Parametrize the contour consisting of the perimeter of the square w square with vertices- the length of this i, 1 + i, and-1 + i traversed once in that order. What is t contour?

Answers

Answer 1

The square with vertices at i, 1+i, -1+i, and -i can be parametrized as follows:

Starting from the vertex at i, we can move along the edges of the square in a counterclockwise direction. Let's call this parameterization as r(t), where t ranges from 0 to 4.

For 0 ≤ t < 1, we move from i to 1+i along the line segment joining these points:

r(t) = i + t(1+i - i) = i + ti

For 1 ≤ t < 2, we move from 1+i to -1+i along the line segment joining these points:

r(t) = (1+i) + (t-1)(-2i) = -t + 2 + i

For 2 ≤ t < 3, we move from -1+i to -i along the line segment joining these points:

r(t) = (-1+i) + (t-2)(-1-i + 1-i) = -1 + (3-t)i

For 3 ≤ t < 4, we move from -i to i along the line segment joining these points:

r(t) = (-i) + (t-3)(i + 1+i) = (t-2)i

Therefore, the parameterization of the contour is:

r(t) = { i + ti for 0 ≤ t < 1

{ -t + 2 + i for 1 ≤ t < 2

{ -1 + (3-t)i for 2 ≤ t < 3

{ (t-2)i for 3 ≤ t < 4

And the contour C is the set of all points r(t) as t ranges from 0 to 4:

C = {r(t) : 0 ≤ t ≤ 4}

Note that we use the closed interval [0, 4] for the parameter t because we want to traverse the perimeter of the square once in a counterclockwise direction.

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Related Questions

In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as:

Answers

In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.

Leitmotiv, from the German "leading motive," is a recurrent musical motif that typically appears in operas but can also be found in symphonic poems.Overture to a concert. Romantic-era concert piece for orchestra in one movement, frequently based on a literary program.

What is serious opera called?

Opera seria, or "serious opera," is an Italian operatic genre that was popular in 18th-century Europe. The genre is commonly referred to as Neapolitan opera since it first appeared in the late 17th century, particularly in the works of Alessandro Scarlatti and other composers based in Naples.

What is Wagnerian leitmotif?

A theme of easily recognizable melodic, rhythmic, or harmonic identity, first used in connection with a certain character of incident, and which returns time and time again, always with a recollection of the original association. The term was coined by the Wagnerian scholar Hans von Wolzogen.

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Please help
The area of a circle is 354 cm². Find in degrees and minutes, the angle subtended at the centre of the circle by a 2.9cm arc.

Answers

The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.

What is the measure of the central angle of a circular section?

In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:

r = √ (A / π) (1)

r = √ (354 / π)

r ≈ 10.615 cm

Then, the measure of the central angle in radians is found by the equation of circular arc:

θ = s/r

θ = 2.9 cm / 10.615 cm

θ = 0.273 radians

Finally, we convert the angle into DMS system:

θ = 0.273 rad × 180°/π

θ = 15.641°

Degrees: 15°

Minutes and seconds: 0.641° (38.46')

Minutes: 38'

Seconds: (0.46' = 27.6'')

The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.

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How to represent 5 rational numbers on line. the numbers should be of form p/q where p or q should be a taxicab number. the fraction can be then reduced to its standard form. write about the taxicab numbers in brief.

Answers

The five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.

According to the question,

To represent 5 rational numbers on line, the numbers should be of form p/q where p or q should be a taxicab number.

A taxicab number is a smallest integer can be expressed as a sum of two positive integer cube.

The most famous taxicab number is 1729. Thus,

1729 = 1³ + 12³

1729 = 9³+ 10³

Now, 2 = 1³ + 1³ so, 2 is the first taxicab number. Therefore, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1.

In 1/1729 -> 1729 is taxicab number

In 1/2 -> 2 is taxicab number

In 3/2 -> 2 is taxicab number

In 1/1729 -> 2 is taxicab number

In 1729/1 -> 1729 is taxicab number

Hence, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.

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Simplify 4/9 + 1/3
A 5/12
B 7/9
C 1 1/9
D 15/9

Answers

Answer:

B) 7/9

Step-by-step explanation:

Fraction addition: If the denominators are not same, find the LCM of the denominators.

LCM of 3 and 9 is 9.

Now, find equivalent fractions with denominator as 9.

[tex]\sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\[/tex]

[tex]\sf =\dfrac{3}{9}[/tex]

Now add.

[tex]\sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\[/tex]

[tex]\sf =\dfrac{7}{9}[/tex]

4/9 + 1/3 = (12 + 9)/9x3 = 21/27
7/9

What is the solution to this system of equations x-2 y=15 2x+4y=-18

Answers

Answer:

(3, - 6 )

Step-by-step explanation:

x - 2y = 15 ( add 2y to both sides )

x = 2y + 15 → (1)

2x + 4y = - 18 → (2)

substitute x = 2y + 15 into (2)

2(2y + 15) + 4y = - 18 ← distribute parenthesis and simplify left side

4y + 30 + 4y = - 18

8y + 30 = - 18 ( subtract 30 from both sides )

8y = - 48 ( divide both sides by 8 )

y = - 6

substitute y = - 6 into (1)

x = 2(- 6) + 15 = - 12 + 15 = 3

solution is (3, - 6 )

Answer:

x is 3 y is -6 I really hope this helps

If A and B are independent events and P(A)=0.25 and P(B)=0.333, what is the probability P(ANB)?
a) 1.33200
b) 0.75075
c) 0.08325
d) -0.0830

Answers

The probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.

For any two events A and B, the probability of event A and B, that is, P(A ∩ B) is given as:-

When the events are dependent, P(A ∩ B) = P(A).P(B|A).When the events are independent, P(A ∩ B) = P(A).P(B).

In the question, we asked the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333.

We know that when the events are independent, P(A ∩ B) = P(A).P(B).

Thus, P(A ∩ B) = (0.25)*(0.333),

or, P(A ∩ B) = 0.08325.

Thus, the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.

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Someone help me out on these 2 geometry questions, ASAP!!!
“Complete the proofs”

Answers

Question 11

1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)

4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)

Question 12

1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)

2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)

4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)

5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)

6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)

7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)

Note: I changed the names of the segments in Question 11 because of the word filter.

What value of k will result in the quadratic having one rational solution if 4x2+kx+4=0?

Answers

The value of 'k' in the quadratic Equation [tex]4x^{2}+kx+4=0[/tex] having one rational solution is k is 8.

What is a Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of the type [tex]f(x) = ax^{2} + bx + c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.The standard form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex] .

Here, the given equation is [tex]4x^{2}+kx+4=0[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 4

b = k

c = 4

The given quadratic is having one rational solution, which means [tex]b^{2} -4ac=0[/tex]

Therefore,

[tex]k^{2} -4 \times 4\times4=0\\k^{2} -64=0\\k^{2} =64\\k=\sqrt{64} \\k=8[/tex]

Therefore, the value of k is 8.

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On a piece of paper, graph y ≤ -2x. Then determine which answer matches
the graph you drew.

Answers

Answer: Graph provided below.

Step-by-step explanation:

Draw the graph of y = -2x and then shade the region below it because y is less than and equal to -2x. To draw the graph of y = -2x, plug in x values into the equation and plot the corresponding coordinates. See this video on how to graph linear equations:

https://www.khanacademy.org/math/in-in-grade-9-ncert/xfd53e0255cd302f8:linear-equations-in-two-variables/xfd53e0255cd302f8:graph-of-a-linear-equation-in-two-variables/v/graphs-of-linear-equations

Gavin has nickles, dimes, and quarters in the ratio of 1:3:6 if 57 of Gavin's coins are dimes how many nickels and quarters does Gavin have?

Answers

Answer:

Gavin has 19 nickels & 114 quarters

Step-by-step explanation:

N : D : Q

1 : 3 : 6 = 57

x : 57 : y

57 / 3 = 19

1 x 19 : 3 x 19 : 6 x 19

19 : 57 : 114

Find the vertex and axis of symmetry

Answers

Answer:

Below in bold.

Step-by-step explanation:

f(x) = 2x^2 - 12x + 24

Convert to vertex form:

f(x) = 2(x^2 - 6x) + 24

= 2[(x - 3)^2 - 9] + 24

= 2(x - 3)^2 - 18 + 24

= 2(x - 3)^2 + 6

So the vertex is at (3, 6) and the axis of symmetry is x = 3.

Find the missing side length of the triangle.

Answers

SOLUTION :

c² = 5² + 5²

c² = 25 + 25

c² = 50

c = √50 ft

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Javier will evaluate the expression 2a(to the power of 3) - 1 for a = 2. Once he submitted 2 for a in the expression, what is the next step Javier needs to take in order to evaluate the expression?

Answers

The next step Javier needs to take in order to evaluate the expression is to simplify it to it's lowest term. Details below

Data obtained from the questionExpression = 2a³ - 1Evaluation =?

How to evaluate the expression

From the question given, we were told that Javier submitted 2 for a

Thus, the new expression becomes

2 × 2³ - 1

Recall

Aⁿ × Aᵐ = Aⁿ⁺ᵐ

Thus,

2 × 2³ = 2¹⁺³ = 2⁴

Therefore,

2 × 2³ - 1 = 2⁴ - 1

But

2⁴ = 16

Thus,

2⁴ - 1 = 16 - 1

2⁴ - 1 = 15

Therefore,

2 × 2³ - 1 = 15

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What is the missing letter in the pattern below?

t, s, r, q, _, o, n, m,...

A. u

B. p

C. l

D. v

Answers

The missing letter is p. The correct option is B. p

Letter pattern

From the question, we are to determine the missing letter in the given pattern

The given pattern is

t, s, r, q, _, o, n, m,...

Consider the English alphabet

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z.

If we study the pattern, we will realize that the alphabets are in the reverse order.

Hence, the missing letter is p. The correct option is B. p

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5th grade algebra. Pls help with these am offering brainliest + bonus points! :D

Answers

Answer:

3. 6 5. 3

Step-by-step explanation:

PEMDAS

3. 0.5 x (24) / 3 + 2

12/3 +2

4 + 2

5. (4 + 6/3) x 0.5

(4 + 2) x 0.5

6 x 0.5

Answer: number 3. is 6 and number 5. is 3

hope it helped

Use cylindrical coordinates to find the volume of the region in the first octant bounded by the cylinder r and the plane z.

Answers

The volume of the region in first octant is 9.

Given that the region in the first octant bounded by the cylinder r=3 and the plane z=y.

The graph is shown below.

we are given that first octant is bound by r=3 and z=y

We will use the conversion formula, i.e.

x²+y²=r² where x=rcos∅ and y=rsin∅

Firstly, we will find bound octant

0≤∅≤π/2

0≤r≤3

0≤z≤r sin∅

Now, we can set up integral

[tex]V=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}\int_{0}^{rsin(\theta)}rdzdrd\theta[/tex]

Further, we can solve it.

Firstly, we solve integral for z then we solve for r and after that we will solve for ∅, we get

[tex]\begin{aligned}V&=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}r^2 \sin (\theta)dr d\theta\\&=\int_{0}^{\frac{\pi}{2}}\frac{1}{3}r^3\sin \theta d\theta\left|_{0}^{3}\\ &=\int_{0}^{\frac{\pi}{2}}\left(\frac{1}{3}\sin\theta d\theta(27-0)\right)\\ &=\int_{0}^{\frac{\pi}{2}}9\sin \theta d\theta\\ &=0-(-9)\\ &=9\end[/tex]

Hence, the volume of the region in the first octant is bounded by the cylinder r=3 and the plane z=y is 9.

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What is the coordinate point of the linear function 5x+3y=15

Answers

Answer: Y-intercept: (0,5) X-intercept: (3,0)

Step-by-step explanation: Set x and y equal to 0.

Find the volume of the pyramid. Round to the nearest tenth if necessary. hurry!!

Answers

Answer:

Step-by-step explanation:

All pyramids have a volume as one-third of a prism with the same base area and the same height.

This will make the formula for the volume [tex]\frac{1}{3}(base*height)[/tex]. We already know the height of the pyramid is 10, but the area of the base for this rectangle would be its length and its width. Let's calculate this:

[tex]7*2.3=16.1\hspace{0.1cm}in^2[/tex]

Let's put these values back into the formula:

[tex]V=\frac{1}{3}(16.1*10)\\ V=\frac{1}{3}(161)\\ V= 53.7\hspace{0.1cm}in^3[/tex]

Solve:
-5/2 a + 5 = 25

a =

Answers

Answer:

A = -8

You're welcome! :)

Answer: a = -8

Step-by-step explanation:

Combine multiplied terms into a single fraction

then find a Find common denominator for the fraction

then Combine fractions with common denominator,

Multiply the numbers, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator,

Multiply the numbers making your equation like this -5a+10=50

subtract 10 by both sides and then you will need to simplify making it

-5a + 40 then you divide them both by the same factor which is -5 then you simplify again making the answer to your question -8

Which ordered pairs are in the solution set of the system of linear inequalities?

y > Negative one-halfx

y < One-halfx + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.
(5, –2), (3, 1), (–4, 2)
(5, –2), (3, –1), (4, –3)
(5, –2), (3, 1), (4, 2)
(5, –2), (–3, 1), (4, 2)

Answers

The ordered pairs (5 , -2) , (3 , 1) , (4 , 2) are in the set of the solution (Option C)

What is an ordered pair?

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order.

It aids visual comprehension by locating a point on the Cartesian plane.

How do we arrive at the solution?

The first line has negative slope and passing through points (0 , 0) and (4 , -2)

That is y > (-1/2)x

The second line has positive slope and passing through points (-2 , 0) and (2 , 2)

That is: y < (1/2)x + 1.

- Refer to the accompanying diagram to discover the common component of the solutions.

- The inequity is shown by the red shading.

- The inequity is shown by the blue shading.

- The two-colored shaded area reflects the common solutions to the two inequalities.

- Let's discover the ordered pairs in the system of linear inequalities' solution set.

- Points (-4, 2), (-3, 1), (4, -3) define the common shaded area.

- Points (5, -2), (3, 1), (3, -1) (4 , 2)

As a result, Point (5, -2) is in the darkened region.

As a result, Point (3, 1) is in the darkened area.

As a result, Point (4, 2) is in the darkened area.

As a result, the ordered pairings (5, -2), (3, 1), (4, 2) are in the solution set.

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Transformation example

Answers

Answer:

Rotation, Reflection, Dilation.

Step-by-step explanation:

Georgie buys a pack of chocolate which has 18 small chocolate bars. She ate three bars in the morning, Later in the
day, Georgie's brother ate three fifth of the chocolates bar that were left, what fraction of the chocolate bars is left in
the packet?

Answers

So if Georgie inceptively eats three small chocolate bars that would make fifteen remaining.

So if Georgie’s brother ate 3/5 you would figure out how many candy bars he ate by:

15 multiplied by the 3/5 = 9

So out of the 18 candy bars Georgie ate 3 and Georgie’s brother ate 9.

Geometric series
2 + 6 + 18 + 54 + ... , find tn

Answers

The function that gives the value of tn for the geometric series is presented as follows;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

How can the expression that represents the geometric series be found?

The given geometric series is presented as follows;

2 + 6 + 18 + 54 +...

From the above series, we have;

First term, a = 2

Common ratio, r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3

The nth term of the geometric series is therefore;

[tex]t_n = a \cdot r^{(n - 1)} [/tex]

Which gives;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

Where, tn is the nth term

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1/5n+3/5n=7/9

Can you help?

Answers

The value of n in 1/5n+3/5n=7/9 is 35/36

How to solve the equation?

The equation is given as:

1/5n+3/5n=7/9

Multiply through by 5

n + 3n = 35/9

Evaluate the sum

4n = 35/9

Divide both sides by 4

n = 35/36

Hence, the value of n in 1/5n+3/5n=7/9 is 35/36

Answers

The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

What is the measure of the missing interior angle in a heptagon?

Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:

θ = (n - 2) · 180°, where n is the number of sides of the polygon. (1)

If we know that n = 7, then sum of the internal angles in the heptagon is:

θ = (7 - 2) · 180°

θ = 900°

And the measure of the final interior angle is found by subtraction:

θ₇ = 900° - 776°

θ₇ = 124°

The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

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please help!
A) A top-class tennis player can serve the ball, of mass 57 g, at an initial horizontal speed of 50 m/s. The ball remains in contact with the racket for 0.05 s. Calculate the average force exerted on the ball during the serve.

B) A motor car of mass 3000 kg moving with 72 km h-1 made to reduce its speed to 18 km h^-1, in 40 s, by applying brakes. Find the resistive force.

Answers

The average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

Force

a. Average force

Using this formula

Force (F) = Mass ×Acceleration

Where:

Mass (m) = 57 g = 57 / 1000= 0.057 Kg

Acceleration (a) = u / t = 50 / 0.05 = 1000 m/s²

Let plug in the formula

Force (F) = 0.057 × 1000

Force (F) = 57 N

b. Resistive force

F = m(v – u) / t

Where:

Force (F) = ?

Mass (m) = 3000 Kg

Initial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/s

Final velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/s

Time (t) = 40s

Let plug in the formula

Force = 3000(5 – 20) / 40

Force = 3000(-15) / 40

Force=-45,000/40

Force = -1125 N

Therefore the average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

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Can anyone tell me how to solve this with step by step and show work
Also apparently the answers are A and C but I need to know how to get to the answer

Answers

Answer is A and C
Imagine your square has an area of 64,
That means it’s sides are 8 x 8
So only rectangles that are 8inches x 8 inches or less will fit. A and C have these dimensions, they will fit. The other two will not. See my attachment, the green rectangle must fit inside the 8 x 8 square.

A streetlight is at the top of an 18ft tall pole. A woman 6 ft tall walks away from the pole at a speed of 4 ft/sec along a straight path. How fast (in ft/sec) is the tip of her shadow moving away from the pole when she is 45 ft from the base of the pole

Answers

The woman's shadow is moving away from the pole at the speed of 4 feet/sec.

Calculating the value of shadow speed

The height of a pole-mounted street light = 18 ft

The height of a lady = 6 ft

The woman is moving quickly and directly away from the pole. Her speed = 4ft/sec.

The woman's distance from the pole at the precise moment question want to know the speed of the woman's shadow's leading edge = 45ft

A woman standing 6 feet tall moves away from the pole in a straight route at a pace of 4 feet per second. If we assume that t is the passing time in seconds and that x is the distance in feet between the pole and the lady, we are informed that dx/dt=4 ft/sec.

Therefore, it is concluded that the final answer is 4 ft/sec.

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PLEASE ANSWERERRREEERRR

Answers

the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

How to get a perfect square?

A perfect square is the product of a number and itself.

As you can see in the example, 16 is a square number. Then let's try to get 16.

To get 16 we can use the difference:

20 - 4

So the first therm needs to be equal to 20, and the second equal to 4.

To write 20 in scientific notation we have:

[tex]2*10^1[/tex]

To write 4 in in scientific notation:

[tex]4*10^0[/tex]

Then the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

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A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles. (4 points)
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
show all work
insert picture of the tree diagram pls

Answers

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

How to determine the possible outcomes?

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL