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The interquartile range of the data will be 0.215.

The lower half is:

7.86, 7.87, 7.99, 8.03

The median of the lower half is:

(Q1) = (7.87 + 7.99) / 2 = 7.93

The upper half is:

8.06, 8.08, 8.09, 8.20, 8.43

The median of the upper half is:

(Q3) = (8.09 + 8.20) / 2 = 8.145

The IQR is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215

Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955

Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795

None of the data points fall outside these thresholds, so there are no outliers in this data set.

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We can see that the percentage is 20%, then 20 percent of the students got a 10.

To find this, we need to use the formula:

Percentage = 100%(number of students with a 10)/(total number of students)

Here we know the that the revelant numbers are:

Number of students with a 10 = 12

total number of students in the class = 60

Replacing that in the formula we will get the percentage:

P  = 100%*(12/60)

P = 20%

So 20% of the total number of students got a 10.

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Keyboards A and B are significantly different from one another

The F ratio has been found to be 4.30, equating to the MS between treatments divided by MS error resulting in a value of 2082/484. In order to seek out the critical value for F at an alpha level of 0.05 within degrees of freedom between treatments (2) and degrees of freedom error (3), we must consult the F-table, revealing it to be 5.14.

We reach the conclusion that rejecting the null hypothesis would not prove necessary as there appears to be no great significance when it comes down to the number of errors made with the three concerned keyboards.

Tukey's HSD signifies 2.0, indicating any distinction of means exceeding such scores is considered noteworthy. Calculating pairwise comparisons can enlighten us as to which keyboards are significant from one another:

Comparing Keyboard A versus Keyboard B: The difference was calculated using |25-6| / ✓(484/6*(1/6+1/6)) = 3.03, determining its significance surpassing Tukey's HSD (2.0).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Its simple, you need to find x

4 days the same amount of time (x) gives 48 min
4x = 48

x = 48/4

x = 12

then to get the amount of minutes in 9 days it would be:

9x=days

9(12)=108

the answer would be 108 min

Answer:

108 mins

Step-by-step explanation:

48 mins/4 days = x mins/9 days

4x= 432

x=108 mins

The estimate of the cost for a 20-ft cord is given as follows:

$74.66.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points in the context of the problem are given as follows:

(3, 12.75), (5, 16), (6, 25.99), (50, 185).

Inserting these points into a calculator, the regression equation is given as follows:

y = 3.6794x + 1.06462.

Hence the estimate of the cost for a 20-ft cord is given as follows:

y = 3.6794(20) + 1.06462

y = $74.66.

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The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.

The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:

m = slope of the line

b = the y-intercept

Given the following:

slope (m) = -2/5.

y-intercept (b) = -4

To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:

y = -2/5x - 4

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Given the above model, we can state that it's predictions were accurate.

The model uses the variable x which represents no. of years from 1970 to 2010

2010 -1970 = 40
P + (x/2) = 44

P + 40/2 = 44

P + 20 = 44
P = 44 - 20
p = 24

The model, it predicted 24% of the population would be smoking in this city in the year 2010. Whereas the data from the graph tell us that

28 %  of the adults actually smoked in the city in 2010. Hence the model is accurate .

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Full Question:

The mathematical model

p+ x/2 =44

Describes the percentage, p, of adults who smoked cigarettes x years after 1970

Does the mathematical model underestimate or overestimate the percentage of adults who smoked cigarettes in 2010? By how much?

This is a word problem involving supplementary angles. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.

Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:

x=6(180−x)−590

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

xx7xxx​=6(180−x)−590=1080−6x−590=490=7490​=70​

Therefore, the measure of the angle is 70°.

we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .

what is equation ?

An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition

In the given question,

Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:

3 / 15 = 0.2 or 20%

Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.

So, the expected number of white horses among the next 20 horses that come to board is:

20 x 0.2 = 4

Therefore, we should expect 4 white horses among the next 20 horses that come to board.

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The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.

The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.

Slope of a line (m) = change in y / change in x = rise / run

The red line in the image below represents the rise of the line while the blue line represents the run of the line.

The rise = 3 units

The run = 4 units

Therefore, we have:

Slope (m) = rise/run = -3 units / 4 units

Slope (m) = -3/4.

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Answer:

Step-by-step explanation:

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Answer:

To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.

First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:

- 70x + 40y = 230

- 32x - 40y = 76

Adding these two equations, we get:

- 102x = 306

Dividing both sides by 102, we get:

- x = 3

Now we can substitute this value of x into either equation to find the value of y. Using the first equation:

- 7(3) + 4y = 23

- 21 + 4y = 23

- 4y = 2

- y = 1/2

Therefore, the point of intersection is (3, 1/2).

Answer:

Step-by-step explanation:

The statement that is true about the given circle equation is:

Option A: The circle is centered at (−6, 3) and has a radius of 11.

The standard form for finding the equation of a circle is given by the expression:

(x - h)² + (y - k)² = r²

where:

(h, k) represents the coordinates of the center of circle

r represents the radius of the circle

We are given the equation of the circle as:

(x - 6)² + (y - 3)² = 121

Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:

(x - 6)² + (y - 3)² = 11²

Comparing with the standard form of equation of a circle gives:

Coordinates of center = (-6, 3)

Radius = 11

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The relative frequency of customers ordering five hot dogs is 7%, option B is correct.

To find the relative frequency of customers ordering five hot dogs, we need to divide the frequency of customers who ordered five hot dogs by the total number of customers.

The total number of customers is the sum of the frequencies in the table:

Total frequency = 90 + 45 + 18 + 18 + 14 + 13 = 198

The frequency of customers ordering five hot dogs is 14, so the relative frequency is:

Relative frequency of customers ordering five hot dogs = (frequency of customers ordering five hot dogs) / (total frequency) = 14 / 198 = 0.0707

To express this as a percentage, we can multiply by 100:

Relative frequency of customers ordering five hot dogs = 0.0707 * 100% = 7.07%

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Answer: 5

Step-by-step explanation:

They are the points

The appropriate measure of variability for the data shown and its value is A. The range is the best measure of variability and equals 600.

The range is one of  the three measures of variability.

The range shows the difference between the highest value and the lowest value in a data set.

The other measures of variability are the IQR (Interquartile Range) and the the Standard Deviation.

Highest value = 800 m

Lowest value = 200 m

The range = 600 m (800 - 200)

IQR = 400 (600 - 200)

Mean = 567 (3,400 ÷ 6)

Median = 625 [(650 + 600) ÷ 2]

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The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

To obtain measures of spread, we can use the dot plot to visualize the frequency of each observation in the data-set, and then calculate the interquartile range (IQR).

For a group of 15 students, we can find the quartiles as follows:

The first quartile (Q1) is the median of the first half of the data-set, which consists of the first seven students.

Looking at the dot plot, the fourth dot represents the median of the first half. For Bus 14, Q1 = 12. For Bus 18, Q1 = 9.

The third quartile (Q3) is the median of the second half of the data-set, which consists of the last seven students. Looking at the dot plot, the eleventh dot represents the median of the second half. For Bus 14, Q3 = 18.

For Bus 18, Q3 = 16.

We can then calculate the IQR as the difference between Q3 and Q1:

For Bus 14, IQR = Q3 - Q1 = 18 - 12 = 6.

For Bus 18, IQR = Q3 - Q1 = 16 - 9 = 7.

Based on the IQR values, we can conclude that Bus 14 is more consistent than Bus 18, as it has a lower IQR.

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The graphed line of the equation is attached 2x + 3y = -6

A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:

ax + b = 0

The given equation 2x + 3y = -6 can be rearranged to get

y = -2/3x - 2

The x variables is plugged in to solve for y and used for the table of values for the graph

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The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.

The length of an arc in a given circle can be calculated by applying the formula as expressed below:

Length of arc (s) = ∅/360 * 2πr, where:

Reference angle = ∅

Radius of the circle = r.

Given the parameters:

Radius (r) = 16 cm

Reference angle (∅) = 40 degrees.

Plug in the values:

Length of the arc (s) = 40/360 * 2 * π * 16

Length of the arc (s) = 3.6π cm

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Answer:

To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?

Step-by-step explanation:

The team made approximately 773 runs in the match.

Let's start by setting up an equation to represent the information given in the problem.

Let's call the total runs made by the team "T".

37% of T = 286

To solve for T, we can start by converting the percentage to a decimal:

37% = 0.37

0.37T = 286

Now we can solve for T by dividing both sides of the equation by 0.37:

T = 286 ÷ 0.37

T ≈ 773.0

Therefore, the team made approximately 773 runs in the match.

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The cost of each admission tickets is 37.5 dollars.

Ms Boi spent a total of 175 dollars for 4 admission ticket and for parking at a baseball game. The cost of each admission ticket was the same amount, including tax. The cost of the parking was 25 dollars.

Therefore, the equation that can be use to determine the cost, i of each admission ticket can be represented as follows:

Therefore,

175 = 4i + 25

subtract 25 from both sides of the equation

175 = 4i + 25

175 - 25 = 4i + 25 - 25

150 = 4i

divide both sides by 4

i  = 150 / 4

i = 37.5 dollars

Therefore,

cost of each admission ticket = 37.5 dollars

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Answer:

f(x) = x^3 - x^2 + 16x - 16

Step-by-step explanation:

If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.

To find the polynomial, we can multiply these factors together:

(x - 1)(x - 4i)(x + 4i)

= (x - 1)(x^2 - (4i)^2)

= (x - 1)(x^2 + 16)

= x^3 + 16x - x^2 - 16

So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:

f(x) = x^3 - x^2 + 16x - 16

the value of 4% as a fraction is 1/25

4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.

Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Answer:

False.

Step-by-step explanation:

A integer in math is defined as a whole number. Therefore, the presence of fractions (which, in this case, is 1/2) and decimals, would mean that the term is in fact, not a integer.

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The value of the expression 5w–4w–w+6w is 6w

When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

For example, 2( 3a+5) can be simplified by using 2 to multiply both 3a and 5. This will give 6a+10. This means that the simplification of 2(3a+5) = 6a+10.

Similar , 5w-4w-w+6w can be simplified into:

5w+6w-4w-w

= 11w-5w

= 6w.

Therefore,the value of the expression 5w–4w–w+6w is 6w

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