Once medicine X is injected, the amount of it in a person's bloodstream decays at a rate of 4.8% per hour. A patient was injected with 611 mg dose of medicine X. How many hours will it take for the amount of medicine X in the bloodstream to drop to 252mg ?

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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The volume of the cylinder can be obtained from the calculation as  1356 \(cm^3\)

We know that the volume of the cylinder is;

π (pi) is a mathematical constant approximately equal to 3.14159

r is the radius of the cylinder's base (the distance from the center to the edge of the circular base)

h is the height of the cylinder (the distance between the bases)

By substituting the appropriate values for the radius and height into the formula, you can calculate the volume of the cylinder.

V = π\(r^2\)h

V = 3.14 *\((12/2)^2\) * 12

h = 1356 \(cm^3\)

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Answer:

Step-by-step explanation:

No, this is not correct.

Step 1: Find the directional distance from every vertex on the blue image to  the center, Point C.

Point A is 1 unit left and 4 units upwards to Point C.

Point B is 4 units right and 5 units upwards to Point C.

Point C is the center of the dilation, so that point will not change.

Step 2: Apply the scale factor to the directional distances to know the distances of the new images.

The scale factor is 2 so

Point A' should be 2 units left and 8 units upwards to Point C.

Point B' should 8 units right and 10 units upwards to Point C.

Step 3:  Move the point in respect to Point C.

The new image should have the these points.

One point that is 2 units left and 8 units upwards to Point C.

Another point that is Point B' should 8 units right and 10 units upwards to Point C.

One point that coincides  with  Point C.

The equation y = 2x+3 has infinite solutions.

In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

A number line is a pictorial representation of numbers on a straight line. It’s a reference for comparing and ordering numbers. It can be used to represent any real number that includes every whole number and natural number.

As can be seen, the line for y=2x+3 extends up to infinity all over the number line.

For x=0,y=3, For x=1,y=5, For x=2,y=7

∴ For every value of x, we get the different value of y  

Hence it will have infinitely many solutions.

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Answer:

Step-by-step explanation:

Sammie is x,,,, Jennie is 9 years younger than him. So, Jennie ( y) = x-9

According to second condition eq is

(X-5) = 4(y-5)

Place the value of y in eq 2

You will find x= 17

Put x in eq 1

Y = 8

Answer:

22.)

m/8 = 15/24

8×15= 120

120÷24= 5

m=5

23.)9/p = 4/48

9×48= 432

432÷4=108

p=108

24.) 10.50÷3= 3.50

thats $3.50 per pizza.

9 pizzas= $31.50

plus one pizza aka, 31.50+3.50= $35

therefore, 10 pizzas would cost $35

26.) 5/2 = d-2/4

cross multiply:

5×4=2(d-2)

20= 2(d-2) divide both sides by 2

20÷2 = 2(d-2)÷2

10= d-2 exchange places with d and 10 and change signs

-d= -2-10

-d=-12 change the sign on both sides when the variable is negative.

d=12

a) If each plant is required to reduce its pollution by 5,000 tonnes, we can calculate the pollution control costs for each firm using the given marginal cost curves. For Plant 1, MCC1 = 0.02Q, where Q represents the tonnes of pollution reduction. Similarly, for Plant 2, MCC2 = 0.03Q.

For both firms, since the pollution reduction is fixed at 5,000 tonnes, we substitute Q = 5,000 into the respective marginal cost curves:

MCC1 = 0.02 * 5,000 = $100

MCC2 = 0.03 * 5,000 = $150

Therefore, Plant 1's pollution control costs will be $100 and Plant 2's pollution control costs will be $150.

The graph for Plant 1 will have a linearly increasing slope starting from the origin, and the graph for Plant 2 will have a steeper linearly increasing slope starting from the origin.

b) With a pollution tax of $120 per tonne of pollution emitted, each firm's pollution reduction costs will be affected. The firms will now have to pay the pollution tax in addition to their pollution control costs.

Without considering taxes, Plant 1's pollution control costs were $100, and Plant 2's costs were $150 for a total of $250. However, with the pollution tax, the costs will change. Let's assume the firms still need to reduce their pollution by 5,000 tonnes.

For Plant 1: Pollution control costs = MCC1 * Q = 0.02 * 5,000 = $100 (same as before)

Total costs for Plant 1 = Pollution control costs + (Tax per tonne * Tonnes of pollution emitted)

Total costs for Plant 1 = $100 + ($120 * 5,000) = $610,000

Similarly, for Plant 2: Pollution control costs = MCC2 * Q = 0.03 * 5,000 = $150 (same as before)

Total costs for Plant 2 = Pollution control costs + (Tax per tonne * Tonnes of pollution emitted)

Total costs for Plant 2 = $150 + ($120 * 5,000) = $750,000

The total pollution reduction costs with the tax are now $610,000 for Plant 1 and $750,000 for Plant 2, resulting in higher costs compared to part a. This difference arises because the tax imposes an additional financial burden on the firms based on their emissions.

To support this answer, we can draw two graphs, one for each firm, with the tonnes of pollution emitted on the x-axis and the total costs on the y-axis. The graphs will show an increase in costs due to the tax.

c) In a tradable permit scheme where 6,000 permits are issued, with 3,000 permits to each plant, the pollution reduction costs to each firm without trading can be determined.

Since Plant 1 and Plant 2 each receive 3,000 permits, they can each emit up to 3,000 tonnes of pollution without incurring any additional costs. However, if they need to reduce their pollution beyond the allocated permits, they will have to incur pollution control costs as calculated in part a.

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a. The hours the students spent doing homework is 11 1/3 hours

b. A student spend fewer than 20 minutes on homework

From the question, we have the following parameters that can be used in our computation:

The dot plot

The hours the students spent doing homework is the sum of the time spent

So, we have

Hours = 0 * 1 + 10 * 2 + 20 * 4 + 30 * 5 + 40 * 4 + 50 * 3 + 60 * 2

Hours = 680 minutes

So, we have

Hours = 11 1/3 hours

A student spend fewer than 20 minutes on homework

This is because 20 is less than the average of the dot plot

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Question

If the data in the dot plot show how many minutes students spent on homework the previous night,

(a) how many hours in all did these students spend doing homework?

(b) did a typical student from this group spend more or fewer than 20 minutes on homework?

See attachment

Answer:

n-4=-15

Step-by-step explanation:

Answer:

area of recatangle= 4x^3(x^3+3x^2+2x)

=4x^6+12x^5+8x^4

Five professional development models are selected for comparison. A graphic organizer is created to describe and compare these models. The organizer provides a visual representation of the key features, components, and differences among the models.

The graphic organizer presents the selected professional development models side by side, highlighting their distinct characteristics. Each model is described with its name, key features, and components. The organizer may include information such as the focus of the model, target audience, delivery methods, duration, and expected outcomes.

By comparing these models in a structured manner, educators and professionals can easily identify similarities, differences, and unique aspects of each model. This comparison facilitates informed decision-making when selecting a professional development approach that aligns with specific goals, learning objectives, and organizational requirements.

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It is discovered that there is a 0.3934, or 39.34%. likelihood that a customer waits fewer than 30 seconds using the exponential distribution.

The following equation describes an exponential probability distribution with mean m:

f(x) = μe∧(- μe)

The decay parameter is in the following:

μ = 1/m

When x is less than or equal to a, the probability is given by:

P(X ≤ x) = ∫ f(x) dx (limits 0 → a)\

which can be resolved as follows:

P(X ≤ x) = 1 - e∧(- μe)

Since 60 seconds is the mean in this problem, then decay parameter is:

μ = 1/60

The likelihood that a customer will wait under 39 seconds is:

P(X ≤ 30) = 1 - e∧(- 30/60)

P(X ≤ 30) = 0.3934

Thus, the probability that a consumer will wait less than 30 seconds is 0.3934, or 39.34%.

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Answer:

\(m= -2\frac{1}{13}\)

Step-by-step explanation:

2m-27/3=5m

x3.             x3

2m-27=15m

-2m.     -2m

-27=13m

/13.   /13

-27/13=m

-2 1/13=m

Hopes this helps please mark brainliest

(a) The plot of y versus t for several values of y₀ between 1/2 and 1 shows oscillations with higher y₀ resulting in larger oscillations.

(b) The critical initial population \(y_c\) below which the population becomes extinct is \(y_c\) = 2.5k.

(c) For different values of k, the corresponding critical initial populations \(y_c\) are found

(d) The relationship between the critical initial population \(y_c\) and the predation rate k can be summarized as \(y_c\) = 2.5k.

(a) Plotting y versus t for several values of y₀ between 1/2 and 1:

To solve the initial value problem dy/dt = r(t) * y - k, y(0) = y₀, we need to integrate the differential equation numerically.

Given:

- r(t) = (1 + sin t) / 5

- k = 1/5

We can observe the following:

For each value of y₀ between 1/2 and 1, the population y will exhibit a fluctuating behavior over time. The sine function in r(t) causes the growth rate to oscillate, leading to oscillations in the population as well. The magnitude of the oscillations depends on the initial population y₀.

Higher values of y₀ will result in larger oscillations, while lower values will lead to smaller oscillations. As time progresses, the population may increase or decrease depending on the interplay between the growth rate and the predation rate.

(b) Estimating the critical initial population \(y_c\) below which the population will become extinct:

To estimate the critical initial population \(y_c\), we need to find the value of y₀ for which the population becomes extinct. This occurs when the population y drops to zero or a very small positive value.

For the given differential equation dy/dt = r(t) * y - k, we can see that when y is very close to zero, the rate of decrease (k) dominates over the growth rate (r(t) * y). Therefore, we can set up the following equation:

0 = r(t) * y - k

Solving this equation for y, we find:

y = k / r(t)

Substituting r(t) = (1 + sin t) / 5, we have:

y = 5k / (1 + sin t)

To find the critical initial population \(y_c\), we need to determine the smallest value of y for all t. Since the minimum value of sin t is -1, the smallest value of y is obtained when sin t = -1, yielding:

\(y_c\) = 5k / (1 - (-1))

   = 5k / 2

   = 2.5k

Therefore, the critical initial population \(y_c\) is 2.5 times the predation rate k.

(c) Choosing other values of k and finding the corresponding \(y_c\) for each one:

Let's consider different values of k and calculate the corresponding critical initial population \(y_c\) using the formula derived in part (b):

For k = 1/10:

\(y_c\) = 2.5 * (1/10) = 1/4 = 0.25

For k = 1/4:

\(y_c\) = 2.5 * (1/4) = 5/8 = 0.625

For k = 1/2:

\(y_c\) = 2.5 * (1/2) = 5/4 = 1.25

For k = 1:

\(y_c\) = 2.5 * 1 = 2.5

For k = 2:

\(y_c\) = 2.5 * 2 = 5

For k = 5:

\(y_c\) = 2.5 * 5 = 12.5

These are the corresponding critical initial populations \(y_c\) for different values of k.

(d) Plotting \(y_c\) versus k:

Using the values of \(y_c\) and k calculated in part (c), we can plot \(y_c\) versus k:

k       |   \(y_c\)

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

1/10   |  0.25

1/4    |  0.625

1/2    |  1.25

1       |  2.5

2      |  5

5      |  12.5

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Answer:

Step-by-step explanation:

c=12+5t?

Answer:

\(V=3367.57\ cm^3\)

Step-by-step explanation:

The diameter of a sphere, d = 18.6 cm

Radius, r = 9.3 cm

We need to find the volume of the sphere. The formula for the volume of a sphere is given by :

\(V=\dfrac{4}{3}\pi r^3\\\\=\dfrac{4}{3}\times 3.14\times (9.3)^3\\\\=3367.57\ cm^3\)

So, the volume of the sphere is equal to \(3367.57\ cm^3\).

Answer:

1/2

Step-by-step explanation:

hope it helps :)

Answer:

x > - 16

Step-by-step explanation:

41- 3/4 x < 53

Subtract 41 from each side

41-41- 3/4 x < 53-41

-3/4x < 12

Multiply each side by -4/3, remembering to flip the inequality

-4/3 * -3/4x > 12 * -4/3

x > - 16

The true statement is (a) The rectangular prism boxes should be used because they will cost the company $2. 50 less than using the cylindrical containers.

The given parameters are:

\(Pencils = 2400\) --- the pencils needed

The number of pencils the prism can hold is:

\(Prism =60\)

Divide the number of pencils needed by the number of pencils in 1 rectangular prism, to calculate the number of prisms needed (n1)

\(n_1 = \frac{Pencils}{Prism}\)

So, we have:

\(n_1 = \frac{2400}{60}\)

\(n_1 = 40\)

A rectangular prism costs $0.50.

So, the total cost is:

\(Total\ cost = 40 \times 0.50\)

\(Total\ cost = \$20\)

The number of pencils the cylinder can hold is:

\(Cylinder=80\)

Divide the number of pencils needed by the number of pencils in 1 cylinder box, to calculate the number of cylinders needed (n2)

\(n_2 = \frac{Pencils}{Cylinder}\)

So, we have:

\(n_2 = \frac{2400}{80}\)

\(n_2 = 30\)

A cylinder costs $0.75.

So, the total cost is:

\(Total\ cost = 30 \times 0.75\)

\(Total\ cost = $22.5\)

By comparison, the rectangular prism costs $2.5 less than the cylinder

Hence, the true statement is (a)

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Answer:the equation of the horizontal line passing through (4,7) is y=7 . Note − The equation of a vertical line is always of the type x=k and hence the equation of the vertical line passing through (4,7) is x=4 .

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Answer:

3 and 1/2

Step-by-step explanation:

2 & 1/2 + x = 6

2 & 1/2 = 2.5

rearrange

6 - 2.5 = 3.5

so...

2.5 + 3.5 = 6

Answer:

I attached both the work and explanation down below. Hope it helps!

Answer:

the correct answeria A.pretest sensitization

Answer:

75%

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

The difference is $12 so let's calculate the percent of 12 to 16:

12/16 = 0.75 = 75%

Answer:

Step-by-step explanation:

a) As a fraction of the original price Louisa will pay ...

  0.85c . . . . 85% of the subscription price

__

b) Louisa's expression (-0.15c) tells the amount of the discount, not the cost of the subscription. If Louisa were to write the cost of the subscription, her expression would be ...

  c - 0.15c

__

c) The expression of (a) is the cost of the subscription; the expression Louisa wrote is the amount of cost reduction due to the discount.