Paige can sort her toys in 6 fewer hours that Madison can. When they work together, it
takes them only 4 hours to sort the toys. How long would it take for each of them to sort
the toys alone?

The doubling time for the bacteria population is approximately 0.231 hours.

To find the doubling time for the bacteria population, we can use the formula N = N0e^rt, where:

- N is the final number of bacteria (1 million in this case)

- N0 is the initial number of bacteria

- r is the growth rate (in this case, it is 3, as the population triples every 4 hours)

- t is the time in hours (12 hours in this case)

First, let's find the initial number of bacteria, N0. Since the population triples every 4 hours, we can calculate N0 by dividing the final number of bacteria by the growth rate raised to the power of the number of time intervals.

N0 = N / (r^t/4)

N0 = 1,000,000 / (3^(12/4))

N0 = 1,000,000 / (3^3)

N0 = 1,000,000 / 27

N0 ≈ 37,037

Now, let's find the doubling time, which is the time it takes for the population to double.

We can rearrange the formula N = N0e^rt to solve for t:

t = ln(N/N0) / r

t = ln(2) / 3

t ≈ 0.231 hours

So, the doubling time for the bacteria population is approximately 0.231 hours.

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Answer:

75,76,84,85,87,88,90,91,92,94,99

Step-by-step explanation:

None of the options is correct

To find the number of distinct memorable telephone numbers, we need to consider the possibilities for the prefix sequence. Since each digit can be any of the ten decimal digits, there are 10 options for each digit in the prefix sequence.

Now, we need to consider the two possibilities:
1) The prefix sequence is the same as the first sequence.
2) The prefix sequence is the same as the second sequence.

For the first sequence, there are 10 options for each of the 3 digits in the prefix sequence. Therefore, there are 10^3 = 1000 possible numbers.

For the second sequence, there are also 10 options for each of the 4 digits in the prefix sequence. Therefore, there are 10^4 = 10000 possible numbers.

Since the telephone number can be memorable if the prefix sequence is exactly the same as either of the sequences or both, we need to consider the union of these two sets of possible numbers.

The total number of distinct memorable telephone numbers is 1000 + 10000 = 11000.

Therefore, the correct answer is not among the options provided.

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The Graham's scan algorithm calculates the convex hull of a set of points, which guarantees a convex polygon. The smallest area polygon containing the set of points is not the convex hull of those points.

To demonstrate that the smallest area polygon containing a set of points may not always be a convex hull of that set of points, let's consider a simple example.

Suppose we have a set of four points: A, B, C, and D, arranged in a square formation, as shown below:

A----B

|    |

|    |

D----C

If we calculate the convex hull of these points using the Graham's scan algorithm, we would obtain the convex hull as ABCDA, which is a square.

However, if we look for the smallest area polygon that contains these points, we can find a non-convex polygon. By connecting the points A, B, C, and D in that order, we form a quadrilateral:

A----B

\  /

 \/

 /\

/  \

D----C

This quadrilateral, ABCD, is not convex, as it has an internal angle greater than 180 degrees.

Hence, in this example, the smallest area polygon containing the set of points is not the convex hull of those points. This example demonstrates that the smallest area polygon can be non-convex, and the convex hull may not always provide the minimum area solution.

The Graham's scan algorithm specifically calculates the convex hull of a set of points, which guarantees a convex polygon. However, to find the smallest area polygon, other techniques or algorithms need to be applied.

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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Answer:

-4

Step-by-step explanation:

14b = -56

divide by 14

-56 ÷ 14 = -4

b = -4

I hope this helps!

Answer:

b = -4

Step-by-step explanation:

\(14b = -56\\\\rule{150}{0.5}\\\frac{14b=-56}{14}\\\\ \boxed{b = -4}\)

Hope this helps.

The height of the altitude of the given equilateral triangle is: 5√3 inches

We know that the sides of an equilateral triangle are equal and as such since we are given one side as 10 inches, then all the three sides will measure 10 inches.

Now, the altitude can be gotten by getting half the length of one side and using Pythagoras theorem to get the altitude.

Thus, if the altitude is denoted by h, then we have that:

h = √(10² - 5²)

h = √75

h = 5√3 inches

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Answer:

40 minutes is your answer

Answer: It will take a 1/2 hour or 30min to paint one full wall.

Answer:

140,000

Step-by-step explanation:

We know that the number is 143,699.

We are asked to round to the nearest ten thousand, which is the number bolded:

143,699

This means we have to look at the number to the right of the 4, which is 3.  If this number is below "5", then we round down to get 140,000.  

If this number was (and it's NOT) above "5" or "5" itself, we would round up to 150,000.  

Since "3" is below "5", we would round down to 140,000.

Hope this helps! :)

The number of groups of 3/4 that are in 11/4 will be 3 2/3.

It should be noted that from the information, we want to know the number of groups of 3/4 that are in 11/4.

This will be:

= 11/4 ÷ 3/4

= 11/4 × 4/3

= 11/3

= 3 2/3

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How many groups of 3/4 are in 11/4.

Answer:

4/3

Step-by-step explanation:

i did this on khan so ye :/

Answer:

The slope of the line=4/5

Step-by-step explanation:

The formula y=mx + b is set up in slope-intercept form, where m=slope and b=y-intercept

y=mx + b

b= -3

m= 4/5

Note: b can be negative or positive

Therefore, the slope=4/5

The distances between each pair of points are as follows:

1. (1, -4.6) and (3, -7): 3.12 (rounded to two decimal places)

2. (-6, -5) and (2, 0): √89 (exact value)

M = (-12, -1) and M = (4, 0): √257 (exact value)

4. (0, -8) and (3, 2): √109 (exact value)

3. (-1, 4) and (1, -1): √29 (exact value)

We may use the distance formula to calculate the separation between each pair of points:

d = √((x₂ - x₁)² + (y₂ - y₁)²),

where the two points' coordinates are represented by (x1, y1) and (x2, y2), respectively.

Let's determine the separation between each pair of points:

1. (1, -4.6) and (3, -7):

d = √((3 - 1)² + (-7 - (-4.6))²)

= √(2² + (-2.4)²)

= √(4 + 5.76)

= √9.76

= 3.12 (rounded to two decimal places)

2. (-6, -5) and (2, 0):

d = √((2 - (-6))² + (0 - (-5))²)

= √(8² + 5²)

= √(64 + 25)

= √89 (exact value)

M = (-12, -1) and M = (4, 0):

d = √((4 - (-12))² + (0 - (-1))²)

= √(16² + 1²)

= √(256 + 1)

= √257 (exact value)

4. (0, -8) and (3, 2):

d = √((3 - 0)² + (2 - (-8))²)

= √(3² + 10²)

= √(9 + 100)

= √109 (exact value)

3. (-1, 4) and (1, -1):

d = √((1 - (-1))² + (-1 - 4)²)

= √(2² + (-5)²)

= √(4 + 25)

= √29 (exact value)

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The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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Answer:

y = 25

Step-by-step explanation:

Given y = kx and k = 5 then

y = 5x ← equation of variation

When x = 5 , then

y = 5 × 5 = 25

Answer:

hope it helped

have a nice day mate

Answer:

y = -3/4x + 9

Step-by-step explanation:

first, find the slope by taking the difference of the y-values / difference of the x-values

(-3-12) / (16-(-4)) which equals -15/20 or -3/4

now use that value to represent the 'm' in the formula in order to find 'b'

y = mx + b

-3 = -3/4(16) + b

-3 = -12 + b

9 = b

y = -3/4x + 9

Answer: 9 cups

Step-by-step explanation:

12*6=72

72/ 8 oz

Considering the perimeter of the rectangular table, it is found that 36 ballons are needed.

The perimeter of a rectangle of length l and width w is given by:

P = 2(l + w).

In this problem, the dimensions of the table are l = 8 ft and w = 4 ft, hence the perimeter is of:

P = 2(l + w) = 2 x 12 = 24 ft.

Ballons will be attached 8 inches = 2/3 feet along the perimeter, hence the number of ballons needed is given by:

\(n = \frac{24}{\frac{2}{3}} = 36\)

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The average velocities over the given intervals are: a. 15.85 m/s, b. 20.6 m/s, c. 20.85 m/s, d. 24.97 m/s.

Determine the change in height and time interval for each interval.

Given the formula for height as s(t) = -4.9t^2 + 45t, we need to calculate the change in height and the time interval for each specified interval.

Calculate the average velocity for each interval.

To find the average velocity, we divide the change in height by the corresponding time interval. This gives us the average rate of change of height over that interval.

Then, calculate the average velocities for each interval.

a. From t=1 to t=3:

The change in height is s(3) - s(1) = (-4.9(3)^2 + 45(3)) - (-4.9(1)^2 + 45(1)) = 64.8 - 33.1 = 31.7 m.

The time interval is 3 - 1 = 2 seconds. Average velocity = 31.7 m / 2 s = 15.85 m/s.

b. From t=2 to t=3:

The change in height is s(3) - s(2) = (-4.9(3)^2 + 45(3)) - (-4.9(2)^2 + 45(2)) = 64.8 - 44.2 = 20.6 m.

The time interval is 3 - 2 = 1 second. Average velocity = 20.6 m / 1 s = 20.6 m/s.

c. From t=2.5 to t=3:

The change in height is s(3) - s(2.5) = (-4.9(3)^2 + 45(3)) - (-4.9(2.5)^2 + 45(2.5)) = 64.8 - 54.375 = 10.425 m.

The time interval is 3 - 2.5 = 0.5 seconds. Average velocity = 10.425 m / 0.5 s = 20.85 m/s.

d. From t=2.9 to t=3:

The change in height is s(3) - s(2.9) = (-4.9(3)^2 + 45(3)) - (-4.9(2.9)^2 + 45(2.9)) = 64.8 - 62.303 = 2.497 m.

The time interval is 3 - 2.9 = 0.1 seconds. Average velocity = 2.497 m / 0.1 s = 24.97 m/s.

Now, close to t=3, the average velocities are decreasing. This suggests that the projectile is slowing down as it approaches its highest point.

This is expected because the height function is a quadratic equation, and the vertex of the parabolic path represents the maximum height reached by the projectile.

As the time approaches t=3, the projectile is nearing its peak and experiencing a decrease in velocity.

ii. To calculate the instantaneous rate of change (velocity) at t=4

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Answer:

78.5

Step-by-step explanation: The equation to find the circumference is C=2pie times radius and radius is half of the diameter which is 12.5 then multiple it by 2=25 then multiple it by pie(3.14)=78.5

Answer: True

Step-by-step explanation: because bias can lead to personal errors

Answer:

your answer is 5.............

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The Correct choice is :

Solution is in attachment ~

Answer:

If g(t) = t^2 - 5t, then G = t - 5

If f(t) = 2t + 4, then F = 2( t + 2) / t (over t)

If (g * f)(5), then 5gf

Step-by-step explanation:

Step-by-step explanation:

135+k=180(sum of angles on a straight line)

k=180-135

k=45

so now u can use k to solve for x

k+9x is also on a straight line

so k+9x=180

we know k so substitute the value in the equation

45+9x=180

9x=180-45

9x=135

\( \frac{9x}{9} = \frac{135}{9} \)

cancel 9 will divide 135 15 times

therefore x=15 degrees

Answer:

yes is correct 6/6 = 1 / 3*2=6 =1

Answer:

nonsense. what's the difference between 6/6 or 1 .

Therefore, the solution to the system of linear equations is: x₁ = -5, x₂ = 11, x₃ = -18.

To solve the system of linear equations:

3x₁ + 2x₂x₃ = 10

-x₁ + 3x₂ + 2x₃ = 5

x₁ - x₂ - x₃ = -1

We can use various methods such as substitution, elimination, or matrix methods. Here, we'll use the elimination method.

Step 1: Multiply the second equation by 3 and add it to the first equation:

3x₁ + 2x₂x₃ = 10

-(3x₁ - 9x₂ - 6x₃ = 15)

-7x₂ - 4x₃ = -5 (Equation A)

Step 2: Multiply the third equation by 3 and add it to the first equation:

3x₁ + 2x₂x₃ = 10

(3x₁ - 3x₂ - 3x₃ = -3)

-x₂ - x₃ = 7 (Equation B)

Step 3: Add Equation A and Equation B:

-7x₂ - 4x₃ = -5

+(-x₂ - x₃ = 7)

-8x₂ - 5x₃ = 2 (Equation C)

Step 4: Multiply Equation B by 8 and subtract it from Equation C:

-8x₂ - 5x₃ = 2

+8x₂ + 8x₃ = -56

3x₃ = -54

Step 5: Solve for x₃:

x₃ = -54/3

x₃ = -18

Step 6: Substitute the value of x₃ back into Equation B to solve for x₂:

-x₂ - x₃ = 7

-x₂ - (-18) = 7

-x₂ + 18 = 7

-x₂ = 7 - 18

-x₂ = -11

x₂ = 11

Step 7: Substitute the values of x₂ and x₃ into Equation A to solve for x₁:

-7x₂ - 4x₃ = -5

-7(11) - 4(-18) = -5

-77 + 72 = -5

-5 = -5

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Answer:

B

Step-by-step explanation:

6x + 30 + 4x = 10(x+3)

10x + 30 = 10x + 30

0 = 0

Answer:

210

Step-by-step explanation:

188 = U - 22

+22       +22

210 = U

U represents the Utah jazz

Answer: it’s 9

Step-by-step explanation:

54 divined by 6 = 9