 0.25, as we have 4 cases all equally probable.

Now, we are said that a student is  64% likely to join the marching band.

∴ Probability( A student joins marching band) = 64% = 64/100 = 0.64.

We are asked to find the probability of the intersection that a student is a junior and participates in the marching band.

Probability( A student is a junior and joins marching band) =  Probability( A student joins marching band)* Probability( A student is a junior)

∴ Probability( A student is a junior and joins marching band) = 0.64*0.25 = 0.16

∴ Probability of the intersection of being a junior and participating in marching band = 0.16

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The coordinate of B is (-3, -3.5).

Let's use this concept to solve the problem at hand. We know that M is the midpoint of line segment AB, which means that the distance from A to M is equal to the distance from M to B. We can use this information to set up an equation:

distance from A to M = distance from M to B

We can calculate the distance between two points using the distance formula:

distance between points (x1, y1) and (x2, y2) = √[(x2 - x1)² + (y2 - y1)²]

Plugging in the given values, we get:

distance from A to M = √[(0 - (-7))² + ((-2) - 1)²] = √[49 + 9] = √58

Let the coordinate of B be (x,y). Using the distance formula, we can calculate the distance from M to B:

distance from M to B = √[(y - 0)² + (x - (-2))²]

Setting up the equation, we get:

√[(y - 0)² + (x - (-2))²] = √58

Squaring both sides, we get:

(y - 0)² + (x + 2)² = 58

Expanding the squared terms, we get:

y² + x² + 4x + 4 = 58

Simplifying, we get:

x² + y² + 4x - 54 = 0

Now we have an equation with two variables, x and y. We need another equation to solve for both variables. Since we know that the midpoint of AB is (-2,0), we can use this information to set up another equation:

midpoint of AB = (1,-7) + (x,y) / 2

Simplifying and rearranging, we get:

2x - 1 = -4

2y + 7 = 0

Solving for x and y, we get:

x = -3

y = -3.5

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\(8.3\)

\( \large \frac{83}{10} \)

\(830\%\)

Answer:

Fraction: 8.3x10/10 = 83/10

percentage: 83/10 × 100/1 = 830%

The critical value of the function \(\(y = 3x^2 - 12x - 15\)\)    is \(\(x = 2\)\). To find the critical values, we need to determine the values of \(\(x\)\) where the derivative of the function is equal to zero or undefined.

First, we find the derivative of the function with respect to x,

\(\(y' = 6x - 12\).\)

Next, we set the derivative equal to zero and solve for x:

\(\(6x - 12 = 0\)\\\(6x = 12\)\\\(x = 2\).\)

The critical value is \(\(x = 2\)\).

Therefore, the correct answer is option C: \(\(x = 2\)\).

To verify this, we can substitute the given values of x into the derivative equation:

For option A: \(\(y'(-1) = 6(-1) - 12 = -6 - 12 = -18\)\) (not equal to zero).

For option B: \(\(y'(1) = 6(1) - 12 = 6 - 12 = -6\)\) (not equal to zero).

For option D: \(\(y'(-2) = 6(-2) - 12 = -12 - 12 = -24\)\) (not equal to zero).

Options A, B, and D are incorrect because they do not represent the values where the derivative is equal to zero.

Therefore, the critical value of the function is \(\(x = 2\)\).

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Step1: Pick 2 points in the table:

(0,6) and (4,10)

Step2: Recall the formula for the slope of a line.

Step3: Substitute the values of the coordinates in the above formula.

Step4:

Step5: Invoke the formula for the equation of the line.

Hence, the correct answer is y = x + 6

The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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Answer:

y=-7x-2

Step-by-step explanation:

I assume you need the equation for the line, so that's what I'm solving for here.

1. Start by putting the slope and the coordinates into point slope form, which is y-y1=m(x-x1)

y+30=-7(x-4)

2. Distribute -7 to (x-4) (or multiply x and -4 by -7).

y+30=-7x+28

3. Subtract 30 from both sides to get y by itself.

y=-7x-2

When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle.

\(x\propto \frac{1}{y} \)

We know that the area of a rectangle is given by the product of the length and width of the rectangle.

Area = Length*Width

In this given problem,

The length of the rerectanglctangle is represented by x

and the width of the rectangle is represented by y

If the area of the rectangle is represented by A now.

So by the formula,

A = x*y

When A is constant then,

x = A/y

\(\therefore x \propto \frac{1}{y}\)

So from the above calculation we can conclude that about relation between length and width that,

"When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle."

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Answer:

y=-x+3/2, I hope that I hoped, and by the way, it is NEGATIVE x. It's a little hard to see :P

Answer:

y=2x + (-1)

Slope is m=2 and the y-intercept is b= -1