Answer:
The probability that they purchased a green or a gray sweater is [tex]\frac{12}{31}[/tex]
Step-by-step explanation:
Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]
The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:
P(A∪B)= P(A) + P(B) - P(A∩B)
Where:
P (A): probability of event A occurring.
P (B): probability that event B occurs.
P (A⋃B): probability that event A or event B occurs.
P (A⋂B): probability of event A and event B occurring at the same time.
Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)
In this case, being:
P(A)= the probability that they purchased a green sweaterP(B)= the probability that they purchased a gray sweaterMutually exclusive eventsYou know:
8 purchased green sweaters4 purchased gray sweatersnumber of possible cases= 12 + 8 + 4+ 7= 21So:
[tex]P(A)=\frac{8}{31}[/tex][tex]P(B)=\frac{4}{31}[/tex]P(A⋂B) = 0Then:
P(A∪B)= P(A) + P(B)
P(A∪B)= [tex]\frac{8}{31}+ \frac{4}{31}[/tex]
P(A∪B)= [tex]\frac{12}{31}[/tex]
The probability that they purchased a green or a gray sweater is [tex]\frac{12}{31}[/tex]
Determine whether each relation is a function. Give the domain and range for each relation.
{(3, 4), (3, 5), (4, 4), (4, 5)}
Answer:
Not a function
Domain: {3,4}
Range: {4,5}
Step-by-step explanation:
A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function
For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function
Now let's find the domain and range.
Domain is the set of x values in a relation.
The x values of the given relation are 3 and 4 so the domain is {3,4}
The range is the set of y values in a relation
The y value of the given relation include 4 and 5
So the range would be {4,5}
Notes:
The values of x and y should be written from least to greatest when writing them out as domain and range.
They should be written inside of brackets
Do not repeat numbers when writing the domain and range
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass
Answer:
a. 16 slug b. 3.2 ft
Step-by-step explanation:
a. Total mass of the rod
Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x
So, λ ∝ x³
λ = kx³
Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,
k = λ/x³ = λ/(L/2)³ = 8λ/L³
substituting the values of the variables into the equation, we have
k = 8λ/L³
k = 8 × 2/4³
k = 16/64
k = 1/4
So, λ = kx³ = x³/4
The mass of a small length element of the rod dx is dm = λdx
So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft
M = ∫₀⁴dm
= ∫₀⁴λdx
= ∫₀⁴(x³/4)dx
= (1/4)∫₀⁴x³dx
= (1/4)[x⁴/4]₀⁴
= (1/16)[4⁴ - 0⁴]
= (256 - 0)/16
= 256/16
= 16 slug
b. The center of mass of the rod
Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm = λxdx = (x³/4)xdx = (x⁴/4)dx.
We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft
The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod
= (1/4)∫₀⁴x⁴dx/M
= (1/4)[x⁵/5]₀⁴/M
= (1/20)[x⁵]₀⁴/M
= (1/20)[4⁵ - 0⁵]/M
= (1/20)[1024 - 0]/M
= (1/20)[1024]/M
Since M = 16, we have
x' = (1/20)[1024]/16
x' = 64/20
x' = 3.2 ft
The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 17 minutes.
What is the probability that washing dishes tonight will take me between 14 and 16 minutes?
Give your answer accurate to two decimal places.
The time it takes to wash has the probability density function,
[tex]P(X=x) = \begin{cases}\frac1{17-8}=\frac19&\text{for }8\le x\le 17\\0&\text{otherewise}\end{cases}[/tex]
The probability that it takes between 14 and 16 minutes to wash the dishes is given by the integral,
[tex]\displaystyle\int_{14}^{16}P(X=x)\,\mathrm dx = \frac19\int_{14}^{16}\mathrm dx = \frac{16-14}9 = \frac29 \approx \boxed{0.22}[/tex]
If you're not familiar with calculus, the probability is equal to the area under the graph of P(X = x), which is a rectangle with height 1/9 and length 16 - 14 = 2, so the area and hence probability is 2/9 ≈ 0.22.
If 5000 is divided by 10 and 10 again what answer will be reached
Hey there!
First, divide 5,000 by 10. You will get 500.
Now, 500 ÷ 10, and you will get your answer, 50.
Hope this helps! Have a great day!
Working at home: According to the U.S Census Bureau, 41% of men who worked at home were college graduates. In a sample of 506 women who worked at home, 166 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Solution :
a). The point estimate of proportion of college graduates among women who work at home,
[tex]$\hat p =\frac{166}{506}$[/tex]
= 0.3281
99.5% confidence interval
[tex]$=\left( \hat p \pm Z_{0.005/2} \sqrt{\frac{\hat p (1- \hat p)}{n}} \right)$[/tex]
[tex]$=\left( 0.3281 \pm 2.81 \sqrt{\frac{0.3281 \times (1- 0.3281)}{506}} \right)$[/tex]
[tex]$=(0.3281 \pm 0.0586)$[/tex]
[tex]$=(0.2695, 0.3867)$[/tex]
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Pls help me with this one:(
Answer:
y=-1/7x + 12/7
Step-by-step explanation:
Start by finding the slope
m=(1-0)/(-5-2)
m=-1/7
next plug the slope and the point (-5,1) into point slope formula
y-y1=m(x-x1)
y1=1
x1= -5
m=-1/7
y- 1 = -1/7(x - -5)
y-1=-1/7(x+5)
Distribute -1/7 first
y- 1=-1/7x + 5/7
Add 1 on both sides, but since its a fraction add 7/7
y=-1/7x + (5/7+7/7)
y=-1/7x+12/7
Answer:
Step-by-step explanation:
(-5,1) (2,0)
m=(y-y)/(x-x)
m = (0-1)/2- -5)
m = -1/7
(2,0)
y-0= -1/7 (x-2)
y = -1/7x + 2/7
An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.
y = 40x - 25
y = 25x + 40
y = 25x - 40
y = 40x + 25
Answer:
y = 25x + 40
Step-by-step explanation:
The electrician charges $25 per hour.
The number of hours is x.
Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)
Therefore fee(y) charged by the electrician = $40 + $25x
Hence y = 25x + 40
find the value of the trigonometric ratio
Answer:
15/17
Step-by-step explanation:
sinA = CB/CA =15/17
Answer:
15/17Step-by-step explanation:
sine = opposite / hypotenusesin A = BC/ACsin A = 15/17HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.
Answer:
The unknown is 100
Step-by-step explanation:
A straight line is 180 degrees
We have two angles x, and 80
x+80 = 180
x = 180-80
x= 100
Identify the slope and y intercept of the line with equation 2y = 5x + 4
Answer:
Slope is 5/2
y-intercept is 2
Step-by-step explanation:
Turn the equation into slope intercept form [ y = mx + b ].
2y = 5x + 4
~Divide everything by 2
y = 5/2x + 2
Remember that in slope intercept form, m = slope and b = y-intercept.
Best of Luck!
Answer:
slope: 2.5
y-intercept: 2
Step-by-step explanation:
First isolate the y variable which changes the equation to y=2.5x+2
The equation of a line is mx + b where m is the slope and b and the
y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.
A company wants to decrease their energy use by 17%. If their electric bill is currently $2500 a month, what will their bill be if they are successful
A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?
Answer:
384 cars
Step-by-step explanation:
To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:
34 ⋅ 40 = 1360
As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.
1360 - 976 = 384
Therefore, our answer is 384, specifically, 384 cars.
Answer:
384 cars.
Step-by-step explanation:
40 * 34 - 976
= 1360 - 976
= 384.
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)
(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 3
You're looking for a solution of the form
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]
Differentiating twice yields
[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]
[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]
Substitute these series into the DE:
[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:
[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]
which indicates that the coefficients in the series solution are governed by the recurrence,
[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]
Use the recurrence to get the first few coefficients:
[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]
You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,
-7 = -7/0!
-7/2 = -7/2!
-7/6 = -7/3!
and so on, with only the coefficient in the n = 1 position being the odd one out. So we have
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]
which looks a lot like the power series expansion for -7eˣ.
Fortunately, we can rewrite the linear term as
3x = 10x - 7x = 10x - 7/1! x
and in doing so, we can condense this solution to
[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]
Just to confirm this solution is valid: we have
y = 10x - 7eˣ ==> y (0) = 0 - 7 = -7
y' = 10 - 7eˣ ==> y' (0) = 10 - 7 = 3
y'' = -7eˣ
and substituting into the DE gives
-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0
as required.
Based on what we have learned, how can we ensure that we choose a sample of students that is representative of all 8:00 AM classes that take place on a given morning
Sampling technique is a way of selecting a sample from a given population. The best way to get a sample of students that represents all 8:00 AM classes is by using a stratified sampling technique.
From the complete question, we can summarize the given data as follows:
[tex]Buildings = 3[/tex] ----3 buildings in the college
[tex]Lecture\ Halls =2[/tex] ---- 2 lecture halls in each building
[tex]Capacity = 100[/tex] --- 100 students in each lecture hall
Because the students' lecture halls are not in the same building, the best way to get a sample is as follows:
Divide the students into groups (In this case, the students will be grouped by the buildings of their lecture halls)The number of students in each building is:
[tex]Students = Capacity \times Lecture\ Halls[/tex]
[tex]Students = 100 \times 2[/tex]
[tex]Students = 200[/tex]
There are 200 students in each building
Then select at random an equal proportion of student from each building (say 30 students in each building)The above method is referred to as a stratified sampling technique because the population of the students are divided into groups, before being randomly selected.
Read more about sampling techniques at:
https://brainly.com/question/9612230
[tex] \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = what[/tex]
Answer I'll make and mark as brainlist.
Answer Fast.
Post on - 2 Aug 2021
which one of these points lies on the line described by the equation below y - 5 = 6 ( x - 7 )
Answer:
the answer would be (7,5)
A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?
What is the slope? Please Help
Answer:
-1
Step-by-step explanation:
Pick two points on the line
(0,2) and (2,0)
Using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 0-2)/(2-0)
= -2/2
= -1
Answer:
-1
Step-by-step explanation:
Use two points on the line to find the slope, using rise over run.
We can use the points (0, 2) and (2, 0).
From the first point to the other, the y value decreases by 2 and the x value increases by 2.
Use rise (change in y value) over run (change in x value):
-2 / 2
= -1
So, the slope is -1.
help whats the volume of this
Answer:
93.6
Step-by-step explanation:
The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.
John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?
in the given circle the radius is 9 cm what is its diameter?
Answer:
18
Step-by-step explanation:
The diameter is equal to twice the length of the radius
So if the radius is 9 then the diameter is 9 * 2 = 18
The LARGEST angle has a measure of ______degrees
Answer:
90 i think
Step-by-step explanation:
slope of (30, 600) (75, 1050)
Answer:
y2-y1/x2-x1
y2: 1050
y1:600
x2:75
x1:30
1050-600=450
75-30=45
450/45=10
slope is 10
Answer:
let:
A(30, 600)=(x1,y1)
B((75, 1050)=(x2,y2)
now,
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{1050 - 600}{75 - 30} [/tex]
[tex] = \frac{450}{ 45} [/tex]
[tex] = \frac{10}{1} [/tex]
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
Answer:
A) area decreases
Step-by-step explanation:
Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.
HOPE THIS HELPS
HAVE A GOOD DAY :)
ITS RASPUTIN002
(-72)(-15)= explain
In which direction does the parabola x=2y2+1 open?
A up
B down
C Right
D left
Answer and Step-by-step explanation:
First, we need to set this equation equal to y, which means we need to get y by itself, and all other terms equal to y.
x = [tex]2y^2 + 1[/tex]
Subtract 1, then divide by 2 on both sides.
[tex]x - 1 = 2y^2\\\\\frac{x-1}{2} = y^2[/tex]
Now, take the square root of both sides.
[tex]y=\sqrt{\frac{x-1}{2}}[/tex]
We see that the value with the x (1) is positive, and that we have a square root function, which means the parabola would open to the right.
(If the x value was negative, the square root function's parabola would open to the left)
So, C (Right) is the correct answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
Oh Brian~
I need help again
Answer:
18c^3d^9
Step-by-step explanation:
2c^3 d^2 * 9d^7
We know that we add the exponents when the base is the same
2*9 c^3 d^(2+7)
18c^3d^9
Find the missing segment in the image below
Answer:
The missing segment length is 20.
Step-by-step explanation:
2 is multiplied by 4 to get to 8, so 5 must be multiplied by 4 to get to 20.
Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3
Answer: r = 50 miles/h
Step-by-step explanation:
Let r be the rate of average speed.
Then
r = D/t
r = 150/3
r = 50 miles/h
please click thanks and mark brainliest if you like :)
