write the equation of the line fully simplified slope-intercept form.

\(\bold{\huge{\underline{ Solution }}}\)

We have given one graph which is plot between distance and time. where time is in minutes and distance is in seconds.

According to the graph

1) Between O and A

2) Between A and B

3) Between B to C

4) For covering the First 6 km ,

According to the graph,

5) No, Marellize and wally walk does not from where they have started.

According to the graph

The line between O and A is a straight line graph while A and B is a constant graph.

A graph simply means a pictorial representation of information or data that's given.

In this case, O and A is a straight line graph while A and B is a constant graph. A straight line graph illustrates a linear relationship between between the x and y values.

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(a) If a is finite, then we know exactly how many elements are in a. For example, if a = {1, 2, 3}, then we know that a has three elements. In this case, we can tell exactly how big a is.

(b) If a is countably infinite, then we know that a has the same cardinality (size) as the set of natural numbers.

This means that we can put the elements of an in a one-to-one correspondence with the natural numbers.

For example, if a = {2, 4, 6, ...}, then we can list the elements of an as a_1 = 2, a_2 = 4, a_3 = 6, and so on. In this case, we can tell how big a is, but it's an infinite size.

(c) If a is uncountable, then we know that a is larger than the set of natural numbers. This means that we cannot put the elements of an in a one-to-one correspondence with the natural numbers.

For example, if a is the set of all real numbers between 0 and 1 (excluding 0 and 1 themselves), then there are uncountably many elements in a. In this case, we can't tell exactly how big a is, but we know that it's larger than the set of natural numbers.

(d) Finally, if we don't have any information about a, then we can't tell how big a is. It's possible that a could be finite, countably infinite, uncountable, or even something else entirely.

Without more information, we simply can't say for sure.

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It will take Stan around 2(√34 - 2) minutes to mow the lawn alone, approximately 4.43 minutes

Let's suppose that it will take Stan x minutes to mow the lawn alone.

Hence, Hilda takes half the time as compared to Stan i.e. x/2 minutes.

In other words, Hilda can mow the lawn in half the time taken by Stan.

Work done by both together in 1 minute = 1/x + 1/(x/2)

Multiplying both sides with 2x, we get:

2 + 4 = 4x/x + x/2

Simplifying the above equation, we get:

6 = (8x + x²)/2x

We can rewrite this equation as:

6 = 4x + x²/2

On multiplying both sides by 2, we get:

x² + 8x - 12 = 0

Solving the above quadratic equation, we get:

x = (-8 + √136)/2 or x = (-8 - √136)/2

The negative value of x is not meaningful since we are dealing with time which cannot be negative.

Therefore, the value of x that we get from the above quadratic equation is:

x = (-8 + √136)/2

= 2(√34 - 2) words

Therefore, it will take Stan around 2(√34 - 2) minutes to mow the lawn alone, approximately 4.43 minutes.

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Answer:

x=3, x=-1

Step-by-step explanation:

|x-1|-1=1

Add 1 to each side

|x-1|-1+1=1+1

|x-1|=2

Now set the absolute value to ±2

x-1 = 2     and x-1 = -2

Add 1 to all sides

x-1+1 = 2+1         x-1+1 = -2+1

x=3                       x = -1

Answer:  The mean of data set K is greater than the mean of data set L.

The median of data set K is greater than the median of data set L

Step-by-step explanation:

we need to calculate the mean (average) of each data set and compare them.

Mean of data set K = (28 + 145 + 112 + 57 + 130) / 5 = 112.4

Mean of data set L = (141 + 171 + 68 + 124 + 43) / 5 = 109.4

'Arranging the values in data set K in ascending order, we get:

28, 57, 112, 130, 145

The median of data set K is the middle value, which is 112.

The mean of data set L is 109.4.

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Given statement solution :-The correct answer is: IQR, because Sunny Town is skewed and Desert Landing is symmetric.

Frequency is a count of the number of times a specific event occurs. A Frequency Histogram, then, is a Histogram where the height of each bar is a frequency, or count, of the number of data points within that bar's range.

The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is the IQR (Interquartile Range).

The IQR is a measure of the spread or dispersion of a dataset and is less affected by extreme values or outliers compared to the range. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the dataset.

In this case, the choice of IQR is appropriate because it can handle skewed distributions (like Sunny Town) and symmetric distributions (like Desert Landing) effectively. The IQR provides a robust measure of the spread that is not heavily influenced by extreme values, making it suitable for comparing the consistency of temperature between the two locations.

Therefore, the correct answer is: IQR, because Sunny Town is skewed and Desert Landing is symmetric.

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A) the probability that the month selected for the annual sale will be September or October is 1/6.

A) Since we are interested in the probability of selecting September or October, which are two out of the 12 months, the probability can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 months / 12 months

Probability = 1/6

Therefore, the probability that the month selected for the annual sale will be September or October is 1/6.

B) To calculate the probability, we need to sum the number of days in September and October and divide it by the total number of days in a year (365 or 366 in a leap year).

Probability = (30 + 31) days / 365 or 366 days

Probability ≈ 61/365 or 366

The exact probability will depend on whether it is a leap year or not.

Comparing the answers from part A and part B, we can see that the probability of selecting September or October using days is slightly different from the probability calculated assuming each month has an equal probability of being selected.

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Answer:

Inferential statistic

Step-by-step explanation:

The art of making deductions or data driven predictions from statistical data refers to an aspect of statistics called Inferential statistics. Inferential statistics differs from descriptive statistics which is another aspect which focuses on presenting characteristics of data. Here, we make statistical deductions about the entire population from the results obtained about the sample statistic. In the scenario above, the statistic derived from the sample data will be used to make deductions about the general population of students who park in the university. Therefore, from the statistic obstaied from the sample, we infer about the population.

Answer:

1. m = 6/5 or 1 1/5

2. m = -4/5

Step-by-step explanation:

1.) Find the slope of the line that contains (5,4) and (0,−2).

Slope m = (y2-y1)/(x2-x1)

m = (-2 - 4)/(0 - 5) = -6/-5 = 6/5

m = 1 1/5

2.) Find the slope of the line that contains (6,−2) and (−4,6).

Slope m = (y2-y1)/(x2-x1)

m = (6 - -2)/(-4 - 6) = 8/-10 = -8/10 = -4/5

The value of the integral ∫(π/2 to π/4) csc(t) cot(t) dt is -√2 + 1.

To evaluate the integral ∫(π/2 to π/4) csc(t) cot(t) dt, we can use trigonometric identities and integration techniques.

First, let's rewrite the integrand using trigonometric identities:

Substituting these identities, the integral becomes:

∫(π/2 to π/4) (1/sin(t)) * (cos(t)/sin(t)) dt

Now, we can simplify the expression:

∫(π/2 to π/4) (cos(t)/sin²(t)) dt

To evaluate this integral, we can use the substitution method. Let u = sin(t), then du = cos(t) dt. We need to find the new limits of integration when t = π/2 and t = π/4.

When t = π/2, u = sin(π/2) = 1.

When t = π/4, u = sin(π/4) = 1/√2.

The integral becomes:

∫(1 to 1/√2) (1/u²) du

Simplifying further, we have:

∫(1 to 1/√2) u^(-2) du

Now, we can integrate:

∫(1 to 1/√2) u^(-2) du = [-u^(-1)] evaluated from 1 to 1/√2

Evaluating the definite integral, we have:

[-u^(-1)] from 1 to 1/√2 = [-(1/√2)^(-1) - (-1)^(-1)] = [-√2 - (-1)] = -√2 + 1

Therefore, the value of the integral ∫(π/2 to π/4) csc(t) cot(t) dt is -√2 + 1.

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The formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D

Total tires needed by each car = 4 + 1

= 5

Total number of tires, t needed for c cars.

Number of tires needed, t = Total tires needed by each car × Number of cars produced per day

t = 5 × c

t = 5c

For instance,

if 5 cars are produced per day

Number of tires needed, t = Total tires needed by each car × Number of cars produced per day

t = 5c

= 5 × 5

t = 25 tires

Therefore, the formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D

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Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

Answer:

The correct answer is D because  for example...

Step-by-step explanation:

If b squared minus 4ac is non-negative, so at 0 or greater, we have at least one real solution. If it's less than 0, if it's negative, we have no real solutions!

Hope I was able to help, and I hope you Have a good day! :)

Answer:

Step-by-step explanation:

Step 1: Divide 150 by 100 which will give you 1.5

Step 2: Multiply 1.5 by 12 which will give you 18

Answer: So the answer is 18% is left handed!

If there are 8 men and 5 women , then the number of ways of selecting a 4 people committee is 715 ways  .

The number of ways to select a committee of 4 people from a group of 13 people, where 5 are women and 8 are men, is calculated by Combination ;

where , "n" is = total number of people, "r" is = number of people to be selected,

In this case, we have:

the total number of people is = 8 + 5 ⇒ n = 13 ;

the number of committee member to be selected is "r" = 4 ;

So, the number of ways to select a committee of 4 people from a group of 13 people is  :  ¹³C₄ = 715 ways ;

Therefore, there are 715 ways to select a committee of 4 people from a group of 5 women and 8 men.

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The given question is incomplete , the complete question is

There are 5 women and 8 men is a department . Find the Number of ways can a committee of 4 people be selected ?

The correct box and whisker plot for the given data-set is given by option B, considering the median concept.

It is the 50th percentile of the data-set, the value that separates the bottom 50% from the upper 50%.

A box and whisker plot shows three things:

In this problem, there are 14 values, hence the median is the mean of the 7th and the 8th values, given by:

Me = (150 + 150)/2 = 150.

The 25th percentile is the median of the first six values, given by the mean of the 3rd and 4th elements, hence:

P25 = (142 + 138)/2 = 140.

The 75th percentile is the median of the final six values, given by the mean of the 11th and 12th elements, hence:

P75 = (191 + 175)/2 = 183.

Hence option B is correct.

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The conditional expectation E[Y|X=2] is 11, and the variance of Y, var(Y), is 24, given the linear relationship Y = 15 - 2X and a variance of 6 for X.

The conditional expectation E[Y|X=2] represents the expected value of Y when X takes on the value 2.

Given the linear relationship Y = 15 - 2X, we can substitute X = 2 into the equation to find Y:

Y = 15 - 2(2) = 15 - 4 = 11

Therefore, the conditional expectation E[ Y|X=2] is equal to 11.

To calculate the variance of Y, var(Y), we can use the property that if X and Y are linearly related, then var(Y) = b^2 * var(X), where b is the coefficient of X in the linear relationship.

In this case, b = -2, and the variance of X is given as 6.

var(Y) = (-2)^2 * 6 = 4 * 6 = 24

Therefore, the variance of Y, var(Y), is equal to 24.

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Answer:

18.92

Step-by-step explanation:

It simple mutiplication put it like this and do the math!

   86

X 00.22

---------------           Or do it like 86/0.22

When performing one-dimensional graphical vector addition, the proper starting position for each of the two arrows representing the two vectors being combined depends on the specific scenario.

In general, when adding two vectors in one dimension, you can start both arrows at the same point, such as the origin of a coordinate system. This is commonly done when the vectors are acting in the same direction.

For example, if you have a vector A pointing to the right with a magnitude of 3 units and a vector B pointing to the right with a magnitude of 2 units, you can start both arrows at the same point and draw them to the right, one after the other, with a total length of 5 units.

However, if the two vectors are acting in opposite directions, you can start one arrow at the origin and the other arrow at the endpoint of the first arrow.

For example, if you have a vector A pointing to the right with a magnitude of 3 units and a vector B pointing to the left with a magnitude of 2 units, you can start the arrow for vector A at the origin and draw it to the right for 3 units.

Then, you can start the arrow for vector B at the endpoint of vector A and draw it to the left for 2 units. The resulting vector sum would be the vector connecting the starting point of vector A to the endpoint of vector B.

Therefore, the proper starting position for each of the two arrows representing the two vectors being combined in one-dimensional graphical vector addition depends on their directions. If the vectors are acting in the same direction, you can start both arrows at the same point.

If the vectors are acting in opposite directions, you can start one arrow at the origin and the other arrow at the endpoint of the first arrow.

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The radian measure of the central angle of a circle of radius r=90 inches that intercepts an arc of length s=130 inches is:

1.4444 radians.

To determine the radian measure of the central angle of a circle of radius r = 90 inches that intercepts an arc of length s = 130 inches, you can use the following formula:

θ = s/r

Where, θ = radian measure of the central angle of the circle of radius r.

s = length of the arc.

r = radius of the circle.

Substituting the given values,

θ = s/r

θ = 130/90

θ = 1.4444 radians (rounded to four decimal places).

Therefore, the radian measure of the central angle is approximately 1.4444 radians.

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The length of the Bathroom is 3x - 4 feet and the width of the Bathroom is 5x + 1 feet.

As per the shown figure, the dimensions can be written as follows:

Length of Bedroom = 6x+2

Width of Bedroom = 5x+1

Length of Master Bedroom = 8x-3

Width of Master Bedroom = 5x+1

The length of the Bathroom can be calculated as follows:

Length of the Bathroom = 17x - 5 - (Length of Bedroom + Width of Master Bedroom)

Length of the Bathroom = 17x - 5 - (6x+2+8x-3)

Length of the Bathroom = 17x - 5 - 14x + 1

Length of the Bathroom = 3x - 4

And width of the Bathroom = 5x + 1

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Answer:

  see attached

Step-by-step explanation:

A quadratic relation is a polynomial relation that has a highest degree of 2. Its graph is ⋃-shaped (or ⋂-shaped). That is, it decreases, then increases, or vice-versa.

__

To identify the quadratic relations, you check to see which of them matches the description above.

The highest degrees, left to right, are 1, 3, 2. The right-most equation is a quadratic relation

The left-most graph is ⋃-shaped, so represents a quadratic relation.

The y-values in the left table decrease, then increase, suggesting a quadratic relation. (Those in the right table continue to decrease at a constant rate, which represents a linear relation.)

Check the picture below.

well, the red one is one, now the green one is another and yet if we tiptoe over the circle made by KL we'll always get a right-triangle as you see in the dashed lines, how many? well infinite many.

Answer:

x = -3

There is a base f 5 on the left side, so write the denominator on the right as a base of

5 as well.

5

x

=

1

125

5

x

=

1

5

3

Move the base to the numerator.

5

x

=

5

−

3

If the bases are equal, the indices are equal:

x

=

−

3

Answer:

The answer is 1/625

Step-by-step explanation:

The reason is because 5a = 1/125

Therefore, to find the value of "a" we need to divide!

So, a = 1/125 / 5

           ⇒ 1/125 × 1/5    ( Reciprocal when we divide )                                                        

             ⇒ 1/125 × 5

             → 1/625

I hope this answer helps!

Answer:

A

\({ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p} (m + n - 1)}}\)

Answer:

yh it's A the other guy's right

Step-by-step explanation:

Answer:

A) They have the same y intercept and the same rate of change

Step-by-step explanation:

Write the equation for the line passing through the points (2,4) and (12,7)

Slope \(\frac{7-4}{12-2}\) = \(\frac{3}{10}\) = .3

y intercept  (b)

y = mx + b

Use 2 fox x, 4 for y and .3 for m

y=mx + b

4 = .3(2) + b

4 = .6 + b    Subtract .6 from both sides

3.4 = b

The equation is

y = .3x + 3.4

The two equation are identical so the slope and y intercepts are the same.

compare the y-intercept and the rate of change of the following items. Option (d) The rates of change are the same, but the y-intercepts are different. is correct.

for rates,

we will find the slope of I and II

slope = dy/dx = change in y/change in x

for both of them when we compare the slope, it is 0.3.

for y-intercepts.

equation for II should be formed in order to compare with the y-intercept of I which is  3.4.

y-7=0.3(x-12) .................(i)

so, the y-intercept is 7 for II

thus, the y-intercepts of given eq are not equal.