Larry and Cathy study for a total of 24 hours each week. Larry studies 3 less than twice the hours than Cathy studies. How many hours does Cathy study per week?

The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows

                                  y = 2 (1/5)^x - 5             y = 4^x

Initial value:               2                                    1

base function:        1/5 = decay function       4 = growth function

Translation:             5 units down                    no transformation

A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.

It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.

Decay function are exponential functions with the base function as

This is the opposite of growth function which has values greater than 1

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The addition law is particularly useful when calculating the probability of the union of two events. It allows us to determine the probability of either event A or event B occurring.

This law provides a straightforward method for calculating probabilities in situations where we want to know the likelihood of at least one of the events happening.

The addition law, also known as the sum rule, states that the probability of the union of two events A and B is given by the sum of their individual probabilities minus the probability of their intersection. Mathematically, this can be expressed as P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

When we are interested in computing the probability of the union of two events, the addition law allows us to combine the probabilities of the individual events to obtain the overall probability of at least one of them occurring. It is particularly helpful in situations where the events are not mutually exclusive, meaning that they can occur together or independently.

In contrast, when calculating the probability of the intersection of two events or dealing with conditional events, other rules such as the multiplication rule and conditional probability formulas are more appropriate.

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The height of the tree opposite to the river is (20√3)/3 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

The width of the river here is adjacent and the height of the tree is opposite.

We know, tan = opposite/adjacent.

Therefore, tan30° = opposite/20.

1/√3 = opposite/20.

opposite = 20/√3.

opposite = (20√3)/3 feet.

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The length of the curve \(\(y = 2\sin(\frac{x}{3})\)\) from x = 0 can be found by integrating the square root of the sum of the squares of the derivatives of x and y with respect to x, without using a calculator.

To find the length of the curve, we can use the arc length formula. Let's denote the curve as y = f(x). The arc length of a curve from x = a to x = b is given by the integral:

\(\[L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx\]\)

In this case, \(\(y = 2\sin(\frac{x}{3})\)\). We need to find \(\(\frac{dy}{dx}\)\), which is the derivative of y with respect to x. Using the chain rule, we get \(\(\frac{dy}{dx} = \frac{2}{3}\cos(\frac{x}{3})\)\).

Now, let's substitute these values into the arc length formula:

\(\[L = \int_{0}^{b} \sqrt{1 + \left(\frac{2}{3}\cos(\frac{x}{3})\right)^2} \, dx\]\)

To simplify the integral, we can use the trigonometric identity \(\(\cos^2(\theta) = 1 - \sin^2(\theta)\)\). After simplifying, the integral becomes:

\(\[L = \int_{0}^{b} \sqrt{1 + \frac{4}{9}\left(1 - \sin^2(\frac{x}{3})\right)} \, dx\]\)

Simplifying further, we have:

\(\[L = \int_{0}^{b} \sqrt{\frac{13}{9} - \frac{4}{9}\sin^2(\frac{x}{3})} \, dx\]\)

Since the problem only provides the starting point x = 0, without specifying an ending point, we cannot determine the exact length of the curve without additional information.

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Answer:

Multiply the bottom equation by -3/2 then add the equations.

Multiply the top equation by-3. then add the equations

Step-by-step explanation:

Given the simultaneous equation

2x- 6y=6  ... 1

6x - 4y = 2 ... 2

To eliminate a variable, we have to make the coefficient of one of the variable to be the same.

Multiply equastion 1 by -3

-6x+18y= -18  

6x - 4y = 2

Add the result:

-6x + 6x + 18y-4y = -18+2

18y-4y = -18+2

14y = -18

y = -9/7

Another way is to Multiply the bottom equation by -3/2 then add the equations.

Multiplying equation 2 by -3/2 will give;

6x(-3/2) - 4y(-3/2) = 2(-3/2)

-9x + 6y = -3

Add to equation 1;

2x- 6y=6

-9x + 2x + 0 = -3+6

-7x = 3

x = -3/7

Hence the correct two options are;

Multiply the bottom equation by -3/2 then add the equations.

Multiply the top equation by-3. then add the equations

Answer:

15 nickels, 6 quarters, and 12 dimes.

Step-by-step explanation: i hoped it helped ;)

Given that 1 square mile is approximately equal to 2,589,988 square feet and 1 liter is equal to 33.814 fluid ounces, we can proceed with the conversion.The volume of Alake is approximately 8,472,413,717 liters.

To explain the calculation further, we start by converting the surface area of Alake from square miles to square feet. We multiply the given surface area of 19.0 square miles by 2,589,988 to obtain the surface area in square feet, which is approximately 49,204,778 square feet.

Next, we convert the average depth from feet to liters. Since volume is a three-dimensional measurement, we need to convert the depth to a cubic unit before converting it to liters. To do this, we multiply the average depth of 55.0 feet by the conversion factor of 28,316.8466 to obtain the depth in liters, which is approximately 1,544,426.56 liters.

Finally, we calculate the volume by multiplying the surface area by the average depth. Multiplying 49,204,778 square feet by 1,544,426.56 liters gives us a volume of approximately 8,472,413,717 liters.

This calculation assumes that the shape of Alake is approximately cylindrical, which allows us to multiply the surface area by the depth to estimate the volume. It's important to note that the actual shape of Alake may deviate from a perfect cylinder, which could affect the accuracy of the volume estimation.

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Answer:

y = 4x + 4

Step-by-step explanation:

Plug in your x and y coordinates

8 = 4(1) + b

8 = 4 + b            get your constants together by subtracting 4 from both sides

4 = b

Hope this helps

Answer:

30 books

Step-by-step explanation:

Answer:

-6a2+7ab+b2

Step-by-step explanation:

please mark me as brainlest

Answer:

- 6a^2 + 7ab + b^2

Step-by-step explanation:

3b^2 + 4ab - 2a^2 - ( 4a^2 - 3ab + 2b^2 )

= 3b^2 + 4ab - 2a^2 - 4a^2 + 3ab - 2b^2

= 3b^2 - 2b^2 - 2a^2 - 4a^2 + 4ab + 3ab

= 1b^2 - 6a^2 + 7ab

= - 6a^2 + 7ab + b^2

The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. answer is option (a).

In a histogram, which is a graphical depiction of the distribution of a set of continuous or discrete data, the height of a bar above the bin on the x-axis represents the frequency or count of the data falling within each bin. On the y-axis of the histogram, the frequency or count of the data points that fall into each bin is displayed.

The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. In a histogram, bars are used to illustrate the frequency distribution of a group of continuous or discrete data points.

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The percentage of these funds are expected to be within ±6 standard deviations of the mean is 97.22% (approx).Hence, the required answer is 97.22.

The Chebyshev’s theorem is used to determine the percentage of observations that lie within a certain number of standard deviations of the mean in a set of data.

According to the Chebyshev rule, what percentage of these funds are expected to be within ±6 standard deviations of the mean can be calculated using the formula:

\($$1 - \frac{1}{k^2}$$\)

Where k is the number of standard deviations. For the question, the mean is 7.10 and standard deviation is 3.50.As per the given data, we can find that, the number of standard deviation from the mean is ±6.

Thus, k = 6.

The percentage of these funds are expected to be within ±6 standard deviations of the mean is:

\($$1 - \frac{1}{k^2} = 1 - \frac{1}{6^2} = 1 - \frac{1}{36} = 0.9722$$\)

Therefore, the percentage of these funds are expected to be within ±6 standard deviations of the mean is 97.22% (approx).

Hence, the required answer is 97.22.

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a) Nonzero vector orthogonal to the plane through the point P(0, 0, -3), Q(4,2, 0), and R(3, 3, 1) would be (12, -6, -12)

b) Area of the triangle PQR would be 4.18

What is nonzero vector of orthogonal ?

Taking the cross product of two vectors in the plane yields a non-zero vector orthogonal to the plane across the points. Calculate the difference vector of two of the points, then take the cross product of that difference vector with the difference vector of the third point.

a) A nonzero vector orthogonal to the plane through the points P, Q, and R can be found by taking the cross product of two nonparallel vectors in the plane.

For example, the vector PQ = (4, 2, 0) - (0, 0, -3) = (4, 2, 3) and PR = (3, 3, 1) - (0, 0, -3) = (3, 3, 4). The cross product of these vectors is orthogonal to the plane:

PQ x PR = (12, -6, -12)

2) The area of triangle PQR can be found using the cross product formula for the area of a parallelogram. The area is given by the magnitude of the cross product of two sides of the triangle:

         \(Area =\frac{ |PQ * PR| }{2}\\\\Area =\frac{\sqrt{(12^2 + (-6)^2 + (-12)^2)} }{2}\\\\Area =3 * \sqrt(10) / 2\\\\Area =4.18\)

Thus, Nonzero vector orthogonal to the plane through the point P(0, 0, -3), Q(4,2, 0), and R(3, 3, 1) would be (12, -6, -12) and area of the triangle PQR would be 4.18.

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Answer: the second one

Step-by-step explanation:

because \(-4^{4}\)= -256

Answer:

positive and even

Step-by-step explanation:

.........................

Answer:

ow

Step-by-step explanation:

yess.

Answer: x=-6

Step-by-step explanation:

Let's solve your equation step-by-step.

2(9−x)=3(x+16)

Step 1: Simplify both sides of the equation by distribution

\(2(9-x)=3(x+16)\\(2)(9)+(2)(-x)=(3)(x)+(3)(16)\\18+-2x=3x+48\\-2x+18=3x+48\\\)

Step 2: Subtract 3x from both sides.

\(-2x+18-3x=3x+48-3x\\-5x+18=48\)

Step 3: Subtract 18 from both sides.

\(-5x+18-18=48-18\\-5x=30\)

Step 4: Divide both sides by -5.

\(\frac{-5x}{-5} =\frac{30}{-5} \\x=-6\)

Answer:

base angle of isosceles triangle are equal..

hope it helps

The area of the triangle is 83.14 square centimeters.

If an equilateral triangle is inscribed in a circle of radius R, each side of the triangle measures:

S = R*√3

In this case R = 8cm.

And we know that the area of an equilateral triangle of side length S is:

\(A = \frac{\sqrt{3} }{4} *S^2\)

Replacing what we know in the area formula:

\(A = \frac{\sqrt{3} }{4} *(\sqrt{3}*8cm)^2 = 83.14 cm^2\)

The area of the triangle is 83.14 square centimeters.

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Answer:

C. 17

Step-by-step explanation:

2 + 3n

= 2 + 3*5 ( Plug n = 5)

= 2 + 15

= 17

Rule when rotating a point counterclockwise:

A transformation that revolves a figure around a point is called a rotation. The rotational center is where we refer to it.

Thus, rule when rotating a point counterclockwise:

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Answer: -5=2x+11

Step-by-step explanation:

3x-5=5x+11

subtract 3x to both sides

3x-5 - 3x =5x+11 - 3x

simplify

-5 = 2x +11

answer is -5=2x+11

Answer:

Greater than 10 but less than 100.

Step-by-step explanation:

Answer:

If there are 125 students, then the total time spent studying for the test will be 6,125 minutes. This is because x = (125 students * 637 minutes) / 13 students  = 6,125 minutes.

The ordered pair that is 5 units away is (-1, -3)

What is a line?

A line is a distance between two points.

Analysis:

see attached file.

In conclusion, the ordered pair is (-1, -3)

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Therefore, when the number of copies made in a month is above 4000, company A's charges are higher than company B's charges in the given equation.

Let's start by setting up an equation to represent the cost of renting a copier from each company:

Cost for company A = 0.10x + 200

Cost for company B = 0.05x + 400

where x is the number of copies made in a month.

To find the number of copies above which company A's charges are higher than company B's charges, we need to set the two equations equal to each other and solve for x:

0.10x + 200 = 0.05x + 400

0.05x = 200

x = 4000

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Answer:

8+2=10

Step-by-step explanation:

A negative minus a negative equals a positive. So 8-(-2) would go to 8+2

Answer:

8+2

Step-by-step explanation:

when you multiply a negative by another negative inside of the paranthesies it creates a positive