The amount of caffeine in the body of a healthy adult after drinking espresso decreases exponentially, with a half-life of approximately 666 hours. That is, every 666 hours, the amount of caffeine in the body decreases by 50\PP, percent. Charlotte wants to go to sleep at 11\,\text{pm}11pm11, start text, p, m, end text and does not want more than 202020 milligrams (\text{mg})(mg)(, start text, m, g, end text, )of caffeine in her system at that time. What is the latest time Charlotte can drink a 222-ounce shot of espresso that contains 80\,\text{mg}80mg80, start text, m, g, end text of caffeine

Answer:

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

Step-by-step explanation:

[tex]x+2y=5 \\ \\ 2y=-x+5 \\ \\ y=-\frac{1}{2}x+\frac{5}{2}[/tex]

The slope of the given line is [tex]-\frac{1}{2}[/tex].

This means the slope of any line parallel to the given line is also [tex]-\frac{1}{2}[/tex].

Using point-slope form, the equation is [tex]y-2=-\frac{1}{2}(x-3)[/tex].

Answer:

Sure! Here's a system of equations we can set up to represent this situation:

Let x be the price of a bag of popcorn and y be the price of a drink.

Then we can set up the following system of equations:

x + 3y = 16.50 (equation for Jack's purchases)

2x + 5y = 29.75 (equation for Jill's purchases)

To solve this system of equations, we can use the substitution method.

First, we can solve for x in equation 1:

x = 16.50 - 3y

Then, we can substitute this expression for x into equation 2:

2(16.50 - 3y) + 5y = 29.75

Simplifying this equation, we get:

33 - 6y + 5y = 29.75

Combining like terms, we get:

33 - y = 29.75

Subtracting 29.75 from both sides, we get:

33 - 29.75 - y = -y

Simplifying, we get:

3.25 - y = 0

Subtracting 3.25 from both sides, we get:

-y = -3.25

Dividing both sides by -1, we get:

y = 3.25

So, the price of a drink is $3.25.

Now we can substitute this value for y back into equation 1 to solve for x:

x + 3(3.25) = 16.50

Simplifying, we get:

x + 9.75 = 16.50

Subtracting 9.75 from both sides, we get:

x = 6.75

So, the price of a bag of popcorn is $6.75.

To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope is the coefficient of x when the coeficient of y is 1.

we need change the form.

2y=x+8

y=[tex]\frac{1}{2}[/tex]x+4

so, the slope of a line parallel to the line is 1/2

Select the data for which you want to create a chart slope . Click INSERT > Recommended Charts. On the Recommended Charts tab, scroll through the list of charts that Excel recommends for your data

When you find the chart you like, click it > OK.

The formula for a horizontal line at y=4 is as follows: There is no slope. 4.0 is the y-intercept.

What are the Slope and intercepts ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

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Answer:

62%

Step-by-step explanation:

First, you got the formulate: 1-27%-11%

Second, calculate the difference: 0.73-0.11

Third, the sum is 0.62

Then you multiply 0.62 ×100\100

Write a single fraction: 0.62×100\100

Calculate the product or quotient: 62\100

100% to a percentage: 62%

That is your answer 62%

The correct option is Simpson's Paradox because the concept of the other options don't depict the paradox displayed in the question.

Simpson's paradox

it is simply a phenomenon in probability and statistics, whereby a trend appears in several different groups of data but will disappear or reverse when these groups are combined.

This result is often encountered in many areas of statistics and is very problematic especially when frequency data is given causal interpretations. The paradox can be resolved when causal relations are appropriately addressed in the statistical modeling.

It concluded that treatment B was more successful than treatment A without considering the conditions under which both treatments were carried out neither did it consider the severity of cases of patients involved in the treatment.

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The two-digit number is 34.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The given information can be translated into the following equation:

(10x + y) + (2x - y - 1) = 13

Where x is the tens digit and y is the units digit.

Solving for x and y, we get:

x = 3 and y = 4

So the number is 34.

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Each of the tables is classified as linear or non-linear on the image presented at the end of the answer.

A function is classified as linear or non-linear depending on the rate of change of the function.

If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.

Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.

For example, the top-left function is non linear, as when x changes by one from x = 1 to x = 2, y changes by 3, from y = 1 to y = 4, while when x changes by one from x = 2 to x = 3, y changes by 5.

The bottom-right function is linear, as for each increase of x by 5, the value of y decays by 4.

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Answer: 1.

Step-by-step explanation:

[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]

On a Cartesian (or "coordinate") plane in which  each point is represented by an ordered pair (x , y) belongs to  x coordinate  , y coordinate .

An ordered pair is a set of numbers in which it gives the location of a point on a coordinate plane.

The ordered pair is always expressed exactly the same way (x , y).

The first number  in an ordered pair represents the x coordinate on the plane while the second number in an ordered pair  represents the y coordinate.

The x-coordinate shoes that  how far away the point is horizontally from the x-axis.

The y-coordinate shows that  how far away the point is vertically from the x-axis.

Quadrant I: the upper-right quadrant of the plane in which all points in this quadrant have  the  positive x coordinates and positive y coordinates as { (+,+)}  ,  {(+,+)}

Quadrant II: the upper-left quadrant of the plane in which all points in this quadrant have negative x coordinates and positive y coordinates

{ (+,-)}{ (+,-)}

Quadrant III: the lower-left quadrant of the plane in which  all points in this quadrant have negative x coordinates and negative y coordinates

{ (-,-)}{(-,-)}

Quadrant IV: the lower-right quadrant of the plane in which  all points in this quadrant have positive x coordinates and negative y coordinates

{(+,-)}{ (+,-)}

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The x-intercept in a quadratic formula is where the graph of the function crosses the x-axis.

An x-intercept is a point on the graph of a function where the y-coordinate is equal to zero. In other words, it's a point on the graph where the function intersects the x-axis. The x-intercepts of a quadratic formula can be found by setting the y-value equal to zero and solving for x.

The quadratic formula is typically in the form of ax^2 + bx + c =0, thus by setting y=0 we get x = -b/2a and x = -b/2a, these are the x-intercepts where the graph of the function will cross the x-axis. The x-intercepts are also known as the roots or zeroes of the function, and are important for understanding the overall shape of the graph.

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The error is that the student rounded off the outcome after combining the numbers.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number.

For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

So, we have:

162 + 287 + 395 = 840

The error:

After adding the numbers, the student rounded the result.

If the learner had added the numbers first and then rounded the result, they would have received the correct answer of 850 instead of 840.

When estimating totals, students should be taught to round numbers first before adding them.

Therefore, the error is that the student rounded the outcome after combining the numbers.

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Correct question:
A third-grade student is asked to find the best-estimated answer for the problem below by rounding to the nearest ten.

162 + 287 + 395

The student gets an answer of 840. Which of the following best describes the student's error?

Answer: The middle number is 15

Step-by-step explanation:

45/3= 15 so the three numbers will be around there.

14+15+16= 45

The equation is 80x + 1200 = 3800. And the numbers of at least 30 recliners and 32 sofas the company can have in the shipment.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A company is loading recliners and sofas onto a trailer that has a volume of about, 3800 cubic feet.

Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet.

The company wants the shipment to have at least 30 recliners and more than 25 sofas.

The equation that represents the situation is,

80x + 40y = 3800,

where x is the volume of a sofa and y is the volume of a recliner.

If y = 30 then,

80x + 1200 = 3800

80x = 2600

x = 2600/80

x = 32.5

x ≈ 32

Therefore, 30 recliners and 32 sofas.

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The explanation of four quadrant are explained below.

In the coordinate plane the first coordinate or the x-coordinate will refer to the number which corresponds with the point's horizontal location as determined by the number on the x-axis.

And the second coordinate known as the y-coordinate, will refer to the number which corresponds with the point's vertical location as determined by the number on the y-axis.

By using these x and y values, we have divide the graph, into four part such as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

Here we want to know that each quadrant contains certain directions.

=> Quadrant 1 placed on 0 to 90 degrees.

=> Quadrant 2 placed on 90 to 180 degrees.

=> Quadrant 3 placed on 180 to 270 degrees.

=> Quadrant 4 placed on 270 to 360 degrees.

And the value in the quadrant are like as follows:

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The length of each piece of the sandwich is 0.3125 feet.

A unitary approach is a mathematical technique for finding the value of a single unit and then multiplying it by any number of other units to derive the value of the given units.

Given, Zachary's art club ordered a giant sub sandwich for a party.

Therefore, t6o obtain the length of each piece we have divide the total length of the sandwich by the total number of pieces which is,

= (5/16) feet.

= 0.3125.

So, The length of each piece is 0.3125 feet.

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A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.

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Answer:

-73

Step-by-step explanation:

So to begin you must find where you start on a graph. To do this you can go backwards from your first number and in this situation it would be 14.5 because the slope is -2.5x. I will use y as the answer.

y=-2.5x+14.5

From here you plug in how many terms are neeeded for the correct answer. In this situation there is 35 terms needed.

y=-2.5(35)+14.5

Solve this equation to get your answer.

y=-73

Answer:

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

Given sequence:

This is an AP with the common difference of:

The first term is a = 12.

Use the nth term equation to find the 35th term:

The farmer needs to sow 135 acres of corn and wheat, and 45 acres of wheat.

A linear equation is the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "linear equation in two variables" is the term used to describe the previous sentence, where y and x are variables. Two variables make up bivariate linear equations. Examples include the linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

180 acres total land area

The corn acres should be C.

The wheat acres should be W.

A 180-acre property is planted with wheat and corn by a farmer.

Equation 1: C + W = 180

Corn is grown on three times as many acres as wheat:

Equation 2 is created by substituting C = 3W into Equation 1. The result is:

45 acres is W.

For corn, 135 acres equals C.

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The total area of triangle in square centimeters is 56.7cm squared .The three angles of the triangle add up to 180 degrees.

The term "trigon" is occasionally (though not frequently) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, some of which may be the same.  The three angles of the triangle add up to 180 degrees. With three sides and three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.

here

Area of each triangles is 4.2 x 8.2 or 34.44.

There are two triangles, thus you don't need to divide by two.

In addition, 8.2 is obtained by deducting the top length from the overall length. (13.5-5.3)

rectangle: 22.26 x 5.3

56.7 square meters is the entire area.

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The correct question is

What is the area, in square centimeters, of the triangles are?

a) 5.3 cm

b) 4.2 cm

c) 13.5 cm

5k4h 6r + 7k4h 6r + 5k4h 6r + 7k4h 6r = The perimeter of the rectangle is 24k8h 24r.

1. 5k4h 6r + 7k4h 6r = 12k8h 12r

2. 12k8h 12r + 5k4h 6r = 17k12h 18r

3. 17k12h 18r + 7k4h 6r = 24k8h 24r.

Therefore, the perimeter of the rectangle is 24k8h 24r.

The width of a rectangle is represented by 5k4h 6r, and the length of the rectangle is represented by 7k4h 6r. To find the perimeter of the rectangle, we need to add the width and length of the rectangle together. This can be done by adding 5k4h 6r and 7k4h 6r. The answer to this addition is 12k8h 12r. We then need to add the width and length of the rectangle together again. To do this, we add 12k8h 12r and 5k4h 6r. The answer to this addition is 17k12h 18r. Finally, we need to add the width and length of the rectangle together again. This is done by adding 17k12h 18r and 7k4h 6r. The answer to this addition is 24k8h 24r. Therefore, the perimeter of the rectangle is 24k8h 24r.

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Answer: x = a/b - c

Step-by-step explanation:

First divide by b on each side to get the x by itself.

Then subtract c from both sides to make x the subject of the formula.

Step-by-step explanation:

a = bx + c

the goal is to get to a form with "x = ...".

a - c = bx

(a - c)/b = x

done.

Answer:

y=2x-7

Step-by-step explanation:

y=mx+b  ==> m is the slope and b is the y-intercept

y=(2)x + (-7)  ==> plugin 2 for m=slope and -7 for b = y-intercept

y=2x-7 ==> simplify

Answer:

142%

Step-by-step explanation:

How I got this solution is made it as a ratio, "82.86:195.82".

I then simplified the balance by dividing 82.86 into both sides.

It then equaled around 0.42 (or 42%). Including itself, it got a markup percentage of 142%

The equations are;

a) y = -7/2x - 13

b) -2/7x - 46/7

We know that the equation of the line that we have here can be written in the general form as the equation that is given as; y = mx + c

We have that

m = slope of the line

c = intercept of the line

As such, we have;

-7x-2y=6 or y = 6 + 7x/-2

or

y = -3 - 7x/2

For the parallel line m = - 7/2

y - (-6) = -7/2(x - (-2))

y + 6 = -7/2x - 7

y = -7/2x - 13

For the perpendicular line m = - 2/7

y - (-6) = -2/7(x - (-2))

y + 6 = -2/7x - 4/7

y = -2/7x - 46/7

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The given equation 1 value of F(x) is 0.109 and in equation 2 F(x) is -4 respectively.

Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. This concept is given by the Greek mathematician Hipparchus.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional figures. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.

if x⁰=π in eq1

then [tex]f(x)= sin\ 2 \pi[/tex]

[tex]f(x) = 0.109[/tex]

if x⁰= -1 in eq2

then [tex]f(x)=3(-1)-(-1)^2[/tex]

[tex]f(x) = -4[/tex]

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Whatever the case a quadrilateral has always a sum of interior angles = 360°.

A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.

A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.

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Answer:

x = - √2/2

Step-by-step explanation:

We know that x = rcosθ and y = rsinθ. The unit circle always have radius of 1 unit. Therefore, r = 1 as defined. Hence:

x = cosθ, y = sinθ

x = cosθ, θ = arcsin(y)

x = cos{arcsin(-√2/2)}

Find the measurement or θ that makes sinθ = -√2/2 and that is π + π/4 = 5π/4.

x = cos(5π/4)

And cos(5π/4) = - √2/2 as well. Hence, x = - √2/2.