Answer:
(a) The average number of passengers that will be on each flight is 28.8.
(b) Everyone will have a seat on about 84.4% of the flights.
Step-by-step explanation:
The correct question is:
Suppose that past experience shows that about 10% of passengers who are schedule to take a particular flight fail to show up. For this reason, airlines sometimes overbook flights, selling more tickets than they have seats, with the expectation that they will have some no shows. Suppose an airline used a small jet with seating for 30 passengers on a regional route and assume that passengers are independent of each other in whether they show up for the flight. Suppose that the airline consistently sells 32 tickets for every one of these flights.
(a) On average, how many passengers will be on each flight?
(b) How often will they have enough seats for all of the passengers who show up for the flight?
Solution:
Let the random variable X measure the number of passengers (out of 32) who show up for a flight.
For each passenger there is a 90% chance of showing up, so X is a binomial random variable with n = 32 and p = 0.90.
(a)
The average of a binomial random variable is:
[tex]\text{Average}=np[/tex]
Compute the average number of passengers that will be on each flight as follows:
[tex]\text{Average}=np[/tex]
[tex]=32\times 0.90\\=28.8[/tex]
Thus, the average number of passengers that will be on each flight is 28.8.
(b)
To have enough seats for all of the passengers who show up for the flight, the value of X must be less than or equal to 30.
Compute the value of P (X ≤ 30) as follows:
P (X ≤ 30) = 1 - P (X > 30)
= 1 - P (X = 31) - P (X = 32)
[tex]=1-[{32\choose 31}\ (0.90)^{31}\ (1-0.90)^{32-31}]-[{32\choose 32}\ (0.90)^{32}\ (1-0.90)^{32-32}]\\\\=1-0.122087-0.034337\\\\=0.843576\\\\\approx 0.844[/tex]
Thus, everyone will have a seat on about 84.4% of the flights.
A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 218 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related
Answer:
Step-by-step explanation:
Hello!
Since you didn't upload the data, I'll use my own data to solve the example. The steps will be the same, only the results will change. (see attachment) The hypothesis test will be made using a 5% significance level.
The objective of this exercise is to test if there is an association between two variables:
X₁: The subject is vaccinated, categorized "Yes" and "No"
X₂: The subject got the disease, categorized "Yes" and "No"
These two variables of interest are qualitative categorical and each one of them has two categories.
To test if the variables are associated, considering the type of variables they are, you have to apply a Chi Square test of Independence, where the statistic hypotheses are:
H₀: [tex]P_{ij}= P_{i.} * P_{.j}[/tex] ∀ i= 1, 2 and j= 1, 2
H₁: The variables, vaccination and disease status, are not independent.
α: 0.05
The statistic is
X²= [tex]{r} \atop {i=1} \right.[/tex]∑[tex]{c} \atop {j=1} \right.[/tex]∑[tex]\frac{(O_{ij}-E_{ij})^2}{E_{ij}}[/tex]≈[tex]X^2_{(r-1)(c-1)}[/tex]
i= values in rows
j= values in columns
r= total number of rows
c= total number of columns
This type of test is always one-tailed to the right, meaning that you will reject the null hypothesis to high values of Chi Square. There is only one critical value:
[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{(2-1)(2-1);1-0.05}= X^2_{1*1;0.95}= 3.841[/tex]
The decision rule will be:
If [tex]X^2_{H_0}[/tex] ≥ 3.841, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 3.841, do not reject the null hypothesis.
Using the p-value approach, the decision rule is always the same:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
Before calculating [tex]X^2_{H_0}[/tex], you have to calculate the expected frequencies for all categories using the formula:
Ê[tex]_{ij}[/tex]= [tex]\frac{O_{i.}*O_{.j}}{n}[/tex]
Ê₁₁= [tex]\frac{O_{1.}*O_{.1}}{n}= \frac{82*100}{200} = 41[/tex]
Ê₁₂= [tex]\frac{O_{1.}*O_{.2}}{n}= \frac{82*100}{200} = 41[/tex]
Ê₂₁= [tex]\frac{O_{2.}*O_{.1}}{n}= \frac{118*100}{200} = 59[/tex]
Ê₂₂= [tex]\frac{O_{2.}*O_{.2}}{n}= \frac{118*100}{200} = 59[/tex]
[tex]X^2_{H_0}= \frac{(42-41)^2}{41} + \frac{(40-41)^2}{41} + \frac{(58-59)^2}{59} + \frac{(60-59)^2}{59}= 0.0827[/tex]
The p-value for this test is the probability of obtaining a value as extreme as [tex]X^2_{H_0}[/tex]= 0.0827:
P(X₁² ≥ 0.0827)= 1 - P(X₁² < 0.0827)= 1 - 0.2264= 0.7736
Using the critical value approach: the value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.Using the p-value approach: the p-value is greater than the significance level, the decision is to not reject the null hypothesis.Ata 5% significance level, the decision is to not reject the null hypothesis. You can conclude that the vaccination and the disease status of the subjects are not related. The new vaccine does not affect the chances of the subjects getting the disease.
I hope this helps!
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X>1), n=4, p=0.6.
Answer:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.6)[/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]
We want to find the following probability:
[tex] P(X >1)[/tex]
And for this case we can use the complement rule and we got:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
If f(x) = (x - 3)/(x + 4), find f -1(x).
Answer:
f^-1(x) = (4x +3)/(1 -x)
Step-by-step explanation:
Solve for y:
f(y) = x
(y -3)/(y +4) = x
y -3 = xy +4x . . . . . . multiply by y+4
y -xy = 4x +3 . . . . . . add 3-xy
y(1 -x) = 4x +3 . . . . . factor out y
y = (4x +3)/(1 -x) . . . divide by the coefficient of y
The inverse function is ...
f^-1(x) = (4x +3)/(1 -x)
Check all of the points that are solutions to the system of inequalities.
'X + y 2 2 +4
y< 4
Answer:
C. (5, 3)
D. (7, -1)
Step-by-step explanation:
The requirement that y < 4 eliminates points A, E, F. None of 7, 4, 5 are less than 4.
The requirement that x+y ≥ 6 eliminates point B. 1-1 = 0 is not at least 6.
Points C and D satisfy both inequalities.
Which of the following expressions is equal to -1?
sec90°
sin180°
csc270°
Answer:
csc 270° is the answer.
A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2 comma 6402,640 firms, 709709 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 2929%? Use alphaαequals=0.100.10 to make your decision.
Answer:
Step-by-step explanation:
Using the one sample proportion test:
z = (p-P) / √{P (1-P)/n}
Where p = 709/2640= 0.27, P = 0.29, n= 2640
Thus z = (0.27-0.29) / √{0.29 (1-0.29) / 2640}
z = (-0.02) / √{0.29(0.71) /2640}
z = (-0.02) / √0.00007799
z = (0.02) / 0.0088
z = 2.27
To be able to draw a conclusion, lets find the p value at the 0.1 level of significant: p value is 0.2327. The result is significant as the p value is greater than 0.1 thus we will fail to reject the null and conclude that there is not enough statistical evidence to prove that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%
66 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.8397
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the cards are chosen is not important. Also, they are drawn without replacement. So we use the combinations formula to solve this question.
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]
What is the probability that at least one of the cards drawn is a spade?
Either none is a spade, or at least one is a spade. The sum of the probabilities of these outcomes is 1.
The standard deck has 52 cards, of which 13 are spades. So
Probability that none are spades:
Desired outcomes:
6 cards from a set of 52 - 13 = 39. So
[tex]D = C_{39,6} = \frac{39!}{6!33!} = 3262623[/tex]
Total outcomes:
6 cards from a set of 52. So
[tex]T = C_{52,6} = \frac{52!}{6!46!} = 20358520[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{3262623}{20358520} = 0.1603[/tex]
Probability that at least one is a spade:
1 - 0.1603 = 0.8397
The answer is 0.8397
The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a 1 + be−0.7t where t is measured in hours. At time t = 0 the population is 30 cells and is increasing at a rate of 18 cells/hour. Find the values of a and b.
Answer:
a = 30
b = 6/7
Step-by-step explanation:
The number of yeast cells after t hours is modeled by the following equation:
[tex]f(t) = a(1 + be^{-0.7t})[/tex]
In which a is the initial number of cells.
At time t = 0 the population is 30 cells
This means that [tex]a = 30[/tex]
So
[tex]f(t) = 30(1 + be^{-0.7t})[/tex]
And increasing at a rate of 18 cells/hour.
This means that f'(0) = 18.
We use this to find b.
[tex]f(t) = 30(1 + be^{-0.7t})[/tex]
So
[tex]f(t) = 30 + 30be^{-0.7t}[/tex]
Then, it's derivative is:
[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]
We have that:
f'(0) = 18
So
[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]
Then
[tex]-21b = 18[/tex]
[tex]21b = -18[/tex]
[tex]b = -\frac{18}{21}[/tex]
[tex]b = \frac{6}{7}[/tex]
Parallelogram V W Z X is shown. Point Y is at the bottom center of the shape. Lines are drawn from points V to X through point Y and from points W to Z through point Y. 4 triangles are formed by the lines. If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not? Yes, along with the given information, ZX ≅ ZX by the reflexive property. Yes, the triangles are both obtuse. No, the sides of the triangles intersect. No, there is not enough information given.
Answer:
It's D: No, there is not enough information given.
Step-by-step explanation:
just took the quiz
The correct answer option D which is No, there is not enough information given.
What is parallelogram?A parallelogram is a quadrilateral having four sides with two opposite sides parallel to each other. The sum of the angles suspended by all the four sides of the parallelogram is 360.
Using VX = WZ and m∠ZVX = m∠XWZ, we have a side and an angle. In order to prove the triangles congruent by SAS, we must have two sides and the angle between them. With the information we have now, we would have to have VZ = WX. However, we are not given that information.
We do have that ZX = ZX by the reflexive property, but this is not SAS, as the angle we have is not between the two sides.
Therefore correct answer option D which is No, there is not enough information given.
The complete figure is attached with the answer below.
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9/8+7/40= and does the answer simplify
Answer:
1 3/10
Step-by-step explanation:
9/8 +7/40
Get a common denominator of 40
9/8 *5/5 + 7/40
45/40 + 7/40
52/40
Rewriting as
40/40 +12/40
1 + 3/10
1 3/10
Answer:
1 3/10
Step-by-step explanation:
First, you need to get a common denominator:
8x5=40 <-- common denominator
45/40+7/40= 52/40
yes you can simplify it.
your final answer will be: 1 3/10
URGENT! WILL GIVE BRANLIEST!!! THX TO THOSE WHO ARE WILLING TO TAKE A LOOK. :) 2 QUESTIONS
If the tangent ratio of 0 is 12/5 which angle is 0
FIRST IMAGE
What is the tangent ratio of angle X? SECOND PICTURE
A) tan0=xy/yz
B) tan0=xy/xz
C) tan0=yz/xz
D) tan0=yz/xy
Answer:
1. tan J
2. D. tan(∠x) = yz/xy
Step-by-step explanation:
1. Remember that tangent is opposite over hypotenuse. So 12 has to be opposite of x point. The only point suitable would be point J. Therefore, your answer is for tan∅ is tan J.
2. Same concept here as in 1. Extra: If tan is sin∅/cos∅ on the unit circle, that means yz would have to be sin and yx would have to be cos.
What is the sum of (4x2 – 10x + 3) and (-6x2 + 10x + 12)
Answer:
-2x² + 15
Step-by-step explanation:
Step 1: Add like terms
4x² - 6x² = -2x²
-10x + 10x = 0
12 + 3 = 15
Step 2: Rewrite
-2x² + 15
[tex](8 - 10x + 3) + ( - 12 + 10x + 12)[/tex]
[tex](11 - 10x) + (10x)[/tex]
[tex] 11 - 10x + 10x[/tex]
[tex] = 11[/tex]
For a project in your statistics class you decide to make a histogram of the salary data for players in the National Basketball Association (NBA). Since most of the players in the NBA earn the league minimum based on their years of service and a few superstars earn very high salaries in comparison, which of the following would most likely be a characteristic of your histogram?
a. Skewed-right
b. Skewed-left
c. Symmetric, with a central peak
d. Uniform
Answer:
b. Skewed-left
Step-by-step explanation:
The histogram will be expressed with the x-axis representing the salaries, in growing amount to the right. The y-axis will represent the relative or absolute frequency.
We know that most of the players earn the minimum league wage. Then, we will have a high frequency in the low salaries classes, at the left of the histogram. A few players earn very high salaries, so we will have a right tail with high values for the salaries a little frequency.
There is no symmetry in this histogram and it is not uniform, as there is no representative mean salary.
As most of the data will be close to the left side, we can conclude that the histogram will be skewed-left.
The Histogram of salary data, with most having less salary is RIGHT Skewed
Given : Data of players' salary is concentrated towards towards most players having less ( minimum ) salary.
Right Skewness denotes a distribution where Tail is on the right side. This implies data is highly concentrated toward left side, ie lower independent variable (x - here 'salary') values.
Left Skewness denotes a distribution where Tail is on the left side. This implies data is highly concentrated towards right side, ie higher independent variable (x - here 'salary') values.
In this case : As more players have lower values of independent variable ie salary, so the data will be concentrated at left - having tail at right.
Hence, it will be Skewed Right
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Geometry: Similarity, Congruence, Proofs Question: Why are proofs so picky? Why can’t we just measure the two figures to see if they are congruent?
Answer:
Haha proofs are an interesting thing. Usually, nothing is to scale, which is why you can't measure anything. They are pretty annoying, but it helps to know why certain things are the way that they are and develop justification skills for higher level math.
Sorry to discourage you, but you're going to see "Justify" quite a lot in calculus and beyond which is basically a more informal version of a proof
you can never escape it tbh lol
We can't just measure the two figures to see if they are congruent as congruence is about shape and size.
What is congruence?It should be noted that congruence simply means that the shapes have identical length, angles, and size.
Therefore, we can't just measure the two figures to see if they are congruent as congruence is about shape and size.
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The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side length equal to 5 inches Which calculation will give the total surface area of the solid figure? 5 × 6 × 6 square inches 6 × 5 × 5 square inches 6 × 5 × 5 × 5 square inches 5 × 6 × 6 × 6 square inchesv
Answer:
6 × 5 × 5 square inches
Step-by-step explanation:
The area of one of the figure's 6 squares is the product of its side length, so is ...
5 × 5 square inches
The area of all 6 of those squares is 6 times this, or ...
6 × 5 × 5 square inches
find the values of a and b such that x^2-4x+9=(x+a)^2+b
Answer:
a = -2; b = 5
Step-by-step explanation:
Expanding the right side of the given equation, we have ...
x^2 -4x +9 = x^2 +2ax +a^2 +b
Comparing coefficients, we see ...
-4 = 2a . . . . . coefficient of x term
9 = a^2 +b . . . constant term
The first of these tells us ...
-2 = a . . . . divide by 2
The second of these tells us ...
9 = (-2)^2 +b . . . substitute for a
5 = b . . . . subtract 4
The values of a and b are (a, b) = (-2, 5).
Answer:
a=-2
b=5
Step-by-step explanation:
type this on mathswatch and you will get it right
can someone help please, it wont give me the last mark
Answer:
The explanation is:
All interior angles in an equilateral triangle are congruent, making them all 60° by the sum of angles in a triangle. Because alternate interior angles of parallel lines are congruent, x = 60°.
What is (14x2 + 19x - 3) = (2x+3)?
Answer:
Dear User
Answer to your query is provided below
X = 2/7 or X = -3/2
Step-by-step explanation:
Explanation for the same is attached in image
if 25% or the person'so salary is $135.75 then what is the amount of his full salary?
Answer:
543
Step-by-step explanation:
let x= total salary
0.25x=135.75
x=543
Answer:
[tex]\$ \: 543.00[/tex]
Step-by-step explanation:
[tex]25\% \times x =135.75[/tex]
[tex]1/4 \times x =135.75[/tex]
[tex]0.25 \times x =135.75[/tex]
[tex]x=135.75 \times 4[/tex]
[tex]x=543[/tex]
If the standard deviation of a population is 20 and we take a sample of size 16 from which to calculate a mean, the standard error (the standard deviation of the sample mean) is:
Answer:
36
Step-by-step explanation:
choose the graph of y less than negative x squared plus 4x + 5
Answer:
The 1st graph
Step-by-step explanation:
The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.
Which of the following is the correct graph of the compound inequality 4p + 1 > −15 and 6p + 3 < 45?
The graph of the compound inequality can be seen at the end.
How to get the graph of the compound inequality?Here we have two inequalities that depend on p, these are:
4p + 1 > -15
6p + 3 < 45
First, we need to isolate p on both inequalities.
4p + 1 > -15
4p > -15 - 1
p > -16/4
p > - 4
6p + 3 < 45
6p < 45 - 3 = 42
p < 42/6 = 7
So we have the compound inequality:
p > -4
p < 7
or:
-4 < p < 7
Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.
The graph of the inequality is something like the one below.
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Algebra 1
Function Notation Worksheet Alternate
Name
For #I-8: Evaluate the following expressions given the functions below:
f(x) = x2 – 7
g(x) = -3x - 1
j(x)=2x-9
h(x) = 1
X=
1. g(10) =
2. What is the value of x if g(x) = 16
3. f(3) =
4. What is the value of x if f(x) = 23
X
5. h(-2) =
6. What is the value of x if h(x) = -2
X =
7. |(7) =
8. h(a) =
For #9-12: Translate the following statements into coordinate points:
9. S(-1) = 3
10. g(4) = -1
11. h(2) = 8
12. k(2) = 9
Answer:
None
Step-by-step explanation:
The answers are:
1. g(10) -31
2. x= -17/3
3. f(3)= 2
4.x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = x² – 7
g(x) = -3x - 1
j(x)= 2x-9
h(x) = 1
1. g(10)= -3(10) -1 = -30 - 1= -31
2. g(x) = 16
-3x- 1= 16
-3x = 17
x= -17/3
3. f(3)= (3)² – 7 = 9- 7= 2
4. f(x)= 23
x² – 7= 23
x² = 30
x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
8. S(-1) = 3
The value of function s(a) at a=-1 is 3.
10. g(4) = -1
The value of function g(a) at a=4 is -1.
11. h(2) = 8
The value of function h(a) at a=2 is 8.
12. k(2) = 9
The value of function k(a) at a= 2 is 9.
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which is the greatest 1/12, 1/32, 1/48 or 1/18
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].
Answer:
1/12
Step-by-step explanation:
Start with a number, for example 100.
Now divide 100 by several numbers which are greater and greater:
100/1 = 100
100/2 = 50
100/4 = 25
100/10 = 10
100/100 = 1
As you divide the same number, 100, by a greater number, the result becomes smaller.
As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.
Numbers in order from greatest to smallest:
1/12, 1/18, 1/32, 1/48
Answer: The greatest number is 1/12
Which scenario is the best example of a deus ex machina?
Answer:
D.
Step-by-step explanation:
Deus ex machina is the plot device of using something very improbable to resolve a situation.
What is the product of 5 and 3?
40
0 -13
13
040
Answer:
15 is the answer to the question
Answer:
15, which for some reason does not seem to be an option.
Step-by-step explanation:
Product means to multiply to numbers, items etc.
5 times 3, as you should know, is 15.
Hope this helps.
Find the slope through each pair of two points. Report answers in simplest form.
(-3,6) and (-5,9)
m =
Answer: m=-3/2
Step-by-step explanation:
To find the slope, we use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. With our given points, we can directly plug them into the formula.
[tex]m=\frac{9-6}{-5-(-3)} =\frac{3}{-2}[/tex]
Our slope is m=-3/2.
there are three witches and three children they were going to cross the river with a boat that can carry only two people and if a mother lives her child alone the another witches will kill her son.how will the witches and children cross the river?
Answer:
It will take to long to type it all but i think i figured it out. The children would have to take several trips. 2 kids would go, then one kid goes back to get the other kid, crosses again, then goes back, gets out, and two witches go (the parents of the kids on the other side), leaving one set of witch and child still needing to cross. One of the children on the other side brings the boat back and picks up the left over kid, now just one witch needing to cross, the two kids cross then the one kid with his mother on the other side takes the boat back again to get his mom.
And then when it gets to the other side the witch there eats it
Step-by-step explanation:
To safely cross the river, the witches and children can follow these steps:
Two witches (W1 and W2) cross the river, leaving one witch (W3) behind.
W1 returns alone to the starting side.
W1 and one child (C1) cross the river, leaving C1 on the other side.
W2 takes two children (C2 and C3) across the river, leaving them on the starting side.
W1 and W3 cross the river, leaving C2 and C3 behind.
W1 returns alone to the other side.
W1 and C1 cross the river, leaving W3 on the other side.
W2 and W3 cross the river.
W2 returns alone to the starting side.
W2 and C2 cross the river, leaving C3 behind.
W1 and C3 cross the river
How will the witches and children cross the river?To solve this puzzle, the witches and children can follow these steps to cross the river without any harm coming to the children:
Two witches cross the river: Two witches (W1 and W2) row the boat to the other side of the river, leaving one witch (W3) on the starting side.
One witch returns alone: W1 leaves the other witch (W2) on the other side and rows back alone to the starting side of the river.
One witch and one child cross the river: W1 takes one child (C1) with her and they both row across the river to the other side. W1 leaves C1 on the other side and rows back alone to the starting side.
Two children cross the river: W2, who has been waiting on the other side, takes two children (C2 and C3) and rows across the river to the starting side. W2 leaves C2 and C3 on the starting side and rows back alone to the other side.
Two witches cross the river: W1 returns to the other side and picks up the remaining witch (W3). They both row across the river to the starting side, leaving C2 and C3 on the other side.
One witch returns alone: W1 rows back alone to the other side.
One witch and one child cross the river: W1 takes C1 and rows across the river to the starting side, leaving W3 on the other side.
Two witches cross the river: W2 returns to the starting side and picks up W3. They both row across the river to the other side.
One witch returns alone: W2 rows back alone to the starting side.
One witch and one child cross the river: W2 takes C2 and rows across the river to the other side, leaving C3 on the starting side.
Two children cross the river: W1 returns to the starting side and picks up C3. They both row across the river to the other side.
Now, all three witches and all three children have safely crossed the river without any harm coming to the children.
Read more about river crossing here: https://brainly.com/question/4219673
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An ordinary deck of playing cards contains 52 cards, 26 red and 26 black. If a card is dealt to each of 2 players,.
Find in how many different ways this can be done if the following occur.
a. both cards are red. _____ ways
b. both cards are black _____ways
c. one card is black and the other is red. ________way
Answer:
(a)650 ways
(b)650 ways
(c)676 ways
Step-by-step explanation:
There are 26 red and 26 black cards.
If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.
(a)Both cards are red
If both cards are red:
The first red card can be dealt in 26 ways.
The second red card can be dealt in 25 ways.
Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways
(b)Both cards are black
If both cards are black:
The first black card can be dealt in 26 ways.
The second black card can be dealt in 25 ways.
Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways
(c)One card is black and the other is red.
The red card can be dealt in 26 ways.
The black card can be dealt in 26 ways.
Therefore: Both cards can be dealt in: 26 X 26 = 676 ways
you currently have 24 credit hours and a 2.8 gpa you need a 3.0 gpa to get into the college. if you are taking a 16 credit hours this semester. what gpa must you get in order to raise your gpa to the correct level? set up an equation and use algebra to solve.
Answer:
[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]
And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:
[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]
And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:
[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]
And from the previous result we got:
[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]
And solving we got:
[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]
And then we can find the mean with this formula:
[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]
So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0
Step-by-step explanation:
For this case we know that the currently mean is 2.8 and is given by:
[tex] \bar X = \frac{\sum_{i=1}^n w_i *X_i }{24} = 2.8[/tex]
Where [tex] w_i[/tex] represent the number of credits and [tex]X_i[/tex] the grade for each subject. From this case we can find the following sum:
[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]
And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:
[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]
And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:
[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]
And from the previous result we got:
[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]
And solving we got:
[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]
And then we can find the mean with this formula:
[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]
So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0