Answer:
5,040
Step-by-step explanation:
Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing then there are total m*n ways of doing both things.
Example : If there are 5 path to reach a destination and 3 mode of transport ( bike, car, bicycle) . Then are 5 * 3 ways to reach the destination using the different mode of transport available.
______________________________________
Given no of clarinet players = 7
no of chairs = 7
First player can be seated on seven chairs in seven ways
( for illustration let the seat be a , b, c , d , e , f , g. he can sit on any of the chairs)
since one chair is occupied and 6 chair is available
second player can be seated on 6 chairs in 6 ways
for illustration let the seat be a be occupied then b, c , d , e , f , g are the chairs on which second player can sit.
\
Similarly 3rd, 4th, 5th, 6th and 7th player can be seat on chairs in
5, 4 , 3, 2, and 1 way respectively.
___________________________________________
now using fundamental Counting Principle
since 7 players can sit on chair in
7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in
7 * 6 * 5 * 4 * 3 * 2 * 1 ways = 5, 040 ways
In this exercise, we consider finding the first five coefficients in the series solution of the first-order linear initial value problem (x²+2)y′′ − 6y = 0 subject to the initial condition y(0) = 1, y′(0) = 2. Since the equation has an ordinary point at x=0 and it has a power series solution in the form y = Lim(n=0→[infinity])Σ cₙxⁿ.(1) Insert the formal power series into the differential equation and derive the recurrence relation: cn= __________cₙ₋₂ for n=2,3,⋯ The solution to this initial value problem can be written in the form y(x)= c₀y₁(x)+c₁y₂(x) where c₀ and c₁ are determined from the initial conditions. The function y₁(x) is an even function and y₂(x) is an odd function. For this example, from the initial conditions, we have c₀ = ______ and c₁ = ______. The function y₁(x) is an infinite series y₁(x) = 1+ Lim(n=1→[infinity])Σ aₙx²ⁿNote that the constant c₀ has been factored out. (2) Use the recurrence relation to find the first few coefficients of the infinite series: a₂ = _______, a₄ = _______, a₆ = _______, a₈ = _______.Note that the constant c₀ has been factored out. Finally the polynomial y₂(x)= _______NOTE: The function y₂(x) is an odd degree polynomial with first term x. In other words, note that the constant c₁ has been factored out.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation for the answer to the question
Which two temperatures have a 0 degrees Celsius?
Someone ran 2km someone else ran 3,500 meters what would be that combined
Answer:
5,500 meters or 5.5km
Step-by-step explanation:
1 km is = 1000 meter
2km=2000 meters
2000 +3500 =5,5000 meters
Europeans have been more skeptical than Americans about the use of genetic engineering to improve foods. A sample survey gathered responses from random samples of 824 Americans and 12268 Europeans. (The European sample was larger because Europe is divided into many nations.) Subjects were asked to consider the following issue: Using modern biotechnology in the production of foods, for example to make them higher in protein, keep longer, or change in taste. They were asked if they considered this "risky for society." In all, 432 of Americans and 7629 of Europeans thought the application was risky.
Give a 98% confidence interval for the percent difference (±0.1) between Europe (call them group 1) and the United States:
Answer:
The 98% confidence interval = (-0.14, -0.056)
Explanations:
From the calculations done in the file attached to this solution
Proportions of Americans that considered the application risky = 0.524
Proportions of Americans that did not considerthe application risky = 0.476
Proportions of Europeans that considered the application risky = 0.622
Proportions of Europeans that did not consider the application risky = 0.377
Standard error of the sample proportion using the formula written in the attached file = 0.018
The 98% confidence interval is also calculated as in the attached file and gotten as (-0.14, -0.056)
A company issues 7% bonds with a par value of $200,000 at par on January 1. The market rate on the date of issuance was 6%. The bonds pay interest semiannually on January 1 and July 1. The cash paid on July 1 to the bond holder(s) is:
Answer:
The cash paid to the bondholder on July 1 is Z = $7000
Step-by-step explanation:
From the question we are told that
The percentage bond issued by the company is [tex]n = 7[/tex]%
The par value of the bond is [tex]V =[/tex]$200,000
The market rate is [tex]r = 6[/tex]%
So we are told that the bonds pay interest semiannually on January 1 and July
So the cash paid to the bondholder on July 1 is mathematically evaluated as
Z = [tex]V * \frac{7}{100} * \frac{1}{2}[/tex]
substituting value
Z = [tex]200000 * \frac{7}{100} * \frac{1}{2}[/tex]
Z = $7000
Final answer:
The cash paid on July 1 to bondholders for the company's 7% bonds with a par value of $200,000 is $7,000. This is calculated by first determining the annual interest payment and then dividing by two for the semiannual payment.
Explanation:
Understanding Bond Interest Payments
The question revolves around how much cash is paid to bondholders on July 1 for a company that issued 7% bonds with a par value of $200,000 at par when the market rate was 6%. Since the bonds were issued at par, this implies that the bond's stated interest rate matches the market interest rate at the time of issuance. However, the market rate later does not affect the fixed payments of a bond issued at par.
The interest payment for this bond would be calculated using the face value and the stated annual interest rate, which is then divided by two since interest is paid semiannually. The calculation is as follows:
Calculate the annual interest payment: $200,000 (par value) × 7% (interest rate) = $14,000.Divide the annual interest by two for the semiannual payment: $14,000 ÷ 2 = $7,000.Therefore, the cash paid on July 1 to the bond holder(s) is $7,000.
What is the domain of the function Y equals cube root x
Final answer:
The domain of the function y = x^(1/3) (cube root of x) is all real numbers, which is expressed as (-∞, +∞).
Explanation:
The domain of a function describes all the possible values of 'x' for which the function is defined. In the case of the function y = cubic root of x, which is written as y = x^(1/3), the function is defined for all real numbers because you can take the cubic root of any real number, negative, positive, or zero. Hence, the domain of the function y = x^(1/3) is all real numbers, which mathematically is expressed as (-∞, +∞). This is different from the function y = x^2, where the domain must often be restricted to nonnegative numbers to have a well-defined real inverse function.
Which statement(s) could describe the graph of a nonproportional relationship? Select all that apply
Answer:
A. The positive y-intercept.
D. The y-intercept is negative.
Step-by-step explanation:
The proportional relationship is defined by the graph passing through the origin i.e. the y-intercept is equal to zero.
The equation of y proportional to x relationship is y = kx, which again denotes that the graph passes through the origin (0,0).
Now, the statements that can describe the graph of a non-proportional relationship are
A. The positive y-intercept.
D. The y-intercept is negative. (Answer)
The statements that could describe the graph of a nonproportional relationship include:
A. The positive y-intercept.D. The y-intercept is negative.It should be noted that the proportional relationship is defined by the graph passing through the origin. The equation of y proportional to x relationship is y = kx.
From the information given, the relationship shows that the positive y-intercept and the y-intercept is negative.
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x/-4=-16. Solve for x.
Answer:
64
Step-by-step explanation:
16 *4 is 64 so 64 divide by -4 equals -16.
Hope this helps.
Answer: 64
Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.
On the left side, the -4's will cancel
and on the right side, -16(-4) is 64.
So x = 64.
Please do not try to do this problem in your head.
Show the work that it takes to get x by itself.
Translate the sentence into an inequality.
Six subtracted from c is at least 20.
Answer:
6 - c </= 20
Step-by-step explanation:
A study in 2010 reported that 3 in 4 adults in a relationship met their significant other using an online dating site. Recently a popular magazine 'People' claimed that that number has changed. To test this claim a telephone survey of 600 randomly selected adults in a relationship was completed. Of the 600 adults, 480 said that they met their significant other using an online dating site. Does this provide evidence that the proportion has changed? Use α = 0.05, to test the magazine's claim. Conditions: 1. The sample is 2. n p 0 ( 1 − p 0 ) 10 3. n 0.05 N Hypotheses: H 0 : p 0.75 H 1 : p 0.75 Test Statistic: The test statistic is a test statistic. The value of the test statistic is . p-value: The value of the p-value is . Decision: Because the p-value is than α = 0.05, we the null hypothesis. Conclusion: The data the claim that the proportion has changed
Answer:
Step-by-step explanation:
From the given information,
The required correct answers are,
1. The sample is:
b) simple random sample
2. np0 (1-p0) ___ 10
a) greater than or equal to
3. n ___ 0.05N
b) less than or equal to
Hypotheses:
4. H0:p___0.75
d) =
5. H1:p___0.75
a) ≠
6. The test statistic is a
a) z test statistic
7. test statistic=2.8284
8. p-value=0.0047
Decision:
Because p-value less than Alpha=0.05, we reject null hypothesis.
Conclusion:
The data support the claim that the proportion has changed.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
p = 3/4 = 0.75
For the alternative hypothesis,
p ≠ 0.75
Considering the population proportion, probability of success, p = 0.75
q = probability of failure = 1 - p
q = 1 - 0.75 = 0.25
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 480
n = number of samples = 600
P = 480/600 = 0.8
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.8 - 0.75)/√(0.75 × 0.25)/480 = 2.53
Recall, population proportion, P = 0.75
The difference between sample proportion and population proportion(P - p) is 0.8 - 0.75 = 0.05
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.75 - 0.05 = 0.7
the p for the right tail is 0.75 + 0.05 = 0.8
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the test z score in the right tail 1 - 0.9943 = 0.0057
We would double this area to include the area in the left tail of z = - 2.53. Thus
p = 0.0057 × 2 = 0.0114
Because alpha, 0.05 > than the p value, 0.0114, then we would reject the null hypothesis.
Therefore, at 5% significance level, this data provide evidence that the proportion has changed.
UPOOD
The area of a square is given by s2 and the perimeter is given by 4s, where s is the side length of the square,
If the side length of a square is 4 inches, its area is
16.6 square inches and its perimeter is
074 Inches.
Reset
Next
Answer:
If the side length of a square is 4 inches, it's Area is 16 inches, and Perimeter is 16 inches.
Step-by-step explanation:
Given that the Area = s²
Perimeter = 4s
Side length of the square = s
If the length of a square is 4 inches, then applying the above formulas, we have
s = 4 inches
Area = 4² = 16 inches
Perimeter = 4s = 4×4 = 16 inches
Final answer:
The area of a square with a side length of 4 inches is 16 square inches and its perimeter is 16 inches. Doubling the side length to 8 inches yields an area that is four times greater, 64 square inches, due to the squared relationship between side length and area.
Explanation:
Understanding Square Area and Perimeter
A student has posed a question about the properties of squares. We are given that the side length of a square is 4 inches. From this, we can calculate the square's area and perimeter. The area of a square is found by squaring the length of its side (s2), which in this case would be 4 inches × 4 inches = 16 square inches. The perimeter is the length around the square, calculated by multiplying the side's length by 4, yielding 4 inches × 4 = 16 inches.
By understanding the formulas for area (s2) and perimeter (4s), students can solve many geometrical problems related to squares. For instance, if the dimensions of a square are to be doubled, the new side length would be 4 inches × 2 = 8 inches, resulting in an area of 8 inches × 8 inches = 64 square inches, which is four times the original area, demonstrating that the area scales with the square of the linear dimensions.
the difference of eight and twice a number
Answer:
8 - 2x
Step-by-step explanation:
Let x be the unknown number
difference is subtraction
8 - 2x
What algebraic expression must be subtracted from the sum of Y squared plus 5Y -1 and 3Y squared minus 2Y +4 to give you 2Y squared plus 7Y -2
Answer:
The required expression is:
2Y² - 4Y + 5
Step-by-step explanation:
Given the expression:
(Y² + 5Y - 1) + (3Y² - 2Y + 4)
= 4Y² + 3Y + 3
Subtracting (2Y² - 4Y + 5), we have
2Y² + 7Y - 2
Therefore, the expression:
2Y² - 4Y + 5
must be subtracted from the expression:
(Y² + 5Y - 1) + (3Y² - 2Y + 4)
to give the expression:
2Y² + 7Y - 2
A large van has careened off the road into a ditch, and two tow trucks are attempting to winch it out. The cable from the first winch exerts a force of 900 lb, while the cable from the second exerts a force of 700 lb. Determine the angle of theta for the first truck that will bring the van directly out of the ditch and along the resultant.
Answer:
25
Step-by-step explanation:
Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly costs of $70,000 just to keep the place running. On top of that, your regular cabaret artist is charging you $2900 per performance, and your jazz ensemble is charging $800 per hour. Set up a (monthly) cost function for the scenario. (Let C represent the monthly cost in dollars, x represent the number of performances by the cabaret artist per month and y represent the number of hours of jazz per month.) C(x, y)
Answer:
The monthly cost function for the scenario C(x,y) is;
C(x,y) = 70,000 + 2900x + 800y
Step-by-step explanation:
Let C represent the monthly cost in dollars.
x represent the number of performances by the cabaret artist per month
and y represent the number of hours of jazz per month
Given;
monthly costs of $70,000
regular cabaret artist is charging you $2900 per performance.
Per month = $2900x
your jazz ensemble is charging $800 per hour.
Per month = $800y
The monthly cost function for the scenario C(x,y) is the sum of all the costs;
C(x,y) = 70,000 + 2900x + 800y
382
Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
(x-3)2 + (y – 5)2 = 6
(x - 3)2 + (x - 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Answer:
(x+3)^2 + (y+5)^2 = 36
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--3)^2 + (y--5)^2 = 6^2
(x+3)^2 + (y+5)^2 = 36
The perimeter of a triangle DEF is 81 units. The length of side DE is twice the length of side EF, and the length of side DF is 4 units less than the length of side DE. Let s represent the length, in units, of side EF. Write an equation that can be used to find s
Answer:
5s = 85
Step-by-step explanation:
Perimeter of our triangle = DE + EF + DF = 81 units
We know from the question that
The length of side DE is twice the length of side EF
DE = 2EF
and the length of side DF is 4 units less than the length of side DE
DF = DE - 4
We can replace EF with s in our equations
DE = 2s
And now we can replace DE from the other equation
DF = DE - 4
DF = 2s - 4
If the perimeter of our triangle = DE + EF + DF = 81 units
We will replace the sides with our new values
Perimeter = 2s + s + 2s - 4 = 81
We can put this as our answer, or we can simplify further
Simplify by adding 4 to both sides
2s + s + 2s - 4 + 4 = 81 + 4
Simplify
2s + s + 2s = 85
Simplify
5s = 85
Since the question only asked for an equation, not for us to solve it, we can stop here
(If you wanted to solve for s, just divide both sides by 5)
5s / 5 = 85 / 5
s = 17
Answer:
81 = s + 2s + (2s -4)
Step-by-step explanation:
The range of the secant function is?
Answer:
1. Where are the vertical asymptotes on the graph of the secant function?
choice A: x = π /2 + nπ
2. The range of the secant function is
answer: y ≤ -1 or y ≥ 1
3. What is the period of the secant function?
Choice C : 2π
Step-by-step explanation:
there are 3 questions on this page.
correct on edge
The range of secant is y ≤ -1 or y ≥ 1.
What is a range in the function?The range of a function is the set of its possible output values.
As we know the vertical asymptotes of the secant function
x = π /2 + nπ
and, The range of the secant function is
y ≤ -1 or y ≥ 1
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Nancy shot a 24 on 4 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes?
Answer:
108
Step-by-step explanation:
"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:
score/18 = 24/4
Multiplying by 18, we get ...
score = 18(24/4) = 18(6) = 108
Nancy can expect a score of 108 on 18 holes.
Solve: tan(x)-cos^2(x)=sin^2(x)
Answer:
x = 45 degrees +180 n where n is an integer
Step-by-step explanation:
tan(x)-cos^2(x)=sin^2(x)
Add cos^2(x) to each side
tan(x)-cos^2(x)+ cos^2(x)=sin^2(x)+ cos^2(x)
tan(x)=sin^2(x)+ cos^2(x)
We know that sin^2(x)+ cos^2(x) = 1
tan (x) =1
Take the inverse tan of each side
tan ^-1 ( tan x) = tan ^-1 (1)
x = 45 degrees +180 n where n is an integer
Answer:
Pi/4+kpi
Step-by-step explanation:
X= 45 degrees and on unit circle that is pi/4
What is the volume, in cubic in, of a rectangular prism with a height of 19in, a width
of 17in, and a length of 18in?
Answer:
Use (B*H)H
Step-by-step explanation:
17*18*19
First 17*18= 306
Second is 306*19=5814
*PLS HELP ME WITH MY MATH
The volume of the given rectangular prism will be 5814 inches³.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Volume has units of cube example meter³,cm³, etc.
The volume of the prism = length × height × width.
As per the given,
Length = 18 inches
Width = 17 inches
Height = 19 inches
Volume = 18 x 17 x 19 = 5814 inches³
Hence "The volume of the given rectangular prism will be 5814 inches³".
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Which expression is the result of
10x2 + 50x = ?
Step-by-step explanation:
10x2 + 50x
10x ( x +5)
Is the result
What is the relationship between 1 and 2
Answer:
they are a complimentary couple since both offer examples of their own qualities. Both types are highly dutiful and are attracted to each other
Step-by-step explanation:
hope this helps
~berrian
Final answer:
The relationship between 1 and 2 in mathematics can refer to causality, ratios, probability, physical properties in physics, or reciprocal relationships, depending on the context.
Explanation:
The relationship between 1 and 2 can refer to various mathematical concepts, depending on the context in which these numbers are being used. Here are a few examples:
Causality: In a simple model with objects A and B, an arrow from A to B implies that A is the cause and B is the effect. It's a directional relationship.
Ratio: When we say the ratio between two quantities is 1:2, it implies for every unit of the first quantity, there are two units of the second quantity. In this case, RP1 to Rp2 is 1:2.
Probability: In the context of dice, if the first value is 2, the ratio could describe the possible outcomes when rolling two dice.
Physical properties: Mathematical relationships can be determined for variable pairs in physics such as Pressure (P) versus number of moles (n), or volume (V) versus temperature (T).
Reciprocity: In some mathematical expressions, swapping the subscripts '1' and '2' does not change the relationship, indicating a reciprocal or bidirectional relationship between the two.
Understanding these relationships requires recognizing the context and the mathematical principles that govern them.
What are the me and you
What are the x- and y-coordinates of point E, which partitions
the directed line segment from A to B into a ratio of 1:2?
x = ( min )(x2 – x1) + x1
v = l m on Jiva – vi] + vi
(0, 1)
0 (-1,3)
* (-2,5)
(1,0)
Complete question:
What are the x- and y- coordinates of point E, which partitions the directed line segment from [tex]A\:(- 4,\:9) \:to\: B\:(2,\:- 3)[/tex] into a ratio of 1 : 2.
Answer:
(C) (-2,5)
Step-by-step explanation:
[tex]x = (\dfrac{m}{m+n}) (x_2-x_1) + x_1\\\\y = (\dfrac{m}{m+n}) (y_2-y_1) + y_1[/tex]
[tex](x_1,y_1)=(- 4,\:9),(x_2,y_2)=B\:(2,\:- 3)[/tex]
m=1, n=2
[tex]x = \left(\dfrac{1}{1+2}\right) (2-(-4)) + (-4)\\=\left(\dfrac{1}{3}\right) (2+4)-4\\=\left(\dfrac{6}{3}\right)-4=2-4\\x=-2[/tex]
[tex]y = \left(\dfrac{1}{1+2}\right) (-3-9) + 9\\=\left(\dfrac{1}{3}\right) (-12)+9\\=\left(-\dfrac{12}{3}\right)+9=-4+9\\y=5[/tex]
The x- and y-coordinates of the point E is (-2,5)
A 33 m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36 m . Find the length of the shadow. If necessary, round your answer to the nearest tenth.
Answer:
Hypotenuse = 36 Leg = 33
other leg^2 = 36^2 - 33^2
other leg^2 = 207
other leg = 14.3874945699
other leg = 14.4 (rounded)
Step-by-step explanation:
A chef got 17 bags of onions. The red onions came in bags of 4 and the yellow onions came in bags of 6. If the chef got a total of 88 onions, how many bags of each type of onion did he get?
Answer:
7 bags red onions
10 bags yellow onions
Step-by-step explanation:
If r is the number of bags of red onions, and y is the number of bags of yellow onions, then:
r + y = 17
4r + 6y = 88
Solve the system of equations using substitution or elimination. Using substitution:
r = 17 − y
4(17 − y) + 6y = 88
68 − 4y + 6y = 88
2y = 20
y = 10
r = 7
The chef received 5 bags of red onions and 12 bags of yellow onions.
The question involves solving a system of linear equations to find the number of bags of red onions and yellow onions the chef received. Let's denote the number of bags of red onions as R and the number of bags of yellow onions as Y. We know that:
Each bag of red onions contains 4 onions.
Each bag of yellow onions contains 6 onions.
The chef got a total of 17 bags.
The chef got a total of 88 onions.
Based on this information, we can set up the following equations:
R + Y = 17
(This represents the total number of bags.)
4R + 6Y = 88
(This represents the total number of onions.)
We can solve this system of equations using substitution or elimination. Let's use substitution. First, we can express Y as 17 - R from the first equation:
Y = 17 - R
Now, we substitute Y in the second equation:
4R + 6(17 - R) = 88
By solving this equation, we find that R = 5 and Y = 12. Therefore, the chef got 5 bags of red onions and 12 bags of yellow onions.
If f[6} = x ^ -2x , find: f [6} =
Answer:
1/ 6^12
Step-by-step explanation:
f[x} = x ^ (-2x)
f(6) = 6 ^ (-2*6)
= 6 ^ -12
We know the negative exponent moves it to the denominator
= 1/ 6^12
Timothy creates a game in which the player rolls 4 dice. What is the probability in this game of having exactly two dice or more land on a five?
A. 0.016
B. 0.132
C. 0.868
D. 0.984
Answer:
B. 0.132
Step-by-step explanation:
For each time the dice is thrown, there are only two possible outcomes. Either it lands on a five, or it does not. The probability of a throw landing on a five is independent of other throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
Timothy creates a game in which the player rolls 4 dice.
This means that [tex]n = 4[/tex]
The dice can land in 6 numbers, one of which is 5.
This means that [tex]p = \frac{1}{6}[/tex]
What is the probability in this game of having exactly two dice or more land on a five?
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{2} = 0.116[/tex]
[tex]P(X = 3) = C_{4,2}.(\frac{1}{6})^{3}.(\frac{5}{6})^{1} = 0.015[/tex]
[tex]P(X = 4) = C_{4,4}.(\frac{1}{6})^{4}.(\frac{5}{6})^{0} = 0.001[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.116 + 0.015 + 0.001 = 0.132[/tex]
So the correct answer is:
B. 0.132
The probability of having exactly two dice or more land on a five is: 0.132.
To determine the probability of having exactly two dice or more land on a five when rolling four dice, we first need to calculate the probabilities of each possible outcome involving getting at least two fives.
1: Define the basic probabilities
Each die has 6 faces, so the probability ( p ) of rolling a five on a single die is:
[tex]\[ p = \frac{1}{6} \]The probability \( q \) of not rolling a five on a single die is:\[ q = 1 - p = \frac{5}{6} \][/tex]
2: Define the number of dice rolls
We are rolling 4 dice.
3: Calculate probabilities for 0, 1, 2, 3, and 4 fives
We use the binomial distribution formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]where \( n = 4 \), \( p = \frac{1}{6} \), and \( k \)[/tex] is the number of fives rolled.
Probability of rolling exactly 0 fives (\( k = 0 \)):
[tex]\[ P(X = 0) = \binom{4}{0} \left(\frac{1}{6}\right)^0 \left(\frac{5}{6}\right)^4 = 1 \times 1 \times \left(\frac{5}{6}\right)^4 = \left(\frac{5}{6}\right)^4 \][/tex]
Probability of rolling exactly 1 five (\( k = 1 \)):
[tex]\[ P(X = 1) = \binom{4}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 \]Probability of rolling exactly 2 fives (\( k = 2 \)):\[ P(X = 2) = \binom{4}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^2 = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 \][/tex]
[tex]Probability of rolling exactly 3 fives (\( k = 3 \)):\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \])^1 \]Probability of rolling exactly 4 fives (\( k = 4 \)):[/tex]
[tex]\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \][/tex]
4: Sum probabilities for \( k \geq 2 \)
We need to find \( P(X \geq 2) \), which is:
[tex]\[ P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \][/tex]
5: Perform calculations
[tex]\[P(X = 0) = \left(\frac{5}{6}\right)^4 \approx 0.4823\]\[P(X = 1) = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{125}{216}\right) \approx 0.3858\]\[P(X = 2) = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} \approx 0.1157\][/tex]
[tex]\[P(X = 3) = 4 \times \left(\frac{1}{6}\right)^3 \times \frac{5}{6} = 4 \times \frac{1}{216} \times \frac{5}{6} = \frac{20}{1296} \approx 0.0154\]\[P(X = 4) = \left(\frac{1}{6}\right)^4 = \frac{1}{1296} \approx 0.0008\][/tex]
6: Summing up [tex]\( P(X \geq 2) \)[/tex]
[tex]\[P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \approx 0.1157 + 0.0154 + 0.0008 = 0.1319\][/tex]
Rounding this to three decimal places, we get 0.132.
Thus, the probability of having exactly two dice or more land on a five is:
[tex]\[ \boxed{0.132} \][/tex].
g a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual? A. A residual is a value that is determined exactly, without any error. B. A residual is the amount that one variable changes when the other variable changes by exactly one unit. C. A residual is a value of yminusModifyingAbove y with caret, which is the difference between an observed value of y and a predicted value of y. D. A residual is a point that has a strong effect on the regression equation. b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the ▼ sum of squares sum of the residuals is the ▼ lowest highest possible sum.
Answer:
for the first question we have the "c” as the correct option
residual is a value of y -y^ which is the difference between an observed value of y and predicted value of y
The residual is a value of y -y ^ which is the difference between an observed value of y and predicted value of y, so answer A is false in The residual mo has errors, option B is false because it is not defined as the quantity that changes a variable and it is false that the residual is a point that has a strong effect on the regression
for question two the correct answer is:
the best fitting straight regression line at the scatter plot points is
b) sum of squares and lowest
The residual is the value obtained by subtracting the actual and the predicted value. Therefore, the residual of a linear model can be defined thus ;
Y_actual - Y_predictedThe line if best fit, defines the line which best fits or models a data. It is the line in the the sum of the square is lowest as it tries to minimize the sum of squared error.
Therefore, the correct options are C and (sum of square ; lowest)
Learn more :https://brainly.com/question/18405415
What is better, X-Box or Playstation?! Im thinking about buying one of them. Plz help me decide. !WILL MARK BRAINLIEST!
Answer:
playstation
Step-by-step explanation:
literally everybody owns one lol
Answer:
well i have both
Step-by-step explanation:
heres some pros and cons
PS4 or Xbox One: which one will you choose?
Both Microsoft and Sony's current generation of gaming consoles inspire fierce loyalty from their respective camps. This means, if you're not already Team PlayStation or Team Xbox, it can be difficult to make a decision between the two.
To help you make the impossible choice between Microsoft and Sony's current offerings, we've made a comprehensive list of all the key differences – as well as the similarities – to keep in mind when buying an Xbox One or PS4.
There's certainly no doubt that the PlayStation 4 has taken the lead in sales, but both have their pros and cons – and the mid-gen refresh has certainly given us a lot more to think about when weighing those up.