A line passes through (6, 3), (8, 4), and (n, -2). Find the value of n.

Answer:

Y = -7x + 24

Step-by-step explanation:

Given

The vectors u and v as,

To find the vector representing u+v.

Explanation:

It is given that,

Two vectors u and v are represented as,

Then, the vector representing u+v is given by,

Answer:

56/143

Step-by-step explanation:

For fraction multiplication, multiply the numerators and then multiply the denominators to get

7*8/13*11 = 56/143

This fraction cannot be reduced.

Therefore:

7/13 * 8/11 = 56/143

The use of Arabic numerals in mathematical calculations provides a consistent, efficient, and universal framework for representing, manipulating, and communicating numerical information, contributing to the development and advancement of various fields of mathematics and sciences.

Arabic numerals, also known as Hindu-Arabic numerals, are the number system we commonly use today, consisting of the digits 0-9. They play a crucial role in performing mathematical calculations for several reasons:

1. Positional notation: Arabic numerals utilize a positional notation system, where the value of a digit depends on its position within the number. This allows for concise representation of numbers and makes arithmetic operations like addition, subtraction, multiplication, and division more efficient and intuitive.

2. Flexibility: Arabic numerals are versatile and can represent a wide range of numbers, from small integers to extremely large or small values. This makes them suitable for all types of mathematical calculations, including basic arithmetic, algebra, calculus, and more advanced mathematical concepts.

3. Universality: Arabic numerals are widely adopted and recognized across the world, making them a universal system for mathematical communication. This standardization enables mathematicians, scientists, engineers, and individuals from different cultures and languages to understand and collaborate on mathematical problems without language barriers.

4. Decimal system: Arabic numerals are based on a decimal system, meaning that they operate in multiples of 10. This aligns with our everyday experiences and facilitates easy comprehension and estimation of quantities. It also allows for efficient conversions between different units and simplifies complex calculations involving fractions and percentages.

Overall, the use of Arabic numerals in mathematical calculations provides a consistent, efficient, and universal framework for representing, manipulating, and communicating numerical information, contributing to the development and advancement of various fields of mathematics and sciences.

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The estimated standard error for a sample of n = 9 scores with ss = 288 is 2. Among your choices, it should be B; s2 = 36 and sM  = 2.

Hope that helps!

The percent increase of the money is 208%, then the correct option is C.

We know that the musician starts with $750, that is the initial amount (which is the 100%) and he adds $130 each month for 12 months, then at the end he will have a total of:

$750 + 12*$130 = $2,310

To find the percent increase, we need to use the formula to get:

P = 100%*(final amount - initial amount)/initial amount

Replacing the values that we know we will get:

P = 100%*($2,310 - $750)/$750

P = 208%

Then the correct option is C.

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Answer:

900+ hours

Step-by-step explanation:

The answer given below means that the function is discontinuous at x = -3 and limit does not exist. Hence, the answer is; The value of the given limit does not exist.

Given function is; f(x) = x² - 3x / x² - 9. To find; limx→-3 f(x)

Now, we need to evaluate the function at the given points; x = -2.9, -2.99, -2.999 and x = -3.1, -3.01,-3.001

Using these points, we can create a table of values as follows:

x f(x)-2.9 28.7001-2.99 29.7001-2.999 29.97-3.1 30.9-3.01 30.0101-3.001 30.001

For calculating the value of limit, we use the concept of limits. It states that if a function f(x) approaches a particular value L as x approaches a, then the limit of f(x) as x approaches a is L. Now, we can see that x is approaching -3 from both sides in the given function. Let's evaluate the function for x = -3, we get;

f(-3) = (-3)² - 3(-3) / (-3)² - 9 = 18 / 0, which is not defined.

This means that the function is discontinuous at x = -3 and limit does not exist. Hence, the answer is; The value of the given limit does not exist.

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Answer:

60 cents

Step-by-step explanation:

hhgfghgfgucixoszfup

Answer:

The answer is D. $1.60

Step-by-step explanation:

4 quarters equal $1.00

2 dimes equal .20 (or 20 cents)

6 nickels equal .30 (or 30 cents)

and 10 pennies equal .10 (or 10 cents)

when you add all of this together, you get $1.60 in total, i hope this helps (:

a) The probability that the sample mean will be less than 11 is approximately 0.0062.

b) The probability that the sample variance will be greater than 5 is approximately 0.0823.

a) To find the probability that the sample mean (X) is less than 11, we can use the properties of the normal distribution. We know that the population mean (μ) is 11.4 and the sample size is 16. Since the population is normally distributed, the sample mean will also follow a normal distribution. We can calculate the z-score corresponding to X = 11 , where σ is the population standard deviation and n is the sample size.-0.4714. We can then look up the corresponding cumulative probability for this z-score in the standard normal distribution table or use software to find that the probability is approximately 0.0062.

b) To find the probability that the sample variance (S^2) is greater than 5, we need to use the chisquare distribution. Since the population is normally distributed, the sample variance follows a chi-square distribution with n-1 degrees of freedom, where n is the sample size. In this case, n = 16.. We can then find the cumulative probability for this chi-square statistic with 15 degrees of freedom and find that the probability of having a sample variance greater than 5 is approximately 0.0823.

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Answer:

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Answer:

0.887 kg

Step-by-step explanation:

3.548/4=0.887

Answer:

.887 kg per container

Step-by-step explanation:

Take the total amount of peanut butter and divide by 4

3.548 / 4

.887 kg per container

The bag weight is 1.5 standard deviation below the mean value. Standard deviation is found with the help of variance.

The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.

The mean value is 4.10 ounce

Standard deviation= 0.10 ounce

The formula for the standard deviation is found as;

\(\rm Z= \frac{x-\mu}{\sigma} \\\\ Z= \frac{3.95-4.10}{0.10} Z=\frac{-0.15}{0.10} \\\\ Z=-1.5\)

Hence, the bag weight is 1.5 standard deviation below the mean value.

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Answer:

your picture is blank if you can fix it i will be glad to help you

Step-by-step explanation:

Answer:

First option

Step-by-step explanation:

The line corresponds to the f(x).

Hope this helps

To solve this problem, we have to use the equivalence of each type in dollars.

Taking x, y and z as the number of nickels, dimes and quarters, we have that:

0.05 is the equivalence of one nickel in dollars, same for 0.1 and 0.25 with dimes and quarters respectively.

Now, we know that she has 2 more dimes than nickels:

And 4 more quarters than nickels:

We can use the expression for y and z in terms of x in the first equation to find the value of x (number of nickels):

Once we have found x, we can use it to find y and z using the equations we stated:

It means that Susan has 3 nickels, 5 dimes and 7 quarters.

Answer:

6

Step-by-step explanation:

4 * x + 12= 36

          -12  -12

4x = 24

x= 6

Answer: 6

Step-by-step explanation:

The equation will look like this

n(4)+12=36

n=6

6(4)+12

24+12

36

To construct a 95% confidence interval to estimate the parameter of interest, we need to follow these steps:

1) Check the necessary assumptions:
  - The responses were collected randomly from ann arbor-area collegiate football fans.
  - The sample size, 441 responses, is large enough for the Central Limit Theorem to apply.
  - The responses are independent of each other.

2) Compute the 95% confidence interval to estimate p:
  - The parameter of interest, p, represents the proportion of all ann arbor-area collegiate football fans who give preference to an eight-team playoff format.
  - To calculate the confidence interval, we can use the formula:
    Confidence Interval = sample proportion ± margin of error
   
  - The sample proportion is the number of responders who give preference to an eight-team playoff format divided by the total number of responses, which is 234/441.
    Sample Proportion = 234/441 ≈ 0.530
 
  - The margin of error can be determined by multiplying the critical value by the standard error. The critical value is determined by the desired confidence level, which is 95% in this case. For a 95% confidence level, the critical value is approximately 1.96.
    Critical Value = 1.96
   
  - The standard error can be calculated using the formula:
    Standard Error = sqrt((p * (1 - p)) / n)
    where p is the sample proportion and n is the sample size.
   
  - Plugging in the values, we can calculate the standard error:
    Standard Error = sqrt((0.530 * (1 - 0.530)) / 441)
   
  - Now we can calculate the margin of error:
    Margin of Error = Critical Value * Standard Error
   
  - Finally, we can compute the 95% confidence interval by subtracting and adding the margin of error to the sample proportion:
    Confidence Interval = 0.530 ± Margin of Error
   
  - Calculate the margin of error and the confidence interval using the values obtained from the calculations above.

Please note that the confidence interval is an estimate of the true population proportion and provides a range within which the parameter is likely to fall. It means that we are 95% confident that the true proportion of ann arbor-area collegiate football fans who prefer an eight-team playoff format is within the calculated confidence interval.

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Answer: 90

Step-by-step explanation:

Answer:

The absolute value of -90 is 90

Step-by-step explanation:

-90 is 90 away from 0.

To determine the coordinate of point P after the described rotations, let's go step by step.

First, the point P(3, 5) is rotated 180 degrees clockwise about the point A(3, 2). To perform this rotation, we need to find the vector between the center of rotation (A) and the point being rotated (P). We can then apply the rotation matrix to obtain the new position.

Let \(\vec{AP}\) be the vector from A to P. We can calculate it as follows:

\(\vec{AP} = \begin{bmatrix} 3 \\ 5 \end{bmatrix} - \begin{bmatrix} 3 \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 3 \end{bmatrix}\).

Now, we can apply the rotation matrix for a 180-degree clockwise rotation:

\(\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}\),

where \(\theta\) is the angle of rotation in radians. Since we want to rotate 180 degrees, we have \(\theta = \pi\).

Applying the rotation matrix, we get:

\(\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\pi) & -\sin(\pi) \\ \sin(\pi) & \cos(\pi) \end{bmatrix} \begin{bmatrix} 0 \\ 3 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} 0 \\ 3 \end{bmatrix} = \begin{bmatrix} 0 \\ -3 \end{bmatrix}\).

The new position of P after the first rotation is P'(0, -3).

Next, we need to rotate P' (0, -3) 90 degrees counterclockwise about the point B(1, 1).

Again, we calculate the vector from B to P', denoted as \(\vec{BP'}\):

\(\vec{BP'} = \begin{bmatrix} 0 \\ -3 \end{bmatrix} - \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} -1 \\ -4 \end{bmatrix}\).

Using the rotation matrix, we rotate \(\vec{BP'}\) by 90 degrees counterclockwise:

\(\begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x' \\ y' \end{bmatrix}\),

where \(\theta\) is the angle of rotation in radians. Since we want to rotate 90 degrees counterclockwise, we have \(\theta = \frac{\pi}{2}\).

Using the rotation matrix, we get:

\(\begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} \cos \left(\frac{\pi}{2}\right) & -\sin\left(\frac{\pi}{2}\right) \\ \sin\left(\frac{\pi}{2}\right) & \cos\left(\frac{\pi}{2}\right) \end{bmatrix} \begin{bmatrix} -1 \\ -4 \end{bmatrix} = \begin{bmatrix} 0 & -1 \\ 1 & 0\end{bmatrix} \begin{bmatrix} -1 \\ -4 \end{bmatrix} = \begin{bmatrix} 4 \\ -1 \end{bmatrix}\).

The final position of P after both rotations is P''(4, -1).

Therefore, the coordinate of point P after the rotations is (4, -1).

The answer is that the director can fill the positions in 5040 ways.

A personnel director for a corporation has hired 10 new engineers. If four distinctly different positions are open at a particular plant, in how many ways can the director fill the positions?

The answer is that the director can fill the positions in 5040 ways.

First, let's find out how many ways there are to choose four distinct positions out of the ten engineers. This is a combination problem, so we can use the formula nCr (n choose r), where n is the total number of items and r is the number of items being chosen:

nCr = n! / r!(n-r)!

In this case, n = 10 and r = 4, so:

nCr = 10! / 4!(10-4)! = 10! / 4!6! = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 210

Now, for each of these combinations of positions, there are 10 x 9 x 8 x 7 ways to choose one engineer for each of the four positions.

This is a permutation problem, so we can use the formula nPr (n permute r), where n is the total number of items and r is the number of items being chosen:

nPr = n! / (n-r)!

In this case, n = 10 and r = 4, so:

nPr = 10! / 6! = 10 x 9 x 8 x 7 = 5040

Therefore, the director can fill the positions in 5040 ways.

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The 99th percentile for the mean height of a random sample of 20 adult women is approximately 68.7 inches, which is 3.7 inches above the mean of 65 inches.

The 99th percentile for the mean height of a random sample of 20 adult women can be calculated using the normal distribution. The normal distribution is a bell-shaped curve that describes the probability of a given event occurring. In this case, the mean and standard deviation of the height of adult women is used to calculate the probability of the mean height of a sample of 20 adult women being a certain value. For the 99th percentile, this means that the probability of the mean of the sample of 20 adult women being equal to or less than the value of 68.7 inches is 99%. This value is 3.7 inches above the mean of 65 inches, which is the expected mean height of adult women.

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Answer:

there equal

I think but I'm not sure

Answer:

1008

Step-by-step explanation:

4+4=8

add that to 1000

1000+8=1008

so your answer would be 1008

Answer:

1,008

Step-by-step explanation:

just add 4+4+1000= 1008

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Under the same translation as X and X' the coordinates of Y' = (-2, -4) and Z' = (-4, -1)

What is translation of a point in coordinate system?

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

According to the given question:

It is given about the points X (-4, -2) and X' (-6, -5).

We see that the translation is moving -2 units horizontally to the left and -3 units vertically down.

Therefore, the point Y(0,0)  is translated to Y'(0-2,-1-3) = Y'(-2,-4)

and the point Z(-2,2)   is translated to Z'(-2-2,2-3)  = Y'(-4,-1).

Hence, under the same translation Y' = (-2, -4) and Z' = (-4, -1)

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