Can someone help me I'm stuck.

Alexandria rolled a number cube 60 times and recorded her results in the table.

What is the theoretical probability of rolling a one or two? Leave as a fraction in simplest from​

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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Answer:

130,000

Step-by-step explanation:

Answer:oh hey yulissa ✌️

Step-by-step explanation:

The equation that models the area of the plate is 9h

Given that: Base of a triangular metal plate = 18 cm,

A represents the area, b represents the base, and h represents the height of the plate.

Area of a triangle = 1/2 × base × height

Area of the metal plate =  1/2 × b × h       (where b = 18 cm)

Area of the metal plate =  1/2 × 18 × h = 9 × h = 9h

Thus, 9h is the equation that models the plate

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The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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a. Corrugated Steel Pipe: Assess corrosion, deformation, and blockage; evaluate structural integrity and hydraulic capacity. b. Culvert: Inspect foundations, structural elements, and hydraulic capacity; evaluate cracking, corrosion, erosion, and blockage. c. Retaining Wall: Inspect for cracks, leaning, displacement, and structural stability. d. Pedestrian Bridge: Evaluate structural integrity, deterioration signs, and functionality. e. Highway Bridge: Perform comprehensive inspection of substructure, superstructure, deck, and components; evaluate structural condition, fatigue, corrosion, and deficiencies.

To assess the Bridge Condition Index (BCI) and Criticality Rating for various structures, we need to follow a systematic process. However, please note that the OSIM (Operating and Supportability Implementation Plan) form you mentioned is not a standard industry form for bridge condition assessment. Here's how you can evaluate the BCI and Criticality Rating for each structure:

a) Corrugated Steel Pipe:

b) Culvert:

c) Retaining Wall:

d) Pedestrian Bridge:

e) Highway Bridge:

Once you have conducted the assessments for each structure, you can assign a BCI score to represent their overall condition. The scoring system may vary depending on the specific assessment guidelines used by the bridge management authority or engineering standards in your country.

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Finite-state machines for given inputs: (a) 0s multiple of 3: 3-state machine. (b) At least four 1s: 4-state machine. (c) Exactly one 1: 2-state machine. (d) Begins with 000: 3-state machine. (e) Second is 0, fourth is 1: 4-state machine. (f) 01 pairs or 2 1s + 0s: 3-state machine. (g) Ends in 110: 3-state machine.

To construct finite-state machines that act as recognizers for the given inputs, we can follow these guidelines:

(a) For the set of all strings where the number of 0s is a multiple of 3, we can use a finite-state machine with three states. Start with the initial state, and transition to the next state whenever a 0 is encountered. After three transitions, go back to the initial state. If the machine ends in the accepting state, output 1.
(b) For the set of all strings containing at least four 1s, we can use a finite-state machine with four states. Start with the initial state, and transition to the next state whenever a 1 is encountered. If the machine enters the final state after four transitions, output 1.

(c) For the set of all strings containing exactly one 1, we can use a finite-state machine with two states. Start with the initial state and transition to the final state when the first 1 is encountered. Output 1 only if the final state is reached.

(d) For the set of all strings beginning with 000, we can use a finite-state machine with three states. Start with the initial state and transition to the next state whenever a 0 is encountered. If the machine reaches the final state after three transitions, output 1.

(e) For the set of all strings where the second input is 0 and the fourth input is 1, we can use a finite-state machine with four states. Start with the initial state and transition to the next state based on the inputs. Output 1 only if the machine reaches the final state.

(f) For the set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two 1s followed by any number (including none) of 0s, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

(g) For the set of all strings ending in 110, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

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Finite-state machines (FSMs) can be constructed to act as recognizers for specific patterns in input strings. These are examples of how to construct FSMs as recognizers for different patterns in input strings. Each FSM is designed to produce an output of 1 when the input received matches the description provided.

Let's consider the given cases and construct FSMs for each one.

(a) The set of all strings where the number of Os is a multiple of 3:
To construct an FSM for this, we can keep track of the number of Os encountered so far. Initially, set the count to zero. When an O is encountered, increment the count by one. If the count becomes a multiple of 3, the FSM outputs 1; otherwise, it outputs 0. Reset the count to zero whenever a 1 is encountered.

(b) The set of all strings containing at least four 1s:
To create an FSM for this, we can keep track of the number of 1s encountered so far. Initially, set the count to zero. When a 1 is encountered, increment the count by one. If the count becomes equal to or greater than four, the FSM outputs 1; otherwise, it outputs 0.

(c) The set of all strings containing exactly one 1:
To build an FSM for this, we can have two states: a "no 1 encountered" state and a "1 encountered" state. Initially, start in the "no 1 encountered" state. Whenever a 1 is encountered, transition to the "1 encountered" state. If another 1 is encountered in the "1 encountered" state, transition to a third "more than one 1 encountered" state. In this case, the FSM outputs 0. Otherwise, if no additional 1s are encountered, the FSM outputs 1.

(d) The set of all strings beginning with 000:
To create an FSM for this, start in an initial state. When a 0 is encountered, transition to a second state. If two consecutive 0s are encountered in the second state, transition to a third state. Finally, if a third 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

(e) The set of all strings where the second input is 0 and the fourth input is 1:
To construct an FSM for this, start in an initial state. When the first input is read, transition to a second state. In the second state, transition to a third state if the second input is 0. In the third state, transition to a fourth state if the third input is not 0. Finally, in the fourth state, if the fourth input is 1, the FSM outputs 1; otherwise, it outputs 0.

(f) The set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two Is followed by any number (including none) of Os:
To create an FSM for this, we can have multiple states to represent different scenarios. We start in an initial state and transition to a second state when a 0 is encountered. In the second state, transition back to the initial state if a 1 is encountered. If a 1 is encountered in the initial state, transition to a third state. In the third state, transition to a fourth state if an O is encountered. Finally, if an O is encountered in the fourth state, the FSM outputs 1; otherwise, it outputs 0.

(g) The set of all strings ending in 110:
To construct an FSM for this, start in an initial state. Transition to a second state if a 1 is encountered. In the second state, transition to a third state if a 1 is encountered again. Finally, if a 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

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Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

Step-by-step explanation:

Step one:

given

original price= $60

discount =20% of 60

discount = 20/100*60

discount = 0.2*60

discount = $12

selling price= 60-12= $48

Added price= 10% off $48

Added price= 10/100 *48

Added price= 0.1 *48

Added price= $4.8

new price= 4.8-48=$43.2

the new price of the jacket is $43.2

1. The jacket is now 40% off its original price

40/100*60=$24-----False

2. The jacket now costs $48.00-----False

3.  The jacket is now 72% of its original price= 72/100*60=$43.2----True

4. The jacket now costs $43.20------True

Each side of cube is 100 cm.

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

Given that,

Volume of cube = 1 cubic meter

We know that,

1 m = 100 cm

Also  volume of cube = \(a^{3}\)

Then,

Volume of cube = 1000000 cm

                   \(a^{3}\)  = \(100^{3}\)

                   a = 100 cm

Hence, Each side of cube is 100 cm.

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If a function f contains a local extremum at point c but is not differentiable at c, the correct statement is that the derivative \(f'(c)\) does not exist.

When a function has a local extremum at point c, it means that the function reaches a maximum or minimum value at that point within a certain interval. Typically, at these local extremum points, the derivative of the function is zero. However, this assumption is based on the function being differentiable at that point.

If a function is not differentiable at point c, it implies that the function does not have a well-defined derivative at that specific point. This can occur due to various reasons, such as sharp corners, vertical tangents, or discontinuities in the function. In such cases, the derivative cannot be determined.

Therefore, if f contains a local extremum at c but is not differentiable at c, the correct statement is that the derivative \(f'(c)\) does not exist. This aligns with option D in the given choices. It is important to note that while \(f'(c)\) is typically zero at a local extremum for differentiable functions, this does not hold true when the function is not differentiable at that point.

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Answer:

\(\frac{6}{25}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Exhaustive\ number, n(S)=25}\\\mathrm{Favorable\ cases (E)={[(1,1),(2,2),(3,1),(1,3),(1,2),(2,1)]}}\\\mathrm{No.\ of\ favorable\ cases,n(E)=6\\}\\\therefore \mathrm{Probability\ of\ getting\ total\ of\ less\ than\ 5=\frac{n(E)}{n(S)}=\frac{6}{25}}\)

Answer:

The answer is 35:19

Step-by-step explanation:

First what is a ratio?

A relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4. A ratio can also be expressed as a decimal or percentage.

So as a result

= There are 35 mangoes and 19 strawberries

And since we are comparing mangoes to strawberries

The answer would be

= 35:19

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The lower limit for the standard deviation is always 0, while the upper limit depends on the data and its distribution.

The standard deviation is a measure of the spread or dispersion of a set of data. It is defined as the square root of the variance, which is the average of the squared differences between each data point and the mean of the data. Since the variance involves squaring the differences, it is always positive or zero. Therefore, the standard deviation cannot be negative and has a lower limit of 0.

The upper limit of the standard deviation depends on the data and its distribution. In general, the standard deviation cannot be greater than the range of the data, which is the difference between the maximum and minimum values. For example, if the range of the data is 10 and the standard deviation is 15, then there must be an error or some issue with the data.

However, in some cases, the standard deviation can be much larger than the range of the data. This can happen if the data is highly skewed or has outliers. Skewed data is when the distribution of the data is not symmetrical, and most of the data falls on one side of the mean. In this case, the standard deviation may be much larger than the range of the data, as it takes into account the extreme values.

Outliers are data points that are much larger or smaller than the rest of the data. They can have a significant effect on the standard deviation, as they increase the variability of the data. In some cases, outliers may be errors or anomalies that should be removed from the data set before calculating the standard deviation.

In summary, the lower limit of the standard deviation is always 0, while the upper limit depends on the data and its distribution. In general, the standard deviation cannot be greater than the range of the data, but it can be much larger if the data is highly skewed or has outliers. It is important to consider the context of the data and any potential issues before interpreting the standard deviation.

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Answer:

drawing the graph of \(f(g(x))=\sqrt{|x|}\)

The graph is attached in the images below.

Option A is correct option.

Step-by-step explanation:

We are given:

\(f(x)=\sqrt{x}\) and \(g(x)=|x|\)

We need to find graph of  (fog)(x)

We know that (fog)(x)= f(g(x))

Placing x=g(x) i,e x=|x|

\((fog)(x)= f(g(x))\\f(g(x))=\sqrt{|x|}\)

Now, drawing the graph of \(f(g(x))=\sqrt{|x|}\)

The graph is attached in the images below.

Option A is correct option.

Answer:

The first graph

Step-by-step explanation:

A on edge

therefore the correct answer is c

Answer:

A. The number of days one works out each week.

Step-by-step explanation:

Frequency regarding physical fitness means how frequently you work out each week. Frequency in Physical Fitness is usually measured in days and not weeks. I took the test on K12 and this is what I got:

Explanation

We are given the measure of arc PR = 118°.

We are required to find m∠PQR.

We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:

Hence, the answer is:

But since Q is the measure of the angle, then the final answer is 118°.

We have the next given expression:

(3y+5)(3y+4)

Simplify the expression:

(3y+5)(3y+4) = 3y*3y+*3y*4+*5*3y+5*4

= 9y²+12y+15y+20

=9y²+27y+20

Hence, the expression is a trinomial.

It is degree is given by the largest exponent number.

Then, the degree of the polynomial is 2.

The limit of the sequence of terms of a series is zero, this test alone does not prove that the series converges, and further testing is needed to determine convergence or divergence.

The divergence test is a test used to determine if a series converges or diverges. It states that if the limit of the sequence of terms of a series is not zero, then the series diverges.

The series 3n/(2n + 1) can be simplified to

=3/2 - 3/4n + 3/4n+1.

As n approaches infinity, the terms in the series approach 3/4n, which approaches infinity as n approaches infinity.

Therefore, the limit of the sequence of terms of this series is not zero, and so the series diverges. Thus, the answer to the question is the series diverges.

A more general form of the divergence test states that if the limit of the sequence of terms of a series is not zero, then the series diverges. However, if the limit of the sequence of terms of a series is zero, this test alone does not prove that the series converges, and further testing is needed to determine convergence or divergence.

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If the sum of two integers is 8 and their difference is 6, the integers that we are talking about are 1 and 7

Let the first integer be x

the second integer be y

According to the question,

Sum = 8

x + y = 8 ----- (i)

Difference = 6

x - y = 6 -------(ii)

Add equations (i) and (ii)

2x = 14

x = 14/2

x = 7

Put the above in (i)

7 + y = 8

y = 8 - 7

y = 1

Thus, the integers in the question are 1 and 7

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Answer:

6 hours

Step-by-step explanation:

292-70=222

222/37=6

Answer:i think its 115 degres

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a - b)² = a² + 2ab + b²

Area of square frame =side²

                                   = (2b - 1)²

                                   = (2b)² - 2*2b * 1 + 1²

                                   = 4b² - 4b + 1

Answer:

12 hours

Step-by-step explanation:

79=7x-5

79+5=7x

84=7x

84/7=7x/7

12=x

Answer: 5(4x² + 4x + 1)

Assuming it wants us to simplify it:

Find the common multiple all the numbers have. You can see both 20s have an x but 5 doesnt, so we cannot take that out. However, 5 and 20 are in the 5 times table, So we can take that out and put it outside a bracket.

You then divide 20x², 20x and 5 by 5, which gives us:

5(4x²+4+1)

Since this cannot be simplified any further, this is the answer.

Assuming it wanted us to factorise this.

Answer:

Step-by-step explanation:

The value of X would be 18

x=18

Answer:

14/42, 56/168, 77/231, ...

Step-by-step explanation:

By multiplying both the nominator and the denominator by a same number, we get a different fraction but is equal to the fraction at the start.

7/21 = 7x2/21x2 = 14/42
7x8/21x8 = 56/168
7x11/21x11=77/231

Hope this helps :)

Answer:

\(\frac{3}{20}\)

Step-by-step explanation:

Well you can represent percentages as decimals, by dividing the percentage by 100. This gives us the fraction: \(\frac{15}{100}\)

We can simplify the fraction, by dividing both the numerator and denominator by 5

\(\frac{15}{100}=\frac{15\div5}{100\div5}=\frac{3}{20}\)

Answer:

87.5 scarves in 5 hours

Step-by-step explanation:

35 divided by 2 is 17.5.

17.5 scarves each hour

17.5 multiplied by 5 is 87.5

Answer: 87.5 scarves

Step-by-step explanation:

5 divided by 2 is 2.5

35x2.5=87.5