T/F : The solution set of the linear system whose augmented matrix [a1a2a3b] is the same as the solution set of the equation x1a1+x2a2+a3x3=b

Answer:

True

Step-by-step explanation:

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces

it should be true. Let me know if I'm incorrect.

The quadratic inequality defined on the graph is given as follows:

y ≥ 2/3(x + 3)² - 24.

The coordinates of the vertex of the quadratic function are given as follows:

(-3, -24).

Hence the quadratic function is given as follows:

y = a(x + 3)² - 24.

In which a is the leading coefficient.

When x = 3, y = 0, hence the leading coefficient a is obtained as follows:

0 = a(3 + 3)² - 24

36a = 24

a = 24/36

a = 2/3.

Hence:

y = 2/3(x + 3)² - 24.

The quadratic function has a solid curve, and the values above it are pained, hence the inequality is given as follows:

y ≥ 2/3(x + 3)² - 24.

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Answer: y = 45

Step-by-step explanation:

225/5 = 45

45·5 = 45

Answer:

(B) \(\frac{\sqrt{6} }{9}\)

Step-by-step explanation:

A right circular cone's curved surface area is 12320 cm2. if the base's radius is 56 cm then the height of the right circular cone is 42 cm.

What is curved surface area?

The space occupied by a hemisphere's curved surface is known as the curved surface area. The space occupied by the surface of a three-dimensional object is referred to as its surface area.

Given that,

Curved surface area of right circular cone is 12,320 \(cm^{2}\),

radius of its base is 56 cm

Hence,

Surface area = \(2\pi r^2+2\pi rh\)

Surface area = \(2\pi rh(r+h)\)

12,320 = \(2\times 56\times 3.14 \times (56+h)\)

h = 42 cm

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I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:

2ln5 + ln4 + ln5

Step-by-step explanation:

Think about how we can write 500 in terms of 4 and 5.

\(500 = 5^2*(4*5)\)

So ln(500) can be written as ln(5^2*4*5)

Using log rules \(log_b(x*y)=log_b(x)+log_b(y)\\logb(x^a)=a*log(x)\)

we can rewrite ln(500) to 2ln5 + ln4 + ln5

Answer:

x = 55 ; y = 60

Step-by-step explanation:

Answer: no.

Step-by-step explanation:

it's 1 tenth

Answer:

because they all have 3 corners

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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The classified label for the test data (0,0,0) depends on the value of K. Please provide the value of K to determine the specific classified label.

To classify the test data (0,0,0) using the K-nearest neighbors (KNN) algorithm, we need to calculate the distance between the test data and each point in the training dataset. Then, we select the K nearest neighbors based on the distance metric and assign the majority class label among those neighbors as the predicted label for the test data.

Let's calculate the Euclidean distance between the test data (0,0,0) and each point in the training dataset:

Distance to Class A: sqrt((0-0)^2 + (0-1)^2 + (0-0)^2) = 1

Distance to Class B: sqrt((0-1)^2 + (0-2)^2 + (0-2)^2) = sqrt(5)

Distance to Class C: sqrt((0+1)^2 + (0+1)^2 + (0+1)^2) = sqrt(3)

Now, based on the value of K, we select the K nearest neighbors. Let's assume K=3 for illustration purposes. Among the distances calculated above, the three closest points are from Class A, Class C, and Class C. Therefore, if K=3, the majority class among these three neighbors is Class C, so the classified label for the test data (0,0,0) would be Class C.

The classified label for the test data (0,0,0) when using the K-nearest neighbors (KNN) algorithm depends on the value of K. To determine the specific classified label, please provide the desired value of K.

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The 89 scores are all within one standard deviation of the mean.

The range of data within one standard deviation of the mean is expressed as the mean plus or minus one standard deviation.

Since the mean in this situation is 80 and the standard deviation is 4, the range that falls within the mean's one standard deviation is as follows:

\(80±4 = (76, 84)\)

Therefore, scores A (75) and B (77) are both below this interval, score C (90) is above this interval, and score D (90) is much higher than this interval. Only score E (89) is within this interval

The 89 scores are all within one standard deviation of the mean.

so E) 89 is the right response.

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Catelyn will have approximately $1,647.62 in her account after 3 years of making deposits every 6 months.

To calculate how much Catelyn will have after 3 years, we need to determine the total number of compounding periods and then apply the compound interest formula.

Given:
Principal deposit (P) = $1537
Interest rate (r) = 2.07% per year (expressed as a decimal, r = 0.0207)
Compounding period (n) = 4 times per year (quarterly)
Time (t) = 3 years

First, we calculate the total number of compounding periods:
Number of compounding periods (N) = n * t = 4 * 3 = 12

Next, we can use the compound interest formula to calculate the future value (A):
A = P * (1 + r/n)^(n*t)

Plugging in the values:
A = $1537 * (1 + 0.0207/4)^(4*3)
A = $1537 * (1 + 0.005175)^12
A = $1537 * (1.005175)^12
A ≈ $1,647.62

Therefore, Catelyn will have approximately $1,647.62 in her account after 3 years of making deposits every 6 months.

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Answer:the answer is b good luck

Step-by-step explanation:

The median of the distribution 34 22 13 is 22.

To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.

In this case, the scores are 13, 22, and 34.

After arranging the scores in numerical order, we have 13, 22, and 34.

There are three scores in this set, so the median is the middle score, which is 22.

The median of the set is 22.

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Answer:

\( x = 2 \sqrt{5} \)

Step-by-step explanation:

\( \sin \: 30 \degree = \frac{ \sqrt{5} }{x} \\ \\ \frac{1}{2} = \frac{ \sqrt{5} }{x} \\ \\x = 2 \sqrt{5} \)

The probability that Paul and Yuri get the weather they want = 27/64

Given probability for rain = 75% = 3/4

The total probability is considered as 100% or 1.

So the probability for sunny day = 1 - 3/4 = 1/4

Paul and Yuri want a sunny day from labor day 4 -day weekend.

This means 3 days of rain and 1 sunny day. So 3 times the probability for rain and 1 time the probability for sunny day.

This one sunny day can be chosen from 4 days. In other ways there is 4C1 =4 different ways possible to choose 3 days of rain and 1 sunny day from 4 days.

So finally the probability that Paul and Yuri get the weather they want

= \(\frac{3}{4}^3 \times \frac{1}{4} \times 4\) = 27/64

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The total pressure of a mixture of two gases is the finalized value of the summation of the total pressure of each of the gases.

The total pressure of a mixture of two gases can be expressed in the form of an equation, as below,

Total Pressure = Pressure of Gas 1 + Pressure of Gas 2

It is noteworthy to be mentioned that the partial pressure of an individual gas is completely in contrast to that of the individual pressure of a gas. It can be expressed in the form of an equation, as below,

Partial Pressure = Total Pressure of Gas x Mole Fraction of Gas

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Answer:

819

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

unit mean the unit digit of ...

\(unit(7^0)=unit(1)=1\\unit(7^1)=unit(7)=7\\unit(7^2)=unit(49)=9\\unit(7^3)=unit(7^2)*7=unit(9*7)=unit(63)=3\\unit(7^4)=unit(7^3)*7=unit(3*7)=1\ just\ like\ unit(7^0)\\\)

\(\left \{ \begin {array}{cc}1&if\ n \in 4*\mathbb{N}\\7&if\ n \in 4*\mathbb{N}+1\\9&if\ n \in 4*\mathbb{N}+2\\3&if\ n \in 4*\mathbb{N}+3\\\end {array} \right.\\\\\\unit(7^{7^{7}})=unit(7^{(7^{7})})=unit(7^{823543})=unit(7^3)=3\\\\unit((7^{7})^{7}) =unit(7^{49} )=unit(7^{1})=7\\\)

I have given 2 answers since i don't know what you mean with 7^7⁷.

Answer:

If you multiply 6 by an even number, it will end in the same digit. For example, 6 x 4 = 24, so 4 and the 4 in 24 are the same. The number in the tens place will be half the number in the ones place, so the 2 in 24 is half of 4

The required strength of the doublet for the flow past a cylinder can be determined using the given information. In this case, we assume the flow to be inviscid, irrotational, and incompressible. The stream function for a uniform flow in the horizontal direction is given by ψ = Uy, where U represents the velocity of the uniform flow and y is the vertical coordinate.

To determine the strength of the doublet, we can use the stream function for a doublet, which is given by ψ = -2πKr sin(θ), where K represents the strength of the doublet and θ is the polar angle. The negative sign indicates that the streamlines are clockwise around the doublet.

The flow past a cylinder can be represented by the combination of a uniform flow and a doublet. The doublet is introduced to simulate the circulation around the cylinder. By matching the flow conditions at the surface of the cylinder, we can determine the strength of the doublet required.

To calculate the strength of the doublet, we equate the stream function of the uniform flow at the surface of the cylinder (ψ_uniform) to the sum of the stream function of the doublet and the stream function of the uniform flow (ψ_doublet + ψ_uniform). By solving this equation, we can find the value of K, the strength of the doublet.

In summary, to determine the required strength of the doublet for the flow past a cylinder, we need to solve the equation that equates the stream function of the uniform flow to the sum of the stream function of the doublet and the stream function of the uniform flow. Solving this equation will provide us with the value of the strength of the doublet, which represents the circulation around the cylinder.

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The wall cloud is approximately 3 miles away.

An angle that is formed when an object is viewed above the horizontal is said to be an angle of elevation.

From the details of the question, we can determine the distance of the wall cloud by;

let the distance of the wall cloud be represented by x, applying the trigonometric function;

Sin θ = opposite/ hypotenuse

Sin 11 = 3000/ x

x = 3000/ 0.1908

  = 15722.53

The wall cloud is 15722.53 feet away.

But 1 mile = 5,280 feet. so that;

x = 15722.53/ 5280

  = 2.9778

x = 3 miles

Therefore, the wall cloud is 3 miles away.

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The probability that a flight between New York City and Chicago is less than 135 minutes is 0.6667, or approximately 0.67. This means there is a 67% chance that a randomly selected flight will take less than 135 minutes.

In the given problem, we are told that the time to fly between the two cities follows a uniform distribution, with a minimum of 120 minutes and a maximum of 150 minutes. In a uniform distribution, the probability of an event within a certain range is proportional to the length of that range. Therefore, to find the probability of a flight being less than 135 minutes, we need to calculate the length of the range from 120 to 135 minutes and divide it by the length of the entire distribution, which is 150 - 120 = 30 minutes.

The length of the range from 120 to 135 minutes is 135 - 120 = 15 minutes. Dividing this by the length of the entire distribution gives us 15/30 = 0.5, or 50%. However, since the distribution is continuous and the probability of exactly 135 minutes is zero (as the distribution is uniform), the probability of a flight being less than 135 minutes is slightly greater than 0.5. Thus, the correct answer is approximately 0.67.

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Answer:15 cubic inches

Step-by-step explanation:

so you know one cube is 1/4 cubic inches, that being said 4 cubes=1 cubic inch.

1 column hold 12 individual cubes, 12/4= 3 cubic inches

then you multiply 3 times the number of columns (5)

which gives you 15 cubic inches

Hey there! I'm happy to help!

To find the surface area of a sphere, here is what you do.

You square the radius.

4²=16

You multiply by 4.

16×4=64

And you multiply by pi!

64×π=64π

Therefore, the surface area of the sphere is A. 64π units². It's that easy!

Now you can find the surface area of a sphere! Have a wonderful day! :D

Question :-

Answer :-

\( \rule{180pt}{3pt}\)

Diagram :-

\(\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}\)

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

\(\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}\)

Substitute the given values into the above formula and solve for surface area:

\(\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2\)

\(\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2\)

\(\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi\)

\(\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi\)

\(\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}\)

Therefore :-

\(\\\)

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Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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