Which set of ordered pairs represent a linear function?
{(3, 4), (5,-2), (6,-5), (9, -7)}
{(-2, 8), (1,5), (4,2), (7, -1)}
{(1, 2), (3, 3), (4,4), (7, 6)}
{(-4,4), (2, 3), (4, 2), (5, 1)}

Answer:

\(m=\frac{-3}{-7}\)

Step-by-step explanation:

Given the following question:

Point A = (4, 8) = (x1, y1)
Point B = (-3, 5) = (x2, y2)

In order to find the slope any two points given we use the formula to find slope or rise/run.

\(m=\frac{y2-y1}{x2-x1}\)
\(m=\frac{5-8}{-3-4} =\frac{-3}{-7}\)
\(m=\frac{-3}{-7}\)

The reason why the students answer is incorrect because he substituted incorrectly. More specifically the run part of the formula for slope. The formula for slope goes x2 - x1 which means it should be -3 - 4, not -4 - 3, which will give you the answer -7.

Hope this helps.

Using the hypergeometric distribution, it is found that there is a 0.4953 = 49.53% probability that he will choose exactly 1 dime or exactly 1 quarter.

------------------

The coins are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:  

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)  

The parameters are:

In this problem:

Then:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 1) = h(1,10,4,6) = \frac{C_{6,1}C_{4,3}}{C_{10,4}} = 0.1143\)

\(P(X = 3) = h(3,10,4,6) = \frac{C_{6,3}C_{4,1}}{C_{10,4}} = 0.381\)

\(p = P(X = 1) + P(X = 3) = 0.1143 + 0.381 = 0.4953\)

0.4953 = 49.53% probability that he will choose exactly 1 dime or exactly 1 quarter.

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The proportion of the variation in the y variable that can be explained by the variation in the x variable, known as the coefficient of determination or r², is 23.5%.

This means that approximately 23.5% of the variability in the y variable can be accounted for by changes in the x variable, as indicated by the given regression equation and correlation coefficient.

The coefficient of determination (r²) is obtained by squaring the correlation coefficient (r). In this case, the correlation coefficient is -0.485. When we square -0.485, we get 0.235. This value represents the proportion of the total variability in the y variable that can be explained by the linear relationship with the x variable.

To express this as a percentage, we multiply r² by 100. Therefore, the proportion of the variation in y that can be explained by the variation in x is 0.235 * 100 = 23.5%.

In summary, based on the given regression equation and correlation coefficient, approximately 23.5% of the variation in y can be explained by the variation in the values of x.

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thats the answer just look at the picture :)

for the work

Answer:

Explanation:

Each baking tray can hold 6 muffins.

(a) If Amy bakes 4 tray of muffins, the number of muffins she will have in all will be:

(b)The corner bakery produced 10 times as many muffins

The number of muffins produced by the bakery will therefore be:

the answer is 7x I'll save you some time by not explaining

The number of the smaller squares which would be shaded to represent 0.75% as given in the task content is; 75.

The number of squares to correctly represent 245% on the grid is; 245.

It follows from the task content that; To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares.

Since each Square in the 10 × 10 grid represents 1%, it follows that on division of one of the squares in the grid into 100 smaller squares;

The percentage, 0.75% can be represented by shading 75 smaller squares.

Also, the number of squares to be shaded on 10 × 10 grids to represent 245% according to the task content is; 245. This follows from the fact that, all 100 squares on the on 10 × 10 grids represent 100%.

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The equation y = 2e^0.4t can be rewritten in the form y = a(1+r)' as y = 2(1+0.4)' or y = 2(1-0.4)', where a represents the initial value, r represents the growth or decay rate, and t represents time.

To rewrite the equation y = 2e^0.4t in the form y = a(1+r)' or y = a(1 - r)', we need to express the exponential term in a different format. The exponential function e^x can be represented using the properties of exponents. In this case, we have e^0.4t.

Using the property e^x = (1 + r)^x, we can rewrite the equation as y = 2(1+0.4)' or y = 2(1-0.4)'. Here, a = 2 represents the initial value of y. The term (1 + 0.4)' corresponds to the growth factor, while (1 - 0.4)' represents the decay factor. The exponent 0.4t is now expressed in terms of the growth or decay rate, r.

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The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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In this example, the area of the sails of the scale model would be 1.025 SI units

To determine the area of the sails of the scale model, you'll first need to know the scale ratio between the real Lady Washington and the model.

A scale ratio is expressed as a fraction, such as 1:20, which means that 1 unit on the model represents 20 units on the real object.

Once you have the scale ratio, you'll need to apply the square of this ratio to the area of the sails of the real Lady Washington. For example, if the scale ratio is 1:20, then the ratio for the area calculation will be (1/20)^2, or 1/400.

Now, simply multiply the area of the real sails (410 SI units) by the square of the scale ratio. Using the 1:20 example, you'd calculate:

410 SI units * (1/400) = 1.025 SI units.

. Remember to replace the scale ratio with the actual ratio provided for your specific question.

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Answer:

T(3, 8)

Step-by-step explanation:

Yes, it can.

Use the midpoint formula with points S and Z, and solve for point T.

M( (x_1 + x_2)/2 , (y_1 + y_2)/2 )

Z(3, 5) = ( (3 + x)/2 , (2 + y)/2 )

(3 + x)/2 = 3

3 + x = 6

x = 3

(2 + y)/2 = 5

2 + y = 10

y = 8

T(3, 8)

Answer:

Step-by-step explanation:

You want two unit vectors that make an angle of 60° with v(6, 8).

After we normalize v to a unit vector, we can find the two desired vectors by adding or subtracting 60° from its angle. The normalized vector v is ...

  v = (6, 8)/√(6² +8²) = (3/5, 4/5)

This can be rotated 60° CCW by the transformation ...

  (x, y) ⇒ (x·cos(60°)-y·sin(60°), x·sin(60°)+y·cos(60°)) = (x-y√3, x√3+y)/2

  (3/5, 4/5) ⇒ ((3-4√3)/10, (3√3+4)/10) . . . . 60° CCW from v

It can be rotated 60° CW by the transformation ...

  (x, y) ⇒ (x·cos(60°)+y·sin(60°), -x·sin(60°)+y·cos(60°)) = ((x+y√3, -x√3+y)/2

  (3/5, 4/5) ⇒ ((3+4√3)/10, (4-3√3)/10)

__

Additional comment

When the vector is written as a complex number, it can be rotated by multiplying by 1∠±60° = (cos(60°)±i·sin(60°). That is what the calculator did.

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A 24-hour collection provides a more comprehensive and reliable assessment of certain values.

A 24-hour collection is a better indicator of some values than a random specimen because it provides a more comprehensive and representative sample of the specific substance or parameter being measured.

It captures variations in levels throughout the day and allows for the detection of fluctuations that may not be captured by a single random specimen.

A 24-hour collection involves collecting samples over a full day, typically for substances such as urine or hormones. This method provides a more accurate representation of the average levels of the substance being measured. It takes into account the diurnal rhythm or cyclical variations that may occur throughout the day.

For example, hormone levels often fluctuate throughout the day, with different peaks and troughs at specific times.

By collecting samples at regular intervals over a 24-hour period, a more accurate picture of the average hormone levels can be obtained, allowing for a better assessment of hormonal imbalances or abnormalities.

In contrast, a random specimen may only capture a snapshot of the substance's level at a specific moment, which may not be representative of the overall pattern.

Fluctuations in levels throughout the day can be missed, leading to potential inaccuracies or misinterpretation of the data.

Therefore, a 24-hour collection provides a more comprehensive and reliable assessment of certain values by capturing variations and trends over time, making it a better indicator than a single random specimen.

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the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.

The probability of a randomly selected person having a birthday in August is 1/12. There are 12 months in a year and August is one of them. Therefore, The probability of a randomly selected person having a birthday in August is 1/12 because there are 12 months in a year and August is one of them. Each month has an equal chance of being chosen since they all have the same number of days. This probability remains the same regardless of whether or not it is a leap year. Therefore, the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.The probability of a randomly selected person having a birthday in August is calculated by dividing the number of days in August (31) by the total number of days in a year (365). This works out to be 1/12 or 0.0833 rounded to four decimal places.

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Answer:

Step-by-step explanation:

7fg - g2x2

The type of function represented in the table is linear.

Let's check the type of function represented in the table.

You can tell if a table is linear by looking at how x and y change. If, as x increases by 1, y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.

It can also be found by using the linear equation,

y = mx + b

where

Therefore,

The x increases by y and the y increase by a constant rate of 5.

Therefore, the function represented in the table is linear.

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Answer:

a. ║ x - 23 ║ ≤ 6 b.  17 ≤ x ≤ 29

Step-by-step explanation:

a. Let x be the length of the wall. Since the length of the wall is half the length of the drive way with an absolute deviation of 6 at most, since the drive way is 46 foot long, half of it is 46/2 = 23.

So, 23 ± 6 ≤ x or x - 23 ≤ ±6 or ║ x - 23 ║ ≤ 6

b. Solving the absolute value inequality,

-(x - 23) ≤ 6 and x - 23 ≤ 6

x - 23 ≥ 6 and x - 23 ≤ 6

x ≥ 23 - 6 and x ≤ 23 + 6

x ≥ 17 and x ≤ 29

So 17 ≤ x ≤ 29

0.25 recurring can be expressed as the fraction 25/99.

A fraction is a mathematical expression representing a part of a whole, or a ratio between two numbers. It consists of a numerator, which represents the part or ratio being considered, and a denominator, which represents the whole or total.

To express 0.25 recurring as a fraction, we can use the following method:

Let x = 0.25 recurring

Then 100x = 25.25 recurring (multiply both sides by 100 to move the decimal point)

Subtracting the first equation from the second equation, we get:

100x - x = 25.25 recurring - 0.25 recurring

99x = 25

x = 25/99

Therefore, 0.25 recurring can be expressed as the fraction 25/99.

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Note that if m/3 = 54°, then the measure of each missing angle are given as follows:

a. m<1= 36°

b. m<2= 90°

c. m<4= 36°

d. m<5= 90°

e. m<6= 45°

f. m<7= 126°

g. m<8= 54°

h. m<9= 126°

i. m<10= 45°

j. m<11 = 36°

k. m<12 = 144°

l. m<13 = 36°

m. m<14 = 144°

We are given three clues from which we solve the missing angles.

Clue 1: m∠3 given as 54°

Clue 2: m∠ 2 given as 90°

The two lines that (are now labeled AB and CD are parallel to one another. Thus:

a) ∠1, ∠2, and ∠3 are complimentary, ∠1 = 180 - (90+54) = 36°

b) ∠2 = 90° (given)

c) ∠4 = 36° (Opposite angles) ∠1 ≅ ∠4

d) ∠5 =90°  (Opposite angles) ∠2 ≅ ∠5

e) ∠6 = 54°  (Opposite angles) ∠13≅ ∠6

f) ∠7 = ∠1+∠2 (since Line EF is perpendicular to GH, (∠1+∠2) are corresponding angles to ∠7
g) ∠8 = 54° (∠3 and ∠8 are corresponding angles)

h) ∠9 = 126° (∠9 corresponds to ∠5 and ∠4; an alternate explanation is the angle on straight line (∠8 and ∠9) (180-54 = 126°)

i) ∠10 = 54° (∠6 and ∠10 are corresponding angles)

j) ∠11 = 36° (∠11 and ∠1 are corresponding angles)

k) ∠12 = 144° (∠12 corresponds to (∠2+∠3)

l) ∠13 = 36° ( ∠12 and ∠13 are supplementary angles)

m) ∠14 = 144° (∠12 and ∠14 are opposite angles)

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Answer:

k = 4, t = 2

Step-by-step explanation:

Express 2025 as a product of its prime factors

2025 = \(3^{4}\) × 5², that is

\(3^{4}\) × 5² = \(3^{k}\) × \(5^{t}\)

Comparing exponents of same bases on both sides, gives

k = 4 and t = 2

Proved that AFDC is an isosceles triangle.

A triangle that has at least two sides of equal length is said to be isosceles. The third side of an isosceles triangle is referred to as the base, while the two equal sides are known as the legs. An isosceles triangle has congruent angles on either side of the legs.

Proof that AFDC is an isosceles triangle:

Given: In triangle ABC, AD=BC and AC is congruent to BD.

To prove: Triangle AFDC is an isosceles triangle.

Proof:

Draw a diagram of triangle ABC with AD=BC and AC congruent to BD.

Draw segment CD.

Since AC is congruent to BD, triangle ADC is congruent to triangle BDC by SSS congruence.

Therefore, AD is congruent to BC by corresponding parts of congruent triangles are congruent (CPCTC).

Since AD=BC, triangle AFD is congruent to triangle BFC by AAS congruence.

Therefore, FD is congruent to FC by corresponding parts of congruent triangles are congruent (CPCTC).

Thus, triangle AFDC has two congruent sides (FD and DC) and is therefore an isosceles triangle by definition.

Therefore, AFDC is an isosceles triangle.

Therefore, we have proved that AFDC is an isosceles triangle.

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Answer:

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The angle formed by a tangent and secant is half the difference of the intercepted arcs:

Find the measure of ∠MLJ by substituting 4 for x in the angle measure:

Answer:

18+\(6\sqrt{5}\)

Step-by-step explanation:

Since the helicopter flies east for six miles and north for 12 miles, it flies 18 miles. Then on the way back, it flies an unknown amount of miles. the path the helicopter takes is in the form of a triangle, and the path back is the hypotenuse of the triangle. To find the hypotenuse, we can do \(a^2+b^2=c^2\), where c is the hypotenuse. We do

\(6^2+12^2=c^2\\36+144=c^2\\180=c^2\\\sqrt{180}=c\\ 6\sqrt{5}=c\)Therefore, the total distance flown by the helicopter is 18+\(6\sqrt{5}\).  

Answer:

y = -x -7

Step-by-step explanation:

-5 = -1(-1) + b

-7 = b

y = -x -7

Answer:

y=−x−6

Step-by-step explanation:

b=−5−(−1)x(−1)=−6.

so  y=mx+b.

y=−x−6.

Answer:

The slope of the line is m=−1.

The equation of the line in the slope-intercept form is y=−x−6.

A student drove from her home to the university and get back to her home. The distance of her home and the university is 12 km. Her average speed for the entire trip is:  3.16 km/hours

The relation between speed, distance, and time is given by:

d = v x t

Where:

d = distance

v = speed

t = travelled time

In this problem, the distance of round trip, from her home to university and back home is:

d = 2 x 12 km = 24 km

The time needs to make this round trip = t = 7.6 hours

Hence, the average speed is:

average speed = distance/time

average speed = 24 / 7.6

average speed = 3.16 km/hours

Your question is incomplete. Most likely it was:

A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km.

(c) if she drove back home using the same path she took out to the university and arrives 7.6 h after she first left home, what was her average speed for the entire trip, in kilometers per hour?

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The gravitational potential energy of the stone-Earth system can be calculated before the stone is released, after it reaches the bottom of the well, and the change in gravitational potential energy during the process.

Gravitational potential energy is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.

(a) Before the stone is released, it is held 11 m above the top edge of the well. The mass of the stone is 0.25 kg, and the acceleration due to gravity is approximately 9.8 m/s². Using the formula, the gravitational potential energy is calculated as PE = (0.25 kg)(9.8 m/s²)(11 m).

(b) After the stone reaches the bottom of the well, its height is 7.3 m. Using the same formula, the gravitational potential energy at this point is given by PE = (0.25 kg)(9.8 m/s²)(7.3 m).

(c) The change in gravitational potential energy can be determined by subtracting the initial potential energy from the final potential energy. The change in gravitational potential energy is equal to the gravitational potential energy after reaching the bottom of the well minus the gravitational potential energy before the stone was released.

By calculating these values, we can determine the specific numerical values for (a), (b), and (c) based on the given data.

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Answer:

Y = 2

X = 6

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

13

Step-by-step explanation:

4^2 is 16

16-3=13

that's all that you have to do you replace the x with 4 and do a normal equation

Answer: y=13

Y=(4)^2-3

y=16-3

y=13