Use substitution to solve each system of equations.
Explain step by step and I'll mark you Brainliest.

16x - 4y = 18
x = -6y - 7​

Where the above are given,

10. The nurse should give 2.45ml of the liquid medication.

11. The nurse can give 24ml of meperidine in 24 hours.

12. The patient should take 42 tablets of the antibiotic.

13. The IV rate is 100ml/hr at 1500gtt/min with a 15gtt/ml drip factor.

14. Each dose of codeine contains 15000mg.

15. The patient should be given 2.67oz (approximately) of the cough syrup.

10. To determine how much   of the liquid should be given, we can set up a  proportion

1g/3.5ml = 700mg/x

Cross-multiplying,

1g * x = 700mg * 3.5ml

x = (700mg * 3.5ml) / 1g

x = 2450mg*ml/g

Therefore, the amount of liquid to be given is 2.45ml.

11. The order states meperidine 75mg IM every 6 hours PRN pain, and the pharmacy sends a vial that contains 25mg/2ml. To calculate how many ml can be given in 24 hours, we need to consider the frequency and duration.

In 24 hours, there are 24/6 = 4 doses to be given. Each dose contains 75mg of meperidine.

To find the volume (ml) of each dose, we can set up a proportion  -

25mg/2ml = 75mg/x

25mg * x = 75mg * 2ml

x = (75mg * 2ml) / 25mg

x = 6ml

12.  To calculate the number of tablets the patient should take, we need to consider the dosage and the duration.

Each tablet contains 250mg of the antibiotic.

To find the number of tablets for the total dosage, we can set up a proportion  -

250mg/1 tab = 0.75g/x

250mg * x = 0.75g * 1 tab

x = (0.75g * 1 tab) / 250mg

x = 0.003 tab

Since we cannot take a fraction of a tablet, the patient should take 1 tablet every 4 hours for 7 days, resulting in a total of 1 * 6 * 7

= 42 tablets.

13.  To determine the IV rate, we need to calculate the number of drops per minute.

The formula to calculate the IV rate in drops per minute (gtt/min) is -

IV rate (ml/hr) = Total volume (ml) / Total time (hr)

IV rate (gtt/min) = IV rate (ml/hr) * Drop factor (gtt/ml)

IV rate (ml/hr) = 1000ml / 10hr = 100ml/hr

IV rate (gtt/min) = 100ml/hr * 15gtt/ml =

1500gtt/min

Therefore, the IV rate is 100ml/hr at 1500gtt/min.

14. To determine the   amount of milligrams of  codeine in each dose, we need to convert grams to milligrams.

1  gram (g) = 1000   milligrams (mg)

15 grams (gr) = 15 * 1000mg = 15000mg

Therefore, each dose contains 15000mg of codeine.

15. To calculate how much cough syrup should be given in ml's, we can set up a proportion -

225mg/1oz = x ml/600mg

225mg * x = 1oz * 600mg

x = (1oz * 600mg) / 225mg

x = 2.67oz

Therefore, 2.67oz of cough syrup should be given in ml's.

Learn more about cough syrup:
https://brainly.com/question/17327689
#SPJ4

Answer:

\(\huge\boxed{C.\ -x^3-2x-12}\)

Step-by-step explanation:

\((x+2)(-x^2+2x-6)\\\\=(x)(-x^2)+(x)(2x)+(x)(-6)+(2)(-x^2)+(2)(2x)+(2)(-6)\\\\=-x^3+2x^2-6x-2x^2+4x-12\\\\\text{combine like terms}\\\\=-x^3+(2x^2-2x^2)+(-6x+4x)-12\\\\=-x^3-2x-12\)

Answer:

first 2 hours: 276m

first 5 hours: 690m

15 minutes: 34.5m

Step-by-step explanation:

take the total distance climbed and divide it by the total time. this gives you 138m per hour climbed. just multiply this by your hours needed. divide by 4 to find the 15 minute distance.

The results are:

They climbed in the first two hours = 276 meters

They climbed in the first 5 hours = 690 meters

They climbed in the final 15 minutes = 34.5 meters.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

In 2011, a professional climber scaled the outside of the Burj Khalifa, making it all the way to 828 meters (the highest point on which a person can stand) in 6 hours.

Assuming they climbed at the same rate the whole way.

So, the unit rate,

= 828/6

= 138 meters per hour.

And 138/60 = 2.3 meter per minute.

They climbed in the first two hours,

= 2 x 138

= 276 meters.

They climbed in the first 5 hours,

= 5 x 138

= 690 meters.

They climbed in the final 15 minutes,

= (15 x 2.3)

= 34.5

= 34.5 meters.

Therefore, the results are 276 meters, 690 meters and 34.5 meters in the order.

To learn more about the multiplication;

https://brainly.com/question/19634536

#SPJ2

The cpk for this process is 0.5.

To calculate the cpk for this process, we first need to calculate the process capability index (cp) using the formula:
cp = (USL - LSL) / (6 × sigma)
where USL is the upper specification limit (48), LSL is the lower specification limit (30), and sigma is the process standard deviation (4).
cp = (48 - 30) / (6 × 4)
cp = 18 / 24
cp = 0.75
Next, we can calculate the cpk using the formula:
cpk = min[(USL - mean) / (3 × sigma), (mean - LSL) / (3 × sigma)]
cpk = min[(48 - 42) / (3 × 4), (42 - 30) / (3 × 4)]
cpk = min[6 / 12, 12 / 12]
cpk = min[0.5, 1]
cpk = 0.5

To know more about process capability index visit:

https://brainly.com/question/29317659

#SPJ11

Answer:

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Step-by-step explanation:

In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?

(1) The teacher distributed 180 candies and 40 bars.

(2) The total number of items received by each student was less than 20.

A Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked.

B Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient to answer the question asked.

C BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D EACH statement ALONE is sufficient to answer the question asked.

E Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

180 candies and 40 bars

The highest common factor of 180 candies and 40 bars = 20

Answer:

16 cubic units

Step-by-step explanation:

\(\displaystyle V=\int^b_aA(x)\,dx\\\\V=\int^6_2(\sqrt{x})^2\,dx\\\\V=\int^6_2x\,dx\\\\V=\frac{1}{2}x^2\biggr|^6_2\\\\V=\frac{1}{2}(6)^2-\frac{1}{2}(2)^2\\\\V=\frac{1}{2}(36)-\frac{1}{2}(4)\\\\V=18-2\\\\V=16\)

A(x) represents the area of the cross-section, so in this case, we square \(\sqrt{x}-0\) which is just \(\sqrt{x}\)

Answer:

16.66cm²

Step-by-step Explanation:

Given:

∆LMN with m<N = 38°

Length of side NL = 7.2cm

Length of side ML = 4.8cm

Required:

Area of ∆MNL

Solution:

Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b

Where sin(A) = Sin(M) = ?

a = NL = 7.2cm

sin(B) = sin(N) = 38°

b = ML = 4.8cm

Thus,

Sin(M)/7.2 = sin(38)/4.8

Cross multiply

4.8*sin(M) = 7.2*sin(38)

4.8*sin(M) = 7.2*0.6157

4.8*sin(M) = 4.43304

Divide both sides by 4.8

sin(M) = 4.43304/4.8

sin(M) = 0.92355

M = sin-¹(0.92355) ≈ 67.45°

Step 2: Find m<L

angle M + angle N + angle L = 180 (sum of angles in a triangle)

67.45 + 38 + angle L = 180

105.45 + angle L = 180

Subtract 105.45 from both sides

Angle L = 180 - 105.45

Angle L = 74.55°

Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)

Where,

a = NL = 7.2 cm

b = ML = 4.8 cm

sin(C) = sin(L) = sin(74.55)

Thus,

Area of ∆MNL = ½*7.2*4.8*0.9639

= ½*33.31

= 16.655

Area of ∆MNL ≈ 16.66cm²

Answer:

7<x-5

12<x

x>12

Step-by-step explanation:

'I hope my answer helps you'

Question: y = 3cos[6(x-4)] - 5

Answer: 3

Step-by-step explanation:

The reason for this is in order to find amplitude, it's always the number before "cos" or "sin". Also, the "[6(x-4)]" was just a distraction to throw you off

Here's a trick to find everything; amplitude, period, phase sift, etc.:

      y = A sin(B(x + C)) + D

* amplitude is A

* period is 2π/B

* phase shift is C (positive is to the left)

* vertical shift is D

Answer: yes it is

Step-by-step explanation:

Answer:

average rate of change is 1.5

Step-by-step explanation:

looking at the table you can do calculations between each number, then add up all these differences, divide by the total amount of changeschaned you got, and that is the average

Answer:

constant = b = -15

Step-by-step explanation:

3 + b = -12

b = -12 - 3

b = -15

Answer:

8/15

Step-by-step explanation:

2/5 + 2/15

Get common denominator

6/15 + 2/15 = 8/15

Answer:

8/15

Step-by-step explanation:

2/5 + 2/15 =

You need a common denominator. The LCD of 5 and 15 is 15.

= (2 * 3)/(5 * 3) + 2/15

= 6/15 + 2/15

= 8/15

For the given graph,

Axis of symmetry : x = 1

Vertex : (1, 4)

Domain : Set of all real numbers or (-∞, ∞)

Range : {y : y ≤ 4, y ∈ R}

Behavior :

Given a graph of a quadratic function which is a parabola.

The axis of symmetry of a quadratic graph is the line which divides the two parts of the parabola symmetrically.

Here the line x = 1 divides the parabola symmetrically.

So axis of symmetry : x = 1

The x coordinate of the vertex is 1, which is same as axis of symmetry.

From the graph, y coordinate = 4

So vertex is (1, 4).

Domain is the set of all the input values or in this case the x values for which the function is defined.

Here x values range from -∞ to ∞, which is the set of all real numbers.

Range is the set of all y values for the given x values in the domain.

Here y values are all the y values which are less than or equal to 4.

So range is y ≤ 4.

End behavior of the function is that as x tends to positive or negative infinity, y tends to negative infinity.

Learn more about Domain and Range here :

https://brainly.com/question/28135761

#SPJ1

Answer:

okay so first we are given that P(2016) = 500 and

P(2017) = 672

put in the equation Pn+1 = k[Pn + 60]

put Pn = P(2016) = 500 {n = 2016 here. }

and P(n+1) = 672

now , 672 = k [ 500 + 60 ]

672 = 560k

k = 672 ÷560 = 1.2

now, using k = 1.2

put n = 2017 in equation we get,

P(2018) = 1.2[ P(2017) + 60 ]

P(2018) = 1.2 [ 672 + 60 ]

P(2018) = 878

now, similarly put n = 2018

P(2019) = k [P(2018) + 60 ]

P(2019) = 1.2 [ 878 + 60 ]

P(2019) = 1125 (approx.)

Sorry for bad graphic style.. I am not very advanced at this.

Answer:

1126

Step-by-step explanation:

Given formula:

\(P_{n+1}=k(P_n+60)\)

Given information:

Substitute these values into the formula and solve for k:

\(\begin{aligned}P_{n+1} & = k(P_n+60)\\\implies P_2 & = k(P_1+60)\\672 & = k(500+60)\\672 & = 560k\\k & = \dfrac{672}{560}\\k & = 1.2\end{aligned}\)

Substitute the found value of k into the formula:

\(P_{n+1}=1.2(P_n+60)\)

If:

Then:

Use the formula and the value of P₂ to find P₃ and P₄.

\(\begin{aligned}P_{3} & =1.2(P_2+60)\\& = 1.2(672+60)\\& = 878.4\end{aligned}\)

\(\begin{aligned}P_{4} & =1.2(P_3+60)\\& = 1.2(878.4+60)\\& = 1126.08\end{aligned}\)

Therefore, the prediction for the population on 1st March 2019 is 1126 tadpoles (nearest whole number).

If f(x) = sin(x), then the Mean Value Theorem guarantees that somewhere between pi/6 and pi/2, f′(x) is equal to C) 3/2pi

According to the mean value theorem, there must be at least one point

(c, f(c)) on the curve where the tangent is parallel to the secant going through the two supplied points for every function f(x) whose graph goes through the given points (a, f(a)), and (b, f(b)).

We know, f'(c) = [f(b) - f(a)]/(b - a).

Therefore, f'(c) = [sin(π/2) - sin(π/6)]/(π/2 - π/6).

f'(c) = [1 - 1/2]/2π.

f'(c) = (1/2)/(2π/6).

f'(c) = = (1/2)×6/2π.

f'(c) = = 3/2π.

learn more about the mean value theorem here :

https://brainly.com/question/14214076

#SPJ1

hope this helps you (⁠ ⁠´⁠◡⁠‿⁠ゝ⁠◡⁠`⁠)

The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.

To determine the relationship between average fixed cost (AFC) and average total cost (ATC) at a quantity of output of 1,000 units, we need to understand the formulas for AFC and ATC.

AFC is calculated by dividing total fixed cost (TFC) by the quantity of output (Q). ATC is calculated by dividing total cost (TC) by the quantity of output (Q). Mathematically, we have:

AFC = TFC / Q

ATC = TC / Q

Given that AFC is $8 at a quantity of output of 1,000 units, we can substitute the values into the AFC formula:

$8 = TFC / 1,000

Multiplying both sides of the equation by 1,000, we find:

TFC = $8,000

Now, we are given that ATC is $12 at the same level of output. Substituting the values into the ATC formula, we have:

$12 = TC / 1,000

Multiplying both sides of the equation by 1,000, we find:

TC = $12,000

To summarize:

Total fixed cost (TFC) = $8,000

Total cost (TC) = $12,000

Therefore, it follows that the difference between AFC and ATC lies in the variable cost component. The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.

Learn more about average fixed cost here:

https://brainly.com/question/13541145

#SPJ11

The normal distribution is used to estimate the location of the boundaries and shade the corresponding areas for the given statements about Alyse's procrastination habits.

In a normal distribution, the area under the curve represents the probability. To estimate the boundaries and shade the areas, we need to find the corresponding z-scores (number of standard deviations from the mean).

a. Alyse procrastinates less than 10 minutes 10% of the time: To find the z-score for the 10th percentile, we look for the mark on the normal distribution that corresponds to this area. This mark represents the boundary where Alyse procrastinates less than 10 minutes with a 10% probability.

b. She procrastinates more than 60 minutes 60% of the time: To find the z-score for the 60th percentile, we look for the mark on the normal distribution that corresponds to this area. This mark represents the boundary where Alyse procrastinates more than 60 minutes with a 60% probability.

By estimating the z-scores and corresponding marks on the normal distribution, we can label the locations of the boundaries and shade the areas that satisfy each statement about Alyse's procrastination habits.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

To sketch the region bounded by the curves of the pair of functions y = cos x and y = x4 and then find its area, we will first plot the graphs of the functions. We have: For y = cos x.

To find the area of the region bounded by the two curves, we need to determine the limits of integration, which is the point(s) of intersection between the two curves. We can equate the two equations:

cos x = x4

We can solve this equation using a numerical method such as Newton-Raphson method or by guessing and checking.

By guessing and checking, we can see that there is a root between x = 0 and x = 1. Using a graphing calculator or software, we can zoom in and get a better estimate of the root. We can also use the intermediate value theorem to conclude that there is a root between x = 0 and x = 1.

Thus, we have: Area = ∫[0, c] (x4 - cos x) dx where c is the x-coordinate of the point of intersection. We can use a numerical method to approximate this value. Using Simpson's rule with n = 10,

we get: Area ≈ 1.5479 square units.

To know more about graphs visit :

https://brainly.com/question/17267403

#SPJ11

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

Equation in the interval from the rounded answers to the nearest hundredth are t = 1.05 and t = 4.19. The correct solution is t = 1.05 and t = 4.19.

To solve the equation cos t = 1/2 in the interval from 0 to 2π, we can use the unit circle or trigonometric identities.

First, let's find the exact solutions:

cos t = 1/2

Using the unit circle, we know that the cosine of an angle t is equal to the x-coordinate of the point on the unit circle corresponding to that angle.

Since the cosine is 1/2, we need to find the angles where the x-coordinate is 1/2.

In the first quadrant, the x-coordinate is positive, so one solution is t = π/3.

In the fourth quadrant, the x-coordinate is positive again, so another solution is t = 5π/3.

Therefore, the exact solutions are t = π/3 and t = 5π/3.

Now, let's find the rounded answers to the nearest hundredth:

To find the rounded answers, we can use a calculator.

For t = π/3, the rounded answer is approximately 1.05.

For t = 5π/3, the rounded answer is approximately 4.19.

So, the rounded answers to the nearest hundredth are t = 1.05 and t = 4.19.

To know more about interval visit:

https://brainly.com/question/29179332

#SPJ11

The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

To know more about water level visit:

https://brainly.com/question/30015643

#SPJ11

The five values in a summary are the median, the lower and upper quartiles, the maximum and minimum values in the data set. Minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), and maximum value are all listed together in this sequence.

To learn more about minimum value, refer to:

https://brainly.com/question/29409891

#SPJ1

When arranging indistinguishable objects in such a way that no two objects are in the same row or column, the number of possible arrangements depends on the dimensions of the grid.

The number of ways to arrange indistinguishable objects without any repetitions in a grid, such that no two objects are in the same row or column, depends on the dimensions of the grid. Let's assume the grid has M rows and N columns. In this case, the number of possible arrangements can be determined using combinatorics.

To find the total number of arrangements, we start with the first column. There are M choices for the first object in this column. Moving to the second column, there are M-1 choices since we need to avoid repetition within the same row. Continuing this process, the number of choices decreases by 1 for each subsequent column.

Therefore, the total number of arrangements can be calculated as M x (M-1) x (M-2) x ... x (M-N+1), where N is the number of columns. This can be further simplified as M! / (M-N)!, where "!" represents the factorial operation.

In conclusion, when arranging indistinguishable objects in a grid such that no two objects are in the same row or column, the number of possible arrangements depends on the dimensions of the grid. By applying combinatorial principles, the total number of arrangements can be calculated using the formula M! / (M-N)!.

To know more about factorial operation click here:

brainly.com/question/29105321

#SPJ11

Revised probabilities: Bruk - 0.2748, Alemayehu - 0.4533, Yohannes - 0.2719 (order filled correctly), Bruk - 0.4743, Alemayehu - 0.4269, Yohannes - 0.0988 (order filled incorrectly).

If the order was filled correctly and the person who filled it is unknown, the revised probabilities that Bruk, Alemayehu, or Yohannes filled the order can be calculated based on their individual error rates and the proportion of orders they fill.

The probability that Bruk filled the order correctly would be 0.8 (1 - 0.2) * 0.3 = 0.24.

The probability that Alemayehu filled the order correctly would be 0.88 (1 - 0.12) * 0.45 = 0.396.

The probability that Yohannes filled the order correctly would be 0.95 * 0.25 = 0.2375.

Therefore, the revised probabilities are approximately 0.2748 for Bruk, 0.4533 for Alemayehu, and 0.2719 for Yohannes

Learn more about probabilities
brainly.com/question/32004014

#SPJ11

Answer:

4 packages of hot dog buns and 3 packages of hot dogs.

Step-by-step explanation:

Answer:

3 packages of hotdogs.

Step-by-step explanation:

Given that the equation of the line in the diagram is `y = 5 - x`. The line cuts the y-axis at P. So, the coordinates of point P are (0,5) and the gradient of the line is `-1`.

The equation of the line can be written as `y = -1x + 5`.Therefore, the y-intercept of the line is 5. Therefore, the coordinates of point P are (0,5).

To find the gradient of the line, we have to write the equation of the line in the form of `y = mx + c`.

We can rewrite `y = -1x + 5` as `y = (-1)x + 5`.From the above form of the equation, we can see that the gradient `m` is `-1`.Therefore, the gradient of line 1 is `-1`.Hence, the required answer is: Coordinates of point P is `(0,5)`.The gradient of the line is `-1`.

For more questions on: gradient

https://brainly.com/question/29578324

#SPJ8