For the following exercises, determine whether the relation is a function
a) {(5.2),(6,1),(6,2),(4,8)}​

1.904 mcg/kg/min is what the client receives.

The number of mcg/kg/minute = flow rate × concentration ÷ mass of client

Flow rate = 12 ml/ hour = 12 /60 = 1/5 = 0.2 ml/min

Formula:

Concentration = mass of dopamine/volume

mass of dopamine = 800mg

volume = 500ml

Concentration = 800/ 500

= 1.6 mg/ml

= 1.6 × 1000 mcg/mg

= 1600 mcg/mg

Here the mass of the client = 70kg

Now calculating mcg/kg/minute = flow rate× concentration÷ mass of client

= 0.08 ml/min × 1600mcg/ml ÷70 kg

= 320/70

= 1.904 mcg/kg/min

Therefore mcg/kg/min is 1.904.

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Answer:

6 months

Step-by-step explanation:

120 +10x = 204 - 4x

10x + 4x = 204 - 120

14x = 84

x = 6

Answer:

a.\(\frac{58}{78}\)

b. 20

c. \(\frac{20}{78}\)

Step-by-step explanation:

a. 58 of 78 are from state A

b. 78 minus 58 equals 20

c. 20 of 78 are found in states other than state A

The function graphed on the axes below as a piecewise function is,

⇒ y = 6 ; - 1 < x < -3

⇒ y = - x + 2 ;  x ≤ -4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The graph of function is shown in figure.

Here, The graph is a line for - 1 < x < -3 has the points;

⇒ ( - 1, 6) and ( 3, 6)

So, The equation of line passes through the points ( - 1, 6) and ( 3, 6).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (6 - 6) / (3 - (-1))

m = 0 / 4

m = 0

Thus, The equation of line with slope 0 is,

⇒ y - 6 = 0 (x - (-1))

⇒ y - 6 = 0

⇒ y = 6

Here, The graph is a line for  x ≤ -4 has the points;

⇒ ( - 4, -2) and ( -1, -5)

So, The equation of line passes through the points ( - 4, -2) and ( -1, -5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 - (-2)) / (- 1 - (-4))

m = - 3 / 3

m = - 1

Thus, The equation of line with slope -1 is,

⇒ y - (-2) = - 1 (x - (-4))

⇒ y + 2 = - 1 ( x + 4)

⇒ y + 2 = - x - 4

⇒ y = - x + 4 - 2

⇒ y = - x + 2

Thus, The function graphed on the axes below as a piecewise function is,

⇒ y = 6 ; - 1 < x < -3

⇒ y = - x + 2 ;  x ≤ -4

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Answer:

d

Step-by-step explanation:

Answer:

256 DIVIDE BY 8 THEN PLUS 1

Step-by-step explanation:

Probability is given by the expression:

Since, you are the first one to pick a block, the probability would be:

3/8, or 37.5% or 0.375. All that values are the same.

Answer:

the answer is 71

Step-by-step explanation:

423/6

42÷6=7

42-42=0

6÷3=×

30÷6=5

70.5--> 71

Rhines criterion implies that there is a minimum length scale for baroclinic instability to take place, which is given by:

L = 2π/kx = 2π[(N² - f₂²)/(f₁² - f₂²)]¹/²

In a 2-layer channel with a flat bottom and infinite width in y, the dispersion relation for baroclinic instability is given by:

ω = kx[(f₁² - f₂²)/(N² - f₂²)]¹/²

Where ω is the frequency, kx is the wavenumber in the x-direction, f₁ and f₂ are the Coriolis parameters for the upper and lower layers, and N is the buoyancy frequency.

In the presence of rotation, the minimum length for baroclinic instability to take place is determined by the condition that the frequency ω must be positive. This means that:

(f₁² - f₂²)/(N² - f₂²) > 0

or equivalently:

f₁ > (N²f₂)¹/²

This condition implies that the Coriolis parameter in the upper layer must be greater than the square root of the product of the buoyancy frequency and the Coriolis parameter in the lower layer. This is known as the "Rhines criterion" and represents a necessary condition for the development of baroclinic instability in rotating fluids.

Furthermore, the Rhines criterion implies that there is a minimum length scale for baroclinic instability to take place, which is given by:

L = 2π/kx = 2π[(N² - f₂²)/(f₁² - f₂²)]¹/²

This length scale represents the typical size of the eddies that form due to baroclinic instability in rotating fluids, and is proportional to the inverse square root of the difference between the Coriolis parameters in the upper and lower layers.

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Using the law of sins:

B =sin^−1((sin(A)⋅a)/b) = sin^−1((sin(65)⋅110)/155)=40.03 degrees

B= 40.03 degrees (round as needed)

Answer:

redoing as sum ans appears to be not right...

Step-by-step explanation:

1. Which function pass through the points (1, 4), (2, 9), and (3, 16)?

A.y = (x + 1)2

B.y = (x + 3)2

C.y = 7x - 5  

substitute x=1 n y=4, the only correct fn is A

2.Suppose that after swimming 1 lap in a pool, you can swim 10 laps in an hour. What is an equation that represents the total number of laps you have swam y in terms of the number of hours x?

A.y(x) = 10 + x

B.y(x) = 10(x + 1)

C.y(x) = 10x + 1

10 laps in an hour so in x hours , u swim 10x laps

total no. of laps, y=10x+1 where 1 is the initial lap already swum.

3.Is the following an arithmetic sequence? If so, what is the common difference? {4, 2, 0, -2, -4, -6, …}

Yes, d = -2

No

Yes, d = 2

each no is 2 smaller than the one before it: 2-4=0-2=-2-0=-2

so ans is yes, its an arith sequence n d = -2

Which function has the following graph?

a. y = -2x + 4  

b. y = 2x + 4  

c. y =12x + 4

no idea as there is no graph

What is the slope of the line containing (3, 5) and (2, 7)?

a. m = 2  

b. m = -2  

c. m = 125

slope, m = (7-5)/(2-3) = -2

The graph of a line passes through the point (-3, 2) and has a slope of 4. What is an equation of the line?

y = 4x - 10

y = 4x - 11

y = 4x+ 14

slope of 4 so the eqn is y = 4x + c

put x=2 n y=-3 into it,  -3 = 4(2) + c

c = -11

ans is y = 4x - 11

Which line is parallel to y = 4x - 2?

y = -14x + 3

y = -4x + 5

y = 4x + 5

y = 4x + 5 has the same slope i.e. parellel to y = 4x -2

Which system of equations has (2, 3) as a solution?

a. y = 2x - 1  

y = x + 1  

b. y = 2x + 1  

y = x - 1  

c. y = 4x - 5

y = 2x

put x=2 n y=3 in, the only eqns that fit are a.

The distance between the church and the art gallery is approximately 1102.19 meters, obtained using trigonometric calculations.

To find the distance between the church and the art gallery, we can use trigonometry and the information given about the angles of depression.

Let's assume that the distance between the church and the art gallery is x meters.

When the balloon is at a height of 900m, the angle of depression to the church is 28 degrees. This forms a right triangle with the height of the balloon (900m) as the opposite side and the distance to the church (x) as the adjacent side. Using trigonometry, we can find the adjacent side as x = 900 / tan(28°).

Similarly, when the balloon rises to a height of 1000m, the angle of depression to the art gallery is 19 degrees. Again, this forms a right triangle with the height of the balloon (1000m) as the opposite side and the distance to the art gallery (x) as the adjacent side. Using trigonometry, we can find the adjacent side as x = 1000 / tan(19°).

Now, we have two equations for x, obtained from the two different heights of the balloon. By solving these equations, we can find the value of x, which represents the distance between the church and the art gallery.

Using these calculations, the distance between the church and the art gallery is approximately 1102.19 meters.

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Answer:

Plot the points (3, 6), (−3, 6), (–3, 1), and (3, 1) on the coordinate plane. Then complete the sentences.

The first number in each pair of coordinates is the

✔ x-coordinate

.

The second number in each pair of coordinates is the

✔ y-coordinate

.

A

✔ rectangle

can be formed by connecting all four points.

Complete sentence is,

To plot the point, start at the origin. Move 3 units right and Move 6 units upwards to plot a point (3  6).

A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.

The given point is,

⇒  (3, 6).

Hence, The coordinate plane to plot the point (3, 6) is shown below.

To plot the graph of point (3, 6) on coordinate plane,

Thus, Complete sentence is,

Start at the origin. Move 3 units right and Move 6 units upwards to plot a point (3  6).

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Complete question,

Use the coordinate plane to plot the point (3, 6). Then complete the statements that explain how to plot the point. Start at the ____ Move 3 units ____ Move 6 units ____ Plot a point ____

Answer:

I think it's $50.18 I'm not sure . hope that I helped you .

True solution is a homogeneous mixture of two or more substances in which the particles of solute are dispersed uniformly throughout the solvent. An example of a true solution is a mixture of salt and water.

True solution is a type of homogeneous mixture in which the particles of solute ( the substance that is dissolved ) are dispersed uniformly throughout the solvent (the substance that is doing the dissolving). The particles of solute are too small to be seen with the eye and the mixture appears to be one single substance. An example of a true solution is a mixture of salt and water. The salt molecules are dispersed evenly throughout the water, producing a salty taste throughout the entire solution.

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If the interest is compounded continuously, an investment account with the same initial investment and the same APR will have the highest APY.

APY (Annual Percentage Yield) is the effective annual rate of return after compounding. The higher the APY, the more frequently the interest is compounded.

Compounding yields the highest APY because it effectively provides an infinite number of compounding periods. Compounding daily, monthly, or annually yields lower APYs than compounding continuously.

An investment account is a type of financial product that allows people to save or invest money in the hopes of earning a profit. Individual retirement accounts (IRAs), brokerage accounts, savings accounts, and other types of investment accounts are available.

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Answer: -12 x 4

Step-by-step explanation:

12 times 4 is 48

Rule: A negative multiplied by a positive, will always give you a negative.

So, -12 is a negative number and 4 is a positive number.

Negative x Positive = Negative

Positive x Negative = Negative

-12 x 4 = -48

Answer:

2 - \(\sqrt{52}\) and 2 + \(\sqrt{52}\)

Step-by-step explanation:

let the 2 numbers be x and y , then

x + y = 4 ( subtract x from both sides )

y = 4 - x → (1)

xy = - 48 → (2)

substitute y = 4 - x into (2)

x(4 - x) = - 48

4x - x² = - 48 ( multiply through by - 1 )

x² - 4x = 48

solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2) x + (- 2)² = 48 + (- 2)²

(x - 2)² = 48 + 4 = 52 ( take square root of both sides )

x - 2 = ± \(\sqrt{52}\) ( add 2 to both sides )

x = 2 ± \(\sqrt{52}\)

substitute this value into (1)

y = 4 - (2 ± \(\sqrt{52}\) ) = 4 - 2 ± \(\sqrt{52}\) = 2 ± \(\sqrt{52}\)

then the 2 numbers are

2 - \(\sqrt{52}\) and 2 + \(\sqrt{52}\)

Answer:

Nnnnnnnnnnnn

Step-by-step explanation:

L bozo

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.

From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:

585.43 + x - 302.05 ≥ 300

Collect like terms

x ≥ 300 - 585.43 + 302.05

x ≥ $16.62

She's needs to deposit at least $16.62.

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The spinner given in the question has four equal sections. The spinner can be used to play a board game where players take turns spinning and moving their game pieces based on the result of their spin.

Each section is colored differently, and each section has a label. The possible moves based on the spinner are - a) Move forward 2 spaces. b) Move forward 3 spaces. c) Move backward 1 space.d) Stay in the same position.So, the main answer is - all the given moves are valid based on the spinner. The spinner is divided into four equal sections, each with an equal chance of being selected. All four moves have an equal probability of being selected. Thus, it is a fair spinner and players can use it for their board games.

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First answer is:

150

Second answer is:

B. Is is the common difference.

Answer:

Results are below.

Step-by-step explanation:

It is not clear what the question is. But, I will assume that we need to calculate the future value of each investment at age 65.

First, we need to calculate the future value of the monthly deposit made by Ben. We will use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit= 500

Interest rate (i)= 0.11/12= 0.0092

Number of months (n)= (26 - 19)*12= 84

FV= {500*[(1.0092^84) - 1]} / 0.0092

FV= $62,944.74

Now, the future value of the investment of Ben at age 65:

FV= PV*(1 + i)^n

n= (65 - 26)*12= 468 months

FV= 62,944.74*(1.0092^468)

FV= $4,574,131.31

Finally, the future value of the investment for Arthur:

i= 0.0092

n= (65 - 27)*12= 456

A= 500

FV= {500*[(1.0092^456) - 1]} / 0.0092

FV= $3,484,032.07

\( \to \sf6x - 3(2x - 1)\)

\( \\ \\ \)

\( \to \sf6x - 6x + 3\)

\( \\ \\ \)

\( \to \sf0 + 3\)

\( \\ \\ \)

\( \to \sf 3\)

In geometry, there are several ways to prove that two triangles are congruent, which means that they have the same size and shape. Here are three common methods for proving triangle congruence SSS congruence, ASA congruence, and SAS congruence.

Side-Side-Side Congruence: If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent. This can be written as:

If AB = DE, AC = DF, and BC = EF, then ∆ABC ≅ ∆DEF

Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. This can be written as:

If ∠A = ∠E, ∠B = ∠F, and AC = EF, then ∆ABC ≅ ∆DEF

Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. This can be written as:

If AB = DE, ∠A = ∠E, and BC = EF, then ∆ABC ≅ ∆DEF

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7x - 2y = -4 (1)

-x - y = 7 (2)

To use the substitution method we will find y in the second equation

-x - y = 7 .......... add x to both sides

-x + x - y = 7 + x

-y = 7 + x ......... (3)

Substitute (3) in (1)

7x + 2(7 + x) = -4

7x + 2(7) + 2(x) = -4

7x + 14 + 2x = -4

Add the like terms

(7x + 2x) + 14 = - 4

9x + 14 = -4

Subtract 14 from both sides

9x + 14 - 14 = -4 - 14

9x

Probabilities are used to determine the chances of events

The probability of choosing a cat or dog is 1/2

The distribution of the animals is given as:

Dogs = 9

Cats = 6

Gerbils = 8

Parrots = 7

The number of cats or dogs is:

Cats or dogs = 6 + 9

Evaluate the sum

Cats or dogs = 15

There are 30 animals.

So, the probability that a selected animal is cat or dog is:

p = 15/30

Simplify

p = 1/2

Hence, the probability of choosing a cat or dog is 1/2

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A coach may use 240 different player combinations on the rink.

What are some permutation and combination examples?

The arrangement of people, numerals, numbers, alphabets, letters, and colors are a few examples of permutations.

Combinations include picking the meal, the cuisine, the attire, the subjects, and the team, for instance.

Forward 6C3 = 20

Defence 4C2 = 6

Golie 2C1 = 2

No. of possible Combination = 20 * 6 * 2 = 240

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The congruence theorem that justifies the similar triangles of triangles EFH and GFH is given as follows:

D. AAS.

For the triangles EFH and GFH in this problem, we have that:

These three features are used to identify the congruence theorem as follows.

Then the congruence theorem that justifies the similar triangles of triangles EFH and GFH is the Angle-Angle-Side theorem, given by option D, as:

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