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 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times.

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

Bus 47, with an IQR of 8
Bus 14, with an IQR of 6
Bus 47, with a range of 8
Bus 14, with a range of 6

Answer:

To divide fractions, we can use the reciprocal (or multiplicative inverse) of the second fraction and then multiply the two fractions.

So to solve ⅚ ÷ ⅔, we can write it as:

⅚ ÷ ⅔ = ⅚ × (⅔)⁻¹

where (⅔)⁻¹ is the reciprocal of ⅔, which is 3/2.

So we have:

⅚ ÷ ⅔ = ⅚ × (⅔)⁻¹ = ⅚ × 3/2

We can simplify this expression by canceling out a common factor of 2 in the numerator and denominator:

⅚ ÷ ⅔ = ⅚ × (⅔)⁻¹ = ⅚ × 3/2 = (⅚ × 3) / 2 = 9/12

Therefore, another way to solve ⅚ ÷ ⅔ is the equation:

⅚ ÷ ⅔ = 9/12

Answer:

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

Inverse variation equation:

We have:

Substitute initial values and find the value of k:

The equation now becomes:

Find the value of V when P = 5:

Hence the answer is 166.4 in³.

Ll término general de la sucesión 4, 9, 14, 19, 24 es an = 5n - 1.

La sucesión 4, 9, 14, 19, 24 es una progresión progresión aritméticacon una diferencia común de 5.

El término general de una progresión aritmética se puede encontrar utilizando la fórmula:

an = a1 + (n - 1)d

donde:

an = el término general que se desea encontrar

a1 = el primer término de la progresión

n = la posición del término que se desea encontrar

d = la diferencia común de la progresión

En este caso, a1 = 4 y d = 5. Para encontrar el término general para cualquier posición n, podemos sustituir estos valores en la fórmula y simplificar:

Por lo tanto, el término general de la sucesión 4, 9, 14, 19, 24 es an = 5n - 1.

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Answer:

Unfortunately, none of the answer choices match. A correct ratio would be 1:2.

Step-by-step explanation:

Let the perimeter of each isosceles triangle be "2x". Since ABC is equilateral, each of its sides is also "2x".

The perimeter of the pentagon is the sum of the perimeters of the triangles, which is 6(2x) = 12x.

Since ABC is equilateral, its perimeter is 6x (since it has three sides of length 2x).

Therefore, the ratio of the perimeter of ABC to the perimeter of ABCDE is (6x)/(12x) = 1/2, simplifying this ratio gives 1:2.

Therefore, the correct answer is not given in the options.

Answer:

Step-by-step explanation:

4/9

By the number of red marbles taken out, we expect that 12/27=4/9 of the marbles are red. Therefore, the probability of the next marble being red is 4/9.

The mean and standard deviation are used to compare the centers and ranges of two symmetric distributions because they provide a measure of position and variability that are consistent with normally distributed data.

When the data are approximately normal, the mean is a good measure of the center of the distribution, and the standard deviation is a good measure of the spread of the distribution.

By comparing the means and standard deviations of two symmetric distributions, we can know their similarity or difference in terms of central tendency and variability.

On the other hand, a five-digit summary (minimum, Q1, mean, Q3, maximum) is used to compare the center and difference of two skewed or outlier distributions.

The five-digit summary provides a way to summarize the key characteristics of a distribution, and it is more robust for outliers than for mean and standard deviation.

By comparing the median and interquartile range (IQR) of two skewed or outlier distributions, we can tell their similarities or differences in terms of central tendency and variability.

In summary, mean and standard deviation are suitable for comparing centers and ranges of normally distributed data, while five-digit summaries are more suitable for comparing centers and ranges of skewed distributions.

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Answer:

The shape in the image is a trapezoid. It is a quadrilateral with one pair of parallel sides.

Step-by-step explanation:

Therefore , the correct option is A Dimension of exisiting patio is 6feet by 8feet.

Ms. Khan wants to add x feet onto each side of an existing  patio, then the area of the existing patio is (x-2)² square feet.

Define square feet?

In the United States, Canada, China, and the United Kingdom, the square foot  is a commonly used imperial measure of area. Its emblem is a straightforward square with a vertical line cutting it in half .

The Imperial system uses a combination of feet, inches, miles, and gallons.

So,

we can write (x-2)² = x²+14x+48.

Expanding the left side gives us x²-4x+4 = x²+14x+48.

Simplifying gives us 18x = 44.

Therefore, x = 11/4.

The dimensions of the square patio are (11/4 - 2)×2 feet by (11/4 - 2)×2 feet which is equal to( 3/4)×2 feet by 6/8

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Solve and get |3x - 0.5| > 1.5: x < -0.333 or x > 1, The solution to |3x - 0.5| = 1.5 is: x = 0 or x = 1, The solution to |3x - 0.5| < 1.5 is: -0.333 < x < 0.833

Depending on whether the expression contained in the absolute value is positive, negative, or zero, there are three scenarios that need to be taken into account in order to system of equations the absolute value inequalities involving |3x - 0.5|.

Example 1: (3x - 0.5) > 0

The absolute value expression in this situation is reduced to 3x - 0.5. We thus have:

3x - 0.5 > 1.5

When we solve for x, we get x > 1.

Example 2: (3x - 0.5) < 0

The absolute value expression in this situation is -(3x - 0.5), which is equivalent to -3x + 0.5. We thus have:

-3x + 0.5 > 1.5

The result of solving for x is: x -0.333

Example 3: (3x - 0.5) = 0

The equation for the absolute value in this situation is |0|, which equals 0. The result is either 3x - 0.5 = 1.5 or 3x - 0.5 = -1.5.

The results of each equation's x term are: x = 1 or x = 0.

As a result, the answer to |3x - 0.5| > 1.5 is either x -0.333 or x > 1.

x = 0 or x = 1 is the answer to the equation |3x - 0.5| = 1.5.

The answer to the equation |3x - 0.5| 1.5 is: -0.333 x 0.833

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Addie measured her height on her 5th birthday, she was 44 4/5 inches tall. Each year, Addies grew 2/5 inch.  Addie height on her 12th birthday is 47 2/5 inches.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and understand mathematical relationships. In algebra, variables are used to represent unknown values, and equations are used to express relationships between these variables.

Algebra involves the use of mathematical operations such as addition, subtraction, multiplication, and division, as well as the use of exponents, logarithms, and other advanced mathematical concepts. Algebraic equations can be solved using various methods, such as substitution, elimination, and graphing.

Algebra has numerous practical applications in various fields, including science, engineering, economics, and finance. It is used to model and solve real-world problems, analyze data, and make predictions. Algebra is also an essential foundation for more advanced mathematical topics, such as calculus, linear algebra, and abstract algebra.

Addie was 44 4/5 inches tall on her 5th birthday. From her 5th to 12th birthday, she grew for 7 years, so her height increased by 7 * (2/5) = 2.8 inches.

Adding this to her height on her 5th birthday, we get:

44 4/5 + 2.8 = 47 2/5

Therefore, Addie was 47 2/5 inches tall on her 12th birthday.

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The ladder reaches the wall at a height of 8.66 from the ground. We solve this problem with an understanding of trigonometry.

From the given situation, we can construct a right-angled triangle where the base is the distance between the ladder and the wall, the hypotenuse is the length of the ladder i.e. 10 feet and the height up to which it reaches is perpendicular (let's assume that to be x).

We can use trigonometry's sine relation to solve this problem, according to which,

sine(60°)=perpendicular/hypotenuse

sin(60°)=x/10

0.866=x/10

so,

x=10×0.866

x=8.66

Hence, we find that The ladder reaches the wall at a height of 8.66 from the ground.

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As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution. Correct option is D.

This is known as the central limit theorem, which states that the sampling distribution of the sample mean is approximately normal regardless of the underlying population distribution, as long as the sample size is sufficiently large.

The central limit theorem is a fundamental result in statistics and has many practical applications. For example, it allows us to use the normal distribution to make inferences about population parameters based on sample statistics, such as constructing confidence intervals or conducting hypothesis tests.

On the other hand, the binomial distribution describes the number of successes in a fixed number of independent trials with a constant probability of success, while the Poisson distribution describes the number of rare events that occur in a fixed interval of time or space.

The hypergeometric distribution describes the probability of drawing a specified number of objects of interest from a population of known size without replacement. These distributions are not related to the sampling distribution of the sample mean and do not converge to a normal distribution as the sample size increases.

Therefore, the correct option is D.

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Complete question is:

As the sample size becomes larger, the sampling distribution of the sample mean approaches a .

a. binomial distribution

b. poisson distribution

c. hypergeometric distribution

d. normal distribution

Vanessa would need to drink about ten cups of liquid to replace the weight she lost while running.

The amount of water needed to be drank is approximately 2 cups of water are required for every pound of body weight reduced.

Vanessa would need to drink about ten cups of liquid to replace the weight she lost while running.

Refilling fluid: To add fluid to something that has been drained, in particular: to replace any fluids the body has lost from dehydration. assist a patient in hydrating.

Oral rehydration solutions (ORSs), which include Pedialyte, are used to treat dehydration. ORSs, which help replace lost fluids, include the correct ratio of salt, sugar, potassium, and other minerals.

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Complete question - A general rehydration recommendation after exercise is 2.5 cups of fluid for every 1 pound of body weight lost. Using this guideline, how much fluid would Vanessa need to consume to make up for the weight that was lost during her run?

Calculation: 2 cups x lbs of body weight lost = cups of water needed

A. Approximately 4 cups of fluid

B. Approximately 8 cups of fluid

C. Approximately 6 cups of fluid

D. Approximately 10 cups of fluid

7. Vanessa asks if she should start using sports drinks. Which of the following would best answer Vanessa's question?

A. A sports drink is not beneficial for you at this time and may provide unnecessary calories.

B. A sports drink would be beneficial to replace fluid and electrolytes when exercising for less than 30 minutes.

C. A sports drink would be beneficial on days when you are exercising for over an hour at a higher intensity.

8. If Vanessa uses a sports drink in the future, how much glucose, sodium and potassium should be provided per 24 fluid ounces of sports drink?

A. No more than 30 g of glucose, 450 g of sodium and 225 mg of potassium.

B. No more than 75 g glucose, 150 mg sodium, 175 mg potassium.

C. No more than 15 g of glucose, 500 mg sodium, 200 mg potassium.

D. No more than 45 g of glucose, 225 mg of sodium and 275 mg of potassium.

The area of Triangle B is 2 times greater than the area of Triangle A.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

Area of the triangle = 1/2 h*b

For Triangle A, the area is:

Area_A = 1/2 * b * h

For Triangle B, the area is:

Area_B = 1/2 * b * 2h = b * h

So, the area of Triangle B is twice the area of Triangle A.

Therefore, the area of Triangle B is 2 times greater than the area of Triangle A.

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Step-by-step explanation:

There are  1+ 3+ 4 = 8 parts to divide

80 / 8 =  £ 10  for each part

                          1 part    = 1 x 10  = £ 10

                           3 parts = 3 x 10 = £ 30

                          4 parts = 4 x 10 = £ 40

Answer:

10

Step-by-step explanation:

1+3+4=8

80/8=10

Answer:

Step-by-step explanation:

by identity       a²-b² =(a-b)(a+b)

9x² = (3x)²

4(y+2x)² = 2²(y+2x)² = (2(y+2x))²=(2y+4x)²

so : a = 3x   and b = 2y+4x

put a and b in this identity     a²-b² =(a-b)(a+b) ....continu

The area of triangle XYZ when using YZ as the base, can be found to be 24 square units.

To find the area of triangle XYZ, we can use the Shoelace Theorem (also known as the Surveyor's Formula). Given the coordinates of the vertices, the area of the triangle is:

Area = (1/2) x |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|

Plugging in the coordinates:

Area = (1/2) x |(2(9 - 1) + 10(1 - 5) + 6(5 - 9))|

Area = (1/2) x |(2(8) - 10(4) + 6(-4))|

Area = (1/2) x |(16 - 40 - 24)|

Area = (1/2) x |-48|

Area = 24 square units

The area of triangle XYZ is 24 square units.

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The number of people who don't use any alternative transportation mode is 18 people.

To find the number of people who don't use any alternative transportation mode we can use the principle of inclusion and exclusion (PIE) method.

adding the number of people who use each mode:

walk = 144

bus = 102

bicycle = 105

Next, subtract the number of people who use two modes:

walk and bus = 78

walk and bicycle = 65

bus and bicycle 45

adding people who use all three modes:

all three modes of transportation = 34

Therefore, the total number of people who use at least one alternative mode of transportation is:

= 144 + 102 + 105 - 78 - 65 - 45 + 34

= 197

To find the number of people who don't use any alternative transportation. we need to subtract the number of people who use at least one alternative mode of transportation from the total number of people in the survey:

= 215 - 197

= 18

Therefore, The number of people who don't use any alternative transportation mode is 18.

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a) The necessary sample size for a 95% confidence interval with an interval width of no more than 6% is 147.

b) The necessary sample size for a 99% confidence interval with an interval width of no more than 6% is 263.

(a) To find the necessary sample size for future surveys such that a 95% confidence interval for p has an interval width of no more than 6%, we use the formula:

n = (Zα/2/ME)² × p(1-p)

where Zα/2 is the Z-score for the desired confidence level (1.96 for 95% confidence), ME is the margin of error (0.06), and p is the estimated proportion of patients with pain relief from the pilot survey (14/20 = 0.7). Substituting these values into the formula, we get:

n = (1.96/0.06)² × 0.7(1-0.7) = 146.95

Therefore, This sample size is larger than the sample size in problem 4.6-21(a), which was 100.

(b) To find the necessary sample size for future surveys such that a 99% confidence interval for p has an interval width of no more than 6%, we use the same formula as above but with a Z-score of 2.576 for 99% confidence:

n = (2.576/0.06)² × 0.7(1-0.7) = 262.43

Therefore, This sample size is larger than the sample size in problem 4.6-21(b), which was 176.

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Answer:

You may see many real-life examples of collinearity such as a group of students standing in a straight line, a bunch of apples kept in a row, next to each other, etc. In geometry, two or more points are said to be collinear, if they lie on the same line.

Step-by-step explanation:

Hope this helps!=D

The required 99% confidence interval representing the true proportion of all college students owns a car lies between the range of 0.3253 and 0.4283.

Sample size n = 319

Students who own a car represents the number of successes x = 120  

Confidence interval =  99%

True proportion p of all college students who own a car.

The formula for the confidence interval for a population proportion is,

p1± zα/2 × √(p1(1-p1)/n)

where p1 is the sample proportion,

zα/2 is the z-score corresponding to the desired level of confidence interval 99%.

First, we find the sample proportion,

p1 = x/n

    = 120/319

    ≈ 0.3768

z-score corresponding to a 99% confidence level.

This is a two-tailed test,

Split the alpha level evenly between the two tails.

α/2 = (1 - 0.99) / 2

     = 0.005,

The z-score that encloses 0.005 in each tail of the standard normal distribution.

Using a standard normal table ,

zα/2 = 2.576.

Substituting the values into the formula, we get,

p1 ± zα/2 × √(p1(1-p1)/n)

= 0.3768 ± 2.576×√(0.3768(1-0.3768)/319)

= 0.3768 ± 0.0515

99% confidence interval for the true proportion p of all college students who own a car is,

0.3253 ≤ p ≤ 0.4283

Therefore, 99% confidence interval that the true proportion of all college students who own a car lies between 0.3253 and 0.4283.

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The correct number line that shows the solution to the inequality y - 2 < -5 is the first option: "A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded."

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The inequality can be rewritten as y < -3, which means that y is less than -3. The open circle at -3 indicates that -3 is not included in the solution set, and everything to the left of it, which represents numbers less than -3, should be shaded.

Therefore, the correct number line that shows the solution to the inequality y - 2 < -5 is the first option: "A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded."

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The domain of the function is all real numbers greater than or equal to 1, or in interval notation: the correct answer is (d) x2≥7.

The domain of a function is the set of all possible values of the independent variable (usually denoted by "x") for which the function is defined. It is the set of all input values for which the function produces a valid output value.

For example, consider the function f(x) = 1/x. The domain of this function consists of all real numbers except for 0, since division by zero is undefined. Therefore, the domain of the function is:

Domain(f) = {x | x ≠ 0}.

In the given question,

The square root function is defined for non-negative values of its argument. Therefore, the expression inside the square root must be greater than or equal to zero.

x + 6 - 7 ≥ 0

Simplifying the inequality, we get:

x - 1 ≥ 0

x ≥ 1

Therefore, the domain of the function is all real numbers greater than or equal to 1, or in interval notation:

[1, ∞)

So the correct answer is (d) x2≥7.

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Answer:

2x

Step-by-step explanation:

(12x^2-10x)/6x-5

10.6 is the height, of the triangular wall .

What is known as a triangle?

The three vertices of a triangle make it a three-sided polygon. The triangle's angles are formed at a point where the three sides are joined end to end.

                               The triangle's three angles add up to a total of 180 degrees. the three different kinds of triangles that are classified according to the size of their biggest angle. These triangles are the acute, right, and obtuse triangles.

Area = 1/2 * b * h

64 = 1/2 *12 * h

64 * 2/12  = h

    h = 10.66

13) 3y+ 6 = 2x

      3y = 2x - 6

       y = 2/3x - 2

compare with y= mx + c

        slope = 2/3

           c = -2

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The given statement that 'the one-sample z-test is used when the population standard deviation is unknown.' is true.

Z-test is used to test hypotheses about the population means when we don't have any information about the population standard deviation and the sample size is huge. According to the given statement, the standard error of the mean can be estimated with the help of sample standard deviation, and the test statistic can be approximated by a standard normal distribution.

In another case where the sample size is too small, T-test should be used instead of Z-test. This is encouraged because of increased efficiency.

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The missing values of the proportion are;

a. 18

b. 19.5

c. 45%

d. 180

The percentage of a number can be defined as the fraction of a number and hundred.

It is represented with the symbol, %.

From the information given, we have that'

1. 6% of 30

This is represented as;

60 /100 × 30

Multiply the values

18

2. 65% of 30

This is represented as

65/100 × 30

Multiply the values

1950/100

19.5

3. 18/40 × 100

Multiply the values

1800/40

45%

4. 81 = 45/100x

cross multiply the values

x = 180

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Answer:

1/10 of the circle (36° central angle).

Step-by-step explanation:

2/20 = 1/10

A circle has 360 degrees, so the central angle will be 1/10 × 360° = 36°.

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] {\color{hotpink}\bigstar} {\boxed{\sf {\green{ slope : m = \: \frac{y_2 - y_1}{x_2 - x_1} }}}}[/tex]

Solution:-

[tex] \sf \: m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex] \: [/tex]

where ,

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \sf \: m = \frac{( -2 ) - ( -3 ) }{1 - 2} [/tex]

[tex] \: [/tex]

[tex] \sf \: m = \frac{ - 2 + 3}{ \: 1 - 2} [/tex]

[tex] \: [/tex]

[tex] \sf \: m = \cancel \frac{1}{ - 1} [/tex]

[tex] \: [/tex]

[tex] \underline{\boxed{ \sf{ \blue{ \: m = -1 \: }}}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)