What is the value of (-6 + 2i) - (7 - 8i)?
0 -1 + 61
O 1 - 6i
0-13 + 10i
13 + 10i

Answer:

1/20

Step-by-step explanation:

Answer:

1/20

Step-by-step explanation:

100/5 = 20

1/20 is the simplest fraction

No, it does not necessarily imply that any random variable X defined from S will have an infinite set of possible values.

For instance, consider a random variable X that takes values from the set of natural numbers S = {1, 2, 3, ...}. We can define X as follows: X(n) = n for any n ∈ S.

Although S is an infinite set, X can only take values in S, which is also an infinite set, but not a larger one. Therefore, X has a countable (finite or infinite) set of possible values.

In general, the set of possible values of a random variable depends on how the variable is defined and not just on the size of the sample space.

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Answer:

58-52

Step-by-step explanation:

the answer is 6

Answer is in the picture.

Answer: -626

Step-by-step explanation: (34)+(−33)(2)(2)(5)

34+(−66)(2)(5)

34+(−132)(5)

34+−660

−626

There are 8,640 ways the five people can be seated in the eight empty seats.

To determine the number of ways the five people can be seated in eight empty seats, we can use the concept of permutations.

Since the order in which the people are seated matters, we need to calculate the number of permutations of five people taken from eight seats.

The formula for permutations is given by:

P(n, r) = n! / (n - r)!

where n represents the total number of items and r represents the number of items taken at a time.

In this case, we have 8 empty seats (n) and want to seat 5 people (r). Therefore, we can calculate the number of ways as:

P(8, 5) = 8! / (8 - 5)!

= 8! / 3!

= (8 * 7 * 6 * 5 * 4 * 3!) / 3!

= 8 * 7 * 6 * 5 * 4

= 8,640

Hence, there are 8,640 ways the five people can be seated in the eight empty seats.

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Answer:

Player B.

Step-by-step explanation:

Player A has a mean score of 25.

Let's calculate Player B's mean score and compare it to Player A's.

23 + 27 + 28 + 22 + 25 / 5 = 125 / 5 = 25.

So, Player A and Player B have the same mean score.

This doesn't tell the scout which player is "better", so let's look at the variance.

The other statistic given for Player A is the standard deviation for their points. The given number is 4. Let’s calculate the standard deviation for Player B, and compare it to player A.

Recall that we add up the squares of the difference between each score and the mean, divide it by the total number of data, and square root that. So, the standard deviation for player B is sqrt(2^2 + 2^2 + 3^2 + 3^2 + 0^2 / 5) = sqrt (26/5) = sqrt (5.2) = 2.3.

Excellent. We have player A’s standard deviation, as well as player B’s standard of deviation. Since player B’s standard deviation is less than player A’s, it can be inferred that player B has more consistent results than player A, and the scout should get Player B.

Hope this helps!

Cylindrical coordinates use coordinates that consist of A radial distance and two angles. The correct answer is C.

Cylindrical coordinates consist of a radial distance, an angle in the horizontal plane (usually denoted as θ), and a vertical distance (usually denoted as z). The radial distance represents the distance from a reference point (usually the origin) to a point in the cylindrical coordinate system.

The angle θ represents the rotation around the vertical axis, while the vertical distance z represents the height or elevation above the horizontal plane.

So, in cylindrical coordinates, we specify a point by its radial distance, angle, and height. This system is particularly useful when dealing with cylindrical or rotational symmetry, as it allows for a more straightforward representation and calculation of quantities in such systems.  The correct answer is C.

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Cylindrical coordinates consist of a radial distance and two angles. One angle is measured from a chosen direction in the plane perpendicular to the 'vertical' axis, and the other angle or height gives the vertical position above or below the plane.

Cylindrical coordinates are commonly used in mathematics and physics to represent the position of a point in a three-dimensional space. They consist of a radial distance and two angles. The radial distance is the distance of the point from the origin. The first angle is measured in the plane perpendicular to the vertical axis from a designated direction, usually the positive x-axis. The second angle, often represented as z, gives a vertical position above or below the plane, which is the height of the point.

So the correct answer to your question would be option (C): Cylindrical coordinates use a radial distance and two angles.

These types of coordinates are useful in certain real-world situations. For example, when representing the location of a point on earth using latitude (angle), longitude (angle), and altitude (radial distance).

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Answer: 4

Step-by-step explanation: We can actually make the two equal each other like so:

3d-4=12d/6

Multiply both sides by 6:

18d-24=12d

Add 24 to both sides:

18d=12d+24

Subtract 12d from both sides:

6d=24

Divide by 6:

d=4

4

Answer:

4550m ; 4

Step-by-step explanation:

Recall

1 hectometre = 100m

1 decameter = 10m

Distance from shore to center of island = 37hm

Another 85 decameter toward stge se direction

Therefore total metres it will travel in other to get to the treasure :

37 hectometre + 85 decameter

(37 * 100)m + (85 * 10)m

3700m + 850m = 4550m

In kilometers :

1000 meters = 1 kilometers

4550 meters =

(4550 / 1000)meters

= 4.55km

Answer: 2nd / (B)

Step-by-step explanation:

Answer:

rectangle

Step-by-step explanation:

the question is asking what the shape of the cross section would be if it was perpendicular to the base. imagine a cylinder that you could slide a piece of paper into. what would be inside the cylinder? perpendicular to the base, it would be a rectangle. if it was parallel to the base, you'd then have a circle.

The area of the mural opening in terms of x is (4x²-54x+180).

According to the question,

Length of the mural = 15ft.

width of the frame = x

The wooden frame will reduce the area of the mural opening, by reducing the length and breadth of the opening.

∴ Length of the opening of the mural opening = (15 - x - x) ft.

                                                                             = (15-2x) ft.

Also, the breadth of the mural frame = 12 ft.

again, the width of the wooden frame will reduce the breadth of the mural opening.

∴ The breadth of the mural opening = (12-x-x) feet.

                                                            = (12-2x) feet.

Now, we know that,

the area of a rectangle = Length × Breadth

                                      = (15-2x)×(12-2x)

                                      = 4x²-54x+180

Hence, the area of the mural opening in terms of x is (4x²-54x+180).

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According to the question The formula \(\(C(t) = \frac{{0.000001 - 0.000001 \cdot e^{-0.005t}}}{{0.005}}\)\)  for the concentration. the initial value problem for the contaminant concentration \(\(C(t)\)\) in the pond is:

\(\(\frac{{dC}}{{dt}} = 0.000001 - \frac{{0.5C}}{{100}}\)\)

Let's denote \(\(V(t)\)\) as the volume of water in the pond at time \(\(t\)\) and \(\(C(t)\)\) as the concentration of the toxic chemical in the pond at time \(\(t\).\)

The rate at which the contaminant enters the pond can be calculated by multiplying the volumetric flow rate of the contaminated water \((\(0.5 \, \text{m}^3/\text{min}\))\) by the concentration of the toxic chemical \((\(0.0002 \, \text{kg/m}^3\)):\)

\(\(\text{Rate of inflow} = 0.5 \, \text{m}^3/\text{min} \times 0.0002 \, \text{kg/m}^3\)\)

The rate at which the contaminant leaves the pond is given by the volumetric flow rate of the outflowing water, which is also \(\(0.5 \, \text{m}^3/\text{min}\)\), multiplied by the concentration \(\(C(t)\)\) in the pond.

Therefore, the rate of change of the contaminant concentration in the pond can be expressed as:

\(\(\frac{{dC}}{{dt}} = \frac{{\text{Rate of inflow}}}{{V(t)}} - \frac{{\text{Rate of outflow}}}{{V(t)}}\)\)

Since the volume of the pond \(\(V(t)\)\)  remains constant at \(\(100 \, \text{m}^3\),\) the initial value problem for the contaminant concentration becomes:

\(\(\frac{{dC}}{{dt}} = \frac{{0.5 \, \text{m}^3/\text{min} \times 0.0002 \, \text{kg/m}^3}}{{100 \, \text{m}^3}} - \frac{{0.5 \, \text{m}^3/\text{min} \times C}}{{100 \, \text{m}^3}}\)\)

To find the equilibrium concentration, we set \(\(\frac{{dC}}{{dt}}\)\) to zero and solve for \(\(C\):\)

\(\(\frac{{0.5 \times 0.0002}}{{100}} - \frac{{0.5 \times C}}{{100}} = 0\)\)

Simplifying the equation, we get:

\(\(0.0001 - \frac{{C}}{{200}} = 0\)\)

Solving for \(\(C\)\), we find the equilibrium concentration:

\(\(C = 0.0001 \times 200\)\)

The equilibrium concentration is \(\(C = 0.02\), \(\text{kg/m}^3\).\)

To determine the stability of the equilibrium, we can analyze the sign of \(\(\frac{{dC}}{{dt}}\)\)around the equilibrium concentration.

Taking the derivative of \(\(\frac{{dC}}{{dt}}\)\) with respect to \(\(C\)\), we have:

\(\(\frac{{d}}{{dC}}\left(\frac{{dC}}{{dt}}\right) = -\frac{{0.5}}{{100}}\)\)

Since the derivative is negative, the equilibrium concentration of \(\(C = 0.02 \, \text{kg/m}^3\)\) is stable.

Therefore, the initial value problem for the contaminant concentration \(\(C(t)\)\) in the pond is:

\(\(\frac{{dC}}{{dt}} = 0.000001 - \frac{{0.5C}}{{100}}\)\)

The initial value problem for the contaminant concentration \(\(C(t)\)\) in the pond is given by \(\(\frac{{dC}}{{dt}} = 0.000001 - \frac{{0.5C}}{{100}}\)\) with the initial condition \(\(C(0) = 0\).\)

Solving this differential equation yields the formula \(\(C(t) = \frac{{0.000001 - 0.000001 \cdot e^{-0.005t}}}{{0.005}}\)\)  for the concentration in the pond at any time \(\(t\).\)

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(a). The speed of the shock wave can be determined by setting [u]s = 0.

(b). The initial value problem u(0,x)={a,b,​x<0,x>0 has been solved.

(a) To determine the Rankine-Hugoniot condition for the speed of a shock, we consider the conservation of mass across the shock wave.

The given equation is:

ut + u^2ux = 0

The Rankine-Hugoniot condition for the conservation of mass is: [u]s = 0

where [u]s represents the jump in fluid velocity across the shock wave.

In this case, the equation is already in conservative form, so we can directly apply the Rankine-Hugoniot condition. Therefore, the speed of the shock wave can be determined by setting [u]s = 0.

(b) Now let's solve the initial value problem u(0, x) = {a, b} for two cases:

(i) |a| > |b|:

In this case, we have a shock wave. The solution will consist of a shock wave moving to the right with velocity s.

(ii) |a| < |b|:

In this case, we have a rarefaction wave. To determine the shape of the rarefaction wave, we can use Exercise 2.3.15, which involves solving the characteristic equations for the given PDE.

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Answer:

Its B.

Step-by-step explanation:

Emath.com- Parabola calculator

Answer:

It's a linear expression.

Answer:

linear binomial

Step-by-step explanation:

I got it right in Grandpoint.

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

Let  

n

be the least of the three consecutive integers. Then the integers are  

n

,

n

+

1

, and  

n

+

2

, and we have that

n

+

(

n

+

1

)

+

(

n

+

2

)

=

−

93

⇒

3

n

+

3

=

−

93

⇒

3

n

=

−

96

⇒

n

=

−

32

Substituting that into  

{

n

,

n

+

1

,

n

+

2

}

, we get the solution set  

{

−

32

,

−

31

,

−

30

}

Step-by-step explanation:

IDK WHY ITS SPREAD APART

Answer:

I answered #1 on a previous question

2) A

Step-by-step explanation:

2) So the formula for consecutive integers is x+x+1+x+2 and so on.

So we know there are 6 integers so the final would be x+5.

so the sum of the final and the first is x+5+x=1

Simplify the equation and solve

2x+5=1

2x=-4

Divide 2 on both sides

x=-2

so -2 is the least Interger of all.

Check: Use the equation x+5 since it’s the greatest,  so since x is -2 subsitute and you’ll get -2+5 you'll get 3 and 3+-2=1

Thus, the probability that it will rain on exactly one of the five days during the Hiking Club's camping trip in the State park is approximately 4.38%.

We can use the binomial probability formula to calculate the probability of rain on exactly one of the five days during the Hiking Club's camping trip in the State park. The formula is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:
- P(X = k) is the probability of k successes (rain) in n trials (days)
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success (rain) on any given day (66% or 0.66)
- n is the number of trials (5 days)
- k is the number of successes (1 day with rain)

Plugging the values into the formula, we get:

P(X = 1) = C(5, 1) * 0.66^1 * (1 - 0.66)^(5 - 1)

First, we find the number of combinations C(5, 1) which is 5.

Next, we calculate the probabilities:
0.66^1 = 0.66
(1 - 0.66)^4 = 0.34^4 = 0.0133

Now, we multiply everything together:

P(X = 1) = 5 * 0.66 * 0.0133 ≈ 0.0438

So, the probability that it will rain on exactly one of the five days during the Hiking Club's camping trip in the State park is approximately 4.38%.

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Using the Fundamental Counting Theorem, it is found that 6 different possible outcomes are there.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem:

Then, the number of outcomes is given by:

N = 2 x 3 = 6.

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Answer:

4.29 , 4.49

Step-by-step explanation:

Answer:

 -y • (6x^2 + 3xy - 4)

Step-by-step explanation:

Logarithms are a useful tool in determining the acidity or basicity of a solution. pH is a measure of the concentration of hydrogen ions in a solution and is calculated using the formula pH = -log[H+].

A solution with a pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

Using logarithms, we can determine the pH of 7 solutions ranging from strong acid to neutral to strong base. To do this, we need to measure the concentration of hydrogen ions in each solution and then use the formula above to calculate the pH.

For example, if we have a solution with a hydrogen ion concentration of 0.001 M, we can calculate the pH as follows:

pH = -log(0.001) = 3

This solution would be considered a strong acid, as it has a pH below 7. Similarly, a solution with a hydrogen ion concentration of 10^-7 M (which is the same as a concentration of 1x10^-7 M) would have a pH of 7 and would be considered neutral.

Finally, a solution with a hydrogen ion concentration of 10^-11 M would have a pH of 11 and would be considered a strong base.

In summary, using logarithms, we can determine the acidity or basicity of a solution by calculating its pH. A pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

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6-4+2x=0

2+2x=0

-2(-1-x)=0

Step-by-step explanation:

not possible

The specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

For a two-tailed hypothesis test, an appropriate null hypothesis indicating that the population correlation is equal to zero would be:

H₀: ρ = 0

where ρ represents the population correlation coefficient.

This null hypothesis states that there is no significant correlation between the two variables being analyzed.

In a two-tailed hypothesis test, the alternative hypothesis would be that there is a significant correlation, either positive or negative, between the two variables:

Hₐ: ρ ≠ 0

This alternative hypothesis states that there is a significant correlation between the two variables, but does not specify the direction of the correlation.

It's important to note that the specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

Additionally, the choice of null and alternative hypotheses will affect the statistical power of the test, which is the probability of correctly rejecting the null hypothesis when it is false.

Hence, the specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

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Complete Question:

For a two-tailed hypothesis test, which of the following would be an appropriate null hypothesis indicating that the population correlation is equal to o?

A. H₀: 1 = 2, B. H₀ : M₁ = M₂ C. H₀: O = 0  

D. None of the options above are correct.

Yes, these data support the scientist's belief that large islands are more effective at protecting at-risk species than small islands. To provide statistical justification, we can compare the probability of extinction for each island size: For large islands, the probability of extinction is 19/208, or approximately 0.091. For small islands, the probability of extinction is 66/299, or approximately 0.221.

The data provided can support the scientist's belief that large islands are more effective than small islands for protecting at-risk species. We can use the concept of probability to calculate the likelihood of extinction for both large and small islands.

For the large island, the probability of extinction for any given species is 19/208 or approximately 0.091. For the small island, the probability of extinction for any given species is 66/299 or approximately 0.221.

Comparing these probabilities, we see that the probability of extinction is higher for at-risk species on small islands than on large islands. This supports the scientist's belief that large islands are more effective for protecting at-risk species.

Additionally, we can use statistical tests such as a chi-square test or a two-sample t-test to confirm whether the difference in extinction rates between large and small islands is statistically significant.

These tests would require more information such as sample size and variance, but based on the provided data alone, the probability calculations suggest that the scientist's belief is supported.

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Given:

Cards labelled 1, 3, 5, 6, 8 and 9.

A card is drawn and not replaced. Then a second card is drawn at random.

To find:

The probability of drawing 2 even numbers.

Solution:

We have,

Even number cards = 6, 8

Odd numbers cards = 1, 3, 5, 9

Total cards =  1, 3, 5, 6, 8 and 9

Number of even cards = 2

Number of total cards = 6

So, the probability of getting an even card in first draw is:

\(P_1=\dfrac{\text{Number of even cards}}{\text{Number of total cards}}\)

\(P_1=\dfrac{2}{6}\)

\(P_1=\dfrac{1}{3}\)

Now,

Number of remaining even cards = 1

Number of remaining cards = 5

So, the probability of getting an even card in second draw is:

\(P_2=\dfrac{\text{Number of remaining even cards}}{\text{Number of remaining total cards}}\)

\(P_2=\dfrac{1}{5}\)

The probability of drawing 2 even numbers is:

\(P=P_1\times P_2\)

\(P=\dfrac{1}{3}\times \dfrac{1}{5}\)

\(P=\dfrac{1}{15}\)

Therefore, the probability of drawing 2 even numbers is \(\dfrac{1}{15}\). Hence, the correct option is (b).