a study was conducted to determine if drinking a cup of tea before bedtime helped with falling asleep faster. after randomly assigning 50 people to one group that received tea before bedtime and 50 other people to a group that did not receive tea before bedtime, the researcher then compared the amount of time it took for each person to fall asleep. what is the explanatory variable? the 50 individuals in both groups the amount of time it took to fall asleep if a subject received tea and how long it took for that individual to fall asleep if subject received tea

Answer:

Step-by-step Explanation:

In a Cartesian plane, we learn many such terms which represent a point, or a line, or cooridnates of some points etc\(.\)

Such terms are:

A possible coordinate pair for vertex N in square MNPQ can be (5, 3).

Since the square has an area of 9 square units, each side of the square must have a length of √9 = 3 units. Given that vertex M is located at (2, 3), we can determine the position of vertex N by moving three units to the right from vertex M. Thus, the x-coordinate of vertex N will be 2 + 3 = 5. Since the y-coordinate remains the same, the y-coordinate of vertex N will be 3.

Therefore, a possible coordinate pair for vertex N is (5, 3). This coordinates form a square with vertex M at (2, 3) and an area of 9 square units.

To learn more about coordinate click here:

brainly.com/question/22261383

#SPJ11

Answer:

MN = 7 cm

Step-by-step explanation:

Well the volume we can separate into pieces

first the ABCDEFGH (? you know this cuboid)

which has a volume of

\(V = AB\cdot BC\cdot CH\\\\V = 3*6*(3+JY+4)\)

if you ask where does the 4 come from

it comes from LP = KB = YC and JY + YC =JC

so

\(V = 18(7+MX)\)

this is because JY = MX

the other volume is of BCNPKLXY (hope you understand which one)

and the volume is

\(V = BP*PN*NX\\\\V=8*6*4\\\\V = 192\)

and the last one is KYXLMJ (the top "triangle")

the volume is

\(V = \frac{LX*XM}{2}*LK\\\\V = \frac{6*MX}{2}*8\\\\V= 6*4*MX\\\\V=24MX\)

so now add them up

and has to equal 444

\(V_T = 18(7+MX)+192+24MX\\\\V_T = 126+18MX+192+24MX\\\\V_T = 318+42MX\\\\444=318+42MX\\\\444-318=42MX\\\\126=42MX\\\\MX = 3\)

and finally we know that MN = MX + XN = 3+4 = 7

so here is our answer MN = 7 cm

a couple of notes

\(1.\:\angle LXM = 90\\\\2.\:\angle KYX = 90\)

3. the units don't matter due to the fact that everything is in cm

4. see the picture below to get a better idea of which prism I am talking of

5. tell me if you have questions :D

A real word problem that can be represented by the division problem 38/5 = 7 R 3, where rounding the quotient up to 8 makes sense:

Problem:

A group of 38 students is going on a field trip, and they need to be divided into groups of 5. How many complete groups can be formed, and how many students will be left over?

A real-world problem that can be represented by the division problem 38/5 = 7 R 3, where rounding the quotient up to 8 makes sense:

Problem:

A group of 38 students is going on a field trip, and they need to be divided into groups of 5. How many complete groups can be formed, and how many students will be left over?

Solution:

To solve this problem, we perform the division 38 ÷ 5. The quotient represents the number of complete groups that can be formed, and the remainder represents the number of students left over.

38 ÷ 5 = 7 R 3

In this case, the quotient is 7, which means we can form 7 complete groups of 5 students each. However, there are 3 students left over, which cannot form a complete group of 5.

Now, let's consider rounding the quotient up to 8 instead of using the exact value of 7. Rounding up to 8 would mean that we create an additional group even though it may not be complete.

If we round up to 8, we can form 8 groups of 5 students each, accommodating a total of 40 students (8 × 5 = 40). With this arrangement, we would have 2 extra students (40 - 38 = 2) in the last group.

Rounding up to 8 allows us to ensure that all 38 students are accommodated, even if it means having a few extra students in the last group. This rounding method ensures that no students are left out and provides a solution that makes sense in the given context.

For more such information on: word problem

https://brainly.com/question/21405634

#SPJ8

The functions best model this scenario are:

For x < 4, C(x) = 4.25x.

For x ≥ 4, C(x) = 3.75x - 2.

Where x is the number of rental hours.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

Cost of rent kayaks per hour = $4.25

If a customer rents for four or more hours.

The cost per hour = $3.75

And,

Discount = $2 off.

Now,

C(x) = the total cost and x represents the number of rental hours.

We can make an equation as:

For x < 4,

C(x) = 4.25x

For x ≥ 4

C(x) = 3.75x - 2

Thus,

For x < 4, C(x) = 4.25x.

For x ≥ 4, C(x) = 3.75x - 2.

Where x is the number of rental hours.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

2.22

Step-by-step explanation:

4/9 x 5

Answer:

Step-by-step explanation:

The tuna can has a shape of a cylinder, and the area of the  tuna lablel is the  lateral surface area of the can

\(A=2\pi rh\)

Data

diameter d= 6.5cm

radius r = \(\frac{diameter}{2}\)= \(\frac{6.5}{2} = 3.25cm\)

height h= 3cm

leteral surface area

\(A=2*3.142*3.25*3\\= 61.269\\=61.27cm^2\)

Answer:

x = 8.98782862707

Step-by-step explanation:

Base on the given we can infer that we are solving for x:

Given equation:

1000x+27x+5.5=9236

Combine similar terms

1027x + 5.5 = 9236

Subtract both side by 5.5

1027x + 5.5 = 9236

             -5.5      -5.5

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

1027x = 9230.5

Now divide both sides by 1027x

9230.5 / 1027

x = 8.98782862707

[RevyBreeze]

Answer:

6

Step-by-step explanation:

3 x 2 x 1

first strip you can have 3 options

second only 2 options left

last one, only 1 choice

RBY

RYB

BRY

BYR

YRB

YBR

Answer:

6 flags

Step-by-step explanation:

The flag must have stripes of 3 different colors.

Ways to arrange each stripe :

Stripe 1 x Stripe 2 x Stripe 3

Note that the line is a horizontal line, passing through the point (0, 1) in the y-axis.

All points of this line have 1 as their y-coordinate. That is, this line contains points like (-3, 1), (-1, 1), (5, 1), (17, 1)... etc.

Thus, this is the line where y is always 1, this is the line y=1.

To learn more about vertical line refer to:

https://brainly.com/question/1821791

#SPJ1

Each and every point along this line has a y-coordinate of 1. This line has points like (-3, 1), (-1, 1), and (5, 1), for example (17, 1).

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept.

A sleeping line is a line that is horizontal. From left to right or right to left, it is a straight line. The word "horizon," which refers to the line where it appears that the earth and sky are meeting in the distance, is the ancestor of the word "horizontal." A horizontal line is a straight line that is perpendicular to the x-axis and contains points with identical y-coordinates throughout.

Vertical lines are straight lines that are mapped from top to bottom, whereas horizontal lines are straight lines that are mapped from left to right. In coordinate geometry, the horizontal line is the line parallel to the x-axis, while the vertical line is the line parallel to the y-axis.

To learn more about equation of the line refer to:

https://brainly.com/question/18831322

#SPJ1

Answer:

infinite solutions

Step-by-step explanation:

3(12x2+x+1)+12(12x2+x+1)=15(12x2+x+1)

Combine like terms

3(12x2+x+1)+12(12x2+x+1)=15(12x2+x+1)

15(12x2+x+1) = 15(12x2+x+1)

Divide by 15

(12x2+x+1) = (12x2+x+1)

Since they are the same

x can be any real value

Answer:

All real values of x

Step-by-step explanation:

3(12x²+x+1)+12(12x²+x+1)=15(12x²+x+1)

(12x² + x + 1)(3+12) = 15(12x²+x+1)

15(12x²+x+1) = 15(12x²+x+1)

Since both sides are identical, all real values of x will satisfy the equation

The correct answer is (d) Those values of a for which the numerator of the function r is not zero.

For a rational function r(x), the limit of r(x) as x approaches a can be determined by evaluating r(a) if the numerator of the function is not zero. This is because when the numerator is not zero, the limit of the function is defined and equal to the value of the function at that point.

However, if the numerator of the function is zero, then further analysis is required to determine the limit. In this case, the limit may be defined or undefined, depending on the behavior of the function as x approaches the point of interest.

In general, for a rational function, the limit exists and is equal to the value of the function at that point if and only if the numerator of the function is not zero at that point.

Learn more about numerator :

https://brainly.com/question/7067665

#SPJ4

Answer:c

Step-by-step explanation:

Answer:

the answer is d to the qu5

Answer:

The answer is c

Step-by-step explanation:

I took the quiz on K12

The inequality in a standard form that describes this situation is,

52000x + 84000y < 830000.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

From the given information, x = the number of junior programmers y = the number of senior programmers,

The inequality that represents the situation is,

52000x + 84000y < 830000.

learn more about inequalities here ;

https://brainly.com/question/30231190

#SPJ1

Answer:

420

Step-by-step explanation:

if we add 30 to each of the length of speech, we get 420 seconds

Answer:

36

Step-by-step explanation:

4x +x = 180
5x=180
x=180/5
x=36

Expansion : \((x+1)(x+9) = x(x+9) + 1(x+9) = x^{2} +9x + x + 9\)
Simplify : \(x^{2} +10x + 9\)

Answer:

\(\huge\boxed{ \bf\:x^{2} + 10x + 9}\)

Step-by-step explanation:

\((x + 1)(x+9)\)

Let's expand it at first.

\((x + 1)(x + 9)\\= x (x + 9) + 1 (x + 9)\\= x^{2} + 9x + x + 9\)

Now, simplify it.

\(x^{2} + x + x + 9\\= \boxed{ x^{2} + 10x + 9}\)

\(\rule{150pt}{2pt}\)

The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

Learn more about functions on:

brainly.com/question/25638609

#SPJ1

Answer:

1599995904

Step-by-step explanation:

first, you must do the top part of the fraction. you can start by doing the power numbers such as 2 power 4, 4 power 6 and 4 power 4.

the complete answer for the top part is: 12x 16x 4069x 8x 2x 256 which equals: 3199991808

then, you must divide by 2 which gives you the answer of: 1599995904

In the 10th week, the sale (S) would have been 6.

To obtain the week in which the sale (S) is equal to 6, we need to solve the equation:

\(\[ 6 = \frac{120t}{t^2 + 100} \]\)

First, let's multiply both sides of the equation by (t² + 100) to eliminate the denominator:

6(t² + 100) = 120t

Expanding the equation:

6t² + 600 = 120t

Rearranging the equation:

6t² - 120t + 600 = 0

Dividing the equation by 6 to simplify:

t² - 20t + 100 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula.

\(\[ t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]\)

In this case, a = 1, b = -20, and c = 100.

\(\[ t = \frac{-(-20) \pm \sqrt{(-20)^2 - 4 \cdot 1 \cdot 100}}{2 \cdot 1} \]\)

Simplifying the equation further:

\(\[t = \frac{{20 \pm \sqrt{{400 - 400}}}}{2}\]\)

\(t = \frac{{20 \pm \sqrt{0}}}{2}\)

\(t = \frac{{20 \pm 0}}{2}\)

\(t = \frac{{20}}{2}\)

t = 10

We have obtained t = 10 as the solution to the equation.

This means that in the 10th week after the introduction of the product in the market, the sale would have been 6.

To know more about quadratic formula refer here:

https://brainly.com/question/22364785#

#SPJ11

The exponential function that is used to determine how much of the isotope is left after x number of half-lives is:

\(A(x) = 90(0.5)^x\)

5.625 mg would be left after 70 days.

A decaying exponential function is modeled by:

\(A(t) = A(0)(1 - r)^t\)

In which:

In this problem, considering that it has 90 mg, and the half-life means that r = 0.5, the equation is:

\(A(x) = A(0)(1 - r)^x\)

\(A(x) = 90(0.5)^x\)

70 days is 70/17.5 = 4 half-lifes, hence:

\(A(4) = 90(0.5)^4 = 5.625\)

5.625 mg would be left after 70 days.

More can be learned about exponential functions at https://brainly.com/question/25537936

The internal angle of a regular polygon is equal to 108°. A 5-sided polygon is a pentagon.

An -sided polygon with regular sides that are all the same length and symmetrically arranged around a common center is known as a regular polygon (i.e., the polygon is both equiangular and equilateral).

Only a few regular polygons are "constructible" with the compass and straightedge of classical Greece.

A regular polygon's interior angle measures 108°.

The pentagon is a 5-sided polygon.

A two-dimensional closed figure with three or more straight sides is called a polygon.

A polygon is any shape with straight edges, such as a triangle or rectangle.

Figures with open sides or any curved sides are not considered to be polygons.

Therefore, the internal angle of a regular polygon is equal to 108°. A 5-sided polygon is a pentagon.

Know more about a regular polygon here:

https://brainly.com/question/1592456

#SPJ4

A tape diagram to represent 8-2+2 will be:

 +-----+-----+-----+-----+-----+-----+-----+-----+

 |     |     |     |     |     |     |     |     |

 +-----+-----+-----+-----+-----+-----+-----+-----+

  ^                                   ^

  |                                   |

  |                                   |

 8-2                                 +2

  |                                   |

  |                                   |

  v                                   v

 +-----+-----+                       +-----+

 |     |     |                       |     |

 +-----+-----+                       +-----+

    6                                 2

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.

In this diagram, the first segment with 8 boxes represents the starting quantity of 8. Then, we subtract 2 from that by crossing out 2 boxes, leaving us with 6. Finally, we add 2 by drawing a new segment of 2 boxes, bringing us to a total of 8.

Learn more about tape diagram on:

https://brainly.com/question/26354395

#SPJ1

Answer:

Step-by-step explanation:

We can find the longest side I.e. Hypotenuse using pythogorean theorem.

\( {8}^{2} + {15}^{2} = {x}^{2} \\ 64 + 225 = {x}^{2} \\ 289 = {x}^{2} \\ x = \sqrt{289} \\ x = 17\)

This is your answer hope it helps :)

Answer:

17?

Step-by-step explanation:

a squared + b squared = c squared (hypothenuse longest side)

square them, then add them and square root them.

Using the Horner's algorithm, the value of p(4) is -16

To use Horner's algorithm to find p(4) for the given polynomial p(z) = 3z^5 – 7z^4 – 5z^3 + z^2 - 8z + 2, we start by writing out the polynomial in a specific form:

p(z) = ((3z - 7)z + 5)z^2 + (z - 8)z + 2

This form of the polynomial is obtained by factoring out the highest degree term and then factoring out the resulting factor from each subsequent term. The coefficients of these factors are then used as the new coefficients in the Horner's algorithm.

Now, to evaluate p(4) using Horner's algorithm, we start with the coefficient of the highest degree term, which is 3:

Step 1: Set x = 4 and initialize a variable, let's say 'result', to 0.

Step 2: Multiply the current result by 4, and then add 3. Set this value to be the new result.

result = 3 × 4 + 0 = 12

Step 3: Move on to the next coefficient, which is -7. Multiply the current result by 4 and add -7. Set this value to be the new result.

result = (-7) × 4 + 12 = -16

Step 4: Move on to the next coefficient, which is 5. Multiply the current result by 4 and add 5. Set this value to be the new result.

result = 5 × 4 - 16 = 4

Step 5: Move on to the next coefficient, which is 1. Multiply the current result by 4 and add 1. Set this value to be the new result.

result = 1 × 4 + 4 = 8

Step 6: Move on to the next coefficient, which is -8. Multiply the current result by 4 and add -8. Set this value to be the new result.

result = (-8) × 4 + 8 = -24

Step 7: Move on to the last coefficient, which is 2. Multiply the current result by 4 and add 2. Set this value to be the new result.

result = 2 × 4 - 24 = -16

Learn more about Horner's algorithm here

brainly.com/question/28699520

#SPJ4

The given question is incomplete, the complete question is:

Use Horner's algorithm to find p(4), where p(z) = 3z^5 – 7z^4 – 5z^3+z^2 - 8z +2

The relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly is 92.16%.

The term 'relative' refers to an event that is being thought of in relation to or in proportion to another event.

As, per the given question.

The minimum standard for moderate-intensity aerobic activity weekly is 150 min.

All the values which are less than 150 min will be considered as the below specified standard for moderate-intensity aerobic activity.

The relative frequency for 0 - 49 min is 47.54%.

The relative frequency for 50 - 99 min is 32.77%.

The relative frequency for 99 - 149 min is 11.85%.

Thus, the cumulative of all relative frequencies will be;

= 47.54% + 32.77% + 11.85%

= 92.17%

Therefore, the percentage of adults who get less than the recommended amount of moderate-intensity physical activity per week is 92.16%.

To know more about the relative frequency, here

https://brainly.com/question/1094036

#SPJ4

The complete question is -

The center for disease control and prevention (cdc) states that adults should engage in at least 75 min of vigorous-intensity aerobic activity or 150 min of moderate-intensity aerobic activity weekly. researchers gathered data from a random sample of adults who participated in the 2011–2012 national health and nutrition examination survey (nhanes).

What is the relative frequency of adults who are engaging in less than the minimum amount of recommended moderate-intensity physical activity weekly (less than 150 min)? Give your answer to two decimal places.

Answer:

it is a

Step-by-step explanation:

I might not know but I guess the answer is D

Besides vertical asymptotes, the zeros of the denominator of a rational function give rise to vertical holes or removable discontinuities in the graph of the function.

When the denominator of a rational function becomes zero at a specific value of x, it results in an undefined value for that particular \(x\) value. This means that the function is not defined at that point, creating a potential discontinuity.

However, in some cases, the numerator of the rational function may also have the same zero value as the denominator, which cancels out the undefined behavior and makes the function well-defined at that point. These canceled zeros give rise to vertical holes in the graph.

A vertical hole occurs when there is a "hole" or an open circle in the graph of the rational function at the x value where the denominator is zero. This indicates that the function has a removable discontinuity at that point.

To clarify, if the zero of the denominator is not canceled out by the numerator, it results in a vertical asymptote. On the other hand, if the zero of the denominator is canceled out by the numerator, it leads to a vertical hole or a removable discontinuity in the graph of the function.

Therefore, the zeros in the denominator of a rational function result in vertical holes or detachable discontinuities on the graph of the function in addition to vertical asymptotes.

Learn more about asymptotes on:

https://brainly.com/question/30197395

#SPJ11