What is the following product?
√12 √18
O√30
O 5√6
O 6√5
O 6√6

The mass of the drug in the organ at time t depends on the concentration of the drug in the blood entering the organ and the rate at which the blood is entering and leaving the organ. This can be calculated by multiplying the volume of the organ by the concentration of the drug in the blood.

At time t, since the rate at which the blood is entering and leaving the organ is 3 cm^3/sec, the amount of drug in the organ is equal to the amount of drug entering the organ plus the amount of drug that was initially in the organ. As there was no trace of the drug initially, the mass of the drug in the organ at time t is 3 cm^3/sec multiplied by the concentration of the drug in the blood (1/3 gm/cm3) multiplied by the volume of the organ (150 cm^3).

Therefore, the mass of the drug in the organ at time t is 150 gm.

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Answer: below :p

Step-by-step explanation:

First problem is irrational since square roots are part of the irrational group.

Second problem is rational since the decimal is repetitive or repeating in an infinite 363636.

Answer:

14.13 cubic feet of lake water can fill the given balloon.

Step-by-step explanation:

concept used:

volume of sphere = 4/3 \(\pi r^3\)

where r is the radius of sphere

we take \(\pi\) = 3.14

_____________________________________

shape of balloon can be taken as spherical.

Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.

Given radius of balloon = 1.5 feet

Thus, volume of balloon = 4/3 \(\pi\) 1.5^3 = 4/3*3.14*1.5^3

volume of balloon = 42.39/3 = 14.13 cubic feet

Thus, 14.13 cubic feet of lake water can fill the given balloon.

Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

Answer:

a(31) = 84

Step-by-step explanation:

The first term, a(1) is 204, and the common difference is 4.  That is, each new term is 4 less than the previous term.

The rule governing this arithmetic sequence is

a(n) = 204 - 4(n - 1)

and so the 31st term is

a(31) = 204 - 4(30) = 84

The percentage decrease is 19%, the percentage increase is 24%

From the question, we have the following parameters that can be used in our computation:

Initial value = $2.59

Next value = $2.09

Final value = $2.59

The percentage decrease

The percentage of the decrease is then calculated using the following percentage equation

Percentage decrease = (Final amount - Initial amount)/Initial amount * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage decrease = (2.09 - 2.59)/2.59 * 100%

Evaluate

Percentage decrease = -19%

The percentage increase

The percentage of the increase is then calculated using the following percentage equation

Percentage increase = (Final amount - Initial amount)/Initial amount * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage increase = (2.59 - 2.09)/2.05 * 100%

Evaluate

Percentage increase = 24%

The percentage changes are not the same, and the percentage increase is greater

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The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.

The correct answer is 4.

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.

Given information:

- Circle C (cats): 15

- Circle D (dogs): 21

- Circle F (fish): 12

- Overlap of C and F: 2

- Overlap of F and D: 0

- Overlap of D and C: 3

- Overlap of all 3 circles: 1

- Number outside of circles: 14

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.

From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.

To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.

Therefore, from the options given correct one is 4.

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Answer: 4

Step-by-step explanation:

trust me bro

Answer:

c

Step-by-step explanation:

1.2+2.6=3.8

3.8×1.4=5.32

5.32-3.90=1.42

Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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Answer:

Question 2  is $500 and Question 3 is 5

Step-by-step explanation:

The percentage of the distance Dominic is on the path is his distance

travelled as a fraction of the total distance when equivalent to 100.

The distance he has travelled on the path is 8.75 miles.

The given parameter are;

Length of Dominic's path = 12.5 miles

The length of the way Dominic is to the end = 70%

Required:

The distance Dominic has travelled on the path

The distance Dominic has travelled, D is 70% of 12.5 miles.

70% of 12.5 miles = 70% × 12.5 miles = 8.75 miles

The distance Dominic has travelled on the path, D = 8.75 miles

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Answer:

Yes

Step-by-step explanation:

2 x 1/2 = 1

1 x 2 1/2 = 2 1/2

Answer:

Yes

Step-by-step explanation:

2 x 1/2= 1

1 x 2 1/2= 2 1/2

The amount of space or volume inside the box but outside the basketball is 6589.44 cm³.

We have to find the volume of the box and volume of the basketball to determine the space outside it.

Box is in rectangular shape.

Volume of the box = 24 × 24 × 24

                                = 13824 cm³

Basketball is spherical in shape.

Volume of the sphere = 4/3 π r³

                                     = 4/3 π (12)³

                                     = 2304π

                                     = 7234.56 cm³

Amount of space inside the box but outside the basketball is,

13824 cm³ - 7234.56 cm³ = 6589.44 cm³

Hence the required space is 6589.44 cm³.

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Answer:

\(y=\frac{8}{11} x-3\)

Step-by-step explanation:

Plug in the slope and point into the equation y=mx+b to solve for the y-value of the y-intercept. Plug in the x value for x, the y value for y, and the slope for m.

\(5=\frac{8}{11} (11)+b\)

\(5=8+b\)

\(-3=b\)

After solving that, you can plug the slope and y-intercept back into the equation to solve for y.

\(y=\frac{8}{11} x+(-3)\)

\(y=\frac{8}{11} x-3\)

Answer:

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept. We have all the information we need except for the y-intercept, so we can plug in our point to solve for the y-intercept.

------------------------------------Solving for y-intercept------------------------------------

Plugging in the point gives us \(5=8/11*11+b\). Simplifying this equation results in \(5=8+b\). To solve for b, we subtract 8 from both sides, giving us that \(b=-3\).  We now have both the slope and the y-intercept, so our equation is y = 8/11x -3.

Feel free to contact me with any questions about my answer. I hope this helps!

Answer:

x = 45 degrees

Step-by-step explanation:

All angles in a triangle will add up to 180 degrees.  So far we have 57 degree of 180.  We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180.  We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.  

Now, follow this equation to find x:

57 + 78 + x = 180

135 + x = 180

-135        -135

x = 45

The angle that the ramp makes with the ground is approximately 28.07 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):

Sin(θ) = 8/17

We can use a calculator to find the inverse sin of this ratio to get the angle θ:

θ = sin⁻¹(8/17)

θ ≈ 28.07 degrees

Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.

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Answer:

(-3, -10)

Step-by-step explanation:

We are asked to solve the system of equations simultaneously.

We need to equate the equations.

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

Solving :

⇒ -4 + 2x = 4x + 2

⇒ 4x - 2x = -4 - 2

⇒ 2x = -6

⇒ x = -3

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

Finding y :

⇒ y = 4(-3) + 2

⇒ y = -12 + 2

⇒ y = -10

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

Hence, the solution :

(-3, -10)

We have to solve them graphically as per question

Some points has already been found

Graph attached

Solution is

Answer:

0.66 melones por niño o 2/3

Step-by-step explanation:

10/15=2/3=0.66

Answer:It's called the "y intercept" and it's the y value of the point where the line intersects the y- axis. For this line, the y-intercept is "negative 1." You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.

Step-by-step explanation:

The Y intercept of a straight line is simply where the line crosses the Y axis.

Example

Y intercept

In the above diagram the line crosses the Y axis at 1.

The Y intercept is equal to 1 and the point is written as (0,1). Notice that for the y-intercept the x-coordinate of the point is always zero..

Answer:

Step-by-:Three linear relationships are shown. Find the slope of ...

The ordered pair of vertices is ( -1/2, 4) of the feasible set and maximized objective function of 3x + 2y is 7.

To find the vertices of function 3x + 2y, we need to first find the intersection points of the two constraint lines y = -3x + 5 and y = -x + 6, which are the vertices of the feasible set.

Setting the two equations equal to each other, we get:

-3x + 5 = -x + 6

Solving for x, we get:

-2x = 1

x = -1/2

Substituting x = -1/2 into either equation, we get:

y = -3(-1/2) + 5 = 8/2 = 4

So the first vertex is (-1/2, 4).

Next, we can use the given constraint equations to find the remaining vertices of the feasible set:

When y = 0, we have:

0 = -3x + 5

x = 5/3

So the second vertex is (5/3, 0).

When x = 6, we have:

y = -3(6) + 5 = -13

So the third vertex is (6, -13).

Now we can evaluate the objective function 3x + 2y at each of the vertices to determine the maximum value. We have:

3(-1/2) + 2(4) = 7

3(5/3) + 2(0) = 5

3(6) + 2(-13) = 0

Therefore, the maximum value of 3x + 2y is 7, which occurs at the vertex (-1/2, 4).

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_____The given question is incomplete, the complete question is given below:

For the feasible set determine x and y so that the objective function 3x + 2y is The vertices of the feasible set are maximized (Use a comma to separate answers as needed. Type an ordered pair.) The value of x is 6 The value of y is O y=-3x+5 y = -x + 6 feasible set.

Answer:

$48

Step-by-step explanation:

24/3 = 8

8 x 6 = $48

Answer:

48

Step-by-step explanation:

because butterfly method 6 time 24 =144 and didved 144 by 3 which gives you 48

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

The probability about an occurrence in an experiment is the likelihood that the event will occur. Any event's probability is a number between (including all) "0" and "1".

If an event's probability is represented by P(E), then we get

Given data:

Total pennies = 50

number of 1977 dated pennies = 12

probability = favourable outcome / total outcome

probability(1977 dated pennies) = number of 1977 dated pennies/ Total pennies

probability(1977 dated pennies) = 12/50

Divide numerator and denominator by 2.

probability(1977 dated pennies) = 6/25

Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

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4931870234e-238+9273.

well we know that we have 80mL and we also know that those 80mL will represent the "solute" or the 40% of the Tennessee whiskey total which we can say is 100%, so if 80 is the 40%, how much will it be for the 100% in mL?

\(\begin{array}{ccll}mL&\%\\\cline{1-2}80&40\\x&100\end{array}\implies \cfrac{80}{x}=\cfrac{40}{100}\implies \cfrac{80}{x}=\cfrac{2}{5}\implies 400=2x\\\\\\ \cfrac{400}{2}=x\implies \underset{mL}{200}=x\)

Answer:

A) 0.1339

B) 0.8078

Step-by-step explanation:

The Poisson Distribution formula is given by;

P(x; μ) = (e^(-μ) × (μ^(x))/x!

We are given;

Variance = 0.5 per month

Now, in Poisson distribution, variance = mean.. Thus, mean μ = 0.5 per month

A) We want to find the probability that 4 typhoons will hit US in a year.

Thus, x = 4

But since it's for a year, then μ = 0.5 × 12 = 6

So;

P(x = 4) = (e^(-6) × (6^(4))/4!

P(x = 4) = 0.00247875 × 1296/24

P(X = 4) = 0.1339

B) probability that at least 2 typhoons will hit US in a given half-year is;

P(X ≥ 2) = 1 - P(X < 2)

P(X < 2) = P(X = 0) + P(X = 1)

In a half given year, μ = 0.5 × 6 = 3

P(X = 0) = (e^(-3) × (6^(0))/0!

P(X = 0) = 0.0498

P(X = 1) = (e^(-3) × (6^(1))/1!

P(X = 1) = 0.1494

P(X < 2) = 0.0498 + 0.1494

P(X < 2) = 0.1922

P(X ≥ 2) = 1 - 0.1922

P(X ≥ 2) = 0.8078