Answer: The answer is 6
Step-by-step explanation: this is a combination because it is without repetition.
3!/(3-2)!
(3x2x1)/1!
6/1 = 6
So the answer is 6 different ways
According to a recent Census Bureau report, 12.7% of Americans live below the poverty level. Suppose you plan to sample at random 100 Americans and count the number of people who live below the poverty level. a. What is the probability that you count exactly 10 in poverty? b. What is the probability that you start taking the random sample and you find
Answer:
a) [tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]
b) [tex]P(X \leq 10) = 0.2614[/tex]
c) [tex] (1-0.127)^7 (0.127) =0.0491[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=100, p=0.127)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
a. What is the probability that you count exactly 10 in poverty?
For this case we want this probability P(X=10)
[tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]
b. What is the probability that you count 10 or less in poverty? .2614
For this case we want this probability [tex]P(X=\leq10)[/tex]
[tex]P(X\leq10)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)[/tex]
And we can find the individual probabilities like this:
[tex]P(X=0)=(100C0)(0.127)^{0} (1-0.127)^{100-0}=1.263x10^{-6}[/tex]
[tex]P(X=1)=(100C1)(0.127)^{1} (1-0.127)^{100-1}=1.837x10^{-5}[/tex]
[tex]P(X=2)=(100C2)(0.127)^{2} (1-0.127)^{100-2}=0.000132[/tex]
[tex]P(X=3)=(100C3)(0.127)^{3} (1-0.127)^{100-3}=0.000629[/tex]
[tex]P(X=4)=(100C4)(0.127)^{4} (1-0.127)^{100-4}=0.00222[/tex]
[tex]P(X=5)=(100C5)(0.127)^{5} (1-0.127)^{100-5}=0.00620[/tex]
[tex]P(X=6)=(100C6)(0.127)^{6} (1-0.127)^{100-6}=0.0143[/tex]
[tex]P(X=7)=(100C7)(0.127)^{7} (1-0.127)^{100-7}=0.0279[/tex]
[tex]P(X=8)=(100C8)(0.127)^{8} (1-0.127)^{100-8}=0.0471[/tex]
[tex]P(X=9)=(100C9)(0.127)^{9} (1-0.127)^{100-9}=0.0701[/tex]
[tex]P(X=10)=(100C10)(0.127)^{10} (1-0.127)^{100-10}=0.0928[/tex]
And then repplacing we got:
[tex]P(X \leq 10) = 0.2614[/tex]
c. What is the probability that you start taking the random sample and you find the first person in poverty on the 8th person selected? .0491
For this case we need after 7 people , 1 in poverty so we can find this probability like this:
[tex] (1-0.127)^7 (0.127) =0.0491[/tex]
To calculate the probabilities, we can use the binomial probability formula. For part (a), the probability of counting exactly 10 people below the poverty level can be found by substituting the values into the formula. For part (b), the question is incomplete, so a specific answer cannot be provided.
Explanation:To calculate the probabilities, we can use the binomial probability formula:
P(X=k) = C(n,k) * p^k * q^(n-k)
where:
- P(X=k) is the probability of getting exactly k successes
- C(n,k) is the number of ways to choose k items from a set of n items (combination)
- p is the probability of success
- q is the probability of failure (1-p)
In this case, we're interested in finding the probability of counting exactly 10 people living below the poverty level from a sample of 100 Americans, assuming the poverty rate is 12.7%.
To find the probability that exactly 10 people live below the poverty level, we have:
P(X=10) = C(100,10) * (0.127)^10 * (1-0.127)^(100-10)
Using a calculator or combinatorial calculator, we can find that C(100,10) = 17310309456440.
Substituting the values, we have:
P(X=10) = 17310309456440 * (0.127)^10 * (0.873)^90
Calculating this expression gives us the probability of counting exactly 10 people in poverty.
The question appears to be incomplete as it ends with 'you find'. Please provide the complete question for a more accurate answer.
A measure of the degree to which capital wears out or becomes obsolete during a period is:________
Answer:
Depreciation
Step-by-step explanation:
Depreciation can be defined as the measure of the degree to which the economic value of a capital asset of an organization wear and tears over an existing period of time.
For example:
If a Tractor is bought for $15,000 and it has a useful lifespan of ten years, then every year, the value of the tractor will decline by $1,500. After five years, it will be worth $7,500. That is the tractor has depreciated by $7,500.
plz help!!
Points L, M, and N are collinear. If LM = 7 and LN = 12, what is a possible value of MN?
Answer:
There are two possible values: MN=5 or MN=19
Step-by-step explanation:
The points L and N are collinear, so we can visualize them on a right line as in Figure 1.
First suppose that M is between L and N as in Figure 2. Then we can compute the distance between L and N as LN=LM+MN. Substracting LM from both sides, we obtain that MN=LN-LM=12-7=5.
For the other possibility, suppose that M is not between L and N as in Figure 3. Because LM<LN, it's impossible that M is located further to the right than N. Then M isn't at the right of L. Therefore, M is at the left of L, so L is between M and N, so the distance between M and N is given by MN=ML+LN=LM+LN=7+12=19.
When points L, M, and N are collinear and LM=7 and LN=12, the possible values of MN are 5 or 19 depending on the arrangement of the points. If the order is L, M, N then MN = 5 while if the order is L, N, M then MN = 19.
Explanation:In mathematics, collinear points are points that lie on the same line. In your question, three points L, M, and N are collinear. Given that LM = 7 and LN = 12, we want to find the possible length of segment MN.
There are two possibilities based on the relative placement of these points:
If the points are arranged in the order L, M, then N, the length of MN would be the difference of LN and LM i.e., MN = LN - LM which gives us MN = 12 - 7 = 5.If the points are arranged in the order L, N, then M, the length of MN would be the sum of LN and LM i.e., MN = LN + LM which gives us MN = 12 + 7 = 19.Learn more about Collinear Points here:https://brainly.com/question/5191807
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On a county-wide baseball team, the best players were sent from each high school. There are three mutually exclusive categories of players on this team: infielders, outfielders, and pitchers. If the ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3, then if we pick one player at random from the county-wide baseball team, what is the probability that we will pick a pitcher?
Answer:
[tex]P(pitcher)=\frac{20}{53}=0.377[/tex]
Step-by-step explanation:
Data given
Infielders: Outfielders = 7:4
Pitchers:Outfielders= 5:3
We can find a ratio in common for the 3 cases and in order to do this we can put the ratio with the same denominator of outfielders and we can do this:
Infielders:Outfielders x3 = 7:4 *3 = 21:12
Pitchers:Outfielders x4= 5:3 *4 = 15:12
And we have a one combined ratio:
Infielders:Outfielders:Pitchers = 21:12:20
And we have a basis or a total of 21+12+20 =53
And then we can find the probability that we select a pitcher like this:
[tex]P(pitcher)=\frac{20}{53}=0.377[/tex]
The probability of selecting a pitcher from the baseball team is approximately 0.3774 or 37.74%, found by establishing the combined ratio of all players and then calculating the ratio of pitchers to the total number of players.
To determine the probability of selecting a pitcher from the county-wide baseball team, we first need to establish the ratio of all players in their respective categories based on the given ratios. The ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3. We should find a common multiple for the number of outfielders in both ratios so that we can combine them into a single ratio that includes infielders, outfielders, and pitchers.
Let's assume there are 12 outfielders which is a common multiple of both 4 and 3 (the numbers of outfielders in each provided ratio). This would give us 7*3 infielders and 5*4 pitchers when we scale the ratios accordingly.
Therefore:
Infielders = 7 * 3 = 21
Outfielders = 12 (our common multiple)
Pitchers = 5 * 4 = 20
The total number of players on the team would be 21 + 12 + 20 = 53.
The probability of selecting a pitcher would therefore be the number of pitchers divided by the total number of players:
P(Pitcher) = Number of Pitchers / Total Number of Players = 20 / 53.
The probability of selecting a pitcher is approximately 0.3774 (or 37.74%).
Which is the expressions is equivalent to the expression 1/2 cos(4 theta)-(1/2)cos(8 theta)?
Answer:
[tex]sin(6\theta)sin(2\theta)[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{1}{2}cos(4\theta)-\frac{1}{2}cos(8\theta)[/tex]
The expression can be written as
[tex]\frac{1}{2}(cos(4\theta)-cos(8\theta))[/tex]
[tex]\frac{1}{2}(-2 sin (\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2}))[/tex]
Using identity: [tex] cos A-cos B=-2 sin(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]
[tex]-sin(6\theta)sin(-2\theta)[/tex]
We know that
[tex] Sin(-x)=-Sin x[/tex]
By using this property
We get
[tex]sin(6\theta)sin(2\theta)[/tex]
Purchasing a movie combo pack of one popcorn and two drinks from $14 saves $4 compared to purchasing the items individually. If a drink is $5' what is the individual cost of a popcorn
Answer:
the individual price of a popcorn is $8.
Step-by-step explanation:
p+2d=14 is the price with deal
p+2d=14+4 if there was no deal
plug 5 into the equation as d
2(5)+p=18
solve for p.
p=8
YOU GUYS GET NO MOM GET MO DAD GET MO GRANDMA GET NO GRANDPA GET NO CAR GET MO HOUSE…..your mom
To determine customer opinion of their pricing, Greyhound Lines randomly selects 90 busses during a certain week and surveys all passengers on the busses.What type of sampling is used?
Answer: Cluster sampling.
Step-by-step explanation:
Cluster sampling is a sampling technique in statistics in which the researcher splits the entire population into different groups called clusters.After that he randomly select a sample from the clusters from the population and survey all elements of sampled clusters.Researcher performs his analysis on data from the sampled clusters.In the given situation Greyhound Lines randomly selects 90 buses during a certain week and surveys all passengers on the buses.
Here, week= Cluster
Buses = Elements
Therefore , the type of sampling is used = Cluster sampling.
Two identical rubber balls from different heights. Ball 1 is dropped from a height of 159 feet , and ball 2 is dropped from a?height of 246 feet. Use the function f(t) = -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over given time t.
When does ball 2 reach the ground? Round to the nearest hundredth.
Answer:
after 3.92 seconds
Step-by-step explanation:
Fill in the given value of h to find the formula for the height of the ball. Then set the value of that height to zero and solve for t.
[tex]h_2(t)=-16t^2+246\\\\0=-16t^2+246\\\\0 = t^2-15.375 \quad\text{divide by -16}\\\\\sqrt{15.375}=t \quad\text{add 15.375, take the square root}\\\\t\approx 3.92[/tex]
Ball 2 reaches the ground after 3.92 seconds.
Identify each of the following variables as continuous or discrete.
a. The weight of a dog
b. The result of a roll of dice
c. The weight of a bunch of bananas
d. The number of people in line at a box office to purchase theater tickets
Answer:
a) a continuous variable
b) a discrete variable
c) a continuous variable
d) a discrete variable
Step-by-step explanation:
Well first we need to define what are the continuous and discrete variables. Discrete variables are those whose values are obtained by counting, but continuous variables those whose values are obtained by measurement.
a) The weight of a dog can be measured. Therefore, it is a continuous variable.
b) The result of a roll of dice can be counted. Therefore, it is a discrete variable.
c) The weight of a bunch of bananas can be measured. Therefore, it is a continuous variable.
d) The number of people in line at a box office to purchase theater tickets can be counted. Therefore, it is a discrete variable.
The weight of a dog and a bunch of bananas are continuous variables, while the result of a dice roll and the number of people in line are discrete variables.
Explanation:a. The weight of a dog is a continuous variable. It can take on any value within a certain range, such as 12.5 pounds, 20.2 pounds, or 35.7 pounds.
b. The result of a roll of dice is a discrete variable. It can only take on particular values, such as 1, 2, 3, 4, 5, or 6.
c. The weight of a bunch of bananas is a continuous variable. Like the weight of a dog, it can take on any value within a certain range.
d. The number of people in line at a box office to purchase theater tickets is a discrete variable. It can only take on whole number values, like 0, 1, 2, 3, and so on.
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What is the midpoint of BC?
Question 4 options:
(0, 1)
(1, 7)
(1, 3)
(0, 2)
To find the midpoint, add the two x values together and divide by 2, and then do the same with the Y values.
-3 + 3 = 0
0 / 2 = 0, the X value is 0
-1 + 3 = 2
2/2 = 1, the Y value is 1
The midpoint would be (0,1)
Answer:
The answer to your question is (0, 1)
Step-by-step explanation:
Data
B (3, -1)
C (-3, 3)
Formula
[tex]Xm = \frac{x1 + x2}{2}[/tex]
[tex]Ym = \frac{y1 + y2}{2}[/tex]
Substitution and simplification
[tex]Xm = \frac{3 - 3}{2}[/tex]
[tex]Xm = \frac{0}{2}[/tex]
Xm = 0
[tex]Ym = \frac{-1 + 3}{2}[/tex]
[tex]Ym = \frac{2}{2}[/tex]
Ym = 1
Result
(0, 1)
A rocket is launched from the top of a 7ft platform. Its initial velocity is 112 ft per sec. It is launched at an angle of 60° with respect to the ground. (a) Find the rectangular equation that models its path. What type of path does the rocket follow
Answer:
[tex]y=7+1.73x-0.0016x^{2}[/tex]
Parbolic path.
Step-by-step explanation:
This is bidimensional motion, so the equation that relates the vertical and horizontal position is:
[tex]y=y_{0}+(tg(\theta))x-\frac{g}{2(v_{0}cos(\theta))^{2}}x^{2}[/tex]
Here, v₀, θ y g are constants, then we can rewrite (1) as:
[tex]y=a+bx-cx^{2}[/tex]
where:
[tex]a=y_{0}=7 ft[/tex][tex]b=tg(\theta)=1.73[/tex][tex]c=\frac{g}{2(v_{0}cos(\theta))^{2}}=0.0016 \frac{1}{ft}[/tex]Therefore the rectangular equation will be:
[tex]y=7+1.73x-0.0016x^{2}[/tex]
This type of path is a parabolic motion.
I hope it helps you!
\begin{aligned} &y=2x -1 \\\\ &5x-4y=1 \end{aligned} y=2x−1 5x−4y=1 Is (1,1)(1,1)left parenthesis, 1, comma, 1, right parenthesis a solution of the system?
Answer:
Therefore, ( 1 , 1 ) is the Solution to the Given Equations
[tex]y=2x-1[/tex]
[tex]5x-4y=1[/tex]
Step-by-step explanation:
Given:
[tex]y=2x-1[/tex] ..............Equation ( 1 )
[tex]5x-4y=1[/tex] ..............Equation ( 2 )
To Find:
x = ?
y = ?
Solution:
[tex]y=2x-1[/tex] ..............Equation ( 1 )
[tex]5x-4y=1[/tex] ..............Equation ( 2 )
Substituting equation 1 in equation 2 we get
[tex]5x-4(2x-1)=1\\applying\ distributive\ property\ we\ get\\5x-8x+4=1\\\\-3x=1-4=-3\\\\x=\frac{-3}{-3}=1\\ \therefore x = 1\\[/tex]
Substituting 'x' in Equation ( 1 ) we get
[tex]y=2\times 1-1\\\\y=1\\\\\therefore y =1\\[/tex]
Therefore, ( 1 , 1 ) is the Solution to the Given Equations
[tex]y=2x-1[/tex]
[tex]5x-4y=1[/tex]
Need help with two questions please
Answer:
Question 1
since triangles are similar
angle B = angle D
8x + 16 = 120
x = 13
Question 2
Ttiangles are similar
therefore, sides are in ratio
AB ÷ XY = BC ÷ YZ = AC ÷ XZ
substituting all values we get
BC = 22
BC = 22AC = 16
The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles. The wall measures 8 feet by 10 feet. How many mirror tiles will they need to cover the wall?
Answer:80 mirror tiles will be needed to cover the wall is 80
Step-by-step explanation:
The dimension of one wall in living room is 8 feet by 10 feet. The wall is rectangular in shape. The area of a rectangle is expressed as
Length × width. The area of one wall in the living room would be
8 × 10 = 80 feet^2
The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles.
The number of mirror tiles that they will need to cover the wall would be
80/1 = 80 mirror tiles.
The Williams family will need 80 mirror tiles to cover the wall.
The Williams family wants to cover one wall in their living room with 1-foot square mirror tiles. The wall measures 8 feet by 10 feet. To find out how many mirror tiles are needed, we calculate the area of the wall using the formula for area:
Area = length × width
Substituting the given measurements:
Area = 8 feet × 10 feet = 80 square feet
Since each mirror tile covers 1 square foot, the number of mirror tiles required is equal to the area of the wall:
Number of mirror tiles = 80
Therefore, the Williams family will need 80 mirror tiles to cover the wall.
PLLLZZZZ!!! HELP!!! WILL GIVE BRAINLIEST!!!!
Given a polynomial f(x), if (x − 6) is a factor, what else must be true?
A. f(0) = −6
B. f(0) = 6
C. f(−6) = 0
D. f(6) = 0
Answer:
D because x is what you subtract/add to get zero in (x − 6). x - 6 + 6 = 0
That is how the class taught me.
Given the function below, what is the value of g(4)? g(x)=3x2−3x−9 Select one: A. 15 B. 27 C. 38 D. 56
Answer:
B. 27
Step-by-step explanation:
Given: g(x) = 3x² - 3x - 9
g(4) = 3(4)² - 3(4) - 9
g(4) = 48 - 12 - 9 = 48 - 21 = 27
Answer:
Option B). 27 is correct
ie., The value of [tex]g(4)=27[/tex] for the given function.
Step-by-step explanation:
Given function g is defined by [tex]g(x)=3x^{2}-3x-9[/tex]
Now to find the value of g(4):
That is put x=4 in the given function we get
[tex]g(x)=3x^{2}-3x-9[/tex]
[tex]g(4)=(3\times 4^{2})-(3\times 4)-9[/tex]
[tex]=(3\times 16)-12-9[/tex]
[tex]=48-21[/tex]
[tex]=27[/tex]
Therefore [tex]g(4)=27[/tex]
Option B). 27 is correct
ie., The value of [tex]g(4)=27[/tex] for the given function.
A single-celled organism is represented below. Structure X carries out a function most similar to which structure in a human?
Answer: lung
Step-by-step explanation:
Attachedfile/picture shows the structure.
Respiration is a process of degradation of complex organic compound with the production of carbon dioxide, water and energy.
Respiration involves two phases, which are;
(1). External Respiration or Breathing: this is a process in which
animals take oxygen in and release carbon dioxide.
(2). Internal Respiration or Cellular Respiration: this process involve the release of energy from food substance with the release of carbondioxide and and water.
Single celled animals or unicellular animals such as amoeba exchange gases through cell surface. The STRUCTURE X IS THE PLASMA MEMBRANE. There is absorption of of Oxygen from the surrounding air or water,hence, giving out carbondioxide through plasma membrane by Diffusion.
PS: Lung is used in respiration process in Human
Benjamin & Associates, a real estate developer, recently built 195 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total number of bedrooms in the entire complex is 497, how many two-bedroom units are there? How many three-bedroom units are there?
To find the number of two-bedroom and three-bedroom units in the complex, we can set up a system of equations and solve them using substitution or elimination.
Explanation:To solve this problem, we need to set up a system of equations. Let x represent the number of two-bedroom units and y represent the number of three-bedroom units. From the problem, we know that there are a total of 195 condos. So, we have the equation: x + y = 195. We also know that the total number of bedrooms is 497, which can be expressed as: 2x + 3y = 497. We can now solve this system of equations using substitution or elimination to find the values of x and y. When solved, we find that there are 112 two-bedroom units and 83 three-bedroom units in the complex.
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Kanna Kamui let her DS charge for 108 minutes from 05%. What percent charge is Kanna's DS.
Note: A Nintendo DS takes 4 hours to charge fully.
Answer:
The percent charge of Kanna's DS is 50%
Step-by-step explanation:
we know that
A Nintendo DS takes 4 hours to charge fully (100%)
4 hours is the same that 240 minutes
using proportion
Find out what percentage represent 108 minutes
[tex]\frac{100}{240}\ \frac{\%}{min} =\frac{x}{108}\ \frac{\%}{min}\\\\x=100(108)/240\\\\x=45\%[/tex]
Remember that
Kanna Kamui charge her DS from 5%
so
[tex]5\%+45\%=50\%[/tex]
therefore
The percent charge of Kanna's DS is 50%
To figure out the charge percentage of Kanna's DS, we need to know the time it takes for a full charge and the time Kanna's DS was charged. The calculation (108 minutes charged / 240 minutes for a full charge) x 100 gives approximately 45%.
Explanation:The question is asking about the percentage charge of Kanna's DS after being charged for a specific period. First, we need to know how long it takes for a DS to become fully charged, which is 4 hours (equivalent to 240 minutes). Now, Kanna let her DS charge for 108 minutes, and the proportion of time spent charging to the total time needed to fully charge the DS represents the percentage of charge.
So, to calculate this, we would divide the time spent charging (108 minutes) by the total time needed for a full charge (240 minutes) and multiply by 100 to get the percentage.
Therefore, the calculation would be: (108/240) x 100 = 45% (rounding to the nearest whole number).
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Which of the following are steps in the process in solving application problems using the two-order system?
1. Assign two variables for the unknowns.
2. Make a guess for the value of the variables.
3. Write two equations using the assigned variables.
4. Make another guess, based on the results of the first guess. Solve the pair of equations.
Answer:
1 and 3
Step-by-step explanation:
For resolving an application problems using the two - order system, the following steps must be taken:
First assign two variables for the unknowns.
Second write two equations using the assigned variables.
Third solve the pair of equations.
Then, only 1 and 3 are steps in the process in solving application problems, using the two-order system
For a birthday party Mr. Perkins or do you eat chocolate chip cookies and 16 sugar cookies each cookie is the same price he also picks up a cupcake for himself which cost two dollars and $75 the total bill is $44.03 what is the cause of a cookie
Question is not proper, Proper question is given below;
For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?
Answer:
The Cost of the cookie will be $1.72.
Step-by-step explanation:
Given:
Mr Perkins orders 8 chocolate chip cookies and 16 sugar cookies.
Since cost of both the cookies are same then Let us assume the cost of cookies be 'x'.
Total cost of the cookies = [tex](8 + 16)x = 24x[/tex]
Cost of Cup cakes = $2.75.
Total bill he pays = $44.03
We need to find the cost of each cookies.
Now we know that Total bill he pays is equal to sum of Cost of cookies and Cost of Cup cakes he bought.
Framing in equation form we get;
[tex]44.03 = 24x + 2.75[/tex]
Now Subtracting both side by 2.75 using Subtraction property we get;
[tex]2.75+24x-2.75 = 44.03 - 2.75\\\\24x = 41.28[/tex]
Now Dividing both side by 24 using Division property we get;
[tex]\frac{24x}{24} = \frac{41.28}{24}\\\\x=1.72[/tex]
Hence The Cost of the cookie will be $1.72.
If two states are selected at random from a group of 20 states, determine the number of possible outcomes if the group of states are selected with replacement or without replacement.
Answer:
With replacement
21C2 = 210 outcomes
without replacement
20C2 = 190 outcomes
Step-by-step explanation:
For determining the number of possible outcomes you need count the number of possible combinations, because a combination is a selection of a number of items from a set of items where the order of selection does not matter.
The number of possible combinations is calculated thus
nCr = [tex]\frac{n!}{(n-r)!r!}[/tex]
Where n: number of items of the set
r: number of selected items
a) If the group of states are selected with replacement then
(n+r-1)Cr
n = 20 states
r = 2 states
then n +r -1 = 20 +2 -1 = 21
21C2 = [tex]\frac{21!}{(21-2)!2!} = 210[/tex]
b) If the group of states are selected without replacement then
nCr
n = 20
r = 2
20C2 = [tex]\frac{20!}{(20-2)!2!} = 190[/tex]
When two states are chosen with replacement from 20, there are 400 possible outcomes. Without replacement, there are 380 possible outcomes.
Explanation:The question asks for the number of possible outcomes if two states are selected at random from a group of 20 states, with and without replacement. Replacement means a state can be chosen more than once, while without replacement means a state can only be chosen once.
Choosing with Replacement
When selecting with replacement, a state can be chosen, replaced, and then chosen again. Therefore, for each of the two selections, there are 20 possible states that can be chosen. This leads to a total of 20 * 20 = 400 possible outcomes.
Choosing without Replacement
In the scenario where states are chosen without replacement, the number of possible outcomes changes for the second selection because a state cannot be chosen twice. In this case, there are 20 options for the first state and 19 options for the second (since one state has been selected and is not replaced). Thus, the total number of possible outcomes is 20 * 19 = 380.
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A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apples weigh 160 pounds, how much the the truckload of fruit weigh in total
Answer:the truck load of fruit weigh 440 pounces
Step-by-step explanation:
Let the total weight of the truck load of fruit weigh x pounds.
The truck carries apples, grapes, and blackberries in the ratio of 4:3:4
The total ratio is the sum of the proportions of apples, grapes, and blackberries. It becomes 4+3+4 = 11
if the apples weigh 160 pounds, it means that
4/11 × x = 160
4x/11 = 160
4x = 160×11 = 1760
x = 1760/4
x = 440
A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement. a) What is the probability that both balls are white? (Answer may be left as a fraction or as a three-place decimal.) b) What is the probability that both balls are the same color? (Answer may be left as a fraction or as a three-place decimal.)
The probabilities are (a) the probability that both balls are white is 0.058 and (b) the probability that both balls are the same color is 1.904.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement.
Total number of balls : 6+4+3 +1 = 13
(a)
Out of 13 balls,
3 are white, so probability of getting first white ball is,
P(first white) = 3/13
After that 12 balls remaining out of which 3 are white so
P(second white| first white) = 3/12
So required probability is
P(both white) = P(Second white| first white)P(first white) = (3/13) x (3/12) = 0.0576 = 0.058
(b)
Since there is only one green ball, so both balls cannot be same. Therefore,
P(both of same color) = P(both blue)+P(both red)+P(both white) = 0.923+ 0.923+ 0.058= 1.904
The probability that both balls of same color is
P(both of same colors) = 1.904
Therefore, the probabilities are (a) 0.058 and (b) 1.904
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Camilo estimates the weight of the dog . The veterinarian says that the dog weighs 84 pounds . The percent error in Camillo's estimate is less than 10%
Answer:
The estimated weight is in the range:
75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds
Step-by-step explanation:
Since, the maximum error is 10%.
Therefore, the maximum and minimum vales will be 10% more and 10% less than 84 pounds, respectively.
For Maximum Limit:
[tex]Weight_{max}[/tex] = (1.1)(84 pounds)
[tex]Weight_{max}[/tex] = 92.4 pounds
For Minimum Limit:
[tex]Weight_{min}[/tex] = (0.9)(84 pounds)
[tex]Weight_{min}[/tex] = 75.6 pounds
Hence, the estimated weight is in the range:
75.6 pounds [tex]\leq[/tex] Weight [tex]\leq[/tex] 92.4 pounds
Four items are on sale at a local store. A shirt was originally $9.50 and now is $7.60. A pair of jeans were $25.00, and now they are priced $20.00. A pair of boots were $55.00, and they are on sale for $44.00. Do these regular and sale prices represent a proportional relationship
Answer:YES
Step-by-step explanation:
Answer : Yes, regular and sale prices represent a proportional relationship.
Step-by-step explanation :
We have to determine the ratio of regular and sale prices of shirt, jeans and boots .
A shirt was originally $9.50 and now is $7.60.
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 9.50}{\$ 7.60}[/tex]
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]
A pair of jeans were $25.00, and now they are priced $20.00.
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 25.00}{\$ 20.00}[/tex]
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]
A pair of boots were $55.00, and they are on sale for $44.00.
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{\$ 55.00}{\$ 44.00}[/tex]
[tex]\frac{\text{Regular price}}{\text{Sale price}}=\frac{5}{4}[/tex]
From this we conclude that, all the items are in same ratio that means the regular and sale prices represent a proportional relationship.
Hence, yes, regular and sale prices represent a proportional relationship.
Jeremy had a square piece of gift wrapping paper with a side length of x inches that he used to wrap a present. First he cut 6 inches off the right side of the paper and discarded the rectangular scrap. Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap. What expression represents the total area in square inches of the scraps that he discarded? Explain your process and justify your answer.
Answer:
( 9x - 18 ) square inches
Step-by-step explanation:
Data provided in the question:
Side of the square piece of gift wrapping paper = x inches
Now,
According to the question:
He cut 6 inches off the right side of the paper and discarded the rectangular scrap
Therefore,
Dimension of the scrap formed will be 6x square inches
The dimensions of the paper left
Top width will be ( x - 6 ) and the right width will be x
Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap
Therefore,
Dimension of the scrap will be
( x - 6 ) long wide and 3 inches wide
Hence,
The area of the scraps will be
⇒ 6x + 3(x - 6)
⇒ 6x + 3x - 18
⇒ ( 9x - 18 ) square inches
The popuation of monterrey, mexico is 4x10^6 people, and the population of shanghai,china is 2x10^7 people. How many times lager is the population of shanghai compared to monterrey
Answer:
The population of Shanghai is 5 times larger than population of Monterrey.
Step-by-step explanation:
Given:
The population of Monterrey, Mexico is [tex]4\times10^6[/tex] people
The population of Shanghai, China is [tex]2\times10^7[/tex] people.
To find how many times the population of Shanghai is lager than Monterrey.
Solution:
In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and Monterrey.
Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.
Thus, we have:
[tex]\frac{2\times10^7}{4\times10^6}[/tex]
Simplifying by using properties of exponents.
⇒ [tex]\frac{2\times10^{(7-6)}}{4}[/tex] [As [tex]\frac{a^x} ]{a^y}=a^{(x-y)}[/tex]
⇒ [tex]\frac{2\times10^{(1)}}{4}[/tex]
⇒ [tex]\frac{20}{4}[/tex]
⇒ [tex]5[/tex]
Thus, we can say that the population of Shanghai is 5 times larger than population of Monterrey.
Shanghai's population is 5 times larger than Monterrey's.
To find out how many times larger the population of Shanghai is compared to Monterrey, we need to divide the population of Shanghai by the population of Monterrey.
Population of Shanghai: 2x[tex]10^7[/tex] people
Population of Monterrey: 4x[tex]10^6[/tex] people
Now, divide the population of Shanghai by the population of Monterrey:
[tex]2x10^7[/tex] / 4x[tex]10^6[/tex] = (2 / 4) x 10(7-6)
This simplifies to:
0.5 x 101 = 5
Therefore, the population of Shanghai is 5 times larger than the population of Monterrey.
Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?
Answer:
Required equation : [tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
Step-by-step explanation:
It is given that Dale Horton can paint a certain room in 3 hours.
One hour woks of Dale Horton = 1/3
Kathy Garcia can paint the same room in 9 hours.
One hour woks of Kathy Garcia = 1/9
Let together they can paint the same room in t hours.
One hour woks of both = 1/t
[tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
[tex]\frac{1}{t}=\frac{3+1}{9}[/tex]
[tex]\frac{1}{t}=\frac{4}{9}[/tex]
After reciprocal we get
[tex]\frac{t}{1}=\frac{9}{4}[/tex]
[tex]t=2.25[/tex]
1 hour = 60 minutes.
0.25 hour = 15 minutes.
Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
Prove F is close if and only if F is a finite intersection of closed sets finite uniona) trueb) false
Answer:
This statement is true
Step-by-step explanation:
Remember that subset F of a metric (or topological) space X is said to be closed if X-F is open according to the metric (topology) of F.
Let F⊆X. For the "if" part, suppose that [tex]F=F_1\cap F_2\cap \cdots \cap F_n[/tex] where [tex]F_k[/tex] is a closed set for all k. Then by De Morgan's law, [tex]X-F=(X-F_1)\cup(X-F_2)\cup \cdots\cup(X-F_n)[/tex].
Now, since Fk is closed for all k, then X-Fk is open. In every metric (topological) space, the union of an arbitrary family of open sets open sets is open, thus X-F is open, that is, F is closed.
For the "only if" implication, suppose that F is closed. We always have that F=F∩F (y∈F if and only if y∈F and y∈F if and only if y∈F∩F). then F is a finite intersection of closed sets (F and F).