James is making a paper chain from different colored paper strips. He joins the links in the following pattern: red, blue, red, and blue, and so on. Counting from the first link, what color will the 23rd link be?

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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The vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.

A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο parallel bases that are cοngruent circles and a curved lateral surface that cοnnects the bases.

1. The circumference οf the cylinder is given as 13 inches. We knοw that the fοrmula fοr the circumference οf a cylinder is 2πr, where r is the radius οf the cylinder. Sο, we have:

2πr = 13

r = 13/(2π)

Nοw, we can use the fοrmula fοr the vοlume οf a cylinder, which is V = πr²h, where h is the height οf the cylinder:

\(V = \pi (13/(2\pi ))^2(9) = 119.8 cubic inches\)

Sο, the approximate vοlume of the cylinder is 119.8 cubic inches.

2. The diameter οf the cylinder is given as 63.5 cm, which means the radius is 31.75 cm (since the radius is half οf the diameter). The height is given as 28 inches.

The formula fοr the vοlume of a cylinder is \(V = \pi r^2h\), so we can substitute the values we have tο get:

\(V = \pi (31.75)^2(28) = 85816.8 ~cm^3\)

Tο cοnvert this tο cubic inches, we need tο knοw that 1 cubic inch is equal tο 16.3871 cubic centimeters, sο we have:

V = 85816.8/16.3871 ≈ 5235.5 cubic inches

Hence, the vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.

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Answer:

the answer is 157

Step-by-step explanation:

7 +10= 17

17+20=37

37+40=77

77+80=157

157+160=317

At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...

Answer:

The answer is: 13/24

Step-by-step explanation:

Find the LCM of 6 and 8

1/6=4/24

3/8= 9/24

4/24+9/24= 13/24

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

Answer:

20+5

Step-by-step explanation:

Becvause 5 to the second power is 25 and 25 in expanded form is 20+5

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Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

Answer:

The combined total dollar amount Natalie paid for her class fees can be expressed as follows:

118f + 105(15-f)

where f is the number of credit hours Natalie took at Florida State.

Simplifying the expression:

118f + 1575 - 105f

= 13f + 1575

Therefore, the combined total dollar amount Natalie paid for her class fees is $13f + $1575.

Step-by-step explanation:

Answer:

skewed to the right

Step-by-step explanation:

Given that

the mean household income for the last year was $46,200

And, the median was $37,800

In the case when the historgram is prepared so the income would be skewed to the right as the mean i..e $46,200 is more tha the median i.e. $37,800

So, the distribution would be right skewed

Hence, the same would be considered and relevant

The mean of the frequency distribution is 52 degrees. and option A is carrect  . A) The computed mean is close to the actual mean because the difference between the means is less than​ 5%

First, we calculate the class mid-points (x); This is the mean of the class intervals.

For 40 - 44, x = (40 + 44)/2 = 42. This is applied to all other classes.

40 −44 = 42

45 −49 = 47

50 −54 = 52

55 −59 =57

64 −64 = 62

So:

x  42    47     52       57     62

f    22    55    1212     77      11

mean = ∑f(x)/∑f

= (42*22+47*55+52*1212+57*77+62*11)/(22+55+1212+77+11)

= 71604/1377

=52

actual mean = 51.8

and now mean = 52

percentage difference = ((52-51.8)/51.8)*100

= 0.3861 percentage

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Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

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Answer:

Given - Product of 3 no. is 0.084

To find - Third no.

Solution -

Let the third no. be X

0.7 × 0.2 × X = 0.084

0.14 × X = 0.084

X = 0.084 /0.14

X = 0.6

The value of third number is 0.6.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The product of 3 numbers = 0.084

Two of the numbers are 0.7 and 0.2

Now,

Let the value of third number = x

Then, By the given condition we formulate;

0.7 × 0.2 × x = 0.084

0.14 × x = 0.084

Divide by 0.14 in both side,

x = 0.084 ÷ 0.14

x = 0.6

Thus, The value of third number is 0.6.

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According to the line of best fit, the time that the temperature will reach 100°c the boiling point of water is a 5.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

It should be noted that with the increase in time, the temperature increases as well.

Therefore, the time that the temperature will reach 100°c the boiling point of water is a 5.

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A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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So the new coordinates of point C are (1, 2), and the image of Triangle ABC is congruent to the original triangle.

A triangle is a closed, two-dimensional geometric figure with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides or the size of its angles. A triangle with all sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with no sides of equal length is called a scalene triangle. Triangles can also be classified based on the size of their angles, with an acute triangle having all angles less than 90 degrees, a right triangle having one angle equal to 90 degrees, and an obtuse triangle having one angle greater than 90 degrees.

Here,

To find the new coordinates of point C after the rotation and translation, we need to perform each transformation separately and then combine them.

Rotation:

To rotate a point 180° counterclockwise about the origin, we switch the sign of both coordinates. Therefore, the new coordinates of point C after the rotation are (-3, -2).

Translation:

To translate a point to the right 4 and up 4, we add 4 to the x-coordinate and 4 to the y-coordinate. Therefore, the new coordinates of point C after the translation are (1, 2).

To determine if the image of Triangle ABC is similar or congruent to the original triangle, we need to compare the corresponding sides and angles of both triangles.

Since we performed a rotation of 180°, all the angles in the image triangle are congruent to the corresponding angles in the original triangle. Additionally, since we performed a translation, the sides of the image triangle are congruent to the corresponding sides of the original triangle. Therefore, the image triangle is congruent to the original triangle.

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Step-by-step explanation:

first 12^ 12

second 7^11

Answer:

\((x+4)^2+(y-4)^2=16\)

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

Since the circle is tangent to both axes, and the center of the circle is in the second quadrant, the center of the circle lies on the line y = -x.

As the circle is tangent to the x-axis, the distance between the center of the circle and the x-axis is equal to the radius of the circle.

Similarly, as the circle is tangent to the y-axis, the distance between the center of the circle and the y-axis is also equal to the radius of the circle.

Therefore, the center of the circle will be 4 units to the left of the y-axis and 4 units up from the x-axis. Therefore, the coordinates of the center are (-4, 4).

\(\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Substitute the center (-4, 4) and the radius, r = 4, into the standard equation of a circle:

\(\implies (x - (-4))^2+(y-4)^2=4^2\)

\(\implies (x+4)^2+(y-4)^2=16\)

Therefore, the equation of the circle that satisfies the given conditions is:

\(\boxed{(x+4)^2+(y-4)^2=16}\)

Answer:

c = 0.5 cm

Step-by-step explanation:

Using the Sine rule in the triangle, then

=  ( cross- multiply )

c × sin105° = 2 × sin15° ( divide both sides by sin105°

c =  ≈ 0.5 cm ( to the nearest tenth )

Answer:

Step-by-step explanation:

a) To determine the endogenous variables, we need to identify the variables that are determined within the model equation. In the given model, the endogenous variable is Y (output or national income).

b) Let's find Y, C, and T step-by-step:

Start with the equation Y = C + I0 + g0.

Substitute C from the equation C = a + b(y - T).

Y = (a + b(y - T)) + I0 + g0.

Substitute T from the equation T = d + tY.

Y = (a + b(y - (d + tY))) + I0 + g0.

Expand the equation:

Y = a + by - bd - btY + I0 + g0.

Rearrange the equation to isolate Y:

Y + btY = a + by - bd + I0 + g0.

Y(1 + bt) = a + by - bd + I0 + g0.

Y = (a + by - bd + I0 + g0) / (1 + bt).

Now, Y is expressed in terms of the exogenous variables a, b, d, I0, g0, and the endogenous variable Y itself, along with the parameter t.

To find C and T, we can substitute the obtained Y value back into the respective equations:

Substitute Y into the equation C = a + b(y - T):

C = a + b(y - T) = a + b(y - (d + tY)) = a + by - bd - btY.

C = a + by - bd - bt[(a + by - bd + I0 + g0) / (1 + bt)].

Now, C is expressed in terms of the exogenous variables a, b, d, I0, g0, and the endogenous variable Y, along with the parameter t.

Substitute Y into the equation T = d + tY:

T = d + tY = d + t[(a + by - bd + I0 + g0) / (1 + bt)].

Now, T is expressed in terms of the exogenous variables d, t, and the endogenous variable Y, along with the parameters a, b, I0, and g0.

It's important to note that in the given model, there is only one endogenous variable, Y (national income/output). C and T are determined based on the values of Y and the exogenous variables.

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

The plot of the points is shown below:

To find this points on the plane we need to remember that the first coordinate of the point represents the horizontal distance while the second coordinate represents the vertical distance.

The length of Marisa's garden is 10

The given parameters are:

Perimeter = 32 feet

Width = 6 feet

The perimeter is calculated as:'

Perimeter = 2 * (Length + width)

So, we have

2 * (Length + 6) = 32

Divide by 2

Length + 6 = 16

Subtract

Length = 10

Hence, the length of Marisa's garden is 10

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Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)