Let's say x is going to be the number meters of the width of the room:
x: width
Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:
1.8x: lenght
Step 2: relating the expressions for each side to its perimeterWe know that the perimeter of a rectangle is given by
Perimeter = 2· (width + lenght)
We know that the perimeter is 29 meters, then
Perimeter = 29
↓
29 = 2· (width + lenght)
We do know an expression for its width and lenght, we replace them:
29 = 2· (width + lenght)
↓
29 = 2· (x + 1.8x)
Step 3: finding xSince x + 1.8x = 2.8x:
29 = 2· (x + 1.8x)
↓
29 = 2· (2.8x)
↓ 2· 2.8 = 5.6
29 = 5.6x
↓ dividing both sides by 5.6
29/5.6 = 5.6x/5.6
5.2 = x
Final step: finding its dimensionsSince
x: width
then
Width = 5.2 meters
Since
1.8x: lenght
then
Lenght = 1.8 · 5.2 meters = 9.36 meters
Answer: the dimensions of the room are Width = 5.2 meters and Lenght = 9.36 meters
Can I Plss get some help I got stuck I don’t know how to find x
Using Sine of angles to evaluate for x
The formula is,
[tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex]Given:
[tex]\begin{gathered} Opposite=x \\ Hypotenuse=19 \\ \theta=21^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} sin21^0=\frac{x}{19} \\ \therefore x=19\times sin21^0 \end{gathered}[/tex]Simplify
[tex]x=6.80899\approx6.81\text{ \lparen2 decimal places\rparen}[/tex]Hence,
[tex]x=6.81[/tex]On its website a tv station displays temperature data for each hour during the past 24 hours. The data are displayed as using two different functions on a line graph. One function shows the current temperature and the other function shows the historical average. Which quantities are represented by the y-values on the line graph
, Given the question, we are asked to find which of the quantities are represented by the y-values on the line graph .
Explanation
In the question, we are told that the tv station displays temperature data using two different functions on a line graph. One of the functions shows the current temperature and the other function shows the historical average.
A function, by definition, can only have one output value(y) for any input value. In this case the input values are the time the temperature which we result in the output value of the historical average and temperature.
Therefore,
Answer
Option D
write a linear equation to: slope=2 and goes through point (4, 11)
When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:
1. Use the standard form of a linear equation:
[tex]y=mx+b[/tex]You know the value of:
m= 2
y= 11
x= 4
You make a substitution:
[tex]11=(2)(4)+b[/tex]You can find then the value of b:
[tex]11=8+b[/tex][tex]b=11-8=3[/tex]Then you have now the data to form the final linear equation:
[tex]y=2x+3[/tex]Renta scored 409 points in a video game. This was 223 more points than Sadia score (s). Which equation does not represent this situation? And why?
A) 223 = 409 - s
B) s = 409 - 223
C) s = 409 + 223
D) 223 + s = 409
Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409
how do I convert the rectangular equation: x=15 to a polar equation that expresses r in terms on theta?I got r=15 sectheta but wanted to double check
In polar coordinates, the x variable is given as
[tex]x=r\cos \theta[/tex]So, we have the equation
[tex]r\cos \theta=15[/tex]By dividing both sides by cosine of thetat, we get
[tex]r=\frac{15}{\cos \theta}[/tex]since
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]The above result is equivalent to:
[tex]r=15\sec \theta[/tex]Identify the following forms of factoring with the correct method of solving
Given:
There are given the equation:
[tex]90x^3-20x[/tex]Explanation:
To find the factor of the given equation, first, we need to take a common variable from the given equation:
[tex]90x^3-20x=x(90x^2-20)[/tex]Then,
[tex]\begin{gathered} 90x^3-20x=x(90x^2-20) \\ =10x(9x^2-2) \end{gathered}[/tex]Final answer:
Hence, the factor of the given equation is shown below:
[tex]\begin{equation*} 10x(9x^2-2) \end{equation*}[/tex]Hurry Will give 75 points
(Score for Question 3: of 4 points)
3. The equation y = 14x describes the amount of money Louis earns, where x is the number of hours he works
and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl's Earnings
Time (h)
Money earned
($)
Hours 3 5 8 10
Money 54 90 144 180
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl's earnings over time in hours. Remember to label the axes.
Answer:
Carl earns 18 dollars an hour, we can get this by dividing the money earned by time which gets your answer.
Part a: Carl earning per hour is $18.
Part b: More Money is earned by Carl.
Part c: The graph that represents Carl's earnings is drawn.
What is termed as the equation?A mathematical statement consisting of two expressions joined by an equal sign is known as an equation. 3x - 5 = 46 is an example of an equation. We have the value for the variable x as x = 17 after solving this equation.For the given question,
The amount of the money Louis have is defined by the equation.
y = 14xx is the number of hours.y is the amount of money.Carl's Earnings
Time (h) Hours 3 5 8 10
Money earned($) 54 90 144 180
Part a: Carl earning per hour.
For 3 hours Carl earns $54.
For one hour-$54/3 = $ 18.
Part b: More Money is earned by-
For 1 hours Carl earns $8.
For 1 hour Louis earning is y = 14×1 = $14.
Thus, Carl earns more.
Part c: The graph that represents Carl's earnings over time in hours is drawn.
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inserted a picture of the question, can you just answer the question and not ask a lot of questions yes i’m following
Step-by-step explanation:
A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,
so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.
[tex]\frac{360}{9}=40[/tex]Therefore the degrees will a nonagon have rotational symmetry
Hene the correct answer is Option B
The seventh term of a geometric sequence is 1/4 The common ratio 1/2 is What is the first term of the sequence?
Answer:
16
Explanation:
The equation for the term number n on a geometric sequence can be calculated as:
[tex]a_n=a_{}\cdot r^{n-1}[/tex]Where r is the common ratio and a is the first term of the sequence.
So, if the seventh term of the sequence is 1/4 we can replace n by 7, r by 1/2, and aₙ by 1/4 to get:
[tex]\frac{1}{4}=a\cdot(\frac{1}{2})^{7-1}[/tex]Then, solving for a, we get:
[tex]\begin{gathered} \frac{1}{4}=a(\frac{1}{2})^6 \\ \frac{1}{4}=a(\frac{1}{64}) \\ \frac{1}{4}\cdot64=a\cdot\frac{1}{64}\cdot64 \\ 16=a \end{gathered}[/tex]So, the first term of the sequence is 16.
Decide whether or not the number 46/45 Could represent the probability
Solution
- A probability, by definition, is a fraction that is less than or equal to 1.
- The number 46/45 is a number greater than 1.
- Thus, the number 46/45 CANNOT be a probability
Find the equation of the line, in slope-intercept form, that passes through the points (-2, -4) and (2,8).A) y = 1/3x + 22/3B) y = 3x + 14C) y = 3x + 2 D) y = - 3x + 14
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
x1 and y1 are the x and y coordinates of the initial point
x2 and y2 are the x and y coordinates of the final point
From the information given, the initial point is (- 2, - 4) and final point is (2, 8)
Thus,
x1 = - 2, y1 = - 4
x2 = 2, y2 = 8
By substituting these values into the slope formula,
m = (8 - - 4)/(2 - - 2) = (8 + 4)/(2 + 2) = 12/4 = 3
We would find the y intercept, c by substituting m = 3, x = - 2 and y = - 4 into the slope intercept equation. We have
- 4 = 3 * - 2 + c
- 4 = - 6 + c
Adding 6 to both sides of the equation,
- 4 + 6 = - 6 + 6 + c
c = 2
By substituting m = 3 and c = 2 into the slope intercept equation, the equation of the line is
C) y = 3x + 2
The volume of a rectangular prism is 2 x cubed + 9 x squared minus 8 x minus 36 with height x + 2. Using synthetic division, what is the area of the base?
The base area of the prism is 2x² + 5x - 18
How to determine the area of the base?From the question, the given parameters are
Volume = 2 x cubed + 9 x squared minus 8 x minus 36
Height = x + 2
Rewrite properly as
Volume = 2x³ + 9x² - 8x - 36
Height = x + 2
The base area is calculated as
Base area = Volume/Height
Using the synthetic division, we have
Set the divisor to 0
x + 2 = 0
This gives
x = -2
So, we have the representation to be
-2 | 2 9 - 8 - 36
Write out 2
So, we have
-2 | 2 9 - 8 - 36
2
Multiply 2 and -2
This gives
-2 | 2 9 - 8 - 36
-4
2
So, we have
-2 | 2 9 - 8 - 36
-4
2 5
Repeat the process
So, we have
-2 | 2 9 - 8 - 36
-4 -10
2 5 -18
Repeat the process
So, we have
-2 | 2 9 - 8 - 36
-4 -10 36
2 5 -18 0
This means that
Base area = 2x² + 5x - 18
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y = -x +3
x+y = 17
Are these parallel?
Answer:
Yes
Step-by-step explanation:
The equations need to be in slope intercept form. The first equation is but the second one isn't. Solve the second equation for y to put it in slope intercept form.
x + y = 17
x - x + y = 17 - x
y = -x + 17
To determine if they are parallel the slopes need to be the same.
y = -1x + 3
y = -1x +17
The slope are both -1, so they are parallel
Answer:
Yes
Step-by-step explanation:
I need to use my work and I don’t know what to put please help me !!!
We are given the information that Bailey reads 2 and a half books in 3 and a third weeks.
2 and a half books can be seen as 5/2 books, just as follows
[tex]2\frac{1}{2}\text{ = }\frac{4}{2}+\frac{1}{2}\text{ = }\frac{5}{2}[/tex]On the other hand, 3 and a third weeks can be seen as 10/ weeks, just as follows:
[tex]3\frac{1}{3}\text{ = }\frac{9}{3}+\frac{1}{3}=\text{ }\frac{10}{3}[/tex]Next, we just have to use a rule of three, its as follows: "if Bailey read 5/ books in 10/3 weeks, how many books does she reads per week?"
[tex]\begin{gathered} 10/3\text{ --> 5/2} \\ 1\text{ --> x} \end{gathered}[/tex]With that, we proceed with the division:
[tex]\frac{\frac{5}{2}}{\frac{10}{3}}\text{ = }\frac{15}{20}\text{ = }\frac{3}{4}[/tex]That means that Bailey reads 3/4 books per week
Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:
Given:
Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.
The total number of sample space is, N = 10.
Head for female kitten
T for male kitten.
The objective is to find the probability that at least three of the kittens will be male.
Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4
Now, the probability of at least three of the kittens will be male can be calculated by,
[tex]undefined[/tex]Mario bought a $2,300 refrigerator on an installment plan. The installment agreement
included a $230 down payment and 18 monthly payments of $125 each. What is the
total finance charge?
O $180
O $225
O $145
O $195
$225,The term "instalment payments" describes a client paying a bill over a set period of time in incremental amounts. Start billing for nothing. A payment schedule agreed upon by the buyer and seller is known as installment payments.
What is installment payment?
The term "instalment payments" describes a client paying a bill over a set period of time in incremental amounts. Start billing for nothing. A payment schedule agreed upon by the buyer and seller is known as installment payments. Typically, it is mentioned unequivocally in a contract's or invoice's payment terms.
one of a series of regular loan, debt, or other payment installments; also, the system of monthly payments: This kind of installment payment is not subject to an additional cost.
An installment is a portion or segment of something, such as the most recent episode of your favorite TV show or the installment you pay each month toward your credit card debt.
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Find the equation of the linear function x 1 2 3 4 y 1 6 11 16
We solve as follows:
*We determine first the slope (m), that is:
[tex]m=\frac{6-1}{2-1}\Rightarrow m=5[/tex]Now, using the slope and one point of the line, we replace in the following expression:
[tex]y-y_1=m(x-x_1)[/tex]We can use any point of the line, but I will be using the point (1, 1), that is:
[tex]y-1=5(x-1)[/tex]Now, we solve for y:
[tex]\Rightarrow y-1=5x-5\Rightarrow y=5x-4[/tex]Let f(x) = 8x^3 - 3x^2Then f(x) has a relative minimum atx=
1) To find the relative maxima of a function, we need to perform the first derivative test. It tells us whether the function has a local maximum, minimum r neither.
[tex]\begin{gathered} f^{\prime}(x)=\frac{d}{dx}\mleft(8x^3-3x^2\mright) \\ f^{\prime}(x)=\frac{d}{dx}\mleft(8x^3\mright)-\frac{d}{dx}\mleft(3x^2\mright) \\ f^{\prime}(x)=24x^2-6x \end{gathered}[/tex]2) Let's find the points equating the first derivative to zero and solving it for x:
[tex]\begin{gathered} 24x^2-6x=0 \\ x_{}=\frac{-\left(-6\right)\pm\:6}{2\cdot\:24},\Rightarrow x_1=\frac{1}{4},x_2=0 \\ f^{\prime}(x)>0 \\ 24x^2-6x>0 \\ \frac{24x^2}{6}-\frac{6x}{6}>\frac{0}{6} \\ 4x^2-x>0 \\ x\mleft(4x-1\mright)>0 \\ x<0\quad \mathrm{or}\quad \: x>\frac{1}{4} \\ f^{\prime}(x)<0 \\ 24x^2-6x<0 \\ 4x^2-x<0 \\ x\mleft(4x-1\mright)<0 \\ 0Now, we can write out the intervals, and combine them with the domain of this function since it is a polynomial one that has no discontinuities:[tex]\mathrm{Increasing}\colon-\infty\: 3) Finally, we need to plug the x-values we've just found into the original function to get their corresponding y-values:[tex]\begin{gathered} f(x)=8x^3-3x^2 \\ f(0)=8(0)^3-3(0)^2 \\ f(0)=0 \\ \mathrm{Maximum}\mleft(0,0\mright) \\ x=\frac{1}{4} \\ f(\frac{1}{4})=8\mleft(\frac{1}{4}\mright)^3-3\mleft(\frac{1}{4}\mright)^2 \\ \mathrm{Minimum}\mleft(\frac{1}{4},-\frac{1}{16}\mright) \end{gathered}[/tex]4) Finally, for the inflection points. We need to perform the 2nd derivative test:
[tex]\begin{gathered} f^{\doubleprime}(x)=\frac{d^2}{dx^2}\mleft(8x^3-3x^2\mright) \\ f\: ^{\prime\prime}\mleft(x\mright)=\frac{d}{dx}\mleft(24x^2-6x\mright) \\ f\: ^{\prime\prime}(x)=48x-6 \\ 48x-6=0 \\ 48x=6 \\ x=\frac{6}{48}=\frac{1}{8} \end{gathered}[/tex]Now, let's plug this x value into the original function to get the y-corresponding value:
[tex]\begin{gathered} f(x)=8x^3-3x^2 \\ f(\frac{1}{8})=8(\frac{1}{8})^3-3(\frac{1}{8})^2 \\ f(\frac{1}{8})=-\frac{1}{32} \\ Inflection\: Point\colon(\frac{1}{8},-\frac{1}{32}) \end{gathered}[/tex]Given the formula for the nth term, state the first 5 terms of each sequence.t1= 800, tn= -0.25tn-1
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
t1 = 800
tn = - 0.25 tn-1
Step 02:
sequence:
t1 = 800
t2 = -0.25 (800) = - 200
t3 = -0.25 (-200) = 50
t4 = -0.25 (50) = -12.5
t5 = - 0.25 (-12.5) = 3.125
The answer is:
t1 = 800
t2 = - 200
t3 = 50
t4 = -12.5
t5 = 3.125
help me pleaseeeeeeeee
The values of given functions f(-2), f(0) and f(7) when f(x) = 1-6x are 13, 1 and -41 respectively.
According to the question,
We have the following function:
f(x) = 1-6x
Now, we can find the values of each function by putting the numbers in place of x.
Now, in order to find the value of f(-2), we will put -2 in place of x in the given function.
f(-2) = 1-6*(-2)
f(-2) = 1+12
f(-2) = 13
Now, in order to find the value of f(0), we will put 0 in place of x in the given function.
f(0) = 1-6(0)
f(0) = 1-0
(We know that when a number is multiplied with 0 then the result is always 0.)
f(0) = 1
Now, in order to find the value of f(7), we will put 7 in place of x in the given function.
f(7) = 1-6*7
f(7) = 1-42
f(7) = -41
Hence, the values of f(-2), f(0) and f(7) are 13, 1 and -41 respectively.
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the area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.
The formula is
[tex]A=\frac{(a+b)\cdot h}{2}[/tex]To solve for b, first, we multiply the equation by 2
[tex]\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}[/tex]Then, we divide the equation by h
[tex]\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}[/tex]At last, we subtract a from each side
[tex]\frac{2A}{h}-a=a-a+b[/tex]Hence, the final expression is[tex]b=\frac{2A}{h}-a[/tex]The probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, what is the probability that two or more of them will fail the test
If the probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, then the probability that two or more of them will fail the test is 0.41
The probability of failing a test = 0.115
Total number of people = 12
We have to find the probability that two or more of them will fail the test
We know the binomial distribution
P(X≥2) = 1 - P(X<2)
= 1 - P(X=0) - P(X=1)
P(X≥2)= 1 - [tex](12C_{0}) (0.115^0)(1-0.115)^{12}[/tex] - [tex](12C_{1}) (0.115^1)(1-0.115)^{11}[/tex]
= 0.41
Hence, if the probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, then the probability that two or more of them will fail the test is 0.41
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Q1 of the numbers 5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
Answer
Q1 = 10
Explanation
To ontain the Q1, we need to first make sure the numbers are arranged in ascending or descending order.
5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
Q1 is the number that occurs at the (N + 1)/4 position for the distribution.
N = Number of variables = 11
Q1 = (N + 1)/4
Q1 = (11 + 1)/4 = (12/4) = 3rd variable.
5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
The 3rd variable = 10
Hope this Helps!!!
Answer:
10
Step-by-step explanation:
i'm drinking boba and am to lazy to explain.
Please tell me if these are correct if theyre not please help and tell me which ones are the right answers
Answer:
They're correct
Step-by-step explanation:
The measure of angle c below is(Hint: Slide 2)95/640
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the right triangle of the figure
we have
c+d+64=180
we have that
d=90 degrees (right angle)
substitute
c+90+64=180
c+154=180
c=180-154
c=26 degrees
Ex) The function f(x) is shown on the graph. Plot two points on this grid to create the graph of the line that would represent f(x) - 2.
ANSWER and EXPLANATION
We have the graph of the function f(x) given.
We want to find 2 points that will represent f(x) - 2.
This (f(x) - 2) is a transformation of the function f(x).
It is called a vertical translation. It means that the function moves on the y axis.
It is generally represented as:
f(x) + b
Comparing the required translation with the general form, we can conclude that there is a -2 shift on the y axis.
Therefore, to find two points for the new function, we have to simply pick two points from the given graph and subtract 2 from their y coordinates.
Let the two points be:
(0, 1) and (-4, 4)
Therefore, the two points will be:
(0, 1) => (0, 1 - 2) = (0, -1)
(-4, 4) => (-4, 4 - 2) = (-4, 2)
Plotting them:
The green line is the line of the new function.
Determine the prime factorization of 350
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define Prime factorization.
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Examples of prime numbers are 2,3,5,7...etc.
STEP 2: Find the prime factors of the given number
Prime factorization of any number means to represent that number as a product of prime numbers.
We start by dividing the number by the lowest possible prime numbers.
STEP 3: Express 350 as a product of its prime factors
[tex]\begin{gathered} \text{Prime factors}=2,5,5,7 \\ \text{Product of prime factors=}2\times5\times5\times7 \\ =2\times5^2\times7 \end{gathered}[/tex]Hence, the prime factorization of 350 is given as:
[tex]2\times5^2\times7[/tex]In 1980 approximately 4,825 million metric tons of carbon dioxide emissions were recorded for the United States. That number rose to approximately 6,000 million metric tons in the year 2005. Here you have measurements of carbon dioxide emissions for two moments in time. If you treat this information as two ordered pairs (x, y), you can use those two points to create a linear equation that helps you make predictions about the future of carbon dioxide emissions!A) Organize the measurements into ordered pairs. B) Find the slope,C) Set up an equation in point-slope form,D) Show the equation in slope-intercept form,E) Predict emissions for the year 2020,
ANSWER and EXPLANATION
A) To organize the measurements in ordered pairs implies that we want to put them in the form:
[tex](x_1,y_1);(x_2,y_2)[/tex]Therefore, the measurements in ordered pairs are:
[tex]\begin{gathered} (1980,4825) \\ (2005,6000) \end{gathered}[/tex]Note: 4825 and 6000 are in millions (10⁶) of metric tons
B) To find the slope, apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m=\frac{6000-4825}{2005-1980} \\ m=\frac{1175}{25} \\ m=47\text{ million metric tons per year} \end{gathered}[/tex]C) To find the in point-slope form, we apply the formula:
[tex]y-y_1=m(x-x_1)_{}[/tex]Therefore, we have:
[tex]y-4825=47(x-1980)[/tex]Note: the unit is in million metric tons
D) To show the equation in point-slope form, we have to put it in the form:
[tex]y=mx+b[/tex]To do that, simplify the point-slope form of the equation:
[tex]\begin{gathered} y-4825=47(x-1980) \\ y=47x-93060+4825 \\ y=47x-88235 \end{gathered}[/tex]E) To predict the emissions for the year 2020, substitute 2020 for x in the equation above:
[tex]\begin{gathered} y=47(2020)-88235 \\ y=94940-88235 \\ y=6705\text{ million metric tons} \end{gathered}[/tex]That is the prediction for the year 2020.
If ¼ gallon of paint covers 1/12 of a wall, then how many quarters of paint are needed for the entire wall?
We know that
1 quarter gallon of paint ⇄ 1/12 wall
?? ⇄ 1 wall
Now we just divide both sides of the equivalence
[tex]\begin{gathered} \frac{1}{?}=\frac{\frac{1}{12}}{1} \\ \frac{1}{?}=\frac{1}{12} \end{gathered}[/tex]We clear the equation in order to find the unkown value
[tex]\begin{gathered} \frac{1\cdot12}{1}=\text{?} \\ 12=\text{?} \end{gathered}[/tex]Then, we need 12 quarters of paintwhen taking a 19 question multiple choice test ,where each question has 3 possible answers ,it would be unusual to get or more questions correct by guessing alone consider "unusual " to be more than two standard deviations away from expected.
we have that
You have 1 in 3 probability of guessing the correct answer for a single question
you have 19 opportunities to guess
so
19*(1/3)=19/3=18/3+1/3=6 1/3
therefore
would be unusual to get 7 or more questions correct by guessing alone
