A set of data is represented in the stem plot below.

Stem plot with stems of 3, 4, 5, 6, 7, 8, 9. Leaf for stem of 3 is 5. Leaves for stem of 4 are 4, 5. Leaves for stem of 5 are 3, 6. Leaves for stem of 6 are 2, 5. Leaves for stem of 7 are 5, 5, 6. Leaves for stem of 8 are 2, 5. Leaf for stem of 9 is 2.

Key: 3 | 5 = 35

Part A: Find the mean of the data. Show each step of work. (2 points)

Part B: Find the median of the data. Explain how you determined the median. (2 points)

Part C: Find the mode of the data. Explain how you determined the mode. (2 points)

Part D: Compare your values for mean, median, and mode from parts A, B, and C. Which value would best represent the data, and why? Explain using complete sentences. (4 points)

The correct equations are:

1. Two one-step equations:

[tex]\[3x + 2 = 11\]\[5y - 7 = 18\][/tex]

2. Two equations that contain fractions:

[tex]\[\frac{2}{3}x - \frac{1}{4} = \frac{5}{6}\]\[\frac{3}{5}y + \frac{2}{7} = \frac{1}{3}\][/tex]

3. One equation with distributive property:

[tex]\[2(4x - 3) = 10\][/tex]

4. One equation with decimals:

[tex]\[0.5x + 0.25 = 1.75\][/tex]

5. Real-world problem solved by an equation:

A bakery sells cakes for $[tex]15[/tex] each. Let's say the total cost of cakes sold in a day is $[tex]180[/tex]. We can use the equation [tex]\(15x = 180\)[/tex] to find the number of cakes sold, represented by the variable [tex]x[/tex]. Solving the equation, we find [tex](x = 12\)[/tex]), indicating that the bakery sold [tex]12[/tex] cakes that day.

Here's a basic explanation for the real-world problem:

Imagine there is a bakery that sells cakes for $[tex]15[/tex]each. We want to find out how many cakes the bakery sold in a day if the total revenue from cake sales is $[tex]180[/tex]. To solve this problem, we can use an equation. Let's represent the number of cakes sold as [tex]x[/tex].

The equation [tex]\(15x = 180\)[/tex] is used to express that the total cost of the cakes sold [tex](\$15\ per \ cake)[/tex] is equal to $[tex]180[/tex]. To solve the equation, we divide both sides by [tex]15[/tex] to isolate the variable [tex]x[/tex]. The equation simplifies to [tex]\(x = 12\),[/tex] which means that the bakery sold [tex]12[/tex] cakes that day.

By using the equation, we can determine the number of cakes sold based on the given information and calculate the desired result.

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Let's denote the total number of books on the shelf as 'total_books', and the number of new books as 'new_books'.

The number of used books can be calculated as the difference between the total number of books and the number of new books:

used_books = total_books - new_books

To find the ratio of used books to all books on the shelf, we divide the number of used books by the total number of books:

Ratio of used books to all books = used_books / total_books

Substituting the expression for used_books, we have:

Ratio of used books to all books = (total_books - new_books) / total_books

Simplifying further:

Ratio of used books to all books = 1 - (new_books / total_books)

Therefore, the ratio of used books to all books on the shelf is equal to 1 minus the ratio of new books to total books.

Answer: B

Step-by-step explanation:

The coefficients 9 & 6, divided by 3, equal 3 & 2.

For the exponents, if you divide the entire equation by xy, you need to subtract the corresponding exponents of x and y. Subtract the denominator's exponent from the numerator's exponent.

So, for the first part x^8/x^1=x^7

y^2/y^1=y

For the second part: x^3/x=x^2

y^4/y=y^3

So, if you put the coefficients and both parts of the equation together, you get 3x^7y - 2x^2y^3 (answer letter B).

Hope this helped!

The mean weekly expense, after correcting the incorrectly recorded week, is $81.25.

Given that Taylor recorded the past 16 weeks' expenses, excluding the incorrect recording of $90 as $38, we have 15 correct expense values.

Sum of correct expenses = $83.20 * 15 = $1248

Now we need to include the corrected expense of $90 instead of $38.

New sum of expenses = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300

Finally, we calculate the mean by dividing the new sum by the total number of weeks, which is 16.

Mean weekly expense = $1300 / 16 = $81.25

Therefore, the mean weekly expense, after correcting the incorrect recording, is $81.25.

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Answer:

Step-by-step explanation:

32 60 68

The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.

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Answer:

[tex]\huge\boxed{\sf r = 5}[/tex]

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

[tex]\rule[225]{225}{2}[/tex]

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

The sum of 33, 78, 10, 98, and 76 is 295.

Answer:

295

Step-by-step explanation:

add the numbers by using the addiction sign

y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

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

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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Answer:

Part A: The actual measurement of the piece of wood could be between 9.65 and 9.75 inches.

Part B: The measurement has three significant digits.

Step-by-step explanation:

Significant digits are the digits in a number that carry meaning in terms of the precision or accuracy of the measurement. In this case, the number 9.7 has three significant digits, which means that the measurement is accurate to the tenths place.

It will take the truck 9 hours to travel from warehouse A to warehouse B.

To determine the time it takes for the truck to travel from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.

First, let's find the vertical distance between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.

Next, we convert the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.

Now, we can calculate the time it takes to travel this distance. We divide the distance by the speed of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.

Therefore, it will take the truck 9 hours to travel from warehouse A to warehouse B.

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The area of the triangle whose dimensions are given in a vertices form would be = 9

To calculate the area of the triangle, the formula that should be used is the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2

Where; W=A, X= B, Y = C

Ax= 8

By= -2

Cy= -4

BX= 5

Ay = -8

CX= 3

That is:

= 8(-2--4)+5(-4--8)+3(-8--2)/2

= 16+20-18/2

= 18/2

= 9

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The Mayan number || :||- € is equivalent to the base-10 number 1021.

To convert a Mayan number to base-10, use the following steps:

In this case, the values of the digits are as follows:

Ones: 1

Twentys: 0

Four-hundreds: 2

Eight-thousands: 1

The place values are as follows:

Ones: 1

Twentys: 20

Four-hundreds: 400

Eight-thousands: 8000

The final value is calculated as follows:

1 × 1 + 0 × 20 + 2 × 400 + 1 × 8000 = 1021

Therefore, the Mayan number || :||- € is equivalent to the base-10 number 1021.

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Answer:

$3827.00

Step-by-step explanation:

To calculate the total compound amount at the end of six years with an interest rate of 1.5% compounded annually, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Total compound amount

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

In this case:

P = $3500

r = 1.5% = 0.015 (as a decimal)

n = 1 (compounded annually)

t = 6 years

Substituting these values into the formula, we have:

A = 3500 * (1 + 0.015/1)^(1*6)

Calculating this expression, we get:

A ≈ 3500 * (1.015)^6 ≈ 3500 * 1.093717 ≈ 3827.00

Rounding the total compound amount to 2 decimal places, the final value is approximately $3827.00

Answer:
To find the volume of a cone with radius 9 feet and height 4 feet, we can use the formula:

V = (1/3) * π * r^2 * h

Plugging in the values:

V = (1/3) * π * (9^2) * 4

Calculating:

V = (1/3) * π * 81 * 4

V ≈ 108.19 cubic feet

Therefore, the volume of the cone is approximately 108.19 cubic feet (rounded to two decimal places)

The area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.

From the given figure, the dimensions of trapezium are parallel sides a=7 ft, b= 13 ft and height = 5 ft.

Here, area of trapezium = 1/2 (Sum of parallel sides)×Height

= 1/2 ×(7+13)×5

= 1/2 ×20×5

= 50 square feet

Dimensions of triangle are base = 8 ft and height = 6 ft

Area of a triangle = 1/2 ×8×6

= 24 square feet

Therefore, the area of a triangle is 24 square feet and the area of a trapezium is 50 square feet.

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The probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.

If the student randomly orders the events, there is only one correct order out of all possible permutations.

Hence, the likelihood of selecting the accurate sequence is equal to 1 over the total count of potential arrangements.

As there are 5 occurrences, the overall count of conceivable sequences is equivalent to 5 factorial (5!), amounting to 120.

Therefore, the probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.

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On an exam, students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. What is the probability that the student chooses the correct order?

The total invoice is $788.80, we find this by find the cost of each item.

To find the invoice total, we need to calculate the total cost of each item.

For the tablecloth:

Quantity: 16

Unit Price: $35.00

Total Cost = Quantity × Unit Price = 16 × $35.00 = $560.00

For the rings:

Quantity: 8

Unit Price: $6.50

Total Cost = Quantity × Unit Price = 8 × $6.50 = $52.00

For the cups (cases):

Quantity: 4 cases

Unit Price: $25.30

Total Cost = Quantity × Unit Price = 4 × $25.30 = $101.20

For the bowls:

Quantity: 12

Unit Price: $6.30

Total Cost = Quantity × Unit Price = 12 × $6.30 = $75.60

Now, let's calculate the invoice total by adding up the total costs of each item:

Invoice Total = $560.00 + $52.00 + $101.20 + $75.60

= $788.80

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The coordinates of the Triangle RST after it is translated 4 units down and 3 units to the left is the option;

R¢(-7, -2), S¢(2, -1), T¢(-1, -9)

A translation transformation is one in which the location of the pre-image is transformed from its initial location to the destination location.

The coordinates of the vertices of the triangle RST are; R(-4, 2), S(5, 3), T(2, -5)

The translation transformation that is applied on the triangle RST includes;

A vertical translation 4 units downwards

An horizontal translation 3 units to the left

The translation transformation is therefore; T₍₋₃, ₋₄₎

Therefore, applying each transformation, we get;

R(-4, 2) ⇒ T₍₋₃, ₋₄₎ ⇒ R¢(-4 -3, 2 - 4) = R¢(-7, -2)

S(5, 3) ⇒ T₍₋₃, ₋₄₎ ⇒S¢(5 - 3, 3 - 4) = S¢(2, -1)

T(2, -5) ⇒ T₍₋₃, ₋₄₎ ⇒ T¢(2 - 3, -5 - 4) = T¢(-1, -9)

The correct option is therefore, the first option

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Two equivalent expressions for the given expression 14(8 - 16x) + 3x are 112 - 221x and 112 - 221x.

Equivalent expression 1:

Expanding the expression 14(8 - 16x) and combining like terms, we get:

112 - 224x + 3x

Simplifying further, we have:

112 - 221x

Equivalent expression 2:

Distributing the coefficient 14 to both terms inside the parentheses, we have:

112 - 224x + 3x

Combining the terms with the same variable, we get:

112 - 221x

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"dom(R) ⊂ UU R" means that the domain of relation R is a subset of the universal set associated with relation R

The notation "dom(R) ⊂ UU R" refers to the domain of a relation R being a subset of the universal set U.

Let me help you to break it down

1. dom(R): This represents the domain of the relation R. The domain of a relation is the set of all elements that appear as the first component in any ordered pair of the relation.

2. ⊂: This symbol indicates a subset relationship, meaning that the set on the left-hand side is a subset of the set on the right-hand side. In this case, "dom(R) ⊂ U" implies that the domain of relation R is a subset of the universal set U.

3. "UU R": The term "UU R" likely represents the universal set associated with relation R. It indicates the set that contains all possible elements that can be related by R.

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Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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Answer:

1.55

Step-by-step explanation:

2/9=0.22 x 7 =1.55

i hope this helps!

Answer:

A)19.0

B)10.0

Step-by-step explanation:

Using [tex]\frac{1}{2} * absin(C)[/tex]

This is used when you have an angle between two sides

Kindly check the attached image for the solution

Answer:

25%

Step-by-step explanation:

9+3=12 dance people total

divide 3 by 12 to determine debate members over dance members

=.25 or 25%

The sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.

To determine the sequence of transformations that maps triangle ABC onto triangle A'B'C', let's analyze the given coordinate points.

Triangle ABC:

A (-4, 4)

B (-8, 2)

C (-6, -6)

Triangle A'B'C':

A' (4, -2)

B' (2, 2)

C' (6, 0)

By comparing the corresponding vertices, we can identify the transformations:

Translation:

To transform A to A', we can observe that A' is obtained by moving 8 units to the right and 6 units downwards from A. Therefore, the first transformation is a translation by (+8, -6).

Reflection:

Next, we notice that B' is the reflection of B across the y-axis. Thus, the second transformation is a reflection about the y-axis.

Therefore, the sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.

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The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.

To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.

Break down the motion into its components:

1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.

2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.

To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:

AC² = AB² + BC²

AB (paddling east) = 10 mph

BC (wind blowing south) = -5 mph (negative sign due to opposite direction)

AC² = (10 mph)² + (-5 mph)²

AC² = 100 mph² + 25 mph²

AC² = 125 mph²

Taking the square root of both sides:

AC ≈ √(125) mph

AC ≈ 11.2 mph (rounded to the nearest tenth)

Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.

The correct answer is option C: 11.2 miles per hour.

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Answer:

Length of third side = 30 inches

Step-by-step explanation:

We will need a system of equations to find the length of the third side.

First equation:

We know the perimeter of a triangle is simply the sum of its sides.

Thus, since the perimeter is 45, our first equation is x + x + y = 45, which simplifies to 2x + y = 45.

Second equation:

Since we're told that the length of the third side is twice as long as the sum of the congruent sides, our second equation is y = 2(x + x), which simplifies to y = 2(2x) and then finally y = 4x

Method:  Substitution.

We can first solve for x (length of one of the congruent sides) by substituting y = 4x for y in 2x + y = 45:

2x + 4x = 45

6x = 45

x = 7.5

Find y:

Now we can find y (length of the third side) by plugging in 7.5 for x in y = 4x:

y = 4(7.5)

y = 30

Thus, the length of the third side is 30 inches.

Optional Step to check validity of answers.

First equation:  Check that the sum of 7.5, 7.5, and 30 = 45

7.5 + 7.5 + 30 = 45

15 + 30 = 45

45 = 45

Second equation:  Check that 30 is twice the sum of 7.5 + 7.5

30 = 2(7.5 + 7.5)

30 = 2(15)

30 = 30

Thus, our answers are correct and we've correctly determined the length of the third side of the triangle in inches.