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The image of the point (-3,0) after the given transformation is (0,5) and this can be determined by using the rules of transformation.

The following steps can be used to determine the image of the point after transformation:

As per the given data translate the point (-3,0) by (3,5).

\(( x, y )\)  =  \(( x + 3, y+ 5)\)  = (0, 5)

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A mathematical quantity having both direction and magnitude is called a vector.

A vector is a mathematical quantity that has both direction and magnitude. It is often represented graphically as an arrow, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vectors are used in many areas of mathematics and science, including physics, engineering, and computer science. Some common operations performed on vectors include addition, subtraction, dot product, and cross product.

Vectors can also be expressed in various coordinate systems, such as Cartesian, polar, and spherical coordinates, depending on the context and application.

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a) The fire is out of the reach of helicopter 1.

b) Only helicopter 3 can be sent to stop the fire.

We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:

The distance is found by the straight line distance formula, an application of Pythagorean theorem:

a) \(d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}\)

\(d = \sqrt{4^{2}+9^{2}}\)

\(d = \sqrt{97}\)

d ≈ 9.849

The fire is out of the reach of helicopter 1.

b) Helicopter 2

\(d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}\)

\(d = \sqrt{1^{2}+8^{2}}\)

\(d = \sqrt{65}\)

d ≈ 8.062

Helicopter 3

\(d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}\)

\(d = \sqrt{7^{2}+3^{2}}\)

\(d = \sqrt{58}\)

d ≈ 7.616

Only helicopter 3 can be sent to stop the fire.

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Answer:

B) x = -4

Step-by-step explanation:

\(\frac{1}{4}x-\frac{1}{8}=\frac{7}{8}+\frac{1}{2}x\\\\\frac{1}{4}x-\frac{1}{2}x-\frac{1}{8}=\frac{7}{8}\\\\\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8}+\frac{1}{8}\\\\\frac{1}{4}x-\frac{1*2}{2*2}=\frac{7+1}{8}\\\\\frac{1}{4}x-\frac{2}{4}x=1\\\\\frac{1-2}{4}x=1\\\\\frac{-1}{4}x=1\\\\x=1*\frac{-4}{1}\\\\x=-4\)

Answer: x = 2 and y = -4

x + 2y = -6

x = -6-2y

Putting this in value of x in

6x + 2y = 4

6(-6-2y) + 2y = 4

-36-12y+2y = 4

-10y = 4+36

y = 40/(-10)

y = -4

Now putting this value of y in

x + 2y = -6

x + 2(-4) = -6

x -8 = -6

x = -6+8

x = 2

Therefore x = 2 and y = -4

If we put these values we can check this

x + 2y = -6

2 + 2(-4) = -6

2 -8 = -6

-6 = -6

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Answer:

3

Step-by-step explanation:

Answer:

B, 15 pencils

Step-by-step explanation:

Our equation: (5 x 42)/14

42 x 5 = 210

210/14= 15

There are three possible triangles that can be formed using the given measurements.

Measurement is the process of quantifying or comparing the amount, size, or extent of something. It is an important concept for scientists, engineers, and other professionals in order to compare and understand the world around them. Measurement involves the use of physical tools, such as rulers, scales, and protractors, and mathematical equations, such as formulas and equations.

We can use the Law of Cosines to solve for the missing side:

\(b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 43^2 + 15^2 - 2(43)(15)\cos(123^\circ)$\\$b^2 \approx 799.5$\\$b \approx 28.3$\)

Now we can use the Law of Sines to solve for the remaining angles:

\(\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.977$\\$A \approx 79.4^\circ$\\$B \approx 23.6^\circ$\)

So the triangle is \($\triangle ABC$\) where \($A=79.4^\circ$\), \($B=23.6^\circ$\), \($C=77^\circ$\), \($a=43$\), \($b\approx 28.3$\) , and \($c=15$\).

We can use the Law of Cosines to solve for the missing side:

\(b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 36^2 + 47^2 - 2(36)(47)\cos(47^\circ)$\\$b^2 \approx 1666.5$\\$b \approx 40.8$\)

Now we can use the Law of Sines to solve for the remaining angles:

\(\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.647$\\$A \approx 40.9^\circ$\\$C \approx 92.1^\circ$\)

So the triangle is \($\triangle ABC$\) where \($A=40.9^\circ$\), \($B=47^\circ$\), \(C\approx 92.1^\circ, a\ =36$\), \($b\approx 40.8$\),

We can use the Law of Cosines to solve for the missing side:

\(h^2 = k^2 + p^2 - 2kp\cos(K)\\$h^2 = 47^2 + 10^2 - 2(47)(10)\cos(139^\circ)$\\$h^2 \approx 2363.7$\\$h \approx 48.6$\)

Now we can use the Law of Sines to solve for the remaining angles:

So the triangle is \($\triangle KHP$\) were \($K=139^\circ$\), \($H\approx 56.5^\circ$\), \($P\approx 124.5^\circ$\), \($k=47$\), \($h\approx 48.6$\), and \($p=10$\).

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Ron's average speed in bike race was 12miles/hour.

What is speed?

Speed is distance traversed per unit of time. It determines that how fast an object is moving. It is the scalar quantity so it has the magnitude of the velocity vector. It has no  direction. An object moving with higher speed means an object is moving faster. An object with lower speed means it is moving slower. If the object isn't moving at all, it has zero speed that is in rest.

The average speed of an object that travels a distance d in time t is d/t.

Ron finished a 15-mile bike race in 1.25 hours.

Here d= 15 miles and t= 1.25 hours.                                       15/1.25

so, average speed = 15/1.25                                                   = (15×100)/125

Dividing 15 by 1.25 we get,                                                     =12

                               = 12 miles/ hour.

Hence Ron's average speed in bike race was 12miles/hour.

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Answer:

x = 12 cm and y = 24 cm

Step-by-step explanation:

Three sides of the first triangle are 10 cm, 12 cm and 12 cm.

Three sides of second triangle are 20 cm, 12+x cm and y cm.

As these two triangles are similar, it means,

\(\dfrac{10}{20}=\dfrac{12}{12+x}=\dfrac{12}{y}\\\\\dfrac{1}{2}=\dfrac{12}{12+x}=\dfrac{12}{y}\\\\\dfrac{1}{2}=\dfrac{12}{y}\ \text{and}\ \dfrac{1}{2}=\dfrac{12}{12+x}\\\\y=24\ cm\ \text{and}\ 24=12+x,x=12 cm\)

So, the value of x is 12 cm and that of y is 24 cm.

The speed of the star as compared to the speed of the star relative to earth is the frequency of light emitted by the source.

A star moving away from the observer (say on Earth) will have its emitted light red-shifted (move to lower frequency), i.e., the spectrum moving to left if we consider the intensity of light is plotted as a function of frequency with the frequency increasing from left to right.

A star moving towards the observer (say on Earth) will have its emitted light blue-shifted (move to higher frequency), i.e., the spectrum moving to the right if we consider the intensity of light is plotted as a function of frequency with the frequency increasing from left to right.

A star moving perpendicular to the observer (say on Earth) will have its emitted light will no change with respect to the spectrum of the stationary star.

These are due to the Doppler effect, the equation of frequency detected by the observer as

\(f_o = f_s\sqrt{\frac{1-\beta }{1+\beta } }\) where \(\beta = \frac{v}{c}\), v the relative velocity of the moving source (the star here), f^s is the frequency of light emitted by the source.

Hence the answer is the speed of the star as compared to the speed of the star relative to earth is the frequency of light emitted by the source.

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Answer:

5(m+9) = 5m+25

Answer:

5(m+9) = 5m+25

Step-by-step explanation:

durrrrrrrrrrrrrrr

The function of the town's population is an exponential growth

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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Sample size and sample standard deviation are the key information needed for a single-sample t-test.

In the event that you need to compare the test cruel with the populace cruel, and you perform a single-sample t-test rather than a z-test, the vital piece of data that will be lost is the populace standard deviation.

Within the z-test, the populace standard deviation is known and the standard mistake of the cruel is calculated utilizing the populace standard deviation.

In a single-sample t-test, the populace standard deviation is obscure, and the standard mistake of the cruel is evaluated from the test standard deviation. 

Therefore, sample size and sample standard deviation are the key information needed for a single-sample t-test. 

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The main difference between vulnerability scanning and penetration testing is a  vulnerability scan is an automated, high-level test that looks for and reports potential vulnerabilities. A penetration test is a detailed hands-on examination by a real person that tries to detect and exploit weaknesses in your system.

vulnerability scanning:

These scans are typically automated and give a beginning look at what could possibly be exploited.

High-quality vulnerability scans can search for over 50,000 vulnerabilities and are required as per PCI DSS, FFIEC, and GLBA mandates.

penetration testing:

A penetration test simulates a hacker attempting to get into a business system through hands-on research and the exploitation of vulnerabilities. Actual analysts, often called ethical hackers, search for vulnerabilities and then try to prove that they can be exploited. Using methods like password cracking, buffer overflow, and SQL injection, they attempt to compromise and extract data from a network in a non damaging way.

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Step-by-step explanation:

To multiply integers with different signs:

Multiply the absolute values of the integers.

The product is negative if the signs of the integers are different.

The product is positive if the signs of the integers are the same.

Example: (-3) x 4 = -12

The absolute values of -3 and 4 are 3 and 4.

Multiply 3 and 4 to get 12.

The signs of -3 and 4 are different (one negative and one positive).

Therefore, the product is negative (-12).

Equally likely refers to two or more possible outcomes of a given situation that have the same probability or the same likelihood to occur. For example, if you throw a die, there are six possible outcomes. You could get 1, 2, 3, 4, 5, or 6. These outcomes are equally likely to occur.

Answer:

C im pretty sure 7.02 and 0.34

Step-by-step explanation:

Answer:

A. 0.318 and 0.3444...

Step-by-step explanation:

Rational numbers are numbers that can be expressed as fractions. Rational numbers include finite values and repeating decimals that have a pattern.

Because all of the answer choices include decimals that have no predictable pattern of decimals, A must be correct.

0.318 is rational because it is finite. 0.3444... will continue to add 4 on to the end of the number, meaning it is repeating predictably, and it is rational.

Answer:

Step-by-step explanation:

This is an arithmetic sequence, in which a set number is added to the previous term to get the next term. The number added is figured out by subtracting the 1st term from the 2nd term and the 2nd term from the 3rd term.

Now that we know the number is 3, we can complete the sequence:

4, 7, 10, 13, 16, 19, 22

We will add all the terms up to get 91.

A=200,201,202.........,2000

Here, it forms an AP with common difference 1

Let the number of terms in the set be n

\( T_{n} = a+(n-1)d \\\\ 2000= 200+(n-1) \\\\ 200+n-1= 2000 \\\\ => n=2000-199= 1801\)

Hence,n(A)=1801

The relation between the events Y and W prevents us from completing the analysis.

The relation between the events Y and W prevents us from completing the analysis.

Case 1: W is more likely than Y then we have the following analysis:

Z, X, Y, and W are arranged in ascending order of more likeliness.

Case 2: Y is more likely than W then we have the following analysis:

Z, X, W, and Y are arranged in ascending order of more likeliness.

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Answer:

Step-by-step explanation:

Let x be the number of tiles to buy for same cost in both store.

18+0.69 · n = 1.29 · n,

1.29n -0.69n =18 or

0.6n =18

n =18/0.6=30

Therefore, 30 tiles need to buy for same cost in both store.[Ans]

Answer:

I think you need to cross multiply

Jody has created a systematic sampling error by forgetting to include a segment of the population that is relevant to the study.

Systematic sampling is a sampling method where every nth member of a population is selected to be part of the sample. In Jody's case, she forgot to include a specific segment of the population, which means that the sampling process was not systematic. This error can introduce bias and affect the representativeness of the sample.

No calculations are required for this type of error.

Jody's mistake in not including a relevant segment of the population has resulted in a systematic sampling error. To ensure the accuracy and validity of the study, it is important to rectify this error by including the missing segment or adjusting the sampling method accordingly.

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Answer:

2,10

Step-by-step explanation:

we can see where the line touches the x-axis but right at the line making the points have a 0 as the y, (2,0) and (10,0) the others have don´t have 0 in the y place. To make it short there are 2 points touching the x-axis, not above or below but on the line.  

Answer:

34 songs

Step-by-step explanation:

120min/3.53 = 33.99

average length of a song = 3.53 minutes

time duration of flight = 120 minutes

no. of songs that should be put on his playlist

= 120/3.53

= 33.99....

= 34 ( approximately )

Answer:

4, 7

Step-by-step explanation:

x = y + 3

y² + 12 = 4x

using the first equation in the second

y² + 12 = 4(y + 3) = 4y + 12

y² = 4y

y = 4

x = y + 3 = 4 + 3 = 7

Answer:

x + 6 = -6

Step-by-step explanation:

Assuming x = -6

\(x+6=0\)

Subtract 6

\(x+6-6=0-6\)

Simplify arithmetic

\(x=0-6\)

Simplify arithmetic(again)

\(x=-6\)

we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.

Hope this helps, have a great day!

With a ratio of 5 : 3, the amount of cocoa powder used to make the icing is 27g.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other. On the other hand, proportion is the equality of two ratios, such that a : b = c : d.

If the combined weight of the iced cake (batter + icing) is 480 g, of which 15% is cocoa powder, then the total mass of the cocoa powder used is:

total mass of the cocoa powder = 15% of 480g

total mass of the cocoa powder = 0.15(480g)

total mass of the cocoa powder = 72 g

If the amount of cocoa powder used in the batter of a chocolate cake and the amount of cocoa powder used in the icing for the cake is in the ratio 5 : 3, and its total mass is 72g, using proportion, solve for the weight used to make the icing.

a + b = 72   ⇒   a = 72 - b

where a = amount of cocoa powder used in the batter

b = amount of cocoa powder used in the icing

5 : 3 = a : b

5 : 3 = 72 - b : b

5b = 3(72 - b)

5b = 216 - 3b

5b + 3b = 216

8b = 216

b = 27

amount of cocoa powder used in the icing = 27 g

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