What is the slope below?

The coordinates of point T' is (2, -2)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point T (3, -3) is transformed under a dilation of 2/3 with respect to the origin.

So the image point is (kx, ky) = (3 * 2/3, -3 * 2/3) = (2, -2)

So the image point of T under a dilation of 2/3 with respect to the origin is (2, -2)

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A linear function would better approximate the data.

A linear function would better approximate the data described. This is because a linear function has a constant rate of change, while an exponential function has a changing rate of change. For example, if we take the data from 10 K to 15 K, we can calculate the rate of change for each 1 K increase in temperature. The rate of change of volume for a 1 K increase in temperature is calculated by taking the difference between the volumes at the two temperatures and dividing by the difference in the temperatures. With the given data, this would yield a rate of change of 0.7 cm3/K, 0.38 cm3/K, 0.92 cm3/K, 1.4 cm3/K, and 1.6 cm3/K. As we can see, the rate of change does not remain constant, but increases over the temperature range, indicating a nonlinear relationship. Therefore, a linear function would better approximate the data.

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Answer:

Step-by-step explanation:

Add, Added to, the sum of, more than, increased by, the total of, plus. +. Add x to y x + y y added to 7.

Work Shown:

x = initial cost before any discounts

x-100 = cost after taking off $100

0.7(x-100) = cost after taking 30% off from the previous value

Therefore, we end up with h(x) = 0.7(x-100)

Optionally you could distribute to get h(x) = 0.7x-70, but I think the first version of this is a bit more descriptive.

It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

Now, According to the question:

"Information available from the question"

A physicist measures the remaining radioactivity in a sample.

She finds that it reduces by 18% each year.

If there was 1.52 g of radioactive material left after 4 years.

In order to find the initial quality of radioactive material, we will use the formula:

Initial Quality = Final Quantity * (1 - Reduction Rate)^Years

We know that -

The final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.

Initial Quantity = 1.52 g × [tex](1-0.18)^4[/tex]

Initial Quantity = 1.52 g × 0.452

Initial Quantity = 0.68 g

Hence, the initial quantity of the radioactive material is 0.68 g.

b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:

Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)

We know that -

the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).

Years = log(0.2 / 0.0.68) / log(1 - 0.18)

Years = 7.15

Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

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Answer:

1    - 1/3     1/9

Step-by-step explanation:

Common ratio is

 81 * r = - 27

       r= - 1/3

-3 * - 1/3  = 1

1 x - 1/3    = -1/3

-1/3  * - 1/3  = 1/9

The probability of selecting a yellow and then a yellow without replacement is 3/10.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 1

Number of green marbles = 1

Number of yellow marbles = 3

Total number of marbles = 5

The probability of selecting a yellow and then a yellow without replacement.

= 3/5 x 2/4

= 6/20

= 3/10

We are using 2/4 since yellow marbles become 2 and the total marbles become 4 when the condition of without replacement is given.

Thus,

The required probability is 3/10.

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The value that makes the pair of ratios equivalent is x = 7.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

The given pair of ratios is:

12:42 = 2:x

12 /42 = 2/ x

Using cross multiplication we have:

12x = 2(42)

x = 7

Hence the value that makes the pair of ratios equivalent is x = 7.

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(a) The expressions (x + x + x + x) and (4x) are equivalent.

(b) The expressions (5x) and (x + 5) are not equivalent.

Equivalent expressions are expressions that perform the same function notwithstanding their appearance. If two algebraic expressions are equivalent, they have the same value when the variable is set to the same value.

a) True

The expressions (x + x + x + x) and (4x) are equivalent.

Both expressions represent the same mathematical operation, which is adding x four times.

b) False

The expressions (5x) and (x + 5) are not equivalent. They represent different mathematical operations.

The expression (5x) is multiplying x by 5, while the expression (x + 5) is adding x and 5.

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A triangular land has area 336 q meter, perimeter 84 meter and length of an edge 26 meter. The lenght of the remaining two sides are both 29 meters long.

Let's call the length of the remaining two sides x.

Since the perimeter of the triangle is 84, then the sum of all three sides is 84, so:

x + x + 26 = 84

Therefore, the sum of the remaining two sides is:

2x = 84 - 26 = 58

And the length of each remaining side is:

x = 58 / 2 = 29 meters required lenght of the remaining two sides.

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Answer:

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the answer.

3 * 17 = 51

The square root of 51 is: 7.141

7.141 is the geometric mean of 3 and 17.

Step-by-step explanation:

Hope it helps! =D

Answer:

Let x be Jenny's hourly rate. Then Mary's hourly rate is x + 0.2x = 1.2x.

The total amount of money they earned for the hours they worked is the same, so we can set up the equation:

30x + 25(1.2x) = 610

Expanding the second term and solving for x:

30x + 30x = 610

60x = 610

x = 10.17

So Jenny's hourly rate is $10.17 and Mary's hourly rate is $12.20.

The option D. See what x is when y = -5 is not a possible way to evaluate the value of f(-5).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The given function is f(x) = 3x² - 2x + 5.

f(-5) is actually the value of y or f(x) when x = -5.

By substituting -5 in place of x of the function, we will get f(-5).

Also we can find the value of f(-5) by graphing the function and finding the y value corresponding to the x value of -5.

Hence the way that is not possible is option D.

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Gauss-Jordan Elimination is a technique for solving systems of linear equations and for determining the inverse of any invertible matrix.

Gauss-Jordan Elimination is a method for finding the inverse of any invertible matrix and for solving systems of linear equations. It is based on the three simplest row operations one may do on a matrix: Place two of the rows in opposite positions. A nonzero scalar multiplied by one of the rows

Since a similar version was described by Wilhelm Jordan in 1888 in his book "Handbuch der Vermessungskunde" independently of B. I. Clasen, who published something similar in the same year, the procedure known as Gauss-Jordan elimination for converting a matrix into reduced echelon form also includes the name Jordan.

This method, which is also known as row reduction, has two steps: forward elimination and back substitution. These two Gaussian elimination method steps differ from one another not by the operations that can be performed through them but rather by the outcome that is obtained.

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The first derivative will give the slope of the function.

The second derivative will give you the point at which the function is increasing or decreasing the most rapidly.

If the 3rd derivative is negative, the rate of increase at the 2nd derivative point will be maximum; if positive, it will be a minimum.

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable).

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the helix r(t) = cos(πt/2), sin (πt/2),t) intersects the sphere x^2 + y^2 + z^2 = 2 in two points.

the angle of intersection at each point: θ = cos⁻¹ (√2/√π²+4)

the angle of intersection at each point: α = cos⁻¹(-√2 /(√π² +4))

Scientists in the fields of physics, engineering, and biology all do research on helices, which are a significant topic in the theory of curves in differential geometry. Helix (or generic helix) is defined as tangent vector field in 3-dimensional Euclidean space establishing a fixed angle with the curve's direction. A curve for which the tangent forms a constant angle with a fixed line is referred to as a helix or coil.

helix: r(t) = < cos(πt/2), sin(πt/2), t >    sphere: x² + y² + z² = 2

put it in the sphere's equation we get:

next, {cos(πt/2)}² + {sin(πt/2)}² + t² = 2

or, 1 + t² = 2

or, t² = 1

or, t = ± 1

thus, points of intersection r(1) = < cos(π/2), sin(π/2), 1 > = < 0, 1, 1 >

r(-1) = < cos(-π/2), sin(-π/2), -1 > = < 0, -1, -1 >

angle intersection is angle between their tangent:

helix:

r(t) = < -π/2 sin(πt/2), π/2 cos(πt/2), 1 >

r'(1) = < -π/2, 0, 1 > .........(i)

r'(-1) = < π/2, 0, 1 > ......... (ii)

sphere:

f = (x² + y² + z² - 2) = 0

Δf = <2x, 2y, 2z>

Δf (0,1,1) = <0,2,2> ................ (iii)

Δf (0,-1,-1) = <0,-2,-2> .............(iv)

angle between (i) and (iii) (at, t = 1)

cosθ = {r'(1) Δf (0,1,1)} / {|r'(1)| |Δf (0,1,1)|]

θ = cos⁻¹ (√2/√π²+4)

angle between (ii) and (iv) (at, t = 1)

cosα = r'(-1)Δf (0,-1,-1) / ||r'(-1)|| ||Δf (0,-1,-1) ||

cos α = -√2 /(√π² +4)

α = cos⁻¹(-√2 /(√π² +4))

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The logarithm and exponential functions are inverse of each other. The exponential function raises a number to a power and the logarithm gives the power that the number has to be raised to in order to equal a given value. In other words, the exponential function expresses exponential growth, while the logarithm expresses exponential decay.

For example, if y = 2^x, then x = log2(y). This logarithmic relationship is useful in solving exponential problems and understanding exponential dynamics.

In exponential dynamics, logarithms are used to study and model changes that occur at exponential rates, such as population growth or decay, interest rate calculations, and many other real-world applications. The logarithmic relationship helps to simplify the exponential equations and make them easier to work with.

In summary, the logarithm and exponential functions are important in understanding exponential dynamics because the logarithmic relationship helps to simplify exponential problems and make them easier to solve.

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Lukes's age is 47

Gibson's age is 26

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Lukes's age = x

Gibson's age = y

Now,

x + y = 73 ______(1)

x = 2y - 5

Substituting in (1)

2y - 5 + y = 73

3y = 78

y = 26

Now,

x = 2 x 26 - 5

x = 52 - 5

x = 47

Thus,

Lukes's age = 47

Gibson's age = 26

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The formula is also used to ensure that the patient is not overdosed or underdosed ,24.1 kg of body weight, 723 mg of cephalexin should be administered per day.

The conversion from 24.1 kg of body weight to milligrams (mg) of cephalexin administered per day can be calculated using the following formula:

Dose (mg) = Desired dose (mg/kg) x Body Weight (kg).

In this case, the Desired dose is 30 mg/kg. So, to calculate the total dose of cephalexin per day:

Dose (mg) = 30 mg/kg x 24.1 kg

Dose (mg) = 723 mg/day

Thus, for 24.1 kg of body weight, 723 mg of cephalexin should be administered per day.

The formula used in this calculation is a standard formula used to calculate the dose of medication to be administered to a patient based on their body weight. The formula is used to ensure that the patient receives the appropriate dosage of medication and that the medication is safe and effective. The formula is also used to ensure that the patient is not overdosed or underdosed, which can cause side effects or other medical problems.

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Answer:

9c

Step-by-step explanation:

16+25=41

50-41=9

fnfnx

The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞

The Maclaurin series for arctan(x) is an alternating series, meaning that the signs of the terms alternate between positive and negative. The terms of the series also get smaller in magnitude as n increases, so the series converges rapidly for small values of x.

The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞

This Maclaurin series representation of arctan(x8) is useful for approximating the value of the function for small values of x. To obtain more accurate results for larger values of x, one can use more terms from the series or use other numerical methods to calculate arctan(x8).

Therefore, The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞

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Answer: 14 eggs

Step-by-step explanation: Hello!

You know that there are 10 chickens that lay eggs every day.  There are 7 neighbors that she needs to give eggs to so that they each get the same amount otherwise there is one egg left over.  We know that each chicken must produce at least one egg per day, meaning that the bare minimum amount of eggs per day is 10.  Let's try 10.

10/7 = 1 and 3/7.  This means that there would be 3 eggs remaining.  This is not possible.  Let's try 11.

11/7 = 1 and 4/7.  This means there would be 4 eggs remaining.  Let's try 14.

14/7 = 2.  This is the smallest number of eggs for each neighbor to get the same amount of eggs each per day (2).  The smallest number of eggs she needs in total is 14.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

What is weight ?

Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.

The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

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dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.

The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

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The car travel before stopping is 400 meters

The car's initial speed was 80 m/s.

Acceleration/Deferral = 8 m/s2.

The following is the equation of motion for time t and distance s:

v = u + at

s = ut + 1/2 * a * t ^2

v = final velocity = 0 where

Thus, s = 80 * 10 - 1/2 * 8 * 10 *10

= 800 - 400

= 400 meters were covered before stopping, giving us 0 = 80 - 8 * t t

= 80/8

= 10 seconds.

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The full question:

A car moving a straight highway with a speed of 80 m/s is forced to slow down at a rate of 8 m/s^2. How far does a car travel before stopping?

Answer:

y = -4 + 1.4

Step-by-step explanation:

y+3/5 = -4(x-1/2)

y + 3/5 = -4x + 2

y + 0.6 = -4x + 2

y = -4 + 1.4

The statement "The results of the experiment do not agree with the theory, there's something wrong with the experiment" is wrong as it does not indulge any other reasons for the results of the experiment not agreeing with the theory.

This statement assumes that the experiment is always at fault and neglects the possibility that the theory may be incorrect or incomplete.

The outcome of an experiment can be influenced by various factors, such as measurement errors, incorrect experimental design, or limitations of the equipment used.

Thus, it is always important to consider multiple explanations before concluding that there is a problem with the experiment.

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Answer: A) 16.425 in^2.

Step-by-step explanation: The figure is broken down, so let's find the area of the rectangle first. We are given 4 in and 2.3 in, which can be multiplied to get 9.2 in. Now, we need to find the area of the two triangles, but let's start with the one to the left. The area of a triangle is b x h x 1/2. 2.3 in x 2.5 in is 5.75 in, but we need to multiply that by 1/2 which is 2.875 in. Finally, we can find the area of the bottom triangle by using the same formula. 3 in x 2.9 in is 8.7 in, but we need to multiply it by 1/2, which is 4.35 in. Now, all we need to do is add all the areas we found together to get the total area of the figure. 9.2 in + 2.875 in + 4.35 in is 16.425 in^2, which means that option A is your answer.

Let me know if this is right! :)

Answer:

16.425 in²

Step-by-step explanation:

total area of the figure= area of (left triangle+ rectangle+ down triangle)

=1/2*base*height+length*breath+ 1/2*base*height

=1/2*2.5*2.3+4*2.3+1/2*3*(5.2-2.3)

=16.425 in²

Answer:

0.2643

Step-by-step explanation:

Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives Summary: When a fair die is tossed 200 times, the probability of obtaining at most 30 fives is 0.2643.

The composite function which expresses the given correspondence correctly is f of g of x

Composite functions are when the output of one function is used as the input of another. If we have a function f and another function g, the function f g ( x ) fg(x) fg(x), said as “ f of g of x”, or “ f g fg fg of x”, is the composition of the two functions.

The composite function rule shows us a quicker way. If f(x) = h(g(x)) then f (x) = h (g(x)) × g (x). In words: differentiate the 'outside' function, and then multiply by the derivative of the 'inside' function.

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