Write the system first as a vector equation and then as a matrix equation.
7 x 1
plus
x 2
minus
3 x 3
equals
7


3 x 2
plus
2 x 3
equals
0
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Part 1
Write the system as a vector equation where the first equation of the system corresponds to the first row. Select the correct choice below and fill in any answer boxes to complete your choice.

Answer:

[tex]m = \frac{4 - ( \sqrt[3]{ - 6} + 4)}{0 - ( - 6))} = \frac{ \sqrt[3]{6} }{6} = .303[/tex]

So the average rate of change of g(x) over -6 < x < 0 is about .303.

No, any court case should not be based solely on probabilities as probability does not imply certainty.

Compute the probability of another couple being in that area with the same characteristics

CHARACTERISTIC ASSUMED PROBABILITY

Drives a yellow car 1 out of 12

Man over 6 feet tall 1 /10

Man wearing tennis shoes 1/4

Man with beard 1/11

Woman with blond hair 1/3

Woman with hair in a ponytail 1 /13

Women over 6 feet tall 1/100

We will use the multiplication rule as all the characteristics should be present in the couple.

The probability of another couple being in that area with the same characteristics is given as

P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800

The characteristics dependent on the sum of the probabilities is not equal to 1.

The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).

No, any court case should not be based solely on probabilities as probability does not imply certainty.

No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.

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The statement "These lines are perpendicular" is true.

To determine if the two lines are perpendicular, we need to check if the product of their slopes is -1. That is, if:

m1 × m2 = -1

where m1 is the slope of the first line and m2 is the slope of the second line.

The slopes of the two lines are:

m1 = -2/5

m2 = 5/2

So, m1 × m2 = (-2/5) × (5/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular. Therefore, the statement "These lines are perpendicular" is true.

The correct answer is A. true.

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Answer:

1:2

Step-by-step explanation:

If  an ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The  probability is:  84.6%.

In this case, we have:

Population standard deviation (σ): $1200

Sample size (n): 400

Margin of error (E): $80

The standard deviation of the sample mean can be calculated as:

σM = σ / √n = 1200 / √400 = 60

To find the probability that the sample mean is within $80 of the population mean, we need to find the z-scores for the upper and lower limits of the interval:

Lower limit: z = (mean - E - population mean) / σM = (-80) / 60 = -1.3333

Upper limit: z = (mean + E - population mean) / σM = 80 / 60 = 1.3333

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(-1.3333 < Z < 1.3333) = 0.8461

Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.846 or 84.6%.

Interpretation: This means that if we take many samples of 400 railroad-car shipments of ethanol and calculate their mean tariff rates, about 84.6% of these means will be within $80 of the true mean tariff rate of all ethanol shipments. This also means that there is a sampling error of $80, which is the maximum amount by which the sample mean may differ from the population mean due to random sampling variability.

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Answer:

30 minutes

Step-by-step explanation:

1/45 m + 1/90 m = 1

2/9 m + 1/90 m = 1

3/90 m = 1   Multiply both sides by 90/3

90/3 x 3/90 m = 1 x 90/3

m = 90/3

m = 30

Helping in the name of Jesus.

Answer:

D(last option)

Step-by-step explanation:

This question might be a bit confusing since a lot of questions like this one require actually visualizing the question. The man in the lighthouse isn't trying to throw the rope directly in front of him to the birds, but rather to the boat.

The angle of depression here is the angle formed from the rope and the man's line of sight. Therefore, the angle of depression is congruent to the angle's alternate interior counterpart, which is the angle of elevation formed from the boat to the water.

From there, we solve like an angle of elevation question. We have the rope length, which is the hypothenuse, but we need to find the length of the side adjacent to the angle of elevation. So, we use cosine.

We just need to plug in the values here. The measure of the angle goes right next to the trig function we are using, and in cosine, the measure of the adjacent angle goes over the measure of the hypothenuse.

Therefore, the answer is D, or the last option.

Answer:

[tex]\textsf{D)} \quad \cos \left(24^{\circ}\right)=\dfrac{x}{45}[/tex]

Step-by-step explanation:

The angle of depression is the angle between the horizontal line of sight of the man in the lighthouse, and the direct line of sight to the boat below him.

To find how far from land the boat is, we can model the scenario as a right triangle.

The angle of depression (24°) is the angle formed by the hypotenuse and the horizontal leg of the right triangle.

If the distance to throw a rope from the top of the lighthouse to the boat is 45 feet, then the hypotenuse of the triangle is 45 feet.

The distance between the boat and the land is the side adjacent to the angle, so we can find this by using the cosine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given:

Substitute these values into the ratio to create the required equation:

[tex]\large\boxed{\cos \left(24^{\circ}\right)=\dfrac{x}{45}}[/tex]

If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

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Answer:

n + 8

M - x

z - 12

c + d

2f + 20 or 20 + 2f

(x + y)^2 or (x + y) × (x + y)

2mn or 2 × m × n

2b - 6 or 6 - 2b

u^2 + v^2 or v^2 + u^2

(xy)/2 or xy/2

The statement "The capital letter N produces the same capital letter after being rotated 180°" is true.

If you rotate the capital letter N 180°, it will produce the same capital letter, as it has rotational symmetry.

The letter N has a vertical line of symmetry in the center, which means that if you rotate it 180°, it will overlap perfectly with its original position, producing the same letter.

So, the statement "The capital letter N produces the same capital letter after being rotated 180°" is true.

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Answer:

0.506

0.516

0.609

0.615

Step-by-step explanation:

The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [[tex]\bold{x}[/tex]] has the highest power of 3.

Given is the following function with degree of 2 as -

We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.

Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, Final answer:

The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:

0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).

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We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.

It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.

For this, let us consider all the digits from 1 to 9, and their respective sums.

Digit: 1 Sum: 1 (odd)

Digit: 3 Sum: 3 (odd)

Digit: 5 Sum: 5 (odd)

Digit: 7 Sum: 7 (odd)

Digit: 9 Sum: 9 (odd)

Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.

Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.

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An equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y is y = 32x

The equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y, can be obtained using the following formula:

y = r * x

where r represents the rate of printing in pages per minute, which in this case is 32 pages per minute.

Therefore, the equation becomes:

y = 32x

This equation states that the number of pages printed, y, is directly proportional to the print time in minutes, x, at a rate of 32 pages per minute.

For example, if Mr. Hernandez wants to print 128 pages, we can use the equation to find out how long it will take him:

128 = 32x

x = 128/32

x = 4

Therefore, it will take Mr. Hernandez 4 minutes to print 128 pages on his high-speed printer.

In summary, the equation y = 32x represents the relationship between the print time in minutes, x, and the number of pages printed, y, when using a high-speed printer that can produce 32 pages per minute.

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The amount of time it would take to drain the swimming pool is equal to 75 minutes..

Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:

[tex]P(t) = I(1 - r)^t[/tex]

Where:

Next, we would determine the amount of time it would take to have 0 gallons in the swimming pool:

20 gallons = 3 minutes

5,000 gallons = x minutes

20x = 1500

x = 1500/20

x = 75 minutes.

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a) The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.

b) The number of squares that will fit on the land is 61773.

Explain square

A square is a geometric shape with four sides of equal length and four right angles. It is a type of rectangle, but all of its sides are the same length. Squares are used in mathematics to represent and calculate areas and volumes, and they also have applications in architecture and art.

According to the given information

(a) To find the area of the largest squares that will fit on the land, we need to find the greatest common divisor (GCD) of the dimensions 735 and 756, and then square it.

To find the GCD, we can use the Euclidean algorithm:

GCD(735, 756) = GCD(735, 756 - 735) = GCD(735, 21) = GCD(21, 735 - 21 * 35) = GCD(21, 210) = GCD(21, 210 - 21 * 10) = GCD(21, 90) = GCD(21, 90 - 21 * 4) = GCD(21, 6) = GCD(6, 21 - 6 * 3) = GCD(6, 3) = 3

Therefore, the GCD of 735 and 756 is 3. The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.

(b) To find how many squares will fit on the land, we need to divide the total area of the land by the area of each square. The total area of the land is:

735 * 756 = 555960 square meters

The area of each square is 9 square meters, as we found in part (a). Therefore, the number of squares that will fit on the land is:

555960 / 9 = 61773.333...

Since we can't have a fractional number of squares, we need to round down to the nearest integer. Therefore, the number of squares that will fit on the land is 61773.

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Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.

The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.

Here,

The average rent is determined by adding up all the rents and dividing by the total number of rents.

This is known as the mean.

Given that the person's rent increased by

=>$150, $1055 - $905 = $150.

The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.

The mean would therefore rise by

=> $150/10

=> $15.

(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.

The new median would be the middle value of the revised list, which would include the new price of $1055,

if one person's rent increased from $905 to $1055.

The median would rise given that $1055 is more expensive than $1020.

Thus , it increases by.

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The number of hours Matt babysits his sister is 1 and half hours.

Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.

Let the number of half an hours Matt babysits his sister be x.

Matt made $18.50

So, equation is 5.50x+2 =18.50

5.50x=16.50

x=16.50/5.50

x= 3

Which means 1 and half hours he babysits his sister.

Therefore, the number of hours Matt babysits his sister is 1 and half hours.

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the inverse of the function f(x) = 3 + 5x is f^(-1)(x) = (x - 3) / 5.To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x).

what is  inverse of the function  ?

The inverse of a function is a new function that "undoes" the effect of the original function, meaning that if we apply the inverse function to the output of the original function, we get back the input.

In the given question,

To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x). The steps to find the inverse are as follows:

Step 1: Replace f(x) with y.

y = 3 + 5x

Step 2: Solve for x in terms of y.

y - 3 = 5x

x = (y - 3) / 5

Step 3: Replace x with f⁻¹(x) to get the inverse function.

f⁻¹(x) = (x - 3) / 5

Therefore, the inverse of the function f(x) = 3 + 5x is f⁻¹(x) = (x - 3) / 5.

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Answer:

A- 304.8 cm²

Step-by-step explanation:

Find the area for the 4 sides (excluding both the top and base).

(2(12×7.5))+(2(12×5.2)) = 302.8

Answer:

A.  304.8 cm²

Step-by-step explanation:

The rectangular prism has a total of 6 rectangular sides

~   two at the bottom and top both of equal dimensions 5.2 x 7.5

~   two at the front and back both of equal dimensions 12 x 7.5

~    two one on the left side and the other on the right side both of equal dimensions 12 x 5.2

The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces

For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle

Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)

We multiply by 2 since there are 2 of each rectangular surface

2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm²   ANSWER

Answer:

A

Step-by-step explanation:

it is a bar graph because it involves class interval

Answer:

the triangle arereflected across the line y=x

Answer:

To determine the possible values of h, we need to first understand what is meant by the range.

The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.

The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.

So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.

If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.

Therefore, the correct answer is B. 11.

The constant of proportionality of the equation would be = 12.80.

The constant of proportionality of an equation is the figure that represents the ratio that exists between two different variables that has direct proportional relationship.

The amount of money made by an employee is directly proportional to the number of hours they worked.

That is m directly proportional to h

The equation = m = k h. where k = 12.80 = constant of proportionality.

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Answer: 105m

Step-by-step explanation:

Hope this helps! :)

The given parallelogram is not a rectangle.

One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .

The test for a right - angled triangle is the Pythagorean Theorem which is :

Side ² + Side ² = Hypotenuse ²

Using, the dimensions, check to see if there is a right triangle :

7. 2 ² + 9. 1 ² = 12 ²

134. 65 ≠ 144

There is no right angled triangle so this is a parallelogram that is not a rectangle .

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The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).

A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.

A(2,8) R(3,4) G(2,-1) Y(9,7)

Translate it to 4 units left gives the result:

A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)

Now dilate it:

A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)

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Answer:

200

Step-by-step explanation:

Turn the 31% back to a decimal = 0.31

62/ x = 0.31

multiply each side of the equation by x to cancel it out from under the fraction

62 = 0.31x

divide each side by 0.31 to have to x alone

200 = x

Check work:

62/200 = 0.31 x 100 = 31%