Give an example of a matrix A and a vector b such that the solution set of Ax=b is a line in R3 that does not contain the origin.

Note that the prompt is geared at testing the ability of the to understand certain vocabulary terms. The terms are given as follows:

The completed paragraphs are given below.

The first paragraph is completed as follows:

When Dr. Carter is not fulfilling his duties as the professor of paleontology at Ganton College, he is in the jungles of South America supervising excavations of ancient creatures. During the last dig, Dr. Carter recoiled when a poisonous snake tried to bite him. Now he wears tall boots and gloves to obviate the risk of dangerous animals endemic to the region.

He will definitely elicit the need for such safety measures. Some of the incoming scientists will accuse him of self-aggrandizement despite the fact that the sociable doctor always avoids using too much panache when speaking about safety; he'll flaunt his amazing findings when he returns to the campus at the end of the summer. He can put his bombast to better use in the classroom.

The second paragraph is completed as follows:

Baker deigned to give a semi-friendly nod to his Nazi captors, and he immediately suffered the consequences. Baker then endured the loud paroxysm of his cellmates: "What was that? What, are you working for them, too?"

He understood their paranoia. Just weeks before, a(n) mendacious rebel captive had revealed the escape plan to the guard. The prisoners, including Baker, had to abandon months of secrecy and labor that went into the construction of the tunnel. They had not yet regrouped; most of the saturnine prisoners simply lay in their cells, defeated.

Baker sat against the wall and thought about his capture. He had misused the shibboleth that the Nazis used to identify foreign spies. and the lack of orthography on his forged travel documents instantly signaled that he was not the German officer he claimed to have been. They must need information, he reasoned, or they would have executed him by now.

The definition of terms are given as follows:

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The length of the guy wire is approximately 21 feet

From the question, we are to calculate the length of the guy wire.

To calculate the length of the guy wire,

First, we will determine the height of the tower.

Let the height of the tower be h

From the given diagram, we can write that

h/(9 +4) = 5/4

h/13 = 5/4

h = (13×5)/4

h = 65/4

h = 16.25 feet

Let the length of the guy wire be l

Then,

From the Pythagorean's theorem we can write that

l² = 16.25² + (9+4)²

l² = 264.0625 + 13²

l² = 264.0625 + 169

l² = 433.0625

l = √433.0625

l = 20.81015

l ≈ 21 feet

Hence, the length is approximately 21 feet

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Answer:

here are signs for (A), (B) and (C) hope this helps :)

Step-by-step explanation:

(a) The signs of two rational numbers whose sum is positive can be either both positive or both negative. If the signs are different, the absolute value of one number is greater than the absolute value of the other.

Example:

1/2 + 3/4 = 1/4 (positive sum, both numbers are positive)

-2/3 + 4/5 = 2/15 (positive sum, both numbers are negative)

(b) The signs of two rational numbers whose product is positive can be either both positive or both negative.

Example:

1/3 * 4/5 = 4/15 (positive product, both numbers are positive)

-2/7 * -3/4 = 3/14 (positive product, both numbers are negative)

(c) The signs of two rational numbers whose quotient is positive can be either both positive or both negative.

Example:

2/3 ÷ 1/4 = 8/3 (positive quotient, both numbers are positive)

-5/6 ÷ -2/3 = 5/4 (positive quotient, both numbers are negative)

Answer: True, False, False

Step-by-step explanation:

Answer:

8. true

9. false

10. false

Answer:

x = 12

The sum of ∠A and ∠C is 90°.

Step-by-step explanation:

Interior angles of a triangle sum to 180°.

[tex]\implies m \angle A + m \angle B + m \angle C = 180^{\circ}[/tex]

From inspection of the given right triangle:

Substitute the given angles into the equation and solve for x:

[tex]\implies m \angle A + m \angle B + m \angle C = 180^{\circ}[/tex]

[tex]\implies (2x+1)^{\circ} + 90^{\circ} + (5x+5)^{\circ} = 180^{\circ}[/tex]

[tex]\implies (2x+1)^{\circ} + 90^{\circ} + (5x+5)^{\circ}-90^{\circ} = 180^{\circ}-90^{\circ}[/tex]

[tex]\implies (2x+1)^{\circ} + (5x+5)^{\circ} = 90^{\circ}[/tex]

[tex]\implies 2x+1 + 5x+5 = 90[/tex]

[tex]\implies 2x+ 5x+1 +5 = 90[/tex]

[tex]\implies 7x+6 = 90[/tex]

[tex]\implies 7x+6 -6= 90-6[/tex]

[tex]\implies 7x=84[/tex]

[tex]\implies 7x\div7=84\div7[/tex]

[tex]\implies x=12[/tex]

Therefore, the value of x is 12.

To find the measure of each angle, substitute the found value of x into the expression for each angle:

Answer:

[tex]x = 12[/tex]

Step-by-step explanation:

A right angled triangle is given to us and we need to find out the value of " x " . The two unknown angles are (2x + 1)° and (5x + 5)° .

We know that, the Angle sum property of a triangle is 180° . So the sum of all the given angles inside the triangle will be 180° .

And as per question one of the angle is 90° . So the sum of other two angles will be 90° .

Hence ,

2x + 1 + 5x + 5 + 90 = 180

7x + 96 = 180

7x = 180 - 96

7x = 84

x = 84/2

x = 12

Hence the value of x is 12 .

And we are done!

The statement "The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small. " is false.

What is meant by the central limit theorem?

According to the central limit theorem, a statistical theory, samples with large sample size and a finite variance will have a normal distribution and a mean that is about equal to the mean of the entire population. The central limit theorem proves that, in many circumstances, given identically distributed independent samples, the standardised sample mean tends towards the conventional normal distribution even though the original variables themselves are not normally distributed.

Since the given sample is small, the histogram will not have a bell shape.

This is because according to central limit theorem, the normal approximation may not be very accurate when the sample size is small, Yet, the normal approximation gets better as the sample size increases.

Therefore the statement "The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small. " is false.

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The radius of the circle is solved to be

The radius of the circle is using the formula for length of arc

= theta / 360 * 2πr

For angles in radian we have that

= theta * radius

Form the problem we have that

arc length is 11π/3

theta = 11π/6 radians

hence

11π/3 = 11π/6 * radius

radius = 2

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Answer:

The probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).

Step-by-step explanation:

Given that Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates, the total number of chocolates in the box is:

[tex]\implies \sf Total=6 + 4 + 8 = 18[/tex]

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Therefore, the probability that the first chocolate Bob eats will have almonds is:

[tex]\implies \sf P(first\;almond)=\dfrac{6}{18}[/tex]

As Bob has eaten one almond chocolate there are now 5 chocolate covered almonds left and a total of 17 chocolates.  Therefore, the probability that the next chocolate Bob eats will have almonds is:

[tex]\implies \sf P(second\;almond)=\dfrac{5}{17}[/tex]

To find the total probability for two or more events, multiply the probabilities.  Therefore, the probability that the first two chocolates Bob eats will have almonds is:

[tex]\begin{aligned}\implies \sf P(first\;almond)\;and\;P(second\;almond) & =\dfrac{6}{18} \times \dfrac{5}{17}\\\\ &=\dfrac{30}{306}\\\\&=\dfrac{5}{51}\\\\&=0.0980392...\\\\&=9.80392...\%\end{aligned}[/tex]

Therefore, the probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).

Answer:

24 years old

Step-by-step explanation:

Jim = 2x + 4

Mark = x

Sum of their ages = 34

2x + 4 + x = 34

2x + x = 34 - 4

3x = 30

3x / 3 = 30 / 3

x = 10

Mark = 10 years old

Jim = 2x + 4

= 2 ( 10 ) + 4

= 20 + 4

= 24

Therefore, Jim is 24 years old

The vertex form of the quadratic equation g is:

g(x) = 25*(x - 4)²

We start with the parent quadratic function:

f(x) = x²

We know that first we apply a translation of 4 units to the right, so we will get:

g(x) = f(x - 4)

And then we compress it horizontally by a factor of 5, then we can write:

g(x) =f( 5(x - 4))

Replacing the actual function we will get:

g(x) = ( 5*(x - 4))²

Distributing the exponent we will get:

g(x) = 5² *(x - 4)²

g(x) = 25*(x - 4)²

That is the quadratic equation in vertex form.

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Answer:

1 milliliter = 0.00105669 liquid quart

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Converting these units:

Therefore, for every 1 milliliter it is equivalent to 0.00105669 liquid quart.

The number of ways two names can be chosen from 76 in a raffle where only one entry is allowed is 3,025.

This can be calculated by using the combination formula: nCr = n!/(r!(n-r)!), where n is the total number of names (76) and r is the number of names to be chosen (2). The calculation for the same is written out below:

nCr = 76!/(2!(76-2)!)

= 76!/(2!*74!)

= 3,025.

This means that there are 3,025 possible combinations of two names that can be chosen from the 76 names if only one entry is allowed per person.

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Answer:

B. Jamie is incorrect. Since spinning a number from 1-3 is certain, the probability is 1.

Step-by-step explanation:

Probability is on a scale of 0 to 1, with 0 being impossible, and 1 being certain.

As the possibility of spinning and landing on a number less than or equal to 3 is 100%, as all numbers on there are less than or equal to 3, the probability would be 1, not 3.

By looking at the data under PURCHASE BEHAVIOR, we can see that the consumers in this segment purchase a backpack at a range of purchase every five years. The Option E is correct.

We have several factors that can determine a consumer's purchase interval, including:

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Answer:

Step-by-step explanation:

answer is c. once every year

Answer: The price is now 1.5 of what it was before is the correct answer.

Step-by-step explanation:For the given situation,

The statement is given as price increased by 1/2.

Let us assume, we have an item costs 1$.

Now the price is increased by 1/2, so we need to add the fraction to 1.

Answer:

x = 50°

d = 40°

Step-by-step explanation:

  Quadrilaterals are four-sided polygon and the sum of all the interior angles is 360°

      Sum of all angles of quadrilateral = 360°

                    60° + x + 3x + 2x = 360

                                  60 + 6x = 360

Subtract 60 from both sides,

                                          6x = 360 - 60

                                          6x = 300

Divide both sides by 6

                                            x = 300 ÷ 6

                                            x = 50°

b)  120° + 110° + 90° + d= 360°

                       320 + d  = 360

   Subtract 320 from both sides,

                                  d = 360 - 320

                                  d = 40°

The relation can be a function is discussed below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Given:

We Know that in a function a input have only one output.

There no input value whose have the two distinct output at a same time.

We have attached question is not understood.

let us take example

Is A = {(1, 5), (1, 5), (3, -8), (3, -8), (3, -8)} a function?

We write the above data in table format then

x     y

1     5

1     5

3     -8

3     -8

3     -8

Here we have input value 1 have two outputs but same value 5.

Thus, the Given relation A is a function

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The possibility of any other range other than 13-6 through 17-10 with several recurring values (mode) is not possible because mean 12 is the median. Hence, I went with 16 and 9.

The mean of a dataset, sometimes referred to as the arithmetic mean, is the sum of all results multiplied by the number of values . This is the most popular way to measure central tendency and is sometimes refereed to as the "mean." This is obtained by dividing the total total of values within the dataset by the sum of the values. Calculations may be performed using both raw data and information that has been compiled into frequency tables. The average of a number is referred to as average. Calculating the following is easy: After adding all the digits, divide by the number of digits. the sum split by the count.

The query is not complete. It would still be 9 and 16 if the question asked for the two numbers that may represent the lowest and highest scores.

9 numbers in total. List them in descending order. Your Median is the middle number. The gap between the greatest and the lowest number called the range. The probabilities are therefore 8-1, 9-2, 10-3, 11-4, 12-5, 13-6, 14-7, 15-8, 16-9, 17-10, 18-11, and 19-12. The possibility of any other range other than 13-6 through 17-10 with several recurring values (mode) is not possible because 12 is the median. Hence, I went with 16 and 9.

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Answer:

h = 12 feet

Step-by-step explanation:

using the right triangle shown in the diagram.

the base of the triangle is half the measure of the base of the square side.

then base of triangle = [tex]\frac{1}{2}[/tex] × 32 = 16 feet and hypotenuse = 20 feet

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² + 16² = 20²

h² + 256 = 400 ( subtract 256 from both sides )

h² = 144 ( take square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12

the height h of the pyramid is 12 feet

Answer:

67°

Step-by-step explanation:

Sum of the interior angles of a triangle = 180

To find x, set the sum of the supplementary angles to the 3 shown angles (x-6, x+9, x) equal to 180:

180 = (180-x+6) + (180-x-9) + (180-x)

180 = 536 - 3x

-357 = -3x

x = 119

119 - 6 = 113    this is the angle supplementary to ∠LMN, therefore:

m∠LMN = 180 - 113 = 67°

The table mentioned in the question is not provided. However, we can use the following formula to find the probability of two independent events occurring together:

P(A and B) = P(A) x P(B)

Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.

Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).

The probability of flipping a fair coin and getting heads is 1/2.

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:

P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16

So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

The probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

Given that, a spinner is spined and coin is flipped,

P(A and B) = P(A) x P(B)

Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.

Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).

The probability of flipping a fair coin and getting heads is 1/2.

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:

P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16

So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

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Each angle in a regular polygon with 5 sides measures 108 degrees.

A polygon is a closed shape with straight sides. A regular polygon is a polygon where all sides are of equal length and all angles are of equal measure.

To find the measure of each angle in a regular pentagon, we can use the formula:

angle measure = (n-2) x 180 / n

where n is the number of sides.

Substituting n=5 into the formula gives:

angle measure = (5-2) x 180 / 5

Subtract the terms

= 3 x 180 / 5

= 540 / 5

Divide the numbers

= 108 degrees

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In the model above, the 8 that the arrow points to is 1/10 times the 8 to the left of the arrow and 10 times the 8 to the right of the arrow.

In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

Generally speaking, the place value of the 8 that the arrow points to is tens and as such, we have the following:

8 = 80 × 1/10

8 = 0.8 × 10

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The quadratic equations with roots that are whole numbers and fractions are listed below:

Case 2: 9 · x² - 78 · x - 27 = 0

Case 3: 7 · x² - 26 · x - 8 = 0

Case 4: 4 · x² + 2 · x - 32 · x - 16 = 0

Case 6: 4 · x² - 5 · x - 6 = 0

Case 7: 7 · x² + 38 · x - 24 = 0

In this problem we find eight cases of quadratic equations of the form a · x² + b · x + c = 0, where a, b, c are real coefficients. All roots can be found by means of algebra properties:

Case 1

5 · x² + 8 · x + 4 = 0

5 · [x² + (8 / 5) · x + 4 / 5] = 0

5 · (x + 4 / 5 - i 2 / 5) · (x + 4 / 5 + i 2 / 5)

Case 2

9 · x² - 78 · x - 27 = 0

9 · [x² - (26 / 3) · x - 3] = 0

9 · (x - 9) · (x + 1 / 3) = 0

Case 3

7 · x² - 26 · x - 8 = 0

7 · [x² - (26 / 7) · x - 8 / 7] = 0

7 · (x - 4) · (x + 2 / 7) = 0

Case 4

4 · x² + 2 · x - 32 · x - 16 = 0

4 · x² - 30 · x - 16 = 0

4 · [x² - (15 / 2) · x - 4] = 0

4 · (x - 8) · (x + 1 / 2) = 0

Case 5

2 · x² - 20 · x + 32 = 0

2 · (x² - 10 · x + 16) = 0

2 · (x - 8) · (x - 2) = 0

Case 6

4 · x² - 5 · x - 6 = 0

4 · [x² - (5 / 4) · x - 3 / 2] = 0

4 · (x - 2) · (x + 3 / 4) = 0

Case 7

7 · x² + 38 · x - 24 = 0

7 · [x² + (38 / 7) · x - 24 / 7] = 0

7 · (x - 4 / 7) · (x + 6) = 0

Case 8

x² - 5 · x - 6 = 0

(x - 6) · (x + 1) = 0

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A p-value two-tailed calculator is a statistical tool used to calculate the p-value for a two-tailed test of a population mean or proportion.

A p-value two-tailed calculator is an online tool used in statistical analysis to determine the probability value of a two-tailed hypothesis test. This calculator helps researchers and analysts to determine if there is a significant difference between two population means or proportions. It calculates the p-value, which is the probability of obtaining results as extreme or more extreme than the observed results under the null hypothesis.

Users input sample data, population parameters, significance level, and type of test to obtain the calculated p-value. This tool is essential in hypothesis testing in fields such as psychology, medicine, and economics.

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Answer:

(p • q)(x) =  3x² + 2x + 4

Step-by-step explanation:

(p • q)(x) same as p(q(x)) is the composite function obtained by applying the expression for q(x) in place of x in p(x)

We have
p(x) = x + 4

q(x) = 3x² + 2x

To find (p • q)(x)

wherever there is an x in p(x) substitute with 3x² + 2x

(p • q)(x)   =  x + 4

                =  (3x² + 2x) + 4

                =   3x²  + 2x + 4

Answer:

See below

Step-by-step explanation:

1. The sum of two numbers is 72. Lets say the two numbers are x and y:

   x + y = 72

If one number is 3 times the other,

  x = 3y

what is the largest number?

 Substitute the second into the first expression

x + y = 72

3y + y = 72

4y = 72

 y = 18

2.  From 6:30am to noon is 5 1/2 hours.  From noon to 1:30 is another 1 1/2 hours.  The sum is (5.5 + 1.5) = 7 hours

3.  I'm assuming the bottom two angles are the same (diffiuclt to read).  If so, we know that the sum of the interior angles of a triangle is 180 degrees.  

        2x + x + x = 180

        4x = 180

          x = 45 degrees

4.  (1.5 meters)*($22.50/meter) = $33.75

5.  (0.5 L)*(1000 ml/L) = 500 ml