Answer:
[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls
Step-by-step explanation:
The selection is from a sample without replacement, so we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
All girls from the first group:
20 students, so [tex]N = 20[/tex]
10 girls, so [tex]k = 10[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_1 = P(X = 5) = h(5,20,5,10) = \frac{C_{10,5}*C_{10,5}}{C_{20,5}} = 0.0163[/tex]
All girls from the second group:
20 students, so [tex]N = 20[/tex]
5 girls, so [tex]k = 5[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_2 = P(X = 5) = h(5,20,5,5) = \frac{C_{5,5}*C_{15,5}}{C_{20,5}} = 0.00006[/tex]
All girls from the third group:
20 students, so [tex]N = 20[/tex]
8 girls, so [tex]k = 8[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_3 = P(X = 5) = h(5,20,5,8) = \frac{C_{8,5}*C_{12,5}}{C_{20,5}} = 0.0036[/tex]
All 15 students are girls:
Groups are independent, so we multiply the probabilities:
[tex]P = P_1*P_2*P_3 = 0.0163*0.00006*0.0036 = 3.52 \times 10^{-9}[/tex]
[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls
solve d+7=13 please!!!
Answer:
d=6
Step-by-step explanation:
d+7=13
-7 -7
-----------
d=6
Answer:
hi
Step-by-step explanation:
[tex]d + 7 = 13 \\ d = 13 - 7 \\ d = 6[/tex]
have a nice day bye
Use the distributive property to create an equivalent expression for -6(7t - 4). Make sure you answer is in the form shown below
Answer:
-42t + 24
Step-by-step explanation:
-6(7t-4)= -42t + 24
-6 x 7t = -42t
-6 x -4 = +4
Pls solve this
A) 16
B) 8
C) 4
D) 2
A recent drug survey showed an increase in use of drugs and alcohol among local high school students as compared to the national percent. Suppose that a survey of 100 local youths and 100 national youths is conducted to see if the percentage of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them.
Required:
Conduct a hypothesis test at the 5% level.
Answer:
We fail to reject H0
Step-by-step explanation:
Null hypothesis : H0 : Plocal ≤ Pnational
Alternative hypothesis : H1 : Plocal > Pnational
Plocal = P1 = 65/100 = 0.65
Pnational = P2 = 61/100 = 0.61
n1 = 100 ; n2 = 100
Mean, m = P1 - P2 = 0.65 - 0.61 = 0.04
The standard deviation : = sqrt(Variance)
Variance = P1(1 - P1) /n1 + P2(1 - P2) /n2
Variance = 0.65(0.35)/100 + 0.61(0.39)/100
Variance = 0.002275 + 0.002379 = 0.004654
Standard deviation (s) = √(0.004654) = 0.06822
Z = m/s = 0.04 / 0.06822 = 0.586
Using the p-value from Z score calculator :
Hence, Pvalue for a Zscore 0.586 at 5% = 0.278938
Since ;
P-value is > α ; 0.278938 > 0.05
Then we fail to reject H0
1. Use the Pythagorean
Theorem to determine if a
triangle with side lengths 6ft.,
6ft., 8ft. is a right triangle.
Answer:
Not a right triangle
Step-by-step explanation:
[tex] {6}^{2} + {6}^{2} = 36 + 36 = 72...(1) \\ \\ {8}^{2} = 64....(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ {6}^{2} + {6}^{2} \neq {8}^{2} \\ \\ [/tex]
Hence, triangle with side lengths 6ft.,
6ft., 8ft. is not a right triangle.
The population of a town is increasing by 2% each year. The current population is 12,000. How many people will there be in 4 years?
Answer:
12989 people
Step-by-step explanation:
f(x)=a(1+r)^x
a= the amount you start with
r=is the rate that it is growing
x= time intervals
12000(1+0.02)^4=12989
What is the slope of the line below?
(2, 2)
(1,-1)
A. negative
B. positive
C. Zero
D. undefined
Please answer
(Will give brainlst)!!
Answer:
D
Step-by-step explanation:
Should work i got and 80 on that one
2 points
4. In 2016, a school started its own aquarium with x fish. In 2019, there
were x^2 fish in the same aquarium. There were 144 fish in 2019. How
many fish were there in 2016? Show your work *
Answer:
171 fish
Step-by-step explanation:
512/3=170.667 (keeps going on but I just rounded it to add 1 to the total of 170) so that is why 171 is the answer.
Please help with my question
V=1/3pir2h h = what ?
Answer:
(3/1)V=(3/1)(1/3pir^2h) 3V=pir^2h (1/pi)(3V)=(1/pi)(pir^2h) 3V/pi=r^2h (1/r^2)(3V/pi)=(1/r^2)(r^2h) 3V/pir^2=h . Check by plugging (h=3V/pir^2)
Step-by-step explanation:
Can someone guide me through this progress?
Oliva buys a 5-piece living room set from a furniture store offering 0% interest for 9 months. Calculate the average monthly payment she should make to avoid paying deferred interest charges for the $4,999 set.
A.
$277.72
B.
$416.58
C.
$555.44
D.
$833.17
4/5x 2 1/3
Simplify and write the steps thanks:)
How can I solve this problem?
In triangle ABC, the size of angle B is 4 times the size of angle A, and the size of
angle C is 1° less than 5 times the size of angle A.
Find the size of the angles.
Answer:
A=18.1, B=72.4, and C=89.5
Step-by-step explanation:
Where A, B and C represent their respective angles:
We are given that:
B=4A
C=5A−1
And since ABC make up a triangle, we know that:
A+B+C=180
Since we have three variables and three equations, we can solve for A, B, and C. To solve for A:
Take the equations B=4A and C=5A−1, and plug B and C into the last equation:
A+B+C=180
A+4A+5A−1=180
10A – 1 + 1 = 180 + 1
10A=181
10 /10 x A = 181/10
A = 18.1
Then we can plug this value into the first two equations to solve for B and C:
B=4A
B=4(18.1)=72.4
C=5A−1
C=5(18.1)−1= 90.5 - 1=89.5
So A=18.1, B=72.4, and C=89.5
Hope this helps!
The size of ∠A is 18.1°.
The size of ∠B is 72.4°.
The size of ∠C is 89.5°.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle ABC
∠A = x
∠B = 4x
∠C = 5x - 1
Now,
The sum of all the angles in a triangle is 180.
This means,
x + 4x + 5x - 1 = 180
10x - 1 = 180
10x = 181
x = 18.1
Now,
∠A = 18.1°
∠B = 4 x 18.1 = 72.4°
∠C = 5 x 18.1 - 1 = 89.5°
Thus,
The sizes of the angles are:
18.1°, 72.4°, and 89.5°
Learn more about triangles here:
https://brainly.com/question/25950519
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4. Tisha has two bags of marbles like the ones
shown below.
Bag 1
Bag 2
Blue
Blue
Yellow
Red
Blue
Blue
Rod
Blue
Yellow
Red
Tisha will randomly select 1 marble from each
bag. What is the probability that Tisha will select
a blue marble from each bag?
Answer:
A. 0.25
B. 0.5
C. 0.6
D. 0.1
Please help
Answer:
0.25
Step-by-step explanation:
Bag 1 :
Number of marbles = 6
Number of Blue marbles = 3
Bag 2:
Number of marbles = 4
Number of Blue marbles = 2
Recall :
Probability = required outcome / Total possible outcomes
For Bag 1:
P(blue) = Number of Blue marbles / total marbles
P(blue) = 3 / 6 = 1/ 2
For Bag 2:
P(blue) = Number of Blue marbles / total marbles
P(blue) = 2 / 4 = 1/ 2
Probability of a picking a blue marble from each bag :
1/2 * 1/2 = 1/4 = 0.25
Mid-Mod 3 Review
Name
1 Lisa used 5 orange juice containers, From the fust container, she poured out gallon of
orange juice. She then poured out 'h gallon from each of the four remaining containers,
a. How much orange juice did Lisa pour out in all? Show and label all your work.
-3(4s-1)-3=-3(6s+6)-3
Answer:
I think its 6 not sure
Step-by-step explanation:
The product of a real number and another real number that is 6 less than the first equals 6. What are the numbers?
Answer:
[tex]3+\sqrt{15} \\3-\sqrt{15}\\[/tex]
Step-by-step explanation:
if ax=6 and a = x-6...
x(x-6) = 6
Completing the square is a process such that [tex](x^2+2bx)=(x+b)^2-b^2[/tex]
Ignoring leap days, the days of the year can be numbered 1 to 365. Assume that birthdays are equally likely to fall on any day of the year. Consider a group of 10 people, of which you are not a member. The sample space consists of all possible sequences of 10 birthdays (onefor each person).
a. Define the probability function P for S.
b. Consider the following events:
1. "someone in the group shares your birthday";
2. "some two people in the group share a birthday";
3. "some three people in the group share a birthday". Carefully describe the subset of S that corresponds to each event.
c. Find an exact formula for P(A). What is the smallest m such that P(A) > .5?
d. Justify why m is greater than 365 without doing any computation. (We 3 are looking for 2 a short answer giving a heuristic sense of why this is so.)
e. Find an exact formula for P(B).
Answer:
Follows are the solution to the given question:
Step-by-step explanation:
They can count the days of the year 1 to 365. The random project consists of drawing a sample of n objects from D where elements are n people's birth in a group but instead, D = {1,....365}. And then there's the issue.
[tex]S=365^n[/tex]
This because the list of future birthdays of n people was its test point; therefore m points will be in the sequence so each point contains 365 distinct outcomes. The probability function P for \Omega is that any event is likely to happen in 365 days.
[tex]P(x)=\frac{1}{365^{n}}[/tex]
if x is between 1 and 365 as well as the occurrence is just all similarly possible
In point i:
That somebody mentions their birthday throughout the party
Guess I was born on day b. Therefore the consequence of "x is in A" is "b is now in the series of x," which is to say, b = bk for some amount k approximately 1 and n.
In point ii:
Any 2 persons share the same birthday at this party". A result x is in B" means which "two of entries in x are same." This means that perhaps the outcome x is in B if or only if bj = bk is in B of two numbers j, and k of 1, of two. , no, n.
In point iii:
Many three students share the same birthday with both the party. The consequence is x at the level of C only when bj = bk = bl at three (different) indices, j, k, l, 1. , no, n.
3. Technology required. Gateway Arch in St. Louis, Missouri, is 630 feet tall. Priya can look
up at a 50 degree angle to see the top of the arch. How far away from the base of the
arch is she standing?
Priya is standing 528.63 feet away from the base of Gateway Arch in St. Missouri.
What is trigonometry?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given parameters:
Height of the Gateway Arch in St. Missouri = 630 feet.
Priya have to look up at a 50° angle to see the top of the arch.
Now from definition of tanθ in trigonometry:
tan50° = height of the Gateway Arch in St. Missouri ÷ distance of Gateway Arch in St. Missouri
hence, distance of Gateway Arch in St. Missouri = height of Gateway Arch in St. Missouri ÷ tan50°
= 630 feet ÷ tan50°
= 528.63 feet.
Hence, she is standing 528.63 feet away from the base of Gateway Arch in St. Missouri.
Learn more about trigonometry here:
https://brainly.com/question/29002217
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rewrite a^5 x a^-3 in the form a^n
Answer:
The answer is A^2
Step-by-step explanation:
When you are dividing, You subtract exponents if they have the same base.
The base (variables) are the same. So you subtract the powers.
Which are 5 and -3. You subtract those two powers 5 minus negative -3 which gives you 2. So it's a^-2
Sorry for the long explanation I hope you understand it. And if I made it harder to understand the answer sorry oops have a good day and stay safe ;D.
Estimate. −49100+1021= ________
Answer:
-48079
Step-by-step explanation:
-(49100-1021)
-48079
PLEASE HELP !!! ILL GIVE BRAINLIEST!! *DONT SKIP* ILL GIVE 40 POINTS.
Answer:
-35 i think
Step-by-step explanation:
hope dis helps
Can you please help me understand this question please?
Answer:
B
u just subsitute in each inequality form and so u will find the only one that is right is letter b
-4 is x
-2 is y
6. ¿Cuál de los siguientes polígonos tiene el mayor área? A. Un rectángulo que mide 3.25 pulgadas de ancho y 6.1 pulgadas de largo.
B. Un cuadrado con lado de longitud 4.6 pulgadas.
C. Un paralelogramo con una base de 5.875 pulgadas y una altura de 3.5 pulgadas.
D. Un triángulo con una base de 7.18 pulgadas y una altura de 5.4 pulgadas.
Answer:
1.A
Step-by-step explanation:
yan po ang Tama po ang sagot..ko
three corners of a square are (1, 7), (5, 3), and (9, 7). What are the coordinates of the fourth corner of the square?
Answer:
i think the answer is 8
Step-by-step explanation:
Answer:(13, 3)
maybe
Hope it helps
How do you do these questions?
Answer:
a) - 7 dollars
b) 24.30 dollars
c) - 5 dollars
Step-by-step explanation:
b) 27 / 10%
Divide 27 by 10/100 by multiplying 27 by the reciprocal of 10/100.
27 x 100/10
Multiply 27 and 100 to get 2700.
2700/10
Divide 2700 by 10 to get 270.
270
Divide 270 by 100 to get 2.7
Subtract 27.00 - 2.7 = 24.30
24.30
PLEASE HELP ME 20 POINTS + BRAINLIEST
Answer:
C
Step-by-step explanation:
By tracing the figure, we see that we go around a semicricle twice and go in a straight path twice. So the perimeter of this figure consists of two semicircles and two line segments, hence the answer is C.