A tooth-whitening gel is to be tested for effectiveness. A group of 85 adults have volunteered to participate in the study. Of these, 43 are to be given a gel that contains the tooth-whitening chemicals. The remaining 42 are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals. A standard method will be used to evaluate the whiteness of teeth for all participants. Then the results for the two groups will be compared. 1. After the treatment period, compare the whiteness of the 43 treated adults. 2. A placebo is not being used. 3. After the treatment period, compare the whiteness of the two groups. 4. Randomly select 85 adults to be given the treatment gel. 5. The remaining 42 adults receive the placebo gel. 6. Randomly select 43 adults to be given the treatment gel.
Answers
Answer:
(a) 3, 5 and 6
Step-by-step explanation:
In the experiment, 43 are to be given a gel that contains the tooth-whitening chemicals while the remaining 42 are to be given a placebo. Therefore, a placebo is used.
The 43 that will receive the gel are to be selected randomly.
After the experiment, the whiteness of the two groups will be compared to see the effect of the gel.
Therefore for the experiment to be completely random, 3, 5, and 6 apply.
(b)
For the experiment to be double-blind, the researchers who will evaluate the whiteness and interact with the subjects, and the subjects would not know which subjects received either the whitening gel or the placebo.
Related Questions
Evaluate your answers as a fraction in simplest form. (1/3)4
Answers
The Solution.
The given fraction is
\((\frac{1}{3})^4\)\((\frac{1}{3})^4=(\frac{1}{3})^{}\times(\frac{1}{3})^{}\times(\frac{1}{3})^{}\times(\frac{1}{3})=\frac{1}{3\times3\times3\times3}=\frac{1}{81}\)So, the correct answer is 1/81
Work with a partner. A train travels 50 miles every 40 minutes. To determine
the number of miles the train travels in 90 minutes, your friend creates the
following table.
please help!!
Answers
To create a table you can do
50:40
100:80
112.5:90
We can find the answers by multiplying the original ratio 50:40 by 2.25 we do this because 90 minutes is 2.25 times longer than 40 minutes.
angles on a line and at a point
work out the size of angle x
Answers
Answer:
WHAT ANGLE THERE IS NO ANGLE
Step-by-step explanation:
A company currently has an advertisement that covers a billboard that is 30 ft wide by 50 ft high. The company wants to reduce the same advertisement to fit on a new billboard that is 25 ft wide by 30 ft high What are the dimensions of the largest advertisement that will fit on the new billboard without cropping the advertisement?
Answers
Because that is the biggest billboard
20. Sketch the level curve of the function f(x, y) that contains the point (5,0).
f(x, y) is shown in the picture attached.
Answers
At the given point,
\(f(5,0) = \dfrac1{\sqrt{5^2 + 0^2 - 9}} = \dfrac1{\sqrt{16}} = \dfrac14\)
Then the level curve is
\(\dfrac1{\sqrt{x^2 + y^2 - 9}} = \dfrac14 \\\\ \implies \sqrt{x^2 + y^2 - 9} = 4 \\\\ \implies x^2 + y^2 - 9 = 4^2 \\\\ \implies x^2 + y^2 = 25 = 5^2\)
which is a circle centered at the origin with radius 5 - quite easy to sketch.
There are 4 red balls and 6 green balls in a bag.
You reach in the bag and take out 3 balls without looking.
What is the probability that all three of the balls you take out are red?
Answers
\(\frac{1}{30}\)
Step-by-step explanation:From the question, in the bag there are;
4 red balls
6 green balls
10 balls in total.
Now, reaching in the bag and taking out 3 balls without looking, the probability that all three balls are red, can be analyzed as follows;
All three red means;
The first ball is red,
The second ball is red and;
The third ball is red.
i. First you take out a ball from a total of 10 balls. The probability P⁰(R) of having a red ball is given as;
P⁰(R) = \(\frac{possible-space}{total-space}\)
Since there are 4 red balls, the possible-space is 4
Also, since there are a total of 10 balls, the total-space is 10
P⁰(R) = \(\frac{4}{10} = \frac{2}{5}\)
ii. Secondly, you take out a ball from a remaining total of 9 balls. The probability P¹(R) of still having a red ball is given as;
P¹(R) = \(\frac{possible-space}{total-space}\)
Since there are 3 red balls remaining, the possible-space is 3
Also, since there are a remaining total of 9 balls, the total-space is 9
P¹(R) = \(\frac{3}{9} = \frac{1}{3}\)
iii. Thirdly, you take out a ball from a remaining total of 8 balls. The probability P²(R) of still having a red ball is given as;
P²(R) = \(\frac{possible-space}{total-space}\)
Since there are 2 red balls remaining, the possible-space is 2
Also, since there are a remaining total of 8 balls, the total-space is 8
P²(R) = \(\frac{2}{8} = \frac{1}{4}\)
Therefore, the probability P(R) of taking out three red balls without looking is given by the product of the probabilities described above. i.e
P(R) = P⁰(R) x P¹(R) x P²(R)
P(R) = \(\frac{2}{5} * \frac{1}{3} * \frac{1}{4} = \frac{1}{30}\)
Simplify:
6x + 2 - 1 - 4 - 3 - 2x + 2
Answers
Answer:
4x - 4
Step-by-step explanation:
Combine like terms. Like terms are terms with the same variable as well as the same amount of variables:
6x - 2x + 2 - 1 - 4 - 3 + 2
(6x - 2x) = 4x
(2 - 1 - 4 - 3 + 2) = (2 + 2) + (-1 - 4 - 3) = (4) + (-8) = -4
4x - 4 is your answer.
~
The simplified form of the expression is 4x - 4.
Here, we have,
To simplify the expression 6x + 2 - 1 - 4 - 3 - 2x + 2, we can combine like terms and perform the necessary calculations.
Step 1: Combine the like terms with the same variable, which are the terms with x:
6x - 2x = 4x.
Step 2: Combine the constant terms:
2 - 1 - 4 - 3 + 2 = -4.
Putting it all together, we have:
6x + 2 - 1 - 4 - 3 - 2x + 2 = 4x - 4.
Therefore, the simplified form of the expression is 4x - 4.
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The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
1.72 1.8 1.86 1.88 1.74 1.86
What is the mean height of the ocean's first high tide for the 6 days?
1.81 meters
1.83 meters
1.86 meters
1.87 meters
Answers
The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
Number of days = 1 2 3 4 5 6 Total = 6
1.72 1.8 1.86 1.88 1.74 1.86
What is average?
The average of the values is the ratio of the total sum of values to the number of values.
Since the mean of the heights of the tides,
= sum of heights / number of heights observation
= (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters
Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
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what is most likely the slope of the line graphed above
Answers
To calculate the slope of a line on the coordinate grid, we start by identifying two points anywhere along the line.
On this line given, two points are located at the following coordinates;
\(\begin{gathered} A=(-3,0) \\ B=(0,1) \end{gathered}\)Note however that, we can equally use any other points but other points would turn out to have fractions or decimals. Hence, for the sake of making our calculations less cumbersome, we have identified two points that lie on exact positions without any decimal or fractions.
The formula to calculate the slope shall be;
\(m=\frac{y_2-y_1}{x_2-x_1}\)Where the varaibles are;
\(\begin{gathered} (x_1,y_1)=(-3,0) \\ (x_2,y_2)=(0,1) \end{gathered}\)The slope now becomes;
\(\begin{gathered} m=\frac{1-0}{0-\lbrack-3\rbrack} \\ m=\frac{1}{0+3} \\ m=\frac{1}{3} \end{gathered}\)ANSWER:
The slope is 1/3
The correct answer is option A
Solve Trig equation
2cos0 = 1
Answers
Answer:
θ = 60 degrees
If needed in radians:
θ = π/3
Step-by-step explanation:
2cos(θ) = 1
We are solving for theta.
We can divide 2 on both sides.
2cos(θ) = 1
/2 /2
cos(θ) = 1/2
Now we can use Inverse of cosine to isolate theta.
θ \(= cos^-^1(1/2)\)
θ = 60 degrees
If needed in radians:
θ = π/3
dividing 1/9 is equal to multiplying by
Answers
Answer: 9
Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:
10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.
Now lets try it with 1/9.
X divided by 1/9 = X times 9/1.
So dividing by 1/9 is equal to multiplying by 9.
Please help me 10 Stars granted image attached below
Answers
Answer:
(-1/2,0)
Step-by-step explanation:
Rewrite this non-statistical
question as a statistical
question.
How many brothers do you
have?
Answers
Answer:
0
Step-by-step explanation:
Which transformation on the coordinate plane is a dilation?
Answers
Answer:
it is the last one
Step-by-step explanation:
A dilation is an enlargement or reduction of an object by a scale factor and with a center of dilation.
Which number is rational?
Please help me
Answers
Answer:A
Step-by-step explanation:
Please help 30 points for a quick response!!
Answers
Will mark as brainlist answer quickly
4 Read the following description of the knarr. "
The knarrs would have looked
similar to the drekars except they were longer, fatter and taller, and the space
dedicated to cargo left less room for oarsmen. These were the backbones of the
Viking empire, which they used to carry everything from gold coins to timber, spices
and fine fabrics."
What can you infer about the knarrs?
A: They were not designed for warfare.
B : They were faster than the drekars.
C: They were designed to carry soldiers.
D: They were used for the same purpose as drekars.
Answers
Answer:
A, they were not designed for warfare.
Step-by-step explanation:
The description describes the knarrs as cargo ships. "they used to carry everything from gold coins, to timber, spices, and fine fabrics."
Nothing there mentions soldiers or weapons.
I really need help on this question, is turning my mind around
Answers
Answer: \(192 \text{ cm}^2\)
Step-by-step explanation:
The area of each of the two triangular faces is \(\frac{1}{2}(8)(3)=12 \text{ cm}^2\).
The area of each of the two rectangular side faces is \((12)(3)=36 \text{ cm}^2\).
The area of the rectangular bottom face is \((12)(8)=96 \text{ cm}^2\).
So, the surface area is \(2(12)+2(36)+96=192 \text{ cm}^2\).
derivate (cos(3x^2). (5x^3 -1)^1/3 +sin 4x^3)^4
\( \: \: \: \: find \: first \: derivative \\ ( cos(3x {}^{2} ) \times ( \sqrt[3]{5x {}^{3} - 1} ) + \sin(4x {}^{3} ) {}^{4} \)
Answers
Answer:
Step-by-step explanation:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)
Lets look at the derivative part:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)
\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)
Substituting in eq(1), we have:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)
Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9
Answers
Answer:
\(y = \frac{2}{3} x - 3 \frac{2}{3} \)
Step-by-step explanation:
Let's rewrite the given equation in the form of y= mx +c, where m is the gradient while c is the y-intercept.
2x -3y= 9
3y= 2x -9
Divide by 3 throughout:
\(y = \frac{2}{3} x - 3\)
Thus, the gradient of given line is ⅔.
Parallel lines have the same gradient.
Therefore, gradient of line is ⅔.
Substitute m=⅔ into the equation:
\(y = \frac{2}{3} x + c\)
To find the value of c, substitute a pair of coordinates.
When x=4, y= -1,
\( - 1= \frac{2}{3} (4) + c \\ - 1 = \frac{8}{3} + c \\ c = - 1 - \frac{8}{3} \\ c = - 3 \frac{2}{3} \)
Substitute the value of c:
\(y = \frac{2}{ 3} x - 3 \frac{2}{3} \)
SOLVE the equation. Use factoring techniques (3x - 1)^2 - 16 = 0X= Smaller value X= Larger value
Answers
Given the equation;
\((3x-1)^2-16=0\)We shall start by expanding the parenthesis as follows;
\(\begin{gathered} (3x-1)^2=(3x-1)(3x-1) \\ (3x-1)^2=9x^2-3x-3x+1 \\ (3x-1)^2=9x^2-6x+1 \end{gathered}\)The equation can now be re-written as follows;
\(\begin{gathered} 9x^2-6x+1-16=0 \\ 9x^2-6x-15=0 \\ \text{Divide all through by a common factor which is 3;} \\ \frac{9x^2}{3}-\frac{6x}{3}-\frac{15}{3}=0 \\ 3x^2-2x-5=0 \\ \text{ Since the coefficient of x}^2\text{ is greater than 1,} \\ \text{ Multiply the constant (-5) by the coefficient of x squared (3)} \\ \text{The constant now takes the value -15} \\ \text{Two factors of -15 when added together to give -2 are,} \\ 3\text{ and -5} \end{gathered}\)Therefore, we now have;
\(\begin{gathered} 3x^2-2x-5=0 \\ 3x^2+3x-5x-5=0 \\ 3x(x+1)-5(x+1)=0 \\ (3x-5)(x+1)=0 \\ \text{Therefore;} \\ (3x-5)=0,(x+1)=0 \\ 3x=5,x=-1 \\ x=\frac{5}{3},x=-1 \end{gathered}\)ANSWER:
\(\begin{gathered} \text{Smaller value; x}=-1 \\ \text{Larger value; x}=\frac{5}{3} \end{gathered}\)which is the real world situation that can be described by a linear inequality
Answers
Answer:
Pretty sure it's B
Step-by-step explanation:
Everything else would be more like an equation. I think B is the only inequality.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Answer:
i think the answer is something like maybe if the artist is really good at doing something well and looking good
this question is hard
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answers
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
Which theme is found in this story The Lucky Ticket
Answers
Answer:
In "The Lottery Ticket", Chekhov develops the theme that the love of money can destroy one's satisfaction.
Rena, a pharmacy technician, is looking to make a 45%
solution. She has the alligation pictured below.
A.
20
45
Which solution can be used to fill in location A?
O 35
O 40
O45
O 55
Answers
The solution that can be used to fill in location A is 45%.
In this case, Rena is trying to make a 45% solution. The alligation diagram shows two solutions with concentrations of 20% and 45%. The concentration at location A represents the concentration of the final mixture.
To determine the concentration at location A, we can visually observe the positioning of the concentrations on the diagram. The closer a concentration is to location A, the more it contributes to the final mixture.
In this case, the concentration of 45% is closer to location A than the concentration of 20%.
This means that more of the 45% solution should be used in the mixture to achieve a 45% concentration.
Therefore, the solution that can be used to fill in location A is 45%.
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Plant Type Number tomato 8 squash 4 cucumber 16 rosemary 22 he The table above shows the number of each type of plant in Robert's garden. What is the ratio of the total number of plants in Robert's garden to the number of tomato plants? OA. 25:2 OB. 25:8 OC. 25:4 OD 23:2
Answers
Answer:
C. 25:4
Step-by-step explanation:
Total number of plants in Robert's garden = 8 + 4 + 16 + 22
= 50
Number of tomato plants in Robert's garden = 8
Ratio of total number of plants to the number of tomato plants = 50 : 8
Simplify
50 : 8 = 25:4
EASY POINTS!
Winter has just begun. After one week, the temperature decreased by 46.8° with a
percent change of 72%. What was the temperature at the beginning of the week and
what is the temperature now?
Answers
Answer:Can somebody also help me with this. i'm confused please hurry!
Step-by-step explanation:
Consider the line 5x+2y=−4. What is the equation of the line parallel to the given line that passes through the point (−2, 6) in slope-intercept form? Enter your answer by filling in the boxes to complete the equation.
Answers
Answer:
y = -5/2x +1
Step-by-step explanation:
You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.
Parallel lineThe equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:
5(-2) +2(6) = c
-10 +12 = c
2 = c
Now we know the equation of the parallel line can be written as ...
5x +2y = 2
Slope-intercept formSolving for y puts this in slope-intercept form:
2y = -5x +2 . . . . . . . . subtract 5x
y = -5/2x +1 . . . . . . . . divide by 2
We don't know what your boxes look like, but we can separate the numbers to make it look like this:
\(\boxed{y=\dfrac{-5}{2}x+1}\)
#95141404393
Find the perioa
equation.
llowing
y = 2 cos(5x + 3) - 6
77
Period = [2]T
Give your answer in simplest form.
![Find the perioaequation.llowingy = 2 cos(5x + 3) - 677Period = [2]TGive your answer in simplest form.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/LQPTncYwbgWAlBk9oUI1EamQ5J0oFRZg.png)
Answers
Answer:
In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.
The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.
The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.
So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:
T = 2π / 5
This is the simplest form for the period of the given function.