Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)

The line plots represent data collected on the travel times to school from two groups of 15 students.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.

Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.

Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24

If an acute angle increases, then its supplement decreases.

To give you a short quick answer, the supplement is going to have to decrease or get smaller.

Example

Suppose the acute angle is 10 (anything under 90 will do).

Then the supplement is going to be 180 - 10 = 170

Now suppose the acute angle increase to 50 degrees.

That means the supplement will go from 180 - 50 = 130

Conclusion

As the acute angle gets bigger, the supplement gets smaller. This is an important idea to get clear. Bigger and Smaller or More or Less can be ugly little words, so anytime you come across them, pay attention. It will make your life in science so much easier

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The power from the main engines, P = 0.

What is power?

Let P be the power from the main engines. Then, the total power of the space shuttle during launch is:

Total power = Power from solid rocket boosters + Power from main engines

Total power = 9,750,000,000 watts + P

We can isolate P by subtracting the power from the solid rocket boosters from both sides:

P = Total power - Power from solid rocket boosters

P = (9,750,000,000 watts + P) - 9,750,000,000 watts

P = P

Simplifying, we get:

P = 0

This means that the power from the main engines is zero. However, this result is not realistic since the space shuttle requires power from both the solid rocket boosters and the main engines to launch. Therefore, there may be an error in the given information or additional information is needed to accurately solve the problem.

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Answer:

Its value is approximately:

G = 6.6743 x 10^-11 m^3 kg^-1 s^-2

Step-by-step explanation:

The value of G is the gravitational constant, which is a physical constant that appears in the law of universal gravitation. Its value is approximately:

G = 6.6743 x 10^-11 m^3 kg^-1 s^-2

This value is used to calculate the force of gravitational attraction between two objects, given their masses and the distance between them. The gravitational constant is a fundamental constant of nature and is important in many areas of physics, including astrophysics, cosmology, and mechanics.

The new coordinates for point D after the rotation are (-4, 3).

To find the coordinates of each point after quadrilateral ABCD is rotated 270° counterclockwise about the origin, we can use the following formula:

(x', y') = (-y, x)

where (x, y) are the original coordinates of the point and (x', y') are the new coordinates after the rotation.

Starting with point A, which has coordinates (2, 1), we plug in the values into the formula:

(x', y') = (-y, x)
(-1, 2)

So the new coordinates for point A after the rotation are (-1, 2).

Moving on to point B, which has coordinates (4, 3), we apply the same formula:

(x', y') = (-y, x)
(-3, 4)

Therefore, the new coordinates for point B after the rotation are (-3, 4).

For point C, which has coordinates (5, 6), we get:

(x', y') = (-y, x)
(-6, 5)

Hence, the new coordinates for point C after the rotation are (-6, 5).

Finally, for point D, which has coordinates (3, 4), we have:

(x', y') = (-y, x)
(-4, 3)


So, the coordinates of each point after quadrilateral ABCD is rotated 270° counterclockwise about the origin are:

A' = (-1, 2)
B' = (-3, 4)
C' = (-6, 5)
D' = (-4, 3)

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If a person has a slow reaction time that puts them in the top 10% of responses, it means that their reaction time is slower than 90% of the population.

The value that separates the top 10% of responses from the bottom 90% is determined by the distribution of reaction times in the population.

Assuming a normal distribution of reaction times, the value that separates the top 10% of responses from the bottom 90% is the 90th percentile. This means that 90% of the population has a reaction time below this value, while the top 10% have a reaction time equal to or above it.

The specific value that separates the top 10% from the bottom 90% can vary depending on the population being studied and the task being performed. However, in general, a value around 1.5 standard deviations above the mean reaction time would be a reasonable estimate for the 90th percentile.

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The expected value of the number of games played is 5.5 games, and the variance is 1.25.

To find the expected value of the number of games played, we need to consider all the possible ways the match can end. Since the match is a best of 7, one team needs to win at least 4 games. The possible outcomes are:

Team A wins in 4 games: AAAA

Team A wins in 5 games: AABAA or ABAAA

Team A wins in 6 games: ABAABA, ABABAA, or ABBAAA

Team A wins in 7 games: ABABABA, ABABAB, ABBABAA, or ABBABAAA

Similarly, we can list the possible outcomes for Team B winning in 4, 5, 6, or 7 games. However, since both teams are equally likely to win each game, the probability of each outcome is the same. Therefore, the expected value of the number of games played is:

E(X) = (41/8) + (52/8) + (63/8) + (72/8) = 5.5 games

To find the variance, we need to first calculate the squared deviation from the expected value for each outcome. For example, for the outcome AABAA, the deviation is (5-5.5) = -0.5, and the squared deviation is (-0.5)^2 = 0.25. We can then multiply each squared deviation by the probability of that outcome and sum them up,

Var(X) = (1/8)(4-5.5)^2 + (2/8)(5-5.5)^2 + (3/8)(6-5.5)^2 + (2/8)(7-5.5)^2

= 1.25

Therefore, the expected value of the number of games played is 5.5 games, and the variance is 1.25.

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a)Since the height of the basketball is only 6.3 feet when it reaches a height of 17 feet at t = 0.23 seconds, the teenager will not make the basket.

b) To find the height of the teenager, we need more information, such as their arm span or jumping ability.

what is  height ?

Height is the measurement of how tall someone or something is, typically referring to the distance from the bottom to the top of an object or person. It can be measured in different units, such as feet, meters, or centimeters

In the given question,

a. To determine if the teenager will make the basket, we need to see if the height of the basketball when it reaches the hoop, which is at a height of 17 feet, is greater than or equal to 17 feet. So, we set h(t) = 17 and solve for t:

-16t² + 20t + 5.5 = 17

-16t² + 20t - 11.5 = 0

Using the quadratic formula, we get:

t = (-20 ± sqrt(20² - 4(-16)(-11.5))) / (2(-16))

t ≈ 1.79 or t ≈ 0.23

Since the basketball will reach a height of 17 feet at two different times, we need to determine the height of the basketball at each of these times and see if it is greater than or equal to 17 feet.

When t = 0.23 seconds:

h(0.23) = -16(0.23)² + 20(0.23) + 5.5 ≈ 6.3 feet

When t = 1.79 seconds:

h(1.79) = -16(1.79)² + 20(1.79) + 5.5 ≈ 17.1 feet

Since the height of the basketball is only 6.3 feet when it reaches a height of 17 feet at t = 0.23 seconds, the teenager will not make the basket.

b. To find the height of the teenager, we need more information, such as their arm span or jumping ability. The function h(t) represents the height of the basketball, not the height of the teenager.

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Answer:

1, 2, 3, 5

Step-by-step explanation:

B) 0.18

To convert 2/11 into decimal form, divide 2 by 11 using a calculator or long division.

The result is 0.18181818... (the pattern of 18s repeats indefinitely).

Therefore, 2/11 as a decimal is approximately 0.1818 (rounded to four decimal places).

Answer:

B. [tex]0.\overline{18}[/tex]

Step-by-step explanation:

2/11 in decimal form is a set of repeating 18's:

0.181818181818...

This can be represented using bar notation, where digits under the bar repeat infinitely:

[tex]0.\overline{18}[/tex]

__

Extra note:

A trick for fractions with 99 in the denominator is that, when the fraction is converted into a decimal, the numerator of the fraction is the repeating two digits.

In this problem, when we convert 2/11 to 99ths:

[tex]\dfrac{2}{11} \cdot \dfrac{9}{9} = \dfrac{18}{99}[/tex],

we can see that 18 is in the numerator, so that is the repeating part of the decimal [tex]0.\overline{18}[/tex].

We can conclude that Bus 14 typically has the faster travel time since its median is lower than that of Bus 47.

When data are sorted in ascending or descending order, the median, a measure of center, indicates the dataset's middle value. Extreme numbers or data outliers have no impact on it.

From the given information, we know that the median travel time for Bus 47 is 16 and the median travel time for Bus 14 is 14.

What is median?

When values are arranged in order of magnitude, the median, a measure of central tendency, indicates the midpoint of the dataset. You must organise the values in ascending order from smallest to largest before determining the middle value to determine the median.

The mean, on the other hand, is affected by extreme values or outliers in the data, which can skew the value. Therefore, we cannot solely rely on the mean to compare the travel times of the two buses. However, for completeness, we also have the mean travel times of Bus 47 and Bus 14, which are both given as 16 and 14, respectively.

Therefore, we can conclude that Bus 14 typically has the faster travel time since its median is lower than that of Bus 47.

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The work required to lift the entire chain to the top of the building is 1,662.9 ft-lbs.

The work required to lift the chain to the top of the building is equal to the potential energy gained by the chain, which is given by

potential energy = mass × gravity × height

where mass is the mass of the chain, gravity is the acceleration due to gravity (32.2 ft/s^2), and height is the length of the chain (18 feet) since it is being lifted vertically.

First, we need to find the mass of the chain. We can use the fact that the weight of the chain is 93 pounds to find the mass using the formula

weight = mass × gravity

Rearranging this formula to solve for mass, we get

mass = weight / gravity

Substituting the given values, we get

mass = 93 pounds / 32.2 ft/s^2 = 2.89 slugs

Now we can calculate the potential energy of the chain using the formula

potential energy = mass × gravity × height

Substituting the values we have calculated, we get

potential energy = 2.89 slugs × 32.2 ft/s^2 × 18 feet = 1,662.9 ft-lbs

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Answer:

B

Step-by-step explanation:

The independent variable is t (time) because no matter what happens the weeks will still pass. The dependent variable is b (balance) because it depends on the amount of time passed. You can see that after every week the balance decreases by 50. So when the independent variable increases by 1, the dependent variable decreases by 50.

Answer:

6000

Convert 8 and 10 to a decimal

8=0.8

10=0.1

0.1*0.8=0.8

4800/0.8=6000

Step-by-step explanation:

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Answer:

y = x - 5

Step-by-step explanation:

y = x -6

y = MX +C

.: m = 1 ( where m is the gradient of the line)

Let gradient = gradient 2 ( because the lines are parallel to each other)

m1= m2

1= y- y1 / x - x1

( 9,4) = ( x1 , y1 )

.: 1= y - 4 / x - 9

Cross multiply

1( x -9) = y - 4

x - 9 = y - 4

y = x - 9 + 4

y = x - 5

.: The equation of the line is y = x -5

The answer can also be written as y - 4 = 1( x -9)

Answer:

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

Answer: 61.56%

Step-by-step explanation:

To find what percent 39.4 is of 64, we can use the following formula:

(percent / 100) * 64 = 39.4

Solving for percent, we get:

percent = (39.4 / 64) * 100

percent = 0.615625 * 100

percent = 61.56 (rounded to the nearest hundredth)

Therefore, 39.4 is approximately 61.56% of 64 when rounded to the nearest hundredth.

The range of the parabola is (-∞, -2). So correct option is A.

A parabola is a U-shaped curve that is defined by a quadratic equation of the form y = ax² + bx + c, where a, b, and c are constants. The graph of a parabola is symmetric around a vertical line called the axis of symmetry, which passes through the vertex of the parabola. The vertex is the point on the parabola where it changes direction.

The shape and position of a parabola depend on the values of the coefficients a, b, and c. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The value of b determines the horizontal position of the vertex, and the value of c determines the vertical position of the vertex.

Parabolas have many applications in mathematics, physics, engineering, and other fields. For example, the trajectory of a projectile launched into the air can be modeled by a parabolic curve, and the reflector dish of a satellite dish antenna is shaped like a parabolic curve to focus incoming signals at a single point.

The range of the parabola is (-∞, -2). So correct option is A.

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Answer:

The answer to the expression 448m^2−49.81m is 448m^2 - 49.81m. It cannot be simplified further without knowing the value of m.

The word phrase "negative one fifth is bigger than or equal to the product of negative two thirds" is represented by the inequality "1/5 ≥ (-2/3) x," and its solution is x ≥ 3/10.

The inequality that symbolises the word phrase as supplied in the task content must be determined, as is evident from the assignment's content.

Negative one fifth is more than or equal to the product of negative two thirds and a number, which is how the disparity is expressed.

Therefore,

Let the number = y

- 1 / 5 ≥ - 2 / 3 × y

- 1 / 5 ≥ - 2 / 3 y

Now, multiply both sides of the inequality by - 3 / 2

Therefore,

- 1 / 5 (- 3 / 2) ≤ y

3 / 10 ≤ y

y ≥ 3 / 10

Therefore, y is greater than or equal to three tenths.

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Answer:

To find the cubic function with the given roots, we can use the factored form of a cubic function:

f(x) = a(x - r1)(x - r2)(x - r3)

where r1, r2, and r3 are the roots of the function.

Substituting the given roots, we get:

f(x) = a(x + 9)(x + 5)(x - 3)

To find the leading coefficient a, we need to use the y-intercept of the function, which is given as -27.

When x = 0, the function becomes:

f(0) = a(9)(5)(-3) = -27

Simplifying and solving for a, we get:

a = -27 / (9)(5)(-3) = 0.6

Rounding to two decimal places, the leading coefficient of the cubic function is a = 0.60.

Answer:

[tex] \sqrt{ {(0 - ( - 7))}^{2} + {( - 1 - ( - 2))}^{2} } [/tex]

[tex] \sqrt{ {7}^{2} + {1}^{2} } [/tex]

[tex] \sqrt{49 + 1} = \sqrt{50} = 5 \sqrt{2} [/tex]

5√2 units is about 7.07 units.

The solution to the system of Equations is x = 1 and y = -2.

Binh was solving a system of equations using the graphing method. This method involves graphing the given equations and finding the point where the graphs intersect. In this case, Binh incorrectly graphed the equation y = x - 3.

To solve the system correctly, Binh should follow these steps:

1. Rewrite the equation, if needed, in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The given equation, y = x - 3, is already in this form.

2. Determine the slope (m) and the y-intercept (b) of the equation. For the equation y = x - 3, the slope (m) is 1 and the y-intercept (b) is -3.

3. Graph the equation by first plotting the y-intercept on the y-axis and then using the slope to find additional points on the graph.

4. Repeat steps 1-3 for the second equation in the system.

5. Observe where the graphs intersect. This point represents the solution to the system of equations.

In this case, Binh should have found the point of intersection to be (1, -2). This means that the solution to the system of equations is x = 1 and y = -2. By accurately graphing the equations and finding the correct point of intersection, Binh can ensure that they have solved the system of equations correctly.

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{JK}\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{49} \end{cases} \\\\\\ JK=\sqrt{ 5^2 + 4.9^2}\implies JK=\sqrt{ 25 + 24.01 } \implies JK=\sqrt{ 49.01 }\implies JK\approx 7[/tex]

Answer:

The cost of 4 dozen eggs is 4 * $1.25 = $5.

The cost of half a gallon of milk is $2.97.

The total cost of the eggs and milk is $5 + $2.97 = $7.97.

Since Chase has only $10, the minimum price for a dozen eggs is $10 - $7.97 = $2.03.

So the answer is 2.03

Step-by-step explanation:

Based on the lengths of the sides, we can see that the triangle is scalene. Based on the slopes of the sides, we can see that the triangle is acute since all the slopes are negative or less than 1.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the desired slopes and lengths of the triangle formed by the points M(-7, 8), N(-1, 9), and O(0, 3), we can use the distance formula and the slope formula.

Distance formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, we can find the lengths of the sides of the triangle:

Length of MO:

d(MO) = √((0 - (-7))² + (3 - 8)²) = √(7² + 5²) = √(74)

Length of NO:

d(NO) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)

Length of MN:

d(MN) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)

Slope formula:

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Using this formula, we can find the slopes of the sides of the triangle:

Slope of MO:

m(MO) = (3 - 8) / (0 - (-7)) = -5/7

Slope of NO:

m(NO) = (9 - 8) / (-1 - (-7)) = 1/6

Slope of MN:

m(MN) = (9 - 8) / (-1 - (-7)) = 1/6

Characterization of the triangle:

Based on the lengths of the sides, we can see that the triangle is scalene (no two sides have the same length). Based on the slopes of the sides, we can see that the triangle is acute (all angles are less than 90 degrees) since all the slopes are negative or less than 1. Additionally, we can see that the side MO is the longest side of the triangle, and since the slope of MO is negative, we can conclude that the angle opposite side MO is the largest angle in the triangle.

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A one-tailed test of significance could be used whenever the researcher is interested in predicting a direction for the difference.What is a one-tailed test?A one-tailed test is a statistical hypothesis test in which the critical region of a parameter's distribution is only one-sided, indicating that it is either higher or lower than the values obtained from sample data.

A one-tailed test is also known as a one-sided test or a directional hypothesis test.It is used when the research hypothesis states a direction for the population parameter (i.e., greater than or less than a specific value).

For example, if we want to test whether a new drug reduces blood pressure, we could conduct a one-tailed test with the null hypothesis stating that the drug has no effect on blood pressure, and the alternative hypothesis indicating that the drug lowers blood pressure. In this scenario, a one-tailed test will be suitable.

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Answer:

Step-by-step explanation:

Answer:

x=5.8

Step-by-step explanation:

a^2+b^2=c^2

3^2+5^2=x^2

9+25 = 34

[tex]\sqrt{34)[/tex] = 5.8

Answer:

[tex]17\sqrt{2}[/tex]  or approximately 5.83

Step-by-step explanation:

The triangle is a right triangle so we use Pythagorean theorem to find the missing side.

[tex]a^{2} + b^{2} =c^{2}[/tex]

x is the hypotenuse so that has to be the value of c but the other two sides are interchangeable.

[tex]3^{2} + 5^{2} = x^{2}\\\\9+25=x^{2} \\\\34=x^{2} \\[/tex]

Square both sides to isolate the x.

[tex]\sqrt{34} =x[/tex]

Simplify

[tex]17\sqrt{2} =x\\[/tex]