Meg colored 3/8 of the tiles for a class art project. Max colored 4/15 of the tiles. What fraction of the tiles did Meg and Max color in all?

The given equation x/4 - y = -2(x/y) can be expressed in a verbal sentence as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.

How to express the mathematical equation in the form of a verbal sentence?    

To express the mathematical equation in the form of a verbal sentence, we have to express the operations by using sentences.

Let's take an example,

                   x + y = 4.

Then the verbal form will be the sum of two numbers is 4.

Hence, the given expression can be expressed as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.

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The probability of getting at least one even number and at least one odd number is (3/4).

What is the probability of getting an even number in a single-dice throw?

If we throw a die, we have six possible outcomes: {1,2,3,4,5,6}. Now:

P(E) = Favourable outcomes / Total outcomes

     = 3/6

     = 1/2

As per the question, we need at least one even number and one odd number in three throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting an even number and B be the event of getting an odd number on the dice.

P(A) = P(B) =  1/2

So, we need to have events occur like:

ABA or ABB (with all their possible combinations)

So, P(A∩B∩A) = (1/2)*(1/2)*(1/2) = 1/8

P(A∩B∩B) = (1/2)*(1/2)*(1/2) = 1/8

Possible number of combinations of ABA = 3

Possible number of combinations of ABB = 3

So, required probability = 3*(1/8) + 3*(1/8)

= 6/8

= 3/4                          

So, the Required probability is (3/4)

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Based on the given CDI and BDI values, investing in Segment 2 would be more advantageous for the brand.

Brand X's growth can be determined by analysing  CDI (Category Development Index) and BDI (Brand Development Index) in two segments, Segment 1 and Segment 2.

Segment 1 has a CDI of 125 and a BDI of 95, while Segment 2 has a CDI of 85 and a BDI of 110. Based on the CDI and BDI values, Segment 2 appears to be a more favourable investment opportunity for the brand because the BDI is higher than the CDI.

CDI is an index that compares the percentage of a company's sales in a specific market area to the percentage of the country's population in the same market area. It provides insights into the market penetration of the brand in relation to the overall population.

BDI, on the other hand, compares the percentage of a company's sales in a given market area to the percentage of the product category's sales in that same market area. It indicates the brand's performance relative to the product category within a specific market.

A higher BDI suggests that the product category is performing well in the market area, indicating a higher growth potential for the brand. Conversely, a higher CDI indicates that the brand already has a strong presence in the market area, implying limited room for further growth.

Therefore, The higher BDI suggests a stronger potential for growth in this market compared to Segment 1, where the CDI is higher than the BDI. By focusing on Segment 2, the brand can tap into the market's growth potential and expand its market share effectively.

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The diagonals of rectangle are congruent.

We should know that a rectangle is a plane shape with four sides, four vertices and four angles.

Using a rectangle with the lettering ABCD

The diagonal AC divide the rectangle into two right angled triangles

<ADC = 90⁰

In the rectangle, AD=BC and AB=CD

Also, The same diagonal AC has another right angled triangle ABC with <ABC=90⁰

Similarly, diagonal BD divides the rectangle into two right angled triangles of ΔBAD and ΔBCD with a common hypothenuse of  BD

Hence AB=CD and AD= BC

Therefore, the two diagonals are congruent

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1. Minimize w = -2y₁ - 5y₂

2. Maximize w = 2y₁ + 5y₂

3. Minimize w = 5y₁

1. Dual of primal LP:
a) The primal LP is:
Maximize z = -5x₁ + 2x₂
Subject to:
-1x₁ + 1x₂ ≤ -2
2x₁ + 3x₂ ≤ 5
x₁, x₂ ≥ 0

To write the dual LP, we need to change the objective function and constraints. The objective function of the dual LP is to minimize the sum of the products of the dual variables and the primal constraint coefficients.

The constraints of the dual LP correspond to the primal LP's objective coefficients.

The dual LP for the given primal LP is:
Minimize w = -2y₁ - 5y₂
Subject to:
-y₁ + 2y₂ ≥ -5
y₁ + 3y₂ ≥ 2
y₁, y₂ ≥ 0

b) The primal LP is:
Minimize z = 6x₁ + 3x₂
Subject to:
6x₁ - 3x₂ + x₃ ≥ 2
3x₁ + 4x₂ + x₃ ≥ 5
x₁, x₂, x₃ ≥ 0

The dual LP for the given primal LP is:
Maximize w = 2y₁ + 5y₂
Subject to:
6y₁ + 3y₂ ≤ 6
-3y₁ + 4y₂ ≤ 3
y₁ + y₂ ≥ 1
y₁, y₂ ≥ 0

c) The primal LP is:
Maximize z = x₁ + x₂
Subject to:
2x₁ + x₂ = 5
3x₁ - x₂ unrestricted

The dual LP for the given primal LP is:
Minimize w = 5y₁
Subject to:
2y₁ + 3y₂ ≥ 1
y₁ - y₂ unrestricted
y₁, y₂ ≥ 0

These are the dual LPs for the given primal LPs.

The dual LPs are obtained by changing the objective function and constraints of the primal LPs.

The objective function of the dual LP is the opposite of the primal LP's objective function, and the constraints of the dual LP correspond to the primal LP's objective coefficients.

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Answer:

d 91

Step-by-step explanation:

she is reaching it perfectly at this height in the problem, its super easy

===========================================================

Explanation:

The proof of this is as follows

p, q, r and s are integers

q and s cannot be zero

A = some rational number = p/q

B =  some other rational number = r/s

A*B = (p/q)*(r/s) = (p*q)/(r*s)

The result is of some form integer/integer, where the denominator is nonzero. This shows that A*B is rational.

Therefore,

rational*rational = rational

---------------

A few examples:

Side note: any whole number is a rational number. For instance, the number 7 can be thought of as the fraction 7/1 or 14/2 or 21/3 and so on.

a. The efficiency of Expedition Everest is approximately 87.8%.

b. The utilization of Expedition Everest is approximately 94.7%.

c.  The demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.

To calculate the efficiency and utilization of Expedition Everest, we need to compare the actual number of riders with the design capacity and effective capacity.

Given:

Demand = 3,000 riders/hour

Average riders = 1,800 riders/hour

Design capacity = 2,050 riders/hour

Effective capacity = 1,900 riders/hour

a. Efficiency:

Efficiency is calculated as the average riders divided by the design capacity, multiplied by 100%.

Efficiency = (Average riders / Design capacity) * 100%

= (1,800 / 2,050) * 100%

≈ 87.8%

Therefore, the efficiency of Expedition Everest is approximately 87.8%.

b. Utilization:

Utilization is calculated as the average riders divided by the effective capacity, multiplied by 100%.

Utilization = (Average riders / Effective capacity) * 100%

= (1,800 / 1,900) * 100%

≈ 94.7%

Therefore, the utilization of Expedition Everest is approximately 94.7%.

c. Capacity Analysis:

To determine if the operation is overcapacity or undercapacity, we compare the demand with the effective capacity.

Demand > Effective capacity

3,000 > 1,900

Since the demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.

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Answer:

24 degrees

Step-by-step explanation:

The sum of the exterior angles of a triangle is 360 degrees

2x + 6x + 7x = 360

15x = 360

x = 24

Answer:

x=24

Step-by-step explanation:

2x+6x+7x=360
15x=360

15x/15=360/15
x=24

Answer:

w= -2

Step-by-step explanation:

3w + 2 = 8 + 6w

Subtract 3w from each side

3w-3w + 2 = 8 + 6w-3w

2 = 8+3w

Subtract 8 from each side

2-8 = 8-8+3w

-6 = 3w

Divide each side by 3

-6/3 = 3w/3

-2 =w

Answer:

Your y intercept is 1.

Step-by-step explanation:

slope is y2-y1 over x2-x1, or 2.

slope intercept formula is y=mx+b, and if you plug values into formula you get 3=2(1)+b

and if you solve that, 2x1=2, 3-2=1.

then you get 1 as your y intercept.

Answer:

C. 6/48

Step-by-step explanation:

mutliply both numerator and denominator

Answer:

your mom

1234567891011

The order of events from least likely to most likely are as follows:

The reason for this order is because of the chances of each event occurring. Event D has the least chance of occurring because no numbers in the set have a value less than or equal to 0. Event A is the next least likely because only one number in the set is greater than 0, which is the number 1. Event C is the next least likely because only two numbers in the set are at least 2 (2 and 3). Event B is the next least likely, as there are only five even numbers in the set (2, 4, 6, 8, and 10). Events E, F, G, and H are the most likely to occur, because of the number of numbers that are divisible by 3, and 5, and are prime numbers.

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Using a z-table, we find that the middle 70% of the waiting time for heart transplants for people aged 35-49 lies between approximately 230.67 days and 230.67 days.

To determine the values between which the middle 70% of the waiting time lies, we need to find the boundaries of the central 70% of the normal distribution.

First, we'll find the z-scores corresponding to the lower and upper percentiles of the middle 70%. The lower percentile will be (100% - 70%)/2 = 15%, and the upper percentile will be 100% - (100% - 70%)/2 = 85%.

Using a z-table or statistical software, we can find the z-scores associated with these percentiles. For the lower percentile (15%), the z-score is approximately -1.036, and for the upper percentile (85%), the z-score is approximately 1.036 (since the standard normal distribution is symmetric).

Next, we'll use these z-scores to calculate the corresponding waiting time values.

Lower value:

Lower Value = Mean - (Z-score * Standard Deviation)

Lower Value = 204 - (-1.036 * 25.7)

Lower Value = 204 + 26.67

Lower Value ≈ 230.67

Upper value:

Upper Value = Mean + (Z-score * Standard Deviation)

Upper Value = 204 + (1.036 * 25.7)

Upper Value = 204 + 26.67

Upper Value ≈ 230.67

Therefore, the middle 70% of the waiting time for heart transplants for people aged 35-49 lies between approximately 230.67 days and 230.67 days.

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The area of the surface generated by revolving the curve about the x-axis is equals to the 8760π.

We can compute the surface area of the revolved curve using the integral formula, \(S= 2π \int_{a}^{b} y \sqrt{1+(f′(x))²}dx\)

where √1 + (f'(x))², is an arc length of a curve and

y is the radius of revolution. We have, y = 10√x on [24,75]. Let f(x) = 10√x

=> f'(x) = 5/√x

1 + ( f'(x))² = 1 + (5/√x)² = 1 + 25/x

Also, here a = 24, b = 75 . Substitute the known values in above formula

\(S= 2π \int_{24}^{75} 10 \sqrt{x} \sqrt{1+ \frac{25}{x} }dx\)

\(S= 2π \int_{24}^{75} 10 \sqrt{x} \sqrt{\frac{x + 25}{x} }dx\)

\(S= 2π \int_{24}^{75} 10\sqrt{{25 + x} }dx\)

\(S= 2π [ \frac{20}{3} {(x + 25)}^{\frac{3}{2}}]_{24}^{75} \)

\(S=\frac{40\pi}{3} [ {(75 + 25)}^{\frac{3}{2}} -{(24 + 25)}^{\frac{3}{2}} ] \\ \)

S = 8760π

Hence, required area is 8760π.

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Complete question:

Find the area of the surface generated when the given curve is rotated about the x-axis. y= 10√x on [24,75] The area of the surface generated by revolving the curve about the x-axis is (Type an exact answer using n as needed.)

The value of M and N from the given expression is -10 and -21 respectively

Sum of functions is the addition of expression. Given the expression below;

M = 5(x + 1) and;

N = (6x - 3)

Take the difference of the expressions

M - N = 10

Substitute

5(x+1) - (6x-2) = 10

Expand the expression to have:

5x + 5 -6x + 2 = 10
5x - 6x + 5 + 2 = 10
-x + 7 = 10
-x = 10 - 7
-x = 3
x = -3

Determine the value of M

M = 5x + 5
M = 5(-3) + 5
M = -15 + 5
M = -10

Determine the value of N

N = 6x - 3
N = 6(-3) - 3
N = -18 - 3
N = -21

Hence the value of M and N from the given expression is -10 and -21 respectively

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Since the remaining distance is negative, it implies that Sam has already exceeded his goal distance. Therefore, he doesn't need to walk any further to reach his goal.

To find the remaining distance that Sam needs to walk to reach his goal of (3)1/2 miles, we need to subtract the distance he has already walked from his goal distance.

Sam walks (1)1/8 miles before lunch and 3/4 miles after resting. To calculate the total distance he has walked, we add these two distances:

Total distance walked = (1)1/8 + 3/4

To add these fractions, we need to find a common denominator, which is 8 in this case

Total distance walked = (9/8) + (6/8)

= 15/8

= 1 (7/8)

Now, we subtract the total distance walked from Sam's goal distance:

Remaining distance = (3)1/2 - 1 (7/8)

To subtract fractions, we also need a common denominator. The common denominator is 2 in this case:

Remaining distance = (6/2 + 1/2) - (15/8)

= (12/8 + 1/8) - (15/8)

= 13/8 - 15/8

= -2/8

= -1/4

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Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

B

Step-by-step explanation:

I'm assuming the end point is to draw line CG parallel to AB. Question doesn't specify. Student A is drawing the line CG before the point G has even been determined yet

Answer:

b

Step-by-step explanation:

2/3 because if you look there are 3 answeres and only 2 are mentioned also if you take the number of potted to not potted and summed em up you woukd still have 2/3

Answer:

r = 9.5ft

Step-by-step explanation:

Answer:

∠ A = 60° , ∠ B = 30°

Step-by-step explanation:

using the cosine ratio in the right triangle

cosA = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{7}{14}\) = \(\frac{1}{2}\) , then

∠ A = \(cos^{-1}\) ( \(\frac{1}{2}\) ) = 60°

the sum of the 3 angles in Δ ABC = 180°

∠ A + ∠ B + ∠ C = 180°

60° + ∠ B + 90° = 180°

∠ B + 150° = 180° ( subtract 150° from both sides )

∠ B = 30°

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer: this is true

Step-by-step explanation:

Answer:

The rate of change of function A is greater than the rate of change of function B

Step-by-step explanation:

\(\sf rate \ of \ change=\dfrac{change \ in \ y}{change \ in \ x}\)

Function A

For every increase of 1 unit in x-values, the y-values increase by 3 units.

\(\sf rate \ of \ change=\dfrac{3}{1}=3\)

Function B

For every increase of 1 unit in x-values, the y-values increase by 2 units.

\(\sf rate \ of \ change=\dfrac{2}{1}=2\)

As 3 > 2, the rate of change of function A is greater than the rate of change of function B

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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