f(x) = -x² - 8x - 16; Find ƒ(-3)

Answer:

Step-by-step explanation:

Answer:

y = 40°

z = 140°

x = 100°

Information:

(i) Sum of interior angles of a triangle sum ups to 180°

(ii) On a straight line, the angles sum up to 180°

(iii) One exterior angle is equal to two opposite interior angles.

Here the exterior angle theorem applies.

∠z = 120° + 20°

∠z = 140°

Find the angle C. Here angles lie on a straight line.

∠? + 120° = 180°

∠? = 180° - 120° = 60°

80°, 60° and y are interior angles of a triangle.

y + 80°+ 60° = 180°

y = 180° - 140°

y = 40°

∠? = 40° (vertically opposite angle)

Now,

y + x + 40° = 180°

40° + x + 40° = 180°

x = 100°

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

\(x=2\\y=-2\)

Step-by-step explanation:

\(-8x-8y=0\)

Solve -8x-8y=0 for x

\(-8x-8y+8y=0+8y\)

\(-8x=8y\)

\(x=-1y\)

\(-8x+2y=-20\)

Substitute -1y for x

\(-8(-1y)+2y=-20\)

\(8y+2y=-20\)

\(10y=-20\)

\(y=-2\)

Substitute -2 for y

\(x=-1y\)

\(x=-1(-2)\)

\(x=2\)

X=2

y=-2

please see the attached picture for full solution...

Hope it helps...

Good luck on your assignment....

The midsegment linking the cartesian coordinates of two of a triangle's sides is parallel to the fourth aspect of the triangle, and its length is half that of the third side, according to the midsegment theorem.

The assertions that the Greek mathematician Pythagoras discovered the properties of right-angled triangles in the fifth century BC just did not match up, according to many. Some people think following commentary shows it was a joint effort among his disciples, the Pythagoreans.

Equilateral: equal angles and all three sides. Acute isosceles: two identical sides and angles, both of which are only about 90 degrees. Acute scalene has irregular sides and angles, all of which are under 90 degrees. Obtuse isosceles: two identical sides and angles, one of which is more than 90 degrees.

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Answer:

I can't see the fourth option, but the answer would be C.

Step-by-step explanation:

It's the only graph that fits the question.

Answer:

h = 2.5

Step-by-step explanation:

250 + 200h = 300 + 180h

250 + 200h - 180 = 300 + 180h - 180

250 + 20h = 300

250 - 250 + 20h = 300 - 250

20h = 50

20h ÷ 20 = 50 ÷ 20

h = 2.5

Answer:

90

Step-by-step explanation:

\(\frac{gray}{color}\) = \(\frac{gray}{color}\)

\(\frac{9}{2}\) = \(\frac{x}{20}\)

If you multiply 2 x 10 = 20 ,so

9 x 10 = 90

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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The equations test observation (4, 4) belongs to class 1.

To assign a class to the test observation (4, 4),  to evaluate the equations of the support vector classifiers (SVCs) and determine which one(s) the observation satisfies.

Let's go through each SVC and check if the observation lies on the positive side or the negative side of the decision boundary.

SVC for class 1(+) vs 2(-): 2x + 3y = 0

Substituting the values of x = 4 and y = 4

2(4) + 3(4) = 8 + 12 = 20

Since 20 is positive, the test observation (4, 4) lies on the positive side of this decision boundary.

SVC for class 1(+) vs 3(-): 3x + 2y = 0

Substituting the values of x = 4 and y = 4

3(4) + 2(4) = 12 + 8 = 20

Again, 20 is positive, so the test observation (4, 4) also lies on the positive side of this decision boundary.

SVC for class 2(+) vs 3(-): x + y = 0

Substituting the values of x = 4 and y = 4

4 + 4 = 8

Since 8 is positive, the test observation (4, 4) lies on the positive side of this decision boundary as well.

Based on these results, the test observation (4, 4) satisfies all three decision boundaries and lies on the positive side of each. Therefore,  assign it to class 1, which is the common positive class across all three classifiers.

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Answer

\(\sqrt{63}\)

Step-by-step explanation:

Answer:

\(your \: answers \: are \: correct\)

Acute Angle - An angle less than 90 degrees.

Right Angle - An angle that is exactly 90 degrees.

Obtuse Angle - An angle more than 90 degrees and less than 180 degrees.

Straight Angle - An angle that is exactly 180 degrees

full angle =360

Answer:

Step-by-step explanation:

The classical probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are 8 possible outcomes and 2 of them correspond to a favorable event. Therefore, the classical probability of the event is 2/8, which simplifies to 1/4 or 25%.

In this case, there are 2 favorable outcomes and 8 possible outcomes in the random experiment.

Step 1: Write down the number of favorable outcomes (2) and the total number of possible outcomes (8).
Step 2: Calculate the probability using the formula: Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Step 3: Plug in the numbers: Probability = 2 / 8

Now we can simplify the fraction:

2 / 8 = 1 / 4

As a percentage, 1/4 is equal to 25%.

So, the classical probability of the event is 25%.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

x = 3

Step-by-step explanation:

Given the linear function, f(x) = -4x + 2, for which we must determine the integer value of x that will provide an output of f(x) = -10:

The first step is to substitute the output value, f(x) = -10, into the given function, and solve for its corresponding input value, x:

f(x) = -4x + 2

-10 = -4x + 2

Subtract 2 from both sides:

-10 - 2 = -4x + 2 - 2

-12 = -4x

Divide both sides by -4 to solve for x:

\(\displaystyle\mathsf{\frac{-12}{-4}\:=\:\frac{-4x}{-4} }\)

x = 3

Hence, when x = 3, f(x) = -10.  

Substitute the value of x = 3 into the original function:

f(x) = -4x + 2

f(3) = -4(3) + 2

f(3) = -12 + 2

f(3) = -10  ⇒  f(x) = -10.

Therefore, the input value of x = 3 gives an output value of f(x) = -10.

There may or may not exist a basis for mathbb{R}^2 consisting of eigenvectors for matrix A. Whether or not such a basis exists depends on the matrix A itself. If matrix A is diagonalizable, then it has a basis consisting of eigenvectors. However, not all matrices are diagonalizable. For example, a matrix with only one eigenvalue may not be diagonalizable. Therefore, it is not possible to say for certain whether or not a basis for mathbb{R}^2 consisting of eigenvectors for A exists without more information about A.

If something went wrong in part (b) of the question, it may be due to the fact that the matrix A is not diagonalizable and therefore does not have a basis consisting of eigenvectors. In such cases, the Jordan normal form can be used to find a generalized basis consisting of eigenvectors and generalized eigenvectors. This may be more complicated than simply finding a basis consisting of eigenvectors, as it involves finding additional vectors to complete the basis. If the problem in part (b) assumed that a basis for mathbb{R}^2 consisting of eigenvectors for A exists, then it would not be a valid assumption if A is not diagonalizable.

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Answer:

8 + 8 + 8 =

Step-by-step explanation:

Thirds are when your timing a number three times.

The eight 3s means that the number 3 is repeated eight times.

A set of symbols and guidelines used to represent and work with numbers is known as a number system. The decimal system, which bases itself on the value of 10, is the most widely used number system.

It employs the symbols 0 through 9 to represent numbers. But, there are a lot more number systems that have been created over time and are still employed in a variety of mathematics, computer science, and engineering sectors.

Eight 3s typically means the number 3 is repeated eight times. In mathematical notation, it is often represented as:

33333333

Therefore, the eight 3s means that the number 3 is repeated eight times.

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We can use the F-test to determine the overall significance of the relationship between the number of books students referred to and the number of lectures they attended, and their final grade on the course.

To conduct the F-test, we need to calculate the F-statistic, which is the ratio of the variance between the groups (books and lectures) to the variance within the groups.

Using the data given, we calculate the F-statistic as F = 7.35. This value is compared to the critical value for F at the 0.05 level of significance, which is 3.86. Since the F-statistic is greater than the critical value, we can conclude that there is a significant relationship between the number of books students referred to, the number of lectures they attended, and their final grade on the course.

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Answer:

98°

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary.

As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3.

what is domain of the function?

The domain of a function is the set of all possible values of the input variable (independent variable) for which the function is defined. It is the set of all x-values for which the function produces a valid output. In order to determine the domain of a function, one needs to consider any restrictions or limitations that the function may have.

The given problem is related to the motion of a soccer ball kicked by Lin. The height of the soccer ball (in feet) is a function of time (in seconds), and it is represented by a graph.

Domain: The domain of the function is the set of all possible values of the input variable (time in seconds). In this case, the soccer ball was in the air for 3 seconds, so the domain is [0, 3], which means that the height function is defined for all values of time between 0 and 3 seconds, including 0 and 3.

Range: The range of the function is the set of all possible values of the output variable (height of the soccer ball in feet). In this case, the soccer ball reached a height of approximately 30 ft while it was in the air. Therefore, the range of the function is [0, 30], which means that the height of the soccer ball is defined for all values between 0 and 30 feet, including 0 and 30.

Line of symmetry: The line of symmetry is a vertical line that passes through the vertex of the parabola (in this case, the highest point that the soccer ball reaches). The parabolic graph of the soccer ball's height function is symmetric with respect to the vertical line passing through the midpoint of the domain. Since the domain is [0, 3], the midpoint is (3/2, 0), so the line of symmetry is x = 3/2.

As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3. As the value of x decreases from 3 to 0, the height of the soccer ball increases from 0 to 30 and then decreases again as it hits the ground. The rate of change of the height of the soccer ball is not constant but rather depends on the shape of the parabolic graph of the height function.

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Check the picture below.

Answer:

942.48

Step-by-step explanation:

Answer:

"D"

the start point is below zero and is doing deeper

Step-by-step explanation:

If angle poa is a right angle and if angle poc is three times as large as angle.The measure of angle POC is 270 degrees.

To find the measure of angle POC, we first need to determine the measure of angle POA.

Since angle POA is a right angle, it measures 90 degrees.
Next, we need to find the measure of angle POC.

The question states that angle POC is three times as large as angle POA.

Since angle POA measures 90 degrees, angle POC would be three times that value.
To calculate the measure of angle POC, we multiply the measure of angle POA (90 degrees) by 3:
Angle POC = 90 degrees * 3 = 270 degrees.
Therefore, the measure of angle POC is 270 degrees.

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Answer: Please adjust the 37. The answer would be 40.

Step-by-step explanation:

23 + 17 obviously equals 40.

Answer:

x²-4x+5

Step-by-step explanation:

With each quadratic function, you can simplify it to see the zeros of the function. Because this graph does not touch the x-axis at all, you can cross out all the functions that have a spot on the x-axis. This includes x²-6x+5, -x²-2x+3, x²+4x-5. Also, because the graph is positive, you can cross out any one of the quadratic functions that shows a negative graph with includes -x²-2x+3 and -x²+2x+3. Now that we are left with x²+6x-5 and x²-4x+5, we can plug in the origin (or you could have done this from the start) into the function, and we can see that when you plug in 2 as the x value, only the function, x²-4x+5 gives the y value of 1. Therefore, this is the answer.

Why I did so much work to get to the same place because it is always good to check your work and make sure that nothing that you are doing is wrong.

The major branch of statistics that deals with making inferences about a population based on a sample is called inferential statistics.

In this scenario, you collected data from a sample of eight classmates and calculated the average score to be 65.

Based on this sample, you made an inference about the entire class, stating that the average test score for the whole class was less than 70. This inference is an example of using inferential statistics. Inferential statistics allows us to draw conclusions and make predictions about a larger population based on a smaller sample.

By using statistical techniques and assumptions, we can estimate parameters, such as the population mean, using sample statistics. This helps us make informed decisions and generalizations about a population when it is not feasible or practical to collect data from the entire population.

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The domain of the function \(f(x) = \sqrt{100 - x^2}\) in interval notation is [-10,10].

Given the function in the question:

\(f(x) = \sqrt{100 - x^2}\)

To determine the domain, we set the radicand to greater than or equal to zero and solve for x:

Hence:

100 - x² ≥ 0

Solve for x:

Subtract 100 from both sides:

100 - 100 - x² ≥ 0 - 100

-x² ≥ -100

Divide both terms by -1

x² ≤ 100

Take the square roots

x ≤ ±√100

x ≤ ±10

Hence:

-10 ≤ x ≤ 10

Note, the domain is the value of x that make the expression defined.

In interval notation domain is [-10,10].

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Answer:

ok so 4x-4y=8

4x-4×8=

4x-32

4x-10-32=

-40 -32= -72

Step-by-step explanation:

I think this is right sorry if I'm wrong

Answer:

We need to keep y on the left side only.

so we distribute the 4x to the right side.

that means:

4x - 4y = 8

-4x         -4x

-4y = 8 - 4x

Now we divide by -4 on both sides

y = 8 - 4x/-4

-2 + x is y

Now for number 2:

Let's use -10 for x.

-2 -10 = -12