As a pharmacist, you are responsible for knowing about medication dosage, and how long a dose stays in the patient's system. Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate, and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:
P(t) = 0.5t + 3.45t³ - 96.65t² + 347.7t, when 0 ≤t≤6 . In this function above, P(t) is the amount of medication (in mg) in the
blood stream at time t (in hours).
When put into a graphing software, it looks like this:

1) Why do we only need to look at the interval 0 ≤ t ≤ 6

Answer:

Step-by-step explanation:

x - 3 = 5

(x -3) +3 = 5+3

x - 3 + 3 = 8

so,

x = 8

Answer: 10 cm

Step-by-step explanation:

Given, length=8cm

breadth=6 cm

Pythagoras theorem states that sum of square of base and square of perpendicular height is equal to square of hypotnyse.

Thus, we can write:

Considering, base=length=8cm

Perpendicular=breadth=6cm

Therefore, length of diagonal =√(length∧2+breadth∧2)

                                                 =√(8∧2+6∧2) cm

                                                = 10 cm

Therefore the length of diagonal = 10cm.

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When n is large the distribution of the sample means will approach a normal distribution.

The central limit theorem (CLT) is a statistical theory that predicts that given a large enough sample size from a population with a certain level of variation, the mean of all the samples from that population will be close to the population mean.

To put it another way, the central limit theorem predicts with absolute certainty the form of the distribution of means when we take repeated samples from a certain population. In particular, the distribution of means derived from repeated sampling will tend toward normality as sample sizes increase.

In other words, when n is large, the distribution of the sample means will resemble a normal distribution if we continually pick independent, random samples of size n from any population.

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The probability that the top card is an Ace of Spades and the bottom card is a Queen of Hearts is extremely low, as there are 52 cards in a standard deck of cards and only two of those cards are an Ace of Spades and a Queen of Hearts.

Therefore, the probability of the top card being an Ace of Spades and the bottom card being a Queen of Hearts is 1/2652 or approximately 0.000038%.The probability of getting an Ace of Spades as the top card and a Queen of Hearts as the bottom card is 1/52 x 1/52 = 1/2652. This can be expressed as a percentage by multiplying the fraction by 100 which gives us 0.000038%. The probability that the top card is an Ace of Spades and the bottom card is a Queen of Hearts is extremely low, as there are 52 cards in a standard deck of cards and only two of those cards are an Ace of Spades and a Queen of Hearts.

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The answer in the solution set that makes 4f − 10 = 3f − 18 true is (a) -8

From the question, we have the following parameters that can be used in our computation:

4f − 10 = 3f − 18

And we have the solution set to be

S: {−18, −8, 3, 8}

Subtract 3f from both sides of the equation

So, we have the following representation

f - 10 = - 18

Add 10 to both sides of the equation

This gives

f = -8

Hence, the solution is (a) -8

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In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time

so finding intersection point of the y=4/x and y=16x

4/x=16x

=> [tex]x^{2}[/tex] = 1/4

=> x = 1/2 as x>0

and y=16x

=> y =8

now finding intersection point of y=4/x and y=1/16x

=> 4/x =x/16

=> [tex]x^{2}[/tex] = 64

=> x = 8 as x>0

and y= 4/x

=> y=1/2

now finding intersection point of y=16x and y=1/16x

the intersection point of both line is x=0

so y=16x

=> y=0

so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.

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Answer:

9

Step-by-step explanation:

Consequently, the room has a 7 meter width. The room's length is

[tex]= 7 * 3 meters = 21 meters[/tex]

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Given that the length of the rectangular space is three times its breadth

The chamber has a 56-meter perimeter.

Assume that the room's width is x.

As a result, the room is three times as long.

The room's perimeter is now equal to 2(3x + x).

[tex]Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.[/tex]

Consequently, the room has a 7 meter width.

The room's length is

[tex]= 7 * 3 meters\\= 21 meters[/tex]

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Answer: y=-3x-5

Step-by-step explanation:

(0,-5)   (-1,-2)

[tex]\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}[/tex]

x₁=0     x₂=-1     y₁=-5    y₂=-2

[tex]\displaystyle\\\frac{x-0}{-1-0}=\frac{y-(-5)}{-2-(-5)} \\\\\frac{x}{-1} =\frac{y+5}{-2+5} \\\\-x=\frac{y+5}{3}[/tex]

Multiply both parts of the equation by 3:

[tex]-3x=y+5\\\\-3x-5=y+5-5\\\\-3x-5=y[/tex]

[tex]Thus,\ y=-3x-5[/tex]

The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of each line,

LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,

Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3

Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.

Thus, the solution of the pair of lines has been shown above.

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Answer:

1. $80 dollars for the month she used 3 GB over her data limit.

2. 10x + 50.

Explanation:

1. Autumn used 3 GB data more than her plan offered. $10 dollars a gigabyte of data times 3 gigabytes equals 30, plus 50 dollars for the base smartphone plan (which, off topic, sucks) equals 80 dollars for the month.

2. 10x + 50 means 10 dollars per X gigabytes, plus the base 50 dollars a month Autumn has to pay.

Answer:

Step-by-step explanation:

(-1 - 3)/(3 - 0) = -4/3

y - 3 = -4/3(x - 0)

y - 3 = -4/3x + 0

y = -4/3x + 3

The expression be 1/4(c³+ d²) then the value exists 9.

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right).

The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations.

Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).

Let the given expression be 1/4(c³+ d²)

The value of c = -4 and d = 10

substitute the values in the above equation, we get

Follow the PEMDAS order of operations

Calculate within parentheses  ((-4)³ + (10)²) = 36

1/4((-4)³ + (10)²)

simplifying the above equation, we get

= 1/4 × 36

= 9

Therefore, the correct answer is option B. 9.

The complete question is:

What is the value of this expression when c = -4 and d = 10?

1/4(c³+ d²)

A. 2

B. 9

C. 21

D. 41

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Considering a circle whose equation is (x + 6)² + (y + 8)²  = 9. The radius of the circle is 3 units

Information given in the question

Circle F is represented by the equation (x + 6)² + (y + 8)²  = 9

Equation of a circle is given as

(x - h)² (y - k)² = r²

The equation of the circle is written in standard form is sown above comparing the equation with the given question gives

rewriting the equation

(x + 6)² + (y + 8)²  = 9

(x + 6)² + (y + 8)²  = 3²

comparing shows that r = 3

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Answer:

It costs $0.49 for each avocado and $0.36 for each tomato.

Step-by-step explanation:

This is a system of equations problem.

Let x represent the avocados and y represent tomatoes:

4x + 5y = 3.76  <--- scenario 1

6x + 3y = 4.02 <---- scenario 2

If we graph these out on a graphing calculator, the lines will intersept at point (0.49,0.36)

The x coordinate represents how much it costs for each avacado and the y coordinate represents how much it costs for each tomato

Answer: 9

Step-by-step explanation:

Let's start with what we know. If we have the data set:
63, 53, 20, 10, x

The average is:

(63+53+20+10+x)/5 = 31

We multiply both sides by 5

(65+53+20+10) = 155

146 + x = 155

x = 9

Answer: 3000 years

Step-by-step explanation:

Let y be the number of money and x be the number of years

So we have the equation

y= 6.5x + 10000

Now we put 29500 in the y

29500 = 6.5x + 10000

Subtracted 10000 from both sides

19500 = 6.5x

Divided both sides by 6.5

x = 3000 years

Answer:

first option

Step-by-step explanation:

inequalities of the type | x | > a have solutions of the form

x < - a or x > a

given

| 7 + m | - 4 > 8 ( add 4 to both sides )

| 7 + m | > 12

then

7 + m < - 12 (subtract 7 from both sides )

m < - 19

OR

7 + m > 12 ( subtract 7 from both sides )

m > 5

solution is m > 5 or m < - 19

Answer: If Lin sells b boxes of cookies, she will earn 3.75b dollars. Therefore, the inequality that will be true whenever Lin makes her goal is:

3.75b > 30

This inequality can be read as "the total amount of money Lin earns selling cookies is greater than $30."

Step-by-step explanation:

The equation that represents "Twenty five is one sixth of the number n" is:25 = (1/6) * n

The equation "25 = (1/6) * n" represents the relationship between the number 25 and an unknown number, n. It states that 25 is equal to one sixth of n. In other words, if we multiply the unknown number n by one sixth (or divide n by 6), we will obtain the value of 25. This equation can be used to solve for the value of n by multiplying 25 by 6, which would give us the unknown number. It provides a clear mathematical expression of the given relationship and allows us to find the value of n based on the given condition.The equation states that 25 is equal to one sixth of the number n. This means that if we take one sixth of the value of n, we will get 25 as the result. In other words, if we divide the value of n by 6, the quotient will be 25.

To understand it conceptually, imagine that we have a number n and we want to find one sixth of that number. By dividing the number by 6, we can determine how many equal parts make up the whole number, and one of those parts is equal to 25.

This equation is useful in various situations, such as solving problems involving proportions or determining unknown values when given a fraction of a number.

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1) The relation in the right is not a function.

2) domain

D: {-60, 20, 70}

range

R: {-6, 3, 2, 5}

3) Angelo is correct.

A function is a relation that maps elements from one set called the domain into another set called the range, such each element from the domain is mapped into only one of the elements of the range.

Thus, if an element of the domain is being mapped into two or more elements of the range, then the relation is not a function.

1) If you look at the relationship in the right, you can see that the input -60 is being mapped into two different outputs, this, it is not a function.

2) The domain is the set in the left:

D: {-60, 20, 70}

And the range is the set in the right side:

R: {-6, 3, 2, 5}

3) Angelo is correct, functions are relations,  but not all relations are functions, only the relations that meet the condition written above.

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To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,15);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 15$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$15^2 + b^2 = 15^2$

$225 + b^2 = 225$

$b^2 = 0$

$b = \sqrt{0} = 0$ feet

Therefore, the height of the balloon is 0 feet. This is because the balloon has been pulled up by the wind so that its top is directly above the stake, and therefore its height is 0 feet.

The average number of children in a family under the age of 1818 is 0.76, which is the predicted value of this distribution.

The product of each potential result and its associated probability yields the anticipated value of a probability distribution. The probable outcomes in this scenario are 0, 1, 2, 3, & 4 minors, with the associated probability shown in the table.

We may add the products of each result and its probability to determine the estimated return of this distribution:

Expected value = (0)(0.58) + (1)(0.18) + (2)(0.16) + (3)(0.06) + (4)(0.02)

= 0 + 0.18 + 0.32 + 0.18 + 0.08

= 0.76

Therefore, 0.76 children below the age of 18 per household are the anticipated value of this distribution.

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Answer:

y = 24

y = 2x

Answer:

5

Step-by-step explanation:

There are 6 total skeins, and 1.2 is needed to make one

So you would divide 6 by 1.2

6 / 1.2 = 5

And to confirm it is 5, you can now multiply 5 by 1.2

5 x 1.2 equals 6

Answer: A

Step-by-step explanation:

Answer:

I am not sure which form you want.

Points slope: y -2  = 3(x -4)

Slope intercept:  y = 3x -10

Step-by-step explanation:

Point slope form for the line

y- y = m(x -x)  

slope of 3 and the point (4,2)  Use 4 for x and 2 for y

y -2  = 3(x -4)

Slope intercept form of a line

y = mx + b

2 = 3(4) + b

2 = 12 + b  Subtract 12 from both sides

2 - 12 = 12 - 12 + b

-10 = b

y = mx + b

y = 3x -10

Answer:

Below in bold.

Step-by-step explanation:

The definition of direct variation is  y = kx where k is a constant.

So, if y/x is a constant for the data, we have direct variation.

So, checking the rows in the given table:

y/x = 11/8

y/x = 22/16 = 11/8

y/x = 33/24 = 11/8

- we see that this is direct variation.

So, k = 11/8 and

The equation is

y = (11/8) x

or

y = 11x/8

or

y = 1.375x  in decimal form.

Answer:

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

Direct variation equation:

Use the pairs of coordinates and find the value of k, then compare:

The value of k is same with all ordered pairs and the equation is:

Answer:

Step-by-step explanation:

There are just two triangles stuck together , here.  Don't let that throw you off your game :DD  

solve for a

then b

for a it's  180 = 2*36 +a   ( b/c of the red marks , again)

180 = 72 +a

180-72 =a

108 = a

Now solve for b

180 = 2b + 42  (red marks tell us this formula works,  again)

180-42 = 2b

138 =2b

138/2 =b

69 = b

Do you see , now,  how I get those formulas???

Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.

initial height = 5

final height =20

height to travel =20-5 =15

[tex]15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0[/tex]

solving we get, t = 0.255 or -2.44

since, -2.44 is not possible,

t = 0.255 seconds.

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