Using direct substitution, verify that y(t) is a solution of the given differential equations 17-19. Then using the initial conditions, determine the constants C or c1 and c2.

17. y ′′ + 4y = 0, y(0) = 1, y ′ (0) = 0, y(t) = c1 cos 2t + c2 sin 2t

18. y ′′ − 5y ′ + 4y = 0, y(0) = 1, y ′ (0) = 0, y(t) = c1et + c2e4t

19. y ′′ + 4y ′ + 13y = 0, y(0) = 1, y ′ (0) = 0, y(t) = c1e-2t cos 3t + c2e-3tsin 3t

Answer:

$13847.30, Option B

Step-by-step explanation:

sold toys = 4694

average profit on each toy = $2.95

total profit in the three months = $2.95 * 4694 = $13847.30

Answer:

Total inventory: $175,000

Inventory in the stockroom: $35,000.

Inventory on the selling floor: $140,000.

Step-by-step explanation:

Let x be the the total inventory.

We have been given that in the Holiday Shop the manager wants 20% of the total inventory in the stockroom. You placed $35,000 of inventory in the stockroom.

We can set an equation such that 20% of x equals $35,000.

[tex]\frac{20}{100}\cdot x=\$35,000[/tex]

[tex]0.20x=\$35,000[/tex]

[tex]\frac{0.20x}{0.20}=\frac{\$35,000}{0.20}[/tex]

[tex]x=\$175,000[/tex]

Since $35,000 of inventory in the stockroom, so we will subtract $35,000 from $175,000.

[tex]\text{Amount of the inventory on the selling floor}=\$140,000[/tex]

Therefore, $140,000 of the inventory on the selling floor.

Final answer:

The probability that exactly 10 representatives from the first company and 12 from the second company will be chosen is about 1.288%, calculated using the hyper geometric probability formula.

Explanation:

The question asks for the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen to make presentations at an industry conference. This can be solved using the hypergeometric probability distribution since we are dealing with two groups and selections without replacement. The first group (G1) consists of 12 representatives from the first company, and the second group (G2) consists of 20 representatives from the second company.

The formula for calculating hyper geometric probability is:

[tex]P(X = k) = (C(G1, k) * C(G2, n - k)) / C(G1 + G2, n)[/tex]

Where:

To find the probability, we calculate:

[tex]P(X = 10) = (C(12, 10) * C(20, 12)) / C(32, 22)[/tex]

Plugging in the values gives us:

[tex]P(X = 10) = (C(12, 10) * C(20, 12)) / C(32, 22)[/tex]

= [tex](66 * 125,970) / 645,122,40[/tex]

=[tex]8,309,820 / 645,122,40[/tex]

=[tex]0.01288 or 1.288%[/tex]

Therefore, the probability that exactly 10 representatives from the first company and 12 from the second will be chosen is about 1.288%.

The probability that exactly 10 representatives from the first company and 12 from the second company will be chosen is approximately 0.0716%. This is calculated using the combination formula and the hypergeometric distribution.

We will use the concept of combinations and the hypergeometric distribution.

The total number of ways to select 22 representatives out of 32 (12 from the first company and 20 from the second company) is given by the combination formula  [tex]\( C(n, k) = \frac{{n!}}{{k!(n-k)!}} \)[/tex] . This reflects the entire sample space.

Therefore, the probability P is calculated as:

[tex]\[ P = \frac{{C(12,10) \times C(20,12)}}{{C(32,22)}} \][/tex]

Using a calculator or computing these values manually, we find:

C(12,10) = 66

C(20,12) = 125,970

C(32,22) = 1,166,803,110

Thus, the probability P becomes:

[tex]\[ P = \frac{{66 \times 125,970}}{{1,166,803,110}} \][/tex]

After computation, we get:

[tex]\[ P \approx 0.000716 \][/tex]

Therefore, the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen is approximately 0.000716, or 0.0716%.

Answer:

0

Step-by-step explanation:

4 - 2/2 - 3 =

Follow the correct order of operations. Start with the division.

= 4 - 1 - 3

Now do subtractions from left to right in the order they appear.

= 3 - 3

= 0

Answer: 0

Answer:

The final depth of Melissa is 14 meters below the surface

Step-by-step explanation:

In this kind of problems, involving directions, etc, usually one position is the positive direction and the other position is the negative direction.

In our problem, we suppose that the surface is the positivo zero, above the surface is the positive position(positive depth) and below the surface is the negative directions(negative depth).

The problem states that Melissa is 29 meters below the surface. So, her initial position is 29 meters in the negative direction, so it is equal to -29.

Then, the problem states that Melissa rises upward 15 meters. Upward is the positive direction, so she moved to the positive direction. It means that we are going to do -29+15 = -14 meters.

It means that the final depth of Melissa is 14 meters below the surface

Answer:

You should take 2 tablets of Aspirin.

Six tablets is not the correct dosage.

You should get 4 tablets.

Step-by-step explanation:

You wake up with a fever! All you can find at the store is Aspirin, and the bottle says to take 162 mg. The bottle also says each tablet has 81 mg in each tablet. How many tablets should you take?

This can be solved by this following rule of three.

1 tablet - 81mg

x tablets - 162mg

[tex]81x = 162[/tex]

[tex]x = \frac{162}{81}[/tex]

[tex]x = 2[/tex]

You should take 2 tablets of Aspirin.

The doctor orders 120 mg of medicine to be given twice a day. The nurse comes in with 6 tablets and tells you that there are 30 mg in each tablet. Is this the correct dosage?

We need to see how many mg are in 6 tablets. If there are 120mg in 6 tablets, this is the correct dosage. We verify this by the following rule of three:

1 tablet - 30mg

6 tablets - x mg

[tex]x = 30*6[/tex]

[tex]x = 180[/tex]mg.

In 6 tablets, there are 180mg. So, it is not the correct dosage.

If not, how many tablets should you get?

Knowing that each tablet has 30mg, in how many tablets are there 120mg?

1 tablet - 30 mg

x tablets - 120 mg

[tex]30x = 120[/tex]

[tex]x = \frac{120}{30}[/tex]

[tex]x = 4[/tex]

You should get 4 tablets.

Answer:

we are applying 70 ml during the whole day

Step-by-step explanation:

First, it is necessary to calculate the percentage of the drug that is left in the evening. This is calculated as:

100% - (35% + 25%) = 100% - 60% = 40%

Because,  35% is the percentage of the drug apply at the morning and 25% is percentage of the drug apply at afternoon.

Then, 40% is the percentage of the drug that is left in the evening and it is equivalent to 28 mL. So, the milliliter that we apply during the whole day are the milliliters equivalent to the 100%. We can calculate this by a rule of three as:

40% -------------------- 28 mL

100% -------------------    X

Where X are the milliliters that we apply during the whole day. Solving for X, we get:

[tex]X=\frac{100*28}{40}=70 mL[/tex]

Answer:

The first one: It is in the 500,000 place.

The second one: It is in the 50 place.

Step-by-step explanation:

Answer:

About 139,764,705.9 users were added, on average, per year, from 1995 to 2012.

Step-by-step explanation:

The problem states that in june 2012, about 2.4 billion people used the internet - 100 times more than the number of people who used it in June 1995.

So, in June 2012, 2.4 billion people used the internet.

In June 1995, [tex]\frac{2,400,000,000}{100} = 24,000,000[/tex] = 24 million people used the internet.

About how many people were added on average each year from 1995 to 2012?

[tex]2012 - 1995 = 17[/tex]. There were 17 years between 1995 and 2012.

[tex]2,400,000,000 - 24,000,000 = 2,376,000,000[/tex]. There were  2,376,000,000 internet users added during this 17-year period. To find this number per year, we solve the following rule of three:

1 year - x users

17 years - 2,376,000,000 users

[tex]17x = 2,376,000,000[/tex]

[tex]x = \frac{2,376,000,000}{17}[/tex]

[tex]x = 139,764,705.9[/tex]

About 139,764,705.9 users were added, on average, per year, from 1995 to 2012.

Answer:

If you purchase it, you will save 16.67% of the original price.

Step-by-step explanation:

Percentage problems can be solved as a simple rule of three problem:

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

A percentage problem is an example where the relationship between the measures is direct.

The problem states that the model you really like happens to be on sale for $1200 and it's original price is $1400. It means the you saved $1400-$1200 = $200. Thus, the problem wants to know how much $200 is of $1200. So, we have the following rule of three

$1200 - 100%

200 - x%

1200x = 200*100

[tex]x = \frac{20000}{1200}[/tex]

x = 16.67%.

If you purchase it, you will save 16.67% of the original price.

Answer:

The EMV of this project is -17,500

Step-by-step explanation:

The EMV of the project is the Expected Money Value of the Project.

This value is given by the sum of each expected earning/cost multiplied by each probability.

So, in our problem

[tex]EMV = P_{1} + P_{2} + P_{3} + P_{4}[/tex]

The problem states that there is a 25% chance of Snowmaggedon which will delay the project at a cost of $35,000. Since this is a cost, [tex]P_{1}[/tex] is negative.

[tex]P_{1} = 0.25*(-35,000) = -8,750[/tex]

There is a 10% chance of cost of construction materials dropping saving the project $70,000. A saving is an earning, so [tex]P_{2}[/tex] is positive

[tex]P_{2} = 0.10*70,000 = 7,000[/tex]

There is a 10% probability a labor strike will occur delaying the schedule with a cost of $40,000.

[tex]P_{3} = 0.10*(-40,000) = -4,000[/tex]

There is a 80% chance of new regulations mandated calling for higher inspection standards which will cost an additional $15,000 to mitigate

[tex]P_{4} = 0.80*(-15,000) = -12,000[/tex]

[tex]EMV = P_{1} + P_{2} + P_{3} + P_{4} = -8,750 + 7,000 - 4,000 - 12,000 = -17,500[/tex]

The EMV of this project is -17,500

Answer:

infinitely many

Step-by-step explanation:

there were too many lines

Answer:

The correct option is D) Infinitely many.

Step-by-step explanation:

Consider the provided graph.

The system of equation has the solution at the point where the line intersects.

Now consider the graph of the equation 2x = 2y-6 and y = x+3

By observing the graph it can be concluded that the graph of 2x = 2y-6 and y = x+3 has the same line.

A system of equation have infinitely many solutions if each equations refers to the same line.

Since 2x = 2y-6 and y = x+3 refer the same line. The system has infinitely many solutions.

Hence, the correct option is D) Infinitely many.

Answer:

2

Step-by-step explanation:

Rewriting the expression we have:

[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}[tex]

Then we have the next step by step solution, starting by the insider parentheses:

[tex]\dfrac{\dfrac{[(2\times 4)\times 3]}{12}\times(2\times 6)}{12}=\dfrac{\dfrac{[8\times 3]}{12}\times(12)}{12}=\dfrac{\dfrac{24}{12}\times(12)}{12}=\dfrac{2\times(12)}{12}=\dfrac{24}{12}=2[/tex]

Answer:

1) 35 distinct groups can be formed.

2) 18  distinct groups can be formed containing 2 men and 1 woman.

Step-by-step explanation:

The no of groups of 3 members that can be chosen from 7 members equals no of combinations of 3 members that can be formed from 7 members.

Thus no of groups =

[tex]n=\binom{7}{3}=\frac{7!}{(7-3)!\times 3!}=35[/tex]

thus 35 distinct groups can be formed.

Part b)

Now since the condition is that we have to choose 2 men and 1 women to form the group

let A and B be men member's of group thus we have to choose 2 member's from a pool of 4 men which equals

[tex]\binom{4}{2}=\frac{4!}{(4-2)!\times 2!}=6[/tex]

Let the Woman member be C thus we have to choose one woman from a pool of 3 women hence number of ways in which it can be done equals 3.

thus the group can be formed in [tex]6\times 3=18[/tex] different ways.

Answer:

  all except 5/6

Step-by-step explanation:

All of the numbers listed are in the set of integers, except for the fraction 5/6. It is a rational number, but not an integer.

___

If by "part of integers" you mean that the number can be multiplied by some integer value to make an integer, then 5/6 is "part of 5". It is 1/6 of the integer 5.

If 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained.

The appropriate conclusion is that if 57% of the houses take more than three months to sell, there is a 2.6% chance that a random sample proportion would be as high as or higher than the one they obtained. This means that the result is statistically significant, indicating that the proportion of houses that take more than three months to sell is likely higher than 57%.

Answer:

0 is not an element of an empty set.

Step-by-step explanation:

We are asked to determine whether 0 is not an element of an empty set.

We know that an empty set is an unique set having no elements. The cardinality of an empty set is 0.

Cardinality stands for the count of element is an set. An empty set is denoted by symbols ∅ or { }.

The empty set is like an empty container. The container is there, but nothing is in it.

When 0 is an element of a set, then its cardinality would be 1.

Therefore, 0 is not an element of an empty set.

Answer:

A boxplot offers us information that can be used to compare two variables. In particular, if one variable is quantitative and the other variable is qualitative, a boxplot is generated for each category of the qualitative variable. Therefore, through this graph it is possible to analyze the relationship between the amount of money spent on food and the gender of the person.

A circular diagram offers information for a single variable, especially of a qualitative type.

A histogram offers us information for a single variable, especially quantitative type.

A relational analysis between two variables could be done using options (D) or (E), however one of the variables of interest is of qualitative type and the other is of quantitative type, so the scatterplot and the two-way table.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:  

We are going to take 4 of the 5 even numbers in the box so we have

[tex]5C4=5[/tex]

Case 2: When all 4 numbers are odd:  

We are going to take 4 of the 5 odd numbers in the box, so we have

[tex]5C4=5[/tex]

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

[tex]5C2 * 5C2[/tex]

Remember that we obtain the probability from

[tex]\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}[/tex]

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:  

We are taking 4 of the 10 cards:

[tex]10C_4=210[/tex]

Hence we have that the probability that their sum is even

[tex]\frac{5+5+100}{210}=\frac{11}{21}[/tex]

Final answer:

To find the probability that the sum of the four cards drawn is even, we can break down the problem into two cases: drawing all four even-numbered cards or drawing two even-numbered cards and two odd-numbered cards. Using the multiplication rule, we calculate the probability for each case and add them together to get the total probability.

Explanation:

Total Number of Possible Outcomes: If we draw four cards from a box containing cards numbered 1 to 10, the total number of ways to do this is given by the combination formula,

resulting in  10!/4!(10-4)! = 210 possible outcomes.

Number of Ways to Get an Even Sum:

For the sum of the numbers on the four drawn cards to be even, there are two cases to consider:

1. All four cards have even numbers: There are 5 even-numbered cards out of 10, and we need to choose 4 of them. The number of ways to do this is  =5.

2. Three cards have odd numbers, and one card has an even number:

   There are 5 odd-numbered and 5 even-numbered cards.

   We need to choose 3 odd-numbered cards out of 5 and 1 even-  numbered card out of 5.

  The number of ways to do this is =50

Total Number of Ways for an Even Sum:

Adding the possibilities from both cases, we have a total of 5 + 50 = 55 ways to get an even sum.

The probability is then calculated as the ratio of the number of ways to get an even sum to the total number of possible outcomes:

Probability = Number of Ways to Get an Even Sum/Total Number of Possible Outcomes = 55/210= 11/42

Therefore, the probability that the sum of the numbers on the four drawn cards is even is 11/42.

Answer:

The minimum value of objective function is 5 at x=0 and y=5.

Step-by-step explanation:

The given linear programming problem is

Minimize [tex]z=4x+y[/tex]

Subject to  constraints

[tex]2x+4y\geq 20[/tex]         .... (1)

[tex]3x+2y\leq 24[/tex]          .... (2)

[tex]x,y\geq 0[/tex]

The related line of both inequalities are solid lines because the sign of inequalities are ≤ and ≥. It means the points lie on related line are included in the solution set.

Check both inequalities by (0,0).

[tex]2(0)+4(0)\geq 20[/tex]

[tex]0\geq 20[/tex]

This statement is not true. So, the shaded region of inequality (1) will not contain the origin.

[tex]3(0)+2(0)\leq 24[/tex]

[tex]0\leq 24[/tex]

This statement is true. It means the shaded region of inequality (2) will contain the origin.

[tex]x,y\geq 0[/tex] means first quadrant.

The common shaded region is feasible region. The vertices of feasible region are (0,5), (0,12) and (7,1.5).

Calculate the value of objective function at these vertices.

For (0,5)

[tex]z=4(0)+(5)=5[/tex]

For (0,12)

[tex]z=4(0)+(12)=12[/tex]

For (7,1.5)

[tex]z=4(7)+(1.5)=29.5[/tex]

Therefore the minimum value of objective function is 5 at x=0 and y=5.

Answer:

The value of x is [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Given,

[tex]\frac{1}{250}:2=\frac{1}{150}:x[/tex]

[tex]\frac{1/250}{2}=\frac{1/150}{x}[/tex]

[tex]\frac{1}{500}=\frac{1}{150x}[/tex]

By cross multiplication,

[tex]150x = 500[/tex]

[tex]x=\frac{500}{150}=\frac{500\div 50}{150\div 50}=\frac{10}{3}[/tex]

Answer:

  C)  [tex]\dfrac{2}{3}(6+s)[/tex]

Step-by-step explanation:

The distributive property lets you factor out the common factor of 2/3. The result is ...

   [tex]\dfrac{2}{3}(6+s)[/tex]

The expression  [tex]\(2\cos^2(\theta) - 1\)[/tex] where θ is the lowercase Greek letter theta gives [tex]cos(\theta) = \pm 1/ \sqrt (2)[/tex].

The expression is [tex]\(2\cos^2(\theta) - 1\)[/tex].

Explanation:

1. 2: This is a coefficient that scales the result of the trigonometric function [tex]\(\cos^2(\theta)\)[/tex]. It simply doubles the value of the cosine squared term.

2. [tex]\(\cos^2(\theta)\)[/tex]: This is the square of the cosine of the angle [tex]\(\theta\)[/tex].

The cosine function cos takes an angle as input and returns the ratio of the adjacent side to the hypotenuse in a right triangle with that angle.

3. -1: This is a constant that is subtracted from the result of [tex]\(2\cos^2(\theta)\)[/tex]. Subtracting 1 shifts the trigonometric value downward by one unit on the y-axis.

Add 1 to both sides

[tex]2cos^2(\theta) =1[/tex]

Divide by 2 on both sides

[tex]cos^2(\theta) =1/2[/tex]

Take the square root of both sides

[tex]cos(\theta) = \pm 1/ \sqrt (2)[/tex]

Learn more about Trigonometry here:

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The expression in question pertains to the conservation of momentum in physics, where trigonometric identities can simplify the calculation of particle velocities and directions after a collision. The included equations and concepts such as the conservation of momentum along an axis and the Pythagorean Theorem are essential components for solving problems in high school physics.

The expression 2cos2(θ)−1, where θ is the lowercase Greek letter theta, can be related to conservation of momentum in physics problems, particularly when analyzing collisions in two dimensions. Using trigonometric identities, such as tan θ = sin θ / cos θ, can be a useful technique in simplifying expressions and solving for unknown variables in mechanical physics.

In the context of conservation of momentum, equations may involve cosines and sines of angles representing the directions of particle velocities before and after a collision. For instance, if the scenario requires that the momentum along the x-axis be conserved, substituting sin θ / tan θ for cos θ could lead to simplifications where terms cancel out. A condition such as μ v2 cos(θ1−θ2)= 0 might imply that either the coefficient of friction μ is zero or the velocity component along the x-axis is zero, hence no momentum is transferred in that direction.

It is important to note that inverting mathematical functions is a common approach to solving equations in physics. Like in trigonometry, it may be necessary to 'undo' a function to isolate a variable, as shown in the example involving the Pythagorean Theorem to solve for side length of a triangle.

Answer:

151.

Step-by-step explanation:

50th or Fiftieth Ordinal numbers are just numbers that identify the order of things: Thus having 151 coming before 152.

The ordinal number just before 152nd is 151st.

The ordinal number just before 152nd is 151st. Ordinal numbers are used to indicate position or order, and they are formed by adding the suffix '-st' to the cardinal number. In this case, the cardinal number 152 is changed to the ordinal number 152nd by adding '-nd' suffix. To find the ordinal number just before 152nd, we go one step back and change the '-nd' suffix to '-st', resulting in 151st.

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Answer:

5mL would be required to provide a patient with 0.25 mg of the drug substance.

Step-by-step explanation:

The problem states that an injectable solution contains 25μg of a dug substance in each 0.5 mL, and asks how many milliliters would be required to provide a patient with 0.25 mg of the drug substance.

So, the first step is the conversion of 25ug to mg, since the problem asks the answer in mg.

Each mg has 1000ug. So

1mg - 1000ug

xmg - 25ug

1000x = 25

[tex]x = \frac{25}{1000}[/tex]

x = 0.025 mg

It means that each 0.5mL of the solution contains 0.025mg of the drug. How many milliliters would be required to provide a patient with 0.25 mg of the drug substance.

0.5mL - 0.025mg

xmL - 0.25mg

0.025x = 0.5*0.25

[tex]x = \frac{0.5*0.25}{0.025}[/tex]

x = 10*0.5

x = 5mL

5mL would be required to provide a patient with 0.25 mg of the drug substance.

Final answer:

To provide a patient with 0.25 mg of a drug substance, 5 mL of the injectable solution is required when the solution concentration is 25μg per 0.5 mL.

Explanation:

If an injectable solution contains 25μg of a drug substance in each 0.5 mL, the question asks how many milliliters would be required to provide a patient with 0.25 mg of the drug substance. First, it is important to convert 0.25 mg to micrograms (μg) because the concentration of the drug is given in micrograms. Knowing that 1 mg = 1000 μg, we have:

0.25 mg = 0.25 × 1000 μg = 250 μg.

Next, if 25 μg is in 0.5 mL, we find how many times 25 μg goes into 250 μg to determine the volume needed:

250 μg / 25 μg/mL = 10 times

Since 25 μg is contained in 0.5 mL:

10 × 0.5 mL = 5 mL.

Therefore, 5 mL of the injectable solution is required to provide a patient with 0.25 mg of the drug substance.

Answer:

The area is given by the following integral: [tex]\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx[/tex], which can be approximated by: 0.265313

Step-by-step explanation:

A normal distribution is defined as:

[tex]f(x)=\frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}[/tex]

, where the greek letter sigma stands for the standard deviation and mu for the mean. Since in our problem we have a mean = 31.5 and a standard deviation = 11, then we can write this function as:

[tex]f(x)=\frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}}[/tex]

Now, we need to find the area below this function, between 35 and 45, and in order to do this, we need to integrate the function. The normal distribution does not has an exact closed form integral, therefore we will have to solve the integral in a software that allows for numerical calculations (I used the online software Wolfram|Alpha).

[tex]\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx =0.265313[/tex]

Answer:

The nurse should set the IV pump to deliver 125 ml/hr.

Step-by-step explanation:

The problem states that a nurse is preparing an IV pump to administer 250ml over 2 hours. So how many ml should be administered each hour?

This problem can be solved by this following rule of three.

250 ml - 2 hours

x ml -  1 hours

[tex]2x = 250[/tex]

[tex]x = \frac{250}{2}[/tex]

[tex]x = 125[/tex]ml.

The nurse should set the IV pump to deliver 125 ml/hr.

To determine the intermittent IV infusion rate, divide the total volume of the fluid (dextrose 5% water) by the total time of infusion. Here, it would be 250 ml divided by 2 hours, which equals 125 ml per hour.

To determine how many ml per hour a nurse should set the IV pump to deliver dextrose 5% water (D5W), you should divide the total volume by the total time. In this case, the total dextrose volume is 250 ml and it should be infused over 2 hours. Using the formula:

So, the nurse should set the IV pump to deliver 125 ml per hour of dextrose.

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Answer:

In order to maximize the profit pairs of pants jackets, the manufactures should make 6 pants and 3 jackets.

Step-by-step explanation:

This problem can be solved by a system of first order equations:

I am going to say that [tex]x[/tex] is the number of pants and [tex]y[/tex] is the number of jackets that the manufacturer should make.

The profit will be maximized when all the avaiable time of the sewing operator and the cutter time has been used.

The problem states that there are 60 minutes of sewing operator time available. It takes 8 minutes to sew one pair of ski pants and 4 minutes to sew one jacket. So:

[tex]8x + 4y = 60[/tex]

We can simplify this equation by 4. So:

[tex]2x + y = 15[/tex]

The problem also states that there are 48 minutes of cutter time available. Cutters take 4 minutes on pants and 8 minutes on a jacket. So:

[tex]4x + 8y = 48[/tex]

Again simplifying by 4,

[tex]x + 2y = 12[/tex].

Now we have to solve the following system:

[tex]2x + y = 15[/tex]

[tex]x + 2y = 12[/tex]

I am going to write y as a function of x in the first equation, and replace it in the second.

[tex]y = 15 - 2x[/tex]

[tex]x + 2y = 12[/tex]

[tex]x + 2(15 - 2x) = 12[/tex]

[tex]x + 30 - 4x = 12[/tex]

[tex]-3x = -18[/tex]

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3}[/tex]

[tex]x = 6[/tex]

Now, replacing

[tex]y = 15 - 2x = 15 - 2(6) = 15 - 12 = 3[/tex]

In order to maximize the profit pairs of pants jackets, the manufactures should make 6 pants and 3 jackets.

Answer:

d = 6 sin(2π/7 t + 3π/2)

Step-by-step explanation:

Equation for simple harmonic motion is:

d = A sin(2π/T t + B) + C

where A is the amplitude,

T is the period,

B is the horizontal shift (phase shift),

and C is the vertical shift.

Given that A = 6, T = 7, and C = 0:

d = 6 sin(2π/7 t + B)

At t = 0, the buoy is at d = -6:

-6 = 6 sin(2π/7 (0) + B)

-1 = sin(B)

3π/2 = B

d = 6 sin(2π/7 t + 3π/2)

Notice you can also use cosine instead of sine and get a different phase shift.

d = 6 cos(2π/7 t + π)

You can even use phase shift properties to simplify:

d = -6 cos(2π/7 t)

Any of these answers are correct.

The equation modeling the displacement d of the buoy as a function of time is d(t) = 6 * sin(2π/7 * t) - 6.

To model the displacement d of the buoy as a function of time t, we can use the equation:

d(t) = A * sin(2π/T * t) + C

where A is the amplitude, T is the period, t is the time, and C is the vertical displacement at t = 0 seconds.

In this case, the amplitude A is 6ft, the period T is 7 seconds, and the vertical displacement at t = 0 seconds C is -6ft and the buoy initially moves upward. Therefore, the equation modeling the displacement as a function of time is:

d(t) = 6 * sin(2π/7 * t) - 6

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Answer:

The equation does not have a real root in the interval [tex]\rm [0,1][/tex]

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if [tex]f[/tex] is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in [tex]\rm [0,1][/tex], which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval [tex]\rm [0,1][/tex], which means to evaluate the equation in 0 and 1:

[tex]f(x)=x^3-3x+8\\f(0)=8\\f(1)=6[/tex]

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval [tex]\rm [0,1][/tex]. I attached a plot of the equation in the interval [tex]\rm [-2,2][/tex] where you can clearly observe how the graph does not cross the x-axis in the interval.