Answer:
28. 0.2461 or 24.61%.
29. 0.00058275 or 0.058275%.
Step-by-step explanation:
Question 28:
we can use the binomial probability formula to calculate the probability:
[tex]\boxed{\bold{P(X = k) = (nCk) * p^k * (1 - p)^(n - k)}}[/tex]
Where:
P(X = k) is the probability of getting exactly k successesnCk is the number of combinations of n items taken k at a timep is the probability of a single successn is the total number of trialsIn this case, we have n = 9 babies, and each baby has a 50% chance of being a girl (p = 0.5). We want to find the probability that exactly 4 of them are girls (k = 4).
Using the formula, we can calculate the probability as follows:
[tex]\bold{P(X = 4) = (9C4) * (0.5)^4 * (1 - 0.5)^(9 - 4)}[/tex]
Calculating the values:
(9C4) = 126 (0.5)^4 = 0.0625(1 - 0.5)^(9 - 4) = 0.5^5 = 0.03125Now, we can substitute these values into the formula:
P(X = 4) = 126 * 0.0625 * 0.03125 = 0.2461 or 24.61%
Therefore, the probability that exactly 4 out of 9 babies are girls is approximately 0.2461 or 24.61%.
Question 29:
We need to calculate the number of possible outcomes to calculate this probability, where the gambler correctly predicts the top 3 finishers in order and divides it by the total number of possible outcomes.
The total number of possible outcomes is the number of permutations of 13 horses taken 3 at a time.
This can be calculated as:
[tex]13P3 = \frac{13! }{(13 - 3)! }= \frac{13! }{ 10! }=\frac{13*12*11*10! }{ 10! }= 13 * 12 * 11 = 1,716[/tex]
Now,
To calculate the number of favorable outcomes where the gambler predicts the top 3 finishers correctly, we need to consider that there is only one correct order for the horses to finish.
Therefore, there is only one favorable outcome.
The probability of the gambler winning his bet is given by:
[tex]\boxed{\bold{P\:(winning) = \frac{Number\: of \:favorable\: outcomes }{ Total \:number \:of \:outcomes}}}[/tex]
[tex]P(winning) = \frac{1 }{1,716}=0,00058275 \: or\:0.058275%[/tex]
Therefore, the probability that the gambler will win his bet is approximately 0.00058275 or 0.058275%.
Answer:
28) 0.246 = 24.6%
29) 1/286 = 0.350%
Step-by-step explanation:
Question 28We can model the given scenario as a binomial distribution.
Binomial distribution[tex]X \sim \text{B}(n,p)[/tex]
where:
X is the random variable that represents the number of successes.n is the fixed number of independent trials.p is the probability of success in each trial.Given the probability that a baby is born a girl is 0.5, and the number of babies is 9:
[tex]\boxed{X \sim \text{B}(9,0.5)}[/tex]
where the random variable X represents the number of babies who are girls.
To find the probability that at exactly 4 babies are girls, we need to find P(X = 4).
To do this, we can use the binomial distribution formula:
[tex]\boxed{\displaystyle \text{P}(X=x)=\binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}}[/tex]
Substitute the values of n = 9, p = 0.5 and x = 4 into the formula:
[tex]\begin{aligned}\displaystyle \text{P}(X=4)&=\binom{9}{4} \cdot 0.5^4 \cdot (1-0.5)^{9-4}\\\\&=\dfrac{9!}{4!\:(9-4)!} \cdot 0.5^4 \cdot 0.5^{5}\\\\&=126 \cdot 0.0625 \cdot 0.03125\\\\& = 0.24609375\end{aligned}[/tex]
Therefore, the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.
We can also use the binomial probability density function of a calculator to calculate P(X = 4).
Inputting the values of n = 9, p = 0.5 and x = 4 into the binomial pdf:
[tex]\text{P}(X=4)=0.24609375[/tex]
Therefore, this confirms that the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.
[tex]\hrulefill[/tex]
Question 29To calculate the probability that the gambler will win his bet, we need to determine the number of favorable outcomes (winning combinations) and the total number of possible outcomes.
The gambler wins if he picks the top three horses in any order. There are 6 ways for the three winners to be arranged in the top three.
There are a total of 13 horses in the race.
The number of ways to choose the first-place horse is 13. After the first-place horse is chosen, there are 12 remaining horses, so the number of ways to choose the second-place horse is 12. Finally, after the first two horses are chosen, there are 11 remaining horses, so the number of ways to choose the third-place horse is 11.Therefore, the total number of possible outcomes is:
[tex]13 \times 12 \times 11 = 1716[/tex]
Therefore, the probability that the gambler will win his bet is:
[tex]\begin{aligned} \sf Probability &=\sf \dfrac{Favorable \;outcomes}{Total\;outcomes}\\\\&=\dfrac{6}{1716}\\\\&=\dfrac{1}{286}\\\\ & \approx0.350\%\; \sf (3\;d.p.)\end{aligned}[/tex]
how to graph an inequality y<1-2x
Answer:
Step-by-step explanation:
Find shaded area. Please help!
Answer:
Area of shaded region = 70.88 unit
Step-by-step explanation:
Given:
Height of shaded region = 12 units
Width of shaded region = 8 units
Find:
Area of shaded region
Computation:
Radius of semi circle = Width of shaded region / 2
Radius of semi circle = 8 / 2
Radius of semi circle = 4 unit
Area of shaded region = Area of rectangle - Area of Semi circle
Area of shaded region = [l x b] - [πr² / 2]
Area of shaded region = [12 x 8] - [(3.14)(4)² / 2]
Area of shaded region = 96 - [(3.14)(16) / 2]
Area of shaded region = 96 - 25.12
Area of shaded region = 70.88 unit
Match the vocabulary to the proper definition.
1. a conclusion based on the results of evidence
2. a question that leads individuals towards a certain answer
the collection, organization, and analysis of numerical
3.
information
a sample in which every member of the population has an
4.
equal chance of being selected; unbiased sample
5. a sampling of a population used to make predictions
Answer:
I got an answer
Step-by-step explanation:
1 is inference
2 is biased question as individuals are lead towards an answer that aligns with what the one who made the question wants
3 is statistics
4 is random
5 is survey
whats 1+1 because i think its 11
Answer:
2
Step-by-step explanation:
when i have one fruit and you have another fruit and we add them together they are gonna b two
Sales volume last weekend for four samples, each consisting of five car dealerships, were as follows: Data Point 1 2 3 4 5 Sample 1 21 10 19 35 23 Sample 2 34 44 29 15 30 Sample 3 38 22 29 31 15 Sample 4 47 39 20 16 36 What is the mean of the distribution of sample means
Answer:
Mean of sample means = 22.12
Step-by-step explanation:
Data points 1 2 3 4 5 Sample mean
Sample 1 21 10 19 35 23 21.6
Sample 2 34 44 29 15 30 30.4
Sample 3 38 22 29 31 15 27
Sample 4 47 39 20 16 36 31.6
[tex]Mean of means = \frac{Sum of sample means}{No. of samples}[/tex]
[tex]=\frac{21.6 + 30.4 + 27 + 31.6 }{5} \\= 22.12[/tex]
Answer:
22.12
Step-by-step explanation:
Hope this helps
A package contains 6 cups of cereal. Each serving is 1/4 cup of cereal. How many serving are there in all?
Answer:
1 and 2/4 I think
Step-by-step explanation:
Answer: 24
Step-by-step explanation: 4•(1/4)=1
4•6=24
Marcelo can select from 2 types of oranges and 3 types of peaches. If he randomly selects 1 orange and 1 peach, how many possible choices does he have? ___________ possible choices
Answer:
6 choices
Step-by-step explanation:
Bob mixed 5/8 cup of water and 1/8 cup of lemon juice in a cup. The rest of the mixture was lime juice. How much lime juice did Bob add if the cup was full?
Answer: thats a good question
Step-by-step explanation:
Answer: he will add 2/8 more so it can be full.
Step-by-step explanation: you divide 2/8 by 5/8 and you'll get 1/8.
please give me brainlest
What is the answer please help no links no links please help
Helppp me plsssssss I need this hel me out
take your time please.
Step-by-step explanation:
6/5(4)=24/20
1/2(5)=5/10
3/9(7)=21/63
3/8(5)=15/40
4/3(9)=36/27
2/4(8)=16/32
9/6(2)=18/12
7/5(6)=42/30
4/7(3)=12/21
In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 536 said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12.
a. Test, at the 5% significance level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%.
b. Is the Test Significant? Why or Why not.
Answer:
Yes, result is significant ; PVALUE < α
Step-by-step explanation:
Given :
x = 536
n = sample size = 1012
Phat = x / n = 536 / 1012 = 0.5296 = 0.53
H0 : P0 = 0.5
H1 : P0 > 0.5
Test statistic :
(Phat - P0) ÷ sqrt[(P0(1 - P0)) / n]
1-P0 = 1 - 0.5 = 0.5
(0.53 - 0.5) ÷ sqrt[(0.5*0.5)/1012]
0.03 ÷ 0.0157173
= 1.9087
Pvalue :
Using the Pvalue from test statistic :
Pvalue = 0.02815
To test if result is significant :
α = 0.05
0.02815 < 0.05
Pvalue < α ; Hence, result is significant at α=0.05; Hence, we reject H0.
The relative growth rate for a certain type of bacteria population is 78% per hour. A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture. What is the initial number of bacteria in the culture? us this formula to solve it and show all work A(t) = Pe^(rt).
Step-by-step explanation:
A(t)=P(e^(rt))
Insert the values as follows:
The equation for "continual" growth (or decay) is A = Pe^(rt), where "A", is the ending amount, "P" is the beginning amount (principal, in the case of money), "r" is the growth or decay rate (expressed as a decimal), and "t" is the time (in whatever unit was used on the growth/decay rate).
34820=P(e^((.78)(5)))
34830=P(49.4024)
704.82335
Hope that helps :)
which of the following is the quotient of the rational expression shown below? x/3x-1 ÷ x-2/2x
Step-by-step explanation:
[tex] \frac{x}{3x - 1} \div \frac{x - 2}{2x} = \\ = \frac{x}{3x - 1} \times \frac{2x}{x - 2} = \\ = \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2} [/tex]
What probability statement would you add to P(blue) = 1 10 to make a complete probability model for the event choosing a foam ball at random from the box?
Answer:
The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner.
need answers 2 and 3
Answer:
2. 10^38, or 10 to the power of 38.
3. 10^15, or 10 to the power of 15.
Step-by-step explanation:
2. If you are multiplying two individual 10's with each having its own power, add the powers together to form an answer. DO NOT ADD THE 10'S TOGETHER!!! Since 10^32 is being multiplied by 10^6, you would write it as 10^38.
3. Because you have 10 cubed inside the bracket, with an exponent of 5 outside of the bracket, you multiply the brackets together. DO NOT MULTIPLY 10!!! So, 5 x 3 equals 15, You would get 10^15.
At a camp with 300 campers and 15 counselors, what is the camper-counselor ratio?
Answer:
300:15 = 100:5 = 20:1
Answer = 20:1
The function, f(x), is plotted below.
Evaluate the limits, if they exist. If not, write DNE.
Limit as x approaches negative 1 minusf(x) =
Limit as x approaches 3 plusf(x) =
Limit as x approaches 1 f(x) =
Answer:
1
2
DNE
Step-by-step explanation:
Select the correct an
Sally rents a life jacket for a one-time fee of $5. She then
rents a canoe for $15 per hour. Which expression
represents the total cost, in dollars, to rent the life jacket
and the canoe for h hours?
A. 5+15h
OB. 10h
C. 15+5h
OD. 20h
Answer: The answer for this question is "A": 5 + 15h
Jordan performed an experiment using a number cube. He rolled a number cube 50 times. He found that he rolled a 6 a total of 8 times. What is the experimental probability that he did not roll a 6?
Answer:
Step-by-step explanation:
Total number of rolls = 50
Number of times rolling a 6 = 8 times
Number of times not rolling a 6 = 50 -8 = 42
P(~6) = 42/50 = 0.84
Classify the following triangle. Check all that apply. 60° 8.4 4.2 30" 7.3 A. Acute B. Equilateral C. Obtuse D. Scalene E. Isosceles O F. Right
The given triangle is a right triangle and a scalene triangle.
What is a scalene triangle?A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.
It does not have equal sides. No equivalent angles exist. It lacks a symmetry line. No point symmetry exists. This triangle can have acute, obtuse, or right angles inside of it.
In the given triangle we see that one angle measure is 90 degrees thus, the triangle is a right triangle.
Also, all the sides of the triangle have different lengths. thus the triangle is also a scalene triangle.
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Draw a plane intersecting a cube to get the cross section indicated. rectangle
OA
OB
OC
OD
Please Help! SCAMMERS WILL BE REPORTED! Use Cramer's Rule to solve the following system
-2x- 6y = -26
5x + 2y = 13
Answer:
x=1,y=4
Step-by-step explanation:
x=1,y=4
Q: Find six rational numbers between 3 and 4 .
Answer:
Six rational numbers between 3 and 4 are 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6.
Answer:
six rational numbers between 3 and 4 are 227 , 237 , 247 , 257 , 267 , 277
find the volume if the cylinder. round to the nearest tenth if nessesary.
A. 627.5m^3.
B. 843.4m^3.
C. 986.4^3.
D. 1017.9n^3
Which expression represents the distance between the two numbers on the
number line?
a. -1 + 2.5
b. -1 -2.5
c. 12.5 - (-1)
d. 12.5 -11
Answer:
B.
Step-by-step explanation:
........................
I have a bucket which I use to fill a
paddling pool
I use 19 full buckets of cold water and 8
buckets of hot water, so the pool is full.
The capacity of the pool is 288 litres.
If I poured the water from one bucket into
some glasses, I could fill 32 glasses,
What is the capacity of each glass
in millilitres?
Answer:
35
Step-by-step explanation:
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(i will mark brainly)
Use the table to write a proportion.
Answer:
One proportion is 15 songs / 2.5 hours = 18 songs / h hours.
ok I'll try to answer
first the given 15/2.5=18/h
so the second hour is missing so we have to multiply cross then the result will be
15h=45
divide 15 for 15 and we got h
again divide 45 for 15
[h=3]
Find q. q/32=6 q=? Help
Answer:
q=0
Step-by-step explanation:
Hope this helped!!
the answer is 192
Step-by-step explanation:
q/32 = 6
q = 192
One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 12% of American adults identify themselves as black. Suppose we take an SRS of 1500 American adults and let X be the number of blacks in the sample. Use a Normal distribution to estimate the probability that the sample will contain between 165 and 195 blacks.
Solution :
Given :
p = 12% = 0.12
n = 15..
Mean is defined as the product of a sample size n and the probability p such that :
[tex]$\mu_X = np = 1500 \times 0.12$[/tex]
= 180
Standard deviation may be defined as the square of a product of the sample size n, the probability p and the probability 1-p :
[tex]$\sigma_X = \sqrt{np(1-p)}$[/tex]
[tex]$\sigma_X = \sqrt{1500 \times 0.12 \times (1-0.12)}$[/tex]
≈ 12.5857
The z-score is given by :
[tex]$z=\frac {x- \mu}{\sigma } $[/tex]
[tex]$z=\frac {165-180} {12.5857 }$[/tex]
≈ -1.19
[tex]$z=\frac {x- \mu}{\sigma } $[/tex]
[tex]$z=\frac{195-180} {12.5857 }$[/tex]
≈ 1.19
Now determining the corresponding probability using table :
P (165 ≤ X ≤ 195 ) = P (-1.19 ≤ Z ≤ 1.19 )
= 1-2 x P(Z < -1.19)
= 1-2 x 0.1170
= 1-0.2340
= 0.7660
= 76.60%
Given values,
p = 12%= 0.12
n = 1500The mean will be
→ [tex]\mu x = np[/tex]
By putting the values,
[tex]= 1500\times 0.12[/tex]
[tex]= 180[/tex]
The standard deviation will be:
→ [tex]\sigma x = \sqrt{np(1-p)}[/tex]
[tex]= \sqrt{1500\times 0.12\times (1-0.12)}[/tex]
[tex]= 12.5857[/tex]
The z-score will be:
→ [tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]= \frac{165-180}{12.5857}[/tex]
[tex]= -1.19[/tex]
and,
→ [tex]z = \frac{195-180}{12.5857}[/tex]
[tex]= 1.19[/tex]
hence,
The probability will be:
→ [tex]P(165 \leq X \leq 195) = P(-1.19 \leq Z \leq 1.19)[/tex]
[tex]= 1-2\times P(Z < -1.19)[/tex]
[tex]= 1-2\times 0.1170[/tex]
[tex]= 1-0.2340[/tex]
[tex]= 0.7660[/tex]
[tex]= 76.60[/tex] (%)
Thus the answer above is right.
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