Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.

1. G is incompressible- True

2. F is irrotational- True

3. G is irrotational- False

4. F is incompressible- False

Divergence and Curl In Mathematics, divergence is a differential operator, which is applied to the 3D vector-valued function. Similarly, the curl is a vector operator which defines the infinitesimal circulation of a vector field in the 3D Euclidean space .

So if we calculate for F:

F has a divergence potentially

divF = df/dx + dg/fy + dh/dz

But curl(F )= 0(all cross derivatives df/dy df/dz, dg/dx etc = 0)

For G

G has zero divergence.

divG = df/dx + dg/fy + dh/dz = 0 + 0 + 0 = 0

But it may have a curl.

curl(G) = df/dy may be non-zero

df/dz, dg/dx etc may all be non-zero

Now, we also know that if the divergence is zero, the vector field is incompressible and if the curl is zero, the vector field is irrotational, that is,  

div = 0 = incompressible and

curl = 0= irrotational  

Thus,

1. G is incompressible- True

2. F is irrotational- True

3. G is irrotational- False

4. F is incompressible- False

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A probability is a numerical representation of the likelihood or chance that a specific event will take place.

12% of peanut M&M’s = brown

15% = yellow

12% = red

23% = blue

23% = orange

15% = green

Here, Probability of an event is represented as P

a) P(not green) = 100% - 15%

                        = 85%

                        = 0.85

b) P(yellow or red) = 15% + 12%

                               = 27%

                               = 0.27

c) P(three blue) = 0.23*0.23 *0.23

                         = 0.012 (rounded to 3 decimal places)

d) P(not green if you choose 6 )= [tex](0.85)^{6}[/tex]

                                                    = 0. 377

e) P(at least 1 green if you choose 6 ) = 1 - 0.377

                                                              = 0.623

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[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]

The slope represents the average number of weeks it is Shawn to run laps is true about Shawn's line.

The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.

Given,

Graph to show number of taps he is scheduled to run a week.

True statement is,

The slope represents the average number of weeks it is Shawn to run laps.

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Answer:gat big

Step-by-step explanation:

The correct option C: -4 ≤ x ≤ -2, are the intervals in which the graph is constant.

So, from the shown graph, the horizontal line have the constant function which lies in the intervals -4 ≤ x ≤ -2.

Thus, in the intervals -4 ≤ x ≤ -2, the function is constant.

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Answer:

X=1 Y=0

Step-by-step explanation:

Multiply the second equation (-2x + 8y = -2) by 2 in order to get -4x+16y=-4.
Using this equation, you can eliminate the x

4x - 8y = -4
-4x+16y=-4.
=
8y=0
y = 0

Now, knowing that y=0, plug y into the second equation:

-2x+8(0)=-2
simplify
-2x=-2
lastly, divide both sides by -2
x=1

Answer:

1309.10

Step-by-step explanation:

1200 = 110%

(1200/110)*120 = 1309.10

The critical numbers of the function are; θ = π/6, 5π/6

We are given the trigonometric function as;

f(θ) =  6secθ + 3tanθ ; 0 < θ < 2π

The critical points of a function are defined as those points of the domain where the function is not differentiable or those points for which the derivative is equal to zero.

Let us find the first derivative;

f'(θ) = 6(-sin θ/cos² θ) + 3(1/cos² θ)

f'(θ) = (3 - 6sin θ)/cos² θ

At f'(θ) = 0, we have;

3 - 6sin θ = 0

θ = sin⁻¹(3/6)

Since sin is positive, then;

θ = π/6, 5π/6

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The given expression evaluates to -19.

We have the following expression -

- 6 - 13

The given expression evaluates to -

x = - 6 - 13

x = - 19

Therefore, the given expression evaluates to -19.

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Answer:

y = x - 2

Step-by-step explanation:

Since m = 0, what we have so far is y=x+b

We have a point, which is (3,1)

Substitute the x and y with the x and y values in the coordinate point to solve for b (y-intercept).

1=3+b

1-3=3+b-3                  undo the 3 by subtracting

-2 = b

y = x + -2                   simplify

y = x - 2

The correct answer is A.

500 is the size of the population at the moment of maximum growth.

Given data:

To find the size of the population at the moment when the population is growing most rapidly, we need to determine the maximum value of the derivative dP/dt.

Given the logistic differential equation [tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex], find the derivative by taking the derivative of each term separately:

[tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex]

To find the critical points where the derivative is zero or undefined, set dP/dt equal to zero:

[tex](\frac{1}{10})P - (\frac{1}{5000})P^2=0[/tex]

Simplifying:

[tex](\frac{1}{10})P= (\frac{1}{5000})P^2[/tex]

[tex]10P^2=5000P[/tex]

Dividing both sides by P and rearranging:

[tex]10P(P-500)=0[/tex]

This equation has two solutions: P = 0 and P = 500.

To determine which solution corresponds to the moment when the population is growing most rapidly, examine the second derivative. Taking the second derivative of the logistic differential equation, we have:

[tex]\frac{d^2P}{dt^2} = \frac{1}{10} - \frac{2}{5000}P[/tex]

Evaluating the second derivative at P = 0 and P = 500, we get:

[tex]\frac{d^2P}{dt^2}_{P=0} = \frac{1}{10} - \frac{2}{5000}(0)[/tex]

[tex]\frac{d^2P}{dt^2}_{P=0}= \frac{1}{10} > 0[/tex]

[tex]\frac{d^2P}{dt^2}_{P=500} = \frac{1}{10} - \frac{2}{5000}(500)[/tex]

[tex]\frac{d^2P}{dt^2}_{P=0}= -\frac{1}{10} < 0[/tex]

Since the second derivative is positive at P = 0 and negative at P = 500, the moment when the population is growing most rapidly occurs at P = 500.

Hence, the size of the population at the moment when the population is growing most rapidly is 500.

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By AAS congruence theorem, ΔABD is congruent ΔCDB.

Quadrilateral ABCD is given in the figure.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given, AB║DC

Consider ΔABD and ΔCDB

m∠A=m∠C=90° (Given)

m∠ABD=m∠BDC (Alternate interior angles)

BD = BD (Common)

Using AAS congruence theorem, ΔABD ≅ ΔCDB

Hence, by AAS congruence theorem, ΔABD is congruent ΔCDB.

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Answer:

Step-by-step explanation:

17/5

Answer:

2 and 2/5

Step-by-step explanation:

Answer: 33%

Step-by-step explanation: a third of the items in the bag are pretzels.

The spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.

An average is a single number taken as representative of a list of numbers, generally the sum of the numbers divided by how many numbers are in the list (the arithmetic mean).

The formula to calculate the average of given numbers is equal to the sum of all the values divided by the total number of values. Average = Sum of Values / Number of Values.

So, in this case:

Values: 25, 50, 75

Number of Values: 3

Thus, the average:

Sum of Values / Number of Values = (25 + 50 + 75) / 3 = 50

Hence, the spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.

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28 mph is  the average speed of the bus in mph.

What is speed?

The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.

                                 Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms-1, is the SI unit of velocity.

time = (1+ 1/2)hr = 3/2 hr = 1.5 hr

distance = 42 miles

average speed = total distance/total time

42/1.5 = 28 mph

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The inequality is y > 2x-3

option C is correct

What is inequality in math?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

The line intersects the y- axis at point (0,-3)

i.e., The y-intercept =-3

We know that,

Equation of lime, y= mx + b

                                                        b: y-intercept

                                                         m: Slope of the line

Slope of the line,

m = 0-(-3)/3/2 = 2

m ⇒ 2

∴ Equation of line,  y = 2x - 3

The shaded are is above the line, and line is represented with dotted lines,

hence the inequality is,

y > 2x - 3

Hence, option C is correct

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The possible value of other two angles will be 20 degree.

What are the types of triangle?

Basically, there are six different types of triangles in terms of lengths and measurements of triangle lines or angles. The sum of all interior angles of a triangle is always 180 degrees. This is called the angular summation of the triangle. Depending on the length of the sides, triangles can be divided into three types:

scale

Isosceles

equilateral

It is given that an isosceles triangle has an angle that measures 140°

We know that two sides of isosceles triangle are equal and by the property of triangle we know that angle opposite to equal sides are equal therefore remaning two angles of isosceles triangle will be equal.

Let the angles be x

By angle sum property of triangle

x + x + 140 = 180

2x = 180 - 140

2x = 40

x = 40/2 = 20

Therefore, the possible value of other two angles will be 20 degree.

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Answer: 24

Step-by-step explanation:

A=5 so F(x)=5^2-1

F(x)=24

Answer:

........................

Answer:

8.8 minutes

Step-by-step explanation:

first we figure out how many liters are being lost

57 - 35 = 22

then divide that by 2.5

22 / 2.5 = 8.8

8.8 minutes

Simplify the [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] we will get  20 · √30.

What do you mean by exponent and radicals?

Exponents are a convenient way of describing repeated multiplication of the same number. Radicals include the use of radical characters √

These are sometimes called surdos. The exponent is the power p of an expression of the form [tex]a^{p}[/tex]

The process of raising a base number to a given power is called exponentiation. (where a ≠ 0)

Given:

[tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex]

= (2 × 5)· [tex](\sqrt{10}\times \sqrt{12)}[/tex]

= 10 · [tex]\sqrt{120}[/tex]

= 10 · 2 · [tex]\sqrt{30}[/tex]

= 20 · √30

Therefore, [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] = 20 · √30

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1000 - 180x represents the remaining number of samples after x weeks.

What is exponents?

Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".

Main body:

Consider what is actually happening in the question.

You begin with 1000 samples,  after it decreases to

=1000-18% of 1000

= 820

You can see the pattern shows that the number of samples decreases 18% every week ,1000-18% of 1000 - 18% 0f 1000.

= 1000 - 180x where x denotes number of weeks.

Hence 1000 - 180x represents the remaining number of samples after x weeks.

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Answer:

50%

Step-by-step explanation:

numerator divided by denominator

1 divided by 2  =  .5

.5  x 100  =  50%

Answer:

The current price of sofa is $195.50.

Step by Step explanation:Cost price of the sofa for the store = $200

Now, the store marked it up 15%.

So, marked price of sofa = $200 + 15% of $200

=200 + 30

=$230

Now, it is given that the sofa could not sell at this price. So, the store reduces its price by 15% now.

So, current price of sofa = $230 - 15% of $230

= 230 - 34.5

=$195.5

So, the current price of the sofa is $195.50.

Answer:

159

Step-by-step explanation:

To find half of an amount, multiply the amount by 1/2 which is the same as dividing the amount by 2.

318 × 1/2 =

= 318 ÷ 2

                        159

                   -----------------------

              2  |  318

                   - 2

               ------------

                      11

                    - 10

                   -------

                        18

                      - 18

                      ------

                          0

318 × 1/2 = 318 ÷ 2 = 159

Answer:

[tex]\huge\boxed{\sf v = 0.4\ mph}[/tex]

Step-by-step explanation:

Distance = S = 4/5 miles = 0.2 miles

Time = t = 1/2 hour = 0.5 hours

Speed = v = ?

v = S/t

v = 0.2/0.5

[tex]\rule[225]{225}{2}[/tex]

Answer: 8/5 mph

Step-by-step explanation:

According to definition, an object's speed is determined by:

s=d/t where,

d is the object's travel distance, and t is the amount of time it takes.

We can replace these values with:

Since, s= (4/5) / (1/2) mph

=> s= 8/5 mph

The object's speed to cover 4/5 miles in 30 minutes is: 8/5 mph