suppose that r and y are both differentiable functions of t and are related by the given equation. Use implicit
differentiation with respect tot to determine dy/dt in terms of x,y and dx/dt A. X^2+y^2 = 1
B. 3xy - 3x^2 = 4

Answer:

Step-by-step explanation:

x=57

y=57

z=66

The delivery rate for Famotidine should be set at 2/3 mL/min.

To determine the delivery rate for each scenario, we can use the formula:

Delivery rate = Volume / Time

1. Cefazolin:

Given:

- Dose: 1000 mg

- IV fluid volume: 50 mL

- Infusion time: 30 minutes

Using the formula, the delivery rate for Cefazolin will be:

Delivery rate = 50 mL / 30 min

Simplifying:

Delivery rate = 5/3 mL/min

So, the delivery rate for Cefazolin should be set at 5/3 mL/min.

2. Famotidine:

Given:

- Dose: 20 mg

- IV fluid volume: 10 mL

- Infusion time: 15 minutes

Using the formula, the delivery rate for Famotidine will be:

Delivery rate = 10 mL / 15 min

Simplifying:

Delivery rate = 2/3 mL/min

So, the delivery rate for Famotidine should be set at 2/3 mL/min.

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Answer:

\(y<-2x+6\)

Step-by-step explanation:

The boundary line of a linear inequality passes through the points (3, 0) and (0, 6).

The points (3, 0) and (2, 6) are not solutions of the inequality.

We want to find the equation of the linear inequality.

First, we will simply find the line that crosses the points (3, 0) and (0, 6).

We can determine the slope to be:

\(\displaystyle \frac{6-0}{0-3}=\frac{6}{-3}=-2\)

Notice that (0, 6) is the y-intercept.

Then by the slope-intercept form:

\(y=mx+b\)

Our equation will be:

\(y=-2x+6\)

Now, we will need to determine our inequality sign.

First, (3,0) is on the boundary line yet it is not a solution. Therefore, our line is dotted. That is: we do not have the "or equal to" statement.

So, our inequality signs can only be either < or >.

We are given that (2, 6) is not a solution.

So, we can test for the sign. Substitute 2 for x and 6 for y:

\(\displaystyle 6\text{ }?\text{ }-2(2)+6\)

Evaluate:

\(\displaystyle 6\text{ } ?\text{ } 2\)

Since 6 is not a solution, the above statement needs to be false.

It will be false is the sign is <, since 2 is not greater than 6.

Therefore, our sign is <.

And our inequality is:

\(y<-2x+6\)

Answer:

75 cu in

Step-by-step explanation:

the formula for volume is V = l w h (volume equals length times width times height) and can also be written V = B h (volume equals the area of the base times the height). Notice that the version, V = l w h is only true for rectangular prisms and cubes.

V = L x W x H

V = 5 x 5 x 3

V = 75

Answer: 75 in³

Step-by-step explanation:

    We will use the given formula to solve for volume by substituting and multiplying.

V = LWH

V = (5 in)(5 in)(3 in)

V = 75 in³

A 34_46_37_3÷56×34÷77+34

Answer:

Step-by-step explanation:

Candice = 25mph for 4 hours.

Candice has driven= 25 * 4= 100miles.

Liz =50mph

Liz time to catch up to candice= 50 * 2= 100miles.

Therefore, It would have taken Liz two hours to catch up with Candice

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Step-by-step explanation:

I'm sorry, but the statement you provided is not correct. The transitive property of angle congruence actually states that if ∠QRS ≅ ∠PQR and ∠PQR ≅ ∠XYZ, then ∠QRS ≅ ∠XYZ. In other words, if two angles are congruent to a third angle, then they are congruent to each other.

So, in your statement, if ∠QRS ≅ ∠PQR and ∠PQR ≅ ∠XYZ, then you can conclude that ∠QRS ≅ ∠XYZ.

The height of the container if it's a cylinder with a radius of 3 cm is 5 cm.

The cost of coffee is $2.83.

The height of the container if it's a cylinder with a radius of 5 cm is 1.8 cm.

The cost of hot chocolate powder is $9.90.

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Picking a volume of 45π cm³, the height of this container is given by:

h = V/πr²

Height, h = 45π/π3²

Height, h = 5 cm.

For the cost of coffee, we have:

Cost of coffee = 45π cm³ × $0.02

Cost of coffee = $2.83.

When the radius is 5 cm, the height of this container is given by:

h = V/πr²

Height, h = 45π/π5²

Height, h = 1.8 cm.

For the cost of hot chocolate powder, we have:

Cost of hot chocolate powder = 45π cm³ × $0.07

Cost of hot chocolate powder = $9.90.

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Answer:

1.25p

p+0.25p

Step-by-step explanation:

Answer:

f(x) = -2cos(1/3 x) + 4

Step-by-step explanation:

f(x) ≥ 0 over the interval [-1,1]. This can be solved by using the concept of function.

Local maxima are the points in the interval where the values of the function are always fewer than the values of the function at those points. Local minima, on the other hand, are locations where the function's values around that point are higher than its value there.

At the point when the graph of the function y = f(x) shifts from growing to decreasing, there is a local maximum. The slope of the tangent is 0 at this location. At the point when the graph switches from dropping to growing, there is a local minimum.

The ordered pairs of the given function in table are (-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It is clear from the values of f(x) with respect to x, that the function reaches zero at x = -1, then goes up to 5 at x = 0 and then again reaches zero at

x = 1.

Hence, the value of f(x) remains positive within the interval of [-1,1].

Hence, we can write f(x) ≥ 0 over the interval [-1,1].

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To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .

To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.

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To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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C. A chain-style franchise is a type of franchise where the franchisee produces and sells a franchisor's product using the franchisor's name.

The franchisee operates under the franchisor's established system and business model, including marketing strategies, training programs, and support services. This type of franchise is also known as a product distribution franchise because the franchisee distributes the franchisor's product to customers within a specified territory.

In a chain-style franchise, the franchisor maintains control over the quality and consistency of the product, while the franchisee is responsible for the day-to-day operations of the business. Examples of chain-style franchises include fast-food restaurants, gas stations, and retail stores.

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Answer:

BE = 3.5 m

Step-by-step explanation:

Δ ACB and Δ EDB are similar, so the ratios of corresponding sides are equal, that is

\(\frac{BE}{BA}\) = \(\frac{BD}{BC}\) , substitute values

\(\frac{BE}{21}\) = \(\frac{3}{18}\) ( cross- multiply )

18 BE = 63 ( divide both sides by 18 )

BE = 3.5

The Maximum Independent Set is {3, 4, 6}, the Minimum Vertex Cover is {2, 3, 4, 6} and the Maximum Clique in the following graph is {3, 4, 6}.

Maximum Independent Set:

An independent set of a graph is a set of vertices such that no two vertices are adjacent to each other. The maximum independent set is a set with the highest possible number of vertices in the graph that satisfies this condition.

The maximum independent set of the given graph is {3, 4, 6}.

Minimum Vertex Cover:

A vertex cover is a set of vertices that covers all edges in the graph. The minimum vertex cover is the smallest set of vertices that can achieve this.

The minimum vertex cover of the given graph is {2, 3, 4, 6}.

Maximum Clique:

A clique is a set of vertices in a graph such that every vertex in the set is adjacent to every other vertex in the set. The maximum clique is the largest clique in the graph.

The maximum clique of the given graph is {3, 4, 6}.

Hence, the Maximum Independent Set is {3, 4, 6}, the Minimum Vertex Cover is {2, 3, 4, 6} and the Maximum Clique is {3, 4, 6}.

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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Answer:

b.79

Step-by-step explanation:

if you look at the graph it shows its right below 80

The 79 customers are predicted to use a card to pay on a day when 90 customers pay by cash option (B) is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)

We have a line of best fits:

y = 0.755x + 11.339

Plug x = 90

y =0.755(90) + 11.339

y = 67.95 + 11.339

y = 79.28 ≈ 79

Thus, the 79 customers are predicted to use a card to pay on a day when 90 customers pay by cash option (B) is correct.

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Answer:

y = -3

Step-by-step explanation:

y = x - 7

when x = 4

y = 4 - 7

y = -3

Answer:

See below.

Step-by-step explanation:

If x is 4, then replace x with 4 and simplify.

y=4-7

y=-3

-hope it helps

Answer:

13.5*43=580.5

580.5/1=580.5

Bsically the answer would be 581 titles

Step-by-step explanation:

The answers to all the subparts are:

So, (A) To make the same shade of green:

Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5

Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.

(B) New pair of numbers to make the same green shade:

Old pair:

Another pair:

The new pair would be:

Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.

(C) Proportional relationship:

Old pair:

Proportional relationship will be:

Therefore, the proportional relationship of the table will be x : 5y.

(D) Constant of proportionality:

According to part (C), the Constant of proportionality will be x : 5y.

Therefore, the answers to all the subparts are:

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Answer:

Step-by-step explanation:

Yes

Answer:

a = 0.20 m/s²

Step-by-step explanation:

F = 3 N

m = 15 kg

F = m * a

find mass m:

3 = 15 * a

a = 3 / 15

a = 0.20 m/s²

Step-by-step explanation:

omg it actually got seven lol

Answer:

The answer is (x-6) squared

Answer:

The awnser to this equation is 120 cents

The cost of using a 200-watt television for 30 days, turned on for 2 hours per day, would be $1.20.  

To calculate the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour, we need to find the total energy consumption and then multiply it by the cost per kilowatt-hour.

First, let's find the total energy consumption:

1. Daily energy usage: 200 watts * 2 hours = 400 watt-hours
2. Monthly energy usage: 400 watt-hours * 30 days = 12,000 watt-hours

Now, we need to convert watt-hours to kilowatt-hours:
3. Monthly energy usage in kilowatt-hours: 12,000 watt-hours / 1,000 = 12 kWh

Finally, let's calculate the cost:
4. Cost of using the television for 30 days: 12 kWh * 10 cents per kWh = 120 cents

So, the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour is 120 cents.

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The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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a) The present value of $25,000 due 9 periods from now, discounted at 10%, is approximately $10,593.22.

b) The present value of $25,000 to be received at the end of each of 6 periods, discounted at 9%, is approximately $22,935.35.

(a) Present Value of $25,000 due 9 periods from now, discounted at 10%:

To calculate the present value, we need to discount the future cash flow of $25,000 back to its current value using the given discount rate of 10%. The formula to calculate the present value is:

Present Value = Future Value / (1 + Discount Rate)ⁿ

Where:

Future Value is the amount to be received in the future ($25,000).

Discount Rate is the rate at which we discount the future cash flow (10%).

'n' is the number of periods or years until the future cash flow is received (9 periods in this case).

Let's plug in the values into the formula and calculate the present value:

Present Value = $25,000 / (1 + 0.10)⁹

Calculating the denominator:

(1 + 0.10)⁹ = 1.10⁹ ≈ 2.36

Present Value = $25,000 / 2.36 ≈ $10,593.22

(b) Present Value of $25,000 to be received at the end of each of 6 periods, discounted at 9%:

In this case, we have a cash flow of $25,000 to be received at the end of each of 6 periods, discounted at 9%. Let's calculate the present value:

Present Value = $25,000 / (1 + 0.09)¹ + $25,000 / (1 + 0.09)² + ... + $25,000 / (1 + 0.09)^6

Calculating each discount factor:

(1 + 0.09)¹ ≈ 1.09

(1 + 0.09)² ≈ 1.1881

(1 + 0.09)³ ≈ 1.2950

(1 + 0.09)⁴ ≈ 1.4116

(1 + 0.09)⁵ ≈ 1.5386

(1 + 0.09)⁶ ≈ 1.6765

Plugging in the values and summing them up:

Present Value = $25,000 / 1.09 + $25,000 / 1.1881 + $25,000 / 1.2950 + $25,000 / 1.4116 + $25,000 / 1.5386 + $25,000 / 1.6765

Present Value ≈ $22,935.35

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