in the case of a consistent system where there are more variables than equations, what information is contained in the augmented column of the rref?

The required time after the pebble is thrown will it hit the​ ground is 10 second.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

We have,

Height of waterfall = 1500 feet, Velocity = 20 feet per second.

h = -16t^2 + 20t +1500

What height will the pebble have when it reaches the ground? At h = 0, it will be.

h = -16t2 + 16t + 1500

0 = -16t2 + 16t + 1500

Divide both sides by 4 to simplify things since all three terms share a common component of 4.

0 = -4t2 + 4t + 375

You can either apply the quadratic formula or try to factor this out. I advise using the quadratic formula because factoring 375 is not enjoyable.

t = [-b ± √(b2 - 4ac)] / 2a

Your equation reads a = -4, b = 4, and c = 375.

t = [-4 ± √(42 - 4(-4)(375))] / 2(-4) (-4)

t = [-4 ± √(6016)] / -8

You receive a favourable and a negative response. The positive number serves as your answer, and you can disregard the negative result. I receive a value of about 10 seconds.

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Weight of the Mediam sized fridge in ounces is  3212 ounces

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

The mass in pounds is multiplied by 16 to get the equivalent weight in ounces. The mass represented in ounces will be the outcome.

The gram serves as the fundamental unit of mass in the metric system. Water has a mass of 1 gram if a box with a length of 1 cm on all sides is filled with it.

A system of measurements known as the foot-pound-second system, or FPS system, is based on three basic units: the foot for length, the pound (avoirdupois) for mass or force (see below), and the second for time.

We can convert 200 pounds to ounces = 200*16 = 3200 ounces

Weight of the Mediam sized fridge in ounces is 3200+12 = 3212 ounces

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The diagonal distance from the center of the rectangular field to one of its corners is the square root of the sum of the squares of half of its length and half of its width.

The length of the rectangular field is 104 meters and the width is 76 meters. Half of the length is 104/2 = 52 meters, and half of the width is 76/2 = 38 meters.

The diagonal distance is the square root of the sum of the squares of half of the length and half of the width, so it can be calculated as:

√(52^2 + 38^2) = √(2704 + 1444) = √4148 = 64.4 meters

So the diagonal distance from the central point to a corner flag is 64.4 meters. This is the scale distance, if you want to draw the plan on a 1 cm to 10 m scale, you would multiply this distance by 10 to get the length in cm on the drawing.

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Answer:

length = 40 ft, width = 15 ft

Step-by-step explanation:

Since both rooms are rectangles, we know each side is the same as it's opposing side. So:

Alvin's bedroom perimeter = x+(x-25)+x+(x-25), which can be simplified to 4x+50

Simon's bedroom perimeter = (x+10)+2x+(x+10)+2x+(x+10), which can be simplified to 6x+20

Because the perimeters of the bedrooms are the same, we can set the equations equal to each other. So: 4x+50=6x+20

Then you solve the equation.

4x+50=6x+20

4x+(50-20)=6x(20-20)

4x+30=6x

(4x-4x)+30=(6x-4x)

30=2x

30/2=2x/2

15=x

Now that we know 15 = x, we can plug that in to the original length and width of Alvin's Bedroom:

Length = (x+25) = (15+25) ft = 40 ft

Width = x ft = 15 ft

Therefore, the length of Alvin's bedroom is 40 feet and the width of his bedroom is 15 feet.

At least 72 footprints to construct a 98% confidence interval with a margin of error of less than ±2.5 centimetres.

a. To construct a 95% confidence interval for the mean foot lengths of the adults who used the cave-dwelling, we can use the formula:

Mean ± Z × (Standard deviation/√n)

Where Z is the Z-score for a 95% confidence level (which is approximately 1.96), and n is the sample size.

So, the 95% confidence interval is:

24.8 ± 1.96 × (7.5/√30) = (23.38, 26.22)

This means that there is a 95% chance that the true mean foot length of the adults who used the cave-dwelling falls within the range of 23.38 cm to 26.22 cm.

The assumptions for constructing a confidence interval are that the sample is randomly selected, the sample is large enough (n > 30 is generally considered large enough), and the data is approximately normally distributed.

b. To calculate the sample size needed for a 98% confidence interval with a margin of error of less than ±2.5 centimetres, we can use the formula:

n = (Z^2 × Standard deviation^2)/margin of error^2

Where Z is the Z-score for a 98% confidence level (which is approximately 2.33), and the standard deviation is 7.5 cm.

So, the sample size needed is:

n = (2.33^2 × 7.5^2)/2.5^2 = 71.48

Since the sample size must be a whole number, we would need to analyze at least 72 footprints to construct a 98% confidence interval with a margin of error of less than ±2.5 centimetres.

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--The given question is incorrect; the correct question is

"Anthropologists have discovered a prehistoric cave dwelling that contains a large number of adult human footprints. To study the size of the adults who used the cave-dwelling, they randomly selected 20 of the footprints from the population of all footprints in the cave and measured the length of those footprints. Some statistics resulting from this random sample are as follows.

a. The anthropologists would like to construct a 95 per cent confidence interval for the mean foot lengths of the adults who used the cave dwelling. Construct that 95% confidence interval and interpret the confidence interval as it relates to the problem. (Hint: List out the steps of PANIC to help you through the process. Briefly list off and check the assumptions since you can use your notes on this assignment.)

b. If we assume that the standard deviation of footprints is, in fact, 7.5 centimetres, and we want to construct a 98% confidence interval with a margin of error of less than +2.5 centimetres, at least how many footprints will we need to analyze?"--

Blake flips a fair coin and stops flipping once he gets a head and he gets the minimum of 64 and 2^n, where n is the total number of Blake's flips. The fair value of this game is 7.

In this question, we need to calculate the number of flips of coin that blake did until he gets a head.

We know that each flip has a 50/50 chance of being heads or tails. So, the probability of getting a head on every flip is 0.5

The expected value here is computed as:

= P(n = 1) x (2^1) + P(n = 2) x (2^2)  +  P(n = 3) x (2^3) +  P(n = 4) x (2^4) +  P(n = 5) x (2^5) + P(n >= 6) x (2^6)

= (0.5^1) x 2 + (0.5^2) x 4 + (0.5^3) x 8 + (0.5^4) x 16 + (0.5^5) x 32 + (1 - 0.5 - 0.25 - 0.125 - 0.0625 - 0.03125) x 64

= 5 + 0.03125*64

= 5 + 2

= 7

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When the y = f(x) and y = g(x) graphs intersect, the x and y values on both graphs are exactly the same.

Both graphs have the exact same x and y values when the y = f(x) and y = g(x) graphs cross. So, by figuring out the solution to the equation f(x) = g, we can determine the point or points of intersection (x). We may find the x value(s) of the intersection point(s) by solving this equation.

The (x,y) coordinate pairings for which the input, x, yields the same output value from both functions are known as the points of intersection of two functions, f(x) and g(x).

If A, B, and C are three sets, then all of the elements that are shared by A, B, and C are contained in the set formed by the intersection of these three sets. This can be illustrated as A, B, and C.

Let the two functions be

y = 2x + 1 and

y = x - 2

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Rounding to the nearest tenth, the surface area painted is approximately 263.8 square inches.

12π inches / 2π = 6 inches / 2π = 6 / 2 = 3 inches

So, the radius of the rod is 3 inches.

Next, we find the surface area of one piece of the rod by using the formula for the surface area of a cylinder:

Surface area = 2πr(h + r)

Surface area = 2π * 3 * (4 + 3) = 2π * 3 * 7 = 42π square inches

Finally, we multiply the surface area of one piece of the rod by 2 to find the total surface area painted:

Surface area painted = 42π square inches * 2 = 84π square inches

Using π ≈ 3.14, the surface area painted is approximately 84 * 3.14 = 263.76 square inches.

Therefore, The rounding to the nearest tenth, the surface area painted is approximately 263.8 square inches.

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The minimum number of dots and/or dashes needed so that each letter in the English alphabet can have a unique representation is 4.

We need a code that can handle at least that many characters because there are 26 letters in the alphabet.

One can choose to use one of two symbols in each position, which results in 2^1 = 2 words.

Given two locations and the option to utilize one of two symbols in each, 2^2 = 4 words are produced.

Using one of two symbols in each of the three slots allows for a total of 2^3=8 words.

With 4 positions and the option to use one of two symbols in each, there are 2^4=16 words possible.

The sum of the dots and dashes is

2 + 4 + 8 + 16 = 30

Since there are 26 letters in the English alphabet, 4 dots and/or dashes are required to represent each letter, hence the answer is 4.

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According to the expression, the code will evaluate to false if x is greater than or equal to y, regardless of what the unknown code may be.

The statement "if (x < y & /unknown code/)" will evaluate to false regardless of the unknown code if the value of x is greater than or equal to y.

This code checks if the value of x is less than y. If it is, it will then evaluate the unknown code.

If both the value of x being less than y and the unknown code evaluate to true, the overall expression will be true and the code inside the if statement will be executed.

If either the value of x being less than y or the unknown code evaluates to false, the overall expression will be false and the code inside the if statement will not be executed.

It's important to note that the "&" symbol represents a logical AND operation, meaning that both conditions must be true for the overall expression to be true.

So, even if the unknown code evaluates to true, if the value of x is greater than or equal to y, the expression will still be false.

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Yes, the entire remaining water will fit in one of the half gallon jugs.

Gallon refers to the measure of the liquid.

A litre of water is equivalent to 0.264172 gallons. As a result, if one full litre of water spilled out, you'd be left with 1.73482 gallons of water. Because a half gallon jug can carry 0.5 gallons of water, the remainder 1.73482 gallons of water will certainly fit into one of the half gallon jugs.

A gallon is a term of liquid measurement equivalent to eight pints. It is approximately 4.546 litres in the United Kingdom. It is about 3.785 litres in the United States.

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The area of this heptagon is equal to 455 square units.

Mathematically, the area of a regular polygon can be calculated by using this mathematical expression:

Area of the regular heptagon = 1/2 × n × s × r

Where:

Substituting the given parameters into the area of a regular polygon formula, we have the following;

Area of the regular heptagon = 1/2 × 7 × 10 × 13

Area of the regular heptagon = 455 square units.

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True. Body weight is an example of a discrete variable. A discrete variable is a variable that can only take on certain values.

It can only be counted, not measured. Body weight, for example, can be expressed as an integer value such as 150 pounds or 68 kilograms, but not as a fractional value such as 150.3 pounds or 68.1 kilograms. In other words, the number of possible values for body weight is finite and can be listed out, which makes it a discrete variable.

On the other hand, continuous variables can take on an uncountable number of possible values, such as height or temperature, which can be expressed to an arbitrary degree of precision.

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Answer:

1260 springs

Explanation:

From 1 pm to 6 pm, the machine will work for 5 hours.

In the first part of the day, the machine made 450 paper clips, which took it:

So, the machine will start making springs at 2:30 pm.

From 2:30 pm to 6 pm, the machine will work for 3.5 hours.

During this time, the machine can make:

Therefore, the machine will make 1260 springs by 6 pm.

________________________________________________________

In one hour a machine can make 300 paper clips 300 paper clips or 360 springs. At 1 pm the machine starts working. It makes 450 paper clips and then changes to making springs. How many springs will the machine make by 6 pm?

The machine will make 1260 springs by 6 pm.

We are given that the machine can make 300 paper clips in one hour or 360 springs in one hour.

Let's first find out how many hours the machine will make paper clips before switching to making springs.

We know that the machine has made 450 paper clips. So,

Hence, the machine will make paper clips for 1.5 hours before switching to making springs.

Now, we need to find out how many hours the machine will make springs. We know that the machine starts working at 1 pm and we need to find out how many hours it will work making springs before 6 pm.

There are 5 hours between 1 pm and 6 pm. However, we need to subtract the 1.5 hours that the machine will work making paper clips.

So, the machine will make springs for:

Now, we can use the information that the machine can make 360 springs in one hour to find out how many springs it will make in 3.5 hours.

Therefore, the machine will make 1260 springs by 6 pm.

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The function f(x) is shifted down by 4 units to get g(x).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

g(x) = [tex]9^x[/tex] - 4

and, f(x) = [tex]9^x[/tex]

As, we know that transformation where f(x) - a  shows the function f(x) is shifted down by a units.

Here, the function f(x) is shifted down to 4 units to get the function g(x).

Hence, the shifting is 4 units down.

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The equation of this trend line is N = -2M + 110

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

From the given trend line,

If M is 0, N = 110 = 0 + 110 = -2*0 + 110

If M is 10, N = 90 = -20 + 110 = -2*10 + 110

If M is 20, N = 70 = -40 + 110 = -2*20 + 110

If M is 30, N = 50 = -60 + 110 = -2*30 + 110

So , the equation of this trend line is N = -2M + 110

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Step-by-step explanation: To solve the equation 2x(2x-5)=36, we first need to distribute the 2x:

2x(2x-5) = 2x * 2x - 2x * 5 = 4x^2 - 10x

Now that we have the expanded equation, we can set it equal to 36:

4x^2 - 10x = 36

Next, we'll isolate x by subtracting 36 from both sides:

4x^2 - 10x - 36 = 0

This is a quadratic equation, which we can solve using the quadratic formula or by factoring. Here's one way to solve it using factoring:

(2x-9)(2x+4) = 0

We can set each factor equal to zero and solve for x:

2x-9 = 0, so x = 9/2

2x+4 = 0, so x = -4/2 = -2

So x = 9/2 and x = -2 are the solutions to the equation 2x(2x-5)=36.

Answer:

52

Step-by-step explanation:

yes

This question is mid term factorisation

Answer:

An inequality that represents the weight x of online orders that result in an additional fee would be:

x > 48

This inequality can be read as "x is greater than 48", which represents the weight of the order being over 48 pounds.

To graph this inequality on a number line, we can start by plotting the point 48 on the number line. Then, we can use a solid circle to represent the point 48, since it is included in the solution set. We can then use an arrow pointing to the right of the point 48 to indicate that all values to the right of 48 are also included in the solution set.

Graphically, this inequality can be represented as:

[48(solid circle)------> (x) (values greater than 48)]

Where x is the weight of the package and the solid circle shows that 48 is also included in the solution set.

The towers ZQ and ZR are the closest together.

Triangle is a three-sided polygon which has three vertices.

Solution

If the measure of ZP is x,

Then the measure of ZQ is x-10 and the measure of ZR is x-5.

To find the two towers that are closest together, we need to find the minimum value of the difference between any two angles.

ZP and ZQ: x - (x-10) = 10

ZQ and ZR: (x-5) - (x-10) = 5

So, the towers ZQ and ZR are the closest together, with an angle difference of 5°.

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The Annual Interest is 2%.

Simple interest is the cost of borrowing money that does not take compounding into consideration. In other words, just the principal is affected by simple interest.

Given:

P = $600

As, The difference between the total interest earned after 5 years and the total interest earned after 3 years is $24.

I(5year) - I( 3 year)= 24

R/100 ( 600 x 5 - 3 x 100) = 24

R ( 3000 - 1800) = 2400

R = 2400 / 1200

R= 2%

Thus, the rate is 2%.

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Answer: x-8

Step-by-step explanation:
Remove parentheses.

-8x-12+9x+4

Add -8x and 9x.

x-12+4

Add -12 and 4.

x-8

Answer:

Step-by-step explanation:

4⁴ is the positive exponent of 4² x 4²

An expression is combination of variables, numbers and operators.

The given expression is 4² x 4²

Four square times of four square we have to write in the positive exponent form.

We have a property of exponent that if bases are same then the powers will be added.

4²⁺²

4⁴

Hence, 4⁴ is the positive exponent of 4² x 4²

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Answer:

To get back to sea level, the scientist must now rise a total of 19.2 feet. This is calculated by subtracting the total amount of feet she has descended (37.4 + 8.4 = 45.8 feet) from the total amount of feet she has traveled (37.4 + 19.8 + 8.4 = 65.6 feet). Therefore, 19.2 feet (65.6 - 45.8) must be ascended in order to reach sea level.

An example of a product-of-sum (pos) expression is X = (A + B)(C + D)

From the four expressions, first we eliminate the expressions which do not have the addition operator.

Then we have three expressions:

X = AB + CD

X = (A + B)(C + D)

X = A + B + C

With the remaining expressions we find the expression which is POS (product-of-sum)

An expression X = AB + CD  is in the form of SOP, Sum of products, which will give the sum of the two different multiplications  AB and CD.

An expression X = (A + B)(C + D) is in the form of POS (product-of-sum), which will give the product of two different additions (A + B) and (C + D).

And the expression X = A + B + C is the sum of three different variables.

Thus, X = (A + B)(C + D) is the required expression.

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The complete question is:

Which answer is an example of a product-of-sum (POS) expression?

X = ABC

X = AB + CD

X = (A + B)(C + D)

X = A + B + C

The average speed in the city by the motorist is  45 km/hr.

Velocity is the direction speed of an item in motion as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time.

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common use.

Calculating average speed involves dividing the whole distance traveled by the total time it takes to cover that distance.

The average speed in the open road is x km/hr (say)

Average speed in the city is x - 42 km/hr

The time taken is same to travel 29 km in open road and 15 km in city then

29/x = 15/(x -42)

⇒29x - 29*42 = 15x

⇒14x = 29*42

⇒x = 87 km/hr

The average speed in the city by the motorist is 87-42 = 45 km/hr.

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The number of solutions for the system of equations for this problem, from the first to last, is given as follows:

There are three possible number of solutions for each system of equations, and the cases are presented as follows:

For the second system, we have that:

As 4 and 13 are not multiples, then the system has zero solutions.

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