Find an equation of the plane that passes through the points A = (0,0,1), B=(1,0,0) and C = (0,1,0).

Answer:

Hello!

Yes, these ratios are equivalent!

Step-by-step explanation:

Since, when we multiply both the numerator and denominator by the same number then we get an equivalent fraction.

We use multiplication or division. Whatever you do to one number of the ratio. You have to do the same thing to the other using multiplication or division. And you get an equivalent ratio.

Hope this helps!

The area of the rhombus WXYZ is 48 unit².

From the diagram:

Diagonal WY = 8 units, Diagonal XZ = 6 units, hence:

Area = 8 * 6 = 48 unit².

A rhombus is a special case of a parallelogram. In a diamond, the opposite sides are parallel and the opposite sides are equal in angle. In addition, all sides of the rhombus are the same length and the diagonal bisects at right angles. Diamonds are also known as diamonds.

The diagonals of the rhombus intersect at right angles to form a non-uniform triangle. The opposite angles are equal. However, if all angles of the diamond are 90 degrees, the diamond is said to be square.

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Answer:

9m³n⁴

Step-by-step explanation:

18m^5n^4 = 2×3² m^5n^4

45m^3n^6 = 3²×5 m^3n^6

GFC = 3² m³n⁴ = 9m³n⁴

Answer:

Step-by-step explanation:

The question is not properly structured. Here is the complete question.

For cones with radius 6 units, the equation V=12\pi h relates the height h of the cone, in units, and the volume V of the cone, in cubic units. Sketch a graph of this equation on the axes.

The formula for calculating the volume of a cone is expressed as shown;

\(V = \frac{1}{3} \pi r^{2} h\) where r is the radius and h is the height.

Given radius r = 6units, on substituting;

\(V = \frac{1}{3}*\pi *6^{2}*h\\ V = \frac{36\pi h}{3}\\V = 12\pi h... (1)\)

It can be seen from the derived volume of the cone that it is linear in nature. The volume of the cone has a linear relationship with its height. As the volume increases, the height also increases and vice versa.

Generally for a direct variation

\(if\ y\ \alpha x \ \\y = kx\)

where k is the constant of proportionality. comparing to equation 1, k = 12π.

Find the graph attached

The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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The mood of the argument is categorical and the figure is EIO. To determine the mood and figure of the given argument, we'll first identify the premises and conclusion, and then assign the appropriate categorical proposition to each statement.

The argument can be rewritten as:

Premise 1: Some dictators are not warmongers. (Some D are not W)
Premise 2: No dictators are egomaniacs. (No D are E)
Premise 3: Some egomaniacs are warmongers. (Some E are W)
Conclusion: Some dictators are not warmongers. (Some D are not W)

Now, let's assign the categorical propositions to each statement:
Premise 1: I (Some D are not W)
Premise 2: E (No D are E)
Premise 3: I (Some E are W)
Conclusion: O (Some D are not W)

The mood of the argument is IEO.

Next, we'll determine the figure by looking at the placement of the middle term (E) in the premises:
Premise 2: No D are E (subject-middle term)
Premise 3: Some E are W (middle term-predicate)

The figure is 1 because the middle term is the subject of one premise and the predicate of the other premise.

So, the mood and figure of the argument are IEO-1. Therefore, the correct answer is:

IEO - 1

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The range of the function for this situation is the interval [398.25, 400] gallons.

To determine the range of the function f(x) = 400 - 0.35x for the given situation, we need to find the possible values of the amount of water remaining in the pool.

The function f(x) represents the amount of water remaining (in gallons) after x minutes, where x ranges from 0 to 5.

To find the range of the function, we evaluate f(x) for the extreme values of x in the given range (0 to 5).

For x = 0, the initial amount of water remaining:

f(0) = 400 - 0.35(0) = 400 gallons

For x = 5, the amount of water remaining after 5 minutes:

f(5) = 400 - 0.35(5) = 400 - 1.75 = 398.25 gallons

Therefore, the range of the function for this situation is the interval [398.25, 400] gallons.

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Answer:

12

Step-by-step explanation:

Draw a horizontal line that splits the hexagon in half

x = 180 - measure of a angle in the pentagon - half of the angle in the hexagon

x = 180 - 540/5 - 1/2*(720/6)

x = 180 - 108 - 60 = 180 - 168 = 12

Hope this helps :)

Have a great day

Answer:

Step-by-step expl

2.73 A,16.3 V

Answer:

7 x 50 = 350 $ multiplication

Answer:

- 13p + 8k

Step-by-step explanation:

\(4k-8p+4k-5p\)

\(\mathrm{Group\:like\:terms}\)

\(=-8p-5p+4k+4k\)

\(\mathrm{Add\:similar\:elements:}\:-8p-5p=-13p\)

\(=-13p+4k+4k\)

\(\mathrm{Add\:similar\:elements:}\:4k+4k=8k\)

\(=-13p+8k\)

[RevyBreeze]

The product of 4 1/10 and -3 5/12 is -14 1/120

Fractions are simply described as a subset of a whole or the part of a whole.

They are several types of fractions, some of which includes;

Some examples of mixed fractions; 3 1/4, 5 1/2, 6 1/4

Some examples of simple fractions; 1/2, 1/4, 1/6

Some examples of proper fractions; 3/4, 4/5, 6/7

Some examples of improper fractions; 3/2, 4/3, 6/5

Given the mixed fractions;

4 1/10  ×  -3 5/12

convert to improper fractions

41/10 × - 41/12

Multiply through

- 1681/120

Find the ratio

- 14 1/ 120

Hence, the value is - 14 1/ 120

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Answer: i think the answer to your problem would be 14

Step-by-step explanation: sorry if i'm wrong!

6-5=1

15-1=14

In this case, the polar coordinate of P will be (r, θ), where r represents the distance from the origin to P, and θ represents The angle formed between the positive x-axis and the line segment connecting the origin and P.

To find r, we can use the formula r = √(x^2 + y^2), where x is the x-coordinate (3) and y is the y-coordinate (1) of P. Substituting the values, we get r = √(3^2 + 1^2) = √10.

To find θ, we can use the formula θ = arctan(y/x), where arctan represents the inverse tangent function. Substituting the values, we get θ = arctan(1/3) ≈ 18.43 degrees (or approximately 0.322 radians).

Therefore, the polar coordinate of P is approximately (√10, 18.43°) or (√10, 0.322 rad). This means that P is located at a distance of approximately √10 units from the origin and forms an angle of approximately 18.43 degrees (or 0.322 radians) with the positive x-axis.

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"To determine how reliable a poll is, one must first determine," is a. the margin of error.

All polls contain errors, and the margin of error is a measure of how much the poll results may deviate from the true population values. A larger margin of error means that the poll results are less reliable, while a smaller margin of error indicates greater reliability. While factors such as sample size and standard deviation can also impact the accuracy of a poll, the margin of error is the most important factor to consider when determining its reliability.

The margin of error is a measure of the variability and potential error in poll results due to the randomness of selecting a sample from the population. It provides an estimate of how closely the poll's results represent the views of the entire population. A smaller margin of error indicates a more reliable poll. The standard deviation, inaccuracy rate, and sample size are also important factors, but the margin of error is the key indicator of a poll's reliability.

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Answer:

60

Step-by-step explanation:

The true statements are:

The area under the curve to the left of the pth percentile is equal to p

The area under the curve to the right of the pth percentile is equal to (1-P)

For the first set of statements regarding the standard normal distribution:

1. For z < 0; P(Z < 2) < 0

  - This statement is true. Since z < 0, the probability of Z being less than 2 (a positive value) is less than 0.

2. P(Z < 0) = 0.50

  - This statement is true. For the standard normal distribution, the probability of Z being less than 0 is 0.50 or 50%.

3. P(Z > 0) = 0.0

  - This statement is false. The probability of Z being greater than 0 is not 0.0 but rather 0.50 or 50%.

4. For z > 0, P(Z < 2) < 0.50

  - This statement is true. When z is positive, the probability of Z being less than 2 is less than 0.50.

5. For z > 0, P(Z < 2) > 0.50

  - This statement is false. When z is positive, the probability of Z being less than 2 is always less than 0.50.

6. P(Z > 0) = P(Z < 0) = 0

  - This statement is false. The probability of Z being greater than 0 and less than 0 is both 0.50 or 50%.

Therefore, the true statements are:

- For z < 0; P(Z < 2) < 0

- P(Z < 0) = 0.50

- For z > 0, P(Z < 2) < 0.50

For the second set of statements regarding the pth percentile of a continuous random variable:

1. The area under the curve to the left of the pth percentile is equal to p

  - This statement is true. The pth percentile represents the value below which a certain percentage (p) of the data falls.

2. The area under the curve to the left of the pth percentile is equal to (1-p)

  - This statement is false. The area to the left of the pth percentile is equal to p, not (1-p).

3. The area under the curve to the right of the pth percentile is equal to (1-P)

  - This statement is true. The area to the right of the pth percentile is equal to (1 - p).

4. The area under the curve to the right of the pth percentile is equal to p

  - This statement is false. The area to the right of the pth percentile is equal to (1 - p), not p.

5. The pth percentile is positive

  - This statement's validity depends on the specific distribution being considered. The pth percentile could be positive, negative, or zero, depending on the distribution.

Therefore, the true statements are:

- The area under the curve to the left of the pth percentile is equal to p

- The area under the curve to the right of the pth percentile is equal to (1-P)

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Answer:2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

10 percent of 5 is 0.5

Multiply by 4 for 40%

0.5 × 4 = 2.0

hope this helps...

Answer:

1,6,8

Step-by-step explanation:

Answer:

well there will be a lot of lines , so this one per example y=-3x, so if you add a value just like this -3x +2, this also is parallel to the line 3x+y=8

Answer:

In total, Esme will need to purchase at minimum TWELVE (12) pieces of fence in order to encompass her entire rectangular garden.

Step-by-step explanation:

Let us start off by isolating each of the two different length sides, and figure out which fence pieces can be used to it off.

For the three meter (3 m) side, we could utilize the following THREE (3) pieces...

Adding up those pieces provides us with our desired garden side length...

(1 × 1.8 m) + (2 × 0.6 m) = 3.0 m!

For the six meter (6 m) side, we could utilize the following THREE (3) pieces...

Adding up those pieces provides us with our desired garden side length...

(1 × 1.8 m) + (2 × 2.1 m) = 6.0 m!

We ought to not forget about the opposite sides of the aforementioned, to make up the four sides of the rectangle! In short, we double the number of pieces that we currently have...

In the end, the smallest number of pieces of fence that Esme will need to buy is TWELVE (12), consisting of the following pieces:

I hope this helps! :)

There is enough proof to indicate that the percentage of newsletter readers who possess a Rolls Royce is less than 69%.

The null hypothesis is that p = 0.69, meaning that 69% of the newsletter readers own a Rolls Royce. The alternative hypothesis is that p < 0.69, meaning that less than 69% of the newsletter readers own a Rolls Royce.

We can use a one-tailed z-test to test the hypothesis. Assuming a sample size of n = 100, if we observe fewer than 69 Rolls Royces in our sample, we can reject the null hypothesis.

Using a z-test, we can calculate the z-score by using the formula:

z = (p' - p) / sqrt(p * (1 - p) / n)

where p' is the sample proportion, p is the hypothesized proportion, and n is the sample size.

At a significance level of 0.10, the critical z-value is -1.28. If the calculated z-score is less than -1.28, we can reject the null hypothesis.

If we conduct a survey of 100 newsletter readers and find that 58 of them own a Rolls Royce, the sample proportion would be p' = 0.58. Calculating the z-score, we get:

z = (0.58 - 0.69) / sqrt(0.69 * 0.31 / 100) = -1.83

Since -1.83 is less than -1.28, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that fewer than 69% of the newsletter readers own a Rolls Royce.

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C. Multiplication property

Properties of equality and congruence are properties that show how equations or shapes can be changed but remain equal.

Properties of Equality

Since this question deals with an equation, not a shape, the properties of equality will be used. The most common properties of equality include:

The important thing to note is that whatever is done to one side, must be done to both. No matter what operation it is, if you change the equation you must change both sides equally.

Solving for X

To find the correct property, we need to solve for x. Do this by isolating the variable.

First, let's rewrite the equation.

Now, we need to find a way to isolate the variable. To isolate x, we need to get rid of the denominator, 5. Do this by multiplying both sides by 5. This will cancel out the denominator on the left side. Remember to multiply on both sides.

Then, simplify the equation

To solve this equation, we multiplied both sides by the same number. This matches the definition of the multiplication property of equality, so that must be the correct answer.

1. The first statement is a universally quantified predicate that states for all x, either Px or Dx is true.

2. The second statement is the negation of Da, which means Da is false. From this, we can infer that Pa is true.

1. The first statement, (∀x)(Px v Dx), expresses that for all x, either Px or Dx is true. This means that every element x satisfies the condition of being either Px or Dx. It does not specify which elements satisfy Px or Dx, but it applies to all x universally.

2. The second statement, ~Da, indicates that Da is false. From the negation of Da, we can infer the truth of its negation, which is Pa. Therefore, we can conclude that Pa is true based on the given information.

By combining the conclusions from the two statements, we can deduce the following:

- (∀x)(Px v Dx) is true for all x.

- ~Da is true, which implies Pa is true.

However, there is no direct relation or implication between Pa and the statement GC / Hc. Without further information or logical connections, we cannot derive the conclusion Hc based solely on the given premises.

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Answer:

C. x=4

Step-by-step explanation:

In this graph the x value never changes, it is always equal to four. In this line the slope is undefined and there is no y-intercept. For all straight vertical lines, the equation will be x equals to whatever x value it is.