Mathematics High School

Researchers randomly choose two groups from 15 volunteers. Over a period of 9 weeks, one group watches television before going to sleep, and the other does not. Volunteers wear monitoring devices while sleeping, and researchers record dream activity. Which type of study method is described in each situation?

A. not enough information given
B. survey
C. observational study
D. controlled experiment

Answers

Answer 1
I would say D. controlled experiments

Related Questions

ANYONE WHO KNOWS SURFACE AREA!!!

I need help urgently!

Answers

[tex]A_1=\dfrac{1}{2}\cdot6\cdot5.2=15.6\ cm^2\\\\A_2=\dfrac{1}{2}\cdot6\cdot5=15\ cm^2\\\\A=A_1+3A_2\to A=15.6+3\cdot15=15.6+45=\boxed{60.6\ cm^2}[/tex]

A carpenter earns $18 an hour for a regular work week (40) hours. He earns time and a half for overtime. The weekly wage function is W(h)={                  18h                                         040} where h is the number of hours worked for the week. Find the wage if the carpenter worked 42.5 hours in the week

Answers

18×40=720 regular time
18×1.5=27 overtime per hour
27×2.5= 67.5 overtime

$720+$67.50=$787.50

Final answer:

To find the carpenter's weekly wage after working 42.5 hours, we calculate the regular pay for 40 hours at $18 per hour, which is $720, and then add the earnings from 2.5 hours of overtime at time and a half ($27 per hour), which is $67.5. The total weekly wage is $787.5.

Explanation:

To calculate the weekly wage of the carpenter who worked 42.5 hours, with $18 per hour for the first 40 hours and time and a half for overtime, we will use the wage function provided: W(h) = 18h for hours up to 40, and for hours above 40, it's (18 × 1.5) × (h - 40). Let's apply this to the 42.5 hours worked.

The carpenter's earnings for the regular 40 hours are $720 (which is 40 hours × $18). For the 2.5 hours of overtime, he earns time and a half, which is $27 per hour (18 × 1.5). The overtime earnings are $67.5 (2.5 hours × $27). So, the total wage is:

$720 + $67.5 = $787.5

Therefore, the carpenter's weekly wage for working 42.5 hours at the given rate is $787.5.

PLEASE HELP AS SOON AS POSSIBLE!!!!!!!!!!!!!!!!!! |r+3| ≥7 solve the inequality (please show work and steps )

Answers

|r+3| = (r+3) when r ≥ -3 so for r ≥ -3
                        r + 3 ≥ 7
                               r ≥ 4
|r+3| = -(r+3) when r < -3 so for r < -3
                     -(r + 3) ≥ 7
                         r + 3 ≤ -7
                               r ≤ -10
The answer to this question is r ≤ -10, r ≥ 4
So the solution would be:
|r+3| = (r+3)
r + 3 ≥ 7
  r ≥ 4
|r+3| = -(r+3)
  -(r + 3) ≥ 7
   r + 3 ≤ -7
r ≤ -10
So the answer is r ≤ -10, r ≥ 4

Find the slope of the line on the graph

Answers

find 2 points on the graph where the blue line crosses an X and Y that we know

1st point ( -4,0)
 2nd point (0,3)

slope = change in y over change in x

change in y = 3-0 = 3

change in x = 0 - -4 = 0+4 = 4

slope = 3/4




A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?

Answers

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

[tex]V = xxy = x^{2}y[/tex]

We also know that the bin is constructed from 48 square feet of sheet metal, so:

Surface area of the square base = [tex]x^{2}[/tex]

Surface area of the rectangular sides = [tex]4xy[/tex]

Therefore, the total area of the cube is:

[tex]A = 48 ft^{2} = x^{2} + 4xy[/tex]

Isolating the variable y in terms of x:

[tex]y = \frac{48- x^{2} }{4x}[/tex]

Substituting this value in V:

[tex]V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3} [/tex]

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

[tex]\frac{dv}{dx} = 48-3x^{2} =0[/tex]

Solving for x:

[tex]x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4[/tex]

Solving for y:

[tex]y = \frac{48- 4^{2} }{(4)(4)} = 2[/tex]

Then, the dimensions of the largest volume of such a bin is:

Length = 4 ft
Width =  4 ft
Height = 2 ft

And its volume is:

[tex]V = (4^{2} )(2) = 32 ft^{3}[/tex]

You buy a new yoga ball. The ball has a diameter of 26 inches. What is the volume of the ball? Use 3.14 for pi. Round your answer to the nearest hundredth.

Answers

the formula for volume of a ball is:

V = 4/3 x PI x r^3
 we are told PI = 3.14

the diameter is 26 inches so r ( radius )= 26 / 2 = 13 inches

 now we have V = 4/3 x 3.14 x 13^3

V = 9198.11 cubic inches

Answer:

The volume of the ball is [tex]9,198.11\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a sphere (yoga ball) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

In this problem we have

[tex]r=26/2=13\ in[/tex] -----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}(3.14)(13^{3})=9,198.11\ in^{3}[/tex]

O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale.
Assuming that lines that appear to be tangent are tangent, what is the value of x?

Answers

we know that

The measure of the external angle is the semi difference of the arcs that it covers.
so
see the picture attached to better understand the problem

m AB=128°--------> by central angle
m ACB=360°-128°-----> m ACB=232°
∠x=(1/2)*[m ACB-m AB]
∠x=(1/2)*[232-128]-----> ∠x=(1/2)*104°-----> ∠x=52°

the answer is
∠ x is 52°
The answer is 52°

Hope I helped :)

The function f(x) = 12x + 50 gives the amount of money a worker earns for working x hours per week. What is the inverse function?

Answers

12x + 50 = 62 but you have to multiply x by 12. I don't know what x is so maybe subtract 12 and 50 to get x. 50 - 12 = 38/ 38 x 12 = 456, then divide that by 50. 456 / 50 = 9.12, round up or down and get 9. 9 is your answer!!!


                                                               

2=sqrt P solve for P

Answers

sqrt P = 2
Square both sides;-

(sqrt P)^2 = 2^2

P = 4   Answer
2=√P, to remove √ we need to square both sides of the equation.
2²=(√P)²
4=P

P=4

Hamilton received a 75 on his algebra exam. The professor is allowing students to take a 7-question bonus quiz to improve their algebra exam score. Each question answered correctly on the bonus quiz will add 3 points to the exam score. Hamilton needs to receive at least a 90 on his exam score in order to make an "A" for the semester. If x represents the number of questions answered correctly on the bonus quiz, which of the following inequalities symbolizes this situation?


A. 3x + 75 < 90
B. 7x + 75 > 90
C. 3x + 75 > 90
D. 7x + 75 < 90




Answers

The answer is A.

Since each question answered right would add 3 points, the amount of questions answered correctly would be x. You then going to add that to his original score, 75. He needs at least a 90, so 90 is the lowest test grade he can afford. Therefore, 90 is should be the greatest number since there are no less than, equal to and such. Knowing that, the answer would be A

Hope this helps!

Final answer:

The correct inequality should be 3x + 75 ≥ 90 to indicate Hamilton needs at least 90 on his exam. The closest option given, which is not entirely accurate, is C. 3x + 75 > 90.

Explanation:

To determine the inequality that represents Hamilton’s situation, we need to calculate how many points he requires to reach a score of at least an “A”, which is 90. Each correct bonus question adds 3 points to his exam score of 75. We need to find the number of questions, x, Hamilton must answer correctly to achieve a total score of 90 or more. Therefore, the inequality that encompasses this scenario is 3x + 75 ≥ 90 because each correct answer contributes 3 points towards closing the 15-point gap between his current score and the desired score of 90.

However, the options given do not include the correct representation which would be 3x + 75 ≥ 90. Instead, the closest option is C. 3x + 75 > 90, which would imply that Hamilton must score more than 90, which is not a requirement for making an “A” (as “A” can include exactly 90).

The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area?

Answers

we know that
area of rectangle=length*width
let
x-----> the length side
y-----> the width side
y=13 units

A=2x²-5x
A=x*y------> 2x²-5x=x*13------> 2x²-18x=0-----> x²-9x=0
x*(x-9)=0
the solutions are
x=0
x=9

hence
the dimensions of the rectangle are
length is 9 units
width is 13 units

the area of rectangle is -----> 9*13-----> 117 units²

the answer is 
117 units²

What is the y-intercept of the function f(x) = –2/9 + 1/5

Answers

The equation has no X variable so whatever that adds up to becomes the y-intercept. 

- 2/9 + 1/5 >> - 10/45 + 9/45 = - 1/45 


Your y-int is - 1/45 or (0, - 1/45)

Need help to write equations for 5, 6 & 7

Answers

5)
The x-values go up by 1: -2, -1, 0, 1, 2
The y values are always 3 times the previous value.
This is an exponential function.

[tex] y = a(b)^x [/tex]

We need to find a and b.
Look at x = 0.
For x = 0, y = 4.

[tex] y = a(b)^x [/tex]

[tex] 4 = a(b)^0 [/tex]

Since b^0 = 1, this simplifies to

[tex] 4 = a [/tex]

Now we know a = 4. We have

[tex] y = 4(b)^x [/tex]

Look at x = 1. For x = 1, y = 12.

[tex] 12 = 4(b)^1 [/tex]

[tex] 12 = 4b [/tex]

[tex] b = 3 [/tex]

Now that we know a and b, we can write the function.

[tex] y = 4(3)^x [/tex]

Now that you have the function written out, notice the following.
In the exponential equation we found, the number raised to x
is the number you multiply each y value to get the next y value.
In this case, each y value is 3 times the previous one, so you have 3^x.
The way you find "a" in the exponential equation is to look at the y-coordinate
when x = 0. When x = 0, b^x is 1, so b^x drops out, and you get "a" equal to
the y-value. In this case, when x = 0, y = 4, so "a" is 4.
With b = 3, and a = 4, you can quickly write:
y = 4(3)^x.

What is the standard deviation of the following data set rounded to the nearest tenth? 52.1, 45.5, 51, 48.8, 43.6

Answers

The standard deviation of a set of data is given by
[tex]\sigma = \sqrt{ \frac{1}{N} \sum (x_i - \mu)^2} [/tex]
where
N is the number of data (in this case, N=5)
[tex]x_i[/tex] are the data
[tex]\mu[/tex] is the average value

Let's calculate the average value:
[tex]\mu = \frac{52.1+45.5+51+48.8+43.6}{5}=48.2 [/tex]

And now we can apply the formula to calculate the standard deviation:
[tex]\sigma = \sqrt{ \frac{1}{5} \sum ( x_i - 48.2 )^2} =[/tex]
[tex]= \sqrt{ \frac{1}{5} ( (3.9)^2 + (-2.7)^2 + (2.8)^2 + (0.6)^2 + (-4.6)^2 ) } =[/tex]
[tex]= \sqrt{ \frac{1}{5} (51.86) } =3.2[/tex]

Answer:

Standard deviation is 3.2.

Step-by-step explanation:

Given data is,

52.1, 45.5, 51, 48.8, 43.6,

Let x represents the data points,

Now, mean of the data is,

[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]

Population size, N = 5,

Hence, the standard deviation of the following data set is,

[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]

[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]

[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]

[tex]=\sqrt{10.372}[/tex]

[tex]=3.2205589577[/tex]

[tex]\approx 3.2[/tex]

Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?

I understand the steps where I am stuck is how did you get 2/3/

Answers

Divide the area by the time:

Divide 2 3/4 acres by 4 1/8 hours:

Divide 2.75 acres by 4.125 hours:

2.75 acres
--------------- = 2.667 acres/hour, or 2 2/3 acres / hour.
4.125 hrs

If this is not entirely clear to you, please share the work you've done yourself and I will respond.

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. you choose one marble from the jar at random. what is the theoretical probability of choosing a white marble?

Answers

30+50+20=100 = altogether marbles
P(white)= 20/100 =1/5
P(white)=1/5
[tex]|\Omega|=100\\ |A|=20\\ P(A)=\dfrac{20}{100}=\dfrac{1}{5}=20\%[/tex]

Find the surface area of the equilateral triangular pyramid.

Answers

its 288. just like I answered on the other question you asked thats the exact same thing as this one 

Students washed cars to raise funds for their school. they collected $291 by charging $3.00 per car. how many cars did they wash?

Answers

Divide total money collected by amount charged per car to find number of cars washed.

=$291 total ÷ $3 a car
=97 cars


ANSWER: They washed 97 cars.

Hope this helps! :)

What is cos 45? Please HELP !!!

Answers

Answer:

A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].

Step-by-step explanation:

Given  : Triangle 90 -45 -45 .

To find : What is cos 45.

Solution : We have given

Triangle 90 -45 -45  

Hypotenuse = √2 ,

Adjacent side to 45 degree = 1 .

By the trigonometric ratio : cosine is the ratio of the adjacent side to angle  to the hypotenuse .

Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].

Plug the values  Hypotenuse = √2 , Adjacent side to 45 degree = 1 .

Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].

Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].

The cosine of 45° is √2 / 2.

In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.

In this case, we want to find the cosine of 45°.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.

In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.

Using the formula for cosine, we have:

cos 45° = adjacent side / hypotenuse

Substituting the values, we get:

cos 45° = 1 / √2

To rationalize the denominator, we multiply both the numerator and denominator by √2:

cos 45° = (1 / √2) * (√2 / √2) = √2 / 2

Therefore, the cosine of 45° is √2 / 2.

To learn more about cosine function;

https://brainly.com/question/29277391

#SPJ6

what is the volume , in cubic units , of a pyramid of height 8 and a square base of length 15?

Answers

pretty sure its 48 cm3

Line RS is tangent to circle Q at point R.


What is the measure of ∠SQR ?

Enter your answer in the box.

Answers

If the line RS is tangent to the circle, then it is at a 90 degree angle to the circle at the point of contact.

Now that we know 2 angles, we can find the 3rd:

180 - 90 - 32 = 58

Using the tangent and radius theorem, the measure of ∠SQR is 58°.

What is Circle Geometry??

From the question, we are to determine the measure of ∠SQR

In the given diagram, QR is a radius

By the tangent and radius theorem,

If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another

∴ ∠QRS = 90°

∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)

∠SQR + 32° + 90° = 180°

∠SQR + 122° = 180°

∠SQR  = 180° -  122°

∠SQR  = 58°

Hence, the measure of ∠SQR is 58°.

Learn more on Circle geometry here: https://brainly.com/question/21872415

#SPJ 2

Need this geometry answer quick!

Answers

Since it is a 90° angle it is equal to the sum of 6x° and 4x°, so 6+4=10 and the answer is the second one.
Adjacent angles on a straight line sum up to 180:
90 + 6x + 4x = 180

Combine like terms:
90 + 10x = 180

Subtract 90 from both sides:
10x = 90

Divide both sides by 10:
x = 9

Answer: 9

1/2g^2 + 7/2 + 3g^2- 4/5g + 1/4

Answers

For this case we have the following expression:
 1 / 2g ^ 2 + 7/2 + 3g ^ 2- 4 / 5g + 1/4
 The first thing we must do is to group terms with the same degree:
 g ^ 2 (1/2 + 3) - 4 / 5g + (7/2 + 1/4)
 Then, rewriting we have:
 (7/2) g ^ 2 - (4/5) g + (15/4)
 Answer:
 (7/2) g ^ 2 - (4/5) g + (15/4)
Final answer:

The expression [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4[/tex]5/4 by combining like terms, which include the [tex]g^2[/tex]s and the constants.

Explanation:

The student's question involves combining like terms and simplifying a polynomial expression in mathematics. The expression provided is [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4.[/tex]ed to combine like terms, which involves adding or subtracting the coefficients of terms with the same degree.

First, combine the g2 terms (1/2g2 + 3g2) to get 7/2g2. Next, the constant terms (7/2 + 1/4) are combined to yield 15/4. The term with g, which is -4/5g, does not have a like term, so it remains as it is. After combining like terms, the simplified expression is 7/2g2 - 4/5g + 15/4.

Simplify the trigonometric expression.

Answers

First we are going to find the common denominator of both fractions. To do that, we are going to multiply their denominators:
[tex](1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha [/tex]

Now we can rewrite our expression using the common denominator:
[tex]\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha} [/tex]

Finally, we can use the trig identities: [tex]1-sin^2 \alpha =cos^2 \alpha [/tex] and [tex]sec \alpha = \frac{1}{cos \alpha } [/tex] to simplify our trig expression:
[tex]\frac{2}{cos^2\alpha}=2sec^2 \alpha [/tex]

We can conclude that the correct answer is the fourth one.
1/(1+sin theta) + 1/(1-sin theta) 

THe answer is letter D. 2 sec^2 theta

Hope it help! Goodluck! 

Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12

Answers

x = -19/2
y = -33/2

Start by plugging in the second equation for y in the first equation. Then solve for x. After you can use that value to solve for y. 

Quadrilateral ABCD has the following vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6). Quadrilateral ABCD is a

A. trapezoid
B. parallelogram
C. square
D. rectangle

Answers

In order to get the figure, you have to plot it.

Quadlirateral ABCDwith vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6) is s A. TRAPEZOID

the answer is TRAPEZOID

From a point on a circle, two perpendicular chords are drawn. One is 6 cm from the center and the other one is 3 cm from the center. Find the lengths of these chords.

Answers

The chord 3cm away is 12cm and chord 6cm away is 6cm. 
The two perpendicular chords will create a rectangle with the center. each side will be half of the parallel sides length. 
The chord 3cm away is 12cm and chord 6cm away is 6cm. 
The two perpendicular chords will create a rectangle with the center. each side will be half of the parallel sides length.

If x varies directly as y, and x = 48 when y = 16, find x when y = 5.

A) 5/3

B) 153.6

C) 15

Answers

x =k y
48 = k* 16
k = 3

x=3*5
x=15

Answer:

15

Step-by-step explanation:

x =ky

48 = k16

divide by 16

k = 3

plug k into x=ky

x=3*5

x=15

A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?

Answers

To convert the amount of milk from deciliters to liters we proceed as follows:
1 liter = 10 deciliters
therefore the amount of liters used in making the cake will be found as follows:
5.25/10×1=0.525 liters

Answer: 0.525 liters

An investment of $450 increases at a rate of 6.5% per year. What is the growth factor, b?

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &450\\ r=rate\to 6.5\%\to \frac{6.5}{100}\to &0.065\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=450(1+0.065)^t\implies A=450(\stackrel{growth~factor}{1.065})^t[/tex]
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They left the remaining six petri dishes closed as a control group. When the researchers measured the growth of bacteria two days later, the six dishes that had no hand sanitizer showed the least amount of bacterial growth. The researchers concluded that not using any hand sanitizer would lead to the least bacterial growth. Which statement best explains why the researchers conclusion was not justified? the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours? Explain why the ratio 3 feet / 1 yard has a value of one A financial institution wishes to estimate the mean balance owed by its credit card customers. a random sample of 64 credit card customers was taken. according to the sample results, the average credit card balance is $600. the population standard deviation is known to be $200. construct a 96 percent confidence interval estimate of the true mean population credit card balance for this financial institution. A Elena le ____________ (gustar) leer los libros, pero no le ___________ (interesar) leer las revistas. gusta, interesa gustan, interesan gusta, interesan gustan, interesa What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)? how did congress reinforce its power with the states that seceded La ciudad de mxico es una de las ciudades ms grandes del mundo y con ms __ . castillos habitantes el bosque de chapultepec, ubicado en el centro de la ciudad de mxico, es uno de los lugares ms __ de la ciudad. solitarios concurridos el metro de la ciudad de mxico es una amplia red de trenes y tneles que recorren __ la ciudad de mxico y __ la vida a sus habitantes. toda; facilitan parte de; dificultan los cuatro millones de personas que diariamente transporta el metro de la ciudad de mxico slo son __ por los sistemas de transporte de tokio y mosc. recorridos superados en las estaciones __ los pasajeros pueden cambiar de trenes para llegar fcilmente a su destino. de transbordo subterrneas algunas lneas del metro de la ciudad de mxico no son subterrneas, sino superficiales, es decir, __ al nivel de la calle. paran circulan en algunas estaciones del metro de la capital de mxico hay __ . exposiciones de arte danzas indgenas para las personas mayores de sesenta aos el servicio de transporte del metro es totalmente __ . inseguro gratuito