Using the binomial distribution, it is found that:
a) There is a 0.0501 = 5.01% probability that you need to contact four people.
b) You expect to contact 1.82 students until you find one who lives within five miles of you.
c) The standard deviation is of 1.22 students.
d) 0.3369 = 33.69% probability that 3 of them live within five miles of you.
e) It is expected that 2.75 students live within five miles of you.
For each student, there are only two possible outcomes. Either they live within 5 miles of you, or they do not. The probability of a student living within 5 miles of you is independent of any other student, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
55% live within five miles, hence [tex]p = 0.55[/tex].Item a:
This probability is P(X = 0) when n = 3(none of the first three) multiplied by 0.55(the fourth does live within five miles), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.55)^{0}.(0.45)^{3} = 0.091125[/tex]
[tex]p = 0.091125(0.55) = 0.0501[/tex]
0.0501 = 5.01% probability that you need to contact four people.
Item b:
The expected number of trials in the binomial distribution until q successes is given by:
[tex]E = \frac{q}{p}[/tex]
In this problem, [tex]p = 0.55[/tex], and 1 trial, thus [tex]q = 1[/tex], hence:
[tex]E = \frac{1}{0.55} = 1.82[/tex]
You expect to contact 1.82 students until you find one who lives within five miles of you.
Item c:
The standard deviation of the number of trials until q successes are found is given by:
[tex]S = \frac{\sqrt{q(1 - p)}}{p}[/tex]
Hence:
[tex]S = \frac{\sqrt{0.45}}{0.55} = 1.22[/tex]
The standard deviation is of 1.22 students.
Item d:
This probability is P(X = 3) when n = 5, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.55)^{3}.(0.45)^{2} = 0.3369[/tex]
0.3369 = 33.69% probability that 3 of them live within five miles of you.
Item e:
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
Hence:
[tex]E(X) = 5(0.55) = 2,75[/tex]
It is expected that 2.75 students live within five miles of you.
A similar problem is given at https://brainly.com/question/25343741
Determine whether the ratios 8:7 and 15:14 are equivalent
Answer:
They are not
Step-by-step explanation:
We can see that 14 / 2 = 7, so we can check for the other side by dividing both sides of the ratio by 2:
15:14
\/
7.5:7 ≠ 8:7
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Lindsey drew a scale of a city. the scale of the drawing is 1 inch = 3 yards. If the actual length of a neighborhood park is 114 yards, how long is the park in the drawing?
Answer:
38 in
Step-by-step explanation:
114 yds divided by 3 = 38 in
What is the value of x if a slope is 2, and a line passing through (x, 3) and (1,5).
Answer:
x = 0
Step-by-step explanation:
Slope = change in y/change in x
Slope = 5-3/1-x
2 = 2/1-x
2(1 - x) = 2
2 - 2x = 2
2 = 2 - 2x
0 = -2x
x = 0
-Chetan K
examine the following sequence 1,4,9,16,25…why is 36 the next number in the sequence ? because the pattern is
Answer:
The pattern is adding by consecutive odds.
Step-by-step explanation:
The first odd you start with is 3:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
16 + 9 = 25
25 + 11 = 36
...
Note that each time you add, it is by consecutive odds, meaning that after 36, you are adding 13, then 15, etc.
~
identify the pair of similar triangles in each of the groups of triangle below
Answer:
its triangle ABC and XYZ
Step-by-step explanation:
Evan is landscaping his backyard. The yard is shaped like a rectangle and measures 80 feet by 70 feet. He wants to spread topsoil evenly over the entire surface. One load of topsoil will cover 400 square feet, 4 inches deep. How many loads of dirt does Evan need in order to cover his entire yard?
A. 14
B. 16
C. 18
D. 20
Gabby read 98 pages of a book then stopped. She later decided to continue the book and read 37 more pages every day.
Let d represent the number of days since Gabby decided to continue the book and p represent the total number of pages of the book she had read.
Answer:
number of days = 3
total number of pages=135
Step-by-step explanation:
98÷49= 2
37=1 day
total number of days=3days
Total number of pages read=135 pages
Find the equation of the line with slope 43 and y-intercept (0,−1)
Answer:
y = 43x -1
Step-by-step explanation:
Using slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 43x -1
What is the answer =2^3(10-7)/3*7?
Answer:
the ansewer is 56
Step-by-step explanation:
by appling bodmas rule which means if such type of operation apper in one question we work it step by step first bracket then division next multiplication then addition finaly substruction 2^3(10-7)/3*7(10-7)=32^3(3)/3*73/3=12^3*1*72^3=88*1*7=8*7=56Calculate the average of these values: 38, 48, 58, 68?
Answer:
53 is the average value.
Step-by-step explanation:
To find the average, or mean of multiple values you first add them all up:
38+48+58+68=212
Then you count how many different numbers there are, (there are 4 numbers here, if there are 2 of the same numbers you still count them both, just so you understand).
Then you need to divide the total you got, 212, by the total amount of numbers, 4, to get the average amount, 53.
I hope that my answer has helped you, have a great day, ask any questions you have below.
Find two numbers x and y with a sum of 2 and a difference of 12
Answer:
x = 7
y = -5
Step-by-step explanation:
x + y = 2
x - y = 12
( x + y ) + ( x - y ) = 2 + 12
2x = 14
x = 7
7 + y = 2
y = -5
Check:
7 + -5 = 2
7 - (-5) = 12
Correct
-Chetan K
Company A received 2131 more patents than Company B. Together, they received patents many patents did each company receive?
I need word form and decimal
(I already shaded it in so that is all I need
The shading is correct for each of the three problems. Nice work.
==========================================
Problem 13
Word form = one tenth
Decimal form = 0.1
Explanation: The 1 is in the tenths place for the decimal value 0.1 to represent the fraction 1/10.
==========================================
Problem 14
Word form = eighty-five hundredths
Decimal form = 0.85
Explanation: The 8 is in the tenths place, and the 5 is in the hundredths place. Overall, 0.85 represents 85 out of 100, aka 85/100.
==========================================
Problem 15
Word form = thirty-nine thousandths
Decimal form = 0.039
Explanation: The second zero is in the tenths place. The 3 is in the hundredths place. The 9 is in the thousandths place. The decimal represents 39/1000 which you can think of it as 039/1000.
Violet is playing a board game with her friends. She earned 78 points during the game, and she receives a game-end bonus for achieving her secret objective. With her bonus, Violet came in second place with 91 points. Let b be the number of points Violet earned for the game-end bonus. Write and solve the equation for b.
Answer:
78 + B = 91...
91 - 78 = B
91 - 78 = 13
B = 13
Step-by-step explanation:
40.75 in word form.
Answer:
forty and seventy-five hundredths
Step-by-step explanation:
first number with always stay the same. after decimal each number you go up a thenths place. so in this case ten, hundreths
Find the 91st term of the arithmetic sequence 5, -14, -33, ...5,−14,−33,...
Answer:
1724
Step-by-step explanation:
first find the nth term = -19n+5
then do -19×91+5= 1724
l
Choose all sets that contain the number 5.
Natural numbers
Whole numbers
Integers
Rational numbers
Irrational numbers
Real numbers
Whole numbers
Natural numbers
Real nunbers
there are 98 girls at Ross elementary there are 15 less boys then girls how many boys and girls are at Ross elementary
Answer:
either 98 girls and 83 boys or 181 students in Ross elementary school
Step-by-step explanation:
98-15 is 83 so there are 98 girls and 83 boys there are also 181 students altogether.
what number is its own oppositie?
Answer:
0Step-by-step explanation:
what number is its own oppositie?
The number 0 is the only number that is its own opposite.
Mary was asleep from 9:pm to 5:am. How long was she asleep for?
Answer:
8 hours
Step-by-step explanation:
Answer:
8hours
Step-by-step explanation:
Use the correct trig function to find the value of x. SOH,CAH, TOA
x = 18.4
Step-by-step explanation:
For this problem, we are going to use the cosine function to find x:
[tex]\cos{45°} = \dfrac{adj}{hyp} = \dfrac{13}{x}[/tex]
[tex]\Rightarrow x = \dfrac{13}{\cos45°} = 18.4[/tex]
3/8 is found between which pair of fractions on a number line
Answer:
2/8 and 4/8
Step-by-step explanation:
Answer:
2/8,4/8 or 1/4,1/2
Step-by-step explanation:
3+1=4 3-1=2
2/8=1/4
4/8=1/2
Does anyone know these answers?
Answer:
A
Step-by-step explanation:
We know the answer to the first question is 3 because GC, FB, HD are parallel to AE, so we can eliminate choices B and C, we know D is incorrect because the answer to the third question is 4
Answer:
A. 3, 3, 4Step-by-step explanation:
Parallel segments to AE are:
BF, CG, DH ⇒ 3Parallel segments to EF:
AB, CD, GH ⇒ 3Segments intersecting with EF under right angle:
AE, EG, BF, GH ⇒ 4Correct choice is A
is 15/6 less than 2 13/18
Answer:
no
Step-by-step explanation:
What is the algebraic expression for the following word phrase: "the product of x and the sum of 2 and y"?
Answer:
x(2+y)
Step-by-step explanation:
sum of 2 and y=2+y
product of x=x times expression
:. Answer =x(2+y)
vertex, maximum height, and axis of symmetry
Answer:
19 height
Step-by-step explanation:
sorry but thats all i know
hope it helps, have a nice day/night! :D
Find two numbers x and y with a sum of 200 and a difference of 82
Answer:
Let x be the bigger number, and y be the smaller number.
[tex]x+y=200[/tex]
[tex]x=200-y[/tex]
Since the difference is 82,
[tex]x-y=82[/tex]
Substitute x in:
[tex](200-y)-y=82[/tex]
[tex]200-2y=82[/tex]
[tex]2y=200-82[/tex]
[tex]2y=118[/tex]
[tex]y=59[/tex]
[tex]x=200-59[/tex]
[tex]x=141[/tex]
Pls and thiss I beggg
Answer:
x=115°,y=50°
Step-by-step explanation:
let <B =x
115°+x=180°
x=180°-115°=65°
Since <B=<C
x+65°=180
x=180-65=115°
For y,
y+2(65°)=180°
y+130°=180°
y=180°-130°=50°
The admission fee at a local zoo is $1.50 for children and $3.00 for adults. On a certain day, 2400 people enter the zoo and $4,800.00 is collected. How many children and how many adults?
Answer:
Step-by-step explanation:
c = children
a = adults
2200 people enter the zoo mean :
c + a = 2200
$4,550.00 is collected mean :
1.5 c + 4 a = 4550
Now you must solve system:
c + a = 2200
1.5 c + 4 a = 4550
c + a = 2200 Subtract c to both sides
c + a - c = 2200 - c
a = 2200 - c
1.5 c + 4 a = 4550
1.5 c + 4 ( 2200 - c ) = 4550
1.5 * c + 4 * 2200 - 4 c = 4550
1.5 * c + 8800 - 4 c = 4550
- 2.5 c + 8800 = 4550 Subtract 8800 to both sides
- 2.5 c + 8800 - 8800 = 4550 - 8800
- 2.5 c = - 4250 Divide both sides by - 2.5
c = - 4250 / - 2.5
c = 1700
a = 2200 - c = 2200 - 1700 = 500
1700 children and 500 adults
Proof :
c + a = 1700 = 2200
$ 1.5 * c + $ 4 * a =
$ 1.5 * 1700 + $ 4 * 500 =
$ 2550 + $ 2000 = $ 4550
The number of children and the number of adults are 1600 and 800, respectively.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's optimum is referred to as a direct consequence.
A nearby zoo charges $1.50 for kids and $3.00 for adults to enter. 2400 persons visit the zoo on a certain day, and $4,800.00 is gathered.
Let x be the number of children and y be the number of adults. Then the equation is written as,
x + y = 2400 ...1
1.5x + 3y = 4800
x + 2y = 3200 ...2
Subtract equation 1 from equation 1, then
2y - y = 3200 - 2400
y = 800
Then the value of x is calculated as,
x + 800 = 2400
x = 2400 - 800
x = 1600
The number of children and the number of adults are 1600 and 800, respectively.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
What is the scale factor for the dilation of triangle ABC
to produce triangle A'B'C'?
A. 0.25
B. 0.5
C. 2
D. 3
What is the scale factor for the dilation of triangle ABC
to produce triangle A"B"C?
A. 0.25
B. 0.5
C. 2
D. 3
Answer:
1) B 0.5
2) C 2
Step-by-step explanation:
point A (-2, 2) (0.5) = (-1, 1) A'
point B (-2, -1) (0.5) = (-1, -0.5) B'
point C (3, -1) (0.5) = (1.5, -0.5) B'
point A (-2, 2) (2) = (-4, 4) A'
point B (-2, -1) (2) = (-4, -2) B'
point C (3, -1) (2) = (6, -2) B'