Please help with these! I don't know how they work.

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Probability of choosing an odd number in the second turn is the sum of probabilities of choosing an odd number in second turn given that an odd number or an even number is picked in first turn.

Probability of getting an odd number in the first turn out of 1,2,3,4,5 is [tex]\frac{3}{5}[/tex]

Probability of getting an even number in the first turn out of 1,2,3,4,5 is [tex]\frac{2}{5}[/tex]

Probability of getting an odd number in second turn given that an odd number was picked in the first turn (remaining : 2 odd numbers out of 4) is [tex]\frac{1}{2}[/tex]

Probability of getting an odd number in second turn given that an even number was picked in the first turn (remaining : 3 odd numbers out of 4) is [tex]\frac{3}{4}[/tex]

Total probability is [tex]\frac{3}{5} \times \frac{1}{2}  +  \frac{2}{5} \times \frac{3}{4}  =  \frac{3}{5}[/tex]

The probability of choosing an odd digit in the second draw, considering all scenarios of the first draw, is 0.625.

The student's question pertains to probability in a sequential selection scenario. It involves two sequential selections of digits from a certain set, specifically looking at the situation where an odd digit is selected in the second draw.

To address this, we first acknowledge that there are 5 digits to choose from initially: 1, 2, 3, 4, 5. However, once a digit is chosen and removed, 4 digits remain in the set for the second round of choosing. Among the remaining 4 digits, either two or three of them will be odd, depending on the parity (evenness or oddness) of the first digit chosen.

If an even digit is chosen first, three odd digits (1,3,5) will be left, thus the probability of choosing an odd digit the second time is 3 out of 4, or 0.75. If an odd digit is chosen first, two odd digits will be left, and the probability of choosing an odd digit in the second draw is then 2 out of 4, or 0.5. Finally, we consider the total probability over all possible first draws, yielding (1/2)*0.75 + (1/2)*0.5 = 0.625.

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Answer:

There are 12,565,671,261 ways.

Step-by-step explanation:

Here we have to use the combination and repetition formula.

C(n + r-1, r) = [tex]\frac{(n + r-1)!}{r!(n-1)!}[/tex]

Given: n = 10 (The number of questions)

Each question is worth at least 5 points.

10 questions = 10 *5 = 50

The total = 100

r = 100 - 50

r = 50

Now we can apply the formula.

C(10 + 50 -1, 50) = [tex]\frac{(10 + 50 -1)!}{50!(10 -1)!}[/tex]

C(59, 50) = [tex]\frac{59!}{50!9!}[/tex]

Simplifying the above factorial using the calculator, we get

C(59, 50) = 12,565,671,261

There are 12,565,671,261 ways.

There are 14,441,654 ways to assign scores to the problems on the final exam.

To find the number of ways to assign scores to the problems, we can use the concept of stars and bars. Let's consider each question as a bar and the points as stars. Since each question is worth at least 5 points, we can subtract 5 from each question's score to make sure it is at least 0. Now, we have a total of 100-5*10 = 50 points to distribute among the questions. Using stars and bars, we can find the number of ways to distribute these points.

The total number of ways to distribute 50 points among 10 questions is given by the formula (n+r-1) choose (n-1), where n is the number of questions (10) and r is the total number of points (50). Plugging in these values, we get (10+50-1) choose (10-1) = 59 choose 9 = 14,441,654 ways to assign scores to the problems.

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Answer:

No

Step-by-step explanation:

Just because the derivative is 0 at a point doesn't necessarily mean it is a relative minimum or maximum.  You must be able to evaluate the derivative on both sides of the point to determine if it changes signs.  Since endpoints have only one side, they cannot be relative maximums or minimums.

The number of toddlers at this daycare center is C. 42.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The ratio of toddlers to infants at a daycare center is 7 to 3.

let, There be 'T' number of toddlers and 'I' number of infants.

So, T : I = 7 : 3.

T/I = 7/3.

3T = 7I Or I = 3T/7...(i)

Now, Twelve more infants join the daycare to change the ratio to 7 to 5.

Therefore,

T/(I + 12) = 7/5.

5T = 7I + 84..(ii)

5T = 7(3T/7) + 84.

5T = 3T + 84.

2T = 84.

T = 42.

So, The number of toddlers in this day center is 42.

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Answer:

The probability of a person having a driving accident while intoxicated is 0.07

Step-by-step explanation:

Hi, well, let´s put this on a formula, I think it is the best way to explain it.

[tex]P(A+I)=P(A)+P(I)-P(AorI)[/tex]

Where:

P(A+I) = Probability of having a driving accident while intoxicated.

P(A) = Probability of a person of having an accident.

P(I) = Probablity person being intoxicated.

P(A or I) = Probability of a person for being intoxicated or having an accident.

Therefore, things should look like this:

[tex]P(A+I)=0.12+0.32-0.37=0.07[/tex]

So, the  probability of a person having a driving accident while intoxicated is 0.07.

Best of luck.

The probability of a person having a driving accident while intoxicated is 0.375 or 37.5%.

To find the probability of a person having a driving accident while intoxicated, we can use the formula for conditional probability: P(A|B) = P(A and B) / P(B). In this case, A represents the event of having a driving accident and B represents the event of driving while intoxicated. The probability of driving while intoxicated is given as 0.32, and the probability of having a driving accident is given as 0.12. So, P(A and B) = 0.12 and P(B) = 0.32. Plugging these values into the formula, we get P(A|B) = 0.12 / 0.32 = 0.375. Therefore, the probability of a person having a driving accident while intoxicated is 0.375 or 37.5%.

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Answer:

P(y≤4) = 0.629

Step-by-step explanation:

you can see in attachment.

Answer: a) [tex]\dfrac{32}{243}[/tex] b) [tex]\dfrac{256}{6561}[/tex] c) [tex]\dfrac{128}{6561}[/tex] d) [tex]\dfrac{6305}{6561}[/tex]

Step-by-step explanation:

Since we have given that

Probability that each person agrees independently to be interviewed = [tex]\dfrac{2}{3}[/tex]

(a) 5 names?

If it has 5 names, then the probability would be

[tex](\dfrac{2}{3})^5\\\\=\dfrac{32}{243}[/tex]

(b) What if it has 8 names?

If it has 8 names, then the probability would be

[tex](\dfrac{2}{3})^8=\dfrac{256}{6561}[/tex]

(c) If the list has 8 names what is the probability that the reviewer will contact exactly 7 people in completing her assignment?

[tex]^8C_7(\dfrac{2}{3})^7(\dfrac{1}{3})\\\\=\dfrac{128}{6561}[/tex]

(d) With 8 names, what is the probability that she will complete the assignment without contacting every name on the list?

[tex]1-P(X=8)\\\\=1-^8C_8(\dfrac{2}{3})^8\\\\=1-\dfrac{256}{6561}\\\\=\dfrac{6561-256}{6561}\\\\=\dfrac{6305}{6561}[/tex]

Hence, a) [tex]\dfrac{32}{243}[/tex] b) [tex]\dfrac{256}{6561}[/tex] c) [tex]\dfrac{128}{6561}[/tex] d) [tex]\dfrac{6305}{6561}[/tex]

Luis swam 20440m in those 4 weeks.

Step-by-step explanation:

Distance swam per day = 0.73 km

Time period = 4 weeks

1 week = 7 days

4 weeks = 7*4 = 28 days

Total distance swam = Distance per day * Total days

[tex]Total\ distance\ swam=0.73*28\\Total\ distance\ swam=20.44\ km[/tex]

1 km = 1000m

20.44 km = 20.44*1000

Total distance in meters = 20440 m

Luis swam 20440m in those 4 weeks.

Keywords: multiplication, conversion

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Answer:

32 oz

Step-by-step explanation:

(a) 1000

(b) 11100

(c) 11095.

Step-by-step explanation:  

(a) If A1 is a subset of A2 and A2 is a subset of A3, then all the elements of A1 are in A2 and all the elements of A2 are in A3.

Then, n(A1 n A2) = 100, n(A2 n A3) = 1000 , n(A1 n A3) = 100 and n(A1 n A2 n A3) = 100.

So,  we get

[tex]n(A1\cup A2\cup A3)\\\\=n(A1)+n(A2)+n(A3)-n(A1\cap A2)-n(A2\cap A3)-n(A1\cap A3)+n(A1\cap A2\cap A3)\\\\=100+1000+1000-100-1000-100+100\\\\=1000.[/tex]

(b) If the sets are pairwise disjoint, then

n(A1 n A2) = n(A2 n A3) = n(A1 n A3) = n(A1 n A2 n A3) = 0.

So, we get

[tex]n(A1\cup A2\cup A3)\\\\=n(A1)+n(A2)+n(A3)\\\\=100+1000+10000\\\\=11100.[/tex]

(c) If  there are two elements common to each pair of sets and one element in all three sets, then

n(A1 n A2) = 2,  n(A2 n A3) = 2, n(A1 n A3) = 2 and n(A1 n A2 n A3) = 1.

So, we get

[tex]n(A1\cup A2\cup A3)\\\\=n(A1)+n(A2)+n(A3)-n(A1\cap A2)-n(A2\cap A3)-n(A1\cap A3)-n(A1\cap A2\cap A3)\\\\=100+1000+1000-2-2-2+1\\\\=11100-5\\\\=11095.[/tex]

Final answer:

The number of elements in the union of sets A1, A2, and A3 varies depending on their relationships. For subsets (a), the count is 10,000; for disjoint sets (b), it is 11,100; and when each pair has common elements plus one common to all (c), the count is 11,095.

Explanation:

Finding the Number of Elements in the Union of Sets

To find the number of elements in the union of sets A1, A2, and A3, we need to consider the given conditions.

a) A1 ⊆ A2 and A2 ⊆ A3

Since A1 is a subset of A2, and A2 is a subset of A3, all elements of A1 and A2 are included in A3. Therefore, the

number of elements in A1 ∪ A2 ∪ A3 equals the number of elements in A3, which is 10,000.

b) The Sets Are Pairwise Disjoint

If the sets are pairwise disjoint, this means they share no elements in common. We simply add the number of elements in each set to find the union's total count. This gives us 100 + 1000 + 10,000 = 11,100 elements in the union.

c) Two Elements Common to Each Pair and One in All Three

With two elements common to each pair of sets and one element in all three, we need to subtract the common elements to avoid double-counting. So, A1 ∪ A2 ∪ A3 will have 100 + 1000 + 10,000 - 2 - 2 - 2 + 1 (since 1 element is counted three times, we add it back once) which equals 11,095 elements.

Answer:

No, yes, yes

(-28,-11) and (8.7)

[tex][tex][\frac{-4}{3} ,\infty)[/tex]}[/tex]

Step-by-step explanation:

Given that a line in two dimension is parametrized by

[tex]x=2+6t \\y = 4+3t[/tex]

a) If t is non negative, then (-28,-11) cannot lie on that part

(-28,-11) No because t =-5

(8,7) yes because t =1

(26,16) yes because t = 4

b) when t lies between -2 and 1

we have left end point as

[tex]x=2+6(-2) = -10\\y = 4+3(-2) = -2\\[/tex]

(-10,-2) is left end point

Right end point is when t =1 i.e.

(8,7)

c) when the points should be above x axis, y should be non negative

i.e. [tex]y=4+3t\geq 0\\t\geq [/tex]

So t should lie in the interval

[tex][\frac{-4}{3} ,\infty)[/tex]}

Answer:

1,152

Step-by-step explanation:

The rectangular field have four sides, where the opposite sides of the field are equal

The length of the brick wall that gives the lowest total cost of the fence is 40 meters

Let the length of the rectangular field be x, and the width be y.

Where: y represents the side to be made of brick wall,

So, the perimeter of the field is calculated using:

[tex]\mathbf{P =2x + 2y}[/tex]

And the area is

[tex]\mathbf{A =xy}[/tex]

The area is given as 2400.

So, we have:

[tex]\mathbf{xy = 2400}[/tex]

Make x the subject in

[tex]\mathbf{x = \frac{2400}y}[/tex]

Rewrite the perimeter as:

[tex]\mathbf{P =2x + y + y}[/tex]

The brick wall is $10 per meter, while the wooden wall is $20 per 4 meters

So, the cost function becomes

[tex]\mathbf{C =\frac {20}4 \times (2x + y) + 10 \times y}[/tex]

[tex]\mathbf{C =5 \times (2x + y) + 10 \times y}[/tex]

Open brackets

[tex]\mathbf{C =10x + 5y + 10y}[/tex]

[tex]\mathbf{C =10x +15y}[/tex]

Substitute [tex]\mathbf{x = \frac{2400}y}[/tex] in the cost function

[tex]\mathbf{C =10 \times \frac{2400}{y} +15y}[/tex]

[tex]\mathbf{C = \frac{24000}{y} +15y}[/tex]

Differentiate

[tex]\mathbf{C' = -\frac{24000}{y^2} +15}[/tex]

Set to 0, to minimize

[tex]\mathbf{-\frac{24000}{y^2} +15 = 0}[/tex]

Rewrite as

[tex]\mathbf{\frac{24000}{y^2} =15}[/tex]

Divide through by 15

[tex]\mathbf{\frac{1600}{y^2} =1}[/tex]

Multiply both sides by y^2

[tex]\mathbf{y^2 =1600}[/tex]

Take square roots of both sides

[tex]\mathbf{y^2 =40}[/tex]

Hence, the length of the brick wall should be 40 meters

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Answer:

  Raj can look on his pay stub to find the total is $400

Step-by-step explanation:

The relation between the deposit and the total pay is ...

  deposit = 0.40 × total pay

  total pay = deposit / 0.40 = 160/0.40 = 400

Raj was paid $400 this week.

The net force on the rotor due to the unbalanced samples : 64.4 N

Centripetal force is a force acting on objects that move in a circle in the direction toward the center of the circle  

[tex]\large{\boxed{\bold{F= \frac{mv^2}{R}}}[/tex]

F = centripetal force , N

m = mass , Kg

v = linear velocity , m/s

r = radius , m

The speed that is in the direction of the circle is called linear velocity  

Can be formulated:  

[tex]\displaysyle v=2\pi.r.f[/tex]

r = circle radius  

f = rotation per second (RPS)  

The sample has a mass of 10 mg larger than the opposing sample. If the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm  

Known  

RPM = 70,000, convert to RPS = 70,000: 60 = 1166.6  

r = 12 cm = 0.12 m  

m = 10 mg = 10⁻⁵ kg  

then  

Linear velocity :

[tex]\displaystyle v=2\times 3.14\times 0.12\times 1166.6\\\\v=879.15\:m/s[/tex]

Centripetal force :

[tex]\displaystyle F=\frac{10^{-5}\times (879.15)^2}{0.12}\\\\F=\boxed{\bold{64.4\:N}}[/tex]

the average velocity

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resultant velocity

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velocity position

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Keywords: ultracentrifuge, samples, Centripetal force, linear velocity

The magnitude of the net force on the rotor due to the unbalanced samples is 64.4 Newton.

From the information given, the velocity will be calculated as:

= 2πrf.

where, r = radius = 0.12

f = rotation per second = 70000/60 = 1166.6

Velocity will be:

= 2 × 3.14 × 0.12 × 1166.6

= 879.15 m/s

Therefore, the centripetal force will be:

= [10^-5 × (879.15)²] ) 0.12

= 64.4N

In conclusion, the magnitude of the net force is 64.4 Newton.

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Answer:

D

Step-by-step explanation:

it is a triangle.

Answer:

D. Triangle

Step-by-step explanation:

D. Triangle

Answer:

Remember, a number a is a zero of the polynomial p(x) if p(a)=0. And a has multiplicity n if the factor (x-a) appear n times in the factorization of p(x).

1. Since -2 is a zero with multiplicity 1, then (x+2) is a factor of the polynomial.

2. Since 1 is a zero with multiplicity 2, then (x-1) is a factor of the polynomial and appear 2 times.

3. Since 5 is a zero with multiplicity 3, then (x-5) is a factor of the polynomial and appear 3 times.

Then, the polynomial function with the zeros described above is

[tex]p(x)=(x+2)(x-1)^2(x-5)^3= x^6-15x^5+72x^4-78x^3-255x^2+525x-250[/tex]

Final answer:

The polynomial function with the given zeros -2, 1, and 5, with their respective multiplicities 1, 2, and 3, and leading coefficient 1 is [tex]f(x) = (x + 2)(x - 1)^2(x - 5)^3.[/tex]

Explanation:

To form a polynomial function f(x) with the given zeros and multiplicities, we use the fact that a zero x = a with multiplicity m corresponds to a factor (x - a)^m in the polynomial. Since the leading coefficient should be 1, we simply multiply these factors together. Based on this, the polynomial with zeros -2 (multiplicity 1), 1 (multiplicity 2), and 5 (multiplicity 3) is:

[tex]f(x) = (x + 2)(x - 1)^2(x - 5)^3[/tex]

This polynomial is of degree 6, as the sum of the multiplicities of the zeros (1+2+3) equals the degree.

Answer:

600ft x 1200ft

Step-by-step explanation:

Use derivative optimization to find the maximum area.

I'll call the two same sides "a", and the one different side "b"

The maximum perimeter (including 3 sides) is 2400 ft. so,

2400 = 2a + b

The area is length × width. so,

A = ab

Using substitution to combine the equations,

A = a × (2400 - 2a)

A = -2a² + 2400a

Find the maximum of A by finding the zeros of its derivative.

dA = -4a +2400

0 = -4a + 2400

The maximum occurs at a = 600

Substitute in the perimeter equation to find b.

2400 = 2(600) + b

b = 1200

600 x 1200

Answer:

[tex]\frac{60!}{22!22!16!}[/tex]

Step-by-step explanation:

As given, drug A is to be given to 22 mice, drug B is to be given to another 22 mice, and the remaining 16 mice are to be used as controls.

Required number of ways = Number of ways to select mice that gets drug A x the number of ways for mice that gets drug B x the number of ways the mice gets no drugs.

= [tex]\frac{60!}{22!38!} \times \frac{38!}{22!16!} \times1[/tex]

Solving this we get;

= [tex]\frac{60!}{22!22!16!}[/tex]

= 314,790,828,599,338,321,972,833,000

To find the area of the rectangular field in square meters, we first convert the length and width from kilometers to meters. Then, we multiply the length by the width to find the area. This results in an area of 140,000 m².

To solve this problem, we must first understand what the question is asking. The question is asking for the area of a rectangular field, and the dimensions are given in kilometers. The area is found by multiplying the length times the width of a shape (in this case, a rectangle).

Then, we need to convert the kilometers to meters because the question asks for the answer in square meters. We know there are 1,000 meters in 1 kilometer. Therefore, the length of the field is 0.4 km * 1,000 = 400 meters, and the width of the field is 0.35 km * 1,000 = 350 meters.

The area is found by multiplying the length by the width, which is 400m * 350m = 140,000 m².

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1.

Chance of finding a bug = 0.35

Chance of not finding a bug = 1 - 0.35 = 0.65

Probability of finding a bug in the first 3 programs =

Probability of not finding a bug in 2 out of the 3 and finding a bug in 1.:

0.65^2 * 0.35 = 0.147 = 0.15

Answer is A.

2.

Probability of heads = 0.50

Probability of tails = 0.50

Probability of heads on the fourth attempt = tails x tails x tails x heads = 0.5 x 0.5 x 0.5 x 0.5 = 0.0625

The answer is B.

Answer:

Step-by-step explanation:

incomplete. no results listed below

Answer: 28989675

Step-by-step explanation:

The number of ways to choose r things out of n things ( if order doesn't matter) is given by :_

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given : In the 6/55 lottery game, a player picks six numbers from 1 to 55.

Then , the number of ways to choose 6 numbers out of 55 is  if repetition is not allowed :

[tex]^{55}C_6=\dfrac{55!}{6!(55-6)!}\\\\=\dfrac{55\times54\times53\times52\times51\times49!}{6\times5\times4\times3\times2\times1\times49!}\\\\=\dfrac{55\times54\times53\times52\times51}{6\times5\times4\times3\times2\times1}\\\\=28989675[/tex]

Hence, the player have 28989675 choices.

When repetition is not allowed, a player in the 6/55 lottery game can make 32,468,436 different choices.

When repetition is not allowed, the number of different choices a player has in the 6/55 lottery game can be determined using the concept of combinations. A combination is a selection where the order of the elements does not matter.

To calculate the number of combinations, we can use the formula:

C(n, r) = n! / (r! * (n-r)!)

In this case, n = 55 (total number of choices) and r = 6 (number of choices to be made). Substituting these values into the formula:

C(55, 6) = 55! / (6! * (55-6)!)

Simplifying further:

C(55, 6) = 55 * 54 * 53 * 52 * 51 * 50 / (6 * 5 * 4 * 3 * 2 * 1)

This simplifies to:

C(55, 6) = 32,468,436

Therefore, a player has 32,468,436 different choices in the 6/55 lottery game when repetition is not allowed.

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Answer:

x=7 and y=-1

Step-by-step explanation:

X+Y=6 OR X=6-Y  ...(1)

X-Y=8    ...(2)

substitue X=6-Y in (2)

(6-Y)-Y=8

6-2Y=8

-2Y=8-6

-2Y=2

Y=2/-2\Y=-1 ANS.

for x, substitute Y=-1 in (1) above

X-(-1)=8

X=8-1

X=7 ANS.

Answer:

The answer is SSS.

Step-by-step explanation:

It is proved that △FIJ ≅ △HGJ By Side side Side Congruence Property.

Thus the correct option is D.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given:

In △FIJ and △HGJ

Segment FI  ≅ segment GH

Segment FJ = segment HJ (by definition of midpoint)

Segment GJ= segment IJ (by definition of midpoint)

∴ By Side side Side Congruence Property

△FIJ ≅ △HGJ by SSS

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Answer:

25

Step-by-step explanation:

Final answer:

Kim's original speed was 70 km/h. This was determined by equating the distances driven by both Kim and Maria in terms of Kim's original speed, and the fact they traveled for the same amount of time.

Explanation:

Let's denote Kim's original speed as [tex]\(V_{o}\)[/tex] in km/h. Kim drove for 3 hours at this speed and then slowed down by 15 km/h, driving at [tex]\(V_{o} - 15\)[/tex] km/h for the next 3 hours. Maria, on the other hand, averaged a speed of [tex]\(V_{o} + 5\)[/tex] km/h for the entire 6-hour trip (from 9:00 am to 2:00 pm).

To find the distance, which is the same for both Maria and Kim, we can set up the following equations based on the fact that distance is the product of speed and time: Kim's distance traveled is [tex]3 \(V_{o}\) + 3\((V_{o} - 15)\)[/tex] and Maria's distance traveled is [tex]5\((V_{o} + 5)\)[/tex]. These two expressions should be equal, as they traveled the same route:

[tex]3 \(V_{o}\) + 3\((V_{o} - 15)\) = 5\((V_{o} + 5)\)[/tex]

Simplifying the equation:

[tex]3 \(V_{o}\) + 3 \(V_{o}\) - 45 = 5 \(V_{o}\) + 25[/tex]

[tex]6 \(V_{o}\) - 45 = 5 \(V_{o}\) + 25[/tex]

[tex]Subtracting 6 \(V_{o}\) from both sides:[/tex]

[tex]\(V_{o}\) = 25+45[/tex]

Adding 45 to both sides:

[tex]\(V_{o}\) = 70[/tex]

Kim’s original speed, therefore, is 70 km/h.

Answer: B. 50 and 60

Step-by-step explanation:

Given : There are 9 showings of a film about endangered species at the science museum.

The total number of people saw the film = 459

Also, The same number of people were at each showing.

Then, the number of people were at each showing = Total people divided by Total showings

= 459 ÷ 9 = 51

Also, 50< 51 < 60  [the quotient is between 50 and 60.]

i.e.  About 50 and 60 people were at each showing .

Hence, the correct answer is B. 50 and 60.

Answer:

  1

Step-by-step explanation:

Label the points as in the attachment. Then we have ...

We can form the sum P + R + T and we get ...

  P +R +T = (a+b)/2 +(c+d)/2 +(e+a)/2 = a +(b +c +d +e)/2

We can form the sum Q + S and we get ...

  Q + S = (b+c)/2 +(d+e)/2 = (b +c +d +e)/2

Subtracting the latter sum from the former one gives ...

  P +R +T -(Q +S) = a +(b +c +d +e)/2 -(b +c +d +e)/2 = a

__

So, the value picked by the person with the average "6" was ...

 (7 +1 +5) -(9 +3) = 13 -12 = 1

The person with average "6" picked 1.

_____

The system of equations written in matrix form is shown in the second attachment. The inverse of the coefficient matrix is shown in the third attachment. That is where the sum shown above came from.

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The rest of the picked numbers are ...

  P = 2, b = 13, Q = 14, c = 5, R = 6, d = -3, S = -2, e = 9, T = 10

Answer:

The volume should not be bigger than the volume if the cross section was a square and thus the volume enclosed would be V=12π.

Step-by-step explanation:

using cylindrical coordinates

x= rsin θ

z= rcos θ

y=y

therefore

y+z=4 → y= 4-z = 4-r cos θ

also from x²+z²=4 →  -2≤x≤2 , -2≤z≤2

therefore since y= 4-z  → 6≤y≤2 → it does not overlap with the plane y=1

V=∫∫∫dV = ∫∫∫dxdydz = ∫∫∫rdθdrdy = ∫∫rdθdr   [(y=4-r cos θ,y=1) ∫ dy] =

∫∫[(4-rcosθ) - 1]rdθdr =  ∫∫(3-rcosθ) rdθdr = ∫dθ [r=2,r=0] ∫(3r-r²cosθ) dr

∫ (3/2* 2²- 2³/3 cosθ) dθ =[θ=2π, θ=0] ∫ (6-8/3 cosθ) dθ = 2π*6 - 8/3 sin0 = 12π

thus

V= 12π

to verify it, the volume should not be bigger than the volume if the cross section was a square and thus the volume enclosed would be:

V = [(2-(-2)]² * (6-2) /2 + [(2-(-2)]²  * (2-1) = 4³/2 + 4²*2 = 64 > 12π

Answer:

Option C is right

C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.

Step-by-step explanation:

Given that the  probability of drawing two aces from a standard deck is 0.0059

If first card is drawn and replaced then this probability would change.  By making draws with replacement we make each event independent of the other

Drawing ace in I draw has probability equal to 4/52, when we replace the I card again drawing age has probability equal to same 4/52

So if the two draws are defined as event A and event B,  the events are  independent

C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.