Answer:
A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
B) The method used is Relative frequency approach.
Step-by-step explanation:
From the question, we are told a sample of n kids line up for recess.
Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).
Since we are being asked about 3 kids from the class, let's assign a letter to each kid:
J: John
B: Betty
M: Mary
A) Now, we want to find the probability that Betty is first in line or Mary is last in line.
In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;
P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
Where;
The suffix 1 refers to the first position while the suffix n refers to the last position.
Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)
This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.
B) The method used is Relative frequency approach.
In this method, the probabilities are usually assigned on the basis of experimentation or historical data.
For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.
Also, let n_A be the number of times that A did occur.
Now, the relative frequency would be written as (n_A)/n.
Thus, in this method, we will define P(A) as:
P(A) = lim:n→∞[(n_A)/n]
Given this pair of probabilities, the probability that Mary is the first is n(A) = n-1!, while the probability that Betty is last is n(A) = n-1!
There are n! ways of making this arrangement
We have probability of A: Betty is the first person in this line
Probability of B: Mary is the last person
A U B = p(A) + p(B) - p(A ∩ B)
n(A) = n-1 that is given that Betty is the first person on the line.
then n(A) = n-1!
As the last person on the line P(B) = n-1!
Probability of (A∩B) =( n-2)! this has Mary as the first and Betty as the last person.
Remaining students that would have to be on this line are n-2
Prob(A∪B) = n(A ∪ B)/n!
= 2(n-2)/n(n-1)
What is the probability theory in Mathematics?This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.
Read more on probability here: https://brainly.com/question/24756209
x = 4 7 9 I dont mind for a step by step
Answer:
[tex]\boxed{\sf x = 9}[/tex]
Step-by-step explanation:
According to chord-chord theorem:
=> [tex]x* 2 = 3 * 6[/tex]
=> [tex]2x = 18[/tex]
Dividing both sides by 2
=> x = 18/2
=> x = 9
Find x and y plz help me show work
Answer:
Sorry but the photo is not clear
Sally's paycheck this week was $100. She spent $220.45 for a shirt, $12.95 for a CD, $15 for gasoline, and put the balance in the bank.
a. What percent of her total pay was spent on the shirt?
b. What percent of her total pay did she put in the bank?
Answer:
A) 220.45%
B) 0%
Step-by-step explanation:
A) 220.45 / 100 = 2.2045 * 100 = 220.45%
B) Costs exceeded her paycheck, so 0% of her pay was leftover and put in the bank.
Answer: A) 22.045% , B) 75.16%
I guess its a typo and weekly salary was $1000
So weekly salary = 1000
Spent on shirt = $220.45
Spent on CD = $12.95
Spent on Gasoline = $15
A) 220.45/1000×100
= 22.045%
B) Total spent = 220.45 + 12.95 + 15
= $248.4
Total left with her = 1000 - 248.4
= $751.6
Total percent of pay she put in bank = 751.6/1000×100
= 75.16%
Must click thanks and mark brainliest
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white, and 8 are blue. One is drawn at random. Which color is most likely to be chosen? A. white B. red C. blue D. yellow Include ALL work please!
Answer:
red
Step-by-step explanation:
Since the bag contains more red marbles than any other color, you are most likely to pick a red marble
Which represents the inverse of the function f(x) = 4x?
h(x) = x+ 4
H(x) =x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
h(x)=1/4x
Step-by-step explanation:
function×inverse=-1
4x=-1
Answer:
h(x) = 1/4x
Step-by-step explanation:
y = 4x
x = 4y
1/4 x = y
Mary subscribed to a cell phone plan with a $50 monthly fee and a charge of $0.25 for each minute she talks. Find an equation for the total cost for her plan when she uses minutes.
Answer:
c = 0.25m + 50
Step-by-step explanation:
Let c = cost; let m = number of minutes.
c = 0.25m + 50
Change the following fractions to 24ths.
3/4= ??
5/6= ??
18/24, 20/24
Step-by-step explanation:
3/4=?/24
5/6=?/24
3X6=18
4X6=24
5X4=20
6X4=24
Answer:
7/8 = 21/24
5/6 = 20/24
3/4 = 18/24
Step-by-step explanation:
What you do to the denominator, you do the same to the numerator.
[tex]\frac{7}{8} * \frac{3}{3} = \frac{21}{24}[/tex]
[tex]\frac{5}{6} * \frac{4}{4} = \frac{20}{24}[/tex]
[tex]\frac{3}{4} * \frac{6}{6} = \frac{18}{24}[/tex]
5/2 divided7 ( please dont report, i just can't figure it out! )
Answer:
5/14
Step-by-step explanation:
You multiply the recripricoal in division problems:
5/2 ÷ 7/1 =
5/2 × 1/7 =
5/14
Answer:
5 / 14
Step-by-step explanation:
will make it simple... the technique is to flip the either 5/2 or 7/1
then multiply.
5/2 x 1/7 = 5 / 14
Point g is located at (3,6) on the coordinate plane. Point G is reflected over the x-axis to create point G'. Point G' is then reflected over the y-axis to create point G''. What ordered pair describes the location of G''.
-Answer:
(-3. -6)
Step-by-step explanation:
G (3,6)
x axis reflect
G' (3, -6)
y axis reflect
G'' (-3. -6)
A ladder 10 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 6 ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is 6 feet from the wall?
Answer:
-4.5ft per sec
Step-by-step explanation:
Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).
This forms a triangle with the ladder as the hypothenus of length 10ft
We have dy/dt = 6ft per sec
According to Pythagoras law the relationship between x and y is
(x^2) + (y^2) = (hypothenus ^2) = 10^2
When we differentiate both sides of the equation
2x(dx/dt) + 2y(dy/dt) = 0
dy/dt = (x/y) * (dx/dt)
y= √(10^2) - (6^2) = 8ft
So dy/dt = (6/8)* (6/1)= -4.5 ft per sec
It is a negative rate
Suppose a newspaper wants to conduct a survey on heating oil consumption in Iowa. For the survey, the newspaper randomly picks 26 households. What is the sample distribution of the sample sum
Answer:
noent einda pergnta poudsesrmaesspeeciicofl
Step-by-step explanation:
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
14 80 tiles of side 30cm were used to cover a counter top. Calculate the area of the counter top in square metres.
Answer:
Step-by-step explanation:
1,480 is a lot of tiles. Did you mean 80 tiles?
30 cm = 0.3 m
Area of one tile = 0.3² m² = 0.09 m²
Multiply the number of tiles by 0.09 m².
Which is the correct label of the line? (1 point)
a
AC
O
CD
D
Ο OllA
Answer:
The correct label of the line is CD
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9 } A= {1, 2, 3, 4} and B= {4, 5, 6, 7}. Draw the Venn diagram of A ∩B. Answer with full explanation and diagram will be marked as brainliest for sure!!!
Step-by-step explanation:
Its mean the same number for both A and B which is only 4.
on tuesday, david picked a apples each hour for 5 hours, and elanor picked b apples each hour for 8 hours. which of the following represents the total number of apples picked by david and elanor on tuesday? a) 13ab b) 40ab c) 5a + 8b d) 8a + 5b
Answer:
c) 5a + 8bStep-by-step explanation:
[tex]a \: apples = 1 \: hours\\x \: apples = 5 \: hours\\x = 5a\\Total \:no \:of \:apples \:picked\\\:by \:david \:= 5a\\\\\\b \:apples = 1 \:hour\\x \:apples = 8 hours\\x = 8b\\Total \:no \:of \:apples \:picked\\ \:by \:elanor = 8b\\\\Total \:no \:of \:Apples =5a+8b[/tex]
Given log32≈0.631 and log37≈1.771, what is log314
Answer:
the log to the base 3 of 14 is 2.402
Step-by-step explanation:
You must find a way to indicate that 3 is the base; you cannot run this '3' together with 2, 7 or 14.
Example:
log to the base 3 of 2 = 0.631
log to the base 3 of 7 = 1.771
Note that 2 times 7 is 14. Thus, to obtain the log to the base 3 of 14, we must ADD the two logs shown above:
0.631
+1.771
----------
2.402
Thus, the log to the base 3 of 14 is 2.402.
Check: Does 3^2.402 = 14? YES
I need to know the answer and explaining how to do it please
Answer:
Its 0.11
Step-by-step explanation:
When you divide any number by 10, you just move the decimal place one to the left, as for this number 1.1, you move it one place to the left which makes it 0.11. Mathmatically, to check your work you can do 0.11 x 10 to get 1.1
Mark brainliest and helpful
If $ 10000 is deposited at an "interest rate" of 4% per year, annually compounded, what amount will depositors get after 5 years?
Answer:
PTR upon hundreds .by putting these formulas you can solve ti and is 2000
what is square root of 49 over square root of 1250 simplified
im pretty sure its 0.19 because the sqyare root of 49 is 7. the square root of 1250 is 35.35
7/35.35=0.19
3 log2 (x+1) - 2 = 13
Answer:
Hello,
Answer 31
Step-by-step explanation:
[tex]3*log_2(x+1)-2=13\\\\3*log_2(x+1)=13+2\\\\log_2(x+1)=5\\\\\\x+1=2^5\\\\x=32-1\\\\\boxed{x=31}\\[/tex]
HELP ASAP!!
The equation (blank) has no solution
Answer:
Just to recap, an equation has no solution when it results in an incorrect "equation".
For example:
Equation: x+3 = x+4
Subtract x: 3 = 4???
But clearly, 3 is not equal to 4, so this equation has NO SOLUTION.
Now onto our problem:
13y+2-2y = 10y+3-y
11y+2 = 9y+3
2y=1
y=1/2
9(3y+7)-2 = 3(-9y+9)
27y+61 = -27y+27
54y = -34
y = -34/54
32.1y+3.1+2.4y-8.2=34.5y-5.1
34.5-5.1=34.5y-5.1
5.1=5.1
infinite solutions
5(2.2y+3.4) = 5(y-2)+6y
11y+17 = 11y-10
17 = -10??
That's not true, so the option "5(2.2y+3.4) = 5(y-2)+6y" has no solution.
Let me know if this helps
ILL GIVE BRAINLIEST
Combine like terms.
4x – 7y + 2x – 4 = [ ? ]x + [ ]y + [ ]
Answer:
[6x] + [-7y] + [-4]
Step-by-step explanation:
There are only two like terms in this expression "4x" and "2x." Since they are like terms we can combine them by adding the coefficients and keeping the variable attached. Therefore we can combine 4x and 2x into 6x. Since there are no more like terms, this expression can be simplified to 6x - 7y - 4.
Three measurements are made on each of three individuals in a random sample from a population. X 1 = 2, X2 = 8
and
1
1
187
X3 = 4. The distances d(X1, X2)between X1, X, and d(X2, X3) between X2, X3 respectively are (Use Euclidean inner
L5.
product)
Step-by-step explanation:
here is the answer hope it helps
What is the difference between congurent and similar ?
Answer:
When a shape is congruent they are equal in shape, size, and measure. Although if a shape is similar they will be the same shape, but not the same size, instead they will be proportionate.
Step-by-step explanation:
Answer:
CongruentCongruent figures are identical in size, shape and measure. SimilarTwo figures are similar if they have the same shape, but not necessarily the same size.
Step-by-step explanation:
any equations that equal three?
Solve the following system
3x+y=9
4x-3y=6
Answer:
multiply the first equation with 3, then add the two equations, you'll get the value of x, by putting the value of x in any of the two equations, find y, answer should be this,
x = 33/13,
y = 18/13
Answer:
Step-by-step explanation:
3x+y=9
y=9-3x
4x-3y=6
4x-6=3y
y=(4x-6)/3
y= 4/3x-2
9-3x=4/3x-2
9+2=4/3x+3x
11=13/3x
x=11*3/13
=2.53
y=9-3*2.53
=1.41
can any one give me answer plz?
Answer:
D
Step-by-step explanation:
since
cos(2x) = 1 - 2×sin²(x)
and for x near 0, sin(x) is very similar to x.
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?
(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5
Answer:
(A) 37.5 miles
Step-by-step explanation:
The trains x and y are travelling on tracks starting simultaneously from a from opposite ends of 100 miles roads.
Translate these information into a simple represention to visualize the problem. (Picture below)
■■■■■■■■■■■■■■■■■■■■■■■■■■
First let's calculate the velocity of both trains.
The velocity formula is:
● V = d/t
d is the distance travelled and t is the tile needed to do it.
● V(x) = 100/5 = 20 miles per hour
● V(y) = 100/3 = 33.33.. wich is approximatively 33 after rounding to the nearest unit.
■■■■■■■■■■■■■■■■■■■■■■■■■■
After calculateingboth velocities, Let's find when the trains meet.
First understand what does it mean matematically when both trains meet.
Go back to the representation and notice what happens when the trains meet.
Let t be that moment.
When x and y reches the meeting point at t, the sum of the distances they have travelled is equal to the total distance wich is 100 miles .
We khow that V = d/t so d = V×t
Let's find the expression of the distances both trains travelled when they have met each other.
● d = V(x) × t
● d' = V(y) × t
■■■■■■■■■■■■■■■■■■■■■■■■■■
So the equation will be:
● V(x) × t + V(y) × t = 100
Factor using t
● t (V(x) + V(y) ) = 100
Replace V(x) and V(y) by their values
● t (20+33) = 100
● 53 t = 100
Divide both sides by 53
● 53t /53 = 100/53
● t = 1.88
■■■■■■■■■■■■■■■■■■■■■■■■■
Replace t in the expression of the distance that train x has travelled when meeting y.
● d = V(x) × t
● d = 20 × 1.88
● d = 37.6 wich is approximatively 37.5 miles