A turtle can walk \dfrac{1}{12} 12 1 ​ start fraction, 1, divided by, 12, end fraction of a kilometer in an hour. The turtle is \dfrac15 5 1 ​ start fraction, 1, divided by, 5, end fraction of a kilometer away from a pond. At this speed, how long will it take the turtle to reach the pond?

Answer:Marcel flew 4060 miles for Valentine's Day.

Step-by-step explanation:

For Christmas, Marcel flew 6090 miles from New York to Japan.

For Valentine's Day, Marcel flew from New York to England. The distance from New York to England's is 2/3 of the distance from New York to Japan. This means that the number of miles that Marcel flew for Valentine's Day would be

2/3 × 6090 = 4060 miles

Final answer:

To determine the distance from New York to England, one must multiply the distance from New York to Japan (6090 miles) by 2/3, resulting in 4060 miles. This represents the distance Marcel flew for Valentine's Day.

Explanation:

Marcel's vacation air travel distances involve a mathematical proportion problem. Marcel flew 6090 miles from New York to Japan for Christmas. The question states that the distance from New York to England is 2/3 of the distance from New York to Japan. To find the distance flown for Valentine's Day from New York to England, we multiply the distance from New York to Japan by 2/3.

So, the calculation is: 6090 miles × (2/3). When we perform this multiplication, we find that Marcel flew 4060 miles from New York to England for Valentine's Day.

Answer: 0.1064

Step-by-step explanation:

D= Both Alzheimer's are less than 80years old.

E= Two of 3 people who have Alzheimer's.

P(D | E ) = P ( D ∩ E)

P ( E )

= P ( A ∩ B ∩ C )

P ( A ∩ B ∩ C ) + P ( A ∩ B ∩ C ) + P ( A ∩ B ∩ C )

= Pa * Pb * (1 - Pc ) Pa * Pb * (1 - Pc ) + (1 - Pa ) * Pb * Pc + Pa * (1 - Pb ) * Pc

= 0.0017

=0.0010+0.0017+0.0037

=0.1064

The conditional probability that two individuals with Alzheimer's are both under 80 cannot be precisely calculated without more information about the general probabilities of each condition. However, the general formula for calculating conditional probability is P(A and B) = P(A) * P(B|A).

This is essentially a question about conditional probability. In order to calculate the conditional probability suggested by the question – that is, the probability that both individuals with Alzheimer's disease are younger than 80, given that we know that two people have the disease – we'd need more information about the overall probabilities of having Alzheimer's disease and being under 80. However, if we had this information the formula for conditional probability is P(A and B) = P(A) * P(B|A). In this equation, P(A) would be the probability that a randomly selected individual has Alzheimer's, P(B|A) would be the probability that a known Alzheimer's patient is under 80, and P(A and B) is the conditional probability we're trying to figure out. So, we'd need to multiply P(A) by P(B|A) to get P(A and B)

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Answer:

24

Step-by-step explanation:

The can will hold 75.36 inch³ of soup.

The volume of a cylinder with base radius 'r' and height 'h' is,

V = πr²h. If its base diameter is d, then we have d = r/2.

Given:

Radius = 2 inches

Height = 6 inches

So, Volume of Cylinder = πr²h

Now, put r= 2 inches and h= 6 inches

Then, Volume of cylinder = 3.14 x 2 x 2 x 6

Volume of Cylinder = 3.14 x 24

Volume of Cylinder = 75.6 inch³

Hence, the can hold 75.36 inch³.

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Answer:

Step-by-step explanation:

mean=(5.9+5.7+5.5+5.4+5.7+5.5+5.6+6.2+6.1+5.5)/10=57.1/10=5.71

we assume mean=5.7

x    mean  |x-mean| (x-mean)^2

5.9   5.7      0.2         0.04

5.7   5.7         0            0

5.5   5.7      0.2         0.04

5.4   5.7      0.3         0.09

5.7   5.7         0             0

5.5   5.7      0.2         0.04

5.6   5.7      0.1          0.01

6.2   5.7      0.5         0.25

6.1    5.7      0.4         0.16

5.5   5.7      0.2         0.04

                                --------

                                0.63

standard deviation=√((0.63)/10)=√(0.063)≈0.251

so c

Final answer:

By finding the range of the office workers' heights and applying the range rule of thumb (estimating the standard deviation as approximately one-fourth the range), the calculated standard deviation is rounded to 0.2 feet, matching answer choice (c).

Explanation:

To estimate the standard deviation of the office workers' heights using the range rule of thumb, we first find the range, which is the difference between the maximum and minimum values in the data set. The maximum height is 6.2 feet and the minimum is 5.4 feet, so the range is 6.2 - 5.4 = 0.8 feet.

The range rule of thumb states that the standard deviation can be estimated as approximately one-fourth of the range. Therefore, the estimated standard deviation is 0.8 / 4 = 0.2 feet. When rounded to the nearest tenth, the standard deviation is 0.2 feet, which corresponds to answer choice (c).

Answer: False

Step-by-step explanation:

The phenol would not evaporate or boil and would not reduce in quantity as it has a higher boiling point. So mixing it in different containers would not change the mass of phenol.

Answer:

slope is 5

Step-by-step explanation:

the slope represents the cost of the kayak for as many hours as the person rents it for. the y intersect is 20 because that is the cost just to rent the boat before using it.

Answer:

Step-by-step explanation:

If the relationship between cost and the number of chairs produced is linear, we would write an equation that expresses this relationship in the slope intercept form. It is expressed as

y = mx + c

Where

m represents the slope

c = intercept.

Slope = (y2 - y1)/(x2 - 1)

y2 = final value of y = 4800

y1 = initial value of y = 2200

x2 = final value of x = 300

x1 = initial value of x = 100

Slope, m = (4800 - 2200)/(300 - 100) = 2600/200 = $13 per chair.

To determine the intercept, we will substitute y = 4800, x = 300 and m = 13 into y = mx + c. It becomes

4800 = 13×300 + c = 3900

c = 4800 - 3900 = 900

The equation becomes

y = 13x + 900

To write an equation that expresses the relationship between cost and the number of chairs produced, we need to find the slope and y-intercept of the linear equation. The equation that expresses this relationship is Cost = $26(Number of Chairs) - $400.

We must determine the slope and y-intercept of the linear equation in order to build an equation that describes the link between the price and the quantity of chairs produced.

Slope = Change in Cost / Change in Number of Chairs
Using the given values, the slope is (4800 - 2200) / (300 - 100) = $26 per chair.

Now, let's find the y-intercept. We can use either of the given data points. Substituting the values of one data point, we have:
$2200 = $26(100) + b
b = $2200 - $2600 = -$400.

Therefore, the equation that expresses this relationship is:
Cost = $26(Number of Chairs) - $400.

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Answer:

C. Stratified Sampling

Step-by-step explanation:

Stratified sampling is a sampling method in which the overall population is divided into a number of smaller sub groups.

These smaller sub-groups are called as strata.

These sub-groups are formed on the basis of similar characteristics and attributes shared by the population.

It is also known as proportional random sampling.

Answer:

$111

Step-by-step explanation:

37x3 = 111

111/3 =37

The total restaurant bill that Joan, Melanie, and Sam paid, multiply the amount each person paid ($37) by the number of people (3), resulting in a total of $111.

Joan, Melanie, and Sam have decided to divide the restaurant bill evenly. If each person paid $37, we can determine the total bill by multiplying the amount each person paid by the number of people. Since there are three people, we calculate the total as follows:

Identify the amount each person paid: $37.

Count the number of people: 3 (Joan, Melanie, and Sam).

Multiply the amount paid by each person by the total number of people: $37 x 3 = $111.

Therefore, The total bill at the restaurant was $111.

Answer:

8.4 cm

Step-by-step explanation:

The longest side of an acute isosceles triangle is 12 centimeters.

Let x be the length of the smallest side

Isosceles triangle has one longest side and two smallest sides

so its acute triangle

[tex]c^2<a^2 +b^2[/tex]

where c is the longest side

a  and b are two shortest sides 'x'

[tex]c^2<x^2 +x^2[/tex]

[tex]12^2<x^2 +x^2[/tex]

[tex]144<2x^2[/tex]

divide both sides by 2

[tex]72<x^2[/tex]take square root on both sides

[tex]8.4<x[/tex]

So 8.4 cm

The perimeter of Kayla's garden including the walkway can be calculated using the formula P = 2(4 + 2w) + 2(3 + 2w), where w is the width of the walkway. This can also be rearranged as P = 2*(4 + 3 + 2w + 2w).

The perimeter of a rectangle, like the garden in question, is usually calculated by adding up the lengths of all its sides. In this case, however, the garden is bordered by a walkway of width w. Thus, to calculate the total perimeter, including the walkway, we need to account for this additional width on all four sides of the garden.

The original dimensions of the garden are 4 feet by 3 feet. With the walkway, the new dimensions become (4+2w) feet by (3+2w) feet, because the width of the walkway is added on both sides of the lengths.

Therefore, the two equivalent expressions for the perimeter, P, of Kayla's garden, including the walkway, are P = 2(4 + 2w) + 2(3 + 2w) or simply rearranged as P = 2*(4 + 3 + 2w + 2w). In these expressions, w is the width of the walkway.

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Answer:

  a) 22π cm/s; on the odd half-second (t=0.5, 1.5, 2.5, 3.5, 4.5); at the rest position; zero

  b) 22 cm from the rest position; zero

Step-by-step explanation:

Undamped simple harmonic motion is not complicated. Acceleration is a maximum where the applied force is a maximum, at the extremes of position. Since the position is extreme, the velocity is zero at those points. All of the energy is potential energy.

The speed is a maximum when the object is at the rest position, There is no applied force at that point, and no acceleration. All of the energy has been transformed to kinetic energy.

Part A:

The cart's velocity is given by the derivative of the position:

  s'(t) = -22π·sin(πt)

This has a maximum magnitude (speed) of 22π ≈ 69.1 cm/s, as you have noted.

The speed is a maximum at the rest position. The cart is there on each odd quarter-period, at t=0.5, 1.5, 2.5, 3.5, 4.5 seconds.

The cart's acceleration is given by the derivative of the velocity:

  s'' = -22π²·cos(πt)

On the odd quarter-period, the acceleration is zero.

Part B:

Acceleration is greatest when position is greatest (both are cosine functions). The speed of the cart is zero then (it is a sine function). The sine is at an extreme when the cosine is zero, and vice versa.

_____

The attached graph shows position, velocity, and acceleration (color coded).

To solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. This can be done by finding the derivative of the acceleration function and setting it equal to zero. The value of t that satisfies this equation can then be used to find the position and speed of the cart.

In order to solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. We can do this by finding the derivative of the acceleration function and setting it equal to zero. The derivative of the acceleration function is given by: a'(t) = -22πsin(πt). Setting this equal to zero gives: -22πsin(πt) = 0. Solving for t, we find that t = 1/2.

Now that we have the value of t, we can plug it back into the position function to find the position of the cart when the magnitude of the acceleration is greatest. The position function is given by: s(t) = 22cos(πt). Plugging in t = 1/2, we get: s(1/2) = 22cos(π/2) = 0.

To find the cart's speed when the magnitude of the acceleration is greatest, we can plug t = 1/2 into the velocity function. The velocity function is the derivative of the position function, which is given by: v(t) = -22πsin(πt). Plugging in t = 1/2, we get: v(1/2) = -22πsin(π/2) = 22π.

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Answer:

Trisha made 2 pans of brownies.

Step-by-step explanation:

Let the number of pans of brownies made by Trisha be 'x'.

Given:

Number of pans contributed by Rachel = 5

Number of squares in each pan = 12

Total number of squares (S) = 84

Total number of pans (N) = Number of pans by Trisha (x) + Number of pans by Rachel

So, [tex]N=x+5[/tex] -------- (1)

Total number of squares (S) = Number of squares in each pan × Number of pans (N).

[tex]S = 12N\\84=12N---- (2)[/tex]

Plug in the value of 'N' from equation (1) in equation (2). This gives,

[tex]84=12(x+5)[/tex]

Solve for 'x'.

[tex]12(x+5)=84\\\\x+5=\frac{84}{12}\\\\x+5=7\\\\x=7-5=2[/tex]

Therefore, Trisha made 2 pans of brownies.

Answer:

[tex]\displaystyle g(x) = 2^{x - 3}[/tex]

Explanation:

See above graph

The exponent gives you the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL.

I am joyous to assist you anytime.

Answer:

[tex]y\leq \frac{2}{3}x+\frac{1}{5}[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid line

Find the slope

we have

(0,0.2) and (3,2.2)

[tex]m=(2.2-0.2)/(3-0)=\frac{2}{3}[/tex]

The y intercept b is equal to

[tex]b=0.2=\frac{2}{10}=\frac{1}{5}[/tex]

so

the equation of the solid line  in slope intercept form is equal to

[tex]y=\frac{2}{3}x+\frac{1}{5}[/tex]

step 2

Find the equation of the inequality

we know that

The solution of the inequality is the shaded area below the solid line

therefore

[tex]y\leq \frac{2}{3}x+\frac{1}{5}[/tex]

Answer:

c,y>2/3x-1/5

Step-by-step explanation:

Answer:

The difference between the circumference of the tires is 12.56 inches.

Step-by-step explanation:

Given:

Diameter of old bicycle tires = 12 inch

Diameter of new bicycle tires = 16 inch

We need to find the difference in circumference of the tires.

Solution:

First we will find the circumference of Old bicycle tires.

Circumference can be calculated by π times diameter.

Circumference of Old bicycle tire = [tex]\pi \times 12 = 37.68\ in[/tex]

Now we will find the circumference of new bicycle tire.

Circumference of New bicycle tire = [tex]\pi \times 16 = 50.24\ in[/tex]

Now to find the difference between the circumference of the tires we will subtract Circumference of New bicycle tire from Circumference of Old bicycle tire we get;

framing in equation form we get;

difference between the circumference of the tires = [tex]50.24-37.68 =12.56\ in[/tex]

Hence The difference between the circumference of the tires is 12.56 inches.

Answer:the angles are 12 degrees, 48 degrees and 120 degrees.

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees.

The measures of the angles of XYZ are in the ratio 1:4:10. The total ratio is the sum of the proportion of each angle. It becomes

1 + 4 + 10 = 15

Therefore, the measure of the first angle would be

1/15 × 180 = 12 degrees

Therefore, the measure of the second angle would be

4/15 × 180 = 48 degrees

Therefore, the measure of the third angle would be

10/15 × 180 = 120 degrees

Answer:

Amy's car tank capacity is 16 gallons.

Step-by-step explanation:

Let the capacity of the tank be 'x'

Given:

Amount of gas in the car till it is refilled = [tex]\frac{1}{8}\times x = \frac{1}{8}x \ gallons[/tex]

Amount of gas added = 14 gallons.

We need to find the capacity of the tank.

Solution:

Now we can say that

Total Capacity of the tank is equal to sum of Amount of gas in the car till it is refilled and Amount of gas added.

framing in equation form we get;

[tex]x=\frac{x}{8}+14[/tex]

Combining the like terms we get;

[tex]x-\frac{x}{8}=14[/tex]

Now making the denominators common we will use L.C.M.

[tex]\frac{8x}{8}-\frac{x\times1}{8\times1}=14\\\\\frac{8x}{8}-\frac{x}{8}=14\\\\\frac{8x-x}{8}=14\\\\\frac{7x}{8}=14[/tex]

Now multiplying both side by 8 we get;

[tex]\frac{7x}{8}\times 8=14\times8\\\\7x = 112[/tex]

Now dividing both side by 7 we get;

[tex]\frac{7x}{7}=\frac{112}{7}\\\\x=16\ gallons[/tex]

Hence Amy's car tank capacity is 16 gallons.

Answer:

a.  -i.

Step-by-step explanation:

i^2 = -1 so

i^3 = i^2 * i

= -1 * i

= -i.

Answer:

[tex]a=29000 -1.28*2400=25928[/tex]

Tires that wear out by 25928 miles will be replaces free of charge

Step-by-step explanation:

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".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(29000,2400)[/tex]  

Where [tex]\mu=29000[/tex] and [tex]\sigma=2400[/tex]

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

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

He wants to give a guarantee for free replacement of tires that don't wear weel so then we need to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.90[/tex]   (a)

[tex]P(X<a)=0.10[/tex]   (b)

Because we are interested in the lower tail.

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(z>-1.28)=0.90

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.1[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.1[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=-1.28=<\frac{a-29000}{2400}[/tex]

And if we solve for a we got

[tex]a=29000 -1.28*2400=25928[/tex]

So the value of height that separates the bottom 10% of data from the top 90% is 25928 mi.  

Tires that wear out by 25928 miles will be replaces free of charge

Answer: b) y = negative one fifthx + seven fifths

Step-by-step explanation:

Equation of a line in Slope intercept form : [tex]y=mx+c[/tex]   (1)

, where m is slope and c is constant.

Given : The equation of line LM is [tex]5x - y = -4.[/tex]

Convert it into slope- intercept form, we get

[tex]y=5x+4[/tex]

Comparing it to (1) , we get

[tex]m= 5[/tex]

Let [tex]m_1[/tex] be the slope pf the line perpendicular to LM.

Since the product of slopes of two perpendicular lines is -1.

Therefore , [tex]m_1\cdot m=-1\Rightarrow m_1=\dfrac{-1}{m}=\dfrac{-1}{5}[/tex]

Equation of line passing through (-3,2) and having slope [tex]m_1=\dfrac{-1}{5}[/tex] will be :-

[tex](y-2)=\dfrac{-1}{5}(x-(-3))\\\\ y-2=(-\dfrac{1}{5})(x+3)=\dfrac{-1}{5}x-\dfrac{3}{5}\\\\\ y=\dfrac{-1}{5}x-\dfrac{3}{5}+2=\dfrac{-1}{5}x-\dfrac{10-3}{5}\\\\\Rightarrow\ y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex]

Hence, the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2) is [tex]y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex].

Hence, the correct answer is b) y = negative one fifthx + seven fifths.

We want to find a line perpendicular to 5x - y = -4 that passes through the point (-3, 2). We will find that the line is: y = (-1/5)*x + 7/5

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Such that a line is perpendicular to the above one if and only the slope of this other line is the inverse of the opposite of the above slope, so the perpendicular line will be something like:

y = (-1/a)*x + c

Now we start with the line that we know, we need to find its slope:

5x - y = -4

We need to isolate y

y = 5x + 4

Then the slope of this line is a = 5, so the perpendicular line will be:

y = (-1/5)*x + c

Now we need to find the value of c such that the line passes through (-3, 2), this means that x = -3 and y = 2, then we have:

2 = (-1/5)*-3 + c

2 = (3/5) + c

2 - 3/5 = c

10/5 - 3/5 = c

7/5 = c

Then the equation is:

y = (-1/5)*x + 7/5

So the correct option is b.

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ANSWER:

Carl could divide the circle into a larger even number of congruent sectors. Then each sector would be smaller, and the approximation of the circle’s area will be closer to the actual area of the circle.

STEP BY STEP EXPLANATION :

Area of a Circle by Cutting into Sectors:

1. Cut a circle into equal sectors and the more we divided the circle up, the closer we get to being exactly right.

2.Rearrange the sectors, which resembles a parallelogram.

What are the (approximate) height and width of the parallelogram?

The height is the circle's radius.

The width (actually one "bumpy" edge) is half of the curved parts around the circle. In other words it is about half the circumference of the circle.

We know that:

Circumference = 2 × π × radius

And so the width is about:

Half the Circumference = π × radius

ow we just multply the width by the height to find the area of the rectangle:

Area = (π × radius) × (radius)

= π × radius2

Conclusion

Area of Circle = π r2

Answer: y = 12x + 50

Step-by-step explanation:

Let y represent the cost of having the party.

Let x represent the number of people who would attend the party.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information given

y2 = 590

y1 = 290

x2 = 45

x1 = 20

Slope,m = (590 - 290)/(45 - 20) = 300/25 = 12

To determine the intercept, we would substitute x = 20, y = 290 and m= 12 into y = mx + c. It becomes

290 = 12 × 20 + c = 240 + c

c = 290 - 240 = 50

The equation becomes

y = 12x + 50

Answer:

the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10 (option B , if 60π is changed for 60/π)

Step-by-step explanation:

The volume of a cylinder is

V= π*R²*H  (H=height)

since the length L of the piece of paper is L=2*π*R  →R=L/(2*π) (since is rolled to form the cylinder), then:

V= π*R²*H  = π*L²/(2*π)²*H  = L²*H/(4*π)

with L=10 in and H= 6 in we have

V₂= L²*H/(4*π)

the other way around is changing H for L

V₁= H²*L/(4*π)

the difference between the volumes will be

V₂- V₁ = L²*H/(4*π)  - H²*L/(4*π) = L*H *(L-H)/(4*π)  

replacing values

V₂- V₁ = L*H *(L-H)/(4*π)  = 10*6*(10-6)/(4*π) = 60/π in³  

then the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10

Answer: A two-way table

Explanation:

A two-way table, also known as a contingency table, is used in statistics to present results of an investigation that contain two variables to analyze. The table shows the relationship between the two variables to be able to represent two sets of data under different categories.

The table is composed of two columns and two rows of data, and two columns of labels at the top, and two rows of labels on the left.

In this case, A two-way table would present the two variables to be analyzed; television violence, and domestic abuse.

I hope this information can help you.

In this exercise we have to use the knowledge of plots to write the correct alternative that best matches, thus we can say that:

Number 3

A two-way table exist one habit to display commonness for two different type calm from a single group of human beings. One classification is depicted for one rows and the other happen depicted by the line.

A two-way table, as known or named at another time or place a possibility table, happen secondhand in enumeration to present results of an thorough check that hold two variables to resolve. The table shows the connection middle from two points two together variables expected able to show two sets of information in visible form secondary various classification.

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Answer:

h=2A/b

Step-by-step explanation:

A=1/2bh

Isolate h by moving 1/2 and b to the other side of the equation.

Divide each side by 1/2,which is multiplying by 2, which gives you 2A=bh.Now divide each side by b, which gives you 2A/b=h. Turn it around.

2A/b=h becomes h=2A/b

Answer:

h=2A/b

Step-by-step explanation:

Answer:

a) (n²-n+m²-m)÷((n+m)×(n+m-1))

b)(n²+m²)÷(n+m)

c) part b is larger ,check below.

Step-by-step explanation:

a)If there are n white and m black balls ,total will be n+m balls. Let's find the probability of choosing two balls white.

First ball as white n÷(n+m)  second ball to be white again is n-1÷(n+m-1) the reason why we take away 1 is because we already chose one white ball in the beginning .So the probability will be product of these to get the both balls white.

Let's find the the probability of choosing both black.Same strategy ,first ball black  is m÷(n+m),second ball black is m-1÷(n+m-1).So the probability will be product of these to get the both balls black. We should add the final products and simplify

b)Because this time they are replacing the ball ,we will not take away 1.So to get both white probability is n÷(n+m) times n÷(n+m) .The probability of both black is m÷(n+m) times m÷(n+m).Add the products .

c) b will be always larger,We should compare the final products.

In b  (n²+m²) is divided by (n+m)

In a (n²-n+m²-m)÷((n+m)×(n+m-1))  less amount divided by a bigger value ,so it will result always with a smaller quotient

Answer:

The number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]

Step-by-step explanation:

Given the initially 30 bacteria present in the culture.

Also, the number of bacteria got doubled every hour.

So, using the equation

[tex]A=A_0r^{n-1}[/tex]

Where [tex]A[/tex] is number of bacteria after [tex]n[/tex] hours.

[tex]A_0[/tex] is bacteria present initially.

[tex]r[/tex] is the common ration, in our problem it is given that bacteria doubles every hour. So, [tex]r=2[/tex]

And [tex]n[/tex] is the number of hours. In our problem we need amount of bacteria at the end of [tex]8th[/tex] hours. So, [tex]n=8[/tex]

Plugging values in the formula we get,

[tex]A=30(2)^{8-1}\\A=30\times 2^7\\A=30\times 128\\A=3840[/tex]

So, number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]

Answer: Cluster Sampling

Step-by-step explanation:

In cluster sampling, researcher divides the population into groups ,which are called clusters. Then random sample of clusters are chosen ,and researcher conduct study to collect data about the population.

Here each bus is considered a cluster ,because busses are selected at random ,this sampling would be an example of cluster type of sampling.

Answer:

Water level in the reservoir is falling at the rate of 0.398 ft per minute.

Step-by-step explanation:

From the figure attached,

Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.

Let the level of water in the reservoir after time t is h where radius of the water level becomes r.

ΔABE and ΔCDE are similar.

Therefore, their corresponding sides will be in the same ratio.

[tex]\frac{r}{h}=\frac{4}{10}[/tex]

[tex]r=\frac{2}{5}h[/tex] --------(1)

Now volume of the water V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

From equation (1),

V = [tex]\frac{1}{3}\pi (\frac{2}{5}h)^{2} h[/tex]

V = [tex]\frac{4\pi h^{2}\times h}{75}[/tex]

[tex]\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})[/tex]

[tex]\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}[/tex]

[tex]\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}[/tex]

Since [tex]\frac{dV}{dt}=5[/tex] feet³ per minute and h = 5 feet

[tex]5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}[/tex]

[tex]5=4\pi \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}=\frac{5}{4\pi}[/tex]

[tex]\frac{dh}{dt}=0.398[/tex] feet per minute

Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.