PLEASE HELP WITH QUESTION C

Answer:

50 is not a perfect square

The following are the properties of the given logarithmic function f(x) = -log3x+6:

The function's domain is (0, ∞).

The function's range is  (-∞, ∞) i.e. the set of all real numbers.

At x = 0, the component shows the presence of a vertical asymptote.

The constant reflects the x-axis logarithm.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

We have been given that the function f(x) = -log3x+6

As per the above function,

The function's domain is (0, ∞).

The function's range is  (-∞, ∞) i.e. the set of all real numbers.

At x = 0, the component shows the presence of a vertical asymptote.

The constant reflects the x-axis logarithm.

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(a) The argument of z, given z = (a + ai)(b√3 + bi), is arg \(z = tan^{(-1)}\)((√3 + 1) / (√3 - 1)) and (b) The cube roots of -32 + 32√3i are 4 * [cos(-π/9) + isin(-π/9)], 4 * [cos(5π/9) + isin(5π/9)], and 4 * [cos(7π/9) + isin(7π/9)].

(a) To determine arg z, we need to find the argument (angle) of the complex number z. Given that z = (a + ai)(b√3 + bi), we can expand this expression as follows:

z = (a + ai)(b√3 + bi) = ab√3 + abi√3 + abi - ab

Simplifying further, we have:

z = ab(√3 + i√3 + i - 1)

Now, we can write z in polar form by finding its magnitude (modulus) and argument. The magnitude of z is given by:

\(|z| = \sqrt(Re(z)^2 + Im(z)^2)\)

Since z = ab(√3 + i√3 + i - 1), the real part Re(z) is ab(√3 - 1), and the imaginary part Im(z) is ab(√3 + 1). Therefore, the magnitude of z is:

\(|z| = \sqrt((ab(\sqrt3 - 1))^2 + (ab(\sqrt3 + 1))^2) = ab\sqrt(4 + 2\sqrt3)\)

To find the argument arg z, we can use the relationship:

arg z = \(tan^{(-1)}\)(Im(z) / Re(z))

Substituting the values, we have:

arg z = tan^(-1)((ab(√3 + 1)) / (ab(√3 - 1))) = \(tan^{(-1)}\)((√3 + 1) / (√3 - 1))

Therefore, the argument of z is arg z = \(tan^{(-1)}\)((√3 + 1) / (√3 - 1)).

(b) To find the cube roots of -32 + 32√3i, we can write it in polar form as:

-32 + 32√3i = 64(cosθ + isinθ)

where θ is the argument of the complex number.

The modulus (magnitude) of -32 + 32√3i is:

| -32 + 32√3i | = √((-32)^2 + (32√3)^2) = √(1024 + 3072) = √4096 = 64

The argument θ can be found using:

θ = arg (-32 + 32√3i) = \(tan^{(-1)}\)((32√3) / (-32)) = tan^(-1)(-√3) = -π/3

Now, to find the cube roots, we can use De Moivre's theorem:

\(z^{(1/3)} = |z|^{(1/3)}\)* [cos((arg z + 2kπ)/3) + isin((arg z + 2kπ)/3)]

Substituting the values, we have:

Cube root 1: \(64^{(1/3)}\) * [cos((-π/3 + 2(0)π)/3) + isin((-π/3 + 2(0)π)/3)]

Cube root 2: \(64^{(1/3)}\) * [cos((-π/3 + 2(1)π)/3) + isin((-π/3 + 2(1)π)/3)]

Cube root 3: \(64^{(1/3)}\) * [cos((-π/3 + 2(2)π)/3) + isin((-π/3 + 2(2)π)/3)]

Simplifying further, we have:

Cube root 1: 4 * [cos(-π/9) + isin(-π/9)]

Cube root 2: 4 * [cos(5π/9) + isin(5π/9)]

Cube root 3: 4 * [cos(7π/9) + isin(7π/9)]

These are the cube roots of -32 + 32√3i. To sketch them in the complex plane (Argand diagram), plot three points corresponding to the cube roots \((-32 + 32 \sqrt 3i)^{(1/3)}\) using the calculated values.

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Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

Halving the side of the square, results in the perimeter being halved.

new perimeter = \(\frac{1}{2}\) original perimeter

Answer:

y = 3x -5

Step-by-step explanation:

Use the slope-intercept form:

y = (slope)x + intercept

slope = 3

intercept = -5

Equation in slope-intercept form:

y = 3x -5

Answer:

it is B i am so sorry i calculated wrong but i got it now sorry again

Step-by-step explanation:

and i cant answer y because you didnt give a seperate question. please make one for y so i can answer it :)

Answer:

x=44

Step-by-step explanation:

add 82 and 54 which is 136

then 180 minus 136 because triangles always equal 180°

The magnitude of the number of the minutes in the school is 2.

Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.

There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).

The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.

On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.

The value storage is where you may find the number into the various magnetic.

As a result, the number of minutes spent in school is 2.

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Complete question -

What is the Order of Magnitude of the number of minutes in a school day?

The formula for the surface area of a sphere is derived from the formula for its volume by taking its derivative with respect to the radius.

Deriving the formula for the surface area of a sphere depends on knowing the formula for its volume because it involves taking the derivative of the volume formula with respect to the radius.

The volume formula for a sphere is  \(V = (4/3)πr^3\), where r is the radius, and π is a constant. If we differentiate this formula with respect to r, we get dV/dr = \(4πr^2\), which gives us the formula for the surface area of the sphere, A = \(4πr^2.\)

Therefore, the formula for the surface area of a sphere is derived from the formula for its volume by taking its derivative with respect to the radius.

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Jack will require 6 tsp of baking powder if he uses 9 c of flour.

Given: Jack's pancake recipe calls for 3 cups of flour and 2 teaspoons of baking powder.

The amount of baking powder required if Jack uses 9 c of flour is to be determined.

Solution:

For 3 c of flour, 2 tsp of baking powder is required

2/3 tsp of baking powder is required for 1 cup of flour.

We must now determine how much baking powder to use with 9 cups of flour.

2/3X9 tsp of baking powder is required for 9 cups of flour.

= 6 tsp

Jack will therefore require 6 tsp of baking powder if he uses 9 c of flour.

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I'd say maybe by 5:30 b would

Train B will catch up to Train A at 5:30 PM.

We have,

d = distance covered by both trains when they meet

t = time it takes for train B to catch up to train A

For train A:

Distance = Speed × Time

d = 90t

For train B:

Distance = Speed × Time

d = 100(t - 0.5) (train B departs 30 minutes (0.5 hours) later than train A)

Since both equations represent the same distance, we can set them equal to each other:

90t = 100(t - 0.5)

Let's solve for t:

90t = 100t - 50

10t = 50

t = 5

It will take 5 hours for train B to catch up to train A.

To determine the time when train B catches up to train A, we add the 5 hours to the departure time of train B, which is 12:30 PM:

12:30 PM + 5 hours = 5:30 PM

Therefore,

Train B will catch up to Train A at 5:30 PM.

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Answer:

36

Step-by-step explanation:

6^2=36

Poisson distribution is the measure to summarize the information contained in a probability distribution in a single parameter.

Poisson distribution gives the probability of an event occurring a certain number of times (k) within a specified time period.

It is denoted by λ , which is the mean number of events.

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Blake started with 94 flyers before 14 of them blew away.To solve this story problem, we can follow these steps:

1. Start by identifying the key information provided in the problem:
  - 14 flyers had blown away by the time Blake arrived.
  - Blake put 50 flyers on blue cars, 26 flyers on white cars, and 32 flyers on silver cars.

2. To find out how many flyers Blake started with, we need to determine the total number of flyers he distributed. Add the number of flyers on blue cars, white cars, and silver cars:
  - 50 + 26 + 32 = 108 flyers were distributed.

3. Since 14 flyers blew away, we subtract this number from the total number of distributed flyers to find the initial number of flyers Blake had:
  - 108 - 14 = 94 flyers.

Therefore, Blake started with 94 flyers before 14  them blew away.

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The points (x, y) corresponding to the parameter values t = -2, -1, 0, 1, and 2 are as follows:

   • When t = -2, the point is (10, 1/2).

   • When t = -1, the point is (0, 1).

   • When t = 0, the point is (0, 2).

   • When t = 1, the point is (10, 4).

   • When t = 2, the point is (30, 8).

To find the points (x, y) corresponding to the given parameter values, we substitute each value of t into the parametric equations x = 5t² + 5t and y = 2^(t + 1) and calculate the corresponding x and y coordinates.

   1. For t = -2: Plugging t = -2 into the equations:

x = 5(-2)² + 5(-2) = 20 - 10 = 10

y = \(2^{-2 + 1} = 2^{-1}\) = 1/2

Therefore, when t = -2, the corresponding point is (10, 1/2).

   2. For t = -1: Plugging t = -1 into the equations:

x = 5(-1)² + 5(-1) = 5 - 5 = 0

y = \(2^{-1 + 1} = 2^0\) = 1

So, when t = -1, the corresponding point is (0, 1).

   3. For t = 0: Plugging t = 0 into the equations:

x = 5(0)² + 5(0) = 0 + 0 = 0

y = \(2^{0 + 1} = 2^1\) = 2

When t = 0, the corresponding point is (0, 2).

   4. For t = 1: Plugging t = 1 into the equations:

x = 5(1)² + 5(1) = 5 + 5 = 10

y = \(2^{1 + 1}\) = 2² = 4

Hence, when t = 1, the corresponding point is (10, 4).

   5. For t = 2: Plugging t = 2 into the equations:

x = 5(2)² + 5(2) = 20 + 10 = 30

y = \(2^{2 + 1}\) = 2³ = 8

Therefore, when t = 2, the corresponding point is (30, 8).

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Answer:

11 percent, I believe but you should check with other answers

Step-by-step explanation:

what I did was add the times together and then multiply 7 by 24 and got 168 because they are playing 20 hour a week, then I divided 20 by 168 and got  0.11 so I just turned that into a percent by moving the decimal 2 digits to the right

So, the transformation matrix that takes the unit circle to the given ellipse is:
|  5   -2  |
|  -2   2  |

To compute the matrix of the transformation that takes the unit circle to the ellipse given by the equation 5x^2 - 4xy + 2y^2 = 1, we need to first find the transformation function. We can do this by setting up a system of equations where (x,y) is a point on the unit circle and (u,v) is the corresponding point on the ellipse:

5x^2 - 4xy + 2y^2 = 1
u = a*x + b*y
v = c*x + d*y

where a, b, c, and d are constants that we need to find.

Since (x,y) is on the unit circle, we know that x^2 + y^2 = 1. Substituting the transformation equations into this equation, we get:

u^2 + v^2 = (a*x + b*y)^2 + (c*x + d*y)^2
= (a^2 + c^2)*x^2 + 2*ab*xy + 2*cd*xy + (b^2 + d^2)*y^2
= x^2 + y^2
= 1

Equating the coefficients of x^2, xy, and y^2, we get the following system of equations:

a^2 + c^2 = \sqrt{1}
2*ab + 2*cd = \sqrt{0}
b^2 + d^2 = \sqrt{1}

Solving this system, we get:

a = (2/3)
b = -\sqrt{2/3}
c = \sqrt{1/3}
d = \sqrt{1/3}

Therefore, the transformation function is:

u = \sqrt{2/3}*x - \sqrt{2/3}*y
v = \sqrt{1/3}*x + \sqrt{1/3}*y

To compute the matrix of this transformation, we need to write it in matrix form. We can do this by arranging the coefficients of x and y in a 2x2 matrix:

[ \sqrt{2/3} -\sqrt{2/3} ]
[ \sqrt{1/3}  \sqrt{1/3}  ]

Therefore, the matrix of the transformation that takes the unit circle to the ellipse given by the equation 5x^2 - 4xy + 2y^2 = 1 is:

[ \sqrt{2/3} -\sqrt{2/3} ]
[ \sqrt{1/3}  \sqrt{1/3} ]

To compute the matrix of the transformation that takes the unit circle to the ellipse given by the equation 5x^2 - 4xy + 2y^2 = 1, you can use the following steps:

1. Identify the general form of the ellipse: Ax^2 + Bxy + Cy^2 = 1.
2. Compare the given equation to the general form: A = 5, B = -4, and C = 2.
3. Compute the matrix M as:

M = | A  B/2 |
   | B/2  C |

M = |  5   -2  |
   |  -2   2  |

So, the transformation matrix that takes the unit circle to the given ellipse is:

|  5   -2  |
|  -2   2  |

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A is finite, then X - A is clearly uncountable (since it has the same cardinality as X). If A is countable but not infinite, then X - A is still uncountable (since it has the same cardinality as X). Thus, the only interesting case is when A is countably infinite.

Let X be an uncountable set and A be a countably infinite subset of X. We need to show that X - A is uncountable. By contradiction, assume that X - A is countable. Since A is countably infinite, we can list its elements in a sequence as {a1, a2, a3, ...}. Now, consider the following sequence of sets:S1 = X - {a1}S2 = S1 - {a2}S3 = S2 - {a3}...Sn = Sn-1 - {an}...Observe that each Si is obtained by removing a finite set from X, and hence Si is uncountable. Moreover, Si is a subset of Si-1 for each i, so we have an infinite descending chain of uncountable sets. This contradicts the fact that X is uncountable. Therefore, X - A must be uncountable.Note that this argument works for any uncountable set X, regardless of its cardinality. We only need to assume that A is countably infinite. If A is finite, then X - A is clearly uncountable (since it has the same cardinality as X). If A is countable but not infinite, then X - A is still uncountable (since it has the same cardinality as X). Thus, the only interesting case is when A is countably infinite.

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Answer:

4 Days

Step-by-step explanation:

Day 1: 10+3= 13

Day 2: 13+3=16

Day 3: 16+3=19

Day 4: 19 + 3= 22

Answer:

y = 3x represents the graph. The point (4, 12) is on the line that is not shown on the graph.

Step-by-step explanation:

The equation of the line that  goes through origin= y = mx

Take any to points from the line

(0,0) & ( 2,6)

\(Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{6-0}{2-0}=\dfrac{6}{2}=3\)

Equation of the line:

y = 3x

Plugin x = 4,

y = 3*4 = 12

(4,12) is on the line.

The sphere equation x^2 + y^2 + z^2 = 6z becomes:
ρ^2 = 6ρcos(φ)
The cone equation z = √(x^2 + y^2) becomes:
ρcos(φ) = ρsin(φ)
So, the solid lies within the region described by the inequalities:
ρ ≤ 6cos(φ) and ρcos(φ) ≥ ρsin(φ)
These inequalities, along with 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π, define the solid in spherical coordinates.

To describe the solid in terms of inequalities involving spherical coordinates, we first need to convert the given equations to spherical coordinates. In spherical coordinates, we have:

x = r sinθ cosϕ
y = r sinθ sinϕ
z = r cosθ

Substituting these values in the given equations, we get:

r² sin²θ cos²ϕ + r² sin²θ sin²ϕ + r² cos²θ = 6r cosθ
r cosθ = r² sin²θ cos²ϕ + r² sin²θ sin²ϕ

Simplifying these equations, we get:

r = 6 cosθ / (sin²θ cos²ϕ + sin²θ sin²ϕ + cos²θ)^(1/2)
r cosθ = r² sin²θ

Now, the solid lies inside the sphere x2 + y2 + z2 = 6z, which in spherical coordinates becomes:

r² = 6 cosθ

And the solid also lies outside the cone z = x2 y2, which in spherical coordinates becomes:

r cosθ >= r^4 sin^2(θ) cos^2(ϕ) + r^4 sin^2(θ) sin^2(ϕ)
r >= r^3 sin^2(θ) (cos^2(ϕ) + sin^2(ϕ))
r >= r^3 sin^2(θ)

Combining these inequalities, we get the description of the solid in terms of inequalities involving spherical coordinates:

r >= r^3 sin^2(θ) >= (6 cosθ)^(1/2)

This represents the solid that lies inside the sphere x2 + y2 + z2 = 6z and outside the cone z = x2 y2, in terms of inequalities involving spherical coordinates.

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Answer:

Step-by-step explanation:

Given line with points (-6, -3) and (6, -7)

Slope intercept form:

We can see on the graph that y-intercept is b = -5

The slope is found using slope formula:

Th equation is:

Answer:

3/2

Step-by-step explanation:

Image a bit blurry, but I'm counting whoever wrote this was sane enough to pick integer values.

\(f(2) = 1; f(4)=4\)

Average rate of change is the difference in f divided by the difference in x:

\(\frac{\Delta f(x)}{\Delta x} = \frac{4-1}{4-2} = \frac32\)

Answer:

38

Step-by-step explanation:

LN and ON are equal

you do 3x+5=35 to find x

subtract 5 from both sides

3x=30

x=10

substitute it in for 4x-2

4(10)-2

40-2

38

first NL=ON

then value of x come

now (4*x-2)=38m

the answer is in the picture

Answer:

y=4/5x+B

what is the whole question?

a) The expected winning probability for a single game defined is: $3.59

b) The standard deviation of winning is: $10.11

a) If the game costs $5 to play, the expected winnings are: - $0.79

If the game costs $5 to play, the standard deviation of winning is $11.33.

Because the projected winning value is negative, the game should not be played with a -$5 playtime charge.

The total number of hearts in a deck is 13.

The probability of drawing three hearts is:

P(drawing 3 Hearts)

13 ÷ 52 × 12 ÷ 51 × 11 ÷ 50 = 0.0129

The probability of selecting three black cards is:

A deck of black cards has 26 cards.

P (drew three black cards):

26 ÷ 52 × 25 ÷ 51 × 24 ÷ 50 = 0.1176

Any other draw probability: P(3 hearts) + P(3 blacks) + P(any other draw) = 1.

858 ÷ 66300 + 7800 ÷ 66300 + P(any other draw) = 1

P(any other draw) = 57642 ÷ 66300

For only one game,

E(X) = Σ[ X × p(X)]

E(X) =Σ[(50 × 858 ÷ 66300) + (25 × 7800 ÷ 66300)+0]

E(X) = $3.588

b) The standard deviation is equal to √Var(X)

Var(X) = Σ[ X² × p(X)] - E(X)

Σ[ X² × p(X)] = Σ[(50² × 858 ÷ 66300) + (25² × 7800 ÷ 66300) + 0] = 105.88235

Var(X) = 105.88235 - 3.588 = 102.29435

Winning standard deviation = √102.29435 = $10.114

If the game cost $5 to play :

The total sum won if and only if:

Three sketched hearts = $50 - $5 = $45

Three blacks are drawn for a total of $25 - $5 = $20.

Any other combination drawn = $0 - $5 = -$5

The distribution is as follows:

E(X) = Σ[ X × p(X)]

E(X) =Σ[(50 × 858 ÷ 66300) + (25 × 7800 ÷ 66300) + (-5 × 57642 ÷ 66300)]

E(X) = - $0.7588

The winning standard deviation is:

The standard deviation is equal to √Var(X)

Var(X) = Σ[ X² × p(X)] - E(X)

Σ[ X²×p(X)] = Σ[(50² × 858 ÷ 66300) + (25² × 7800 ÷ 66300) + (-5² × 57642 ÷ 66300)] = 127.61764

Var(X) = 127.61764 - (-0.7588) = 128.37644

The winning standard deviation is:

Std(X) = √Var(X) = √128.37644 = $11.330

With a game cost of - $5, the predicted winnings for a single game are negative, hence you should avoid playing the game.

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The number of trailing zeros at the end of (20!)^2, without explicitly computing the value, is 5.

To determine the number of zeros at the end of (20!)^2 without explicitly computing the value, we need to count the factors of 10 in the number.

A trailing zero is formed when a factor of 10 is present in the number. Since 10 can be expressed as 2 * 5, we need to determine the number of pairs of 2 and 5 factors in (20!)^2.

In the factorial expression, the number of 2 factors is typically more abundant than the number of 5 factors. Therefore, we need to count the number of 5 factors in (20!)^2.

To determine the count of 5 factors, we divide 20 by 5 and take the floor value, which gives us 4. However, there are multiples of 5 with more than one factor of 5, such as 10, 15, and 20. For these numbers, we need to count the additional factors of 5.

Dividing 20 by 25 (5 * 5) gives us 0, so there is one additional factor of 5 in (20!)^2 from the multiples of 25.

Hence, the total count of 5 factors is 4 + 1 = 5, and consequently, there are 5 trailing zeros at the end of (20!)^2 when written in decimal form.

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Answer:

It is the first graph

Step-by-step explanation:

The line under the > and < sign means that it must include the 3 and the 0.  The closed circle is showing that the 3 and 0 or included.

Answer:

It is approximately 1320.25

The covariance is -0.02%, standard deviation is 17.91% and expected return is 9.05%.

1. To determine the covariance between the S&P 500 and REITs and between core bonds and REITs, we can use the formula:

covariance = correlation * standard deviation of S&P 500 * standard deviation of REITs

a) covariance between S&P 500 and REITs:

covariance = 0.74 * 19.45% * 23.17% = 3.14%

b) covariance between core bonds and REITs:

covariance = -0.04 * 2.13% * 23.17% = -0.02%

2. For a portfolio that is 50% invested in an S&P 500 fund and 50% invested in REITs, we can calculate the expected return and standard deviation as follows:

Expected return = 0.5 * 5.04% + 0.5 * 13.07% = 9.05%

Standard deviation = sqrt((0.5 * 19.45%)^2 + (0.5 * 23.17%)^2 + 2 * 0.5 * 0.74 * 19.45% * 23.17%) = 17.91%

3. For a portfolio that is 50% invested in a core bonds fund and 50% invested in REITs, we can calculate the expected return and standard deviation as follows:

Expected return = 0.5 * 5.78% + 0.5 * 13.07% = 9.43%

Standard deviation = sqrt((0.5 * 2.13%)^2 + (0.5 * 23.17%)^2 + 2 * 0.5 * (-0.04) * 2.13% * 23.17%) = 11.88%

4. For a portfolio that is 80% invested in a core bonds fund and 20% invested in REITs, we can calculate the expected return and standard deviation as follows:

Expected return = 0.8 * 5.78% + 0.2 * 13.07% = 6.38%

Standard deviation = sqrt((0.8 * 2.13%)^2 + (0.2 * 23.17%)^2 + 2 * 0.8 * (-0.04) * 2.13% * 23.17%) = 4.84%

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