a particle moves along the x axis with position function x(t)=t^2-8t-1 on the interval

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:

x = ± 8

Step-by-step explanation:

x² = 64 ( take square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8

solutions are x = 8 and x = - 8 ,  since

8 × 8 = 64 and - 8 × - 8 = 64

Answer: In statistics, the term linear model is used in different ways according to the context.

Step-by-step explanation: The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning.

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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Mateo will be able to choose a gym membership plan that best meets his needs and budget.

To help Mateo decide on the best gym membership plan, the following information would be important:

By considering these factors, Mateo will be able to choose a gym membership plan that best meets his needs and budget.

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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

The standard form from (-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) is B) 9[tex]x^{2}[/tex] - 15x - 12.

This is a quadratic equation. To simplify the equation, we need to arrange the equation to be standard form or quadratic equation which is

a[tex]x^{2}[/tex] + bx + c

(-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) = -7x -5 + 9[tex]x^{2}[/tex] - 8x -7

Group of a[tex]x^{2}[/tex] --> It will be 9[tex]x^{2}[/tex]

Group of bx ---> It will be -7x-8x = -15x

Group of c ---> It will be -5-7 = -12

We just combine the group into standard equation

(-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) = -7x -5 + 9[tex]x^{2}[/tex] - 8x -7

                                      = 9[tex]x^{2}[/tex] -15x - 12

So the simplification of equation (-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) is 9[tex]x^{2}[/tex] - 15x - 12, or from the answer, it's B)

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Answer:

9c

Step-by-step explanation:

16+25=41

50-41=9

fnfnx

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 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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The figure below is made of 222 rectangular prisms.

Completed question :

Part D

Wendell plans to paint the doghouse after it’s built. He wants to know what the surface area of the outside of the doghouse will be. To find the surface area, first break up any composite shapes into rectangles and triangles. Which shape is considered a composite shape? When the shape is decomposed, what are the dimensions of the resulting shapes necessary for finding surface area?

Given data :

The volume of a rectangular prism is given as follows.

Volume of a rectangular prism = length x breadth x height

Therefore, the volume of 222 rectangular

prism

= 2 x 2 x 2

= 8 cubic units

Volume of 222 rectangular prisms = 222

×Volume of a rectangular prism

=222× 8

= 1776 cubic units

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Answer:

The surface area is 5,052 inches

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?

Factory should produce 100 high-grade shoes and 200 low-grade shoes for maximum profit.

Let x be the number of high-grade shoes produced, then the number of low-grade shoes produced is at least 2x. The maximum number of shoes the factory can produce is 500, so we have the following constraints:

x + 2x ≥ 500 (production constraint)

x ≥ 100 (delivery constraint)

x ≥ 0 (non-negative constraint)

The profit for each type of shoe is given as birr 2.00 for high-grade shoes and birr 1.00 for low-grade shoes, so the total profit is:

Profit = 2x * 2.00 + 1.00 * 2x = 4.00x + 2x = 6.00x

The objective is to maximize the profit, subject to the constraints above. So, the feasible solution is x = 100, which means the factory should produce 100 high-grade shoes and 200 low-grade shoes. This is the maximum possible profit of 600 birr.

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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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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.

The linear demand equation: x = m(p) + b, where x is the number of occupied units, p is the monthly rent, and m and b are constants and the linear demand equation in this case is:

x = -1.04p + 44.16

To find the linear equation, we need to determine the slope (m) and the y-intercept (b). Using the two points provided, we can write a system of equations:

When p = $780, x = 40 units

40 = m($780) + b

When p = $852, x = 36 units

36 = m($852) + b

Solving for m and b, we get:

m = -1.04 and b = 44.16

So, the linear demand equation is:

x = -1.04p + 44.16

This equation represents the inverse relationship between the monthly rent and the demand, where a higher rent results in a lower demand and vice versa.

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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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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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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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The no of gallon of a 14%-salt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution is 5 gallon

What is Gallon?

The gallon is a volume unit used in imperial and customary units in the United States. There are now three versions in use: the imperial gallon, which is equal to 4.54609 litres

Given

14%-alt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution

.14x +.25*6 = .20(x+6)

.14x + 1.5 = .20x + 1.2

.14x - .20x = 1.2 - 1.5

-0.06x = -0.3

x = 5 gallon

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The no of gallon of a 14%-salt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution is 5 gallon

What is Gallon?

A gallon is a volume unit used in imperial and customary units in the United States. There are now three versions in use: the imperial gallon, which is equal to 4.54609 litres

Given

14%-alt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution

.14x +.25*6 = .20(x+6)

.14x + 1.5 = .20x + 1.2

.14x - .20x = 1.2 - 1.5

-0.06x = -0.3

x = 5 gallon

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x=6 m<ABD=20 *I think*

Step-by-step explanation:

Find x

plug in your answer

Answer:

False - The standard deviation is always positive.

Sister uses 420.76 inches more wire per wall than Poppy.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

We have,

Poppy's diameter = d

Older sister diameter.

D = d + 134

Now,

The circumference of the wall hangings.

= 2πr

= πd

Now,

The circumference of the wall hangings by the older sister.

= πD

= π (d + 134)

The circumference of the wall hangings by the Poppy.

= πd

Now,

The difference between the length of the wire.

= π (d + 134) -  πd

= πd + π x 134 - πd

= 3.14 x 134

= 420.76 inches.

Thus,

Sister uses 420.76 inches more wire.

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1 micrometer equals 1e-6 meters. Dividing by 1000000 will convert your number from micrometers to meters.

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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

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.

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 circumference of the circle with the diagram of 2.25 cm is 14.13 cm.

The circumference, also known as the length of a circle, is its circumference. By using the radius or diameter, we can calculate the circumference of a circle.

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed centre. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "small ring," is the source of the English word "circle."

Given that the diameter of the circle is 4.50 cm. The circumference of the circle is calculated as:-

C = 2πr

C = 2 x π x 2.25

C = 14.13 cm

Therefore, the circumference of the circle with the diagram of 2.25 cm is 14.13 cm.

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Answer: $2171.79

Step-by-step explanation: