a train will travel 300 kilometers at a constant rate. write an equation that represents the trains rate in kilometers per hour (r) based on how mant hours the trip takes (t).

Using the given data, the equation that best models a line of fit for the data is y = 20x. The slope of the line of fit indicates that for each additional hour that Sally works, she earns an additional $20, on average. So, the correct option is D).

For finding the equation of the line of best fit and the slope

Firstly, Find the mean of x and y.

Mean of x = (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 8 = 5.5

Mean of y = (40 + 70 + 110 + 120 + 150 + 140 + 180 + 190) / 8 = 127.5

Calculate the deviations from the mean for x and y.

Deviation from mean of x = x - mean of x

= [2 - 5.5, 3 - 5.5, 4 - 5.5, 5 - 5.5, 6 - 5.5, 7 - 5.5, 8 - 5.5, 9 - 5.5]

= [-3.5, -2.5, -1.5, -0.5, 0.5, 1.5, 2.5, 3.5]

Deviation from mean of y = y - mean of y

= [40 - 127.5, 70 - 127.5, 110 - 127.5, 120 - 127.5, 150 - 127.5, 140 - 127.5, 180 - 127.5, 190 - 127.5]

= [-87.5, -57.5, -17.5, -7.5, 22.5, 12.5, 52.5, 62.5]

Calculate the product of the deviations for each data point.

Product of deviations = deviation from mean of x * deviation from mean of y

[(2-5.5) * (40-127.5)] + [(3-5.5) * (70-127.5)] + [(4-5.5) * (110-127.5)] + [(5-5.5) * (120-127.5)] + [(6-5.5) * (150-127.5)] + [(7-5.5) * (140-127.5)] + [(8-5.5) * (180-127.5)] + [(9-5.5) * (190-127.5)]

= [-135.625, -51.875, 32.625, 28.125, 17.8125, 26.25, 137.8125, 229.0625]

Calculate the sum of the deviations of x squared.

Sum of deviations of x squared = (deviation from mean of x)²

= (-3.5)² + (-2.5)² + (-1.5)² + (-0.5)² + 0.5² + 1.5² + 2.5² + 3.5²

= 70

Calculate the slope of the line of best fit.

slope = sum of products of deviations / sum of deviations of x squared

= (−135.625 + (−51.875) + 32.625 + 28.125 + 17.8125 + 26.25 + 137.8125 + 229.0625) / 70

= 20

Calculate the y-intercept of the line of best fit.

y-intercept = mean of y - slope * mean of x

= 127.5 - 20 * 5.5

= 10

The equation of the line of best fit in slope-intercept form.

y = slope * x + y-intercept

= 20x + 10

Therefore, the equation that best models a line of fit for the data is D) y = 20x, and the slope is 20. So, the correct answer is D).

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The final function for slinky displacement is: 24 sin(t/2 - /2) d(t). This offers the displacement in inches as a function of time in seconds.

A sinusoidal function of the form: can be used to describe the slinky's displacement.

A sin(t + ) = d(t).

where A is the greatest displacement, is the angular frequency (2 divided by the period), and is the phase angle (starting phase).

We know the slinky's greatest displacement (amplitude) occurs at t=0, thus we have:

24 inches = d(0) = A sin()

We also know that the period is T=2 seconds because the time for one oscillation (i.e., one complete cycle) is 2 seconds. As a result, the angular frequency is:

ω = 2π / T = π radians/second

The phase angle can be calculated using the fact that the slinky is at its equilibrium position at t=T/4=0.5 seconds. At this time, the sine function's argument is:

= 2 / T = radians per second

The phase angle can be calculated using the fact that the slinky is at its equilibrium position (zero displacement) at t=T/4=0.5 seconds. At this time, the sine function's argument is:

ωt + φ = π/2

When we substitute the known values, we get:

π/2 + φ = 0.5π

φ = -π/2

As a result, the slinky's displacement function is:

A sin(t/2 - /2) = d(t).

We may utilize the information that the amplitude is 24 inches to calculate A:

A = |24| = 24

As a result, the final function for slinky displacement is:

24 sin(t/2 - /2) d(t)

This offers the displacement in inches as a function of time in seconds.

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The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4  is 0.764 or 76.4%.

The probability is the chance that an expected event occurs out of many possible events.

For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.

The event that the first roll is a total of at least 5 = A

In the event that the second roll is a total of at least 4 = B

The number of faces on each die, n = 6

The probability of event A = ³⁰/₆ = ⁵/₆

The probability of event B = ³³/₃₆ = ¹¹/₁₂

Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ ​× ¹¹/₁₂

= ⁵⁵/₇₂ = 0.764

Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.

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The answer to the question about how many teams completed the escape room in 45 minutes or less is 6.

A dot plot is a type of chart used to display the distribution of a dataset. It is also known as a dot chart, strip plot, or dot graph. In a dot plot, each data point is represented by a dot placed along a horizontal or vertical axis.

Dot plots are useful for showing the distribution of a small to moderate-sized dataset, and are especially helpful when you want to compare the distribution of two or more datasets side by side. They are also useful for identifying outliers or gaps in the data

If we count the amount of dots on 45 and before 45 and add them up, the answer is 6

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Answer:

The range is 37

Step-by-step explanation:

highest - lowest = range

64-27= 37

Hope it helped! :)

The sample space describing all possible outcomes is {1. 2. 3. 4. 5. 6}

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

A number cube with faces labeled from 1 to 6 will be rolled once.

This means that

Sample space = {1. 2. 3. 4. 5. 6}

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

The outcomes for the event of rolling the number 1 ,3 , or 4. is

Outcome = {1, 3, 4} where we have

P(1) = 1/6

P(3) = 1/6

P(4) = 1/6

Altogether, we have

P(1, 3, or 4) = 1/6 + 1/6 + 1/6

P(1, 3, or 4) = 3/6

P(1, 3, or 4) = 1/2

Hence, the probability is 1/2

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Complete question

A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.

Give the sample space describing all possible outcomes.

Then give all of the outcomes for the event of rolling the number 1 ,3 , or 4.

If there is more than one element in the set, separate them with commas.

Answer:

53 es el pr espero que te ayude

Answer:

2, area=42.39 arc length=14.13

3, area=604.9 arc length=71.1

Answer:

B

D

E

( all of the answers (E, D, B) have no real solutions)

Using the ratios, 1 yd/3 feet, 1 mi/5,280 feet, and 200 yards/1 feet, the number of flags required to mark the racecourse with a flag every 200 yards is 22.

Ratios are relative sizes of one quantity or value compared to another.

Ratios are depicted as fractional values using decimals, percentages, or fractions, including the standard ratio form (:).

The total distance of the racecourse = 2.5 miles

The common distance between each flag = 200 yards

1 mile = 1,760 yards

2.5 miles = 4,400 yards

1 yard = 3 feel

The number of flags required to cover the distance = 22 (4,400 ÷ 200)

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The type of pay modeled in the given image is c. Commission pay.

Commission pay is a form of variable pay where the employee is paid based on the percentage of sales that they make. In this case, the y-axis represents the pay earned and the x-axis represents the sales made.

The straight line represents the commission rate, which is constant at 15%. The more sales the employee makes, the more pay they will earn.

Therefore the correct option is C.

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The area of the shaded region is 117.8 m².

Given is a semicircle and a triangle in it, we need to find the area that is shaded,

So, we know that a triangle in a semicircle is always a right triangle whose hypotenuse is the diameter of the semicircle,

So, let us find the hypotenuse of the triangle (diameter of the semicircle) using the Pythagorean theorem,

diameter / hypotenuse = √21.6²+9²

= 23.4m

So the radius = 23.4/2 = 11.7 m

To find the area of the shaded region we will subtract the area of triangle from the semicircle,

So,

Area of the shaded region = π×r²/2 - 1/2×base×height

= 3.14×11.×7²/2 - 1/2×21.6×9

= 215 - 97.2

= 117.8 m²

Hence the area of the shaded region is 117.8 m².

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The probability of randomly selecting a red token would be 0. 30.

First, we know that the experiment was done 2, 000 times;

605 + 342 + 518 + 535 = 2000

The probability that a red token is randomly selected is therefore:

= Red token / Total times

= 605 / 2, 000

= 0. 3025

In fractions, we can make this:

= 605 / 2, 000

= 121 / 400

This is closest to the fraction 3 / 10 which is 0. 30.

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Bob needs to make at least 9 two-point baskets in the second half to break the school record of scoring 30 points in his basketball game.

To break the school record of scoring 30 points, Bob needs to score more than 30 points in his basketball game. Since he scored 13 points in the first half, he needs to score at least 17 points in the second half to break the record.

Let's assume that Bob makes x two-point baskets in the second half. Since each two-point basket contributes 2 points to his score, his total score from two-point baskets would be 2x.

Therefore, to break the school record, we need to solve the following inequality:

2x + 13 > 30

Subtracting 13 from both sides, we get:

2x > 17

Dividing both sides by 2, we get:

x > 8.5

Since Bob cannot make a fractional number of baskets, he needs to make at least 9 two-point baskets in the second half to break the school record.

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There are 960 bikes in the repair department and  1.98% of the bikes need two repairs.

The number of bikes with flat tires only is 0.25x, where x is the total number of bikes

The number of bikes with bent handlebars only is 0.05x

The number of bikes with ripped seats only is 0.1x

The number of bikes that need two repairs is 0.01Tx, where T is the percentage of bikes that need two repairs (expressed as a decimal)

The number of bikes that need all three repairs is 0.0833...x

So we have the equation:

0.25x + 0.05x + 0.1x + 0.01Tx + 0.0833...x = 101

Simplifying and solving for x, we get:

x = 960

So there are 960 bikes in the repair department.

To find the number of bikes that need two repairs, we can use the equation:

0.25x + 0.05x + 0.1x + 0.01Tx = 101 - 0.0833...x

Substituting x = 960, we get:

0.25(960) + 0.05(960) + 0.1(960) + 0.01T(960) = 101 - 0.0833...(960)

240 + 48 + 96 + 9.6T = 101 - 80

9.6T = 19

T = 1.98

About 1.98% of the bikes need two repairs.

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Answer:

3 yards

Step-by-step explanation:

The rule used to obtain the transformed function is given as follows:

g(x) = -0.5f(x).

Examples of transformations are given as follows:

The parent function in this problem is given as follows:

f(x).

The parent function is reflected across the x-axis, hence:

g(x) = -f(x).

The parent function is also compressed by a factor 0.5, hence:

g(x) = -0.5f(x).

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Answer:

Vertex= (-5, 2)

Step-by-step explanation:

The vertex shifts 5 to the right (x-axis), and 2 up (y-axis) from the point of origin. Then plug in the x values to find other y values.

Option B is correct. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.

We are utilizing the rare event rule and subjective estimation to verify the legitimacy of a claim. The assertion states that, within a considerable math class, the mean age of pupils is below 30. When selecting students at random, we observe that their average age is 29.3 years.

Given that the sample's mean age only subtlety fluctuates from the value expected (i.e., 30), the result obtained is not improbable if the premise holds true (thus validating the claim). Furthermore, it would be non-ambiguous even if the proposition is false due to the minuscule difference between 29.3 and 30 years of age.

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I: TRUE - A limit is a value that a function, pattern, or sum of a series approaches as the number of terms or input value increases.

II: TRUE - A limit can also be a value that a function approximates for a specific input value, especially when dealing with continuity or differentiability.

III: FALSE - Although a limit might seem like a value that is never quite achieved, it can be reached or even exceeded, depending on the function and its behavior.

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Answer: 8

Step-by-step explanation:

pemdas its not that deep

Answer:

a. 14:8

b. 6:14

Step-by-step explanation:

all books on the shelf = 6+8=14

a. 14:8

b. 6:14

The expression (32 ÷ (10 - 8)) ÷ 2 - 3 evaluates to 5 and includes the necessary parentheses to achieve this result.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make the value of the expression equal to 5, we can use parentheses to change the order of operations. One possible way to do this is:

32 ÷ (10 - (8 ÷ 2) - 3)

First, we evaluate the expression inside the parentheses:

8 ÷ 2 = 4

10 - 4 - 3 = 3

So now the expression becomes:

32 ÷ 3

=10.67

This is not equal to 5.

To make the value of the expression equal to 5, we need to modify the expression inside the parentheses. One way to do this is:

32 ÷ (10 - (8 ÷ (2 - 3)))

Here, we use the parentheses to change the order of operations so that we subtract 3 from 2 before dividing 8 by the result. This gives us:

8 ÷ (-1) = -8

So now the expression inside the parentheses becomes:

10 - (-8) = 18

So the entire expression becomes:

32 ÷ 18 = 1.78

This is still not equal to 5.

Another way to make the value of the expression equal to 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

Here, we use the parentheses to ensure that we divide 32 by the result of (10 - 8) before dividing the whole expression by 2 and subtracting 3. This gives us:

32 ÷ 2 - 3 = 13

So the entire expression becomes:

13

And this is equal to 5.

Therefore, one possible expression that includes a set of parentheses so that the value of the expression is 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

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The statement that analyzes difference between an irrational number and a rational number is: the expression √25 - √21 can be rewritten as 5 - √21. since the exact value of √21 cannot be found, the difference is irrational, The Option D is correct.

A rational number refers to number that can be expressed as the ratio of two integers where the denominator is not zero. For example 1/2, 3/4, and -5/7  all rational numbers.

Irrational number refers to one that cannot be expressed as a ratio of two integers. Examples include pi (π) and the square root of 2 (√2).

The difference is that one is expressed as a ratio of two integers or a decimal that either terminates or repeats other cannot be expressed as a ratio of two integers and have a decimal representation that does not terminate or repeat.

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Answer:

Step-by-step explanation:

If y varies directly as x, it means that y is directly proportional to x, and we can express this relationship using a proportionality constant k:

y = kx

To find the value of k, we can use the given information that y = 2 when x = 3:

2 = k(3)

Solving for k, we get:

k = 2/3

Now that we know the value of k, we can use the formula to find y when x = 1:

y = (2/3)x

y = (2/3)(1)

y = 2/3

Therefore, when x = 1, y = 2/3.

A graph is a visual representation of data that shows the relationship between two or more variables. It is also known as a chart or plot.Difference in S-P (sec):

The S-P difference is the interval of time between the arrival of the S wave and the P wave at a seismic station.We can observe from the accompanying diagram that the S wave begins to arrive at roughly 16 seconds, and the P wave begins to arrive at roughly 8 seconds. The S-P differential is therefore 16 – 8 = 8 seconds.(mm) Amplitude:

The amplitude of a seismic wave exhibits the greatest departure from the equilibrium position. We can observe from the provided diagram that the wave's maximum displacement is roughly 70 mm. Therefore, the wave's amplitude 70mm.

(km) Distance:

The S-P time difference and a journey time graph can be used to calculate how far the earthquake was from the seismic station.

Using the equation:

Distance is calculated as ((S-P time difference)*(km/sec))

where the travel time graph provides the km/sec value, we obtain:

distance = 56 km (8 * 7).

As a result, the quake's distance from the seismic station is 56 kilometres.

Magnitude (M):

An earthquake's magnitude is a logarithmic scale representation of the energy released by the earthquake. By measuring the greatest wave's amplitude (in mm) and applying the method below, we can determine the magnitude from the provided seismogram:

M = log(A) + 1.5 * log(S-P) - 3.2

where S-P is the S-P time difference in seconds, and A is the amplitude in millimetres. Inputting the numbers provided yields:

M = log(70) + 1.5 * log(8) - 3.2

M ≈ 4.1

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Answer: To solve the system of equations graphically, we need to graph both equations on the same coordinate system and find the point where they intersect. This point will give us the values of x and y that satisfy both equations.

First, we can rewrite the two equations in slope-intercept form:

y = 4x - 1 (equation 1)

y = -x + 4 (equation 2)

Now we can graph both equations on the same coordinate system. To do this, we can plot a few points for each equation and then draw a line through the points. Alternatively, we can use the y-intercept and slope of each equation to graph the lines. For equation 1, the y-intercept is -1 and the slope is 4. For equation 2, the y-intercept is 4 and the slope is -1.

We can see that the two lines intersect at the point (1, 3). Therefore, the solution to the system of equations is x = 1.

Answer:

(x - 8)^2 + (y + 10)^2 = 169

Step-by-step explanation:

you need to do completing the square

x^2 + y^2 -16x + 20y - 5 = 0

(x)^2 - 2(8)(x) + (y)^2 + 2(10)(y) - 5 = 0

(x)^2 + 2(-8)(x) + (-8)^2 - (-8)^2 + (y)^2 + 2(10)(y) + (10)^2 - (10)^2 - 5 = 0

[(x)^2 + 2(-8)(x) + (-8)^2] + [(y)^2 + 2(10)(y) + (10)^2] - (10)^2 - (-8)^2 - 5 = 0

### (a)^2 + 2(a)(b) + (b)^2 = (a + b)^2 ###

(x - 8)^2 + (y + 10)^2 -100 - 64 - 5 = 0

(x - 8)^2 + (y + 10)^2 -169 = 0

(x - 8)^2 + (y + 10)^2 = 169