Answer:
0.1183 = 11.83% probability that both of them have the secret decoder ring.
Step-by-step explanation:
The boxes are chosen without replacement, which means that the hypergeometric distribution is used 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]
In this question:
63 boxes means that [tex]N = 63[/tex]
22 have the secret decoder ring, which means that [tex]k = 22[/tex]
Two are selected, which means that [tex]n = 2[/tex]
What is the probability that both of them have the secret decoder ring?
This is P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,63,2,22) = \frac{C_{22,2}*C_{41,0}}{C_{63,2}} = 0.1183[/tex]
0.1183 = 11.83% probability that both of them have the secret decoder ring.
Need some help on this question
Answer:
9.We know that
6 × 3 = 2 × x
18 = 2x
x = 9
What is the area, in square centimeters, of the shaded part of the rectangle shown below
Answer:
Step-by-step explanation:
i think you forgot to link or import the question
Two methods are proposed for testing a shipment of five items (call them A, B, C, D, and 13). In method 1, an inspector randomly samples two of the five items and tests to see whether either item is defective. In method 2, an inspector randomly samples one item and tests it; the remaining four items are sent to a second inspector who randomly samples one item and tests it. Suppose that only item A is defective in the shipment.
a. What is the probability that item A will be dis-covered by method 1?
b. What is the probability that item A will be dis-covered by method 2?
c. What general statement can you make regarding the effectiveness .of the two methods? Can your statement be extended to methods involving samples of more than two items?
Answer:
a-The probability that item A is discovered as a defective item by method 1 is 0.4
b. The probability that item A is discovered as a defective item by method 2 is 0.4
c-As the probability of detecting A as a defective item is same for the two methods, thus it can be stated that each of the methods is equally effective.
Step-by-step explanation:
a-
The first method where the inspector chooses two of the five items randomly, so the total pairs are as given below:
[tex]N_{total}=n(S_{total})\\N_{total}=n(\{AB,AC,AD,AE,BC,BD,BE,CD,CE,DE\})\\[/tex]
As the total experiments in the overall space is 10 so [tex]N_{total}[/tex] is 10.
As A comes in 4 of these experiments, thus the value of [tex]N_{A}[/tex] is 4.
So the Probability of A is given as
[tex]P(A)=\dfrac{N_{A}}{N_{total}}\\P(A)=\dfrac{4}{10}\\P(A)=0.4[/tex]
The probability that item A is discovered as a defective item by method 1 is 0.4.
b-
Now in order to find the probability of finding item A as defective by method 2, first consider the probability of not finding item A as defective.
This is given as
[tex]P(A)=1-P(A)'[/tex]
Here P(A)' is given as
[tex]P(A)'=P(A)'_{1^{st}}\times P(A)'_{2^{nd}}[/tex]
Here
P(A)'_1st is the probability that the first inspector fails to detect A as a defective item which is given as
[tex]P(A)'_{1^{st}}=1-\dfrac{1}{N_{total\ items}}[/tex]
Here N_total items is 5. so the equation becomes
[tex]P(A)'_{1^{st}}=1-\dfrac{1}{N_{total\ items}}\\P(A)'_{1^{st}}=1-\dfrac{1}{5}\\P(A)'_{1^{st}}=\dfrac{5-1}{5}\\P(A)'_{1^{st}}=\dfrac{4}{5}[/tex]
Similarly
P(A)'_2nd is the probability that the second inspector fails to detect A as a defective item which is given as
[tex]P(A)'_{2^{nd}}=1-\dfrac{1}{N_{total\ items}}[/tex]
Here N_total items is 4 as 1 item has already been checked. so the equation becomes
[tex]P(A)'_{2^{nd}}=1-\dfrac{1}{N_{total\ items}}\\P(A)'_{2^{nd}}=1-\dfrac{1}{4}\\P(A)'_{2^{nd}}=\dfrac{4-1}{4}\\P(A)'_{2^{nd}}=\dfrac{3}{4}[/tex]
So the main equation becomes
[tex]P(A)=1-P(A)'\\P(A)=1-(P(A)'_{1^{st}}\times P(A)'_{2^{nd}})[/tex]
Substituting the values give
[tex]P(A)=1-(P(A)'_{1^{st}}\times P(A)'_{2^{nd}})\\P(A)=1-(\dfrac{4}{5}\times \dfrac{3}{4})\\P(A)=1-\dfrac{3}{5}\\P(A)=\dfrac{5-3}{5}\\P(A)=\dfrac{2}{5}\\P(A)=0.4[/tex]
The probability that item A is discovered as a defective item by method 2 is 0.4.
c-
As evident from the above, that the value of probabilities for both the methods is same therefore the overall effectiveness of each of the methods is same.
Find the length of the cable in the diagram below.
Answer:
13.4
Step-by-step explanation:
it is A square +b square =c square which is just 12×12=144 + 6×6=36 and then add them together which is 180, then just square root 180 can do it for every type of question like that and always remember the longest side is c, and the other two it doesn't matter which is A or B.
PLS HELLP PLS PLS
Aarons bedroom measures. feet by 14 feet by 8 feet. how many cubic feet of space does the room contain? round ur answer to the nearest hundredth
Answer:
it would be 100 rounded because 14x8=112 and 112 is rounded to 100 to the nearest hundreth. Please subscribe to Amiredagoat Yt
Step-by-step explanation:
Can somebody please help me with this whoever answers first gets a thanks and no rush but can you please be quick
Answer:
Bookstore to pet store: Down 6 units
Bookstore to Ice cream shop: Down 1 unit, 5 units to the left
Ice cream shop to pet store: Down 5 units, 5 units to the right
Sorry if this is wrong the image is a little blurry
Kristian spends 45% of his $72 on a computer game. Calculate the price of the computer game
Answer:
$32.40
Step-by-step explanation:
45% = 0.45
72(0.45) = 32.4
Based on the amount Kristian had and the percentage spent on the game, the price of the game is $32.40.
What is the Price of the Game?The price of the game can be found as:
= Amount Kristian has x Percentage spent on game
Solving gives:
= 45% x 72
= $32.40
In conclusion, the price of the game is $32.40.
Find out more about percentages at https://brainly.com/question/11570843
Identify the solutions of the graph. Only put one number in each blank.
___________ ___________
Answers: -2 and 2
Explanation:
The solutions to a graph are the same as the roots, zeros, or x intercepts. The x intercept is the location of the curve where it crosses or touches the x axis. In this case, it does so when x = -2 and x = 2.
The diameter of a circular plate is 12 inches. What is the area of the plate? Round your answer to the nearest tenth of a square inch.
Answer:
Plate Area = PI * radius^2
Plate Area = 3.14159 * 6 * 6
Plate Area = 113.09724 square inches
Plate Area = 113.1 square inches (rounded)
Step-by-step explanation:
Given that cos A 165 and sin B = 72, and that angles A and B are both in
Quadrant I, find the exact value of sin(A + B), in simplest radical form.
Given:
[tex]\cos A=\dfrac{4}{\sqrt{65}}[/tex]
[tex]\sin B=\dfrac{1}{\sqrt{2}}[/tex]
A and B both lies in I quadrant.
To find:
The value of [tex]\sin (A+B)[/tex].
Solution:
We know that, all trigonometric ratios are positive in first quadrant.
[tex]sin^2\theta +\cos^2\theta =1[/tex]
Using this we get
[tex]\sin^2A +\cos^2A =1[/tex]
[tex]\sin^2A +\left(\dfrac{4}{\sqrt{65}}\right)^2 =1[/tex]
[tex]\sin^2A +\dfrac{16}{65}=1[/tex]
[tex]\sin^2A =1-\dfrac{16}{65}[/tex]
Taking square root on both sides, we get
[tex]\sin A =\sqrt{\dfrac{65-16}{65}}[/tex] [Only positive because A lies in I quadrant]
[tex]\sin A =\sqrt{\dfrac{49}{65}}[/tex]
[tex]\sin A =\dfrac{7}{\sqrt{65}}[/tex]
Similarly,
[tex]\sin^2B +\cos^2B =1[/tex]
[tex]\left(\dfrac{1}{\sqrt{2}}\right)^2 +\cos^2B =1[/tex]
[tex]\dfrac{1}{2}+\cos^2B =1[/tex]
[tex]\cos^2B =1-\dfrac{1}{2}[/tex]
Taking square root on both sides, we get
[tex]\cos B =\sqrt{\dfrac{2-1}{2}}[/tex] [Only positive because B lies in I quadrant]
[tex]\cos B =\sqrt{\dfrac{1}{2}}[/tex]
[tex]\cos B =\dfrac{1}{\sqrt{2}}[/tex]
Now,
[tex]\sin (A+B)=\sin A\cos B+\cos A\sin B[/tex]
[tex]\sin (A+B)=\dfrac{7}{\sqrt{65}}\times \dfrac{1}{\sqrt{2}}+\dfrac{4}{\sqrt{65}}\times \dfrac{1}{\sqrt{2}}[/tex]
[tex]\sin (A+B)=\dfrac{7}{\sqrt{130}}+\dfrac{4}{\sqrt{130}}[/tex]
[tex]\sin (A+B)=\dfrac{11}{\sqrt{130}}[/tex]
Therefore, the exact value of [tex]\sin (A+B)[/tex] is [tex]\dfrac{11}{\sqrt{130}}[/tex].
pls helpppp im so stuckk
ahhhhhgggg
Answer:
hmm easy peesy
3x+6= 21
21-6=3x
15=3x
5 = X
meet my dog; (Frankie the sleeping beauty )
Answer:
x = 5
Step-by-step explanation:
Expand:
Use distributive property:
3x + 6 = 21
3x = 15
x = 5
Divide:
(x + 2) = 21/3
x + 2 = 7
x = 5
Check your work:
3(5 + 2) = 21
15 + 6 = 21
21 = 21
Correct
How much water will be needed to completely fill a rectangular tank that has a length of 3 meters a width of 3 meters
and a height of 18 meters?
(A) 162 cubic meters
(B) 24 cubic meters
(C) 324 cubic meters
(D) 108 cubic meters
Answer:
A
Step-by-step explanation:
because when you multiply 3x3 (the base) times 18(the height) you get= 162
The set of ordered pairs {(1,19), (2,23), (3,23), (4,29), (5,31)}
represents the number of tickets sold for a fundraiser. The x-coordinates
represent the day and the y-coordinates represent the number of tickets
sold on that day.
a) Which mapping diagram represents the relation?
Answer:
D
Step-by-step explanation:
1) remember that x indicates the independent variable, while y the dependent variable
2) remember that the first diagram represents the values of x, while the second the values of y
Mapping diagram A represent the number of tickets sold on that day. Therefore, option A is the correct answer.
The given set of ordered pairs are {(1,19), (2,23), (3,23), (4,29), (5,31)}.
What are relations in Math?In math, a relation defines the relationship between sets of values of ordered pairs. The set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.
A mapping diagram consists of two parallel columns. The first column represents the domain of a function [tex]f[/tex], and the other column for its range. Lines or arrows are drawn from domain to range, to represent the relation between any two elements.
Diagram A represents the given ordered pair
Mapping diagram A represent the number of tickets sold on that day. Therefore, option A is the correct answer.
Learn more about the relations here:
https://brainly.com/question/6241820.
#SPJ2
Please help, I will give brainliest!!!
The table models the flight of the projectile from Part A
Which of these statements is true?
A) h(4) < h(20)
B) The flight is symmetric about the line t=10
C) The projectile will hit the ground at some value of t less than 24.
D) If 0<a<12, then h(12-a) = h(12+a).
If 0 < a < 12, then h(12 – a) = h(12 + a) is true. Then the correct option is D.
What is a projectile motion?When a body is thrown in the air at an angle, then the term is known as projectile motion.
The table is given in the question.
A) h(4) < h(20), this statement is incorrect, because the h(4) = h(20).
B) The flight is symmetric about the line t = 10, this statement is incorrect, because symmetric about t = 12.
C) The projectile will hit the ground at some value of t less than 24. This is incorrect, because t > 24.
D) If 0 < a < 12, then h(12 - a) = h(12 + a). This statement is correct.
Then the correct option is D.
More about the projectile motion link is given below.
https://brainly.com/question/11049671
#SPJ1
A cube with sides that are 2 cm has a mass of 48 g and its density would be
___________ g/cm3.
Answer:
6g/cm^3
Step-by-step explanation:
The density of the cube would be 6 grams/cm^3. I got this answer by first finding the volume of the cube, 2^3 which gives me 8 cm as the initial volume of the cube. Then, the 48 grams of mass the cube has allows me to divide 48 / 8 which gave me 6. And 6 would be the density of the cube in grams.
Answer: 6g/cm^3
Hope this helps!
Answer:
p = 6 g/cm³
Step-by-step explanation:
Given: cube sides= 2 cm and 48 g
To find: The cube's density
Formula: [tex]{p} \frac{m}{V}[/tex]
Solution: Measure the height, width, and depth of the shipment in inches.
Multiply the three measurements (height x width x depth).
Divide the total cubic inches by 1,728 (the number of cubic inches in a cubic foot).
Divide the weight (in pounds) of the shipment by the total cubic feet.
p = density
m = mass
V = volume
A sphere has a radius of 5. What is its diameter?
Answer:
D=10
Step-by-step explanation:
Diameter of a Sphere
D = 2 r
D=2(5)
D=10
Answer:
Diameter = 10
Diameter - is the full thing
Radius - Is only half of the diameter.
Step-by-step explanation:
The picture will explain it to you visually
You own a truck that has a trailer in the shape of a rectangular prism. It has a height of 15 m and a length of 40m, and a width of 10 m. If you wish to fill this trailer with 5m x 5m x 5m cubic boxes, how many boxes will fit into
the trailer
Answer:
48 boxes
Explanation:
First, find the volume of the rectangular prism (l*w*h) to find out how much it can hold.
15*40*10= 6,000
Then, find the volume of the cubic boxes (l*w*h) to find how much space each of them take up.
5*5*5= 125
Finally, divide the rectangular prism's volume by the boxes' to find out how many can fit inside.
6,000/125= 48 boxes
For every 3 boys in a class, there are 2 girls.
If there are 20 children in the class, how many girls are in there?
VWXY is a parallelogram. Find the value of n.
Help meeee
Answer:
3.5
Step-by-step explanation:
n+7=3n
7=2n
n=3.5
Answer:
n=7/2
Step-by-step explanation:
n+7=3n
-n -n
7=2n
/2 /2
7/2=n
7 1/2 x 4 1/3 x 3 3/5
Answer:
answer: 117
Hope this helps!
Answer:
117
Step-by-step explanation:
Convert mixed numbers to improper fractions:
7 1/2 = 15/2
4 1/3 = 13/3
3 3/5 = 18/5
15/2 x 13/3 x 18/5
Multiply and cross-cancel:
18/2 x 13/1
Multiply again:
117/1 = 117
What is cot(A)?
A. -3 sqrt 7/7 correct
Step-by-step explanation:
[tex]to \: help \: you \\ \cot(A) = { (\tan(A)) }^{ - 1} = \frac{ \cos(A) }{ \sin(A) } \\ or : \\ \cot(A) = \sqrt{(1 + {( \tan(A) )}^{2} } [/tex]
Answer:
A is correct :)
Step-by-step explanation:
edge 2021
thank you! have a great day
hey guys i'm having a rough night and i can't figure out my homework rn i'm just too stress please help
Answer:
3a) 54/99
3b) 257/999
Hope this'll help you!
WHAT IS THE ANSWER PLSS
Answer: X≥6
Step-by-step explanation:
x/-2≤-3
x≥-3(-2)
X≥6
Please quickly help me with this question please please please please please I’m beggig
Answer:
D: Point A is 1 unit to the right of the origin and point B is 3 units to the right of the origin.
Step-by-step explanation:
The coordinate (1, 3) is in quadrant 1 with a positive y, moving the point up, and a positive x, moving the point right. Because the x is 1, the point moves 1 unit right from the origin.
The coordinate (3, 1) is also in quadrant 1 with a positive y and x, but this time the x is 3, moving the point 3 units right from the origin.
A:Consecutive interior angles
B:Vertical angles
C:Alternate exterior angles
D:Corresponding angles
Answer:
D: corresponding angle
hope it helps.
Answer:
corresponding angles
Step-by-step explanation:
hope it is helpful ><
Two rectangular prisms have the same volume.the first prism has a length of 10 meters a width of 6 meters and a height of 2 meters. The second prism has a length of 6 meters and a width of 4 meters
Answer:
height of second rectangular prism is 5 meters
Step-by-step explanation:
In Mr. Thompson's first period class, there are 6 students with blue eyes, 8 students with brown eyes,
5 students with grey eyes, and 1 student with hazel eyes. If Mr. Thompson selects one student
randomly, what color eyes is the student most likely to have?
Answer:
blue
Step-by-step explanation:
There the most common eyes in the class?
Answer:the student would most likely have blue eyes
Step-by-step explanation:
8/20
6/20
5/20
1/20
Determine the amplitude or period as requested . Amplitude of y = - 1/5 * sin x a - 1/5 1/5 b 5 d. pi/5
Answer:
The amplitude is 1/5
Step-by-step explanation:
Given
[tex]y = -\frac{1}{5}\sin(x)[/tex]
Required
Determine the amplitude
The general cosine function is:
[tex]y = A\sin(k(x + c)) +d[/tex]
Where
[tex]Amplitude = |A|[/tex]
Compare [tex]y = A\sin(k(x + c)) +d[/tex] and [tex]y = -\frac{1}{5}\sin(x)[/tex]
[tex]A = -\frac{1}{5}[/tex]
So:
[tex]Amplitude = |-\frac{1}{5}|[/tex]
[tex]Amplitude = \frac{1}{5}[/tex]
Comcast Corporation is the largest cable television company, the second largest Internet service provider, and the fourth largest telephone service provider in the United States. Generally known for quality and reliable service, the company periodically experiences unexpected service interruptions. On January 14, 2009, such an interruption occurred for the Comcast customers living in southwest Florida. When customers called the Comcast office, a recorded message told them that the company was aware of the service outage and that it was anticipated that service would be restored in two hours. Assume that two hours is the mean time to do the repair and that the repair time has an exponential probability distribution.
a. What is the probability that the cable service will be repaired in one hour or less?
b. What is the probability that the repair will take between one hour and two hours?
c. For a customer who calls the Comcast office at 1:00 P.M., what is the probability that the cable service will not be repaired by 5:00 P.M.?
Answer:
wow that
Step-by-step explanation:
a lot
KM and NP are parallel lines.
Which angles are alternate exterior angles?
Answer:
<MLJ and <NOQ
Step-by-step explanation:
Alternate exterior angles are angles that lie outside of the two parallel lines that are cut across by the transversal line, and are also alternating each other along the transversal
Considering the image and the options given, <MLJ and <NOQ are exterior angles that alternate each other. Therefore, they are alternate exterior angles.