Answer:
their sizes vary
Step-by-step explanation:
their sizes vary
Suppose there is a strong positive correlation between a and b. Which of the
following must be true?
A. An increase in a causes b to decrease.
B. An increase in a causes bto increase.
C. When a increases, b tends to increase.
D. When a increases, b tends to decrease.
ANSWER ASAP WILL GIVE BRAINLIEST
Answer:
B.
Step-by-step explanation:
there is not much to explain.
a strong correlation means there is a direct connection.
so, a change in a causes immediately a change in b.
and positive means that the changes go in the same sign direction. increase => increase. decrease => decrease.
Please answer i will give you brainlest please help me
have attached the solution, couldn't solve 13 and 17 tho, if it helps, then do mark me the brainliest...
Btw, which class r u in?
Step-by-step explanation:
Solve: 3x - 1 = 8(x + 1) + 1
O A. x= -
3
5
O B. x= -2
O C. x = -
CT 00
O D. There are infinitely many solutions.
Answer:
x=-2
Step-by-step explanation:
3x-1=8x+8+1
3x-1 = 8x+9
3x-1+1=8x+9+1
3x= 8x+10
3x-8x=8x+10-8x
-5x=10
-5x ÷-5
10 ÷-5
x=-2
Happy buys 5 litres of milk on Monday and uses a fifths of it. On Tuesday she uses
half of what is left. How many millilitres are left after Tuesday?
it is 2000 ml after she drank it on Tuesday
Answer:
2000 mL
Step-by-step explanation:
1. The amount of milk left after 1/5 is drank is 4 litres, which is 4000 mL.
2. She drinks half of that, so divide 4000 mL by two.
2000 mL are left after tuesday
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
Answer:
a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.
This means that [tex]\mu = 273, \sigma = 100[/tex]
A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 30, s = \frac{100}{\sqrt{30}}[/tex]
The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = 0.88[/tex]
[tex]Z = 0.88[/tex] has a p-value of 0.8106
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.8106 - 0.1894 = 0.6212
0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 50, s = \frac{100}{\sqrt{50}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = 1.13[/tex]
[tex]Z = 1.13[/tex] has a p-value of 0.8708
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = -1.13[/tex]
[tex]Z = -1.13[/tex] has a p-value of 0.1292
0.8708 - 0.1292 = 0.7416
0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 100, s = \frac{100}{\sqrt{100}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value of 0.0648
0.9452 - 0.0648 =
0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
C is actually 0.8904
for anybody else stuck on this wondering why cengage is telling you c is wrong
Assume the random variable X is normally distributed, with mean of 50 and a standard deviation of 9. Find the 9th percentile.
Answer:
37.94
Step-by-step explanation:
the 9th percentile is equal to a zscore of -1.34
-1.34=(x-50)/9
x=37.94
1 cm = 5km scale ratio
Answer: Definition: Ratio of the size of the map to its subject: Scale ... so scale = 1 cm / 100,000 cm = 1/100,000. - Scale ... STEP 1: - 2 cm represents 5 km
Step-by-step explanation:
STEP 1: - 2 cm represents 5 km - (write in full)
- STEP 2: - 1 cm represents 2.5 km - (divide so left side = 1)
- STEP 3: - 1 cm represents 250,000 cm - (convert to same units)
- STEP 4: - scale is 1 : 250,000 - (express as a representative fraction)
determine lcm and HCF of 24 and 26 using prime factors
Answer:
WHAT IS THE FACTOR?
Step-by-step explanation:
PLEASE HELP
Fill in the blanks. Then, choose the property of addition you used.
(a)3+_= 3
(Choose one)
(b)4 + 7) + _1 = 4 + (7 + 3)
(Choose one)
(c)9+8 = 8+_
(Choose one)
Fill in the blank and choose a property
Answer:
3+ 0 = 3
( 4+7) + 3.0 × 1 = 4 + (7+3)
9 + 8 = 8 + 9
Select the correct answer from the drop-down menu.
The measure of the angle between the two sides of the roof is approximately
A. 95.8
B. 91.2
C. 92.9
A family has 5 children. Compute the probabilities of the following events:
All five are born on Friday.
Each one is born on a different day of the week.
Answer:
1/16,807 chance that they all will be born on Friday
Probably 5/7, but don't take my word for it.
Step-by-step explanation:
There are 7 days of the week.
There is a 1/7 chance for one kid to be born on a certain day of the week.
We can attach an exponent of 5 since the 1/7 is a constant, and I'm not going to bother typing the same thing over and over again.
(1/7)^5 = 1/16,807.
The probability of all of them being born on Friday or anyday is 1/16,807.
The probability of each person being born on a different day of the week is probabily going to be 5/7, but it could be different, because you need to factor in the requirement that they are not born on the same day.
I can guarantee that the first question is probably correct, but not the second.
What is the probability that something with a 2.18% chance of occurring happens 3 times out of 194 events
Answer:
0.18431525 = 18.4%
Step-by-step explanation:
General Formula :
total trials Cn⋅p(success)^n⋅p(fail)^total−n
1198144* (.0218)^3 * (1-.0218)^191
what is 221st number out of 5,6,7,8,9
Answer:
221
Step-by-step explanation:
Given sequence is ,
> 5 , 6 , 7 , 8 , 9.
The common difference is 6-5 = 1 .
Therefore , the 221st number will be
> 221 st term = 221 × 1 = 221 .
Hence the 221 st term is 221 .
Answer:
225
Step-by-step explanation:
d = 6 - 5 = 1 (common differences)
a = 5 (first term)
221st term
a+(n-1)d
5 +(221 - 1) 1
5 + 220 =225
Therefore the answer is 225
A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long
will it take for the projectile to reach the ground?
Answer:
Step-by-step explanation:
We will work in the y-dimension only here. What we need to remember is that acceleration in this dimension is -9.8 m/s/s and that when the projectile reaches its max height, it is here that the final velocity = 0. Another thing we have to remember is that an object reaches its max height exactly halfway through its travels. Putting all of that together, we will solve for t using the following equation.
[tex]v=v_0+at[/tex]
BUT we do not have the upwards velocity of the projectile, we only have the "blanket" velocity. Initial velocity is different in both the x and y dimension. We have formulas to find the initial velocity having been given the "blanket" (or generic) velocity and the angle of inclination. Since we are only working in the y dimension, the formula is
[tex]v_{0y}=V_0sin\theta[/tex] so solving for this initial velocity specific to the y dimension:
[tex]v_{0y}=35sin(35)[/tex] so
[tex]v_{0y}=[/tex] 2.0 × 10¹ m/s
NOW we can fill in our equation from above:
0 = 2.0 × 10¹ + (-9.8)t and
-2.0 × 10¹ = -9.8t so
t = 2.0 seconds
This is how long it takes for the projectile to reach its max height. It will then fall back down to the ground for a total time of 4.0 seconds.
the area of triangle
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person.
Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents.
Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
Step-by-step explanation:
Part A.....let P be the number of people that will show up.....so....
The total amount of broccoli needed (in ounces) = 8P ounces
Part B
32 = 8P divide both sides by 8
4 = P so.....4 people can be fed.....!!!
Step-by-step explanation:
My daughter had a quiz today and the 3 questions did not make sense to me. Can anyone decifer how you would solve for the variable on these? I am stumped!!
1) In 10 years, Sara will be 81 older than she is now. How old is Sara now?
2) In 8 years, Sara will be 49 years older than she is now. How old is Sara now?
3) In 11 years, Bob will be 100 years than he is now. How old is Bob now?
Answer:
1 71years
Step-by-step explanation:
x+10=81
x=71
2. x+8=49
x=41
3. x+11=100
x=99
4. Cindy purchased a pair of boots which had a sticker price of $85. Cindy paid $5.95 in sales tax. What was the tax rate on Cindy's purchase?
The system of equations y = negative one-fifth x minus 6 and y = –2x + 3 is shown on the graph below.
On a coordinate plane, 2 lines intersect at (5, negative 7).
According to the graph, what is the solution to this system of equations?
(5, –7)
(–7, 5)
(5, 7)
(7, 5)
Answer:
According to graph, solution is (5, –7)
Answer:
A) (5, –7)
Step-by-step explanation:
I got 100%, please brainlist
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.
Answer:
the operating characteristics have been solved below
Step-by-step explanation:
we have an average of 10 minutes per customers
μ = mean service rate = 60/10 = 6 customers in one hr
the average number of customers that are waiting in line
mean arrival λ = 2.5
μ = 6
[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]
= 6.25/21
= 0.2976
we calculate the average number of customers that are in the system
[tex]L=Lq+\frac{2.5}{6}[/tex]
= 0.2976+0.4167
= 0.7143
we find the average time that a customer spends in waiting
[tex]Wq=\frac{0.2976}{2.5}[/tex]
= 0.1190 hours
when converted to minutes = 0.1190*60 = 7.1424 minutes
[tex]0.1190+\frac{1}{6}[/tex]
=0.2857
probability that arriving customers would wait for the service
= 2.5÷6 = 0.4167
Can someone help me out here? Not sure how to solve this problem or where to start either?
Answer:
19.3 miles per gallon
Step-by-step explanation:
First, subtract 54,042.8-53,737.7. The answer is 305.1
Then, find the unit rate. 305.1/15.8
You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.
That's your answer!
The number of runners in the London Marathon on 25th April, 2010 was 37 527.
Work out an estimate for the number of these runners whose birthday was on that day.
Answer:
Hi 34
Step-by-step explanation:
Hi
a pie chart is divided into four sectors in fig. 12.42. Each sector represents a percentage of the whole. The two larger sectors are equal and each represents x%. What is the angle subtended by one of those larger sectors ?
Answer:
Angle formed by the sector measuring x% will be 126°.
Step-by-step explanation:
Since, sum of all sectors formed in a circle is 100%.
By adding the measures of all the sectors,
x + x + 21 + 9 = 100
2x + 30 = 100
2x = 70
x = 35%
Now we know sum of all the central angles formed at the center of a circle = 360°
Therefore, angle formed by x% = 360° × 35%
= [tex]\frac{360\times 35}{100}[/tex]
= 126°
What is the area of the sector that is not shaded?
12Pi units squared
24Pi units squared
120Pi units squared
144Pi units squared
Answer:
120Pi units squared
Step-by-step explanation:
π*12²*(360-60)/360
= π*144*300/360
= π*144*5/6
= π*720/6
= π*120
= 120π or 120Pi units squared
Answer:
120Pi units squared
Step-by-step explanation:
on edge
3p + 4q = 22
10p + 12 q = 68
What is p and what is q
(Similtaneous equations)
Answer:
q=4
p=2
Step-by-step explanation:
3p+2q=14
10p+6q=44
10(3p+2q=14)
3(10p+6q=44)
30p+20q=140-
30p+18q=132
2q=8
2q/2=8/2
q=4
3p+2*4=14
3p+8=14
3p=14-8
3p/3=6/3
p=2
hope this helps
Answer:
[tex]p=2\\q=4[/tex]
Step-by-step explanation:
One is given the following system of equations,
[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]
The fastest method to solve a system of equations is the method of elimination. This process is manipulating one of the equations, by multiplying or diving it by a value, such that one of the coefficients variables in the equation is the additive inverse of the like term in the other equation. That way, when one adds the equations, one of the variables cancels out. Then one can solve for the other term. Finally, one can back sovle by substituting the value of the solved variable into one of the equations and simplifying to find the value of the other variable.
[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]
Manipulate the first equation so that the variable (q) cancels
[tex](3p + 4q = 22) *(-3)\\\\10p + 12q = 68[/tex]
[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]
Add the equations,
[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]
[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]
Simplify,
[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]
[tex]p=2[/tex]
Backsovle for the variable (p). Substitute the values of (p) into one of the original equations. Then simplify and use inverse operations to solve for the variable (q).
[tex]3p+4q=22[/tex]
Substitute,
[tex]3(2)+4q=22[/tex]
Simplify,
[tex]3(2)+4q=22[/tex]
[tex]6+4q=22[/tex]
Inverse operations,
[tex]6+4q=22[/tex]
[tex]4q=16\\q=4[/tex]
Nine children are to be divided into an A team, a B team and a C team of 3 each. The A team will play in one league, the B team in another, the C team in a third league. How many different divisions are possible
Answer:
The answer is "840".
Step-by-step explanation:
Following are the number of ways in which selecting a team A by 9 children:
[tex]= ^{9_{C_{3}}\\\\\\[/tex]
[tex]=\frac{9!}{3! \times 6!} \\\\=\frac{9\times 8\times 7\times 6!}{3 \times 2\times 1\times 6!}\\\\=\frac{9\times 8\times 7}{3 \times 2\times 1}\\\\=\frac{3\times 4\times 7}{1}\\\\=\frac{84}{1}\\\\=84[/tex]
Following are the number of ways in which selecting a team B by remaining 6 children:
[tex]= ^{6}_{C_{3}}[/tex]
[tex]= \frac{6!}{(3! \times 3!)}\\\\= \frac{6!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{6\times 5 \times 4 \times 3!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{ 5 \times 4 \times 3!}{3!}\\\\= 5 \times 4 \\\\=20[/tex]
Following are the number of ways in which selecting a team C by remaining 3 children:
[tex]= ^{3}_{C_{3}}\\\\=\frac{3!}{3!}\\\\= 1[/tex]
Following are the number of ways in which making 3 teams by 9 children:
[tex]= \frac{(84 \times 20 \times 1)}{3!}\\\\= \frac{(84 \times 20 )}{6}\\\\= 14 \times 20\\\\= 280\\\\[/tex]
(Note: we've split by 3! Because it also is necessary to implement three teams between themselves)
Now 3 leagues have to be played. One is going to be run by each team.
That is the way it is
Different possible divisions
[tex]= 280 \times 3!\\\\= 280 \times (3 \times 2 \times 1)\\\\= 840[/tex]
Samantha acored 15 points in her laat
basketball game. She made 3 free throwa
that are worth 1 point each. The rest of
her pointa came on 2 point field goala,
Write an equation that can be used to find
the number of 2 point field goals that
Samantha made
(uae p as your variable)
Help fasttt
Answer:
15=2p+3
Step-by-step explanation:
State sales tax y is directly proportional to retail price x. An item that sells for 156 dollars has a sales tax of 14.42 dollars. Find a mathematical model that gives the amount of sales tax y in terms of the retail price x .
What is the sales tax on a 320 dollars purchase.
Answer:
The sales tax on a 320 dollars purchase is of $29.6.
Step-by-step explanation:
State sales tax y is directly proportional to retail price x.
This means that:
[tex]y = cx[/tex]
In which c is the constant of proportionality.
An item that sells for 156 dollars has a sales tax of 14.42 dollars.
This means that [tex]x = 156, y = 14.42[/tex]. We use this to find c. So
[tex]y = cx[/tex]
[tex]14.42 = 156c[/tex]
[tex]c = \frac{14.42}{156}[/tex]
[tex]c = 0.0924[/tex]
Then
[tex]y = 0.0924x[/tex]
What is the sales tax on a 320 dollars purchase?
y when [tex]x = 320[/tex]. So
[tex]y = 0.0924(320) = 29.6[/tex]
The sales tax on a 320 dollars purchase is of $29.6.
At a local community college, 57% of students who enter the college as freshmen go on to graduate. Five freshmen are randomly selected.
a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations Round your final answer to 4 decimal places Probability
b. What is the probability that at most four will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)
c. What is the expected number that will graduate? (Round your final answer to 2 decimal places)
Answer:
a) 0.0147 = 1.47% probability that none of them graduates from the local community college.
b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.
c) The expected number that will graduate is 2.85.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
57% of students who enter the college as freshmen go on to graduate.
This means that [tex]p = 0.57[/tex]
Five freshmen are randomly selected.
This means that [tex]n = 5[/tex]
a. What is the probability that none of them graduates from the local community college?
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]
0.0147 = 1.47% probability that none of them graduates from the local community college.
b. What is the probability that at most four will graduate from the local community college?
This is:
[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]
So
[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]
0.9398 = 93.98% probability that at most four will graduate from the local community college.
c. What is the expected number that will graduate?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 5*0.57 = 2.85[/tex]
The expected number that will graduate is 2.85.
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
