A patient is ordered 1.6 g Drug A every 8 hours over a 24
hour period, then 1.6 g every 4 hours for the next three
days. How many grams of Drug A will the patient receive
altogether?

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

To find the rules for (fg)(x) and (gf)(x), we need to evaluate the composite functions.

(fg)(x) = f(g(x)) = f(sqrt(x - 5)) = (sqrt(x - 5))^2 + 5 = x - 5 + 5 = x

(gf)(x) = g(f(x)) = g(x^2 + 5) = sqrt(x^2 + 5 - 5) = sqrt(x^2) = |x|

Therefore, the rules for (fg)(x) and (gf)(x) are:

(fg)(x) = x

(gf)(x) = |x|

Step-by-step explanation:

Answer: The union of the two intervals is (-∞, ∞) which is the set of all real numbers.

The intersection of the two intervals is [0, 2], which is the set of all numbers that are greater than or equal to 0 and less than or equal to 2.

Step-by-step explanation:

You can visualize this using a number line, with the interval (-∞, 2) represented by the set of numbers to the left of 2 and the interval [0, ∞) represented by the set of numbers greater than or equal to 0. The union of the two intervals would be the entire number line, and the intersection would be the numbers between 0 and 2.

Answers:  

Magnitude of force P = 163.041494

Magnitude of resultant force = 184.320997

Values are approximate. Units are in newtons.

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

Explanation:

Let for P be pulled directly to the east. The vector for this force is <x, 0> where x is positive.

The 200 newton force has the vector <200*cos(120), 200*sin(120)>

The resultant vector is <x+200*cos(120),200*sin(120)>. Each component is the sum of the corresponding components of <x,0> and <200*cos(120), 200*sin(120)>

The resultant vector is also <r*cos(70),r*sin(70)>. Note how 70+50 = 120. The 50 degree angle is known, so we effectively do 120-50 = 70 to find the angle of the resultant vector with the positive x axis.

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

The resultant vector expressions we found were

Equate the y components of each resultant vector expression. Solve for r

r*sin(70) = 200*sin(120)

r = 200*sin(120)/sin(70)

r = 184.320997021376

Make sure your calculator is in degree mode.

Let's round this r value to 6 decimal places to simplify things a bit

r = 184.320997

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

Now equate the x components of each resultant vector expression, plug in the r value we found, and solve for x

x+200*cos(120) = r*cos(70)

x+200*cos(120) = 184.320997*cos(70)

x = 184.320997*cos(70) - 200*cos(120)

x = 163.041494

this value is approximate just like r is as well

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

The magnitude of force P is

magnitude = sqrt(x^2+y^2)

magnitude = sqrt(x^2+0^2)

magnitude = sqrt((163.041494)^2+0^2)

magnitude = 163.041494

Which is equal to the x value. This applies because y = 0.

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

The magnitude of the resultant is r = 184.320997 which we found earlier

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

-300r + 15

Step-by-step explanation:

Hope this helps!

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:

f(4)= -10

If g(x) =2, then x=0

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

y = 2x +4

Step-by-step explanation:

m = \(\frac{y_{2} -y_{1} }{x_{2} - x_{1} }\)

y - \(y_{1}\) = m ( x - \(x_{1}\) )

~~~~~~~

(1, 6)

(- 3, - 2)

m = 2

y - 6 = 2 ( x - 1 ) <------ ( point-slope form )

y = 2x + 4  <------- ( slope-intercept form )

2x - y = - 4  <------ ( standard form )

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Then  it would take 116/0.8286 = 140.10 minutes (rounded to two decimal places) or approximately 2 hours and 20 minutes to produce 116 cups of coffee using both machines continuously.

To calculate the time it would take to produce 116 cups of coffee using both machines continuously, we need to first determine how many cups of coffee each machine produces per minute.

For the first machine, it produces 2 cups in 5 minutes, which means it produces 2/5 = 0.4 cups of coffee per minute.

For the second machine, it produces 3 cups in 7 minutes, which means it produces 3/7 = 0.4286 cups of coffee per minute (rounded to four decimal places).

To find out how long it would take to produce 116 cups of coffee using both machines, we need to divide the total number of cups by the combined rate of production.

Combined rate of production = rate of first machine + rate of second machine
= 0.4 + 0.4286
= 0.8286 cups per minute (rounded to four decimal places)

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Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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3.6 years will have passed when 115 grams of thorium 234 is left.

(a) To find the amount of thorium 234 left after 0.5 years, we can substitute t = 0.5 and A0 = 1000 into the given equation and solve for At:

\(A_t = A0e^{(-10.498t)}\\\\A_t = 1000e^{(-10.498(0.5))}\\\\A_t = 679.6\ grams\)

Therefore, approximately 679.6 grams of thorium 234 will be left after 0.5 years.

(b) To find when 115 grams of thorium 234 will be left, we can set At = 115 in the given equation and solve for t:

\(A_t = A_0e^{-10.498t}\\\\115 = 1000e^{-10.498t}\\\\ln(115/1000) = -10.498t\\\\t = 3.6\ years\)

Therefore, approximately 3.6 years will have passed when 115 grams of thorium 234 is left.

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Answer:

-9

Step-by-step explanation:

Answer:

the opposite of division is multiplication

The different 2-member groups that are possible is 28

From the question, we have

Total number of members, n = 8

Numbers to selection, r = 2

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 2

Substitute the known values in the above equation

Total = ⁸C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 8!/(6! * 2!)

Evaluate

Total = 28

Hence, the number of ways is 28

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By graphing

Answer: 1.14

Step-by-step explanation:

25/22 = 1.1363

Answer:(2x+7)+(2x+7)

Step-by-step explanation:

what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

There were 14 players on the soccer team.

In the given problem, the members of a soccer team raised $1210.50 to go to a tournament. They rented a bus for $769.50 and budgeted $31.50 per player for meals. We need to find how many players were on the team.To solve this problem, we can start by subtracting the cost of the bus rental from the total amount raised by the team:$1210.50 - $769.50 = $441Now, we can divide this remaining amount by the amount budgeted per player for meals:$441 ÷ $31.50 = 14Therefore, there were 14 players on the soccer team. We can check our answer by multiplying the number of players by the amount budgeted per player for meals:14 x $31.50 = $441This is equal to the remaining amount after the bus rental was paid, which confirms that our answer is correct.

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Answer:

C. 11

Step-by-step explanation:

15-4=11

After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

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Answer:

True

Step-by-step explanation:

Given data

Diameter =6 yards

Radius R= Diameter/2= 6/2  = 3 yards

R²=3*3=9square yards

Hence R^2 = 9square yards= True

Answer:

True.

Step-by-step explanation:

R² is radius to the second power. You were given the diameter, so the radius will be half of that diameter.

3 to the second power, (or 3 x3), is 9.

Answer:

224

Step-by-step explanation:

360.-136.

Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

<95141404393>

Answer:

um 6/1?

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The slope of a line is the change in the line. It is often referred to as the (\(\frac{rise}{run}\)), the slope of the line can be found using the following formula,

\(\frac{y_2-y_1}{x_2-x_1}\)

The graph of the given line gives one the points (7, 2), (9, 6). Substitute these points into the given formula and solve for the slope,

\(\frac{6 - 2}{9 - 7}\)

Simplify,

\(=\frac{4}{2}\)

\(=2\)