Given P(x), use the Remainder Theorem to find P(3). P(x)=x^4 −2x^3 +2x^2 −4x

ATA is non-singular and det(ATA) > 0.

Let A be an n × n matrix.

We want to show that ATA is non-singular and det(ATA) > 0.

Recall that a square matrix is non-singular if and only if its determinant is nonzero.

Since A is non-singular, we know that det(A) ≠ 0.

Now, we have `det(ATA) = det(A)²`.

Since det(A) ≠ 0, we have det(ATA) > 0.

Therefore, ATA is non-singular and det(ATA) > 0.

If A is a non-singular n x n matrix, show that ATA is non-singular and det(ATA) > 0.

Let A be an n × n matrix.

Since A is non-singular, we know that det(A) ≠ 0.

Thus, we have det(A) > 0 or det(A) < 0.

If det(A) > 0, then A is said to be a positive definite matrix.

If det(A) < 0, then A is said to be a negative definite matrix.

If det(A) = 0, then A is said to be a singular matrix.

The matrix ATA can be expressed as follows: `ATA = (A^T) A`

Where A^T is the transpose of matrix A.

Now, let's find the determinant of ATA.

We have det(ATA) = det(A^T) det(A).

Since A is non-singular, det(A) ≠ 0.

Thus, we have det(ATA) = det(A^T) det(A) ≠ 0.

Therefore, ATA is non-singular.

Also, `det(ATA) = det(A^T) det(A) = (det(A))^2 > 0`

Thus, we have det(ATA) > 0.

Therefore, ATA is non-singular and det(ATA) > 0.

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Answer:

Below

Step-by-step explanation:

Since all angles in a triangle add up to 180 degrees, all you need to do to find the 1 missing angle is to subtract the given values from 180.

17) 180 - 25 - 102 = 53

Angle Q = 53 degrees

18) 180 - 46 - 34 = 100

Angle E = 100 degrees

Hope this helps, good luck!

Answer:

"What are the advantages and disadvantages of each alternative?" would be an appropriate question to evaluate alternatives in the third stage of the rational model of decision making.In the third stage, decision makers generate and evaluate alternative courses of action. They weigh the pros and cons of each alternative, considering factors such as feasibility, risks, costs, benefits, and consequences. By asking about the advantages and disadvantages of each alternative, decision makers can systematically compare and contrast their options, identify potential trade-offs, and select the best alternative based on their criteria and preferences.

Answer:

C. $30

Step-by-step explanation:

So we know that in 2007 the fee was $40 and we want to figure out what is 3/4 of 40.

To solve that we can start off with 40 and divide it by 4. Which is like saying "I'm finding what one fourth of 40 is." The answer to that is 10.

Because 10 is ONE fourth we multiply by 3 to find what 3/4 of 40 is. 10x3=30 and that's why 3/4 of 40 is 30.

Hope that helps and have a great day!  

The scale factor was applied to the first diamond is 2.5

From the question, we have the following parameters that can be used in our computation:

The diamonds

The scale factor is calclated as

scale factor = Diamond 2/Diamond 1

Substitute the known values in the above equation, so, we have the following representation

scale factor = 1.5/0.6

Evaluate

scale factor = 2.5

Hnce, the scale factor is 2.5

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Answer:

-39

Step-by-step explanation:

just plug -3 into x

-4(-3)^2-3=-4*9-3=-36-3=-39

so, g(-3)=-39

hope this helped

The difference of the elevation of the two points, a mountain in the Great Smoky Mountains National Park and gap in the Atlantic Ocean is 30143 feet.

Given that,

Elevation of a mountain in the Great Smoky Mountains National Park = 5651 feet above sea level

Elevation of the gap in the Atlantic Ocean = 24492 feet below sea level

We have to find the difference in the elevation of the two points.

Let s be the sea level.

Elevation of mountain = s + 5651

Elevation of gap in Atlantic Ocean = s - 24492

Difference in the elevation = s + 5651 - (s - 24492)

                                            = 5651 + 24492

                                            = 30143 feet

Hence the difference in elevation is 30143 feet.

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Answer:

90°

Step-by-step explanation:

As given in the figure:

\(AC \perp CE\\

\therefore m\angle ACE = 90\degree \\ \)

Formula is

#1

\(\\ \sf\longmapsto (54-2)180\)

\(\\ \sf\longmapsto 52(180)\)

\(\\ \sf\longmapsto 9360°\)

#2

\(\\ \sf\longmapsto (19-2)180\)

\(\\ \sf\longmapsto 17(180)\)

\(\\ \sf\longmapsto 3060\)

#3

\(\\ \sf\longmapsto 292-2(180)\)

\(\\ \sf\longmapsto 290(180)\)

\(\\ \sf\longmapsto 52200\)

#4

\(\\ \sf\longmapsto (5-2)180\)

\(\\ \sf\longmapsto 3(180)\)

\(\\ \sf\longmapsto 540\)

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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Answer:

slope = 4/1 or 4

Step-by-step explanation:

Answer:

y-intercept = 31

Step-by-step explanation:

The equation of a straight line in slope-intercept form is y = mx + b, where m is the slope, and b is the y-intercept.

As we know that 11 is the slope, our equation now becomes y = 11x + b.

To find b, you take the given point, and plug the numbers in for x and y in the equation. Now x = 7, and y = 108.

Your equation is now 108 = 11(7) + b and you can solve for b, your y-intercept.

108 = 11(7) + b

108 = 77 + b

31 = b

Therefore, your y-intercept is 31.

Answer:

m∠1 = 90°

Step-by-step explanation:

Since the line is tangent to the circle, it creates a perpendicular bisector with the diameter. That means that the m∠1 has to be 90°

Answer:

-4+3n     (if first value corresponds to n=0)

or

-7+3n     (if first value corresponds to n=1)

Step-by-step explanation:

Notice form each term you just need to add 3
For example, the first term is -4, then the second is -4+3=-1

then the third is -4+3+3=2

So you can start from -4 and 3 for each value.

If n=0 is the start value the sequence will be -4+3n

if the first term is n=1  the sequence will be  -4+3(n-1)=-7+3n

So depends if your sequence starts from n=1 or n=0 (which is usually just a convention)

Answer: All in images

Step-by-step explanation:

Answer:

8,000 cm³

Step-by-step explanation:

V = s³

V = (20 cm)³

V = 8,000 cm³

The probability of Pat finishing on or before the 18th house is approximately 0.9978. This problem can be modeled using a geometric distribution, where the probability of success (selling a candy bar) is 0.3 and we want to find the probability of reaching the 8th success.

(a) The probability that Pat sells his last candy bar on the 14th house is:

P(X=14) = (1-0.3)^{13} * 0.3 = 0.002678

(b) The probability of Pat finishing on or before the 18th house is:

P(X≤18) = 1 - P(X>18) = 1 - (1-0.3)^{18} = 0.997805

Therefore, the probability of Pat finishing on or before the 18th house is approximately 0.9978.

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Answer:

3:5 & 12:20

Step-by-step explanation:

There are many more but there are 2 ratios that are equivalent. I got 3:5 by dividing 6 in half and 10 in half. And i got 12:20 bye multiplying 6 by 2 and 20 by 2. Hope this helps :3

3/5

since 6 divided by 2 is 3 and 10 divided by 2 is 5

The coefficient of non-determination that shows unique rather than common variance is 0.64.

The amount of variance that is common among a group of objects is known as common variance. Items with high correlation will have a lot of variance in common. Common-method variance (CMV) is the fictitious "variance that is attributable to the measurement method rather than to the constructs the measures are assumed to represent" or, alternatively, "systematic error variance shared among variables measured with and introduced as a function of the same method and/or source".

Depending on a number of variables, the inter correlations across measures that are impacted by CMV or common-method bias might be inflated or deflated.

The coefficient of non-determination = 100% - coefficient of determination

= 100 -36

= 64%

= 0.64

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The probability that a number selected at random from the first 1000 positive integers is divisible by 6 or 8 is 3/10 or 0.3.

The number of positive integers between 1 and 1000 is 1000. We can divide the number of positive integers by 6 or 8. We can start by dividing the number of positive integers by 6, then by 8.Number of integers divisible by 6:Number of positive integers between 1 and 1000 that are divisible by 6 = (1000 ÷ 6) = 166 2/3So, we can only take the integer value that is 166. The other numbers that follow the integer are not positive integers between 1 and 1000. Therefore, there are 166 positive integers between 1 and 1000 that are divisible by 6.

Number of integers divisible by 8:Number of positive integers between 1 and 1000 that are divisible by 8 = (1000 ÷ 8) = 125So, there are 125 positive integers between 1 and 1000 that are divisible by 8. Counting numbers that are divisible by both 6 and 8:Next, we will find out how many numbers are divisible by both 6 and 8.The least common multiple of 6 and 8 is 24. So, we have to find all positive integers between 1 and 1000 that are divisible by 24.Number of integers divisible by 24:Number of positive integers between 1 and 1000 that are divisible by 24 = (1000 ÷ 24) = 41So, there are 41 positive integers between 1 and 1000 that are divisible by 24.Now we can add up the total number of positive integers between 1 and 1000 that are divisible by 6 or 8.166 + 125 − 41 = 250Therefore, there are 250 positive integers between 1 and 1000 that are divisible by 6 or 8. Finally, we can calculate the probability by dividing the number of positive integers that are divisible by 6 or 8 by the total number of positive integers between 1 and 1000.250 ÷ 1000 = 0.25 or 1/4Therefore, the probability that a number selected at random from the first 1000 positive integers is divisible by 6 or 8 is 3/10 or 0.3.

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The possible approximate lengths of b are: 2.3 units and 7.8 units

We know that the law of sines for triangle is:

The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.

This means, for triangle ABC,

\(\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}\)

where a is the length of side BC,

b is the length of side AC,

c is the length of side AB.

For triangle ABC consider an equation from sine law,

\(\frac{sin~ A}{a} =\frac{sin~ C}{c}\)

here, c = 5.4, a = 3.3, and m∠A = 20°

\(\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}\)

0.3420 × 5.4 = 3.3 × sin(C)

sin(C) = 0.5596

∠C = arcsin(0.5596)

∠C = 34.03°  OR 145.9°

∠C ≈ 34° OR 146°

We know that the sum of all angles of triangle is 180 degrees.

so, ∠A + ∠B + ∠C = 180°

when m∠C = 34°,

20° + ∠B + 34.03° = 180°

∠B = 125.97°

m∠B = 126°

when m∠C = 146°,

20° + ∠B + 146° = 180°

m∠B = 14°

Now consider equation,

\(\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}\)

b × 0.3420 = 0.8090 × 3.3

b = 7.8 units

when m∠B = 14°,

\(\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}\)

b × 0.3420 = 0.2419 × 3.3

b = 2.3 units

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The complete question is:

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.0 units and 4.6 units

2.1 units and 8.7 units

2.3 units and 7.8 units

2.6 units and 6.6 units

Answer:

x=70

z=20

y=30

Step-by-step explanation:

first find x: the sum of straight angle is 180

x+110=180

x=180-110=70

now find z: the sum of the angles of triangle is 180:

x=70, right angle=90

z+70+90=180

find y:

y+110+40=180

y=180-150=30

z=180-160=20

Answer:

x=70 degrees, y= 30 degrees, z=20 degrees

Step-by-step explanation:

110+x=180 => straight angle def.

180-110+40=y => def. of angles in triangle

x( 70 degrees) +90+z=180, z= 20 => angles in triangle

The book that weighs 3/4 pounds is greater than 1/2 pounds.

To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.

Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.

Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.

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Answer:

a = 4

b = 4

Step-by-step explanation:

This is a special right triangle with angle measures of 45° 45° 90° and side lengths x x x√2

The average number of calls per day is approximately 5.298 calls.

To solve this problem, we'll first use the information given about the probability of receiving no calls (0.5%) and the Poisson distribution formula to find the average number of calls per day (λ).

Step 1: Convert the percentage of no calls into a decimal.
0.5% = 0.005

Step 2: Use the Poisson distribution formula for the probability of receiving no calls (k = 0).
P(X = 0) = (e^(-λ) * λ^0) / 0! = 0.005

Step 3: Simplify the equation.
(e^(-λ) * 1) / 1 = 0.005

Step 4: Solve for λ.
e^(-λ) = 0.005
-λ = ln(0.005)
λ = -ln(0.005)

Step 5: Calculate the average number of calls per day.
λ ≈ 5.298

So, the average number of calls per day is approximately 5.298 calls.

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The length of the Cityscape Bike Path exists 3 1/9 miles.

So, we have:

To estimate the length of the Cityscape Bike Path:

Therefore, the length of the Cityscape Bike Path:

Length of Cityscape Bike Path:

Therefore, the length of the Cityscape Bike Path is 3 1/9 miles

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Complete question:
The Cityscape Bike Path is 2 2/3 times longer than the Bay View Bike Path. What is the length of the Cityscape Bike​ Path?

The Bay View Bike path is 7/8 of a mile.

Answer:

here hereh ehreh ehe

Step-by-step explanation: