One pump can empty a pool in 4 days, whereas a second pump can empty the pool in 10 days. How long will it take the two pumps, working together, to empty the pool? (Fractional answers are OK.)

Answer:

The answer to your question is  y = x - 23

Step-by-step explanation:

Process

1.- Get the slope of the line

If two lines are parallels, it means that they have the same slope.

                                 y = 1x - 10

Slope = m = 1

2.- Get the equation of the line

                               y - y1 = m(x - x1)

                               y + 29 = 1(x + 6)                 Substitution

                               y + 29 = x + 6                     Expanding

                               y = x + 6 - 29                      Simplifying

                               y = x - 23

Answer:

y = x - 23

Step-by-step explanation:

All lines parallel to the given line y = x - 10 have the same slope (1), and the same form of equaiton:  y = x + C, where C is a constant.

We know that the new line passes through (-6, -29).  Replacing x with -6, y with -29, we get:

-29 = -6 + C, and thus we find that C = -23.

Thus, the desired equation is

y = x - 23

Answer:

Below.

Step-by-step explanation:

If g(x) is the inverse of g(x) then  g(f(x)) = x.

g(f(x)) =  4 (x + 9)/ 4 - 9

= x + 9 - 9

= x.

So it is the inverse.

Also if you find f((g(x)) it is also = to x.

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: 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:

Step Three is the error

Step-by-step explanation:

right on edge

The student made the first mistake in step 2. Use the change of base formula to rewrite the equations is incorrect.

The reason is that the change of base formula is typically used in logarithms, not when graphing systems of equations.

When solving a system of linear equations by graphing, you would typically write the equations in the form y=mx+b and then graph them on the coordinate plane to find the point of intersection.

The change of base formula is used to convert logarithms from one base to another, not to rewrite equations in general.

In this case, the student simply rewrote the equations using different notation without changing their meaning.

The correct method would be to graph the original equations and identify the x-value at the point of intersection.

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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Answer:

D

Step-by-step explanation:

it is a triangle.

Answer:

D. Triangle

Step-by-step explanation:

D. Triangle

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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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:

pic # 1 answer is B. 81 x pi

pic#3 answer is C. QC

Step-by-step explanation:

pic #1

         the formula to find the area of a circle is pi x the radius to the second power

they give you the diameter. (18)

the radius is half of a diameter (d/2)

so 18/3 = 9

9 to the second power (9 x 9) = 81

so your answer is 81 x pi

pic#2

        I don't much, but i do know they asking for the radius and since the radius is half the diameter of a circle then QC makes sense in my book.

hope this is helpful.

The area of the circle is B. 81 π in²

the line segment representing radii are PC and QC

Area of circle is given by the formula

= π d² / 4

where d = 18 in

= π * 18² / 4

= 81 π in²

When C is the center of the circle. The line segment representing radii are lines from the circumference to the center. These lines includes

PC and QC

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Answer:

25

Step-by-step explanation:

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:

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:

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:

[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: 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.

Final answer:

Sally looked at 48 turkey trees and found 7/8 were too small. By multiplying 48 by the fraction 7/8, we find that 42 trees were too small.

Explanation:

The question asks us to calculate the number of turkey trees that were too small, based on the total number of trees Sally looked at and the fraction that were too small.

Sally looked at 48 trees in total and found that 7/8 of them were too small. To find the number of too small trees, we multiply the total number of trees by the fraction that were too small:

Number of too small trees = Total number of trees × Fraction too small

Number of too small trees = 48 × 7/8

Calculating this gives us:

Number of too small trees = 48 × 0.875

Number of too small trees = 42

Therefore, out of the 48 turkey trees Sally looked at, 42 of them were too small for her Thanksgiving needs.

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:

P(y≤4) = 0.629

Step-by-step explanation:

you can see in attachment.

Answer: 240 people get the news from social media

Step-by-step explanation:

The ratio of the number of people who get their news from social media to the number of people who their news elsewhere is 3:7

Total ratio is the sum of the proportion of those that get their news from social media and those that got their news elsewhere.

It becomes 3+7 = 10

Total number of people in the town is 800

To determine the number of people that got their news from social media, we will divide the proportion of those that get their news from social media by the total ratio and multiply by the total number of people in the town. It becomes

3/10 × 800 = 240

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.

__

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:

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:

a) [tex]P(\bar X>81.5)=1-0.933=0.067[/tex]

b) [tex]P(\bar X<69.5)=0.0062[/tex]

c) [tex]P(73.4<\bar X<84.05)=0.8755[/tex]  

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

[tex]X \sim N(\mu=77,\sigma=27)[/tex]  

And let [tex]\bar X[/tex] represent the sample mean, the distribution for the sample mean is given by:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

On this case  [tex]\bar X \sim N(77,\frac{27}{\sqrt{81}})[/tex]

Part a

We want this probability:

[tex]P(\bar X>81.5)=1-P(\bar X<81.5)[/tex]

The best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we apply this formula to our probability we got this:

[tex]P(\bar X >81.5)=1-P(Z<\frac{81.5-77}{\frac{27}{\sqrt{81}}})=1-P(Z<1.5)[/tex]

[tex]P(\bar X>81.5)=1-0.933=0.067[/tex]

Part b

We want this probability:

[tex]P(\bar X\leq 69.5)[/tex]

If we apply the formula for the z score to our probability we got this:

[tex]P(\bar X \leq 69.5)=P(Z\leq \frac{69.5-77}{\frac{27}{\sqrt{81}}})=P(Z<-2.5)[/tex]

[tex]P(\bar X\leq 69.5)=0.0062[/tex]

Part c

We are interested on this probability

[tex]P(73.4<\bar X<84.05)[/tex]  

If we apply the Z score formula to our probability we got this:

[tex]P(73.4<\bar X<84.05)=P(\frac{73.4-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{84.05-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]

[tex]=P(\frac{73.4-77}{\frac{27}{\sqrt{81}}}<Z<\frac{84.05-77}{\frac{27}{\sqrt{81}}})=P(-1.2<z<2.35)[/tex]

And we can find this probability on this way:

[tex]P(-1.2<z<2.35)=P(z<2.35)-P(z<-1.2)[/tex]

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

[tex]P(-1.2<z<2.35)=P(z<2.35)-P(z<-1.2)=0.9906-0.1151=0.8755[/tex]

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:

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:

  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.

(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.

Final answer:

The volume of the cylindrical water tank is approximately 490 ft³.

Explanation:

To find the volume of a cylindrical water tank, we can use the formula V = πr²h, where r is the radius of the tank and h is the height of the tank. Plugging in the given values, we have V = 3.14 × (5.5 ft)² × 13 ft. Simplifying, we get V ≈ 490 ft³. Rounding to the nearest whole number, the volume of the tank is approximately 490 ft³.

Answer:

C

Step-by-step explanation:

Discrete data includes numbers that are exclusively integers, i.e, ... -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 7 ..... and so on. It do not include the other real numbers that are not integers. You can recognize discrete data, for example, in a grah, as there will be only isolated points and not a continuous line.

The height of a member is continuous as we can have every number between 0 and the top height. There can be 1.50 m, 1.51m, 1.5000001m, 1.65m, 1,644444449, and so on with every number (obviously, we will not have heights of 5.78 m because of simply nature). So, we discard option a.

Exactly the same as heights happens with weight. We can ahve any weight you may imagine from the less weight to the top. 100.45555555 pounds is a posible weight, for example. With this, we discard option b.

The time is also continuous. Lets think in minutes. A runner can register 7 minutes, 7.2 minutes, 7.098686 minutes, and so on for every number. We can use every fraction you imagine. So we can discard options d and e.

However the number of times is discrete, because the number of races are discrete. There are 1, 2, 3, 4,... races. We can not have 5.5 races, it is impossible. So, the number of times a runner finished ahead is discrete. There is no member that finished 7.2 times first, we can find either 7 times or 8 times, but not 7.2. So, option c is the correct.