The data table to the right represents the volumes of a generic soda brand Volumes of soda (oz) 65 80 70 75 70 85 80 75 70 75 65 70 Complete parts (a) through (c) below 508:5 a. Which plot represents a dotplot of the data? 50 60 70 80 9 50 60 70 80 9 Volumes of soda (oz) Volumes of soda (oz) Oc. 50 60 70 80 90 50 60 70 80 9 Volumes of soda (oz) Volumes of soda (oz) b. Does the configuration of the points appear to suggest that the volumes are from a population with a normal distribution? A. Yes, the population appears to have a normal distribution because the dotplot resembles a "bell shape B. No, the population does not appear to have a normal distribution because the frequencies of the volume decrease from left to right. C. No, the population does not appear to have a normal distribution because the dotplot does not resemble a "bell" shape D. Yes, the population appears to have a normal distribution because the frequencies of the volume increase from left to right. c. Are there any outliers? A. Yes, the volumes of 0 oz and 200 oz appear to be outliers because they are far away from the other temperatures O B. No, there does not appear to be any outliers ° C. Yes, the volume of 50 oz appears to be an outlier because it is far away from the other volumes ( D. Yes, the volume of 70 oz appears to be an outlier because many sodas had this as their volume

The triangle congruency postulate that proves both triangles are congruent is: SSS

There are different triangle congruence postulates such as:

SSS: This denotes Side Side Side Congruency Postulate

SAS: Side angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

Now, from the given two triangles, we can see the following:

BC ≅ UW

AC ≅ UV

AB ≅ VW

Thus, the three sides are congruent and as such it is congruent by SSS congruency postulate

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The five number summary is: Minimum: 60 Q1 (first quartile): 63 ,Median: 70Q3 (third quartile): 75, Maximum: 79

To find the five number summary of the data set 72, 60, 64, 75, 79, 63, 70, 61, 78, follow these steps:

1. Arrange the data in ascending order: 60, 61, 63, 64, 70, 72, 75, 78, 79

2. Identify the minimum value (smallest number): 60

3. Identify the maximum value (largest number): 79

4. Calculate the median (middle number): There are 9 data points, so the median is the 5th number: 70

5. Calculate the first quartile (Q1): The lower half of the data set is 60, 61, 63, 64, 70. The median of this lower half is the

middle number, which is 63.

6. Calculate the third quartile (Q3): The upper half of the data set is 70, 72, 75, 78, 79. The median of this upper half is

the middle number, which is 75.

The five number summary is:

Minimum: 60

Q1 (first quartile): 63

Median: 70

Q3 (third quartile): 75

Maximum: 79

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Answer:

x^2 + 7x - 18 = (x + 9)(x - 2)

The difference between length and width is x + 9 - (x - 2) = x + 9 - x + 2 = 11.

After answering the provided question, we can conclude that As a result, equation the cost of 2 pounds of candy is $7.00.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9"[/tex] asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Claim: To calculate the cost of 2 pounds of candy, multiply the cost per pound of candy by 2.

According to the data provided, the cost per pound of candy is $3.50.

Reasoning: In order to determine the cost of 2 pounds of candy, we must first determine the total cost of 2 pounds of candy. Because the price per pound of candy is $3.50, we can calculate the total cost by multiplying the price per pound by the number of pounds. In this case, we want to know how much it costs for two pounds, so we multiply $3.50 by two to get:

2 pounds of candy = $3.50 per pound x 2 pounds = $7.00

As a result, the cost of 2 pounds of candy is $7.00.

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The range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

To find the range of the function f(x) = x + 3, we need to apply the function to each value in the given domain and collect the resulting outputs.

When the domain is {-1, 3, 5, 7}, we have:

f(-1) = -1 + 3 = 2

f(3) = 3 + 3 = 6

f(5) = 5 + 3 = 8

f(7) = 7 + 3 = 10

Therefore, the range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

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The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

What is the Pythagorean theorem?

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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Answer:

[tex]{ \colorbox{lightgreen}{can \: be \: simplified}} \\ \dashrightarrow \: { \sf{ \blue{9x + 6x}}} \: \: \: \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \: \: \: \\ { \sf{ = (9 + 6)x}} \\ { \underline{ \sf{ \: = 15x \: \: \: \: \: \: \: \: \: \: }}} \\ \\ \dashrightarrow \: { \sf{ \blue{4x + x}}} \: \: \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (4 + 1)x}} \\ { \underline{ \sf{ \: = 5x \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \\\dashrightarrow \: { \sf{ \blue{y + 2y}}} \\ \hookrightarrow \: { \mathfrak{simplification}} \\ { \sf{ = (1 + 2)y}} \\ { \underline{ \sf{ \: = 3y \: \: \: \: \: \: \: \: \: \: \: \: }}}[/tex]

[tex]{ \colorbox{lightgreen}{cannot \: be \: simplified}} \\ \dashrightarrow \: { \sf{2x + 3y}} \\ \dashrightarrow \: { \sf{7y + 1 \: \: }} \\ \dashrightarrow \: { \sf{4y + 4x}}[/tex]

The units digit of the 5857th triangular number is 8.

A series of numbers known as triangular numbers may be modelled as the sum of a series of positive integers. The equation Tn = (n(n+1))/2 yields the nth triangular number. The first few triangular numbers, for instance, are 1, 3, 6, 10, 15, and so on. Many mathematical and non-mathematical applications exist for triangular numbers. They can be found, for instance, in the study of geometry, combinatorics, and number theory. They are utilised in algorithms for data searching and sorting in fields like computer science, where they have practical applications.

The nth triangular number is given by the formula:

Tn = (n(n+1))/2

For the given sequence 1,3,6,10,15,21,28,36, the units digit are:

1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, ...

The value of 5857 is congruent to 7 modulo 10.

Thus, the units digit is seventh number in the cycle above, that is 8.

Hence, the units digit of the 5857th triangular number is 8.

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The total number of students in Ms. Persons class is 24.

An equation is simply a mathematical formula that expresses the equality of two expressions.

Given the data in the question:

Lets y be the number of students in the class

Hence:

[tex]75\% \ \text{of y = 18}[/tex]

[tex]\text{Lets find y}[/tex]

[tex](\dfrac{75}{100} ) \times y = 18[/tex]

[tex]75 \times y = 18 \times 100[/tex]

[tex]75 \times y = 1800[/tex]

[tex]y = 1800 \div 75[/tex]

[tex]y = 24[/tex]

Therefore, the total number of students in Ms. Persons class is 24.

Answer:

-24

Step-by-step explanation:

Hey there!

First we need to find the ratio

ratio = -6/-3 = 2

r = 2

-3, -6, -12, ? , -48

T1 = a

T2 = ar

T3 = ar²

T4 = ar³

T5 = ar⁴

And so on...

T1 means first term, T2 means second term

We're finding the fourth term which is T4

Remember T1 = a = -3

So, T4 = ar³

= -3 × 2³

= -3× 8

= -24

Therefore, the fourth unknown term is -24

You're welcome y'all

1 centimeter on the scale drawing of rectangular park represents 15 feet of the actual parking lot.

What is rectangle?

A rectangle is a four-sided flat shape with four right angles. It is a type of quadrilateral. Rectangles have opposite sides that are parallel and equal in length, and all four interior angles are right angles (90 degrees).

We know that the width of the actual parking lot is 48 feet. We also know that on the scale drawing, the width is represented by 3.2 cm. Therefore, we can set up a proportion to find out how many feet are represented by 1 centimeter on the scale drawing:

[tex]$\frac{48 \text{ feet}}{3.2 \text{ cm}} = \frac{x \text{ feet}}{1 \text{ cm}}$[/tex]

where x is the number of feet represented by 1 centimeter on the scale drawing.

We can solve for x by cross-multiplying:

[tex]$48 \text{ feet} \times 1 \text{ cm} = 3.2 \text{ cm} \times x \text{ feet}$[/tex]

Simplifying, we get:

[tex]$x = \frac{48 \text{ feet} \times 1 \text{ cm}}{3.2 \text{ cm}} = 15 \text{ feet}$[/tex]

Therefore, 1 centimeter on the scale drawing represents 15 feet of the actual parking lot.

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Answer:

3. ( 3, -1 )

Step-by-step explanation:

Answer: y=-3/4x-11

Step-by-step explanation: slope= -3/4

y+8=-3/4x+4

y+8=-3/4x-3

y=-3/4x-11

The dimensions of the final flag and the number of pieces of construction paper it took would be 9 inches tall and 18 inches long.

Three (3) pieces of  9" x 12" construction paper are needed.

First, let's find out the dimensions of the flag. The flag is twice as long as it is tall. If the height of the flag is H, then the length L would be 2H.

Since there are three equally sized vertical bars, the length of the flag would be 3 times the width of the green bar:

L = 3(18 - a)

Now, we know that L = 2H. So,

2H = 3(18 - a)

Given that the construction paper is 9" x 12", we can try to create the flag with the minimum amount of overlap a. Since the height of the flag should be equal to the short side of the construction paper, H = 9 inches.

Now we can plug in the value of H in the equation we derived above:

2(9) = 3(18 - a)

18 = 54 - 3a

3a = 36

a = 12

Now we can calculate the dimensions of the final flag:

H = 9 inches

L = 2H = 2(9) = 18 inches

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Answer: 25

Step-by-step explanation:

Let x represent the number of pages Broonzy read last night. Then, 5x represents the number of pages she will read tonight. According to her plan, after reading 5x pages tonight and 10 pages tomorrow night, she will complete the remaining 40 pages. The equation can be expressed as:

x (last night) + 5x (tonight) + 10 (tomorrow night) = 40 (total remaining pages)

Combining the terms, we get:

6x + 10 = 40

Now, let's solve for x:

6x = 30

x = 5

So, Broonzy read 5 pages last night. To determine the number of pages she needs to read tonight, we multiply x by 5:

5x = 5 * 5 = 25

Therefore, Broonzy has to read 25 pages tonight to finish her book according to her plan.

Answer: 298.41 K

Step-by-step explanation:

given from the problem: T=VPC

where C is a constant

plug in knowns to get C

294= (8000)(0.75)C

C=0.049

T=VP(0.049)

T = (7000)(0.87)(0.049)

T = 298.41 K

Answer:

Step-by-step explanation:

the measurements are a Pythagorean triple, therefore it is a right triangle, where 3 and 4 are the legs and 5 is the hypotenuse, we use the formula 1/2 × b × h

A = 1/2 × b × h.

A = 1.5 × 4

A = 6"^2

We can write this expression as a product of two factors:

(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)

HOW TO WRITE expression as a product.?

To write an expression as a product means to represent the expression as the multiplication of two or more factors. The process of writing an expression as a product depends on the type of expression and the algebraic techniques that are available.

Here are some general steps that can be followed to write an expression as a product:

Look for common factors: If there are common factors in the expression, they can be factored out using the distributive property. For example, in the expression 3x + 6, we can factor out 3 to get 3(x + 2).

Use algebraic identities: There are many algebraic identities that can be used to factor expressions. For example, the difference of squares identity (a² - b²= (a + b)(a - b)) can be used to factor expressions that are in the form of a difference of squares.

Look for patterns: Sometimes, expressions can be factored by recognizing patterns. For example, the expression x² + 2x + 1 can be factored as (x + 1)²by recognizing that it is a perfect square trinomial.

Use polynomial division: If the expression is a polynomial with higher degree, polynomial division can be used to factor it into linear and quadratic factors.

Use the quadratic formula: If the expression is a quadratic trinomial that cannot be factored easily, the quadratic formula can be used to find the roots of the equation, which can then be used to write the expression as a product of linear factors.

Overall, writing an expression as a product requires a good understanding of algebraic techniques and a lot of practice.

We can use the formula for the sum of cubes to write the expression as a product:

(a + 1) + x³ = (a + 1 + x)(a² - a x + x²) + x³

Expanding the first factor on the right-hand side using the distributive property, we get:

(a + 1 + x)(a²- a x + x²) + x^3 = a³- a² x + a x² + a² + a x + x²+ x³

Collecting like terms, we can write this expression as a product of two factors:

(a + 1)³ + x³ = (a + x + 1)(a²- a x + x² + x + a + 1)

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Answer:

31

Use Bodmas to solve it

7*3 + 10
21 +10
31

31

You can use BODMAS by arranging it multiplication comes first so 7 times 3 which is 21 so agter that addition comes next so that will be 21 plus 10 which gives 31

Answer: variables

Step-by-step explanation:

mathmeticians made this to where it would leave things out of questions, so factoring would just be your variables my guy

From a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. Therefore, the height of the flagpole is 125.6m.

we can use the trigonometric ratios of Sine, Cosine, and Tangent.

First, we need to draw a right triangle with the given information.

The triangle will have two sides:

the 100m side and the side to the flagpole. We can use the angle of elevation of 54.5 degrees to calculate the side of the triangle opposite the flagpole.

To do this, we use the Tangent ratio and solve for the side opposite the flagpole (the height of the flagpole):

Tangent(54.5) = Height/100

Height = 100*Tangent(54.5)

Height = 100*1.256

Height = 125.6m

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Answer:

-157.7

Step-by-step explanation:

Subtract 12.3 from 23 to get 10.7

10.7 - (166.4 + 2), next add 166.4 and 2 to get 168.4

10.7 - 168.4, finally subtract 168.4 from 10.7 to get -157.7

a. Sketch of a rhombus that is not a square, the line segment JK as one of its diagonals is mentioned below. b. The polygon formed , connecting the consecutive midpoints of each side of a rhombus is a rectangle.

A line segment is a part of a line that is bounded by two distinct endpoints. In geometry, a line is an infinite straight path that extends indefinitely in both directions, but a line segment is a finite portion of that path with a measurable length. The length of a line segment can be determined by measuring the distance between its two endpoints using a ruler or other measuring tool.

a. Here is a sketch of a rhombus that is not a square, using the line segment JK as one of its diagonals. I've labeled the midpoint of each side of the rhombus with M1, M2, M3, and M4:

        M2       x         M3

        .___________.  

        |                        |  

        |                        |  

   M1x          .             x  M4

        |                        |  

        |___________|  

        M4       x           M3

b. The polygon formed by connecting the consecutive midpoints of each side of a rhombus is a rectangle. To see why, let's look at the diagonals of the rhombus. Since the diagonals of a rhombus are perpendicular bisectors of each other, we know that they intersect at right angles, dividing the rhombus into four congruent right triangles. Let's call the point where the diagonals intersect P.

Now, let's look at the line segments that connect the midpoints of opposite sides of the rhombus. These line segments are parallel to each other, and each one connects two midpoints that are equidistant from the intersection point P. Therefore, these line segments are also equidistant from each other, and they divide the rhombus into four congruent rectangles.

Finally, we can see that the polygon formed by connecting the consecutive midpoints of each side of a rhombus is simply a subset of the lines that connect the midpoints of opposite sides. Since these lines form congruent rectangles, we know that the polygon formed by the midpoints is also a rectangle.

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a. Sketch of a rhombus that is not a square, the line segment JK as one of its diagonals is mentioned below.

b. The polygon formed , connecting the consecutive midpoints of each side of a rhombus is a rectangle. Whose image is attached below.

A line segment is a part of a line that is bounded by two distinct endpoints. In geometry, a line is an infinite straight path that extends indefinitely in both directions, but a line segment is a finite portion of that path with a measurable length. The length of a line segment can be determined by measuring the distance between its two endpoints using a ruler or other measuring tool.

a. Here is a sketch of a rhombus that is not a square, using the line segment JK.

b. The polygon formed by connecting the consecutive midpoints of each side of a rhombus is a rectangle. To see why, let's look at the diagonals of the rhombus. Since the diagonals of a rhombus are perpendicular bisectors of each other, we know that they intersect at right angles, dividing the rhombus into four congruent right triangles. Let's call the point where the diagonals intersect P.

Now, let's look at the line segments that connect the midpoints of opposite sides of the rhombus. These line segments are parallel to each other, and each one connects two midpoints that are equidistant from the intersection point P. Therefore, these line segments are also equidistant from each other, and they divide the rhombus into four congruent rectangles.

Finally, we can see that the polygon formed by connecting the consecutive midpoints of each side of a rhombus is simply a subset of the lines that connect the midpoints of opposite sides. Since these lines form congruent rectangles, we know that the polygon formed by the midpoints is also a rectangle.

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[tex]\text{t = total}[/tex]

[tex]\text{equation:} \ t = 25x + 50[/tex]

[tex]m=25[/tex]

[tex]\text{The slope is} \ \bold{25}[/tex]

A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.

This graph represents the solution to this inequality.

What is inequality?

An inequality in mathematics is a relation that compares two integers or other mathematical statements in an unequal way. The majority of the time, height comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

Given inequality:

(-1/4)*(12x + 8) < -2x + 11

First, we need to solve it for knowing the value of x,

So,

(-1/4)*(12x + 8) < -2x + 11

Or, -3x - 2 < -2x + 11

Or, -2 - 11 < -2x + 3x

Or, -13 < x

A ray with a red dot at minus 13, and it passes through minus 5.

Hence the correct answer is C; a straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.

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When examining the plots, only one displays a straight line going from -17 to -5 and a ray going from -13 to -5. (indicating that x can be any value greater than or equal to -13) Thus, option C is correct.

To solve the inequality, we can simplify it by first distributing the -1/4 on the left side:

[tex]-3x - 2 ≤ -2x + 11[/tex]

Next, we can isolate the variable on one side by subtracting -2x from both sides:

[tex]-x - 2 ≤ 11[/tex]

Finally, we can isolate the variable by adding 2 to both sides:

[tex]-x ≤ 13[/tex]

And since we want to solve for x, we need to multiply both sides by -1, which will flip the direction of the inequality:

[tex]x ≥ -13[/tex]

This means that x can be any value greater than or equal to  [tex]-13[/tex] .

Therefore, Looking at the graphs, the only one that shows a straight line passing from -17 to -5 and a ray starting at -13 and passing through -5 (indicating that x can be any value greater than or equal to -13)

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Answer: is it an A.P or G.P

Answer:

4.4 m

Step-by-step explanation:

Area of the wheel of a car= 1.54 m²

Area of a circle= [tex]\pi r^{2}[/tex]

                 1.54= 3.14 x r²

                     r²= [tex]\frac{1.54}{3.14}[/tex]

                     r²= 0.49

                      r= 0.7 m

Circumference of the wheel= [tex]2\pi r[/tex]

                                              = 2 x 3.14 x 0.7

                                              = 4.4 m

∴ the circumference of the wheel is 4.4 m

Step-by-step explanation:

Step 1 :

Break down the fraction with the H.C.F of the numerator and the denominator.

For instance, in Question 5 , the HCF of 20 and 8 is 4. So, 4 will go into 20 five(5) times and 4 will go into 8 two(2) times, leaving 5/2.

Step 2 :

Then 2 (denominator) will go into 5(numerator) two(2) times.

So, you'll get 2 as the whole number .

Step 3:

Multiply the denominator by the whole number (2×2) to get 4.

Then subtract 4 from 5 to get 1 and to form a proper fraction by making 1 the numerator and the 2 the denominator to get 1/ 2

Step 4 :

Then put the 2( whole number) and the 1/2 ( proper fraction) together to get the mixed fraction

Answer:

Step-by-step explanation:

irregular quadrilateral

Answer:

The name of this shape is (Irregular Pentagon)