What is the radius of the circle if the given equation is x2 y2 9?

Answers

Answer 1

The radius of the circle is 3. . The equation for a circle is x2 + y2 = r2, where r is the radius of the circle.

Given equation: x2 + y2 = 9

We can rewrite the equation as (x2 + y2) = 32

This is the equation for a circle, with the radius equal to the square root of 3.

Therefore, the radius of the circle is 3.The circle is the set of all points in a plane that are the same distance from a given point called the center. The equation for a circle is x2 + y2 = r2, where r is the radius of the circle.

Given equation: x2 + y2 = 9

We can rewrite the equation as (x2 + y2) = 32

Since 32 is the square of 3, we can conclude that the radius of the circle is 3. This means that the distance from the center of the circle to any point on the circle is 3 units.

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Related Questions

warm up help plz and thx

warm up help plz and thx

Answers

Answer:

D. for the first one and B. for the second one i think

how do you ensure accurate predictions using data correlation? which are the most effective methods?

Answers

Correlation

The only kind of data generated by observational research is correlations or patterns in the data that have been observed. By using correlations, one variable's value can be used to predict the value of another.

Explanation:

Accurate predictions using data correlation can be ensured by using a variety of methods. Firstly, it is important to ensure that the data is free from errors and is of high quality. This can be done by cleaning and validating the data to remove any inconsistencies and outliers. Secondly, it is important to analyze the data thoroughly and identify any patterns or trends. Furthermore, it is beneficial to use appropriate statistical tests and algorithms such as linear regression, logistic regression, and decision trees to identify the predictive relationships between the variables. Finally, it is important to evaluate the model’s performance to determine the accuracy of the predictions.

The most effective methods for ensuring accurate predictions using data correlation are:

1. Perform Exploratory Data Analysis: Exploratory data analysis is an essential step in any predictive modeling process. It involves exploring the data to identify patterns, trends, and relationships within the data. This helps to identify any potential issues or biases within the data that could affect the accuracy of predictions.

2. Use Statistical Tests: Statistical tests can be used to measure the strength of the relationship between two variables. These tests can help to identify which variables are most strongly correlated with each other and can help to determine which variables should be used in a predictive model.

3. Use Machine Learning Algorithms: Machine learning algorithms can be used to create predictive models that can identify and learn patterns in the data. These algorithms are particularly effective at identifying complex relationships between variables that may not be identified by statistical tests.

4. Validate Predictions: Predictions should always be validated to ensure that they are accurate and reliable. This can be done by comparing the predictions against known outcomes or by testing the model on a separate data set.

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A square-base pyramid has the following measurements: The base edges are 3cm The height of the pyramid is 8cm What is the slant height of the pyramid?

Answers

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

good luck

GOOD AFTERNOON BRAINLIESTS! Please help me with this question! TYSM!
- xXIndieKidXx

GOOD AFTERNOON BRAINLIESTS! Please help me with this question! TYSM! - xXIndieKidXx

Answers

Answer:

Domain: All real numbers ; Range: y> -3

Step-by-step explanation:

The quadrilateral below is a rhombus. Find the missing measures. Any decimal answers should be rounded to the nearest tenth.
NK =
m
NL =
m
ML =
m
JM =
m
m

Answers

A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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solve the equation 3x - 8 = 8x - 7

Answers

Answer:

Im solving for x here u didn't specify so lol

Step-by-step explanation:

3x - 8 = 8x - 7

To clarify the "- 8" and the "- 7" are negatives.

3x - 8 = 8x - 7

Add 7 both sides

3x - 8 = 8x - 7

    + 7         + 7

Now u have

3x - 1 = 8x

Subtract 3x both sides

3x - 1 = 8x

-3x       -3x

You get

- 1 = 5x

Divide by 5 both sides

- 1 / 5 = 5x / 5

-0.2 = x

That's your answer help me out I need points <3

Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values. 2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5 Required: a. Compute the population mean. (Round your answer to 1 decimal place.) b. Compute the standard deviation. (Round your answer to 2 decimal places.) c. If you were able to list all possible samples of size five from this population of 20, how would the sample means be distributed

Answers

Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

What are the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

\(S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23\)

What does the Central Limit Theorem states?

It states that for distribution of sample means of size n:

The mean remains constant.The standard deviation is of S/sqrt(n).

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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Fill in the blank.
-6 + ____ = -6

Answers

Answer:

The answer is 0

Step-by-step explanation: If you have -6 and you want to the answer to be -6, if you add anything to 0, it will be the same sum.

What is the range of f/x )= sin x the set of all real numbers?

Answers

On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = \(-1 < y < 1\)

What is Range?

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The Range of the given function, f(x) = sin(x)

\(-1 < y < 1\)

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(Expected rate of return and risk) B. J. Gautney Enterprises is evaluating a security. One-year Treasury bills are currently paying 4.8 percent. Calculate the investment's expected return and its standard deviation. Should Gautney invest in this security? Probability 0.20 Return - 4% 4% 7% 0.45 0.15 0.20 10% (Click on the icon in order to copy its contents into a spreadsheet.) ...) a. The investment's expected return is%. (Round to two decimal places.)

Answers

The investment's expected return is 5.95%.

Is the investment's expected return favorable for Gautney?

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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a) use the divergence theorem to evaluate fF.ñ ds where F = y³i+zj + zk and S is the surface bounded by the graphs of z=1-x² - y² and z = 0 b) use the stokes theorem to evaluate curlF.ñ ds where F = yi-xj-z²k and S is the part of the surface bounded by z=4-x² - y² and z = 0 oriented upward c) use the stokes theorem to evaluate fF.dr for the vector field F = 2zi + 3xj+yk S is the surface of the paraboloid z=1-x² - y² and C the trace of S in the xy-plane with counterclockwise direction. a) Show that the integral is independent of the path and find its value: (1,2) [(y + 2xy)dx + (x² + x)dy (0,1)

Answers

a) The surface integral using the divergence theorem evaluates to 4/3.

b) The surface integral using the Stokes theorem evaluates to 0.

c) The line integral using the Stokes theorem evaluates to -12.



a) To evaluate the surface integral using the divergence theorem, we first find the divergence of the vector field F, which is 2. The surface S is bounded by z = 1 - x² - y² and z = 0. The outward unit normal vector is n = k since the surface is oriented upward. Applying the divergence theorem, the integral becomes the triple integral of 2 over the volume enclosed by the surface. Integrating 2 with respect to the volume gives the volume V = 2/3. Therefore, the surface integral is 2 times the volume, resulting in 4/3.

b) To use the Stokes theorem, we need to find the curl of the vector field F, which is (2z, 1, -1). The surface S is bounded by z = 4 - x² - y² and z = 0, oriented upward. Applying the Stokes theorem, the integral becomes the line integral of F over the curve C, which is the trace of S in the xy-plane. Since F = yi - xj - z²k, the line integral can be calculated as ∮C (ydx - xdy - z²dz). Considering the parametric representation of the curve C as a circle with radius 2, the line integral evaluates to 0.

c) Using the Stokes theorem, the line integral becomes the surface integral of the curl of F over the surface S. The curl of F is (0, -3, 2). The surface S is the paraboloid z = 1 - x² - y², and the curve C is its trace in the xy-plane. Evaluating the surface integral gives the value of -12.

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What is 14 inches rounded to the nearest inch?

Answers

Answer:

6 inches

Step-by-step explanation:

1 inch = 2.54 cm.

 1 cm = 1/2.54 inches.

14 cm = 14/2.54

14 cm, when rounded to nearest inch, results in around 6 inches.

The shape shown is made up of three similar right-angled triangles.


Click to insert IMC 2022 KF3a


The smallest triangle has two sides of side-length 2, as shown.


What is the area of the shape?

Answers

To calculate the area of the shape made up of three similar right-angled triangles, we need additional information about the scale factor or proportions of the triangles. Without that information, we cannot determine the exact area of the shape.

The given information states that the shape is composed of three similar right-angled triangles, and the smallest triangle has two sides of side-length 2. While we know the dimensions of the smallest triangle, we do not have any information about the scale factor or proportions of the other two triangles. Since the shape is formed by three similar triangles, the areas of the triangles would be proportional, but we cannot determine the exact proportions without additional information. Consequently, we cannot calculate the area of the shape accurately based solely on the given information.

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In ABC, D is a point on AB and E is a point
on AC such that DE is parallel to BC. If AE = 3,
EC = x, ED = x + 1, and CB = x + 5, find the
length of EC. [Only an algebraic solution will be
accepted.]

Answers

The required value of EC is 5 units.

How to find the value of EC?

Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:

AD/DB = AE/EC

We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:

AD = x, DB = x + 5 - x = 5

We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:

AD = ED - AE = (x + 1) - 3 = x - 2

Substituting these values into the proportion, we get:

(x - 2)/5 = 3/EC

Multiplying both sides by 5EC, we get:

x - 2 = 15/EC

Multiplying both sides by EC, we get:

EC(x - 2) = 15

Expanding the left side, we get:

ECx - 2EC = 15

Solving for EC, we get:

EC = 15/(x - 2)

We are given that EC = x, so we can set these expressions equal to each other:

x = 15/(x - 2)

Multiplying both sides by (x - 2), we get:

x(x - 2) = 15

Expanding the left side, we get:

x² - 2x = 15

Bringing all terms to one side, we get:

x² - 2x - 15 = 0

We can factor this quadratic equation:

(x - 5)(x + 3) = 0

Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.

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Mitchell received a stipend at the beginning of the semester to buy textbooks. During the semester, he spent $439.14 on textbooks. He had $144.60 of the stipend left at the end of the semester.

x - $439.14 = $144.60

Answers

The original stipend was $583.74
$294.54 get you a calculator my guy.

Use back-substitution to solve the system. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x2-t and solve for xi in terms of t.) X1-x2=5
x2 = 4 (xi x2) =

Answers

The solution to the system is (X1, x2) = (9, 4).

The given system of equations is:

Equation 1: X1 - x2 = 5

Equation 2: x2 = 4

To solve this system using back-substitution, we start with the second equation, which is already solved for x2. We can directly substitute the value of x2 from Equation 2 into Equation 1.

Substituting x2 = 4 into Equation 1, we get:

X1 - 4 = 5

To isolate X1, we can add 4 to both sides of the equation:

X1 = 5 + 4

Simplifying the right side:

X1 = 9

Therefore, the solution to the system is X1 = 9 and x2 = 4. In other words, the ordered pair (X1, x2) is (9, 4).

This means that if we substitute X1 with 9 and x2 with 4 in both equations, both equations will be satisfied simultaneously. This solution represents the point of intersection of the two lines represented by the equations.

It's important to note that this system has a unique solution since there is only one point where the two lines intersect. If the system had no solution or an infinite number of solutions, the back-substitution method would lead to different outcomes.

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5.explain why reaction rates decline with time and use this information to correctly process the data (by choosing the proper data points to do linear regression

Answers

Reaction rates decline with time because the reactants are consumed over time, reducing the number of reactant particles available for reaction.

What are reactants?

The components that are involved in a chemical reaction are known as reactants. They are the beginning ingredients that are changed into new compounds, known as products, through a chemical process. The left side of a chemical equation is often used to represent reactants, whereas the right side is used to indicate products. The quantity and kind of reactants and products affect the kind of chemical reaction that takes place. Pure substances, such as elements or compounds, or combinations of substances, can function as reactants with time. In a chemical reaction, reactants are changed into products by chemical bonds being broken and formed, releasing or absorbing energy in the process.

How to solve?

As the number of reactant particles decreases, the rate of reaction also decreases. This phenomenon can be observed in many chemical reactions, including reactions that involve the decay of radioactive elements.To correctly process data on the decline of reaction rates with time, it is important to choose the appropriate data points for linear regression. This typically involves selecting data points at regular intervals, such as every minute or every hour, to accurately represent the decline in reaction rates over time. By choosing the right data points and performing linear regression, it is possible to accurately model the decline in reaction rates and make predictions about future reactions.

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need help asap please!

need help asap please!

Answers

Answer:

determinant: -15x = 3; y = 4; z = 1

Step-by-step explanation:

The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.

coefficient matrix, determinant

The first attachment shows the coefficient matrix and its determinant.

__

solution

The solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.

  \(\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}\)

This multiplication is shown in the second attachment. It tells us ...

  \(\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right]\)

need help asap please!
need help asap please!

solve for a and simplify your answer

solve for a and simplify your answer

Answers

The first step let us find the lowest common denominator to get r of the fraction.

⇒In this case the lowest denominator is 3,meaning3 will multiply all the terms in the equation

\(-14(3)=-\frac{4}{3} a(3)\\-42=-4a\)

⇒ Divide all the terms of the equation with the coefficient of the unknown variable to leave it independent.

⇒We are going to divide all the terms of the equation on this case by -4 since it tis the coefficient of the unknown variable

\(-\frac{42}{-4} =-\frac{4a}{-4} \\a=10.5\)

∴a=10.5


Help its for algebra!!!

Help its for algebra!!!

Answers

Answer:

they both last 1,25 hours

Step-by-step explanation:

Friday: 5*A + 3*B =10 hours

Saturday: 2*A + 6*B = 10 hours  --> A = (10-(6*B)) / 2

                                                          A = 5-(3B)

5*(5-3B) + 3B = 10

25 - 15B + 3B = 10

15= 12B

B=1,25 hours

A=5-3*1,25

A= 1,25 hours

The diameter of a circle is 35 cm. find its area to the nearest whole number.

Answers

Answer:

962 cm²

A = 1/4πd²

   = 1/4 × π × 35²

    = 962 cm²

Area of circle = pi * radius ^2

Radius = 35 / 2 = 17.5

pi * (17.5)^2 = 962 square cm

Hope this helps!

A balloon is filled with helium at sea level, and then taken into the mountains to an elevation of 7500 feet. Assuming the temperatures are the same, what will happen to the balloon

Answers

When a balloon filled with helium at sea level is taken into the mountains to an elevation of 7500 feet, several things can happen:

The balloon may expand

As we go higher in altitude, the atmospheric pressure decreases. This means that the pressure outside the balloon is lower at higher elevations compared to sea level. If the pressure inside the balloon remains constant, the difference in pressure between the inside and outside of the balloon increases, causing the balloon to expand.

The balloon may burst:

If the pressure inside the balloon is significantly higher than the pressure outside the balloon at the higher altitude, it may exceed the structural integrity of the balloon, causing it to burst or pop.

The balloon may deflate:

If the pressure inside the balloon is lower than the pressure outside the balloon at the higher altitude, the helium gas inside the balloon may escape, causing the balloon to deflate.

The exact outcome would depend on various factors such as the elasticity and strength of the balloon material, the volume of helium inside the balloon, the temperature, and the atmospheric conditions at the specific altitude. It is important to take into consideration the potential effects of altitude changes when using helium-filled balloons or any other gas-filled containers in different elevations to avoid potential hazards.

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pls help i really need it​

pls help i really need it

Answers

Answer:

I think if you look up the equation on google there is a calculator and you may get some of your answers there

Step-by-step explanation:

k/5 + 8= 23 what solution is k?

Answers

Answer:

k=75

Step-by-step explanation:

\(\frac{k}{5}\)+8=23

(subtract 8 from both sides of the equation)

\(\frac{k}{5}\)+8-8 = 23-8

(simplify)

\(\frac{k}{5}\) = 15

(multiple all terms by the same value to eliminate fractional denominators)

5. \(\frac{k}{5}\) = 5.15

(cancel multiplied terms that are in the denominator, multiply the numbers)

k=75

Use the following building blocks in the right column to assemble a direct proof that the product of two odd numbers is odd Not all blocks belong in the proof. Suppose that the product of two odd numbers is odd. Distributing we get nm-2(2kk)+1 Suppose that nm is odod. By multiplying these equations, we obtain nm = (2k + 1)(29 + 1). By definition of an odd integer, that means that nm is odd. Suppose that n and m are odd numbers. Then n = 2k + 1 for some integer k and m = 2q + 1 for some integer q. Then n 2k + 1 and m-2k + 1 for some integer k.

Answers

Using the following building blocks in the right column to assemble a direct proof that the product of two odd numbers is odd, we have:

Suppose that n \(\alpha\) m is oddThen n = 2k + 1, for some integers k, m = 2q + 1, for some integers qBy multiplying these equations, we obtain mn = (2k +1)(2q + 1)Distributing, we get: nm = 2(2kq + k + q) + 1By definition of odd integers, nm is odd

What is a Mathematical Proof?

A mathematical proof is an inferential justification for a mathematical claim that demonstrates how the premises logically support the conclusion.

The direct proof has been assembled above,

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Use the following building blocks in the right column to assemble a direct proof that the product of

There are 8 women on a bus each of them has 8 bags and each one of those bags has 8 cats in them and each cat has 8 kittens how many legs are on the bus?

Answers

I’m pretty sure the answer is 18,448 legs

8 women*2 legs=16

8*8 bags=64 bags

64*8=512 cats * 4= 2048 legs

512*8=4096 kittens*4=16,384 legs

16,384+2,048+16= 18,448 legs!

Answer: 272 legs on the bus

Step-by-step explanation:

It says the women and cats are on the bus, but it does not say that the kittens are on the bus, so only the women and cat legs will be counted.

Each woman has 2 legs and each cat has 4 legs.

so: 8 x 2 = 16 human legs

     8 bags with 8 cats in each bag = 64 cats

     64 x 4 = 256 cat legs

      16 + 256 = 272 legs

Therefore 272 legs are on the bus.

(1)The figure shows two similar triangles: the smaller triangle has a base length of 8 feet and a height of 5 feet (the height of the boy), whereas the second triangle has a base length of 24 feet and a height equal to that of the tree. How tall is the tree? (A) 15 feet (B) 27 feet (C) 38.4 feet (D) 45 feet 24 ft 5 ft 8 ft​

(1)The figure shows two similar triangles: the smaller triangle has a base length of 8 feet and a height

Answers

Answer:

A

Step-by-step explanation:

since the 2 triangles are similar then the ratios of corresponding sides are in proportion.

let h represent the height of the tree , then

\(\frac{h}{5}\) = \(\frac{24}{8}\) = 3 ( multiply both sides by 5 )

h = 3 × 5 = 15

height of tree is 15 feet

evaluate the cross product (3iˆ 5jˆ)×(−3iˆ 8jˆ), which expands to −9 iˆ×iˆ 24 iˆ×jˆ−15 jˆ×iˆ 40 jˆ×jˆ. write your answer in vector form physics

Answers

The required cross product of given vectors is 39k

What is cross product?

Cross product is a parallel procedure on two vectors in three-layered space. It brings about a vector that is opposite to the two vectors. The Vector result of two vectors, an and b, is meant by a × b. Its resultant vector is opposite to an and b. Vector items are additionally called cross items.

According to question:

A = 3i + 5j , B = -3i + 8j

Then, cross product of A and B,

A×B = i(5×0 - 8×0) - j(3×0 - (-3)×0) + k(3×8 - (-3)×5)

A×B = i(0) - j(0) + k(24 + 15)

A×B  = 39k

Thus, cross product of A and B is 39k

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A survey of the 12th grade students at gaffigan high school found that 84% of the seniors have their driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. To the nearest whole percent, what is the probability that a senior takes the bus to school every day, given that he or she has a driver’s license?.

Answers

The probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

To find the probability that a senior takes the bus to school every day given that he or she has a driver's license, we can use conditional probability.

Let's denote the event that a senior has a driver's license as A and the event that a senior takes the bus to school every day as B. We want to find the probability of event B given event A, denoted as P(B|A).

We are given the following information:

P(A) = 84% = 0.84 (probability of having a driver's license)P(B) = 16% = 0.16 (probability of taking the bus every day)P(A ∩ B) = 14% = 0.14 (probability of having a driver's license and taking the bus every day)

The conditional probability formula states that P(B|A) = P(A ∩ B) / P(A).

Substituting the given values, we have:

P(B|A) = P(A ∩ B) / P(A) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

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Final answer:

The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

Explanation:

To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.

We can use the formula:

P(A|B) = P(A and B) / P(B)

where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.

Plugging in the values into the formula:

P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)

P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

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the vertices of the trapezoid are the origin along with a (4m, 4n), b (4q, 4n), and c (4p, 0). find the midpoint of the midsegment of the trapezoid.

Answers

The midpoint of the midsegment of Trapezoid is   E(2m, 2n) and F (2(q+p), 2n).

According to the question,

The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).

Let mid-point of midsegment of Trapezoid be E and F

Using section formula

E (x- coordinate)= 1*4m + 0 /2

E (x- coordinate)=2m

E (Y- coordinate)= 4n/2

E  (Y- coordinate)=2n

So, the coordinates of E (2m, 2n)

similarly,

F (x- coordinate)= (1*4q + 1*4p)/2

F (x- coordinate)=2(p + q)

F (Y- coordinate)= 4n/2

F(Y- coordinate)=2n

So, the coordinates of F (2(q +p), 2n)

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