2. compare articles i, ii, and iii. rank them in order of length and detail. which is the longest? speculate as to why this is the case.

The volume of the composite shape is

Volume is a measure of three-dimensional space.

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

The shape above shows two cuboid joined together.

volume of the base cuboid = lbh

= 6×3×1 = 18ft³

Volume of the second cuboid = lbh

= 4×3×8 = 96 ft³

volume of the composite shape = 18ft³ + 96ft³

= 114 ft³

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Answer:

Step-by-step explanation:

WX length = Square root 13                                                                                             Slope of WX=-2/3 or -2 divided by 3                                                                  YZ length= Square root 13                                                                                  Slope for YZ= 2 divided by -3 or 2/-3                                                                              Part C should be A since parallel means that they have the same slope and they are congruent side lengths so, hopefully im right? Theorem 7.12 proves it

Answer:

The situation that can be represented by the sum 5.25 ÷ (-1.35) is:

C. Before heating a solution, a scientist measured its temperature to be 5.25 *F. The scientist stopped heating the solution after 1.35 hours. The sum represents the final temperature of the solution.

The possible value of angle X, to the nearest degree is 78°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔXYZ, x = 300 cm, z = 290 cm and ∠Z=109°.

Here, sinX/x=sinZ/z

sinX/300 = sin109°/290

sinX/300 = 0.9455/290

sinX/300 = 0.00326

sinX=0.00326×300

sinX=0.978

∠X=78°

Therefore, the possible value of ∠X, to the nearest degree is 78°.

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Answer:

The number of daisies in the garden is 25 x 60% = 15 flowers.

Step-by-step explanation:

The solution for the number of daisies in the garden is found by multiplying the total number of flowers by the proportion that are daisies.

25 flowers * 60% daisies = 15 daisies

So, there are 15 daisies in the garden.

Answer: Let's call the hourly rate for regular work as "r" and the hourly rate for overtime work as "o".

From the information given, we know that 80 hours of regular work earned Andrew 80 * r = $920.65.

And we also know that 5 hours of overtime work earned him 5 * o = $109.80.

So, combining the two amounts, we have:

80 * r + 5 * o = $1030.45

Now, we can substitute the first equation into the second:

80 * r + 5 * o = $1030.45

80 * r = $920.65

80 * r + 5 * o = $1030.45

5 * o = $1030.45 - $920.65

5 * o = $109.80

Finally, we can solve for the hourly rate of overtime work:

o = $109.80 / 5

o = $21.96/hour

Step-by-step explanation:

Answer:

For the inequality [tex]x \leq 3[/tex], there were no pictures so I created my own number line, check the picture:

Hope it helps! <3

Step-by-step explanation:

Therefore , rounding to the nearest fraction whole number, we would expect about 1696 visitors to purchase exactly one costume next week.

An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction.

Here,

Out of 112 visitors to the website (9 + 95 + 8), 95 purchased exactly one costume.

So the proportion of visitors who purchased exactly one costume is:

95/112 ≈ 0.848

To estimate how many visitors out of 2000 would purchase exactly one costume, we can multiply the proportion by 2000:

0.848 x 2000 ≈ 1696

Rounding to the nearest whole number, we would expect about 1696 visitors to purchase exactly one costume next week.

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Answer: To determine if a set of dimensions is possible for the container, we need to check if it satisfies both the inequality h > 0.3r^2 and the two constraints.

A) radius = 21 inches, height = 21 inches:

The inequality h > 0.3r^2 is satisfied (21 > 0.3 * 21^2).

The height must be no more than 15 inches greater than the radius (21 - 21 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is not satisfied (pi * 21^2 < 36pi).

So, option A is not a possible set of dimensions.

B) radius = 8 inches, height = 21 inches:

The inequality h > 0.3r^2 is satisfied (21 > 0.3 * 8^2).

The height must be no more than 15 inches greater than the radius (21 - 8 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is satisfied (pi * 8^2 >= 36pi).

So, option B is a possible set of dimensions.

C) radius = 7 inches, height = 23 inches:

The inequality h > 0.3r^2 is satisfied (23 > 0.3 * 7^2).

The height must be no more than 15 inches greater than the radius (23 - 7 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is not satisfied (pi * 7^2 < 36pi).

So, option C is not a possible set of dimensions.

D) radius = 9 inches, height = 18 inches:

The inequality h > 0.3r^2 is not satisfied (18 <= 0.3 * 9^2).

The height must be no more than 15 inches greater than the radius (18 - 9 <= 15), which is not satisfied.

So, option D is not a possible set of dimensions.

Therefore, the only possible set of dimensions is B) radius = 8 inches, height = 21 inches.

Step-by-step explanation:

Since the corresponding sides are not proportional, we can say that the triangles are not similar

In similar triangles, corresponding sides are always in the same ratio.

Given are two triangles ΔWUV and ΔXZY.

It is given that -

VW = 60     ZY = 48     YX = 40     VU = 50     UW = 40     XZ = 32

For the triangles to be similar, the corresponding sides will be proportional.

WU/XZ = UV/ZY = WV/XY

40/32 = 50/48 = 60/40

1.25 ≠ 1.044 ≠ 1.5

The corresponding sides are not proportional.

Therefore, since the corresponding sides are not proportional, we can say that the triangles are not similar.

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Sally has 20 water bottles he gives 10 to jerry, then final count of water bottles that Sally has is 10.

What is the addition?

The addition is the process of adding two or more numbers together to get their sum. Addition in math is a primary arithmetic operation, used for calculating the total of two or more numbers. For example, 7 + 7 = 14.

We have given,

sally has 20 water bottles he gives 10 to jerry how many does sally have left?

Sally originally had 20 water bottles.

When she gives 10 water bottles to Jerry, she will have 20 - 10 = 10 water bottles left.

Therefore, the final count of water bottles that Sally has is 10.

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When travelling at 70 mph over a road with a sinusoidal surface, an automobile crosses its peak 1.9556 times every second.

The relation between rectangle side angles and the lengths is examined in the mathematics branch known as trigonometry. The application of geometries in astronomical study gave rise to the county's first appearance in the Hellenistic era, roughly in the third centuries BC. Exact approaches mathematics concentrate on certain right triangle and how they could be applied to calculations. In trigonometry, there are six well-known trigonometric expressions. They are known by their various names and acronyms: sine, cosine, parallel, cotangent, cotangent, and cosecant (csc). The features of all geometric forms are studied in geometry.

given

first convert 40 miles per hour (mph) into feet per second (fps):

1 mile is equal to 5280 feet, and a speed of 40 miles per second is equal to 3600/405280, or 58.6667 feet per second.

Second, determine how many times per second the car will pass a bump:

The vehicle crosses a sinusoidal road with a period of 30 feet, where

P = 30 feet frequency

speed/P = 30/58.667 = 1.9556 times per second.

When travelling at 70 mph over a road with a sinusoidal surface, an automobile crosses its peak 1.9556 times every second.

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According to the table, the values of g(x) are 2 units lower than the corresponding values of f(x).

Translation of functions

When a function is transferred without undergoing any form or rotation changes, it has been "translated." A function may be translated both horizontally and vertically.

According to the question;

The table that illustrates function g(x) is; when the function f(x) is shifted vertically down by 2 units to obtain function g

x = 0, 1, 2, 3

g(x) = -2, 0, 6, 24

By shifting the function f vertically down by 2 units, the function g(x) is produced.

Note that the relationship between the functions g and f is as follows:

g(x) = f(x) -2

Therefore, as seen in the above table, the values of g(x) are 2 units fewer than the corresponding values of f(x).

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Based on the following given inequality; the symbol will be reversed when the variable is isolated

The condition for the symbol of an inequality to be reversed is;

if the variable is isolated and a negative number is used to divide.

The symbols of inequality are;

Greater than >

Less than <

Greater than or equal to ≥

Less than or equal to ≤

Equal to=

–10.5 < 3a

a < -10.5/3

a > -3.5

Yes

b6 ≤ 7

b ≤ 7/6

b ≤ 1.17

No

–4.5c > 9

c > 9/-4.5

c < -2

Yes

–215 ≤ –52d

d ≤ -215 / -52

d ≤ 4.14

No

Hence, the symbol will be reversed when the variable is isolated if the result of the division is negative.

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Answer:

a. 3 heures

b. 3 km

Step-by-step explanation:

a. Pour parcourir 18 km, un randonneur met 18 km / 6 km/h = 3 heures.

b. Pour parcourir une distance en 30 minutes, la vitesse est de 18 km / 3 heures = 6 km/h, donc la distance parcourue en 30 minutes est 6 km/h * 30 min / 60 min = 3 km.

One element within an experiment that allows you to increase the level of certainty in your results and account for random events is the use of a control group.

Level of certainty refers to the degree of confidence or assurance that one has in the accuracy of a particular result, decision, or conclusion. In scientific research, the level of certainty is often expressed as a probability or as a confidence interval, which provides a range of values that are expected to contain the true value with a certain degree of confidence. A higher level of certainty indicates a greater level of confidence that the result is correct, while a lower level of certainty indicates more uncertainty or ambiguity. Factors that can affect the level of certainty in an experiment or measurement include the quality of the data, the size of the sample, the accuracy of the methods used, and the presence of random or systematic errors.

By having a control group, you can compare the results of the experiment against a baseline and isolate any changes caused by the independent variable. Additionally, using a large sample size and repeating the experiment multiple times can also help increase the level of certainty and account for random events.

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The situation that can be modeled by a linear function is:

An amusement park allows 50 people every 30 minutes

Option 3 is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A linear function is a function in the form of f(x) = mx + c.

Now,

1)

The population of bacteria triples every day.

This can be written as a function,

f(x) = M x [tex]3^x[/tex]

Where M is the initial number of bacteria and x is the number of days.

This is an exponential function.

2)

The value of cell phones depreciates at a rate of 3.5% each year.

This can be written as a function,

f(x) = M x [tex]96.5^x[/tex]

Where M is the initial value and x is the number of years.

This is an exponential function.

3)

An amusement park allows 50 people every 30 minutes.

This can be written as a function,

f(x) = 50x

Where x is the number of times of 30 minutes.

This is a linear function.

4)

A baseball tournament eliminates half of its teams after each round.

This can be written as a function,

f(x) = M x [tex](1/2)^x[/tex]

Where x is the number of rounds.

This is an exponential function.

Thus,

An amusement park allows 50 people every 30 minutes can be modeled by a linear function.

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Answer:

56in.²

Step-by-step explanation:

the given figure can be divided into three parts .

( see attachment)

Finding area of I

Area = 7*4

Area = 28 in.²

Area of II

Area = 5 * (7-3) = 5*4

Area = 20 in.²

Area of III

area = 1/2 * 4*4

area = 8in.²

Total area [ 28 + 20 +8] in.² = 56in.²

The measures of both pairs of opposite sides are equal in length using the properties of rotations.

What is rotation?

In mathematics, a rotation is a transformation that spins a shape around an immovable object.

We are given that M is the midpoint of the diagonals.  

Since, M is the midpoint of the diagonals, so, VM = MQ and TM = MN.

Since T and N are equidistant from M, and the measure of ∠TMN = 180°, So, r(180°, M)(T) = N

Similarly, r(180°, M)(V) = Q  

We can rotate every point on TV in this same way.

So,  r(180°, M)(TV) = QN

Similarly, r(180°, M)(TQ) = VN  

Since, the rotations are rigid motions and they preserve distance, so, TV=QN and TQ=VN.

Hence, the measures of both pairs of opposite sides are equal in length.

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In the question, the figure is missing which is attached below

Answer:

showed below

Explanation:

you can start by plotting a dot at (2,0), since the line must go through that point. Since m, the slope, is -2, you can re-write this into a fraction to make it easier, looking like this: -2/1. Slope in general can be written as “rise over run” or “rise/run”, so the numerator is how far you go up on the graph, while the denominator is how far you go over. In this case, the slope is negative, so instead of up and right, the line goes down and right. From (2,0) you would go down by 2, and right by one. At that point you polar another dot. That point is (3,-2). From there, you can take a straight edge and line it up with the two dots and draw your line. It looks like what is in the picture.

Answer:

Rotation

Step-by-step explanation:

Answer: Rotation

Step-by-step explanation:

rotation by 180 degrees is (x,y) => (-x,-y)

Looking at some of the points on A like (-1,-1) we can see B has a point on (1,1) and (-6,-2) B has a point on (6,2) and so on

In this particular study, Selection bias, Response bias, non response bias and Self-selection bias may exist.

There are several biases that may exist in the study:

1. Selection bias: By only calling people whose names were randomly sampled from the phone book, the study may not accurately represent the population of the state as a whole. Mobile phones and unlisted numbers, which may represent a significant portion of the population, are not included in phone books and therefore not included in the sample.

2. Response bias: The study only includes people who answered the phone when the senator's office called. This means that the sample only represents people who were available and willing to participate in the study. People who were not available or unwilling to participate may have different opinions, which would introduce a response bias.

3. Nonresponse bias: People who did not answer the phone when the senator's office called may have different opinions than those who answered. This nonresponse bias can result in an overestimation or underestimation of the true population values.

4. Self-selection bias: By only calling people who answered the phone, the study may only represent those who are interested in politics or are more likely to participate in political surveys. This self-selection bias can result in an overestimation or underestimation of the true population values.

These biases can lead to inaccurate results and conclusions. To reduce these biases, it's important to use a representative sample of the population and to make sure that the sample is selected in a way that minimizes bias

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Answer: 1,000 to 40,300

Step-by-step explanation:  Every major league stadium will let in fans to start the season, but capacities vary, ranging from just over 1,000 to 40,300.

The equivalent equations are:

52 = 8n + 4

4(2n + 1) = 5

4 = 52 – 8n

n = 6

Options A, B, C, and E are the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 5 is an equation.

We have,

A.

52 = 8n + 4

8n = 52 - 4

8n = 48

n = 6

B.

4(2n + 1) = 52

8n + 4 = 52

8n = 52 - 4

8n = 48

n = 6

C.

4 = 52 – 8n

8n = 52 - 4

8n = 48

n = 6

D.

4n = 48

n = 12

E.

n = 6

Thus,

The equivalent equations are:

52 = 8n + 4, 4(2n + 1) = 5, 4 = 52 – 8n, and n = 6.

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Answer:

10.39

Step-by-step explanation:

In a 30-60-90 right triangle, the ratio of the three sides are
√3 : 1 : 2

The longest side is, of course, the hypotenuse

In general, if the hypotenuse is a, The side opposite the 30° angle is a/2 and the side opposite the 60° angle is a(√3/2)

Given a = 12, y = 12/2 = 6

x =  ( √3/2) x 12 = 10.39

Answer: 0.48

Step-by-step explanation:

So the question is asking for the probability of the spinner not  landing on "C" within the 125 tries. So, we can see there are 4 possibilities:

Now, we add up how many times it landed on these 4 possibilities, which is 15 + 12 + 18 + 15 = 60.

To calculate the possibility, we divide the selected possibilities by the total amount of possibilites, which is [tex]\frac{60}{125\\}[/tex], which is equal to 0.48

The probability can you expect the spinner to not land on C is,

⇒ 0.48.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Now, the question is asking for the probability of the spinner not landing on "C" within the 125 tries.

So, we can see there are 4 possibilities:

A , A

A , B

B , A

B , B

Now, we add up how many times it landed on these 4 possibilities, which is,

⇒ 15 + 12 + 18 + 15 = 60.

Thus, To calculate the possibility, we divide the selected possibilities by the total amount of possibilities, which is;

⇒ 60 / 125

⇒ 0.48

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Answer:

(1 +a + b)(1 - a -b)

Step-by-step explanation:

1 - 2ab - (a² +b²) = 1 - 2ab - a² - b²

                           = 1 - (2ab + a² + b²)

                           = 1 - (a + b)²

                           = 1² - (a +b)²    

Identity: x² - y² = (x + y)(x - y)

                          = (1 + (a+b))(1- [a +b] )

                          = (1 +a + b)(1 - a -b)

There were 100 adult tickets sold.

When solving a system of equations with two unknowns, one of the techniques to find the unknown values is the substitution method. In this method, one equation is substituted to the other equation to achieve a final equation that contains only one of the unknowns. The value remaining unknown can be derived directly from the final equation. By substituting the first value to one of the original equations, the other unknown may be derived.

Let A be the number of adult tickets sold and S be the number of student tickets sold.

The total tickets sold is 275.

A + S = 275_________(Eq. 1)

Also, the total sales is $1025.

5A + 3S = 1,025_______(Eq. 2)

From the Equation 1

S = 275 - A     [Subtract A from both sides]

Using this value of S, substitute S in the second equation.

5A + 3(275 - A) = 1,025

5A + 825 - 3A = 1,025

2A = 200 [Subtract both sides 825]

A = 100   [Divide both sides by 2]

Hence, There were 100 adult tickets sold.

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Answer:

11:34 AM

Step-by-step explanation:

To find out the start time of the water fight, we need to subtract the total time it took from the end time.

End time: 1:08 P.M.

Total time: 1 hour and 13 minutes for water balloons + 21 minutes for hoses = 1 hour and 34 minutes

So, we subtract 1 hour and 34 minutes from 1:08 P.M.

1 hour before 1:08 P.M. is 12:08 P.M.

34 minutes before 12:08 P.M. is 11:34 A.M.

Therefore, the water fight started at 11:34 A.M.