5-card hands have at least one club 2023203
5-card hands have at least two cards with the same rank 916,272
N[at least one club] = N[total ways] - N'[at least one club]
= N[total ways] - N[no clubs]
There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.
There are 2598960 possible hands, leaving us with 2598960-575757 ways.
Which is 2023203 hands.
How many 5 card hands will have (at least) two of the same number?
This is a standard deck. Take 2–10 to be what I mean by numbers.
N=∑k=24(91)(4k)⋅(125−k)(41)5−k+[(92)+(91)(41)](42)2⋅(111)(41)
+(91)(42)⋅(121)(43)+(91)(43)⋅(41)(42)
=(760,320+38,016+432)+114,048+2,592+864
=916,272
A standard deck of playing cards contains 13 unique ranks, each with 4 distinct suits. Since we are interested in only pairs from ranks 2 to 10, we shall define A be the collection of the 9 relevant ranks and B be the collection of the 4 ranks (ace, jack, queen, king) where pairs are not a consideration. Collection C is the union of A and B, which contains all 13 ranks.
When computing probabilities we need to select the ranks(s) from a collection and then choose a number of suits (cards). When ranks are chosen from either A or B they are also chosen from C. This is important since we might choose twice from the same collection. For example, we might choose a rank from A for a pair (9 choose 1) and later choose 3 ranks from C for singletons (12 choose 3).
To hopefully make understanding the logic easier, I have first chosen the ranks either from A, B, or C, and immediately following I have chosen the number of cards, which is always choosing from 4 suits. I have inserted a dot between different card selections.
We begin by computing the number of combinations with exactly 2, 3, and 4 of a kind from A. The singletons come from C.
N1=∑k=24(91)(4k)⋅(125−k)(41)5−k=760,320+38,016+432=798,768
We add the case of either two pairs from A or a pair from each of A and B. The singleton comes from C.
N2=[(92)+(91)(41)](42)2⋅(111)(41)=114,048
We add the case of a pair from A and 3 of a kind from C.
N3=(91)(42)⋅(121)(43)=2,592
Finally, we add the case of 3 of a kind from A and a pair from B. Note that the case of both 3 of a kind and a pair from A is the same as the case of both a pair and 3 of a kind from A, which has already been included.
N4=(91)(43)⋅(41)(42)=864
N=N1+N2+N3+N4=916,272
5-card hands have at least one club 2023203
5-card hands have at least two cards with the same rank 916,272
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Complete the equation describing how x
and y are related.
X y
7
9
11_ y = [ ? ]x +
13
15
17
012345
Enter the answer that
belongs in [?].
Enter
Help
Skip
The complete equation is y =2x+7 after substituting the given values.
What is equation?
An equation is a condition on a variable such that two expressions in the variable should have equal value and Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
y = ax+b
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
7 = a(0) + b
b= 7
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
9 = a(1)+b
9 = a+7
a=9-7
a=2
substitute the value of a and b in the equation y = ax + b. we get ,
y = 2x+7
Therefore, the complete equation is y = 2x+7
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A group of researchers investigated the effect of media usage (whether or not subjects watch television or use the Internet) in the bedroom on ""Tiredness"" during the day (measured on a 50 point scale a. Identify each of the variables, state whether the variables are quantitative or categorical, and identify each variable as either explanatory or response variables. nterviewed b. To collect these data, the researchers randomly selected homes to visit and i the adult member of the household whose birthday was nearest. Is this an experiment or an observational study? Briefly explain.
a. Media usage is categorical and Tiredness is quantitative. The effect of media is the explanatory variable and Tiredness is the response variable.
b. Yes, this is an observational study.
What is an Observational Study?In fields including epidemiology, social sciences, psychology, and statistics, observational studies draw conclusions from a sample of the population when the independent variable is not under the researcher's control due to ethical issues or practical constraints.In a normal observational study, participants are assigned to either the treated group or the control group, and the researcher observes how the therapy may influence them.This does not occur in experiments such as randomized controlled trials when each subject is randomly assigned to either a treated group or a control group. Observational studies by their very nature provide difficulties for inferential analysis due to the absence of an assignment process.This research was done via observation. The researchers are not modifying or controlling any variables; instead, they are watching and assessing the correlation between media use and fatigue. By visiting randomly chosen households and interviewing the adult household member with the closest birthday, they are gathering data.
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Find the possible dimensions of the sports field given if the width is at least 50 yards.
click the icon to view the sports field.
select all that apply.
a. width 70 yards, length 9-60 yards
ob. width 45 yards, length 14 - 10d yards
c. width 50 yards, length 13 - 9d yards
od. width 90 yards, length 7-5d yards
By finding the Greatest Common Factor we can conclude that the possible dimensions of the sports field are a width of 70 yards and a length 9-6d yards.
There are two theories needed to solve the problem:
Dimensions of an object are defined as a measure of length, width, or height extended in a certain direction.
The Greatest Common Factor (GCF) of two or more numbers is the largest number that can be evenly divisible by these numbers.
We can assume that the sports field is a rectangle since we know that:
- the width is at least 50 yards
- the area is (630-420d) yard square
To find the dimension of the sports field, we have to find the GCF of 490 and 210, by enumerating their prime factors and multiplying those factors both numbers have in common.
490 = 2 × 5 × 7 × 7
210 = 2 × 5 × 3 × 7
So the GCF is 2 × 5 × 7 = 70
This GCF depicts one of the dimensions of the sports field, which we denote as d₁.
By substituting the value of one dimension, the value of another dimension (d₂) can be obtained:
Area = d₁ x d₂
d₂ = Area / d₁
= (630-420d) / 70
= 9-6d
Thus we can conclude that the possible dimensions of the sports field are width 70 yards and length 9-6d yards.
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the copeland family started out on a family vacation with plans to visit several states. first, mr. copeland drove 163 miles in 3 hours and 49 minutes. then, mrs. copeland took over, driving 411 miles in 6 hours and 27 minutes. what is the family's average speed so far?
The average speed so far is 226.4 miles per hour.
Time taken: 3 hours 49 minutes + 6 hours 27 minutes
= 10 hours 16 minutes
Total distance: 163 miles + 411 miles
= 574 miles
Average speed: 574 miles / (10 hours 16 minutes)
= 226.4 miles per hour
To calculate the average speed of the Copeland family's trip so far, we need to know the total distance they have traveled and the total time they have spent traveling. We can calculate this by adding the distance driven by Mr. Copeland (163 miles) and the distance driven by Mrs. Copeland (411 miles) to get a total distance of 574 miles. Then, we can add the time taken by Mr. Copeland (3 hours 49 minutes) and the time taken by Mrs. Copeland (6 hours 27 minutes) to get a total time of 10 hours 16 minutes. We can then divide the total distance (574 miles) by the total time (10 hours 16 minutes) to get an average speed of 226.4 miles per hour.
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If you dissolved 50g of sugar in 30g of water, what would the sugar concentration be
Mario obtains a 30/7 balloon mortgage to finance $245,500 at 5. 25%. How much principal and interest will he have already paid when his balloon payment is due?
O $113,875. 44
O $112,519. 78
O $127,304. 57
O $216,988. 63
113875.44746 is principal and interest will he have already paid when his balloon payment is due.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. The amount you pay for borrowing money, expressed as a percentage of the entire loan amount, is what you will pay in interest if you are a borrower.
The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). Lenders may charge interest for the use of their money, or borrowers may charge interest for the use of those funds.
=PMT(5.25%/12,12*30,-245500)*12*7
= 113875.44746
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What is ratio grade 7?
Ratio grade 7 is a mathematical concept that involves comparing two or more quantities using a ratio. It is a common part of mathematics curriculums for middle and high school students.
1. A ratio is a comparison of two or more numbers.
2. Ratios can be expressed as a fraction, a decimal, or a percentage.
3. Ratios are used to compare quantities of different kinds and are used to find relationships between them.
4. In grade 7, students will learn about ratios and how to use them to solve various problems. They will also learn about proportionality, rates, and unit rates.
5. Ratios can also be used to compare measurements, such as lengths, weights, and areas.
6. Students will also use ratios to calculate proportions, which can be used to solve problems involving proportional relationships.
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what advantage does a mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving ?
The advantage does a Mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving is explained below.
The term class in math is used to define a grouping of values by which data is binned for computation of a frequency distribution
Here we have to find the advantage does a Mercedes g class 6x6 squared have compared to the 4x4 squared for off road driving
Where we all know that in a 4x4 Transfer Case there is a 50:50 split between Front and Rear axles on the other had in a 6x6 we have the Transfer Case splits the torque 33:66 between Front & Rear Axles.
Then the next one is known as intricate rear Suspension such as Short Radius Arms and coil Springs or elliptical leaf springs/Inverted Leaf Springs.
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I need help please!! assume that the height of your cylinder is 8 inches. consider a as a function of r, so we can write that as a(r)=2πr2 16πr. what is the domain of a(r)? in other words, for which values of r is a(r) defined? part b: continue to assume that the height of your cylinder is 8 inches. write the radius r as a function of a. this is the inverse function to a(r), i.e to turn a as a function of r into. r as a function of a.
a. The domain of a(r) is [tex]A(r)= 2\pi r^{2} + 16\pi r[/tex].
b. The radius r as a function of a is [tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex] .
What In Geometry Is a Cylinder?The three-dimensional solid shape of a cylinder is made up of two circular bases joined by a curving surface that is created by folding a rectangle. A cylinder's top and bottom faces are parallel to one another. There are 3 faces, 2 edges, and 0 vertices in all.
In this question, we must apply our understanding of cylinders to determine the function that most accurately captures its value:
[tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex]
The area domain of A can be represented as:
[tex]A(r)= 2\pi r^{2} + 16\pi r[/tex]
Let's divide the equation by 2π and write A(r) as just A to get:
[tex]r^{2} + 8r = \frac{A}{2\pi }[/tex]
So, after we sum on both sides we get,
[tex]r^{2} +8X +16 =\frac{A}{2\pi } + 16[/tex]
[tex](r+4)^{2} = \frac{A}{2\pi } +16[/tex]
By taking the square root of the previous equation and then figuring out r, we get:
[tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex]
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Express the vector w as a linear combination of u and v. Given:
u = <5, 7> v = <2, 3> and w = <1, 1>.
Vector w can be expressed as w=1u-2v as linear combination of vector u and v.
Vector equation would be w=Au + Bv
[1,1]=A[5,7] + B[2,3]
Here A and B are constants and we are trying to find their values.
We can split two equations as
1=5A+2B → equation a
1=7A+3B → equation b
Solving these equations by elimination method . Multiplying equation a with 3 and equation b with 2.
3=15A+6B
2=14A+6B
1=A → A=1
Putting value of A in equation b:
1=7+3B
1-7=3B
-6=3B
B=-6/3=-2
A = 1 and B = -2 . It means we can write w as 1u - 2v. We can recheck by plugging the values in any of the vector to confirm if the values are correct or not.
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how do I work this out and what is the answer
Answer:
54 cm^2
Step-by-step explanation:
calculate the area of each of the 2 rectangles and add them .
area of rectangle = l × w
so let the area of the big rectangle be A1 and the area of the small one A2 :
A1 = l × w = 11 × 4 = 44 cm^2
A2 = l × w = 5 × 2 = 10 cm^2
then , the area of the shape is = A1 + A2 = 44 + 10 = 54 cm^2
Maria had some postcards for sale. She sold 3/5 of them on monday and the remaining on Tuesday. If she sold 26 postcards. on Tuesday how many did she have at first?
The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.
What are expressions?
The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.
The examples include:
D indicates the cost of each postcard.
35 - 5D is the number of postcards that were sold.
D(35 - 5D) denotes the revenue resulting from the sales.
Describe phrases.
Mathematical assertions called expressions include all of the followings.
Mathematical operator variables for numbers
The phrase is given as follows:
The query leads us to believe that:
D indicates the cost of each postcard
D(35 - 5D) denotes the revenue resulting from the sales.
The highlights listed above indicate that: 35 - 5D reflects the quantity of postcards sold.
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Kenton compared gas mileage for three cars.
Car A—450 miles for 15 gallons
Car B—651 miles for 21 gallons
Car C—598 miles for 23 gallons
Which car has the best rate of miles per gallon?
Car A has the best rate at 30 miles per gallon.
Car B has the best rate at 31 miles per gallon.
Car C has the best rate at 26 miles per gallon.
All three cars had the same rate of miles per gallon.
Answer:
Car B has the best rate
Step-by-step explanation:
A: 450 mi / 15 gal = 30 mi/gal
B: 651 mi / 21 gal = 31 mi/gal
C: 598 mi / 23 gal = 26 mi/gal
31 > 30 > 26
Answer:Car B has the best rate at 31 miles per gallon
Step-by-step explanation: i did my math
How do you know if two ratios are proportional?
Answer: Ratios are proportional if they represent the same relationship.
Step-by-step explanation:
One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
Your shifts productivity is slow because one person is not pulling his shares. the rest of the team is getting upset. what should you be most and least likely to do?
11+4z+z-6
how would I solve this
Answer:
5 + 5z
Step-by-step explanation:
You just combine the like terms:
11 - 5 = 5
4z + 1z = 5z
=
5 + 5z
Triangle GHI is similar to triangle JKL. Find the measure of side KL. Round your
answer to the nearest tenth if necessary.
The length of the side KL for the given similar triangles rounded to the nearest tenth is 10.6 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.
What is the property of similar triangles?When two triangles are comparable, their respective sides and angles are equally spaced out and congruent. This is the property of similar triangles.
Given that the triangle GHI is similar to triangle JKL.
According to the property of similar triangles:
[tex]\frac{GH}{HI} = \frac{JK}{KL} \\\\\frac{45}{34} = \frac{14}{y} \\\\y= \frac{(14)(34)}{45} \\\\y= 10.577[/tex]
Rounding the value to the nearest tenth 10.57 is 10.6.
Hence, the value of side KL is 10.6 units.
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A school board is interested in knowing how the teachers in the school district feel about the new professional development plan. They create a list of the 245 teachers in the district and randomly select 40 names from the list to survey anonymously.
The 40 randomly selected teachers: sample.
The list of all teachers in the school district: frame.
The 245 teachers in the school district: population.
A sample is a subset of a population that is selected for research purposes. In this case, the school board has randomly selected 40 teachers out of the 245 teachers in the district as a sample to survey their opinions on the new professional development plan.
A population is the entire group of individuals or objects that researchers are interested in studying. In this case, the population is all 245 teachers in the school district.
A frame is the list or method used to define the population. In this case, the frame is the list of all 245 teachers in the school district that was used as the basis for selecting the random sample of 40 teachers.
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Calculate the double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1]
The double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1] is: 2*(1/2ln(3) - 1/2ln(1))
To calculate the double integral ∫∫R 2x/1 + xy dA, we need to integrate with respect to x and y over the region R = [0, 2] × [0, 1].
We can solve this by using the order of integration.
First we need to fix the limits of integration with respect to y and then integrate with respect to x.
∫∫R 2x/1 + xy dA = ∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy
∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy = ∫(0 to 1) ( 2*ln(1+xy)|x=0 to 2) dy
∫(0 to 1) ( 2ln(1+2y) - 2ln(1+0) ) dy
= 2*∫(0 to 1) ln(1+2y) dy
= 2*[y*ln(1+2y) - ∫(0 to 1) ln(1+2y) dy] |y = 0 to 1
= 2*[yln(1+2y) - (1/2 ln(3) - 1/2* ln(1))] |y = 0 to 1
= 2*(1ln(3) - 0ln(1) - 1/2* ln(3) + 1/2* ln(1))
= 2*(1/2ln(3) - 1/2ln(1))
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What is the equation of the tangent to the parabola y=4+2x-x^2 such that:
PLEASE HELP 100 POINTS+ BRAINLIEST
Answer:
[tex]\textsf{1)} \quad y=x+\dfrac{17}{4}[/tex]
[tex]\textsf{2)} \quad y=2x+4[/tex]
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve.
At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
[tex]y=4+2x-x^2[/tex]
Differentiate the given function:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]
If the tangent to the parabola forms an angle of 45° with the negative direction of the x-axis, then the gradient of the tangent is 1.
Set the differentiated function to 1 to find the x-value of the point where the gradient of the tangent is 1:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=1[/tex]
[tex]\implies 2-2x=1[/tex]
[tex]\implies -2x=-1[/tex]
[tex]\implies x=\dfrac{1}{2}[/tex]
Substitute x = 1/2 into the given function to find the y-value of the point:
[tex]\implies y=4+2\left(\dfrac{1}{2}\right)-\left(\dfrac{1}{2}\right)^2=\dfrac{19}{4}[/tex]
Therefore, the point at which the tangent of the parabola forms an angle of 45° with the negative direction of the x-axis is:
[tex]\left(\dfrac{1}{2},\dfrac{19}{4}\right)[/tex]Substitute the found point and slope into the point-slope formula to create an equation of the tangent:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-\dfrac{19}{4}=1\left(x-\dfrac{1}{2}\right)[/tex]
[tex]\implies y=x+\dfrac{17}{4}[/tex]
--------------------------------------------------------------------------------------
Given function:
[tex]y=4+2x-x^2[/tex]
Differentiate the given function:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2-2x[/tex]
If the tangent to the parabola is parallel to the line y = 2x - 4 then the gradient of the tangent is 2 (since parallel lines have the same gradient).
Set the differentiated function to 2 to find the x-value of the point where the gradient of the tangent is 2:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2[/tex]
[tex]\implies 2-2x=2[/tex]
[tex]\implies -2x=0[/tex]
[tex]\implies x=0[/tex]
Substitute x = 0 into the given function to find the y-value of the point:
[tex]\implies y=4+2\left(0\right)-\left(0\right)^2=4[/tex]
Therefore, the point at which the tangent of the parabola is parallel to the line y = 2x - 4 is:
(0, 4)Substitute the found point and slope into the point-slope formula to create an equation of the tangent:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-4=2\left(x-0\right)[/tex]
[tex]\implies y=2x+4[/tex]
Find the area of the following figure. Pictures are not drawn to scale. Round answers to the nearest tenth.
The area of the trapezoid is 210 squared '
How to find the area of a trapezoid?
The area of a trapezoid be be calculated using the formula:
A = 1/2(a+b)h
where:
a is the length of one of the parallel sides of the trapezoid
b is the length of the other parallel side of the trapezoid
h is height is the distance between the two parallel sides (perpendicular to the bases)
a = 12', b = 18 + 5 = 23' and h = √(13²-5²) = 12'
A = 1/2(a+b)h
A = 1/2(12+23)12
A = (35)6
A = 210 squared '
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Describe each correlation value.
A. r = 0.921
B. r=-0.873
C. r = -0.281
D. r = 0.303
[Select]
[Select]
[Select]
[Select]
>
>
The correlation coefficient having -negative value means inverse correlation and +positive value means direct relationship.
What Is the Correlation Coefficient?An analytical way to gauge how strongly two variables are linearly related is to use the correlation coefficient. Anywhere between -1 and 1 can be its value. A correlation coefficient of -1 indicates a perfect negative, inverse, or inverse-correlation, where values in one series increase as those in the other decline and vice versa. An exact positive correlation or direct relationship is indicated by a coefficient of 1, or 1. In the absence of a linear relationship, a correlation coefficient of 0 indicates.
When evaluating the level of association between two variables, factors, or data sets, scientists and financiers alike use correlation coefficients. Assuming, for instance, that there is a strong positive correlation between oil prices and forward returns on oil stocks given that high oil prices are advantageous for crude producers
Now,
For
A. r = 0.921 -Direct relationship.
B. r= -0.873 -Inverse relationship.
C. r = -0.281 -Inverse relationship.
D. r = 0.303 -Direct relationship.
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2.) a swim contest of 10 people has three winners. a.) in how many ways can those three winners be chosen?
Answer:
720 Should be the answer I think.
The person is around 2 meters tall and the street light is only 8 meters above the ground. The rate at which the person is walking is 4/3
Step-by-step explanation:
We find the answer by using the equation ds/dt which equals to 4/9.
s represents the length of the shadow while x represents distant of shadow from the street light.
Hence we get x/6 = s/2 so dx/dt putting the values we get 6ds/2dt and the answer is 4/3
By applying the first derivative of distance with respect to time, it can be concluded that the person is walking 4/3 meters per second.
Instantaneous velocity or rate is the first derivative of distance with respect to time. Mathematically it is written v = ds/dt, where v is the velocity, s is the distance and t is the time.
First, we make a simple drawing using the given information:
The walking person = 2 meters tall
The street light = 8 meters above the ground
The walking rate is constant
The person's shadow lengthening rate = 4/9 meter per second = dy/dt
We want to know the walking rate, dx/dt.
We determine the value of y:
8 / 2 = (x + y) / y
8y = 2x + 2y
6y = 2x
y = x / 3
Then we substitute the value of y into the equation:
dy/dx = d(x/3) / dx
= 1/3
Finally, we can get the rate dx/dt:
dx/dt = dy/dt * dx/dy
= 4/9 * 3
= 4/3
Thus, it can be concluded that the person is walking 4/3 meters per second.
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(6-squarre root 8)^2
Answer:
(6-squarre root 8)^2 = 10.058874
Is dividing by 0.5 the same as dividing by 2?
The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers .
Let us understand the Division with the help of example ;
let the number be 10 ;
first we divide the number 10 by 0.5 ;
this can be written mathematically as ⇒ [tex]\frac{10}{0.5}[/tex] ;
⇒ [tex]\frac{10}{\frac{1}{2} }[/tex] = [tex]10\times2[/tex] = 20 ;
So , on dividing 10 by 0.5 , we get the answer as 20 .
Second , the number 10 is divided by 2 ;
this can be written mathematically as ⇒ [tex]\frac{10}{2}[/tex] ;
⇒ [tex]\frac{10}{2 }[/tex] = 5 ;
So , on dividing 10 by 2 , we get the answer as 5 .
Therefore , dividing by 0.5 is not same as dividing by 2 .
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pick a two digit number greater than 49 but less than 65 rewrite your two digit number is a difference of two numbers, show how to use the identity (x - y)² = x² - 2xy + y² to square your number.
Answer This Question Please!!!!!
Answer:
Step-by-step explanation:
none of these the corrct answer is 5
let d be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. what is the standard deviation of d?
A randomly selected subject has a 0.40 probability of completing more tasks than expected in 5 minutes while listening to relaxing music.
The Probability distribution is:
X 1 2 3 4
P(x) 0.20 0.40 0.30 0.10
If listening to soothing music, the expected number of puzzles in 5 minutes can be calculated as follows:
E(x) = ∑x p(x)
⇒ E(x) = 1 ×(0.20) + 2× 0.40 + 3 × 0.30 + 4× 0.1
⇒ E(x) = 0.20 + 0.8 + 0.9 + 0.4
⇒ E(x) = 2.3
Thus, a randomly selected subject could solve 5 puzzles while listening to soothing music. The probability of solving more tasks than expected in a minute is calculated as:
P( X > 2.3) = P(X = 3) + P(X = 4)
= 0.30 + 0.10
= 0.40
Explanation for other option:
(a) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music does not equal 0.1.
(c) 5 randomly selected participants. The probability of completing more tasks than expected in a minute of listening to relaxation music does not equal 0.8.
(d) The probability that a randomly selected participant completes more tasks than expected in 5 minutes while listening to relaxing music is not equal to 1.
(e) The likelihood of randomly selected participants completing more tasks than expected in 5 minutes while listening to relaxing music cannot be determined.
Learn more about Probability:
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What is the actual height of the lighthouse?
Answer:
30 feet
Step-by-step explanation:
The scale factor is 1 inch = 3 feet
So 10 inches = 10 x 3 feet= 30 feet
Height of the lighthouse is 30 feet
