Pablo has drawn Parallelogram ABCD and its diagonals, AC and BD. Using Side-Side-Side, he has proven that A BAD is congruent to A DCB.
Given this, which result is Pablo now able to prove?,
O ABOCAAOB
O ACOB
AAOD
O ZCOB is an acute angle.
O The area of A BOC is equal to the area of A AOB.

The new volume (V₂) will be twice the initial volume (V₁) when the absolute temperature is doubled at constant pressure.

According to Charles's Law, which states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant, if the absolute temperature of a given amount of gas is doubled, the new volume will also double.

V₁ / T₁ = V₂ / T₂

Where:

V₁ and T₁ are the initial volume and absolute temperature respectively,

V₂ and T₂ are the final volume and absolute temperature respectively.

If the absolute temperature is doubled (T₂ = 2T₁),

V₁ / T₁ = V₂ / (2T₁)

By cross-multiplying and simplifying,

V₂ = 2V₁

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Answer:

  B. cos(pi/2) +i·sin(pi/2)

Step-by-step explanation:

You can convert to rectangular and back, or you can use the trig function relations directly.

  w = 4·cis(π/2) = 4i

  z = 3·cis(3π/2) = -3i

Then the sum is ...

  w +z = 4i -3i = i = cis(π/2) . . . . matches choice B

__

An alternative representation of z is ...

  z = -3·cis(π/2)

Then ...

  w +z = 4·cis(π/2) -3·cis(π/2) = cis(π/2)

_____

Additional comment

In the above, we have used cis(α) to represent (cos(α) +i·sin(α)).

The standard deviation of returns is 0.0665 when a person is holding stock and there are three possible outcomes.

To calculate the expected return, we multiply the probability of each state by its corresponding return and sum them up:

Expected return = (20% * 18%) + (55% * 9%) + (25% * -5%)

Expected return = 0.20 * 0.18 + 0.55 * 0.09 + 0.25 * (-0.05)

Expected return = 0.036 + 0.0495 - 0.0125

Expected return = 0.073

The expected return is 7.30%.

To calculate the standard deviation of returns, we need to find the variance first. The variance is calculated as the weighted sum of squared deviations from the expected return:

Variance = (20% * (18% - 7.30%)^2) + (55% * (9% - 7.30%)^2) + (25% * (-5% - 7.30%)^2)

Variance = 0.20 * (0.1077)^2 + 0.55 * (0.0177)^2 + 0.25 * (-0.123)^2

Variance = 0.00232 + 0.000173 + 0.001903

Variance = 0.004423

The standard deviation is the square root of the variance:

Standard deviation = √(0.004423)

Standard deviation = 0.0665

Therefore, the value obtained is 0.0665.

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The crank angle value when the piston is at Top Dead Center (TDC) is 0 radians or 0 degrees. The maximum ratio of the crank radius to the connected length is 0.3.

The crank angle value refers to the angle between the crankshaft and a reference point when measuring the position of the piston. When the piston is at Top Dead Center (TDC), it is at its highest point in the cylinder. The crankshaft is positioned such that the connecting rod is aligned with the crank radius and the piston is at the topmost position. This corresponds to a crank angle value of 0 radians or 0 degrees.

Regarding the maximum ratio of the crank radius to the connected length, this value is given as 0.3. The crank radius is the distance from the center of the crankshaft to the center of the crank pin, and the connected length is the distance from the center of the crank pin to the center of the piston pin. The maximum ratio of 0.3 indicates that the crank radius is 0.3 times the connected length.

It's important to note that these values are specific to the context of the problem statement provided. Different engines or mechanisms may have different values for the crank angle at TDC and the maximum ratio of crank radius to connected length.

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Answer:

5x/3

Step-by-step explanation:

The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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Answer:

The probability of rolling a six on this cube is A. 1/6

Step-by-step explanation:

Just... Think about it. The cube has six sides (the total, or denominator). There is only one six (the numerator). So, the answer is 1/6.

Have a wonderful day/night! <3

Answer: The answer should be B) -3. To solve the equation you have to rewrite the equation.

The absolute value for |4 - 5i| =\(\sqrt{41}\).

Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A negative number has a positive absolute value, too. If x 0, then |x| = -x gives the absolute value of the supplied number.

For illustration, |-2| = 2. No matter what the numerical value's sign, the absolute value is always positive.

Here complex number form =|a+ib|

= |4-5i| Here a=4, b=(-5).

\(|a+ib| = \sqrt{a^{2}+b^{2} } \\\\\sqrt{4^{2}+5^{2} } \\\\\sqrt{16+25} \\\\\sqrt{41} \\\)

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The coordinates of the given triangle after 90° counter-clockwise about the origin are: \(\left[\begin{array}{ccc}-1&-2&-4\\2&4&3\end{array}\right]\)

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices, the coordinates of the vertices of the image are as follows:

(x, y)                               →                (-y, x)

Ordered pair (2, 1)        →           Ordered pair (-1, 2)

Ordered pair (4, 2)        →           Ordered pair (-2, 4)

Ordered pair (3, 4)        →           Ordered pair (-4, 3)

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Therefore, the probability that Team A wins the series given that they have already won the first game is 0.36 or 36%.

To calculate the probability that Team A wins the series given that they have already won the first game, we can consider the different possible scenarios for the remaining games. For Team A to win the series, they need to win at least one of the next two games. Let's analyze the possible outcomes:

Team A wins the second game and wins the series. Team A loses the second game but wins the third game and wins the series. The probability of Team A winning the second game is 0.2, and the probability of Team A winning the third game is also 0.2. Using these probabilities, we can calculate the probability of each scenario:

Scenario 1:

P(A wins second game and wins series) = P(A wins second game)

= 0.2

Scenario 2:

P(A loses second game but wins third game and wins series) = P(A loses second game) * P(A wins third game)

= (1 - 0.2) * 0.2

= 0.8 * 0.2

= 0.16

Now, we can add up the probabilities of both scenarios to find the overall probability that Team A wins the series:

P(A wins series | A wins first game) = P(A wins second game and wins series) + P(A loses second game but wins third game and wins series)

= 0.2 + 0.16

= 0.36

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The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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Answer: \(\frac{1}{6}\)

Step-by-step explanation:

Given

There is half of a steak left for Julie, her brother, and her mom i.e. there are 3 persons to share the steak

So, each family member will get one-third of leftover steak or

\(\Rightarrow \dfrac{\frac{1}{2}}{3}=\dfrac{1}{6}\)

One-sixth of steak

The type of utility that provides fast, friendly service during and after the sale as well as teaching customers to use products over time is the service utility.

What is Utility?

Consumption refers to the usefulness or satisfaction derived from consuming goods and services. It is the ability of a product to satisfy consumers and meet their demands. It is critical to assisting consumers in making choices by providing a sense of satisfaction and need fulfillment. It is possible to classify utility into two categories: form and service. Formal utility refers to the ability of a product to satisfy a need or desire by changing the characteristics of an object to make it more valuable to consumers.

Service Utility

Service utility refers to the additional value that consumers receive as a result of receiving services such as quick and reliable delivery, prompt repair, and courteous and competent customer support. Service utilities can be divided into two types: pre-sale and post-sale.

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Solution:

The solution to the system of an equation using the graphical method is the point on the graph where the two lines intersect

From the image below, the point of intersection of the two lines is at

Hence,

The x-coordinate of the solution to the system of equation is

The angle between two vectors a = 5i + j and b = 2i - 4j is approximately 52.125°.

The angle between two vectors can be calculated using the following formula: cosθ = (a · b) / (||a|| ||b||)

where θ is the angle between the vectors, a · b is the dot product of the vectors, and ||a|| and ||b|| are the magnitudes of the vectors.

In this case, the dot product of the vectors is 13, the magnitudes of the vectors are √29 and √20, and θ is the angle between the vectors. So, we can calculate the angle as follows:

cos θ = (13) / (√29 * √20) = 0.943

The inverse cosine of 0.943 is approximately 52.125°. Therefore, the angle between the two vectors is approximately 52.125°.

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The weight of food packed in certain containers is a random variable with a mean of 16 0z. and a standard deviation of 0.6 oz. If 36 packages are randomly selected, the probability that the mean will be greater than 16.2 oz is 2.28%.

Given that the weight of food packed in containers is a random variable with a mean (µ) of 16 oz. and a standard deviation (σ) of 0.6 oz, we want to find the probability that the mean weight of a sample of 36 packages (n) will be greater than 16.2 oz.
Step 1: Calculate the standard error (SE) of the sample mean.
SE = σ / √n = 0.6 / √36 = 0.6 / 6 = 0.1
Step 2: Calculate the z-score for 16.2 oz.
z = (sample mean - population mean) / SE = (16.2 - 16) / 0.1 = 2
Step 3: Find the probability that the mean weight will be greater than 16.2 oz.
To find the probability for a z-score of 2, we can look it up in a standard normal (z) table or use a calculator that provides the area to the left of the z-score.
Using the table or calculator, we find the area to the left of the z-score 2 is approximately 0.9772. Since we are looking for the probability of the mean weight being greater than 16.2 oz, we want the area to the right of the z-score. To find this, subtract the area to the left from 1:
1 - 0.9772 = 0.0228
So, the probability that the mean weight of the 36 packages will be greater than 16.2 oz is approximately 0.0228 or 2.28%.

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Answer:

Step-by-step explanation:

9 x 7 = 63

9 x 2 = 18

63+18=81

SO we do 9(7+ 2)

HOPE THIS HELPED :DDDD

Answer:

y=-2x+2

Step-by-step explanation:

it has a positive slope

the line should point like this on the graph: picture above

Answer:

B

Step-by-step explanation:

Answer:

I believe the answer is 240.

Step-by-step explanation:

Answer:

240 calories each day

Step-by-step explanation:

According to the information Lacey read, a cat weighing p pounds needs to eat a total of 30p calories each day to stay healthy. Since Lacey's cat, Muffin, weighs 8 pounds, she needs to eat 30 * 8 = <<30*8=240>>240 calories each day to stay healthy. Therefore, Lacey should feed her cat a total of 240 calories each day in order to ensure that it receives the proper nutrition and stays healthy.

Answer:

if you mean 8 divided by 5 then use long division which will result in 1 with a remainder or 3 or 1.6

Answer:

8/5=1.6

Step-by-step explanation:

There's no step by step for explaining this answer. Or nothing that I can think of

Answer:

Step-by-step explanation:

You can use the slope formula:

\(y = mx + b \\ m = slope , b = y-intercept\)

So if the function is :

\(f(x) = \frac{-2}{3} x - 4\)

Then m (the slope) is -2/3

Bisect each angle of the triangle using a compass then where the lines the have been bisected meet up, from there, put the the compass and then your pencil tip on the perimeter of the triangle and draw a circle

Answer:

Para un rectángulo de largo L y ancho W, el área se define como:

A = L*W

Ahora sabemos que nuestro rectángulo tiene un área de 24cm^2

Entonces queremos encontrar 3 pares de valores L y W tal que:

L*W = 24cm

Esto es bastante trivial, podemos simplemente definir una de las dos variables, y así encontrar el valor de la otra.

Por ejemplo, si definimos L = 1cm

tenemos:

(1cm)*W = 24cm^2

W = (24cm^2)/(1cm) = 24cm

Entonces un posible rectángulo tiene un largo de 1cm y un ancho de 24cm

Si tomamos L = 3cm tenemos:

(3cm)*W = 24cm^2

W = (24cm^2)/(3cm) = 8cm

Un rectángulo con 8cm de ancho y 3cm de largo es otra opción.

Si tomamos L = 4cm tenemos:

(4cm)*W = 24cm^2

W = (24cm^2)/(4cm) = 6cm

Un rectángulo con 6cm de ancho y 4cm de largo también es un posible rectángulo.

Así, los 3 rectangulos que se piden pueden ser:

1) largo 1 cm, ancho 24cm

2) largo 3cm, ancho 8cm

3) largo 4cm, ancho 6cm

a) E(2X) = 2E(X) = 2(4) = 8. Therefore, the expected value of 2X is 8.

b) Var(2X) = (2^2)Var(X) = 4(3^2) = 36. Therefore, the variance of 2X is 36.

To derive these answers, we first used the fact that the expected value of a constant times a random variable is equal to the constant times the expected value of the random variable. This is why we were able to obtain E(2X) = 2E(X) = 2(4) = 8.

For part b, we used the fact that the variance of a constant times a random variable is equal to the square of the constant times the variance of the random variable. This is why we were able to obtain Var(2X) = (2^2)Var(X) = 4(3^2) = 36.

In summary, we were able to find the expected value and variance of 2X by using basic properties of expected value and variance.

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Answer:

4 2 and 3 are the exterior angles

Answer:

3.92 x \(10^{12}\)

Step-by-step explanation:

The first factor needs to be a number greater than 0, but less than 10.  That would be 3.92.  Next count how many places you moved the decimal.  In standard notation the decimal should be 12 spaces to the right.  This is the exponent.

Helping in the name of Jesus.

The size of XYZ in the triangle based on the application of trigonometry ratio is 66.4°.

Based on the information given, it should be noted that we can apply trigonometry to solve the triangle.

In this case, the hypothenuse is 15cm and the adjacent is 6cm. The trigonometry ratio will be:

cos = adjacent / hypothenuse.

cos x = 6 / 15

cos x = 0.4

x will be the inverse cos to find the value. This will be 66.4°.

Therefore, the angle is 66.4°.

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