I don’t understand how to simplify this problem.

The probability that the rolls are 1, 2, 3, 4, 5, and 6, in any order is [tex]\frac{1}{46656}[/tex].

A fair die is rolled six times.

The rolls are 1, 2, 3, 4, 5, and 6.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur. The probability of all the events in a sample space adds up to 1.

Hence there is a [tex]\frac{1}{6}[/tex] chance a 1 will be rolled first,  [tex]\frac{1}{6}[/tex] chance a 2 will be rolled second,  [tex]\frac{1}{6}[/tex] that a 3 will be rolled third, etc. Therefore the probability of the sequence appearing is  [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex]. [tex]\frac{1}{6}[/tex].

On each of the six independent rolls there is a probability of 1/6

for rolling the desired number, so by the multiplicative principle, the probability for rolling the required sequence is:

Since each sequence of six rolls is equally likely, the answer is

=[tex](\frac{1}{6} )^{6} =\frac{1}{46656}[/tex]

Therefore, the probability is [tex]\frac{1}{46656}[/tex].

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A rational number p/q has a terminating base 60 representation if q is a factor of 60. This can be proven by noting that q is a factor of p if and only if the remainder of p divided by q is 0. For any base n, q must be a factor of n in order for p/q to have a terminating base n representation.

A rational number p/q has a terminating base 60 representation if q is a factor of 60. This can be proven by noting that q is a factor of p if and only if the remainder of p divided by q is 0. This can be seen by noting that if q is a factor of p, then p can be written as a multiple of q, or p = kq, where k is an integer. Thus, p/q = k, and the remainder of p divided by q must be 0. If q is not a factor of p, then the remainder of p divided by q will not be 0. Thus, for a rational number p/q to have a terminating base 60 representation, q must be a factor of 60. To determine if q is a factor of n for any base n, we must again consider the remainder of p divided by q. If the remainder of p divided by q is 0, then q is a factor of n, and the rational number p/q will have a terminating base n representation. If, however, the remainder of p divided by q is not 0, then q is not a factor of n and the rational number p/q will not have a terminating base n representation.

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[tex]3x+5=3(x-5)[/tex]

Distribute numbers outside of parentheses:

[tex]3x+5=(3)(x)+(3)(-5)[/tex]

[tex]3x+5=3x-15[/tex]

Subtract 3x from both sides:

[tex]3x+5-3x=3x-15-3x[/tex]

[tex]5=-15[/tex]

Subtract 5 from both sides:

[tex]5-5=-15-5[/tex]

[tex]0=-20[/tex]

[tex]\fbox{No solution}[/tex]

Given Tables does not represents a quadratic function.

A set of inputs with one output per input is referred to as a function. Simply put, a function is an association between inputs in which every input is coupled to exactly one output. Each function has a range and a co-domain, or domain.

There are numerous function types in mathematics. Among the crucial types are the following:

An injective function, also referred to as a one-to-one function, is a mapping between two sets that accounts for a range for each domain.

Onto functions or surjective functions when a range to a domain mapping involves more than one element.

A function composed of polynomials is known as a polynomial function.

Inverse functions are those that have the ability to invert other functions.

Now,

As we can see from the image that the graph for the function is a straight line but for quadratic function or parabola the graph is parabolic.

Hence,

          Given Tables does not represents a quadratic function.

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(a) Yes,f(x)=9 since every point on this line would have a y-coordinate of 9.

(b) No. A function can have only one value of y corresponding to each value of x.

A function is an equation where each value of x corresponds to exactly one value of y, This means that different x-values can correspond to the same y value but different y-values cannot correspond to the same x value.

(a)

if f(1)=9and f(2)=9 then both x=1 and x=2 corresponds to y=9.

Since different x-values can go to the same y-value for a function, then it is possible that f(1)=9 and f(2)=9

For example, the function could be the horizontal line

f(x)=9 since every point on this line would have a y-coordinate of 9 .

b) If

f(1)=9 and f(1)=3, then y=3 and y=9correspond to x=1. Since functions cannot have different y-values corresponding to the same x-value, then it is not possible for f(1)=9 and f(1)=3

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The number of the degrees of freedom  for the data given below is 14.

Given that ,

According to data from the US Census Bureau, there are 1.86 children on average in each American home. In a specific city, 15 households were polled.

To find : The degree of the freedom ?

The mean number of children in an

American House hold is 1.86

Polls of 15 households were conducted in a city.

So, No . of households sampled

D = 15

Degrees of freedom of = n- 1

= 15 - 1

=14

Therefore, the degree of the freedom is 14.

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The United States Census Bureau determined that the mean number of children in an American household is 1.86. Polls of 15 households were conducted in a certain city. What is the number of degrees of freedom?

The correct answer is d. 1 Gallon is equal to 4 Quartz.

To determine the correct conversion, we can work backwards from the given answer choices.

a. 100 Fluid Ounces: Since 1 cup equals 8 fluid ounces, 100 fluid ounces would be equivalent to 100/8 = 12.5 cups, which is not one of the answer choices.

b. 8 Pints: Since 1 pint equals 2 cups, 8 pints would be equivalent to 8 * 2 = 16 cups. However, this is not one of the answer choices.

c. 5 Quarts: Since 1 quart equals 2 pints, 5 quarts would be equivalent to 5 * 2 = 10 pints. However, this is not one of the answer choices.

d. 1 Gallon: Since 1 gallon equals 4 quarts, each quart is 2 pints, and each pint is 2 cups, the conversion can be calculated as follows:

1 gallon = 4 quarts = 4 x 2 pints = 8 pints = 8 x 2 cups = 16 cups = 16 x 8

fluid ounces = 128 fluid ounces.

Therefore, the correct answer is d. 1 Gallon.

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The time complexity of uttkonen’s algorithm is option(a) that is

O (n log n)

The time complexity is the number of operations an algorithm performs to complete its task (considering that each operation takes the same amount of time). The algorithm that performs the task in the smallest number of operations is considered the most efficient one in terms of the time complexity.

O(log N) is a common runtime complexity. Examples include binary searches, finding the smallest or largest value in a binary search tree, and certain divide and conquer algorithms. If an algorithm is dividing the elements being considered by 2 each iteration, then it likely has a runtime complexity of O(log N)

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Therefore , the solution of the given problem of mean comes out to be on total  he gets $2.00 from the bags.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations.

Here,

Given :

A ,B , C , D , E, F .

The game is played by choosing 2 bags.

Each of five of bags holds $1.00 and one of the bags total $10.00 .

So, there are 5/6 th bags are average is $1.00 .

Thus , on average if they choose 2 bags is $1.00 each .

on total  he gets $2.00 from the bags.

only 1/6th bag he will get $10.00

Therefore , the solution of the given problem of mean comes out to be on total  he gets $2.00 from the bags.

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Answer:

It's the other way around, subtract 36 from 100, and you will get 8

Step-by-step explanation:

a^2+b^2=c^2

a and b are the sides, and c is the longest side.

6x6=36

10x10=100

100-36=64

square root of 64 is 8

Answer:

--------------------------------

Let the speed of the current be x.

The speed with current is 15 + x and the speed against current is 15 - x.

The time difference to travel the distance of 63 km is 4 hours:

The new bacteria population after 6hours is 101.442 million.

The integration denotes the summation of discrete data. The integral is calculated to find the functions which will describe the area, displacement, volume, that occurs due to a collection of small data, which cannot be measured singularly.

integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

Given initially bacteria 85 million.

and the growing rate of bacteria 10 is given by.

[tex]$f(t)=2 e^{0.1 t}[/tex] million/hour

Let [tex]$y$[/tex] be number of bacteria (In millions) at t hour.

so, [tex]\frac{dy}{dt} =2e^{0.1t}[/tex]

Integrating both side

[tex]$$\begin{aligned}& y=\int 2 e^{0.1 t} d t \\& y=\frac{2 e^{0.1 t}}{0.1}+c \\& y=20 e^{0.1 t}+c\end{aligned}$$[/tex]

So, at t=0, y=85

[tex]$$\begin{aligned}& \Rightarrow \quad 85=20 e^{0.1 \times 0}+c \\& \Rightarrow \quad 85=10+c \\& \ C_2\quad=85-20 \\& \Rightarrow C=65 \\& \Rightarrow y=20 e^{0.1 t}+65 \\& \text { when } t=6 \\& y=20 e^{0.1 \times 6}+65 \\& y=20 x e^{0.1 \times 6}+65 \\& y=36.442376+65 \\& y=101.442376 \\& y \cong 101.442 \text {million bacteria } \\&\end{aligned}$$[/tex]

so, at t=6 hour the population of bacteria are 101.442 million.

Therefore, the new bacteria population after 6hours is 101.442 million.

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Greater than or less than symbols are used when a number is greater or less than another number. A greater than sign (>) is used if the first number is greater than the second number. If the first number is less than the second number, the less than sign (<) is used.

In mathematics, the greater-than sign represents an inequality between two values. A common form of > joining two strokes of equal length at an acute angle on the right is found in documents dating from 1631.

> is the greater than sign. So 9>7 is interpreted as "9 is greater than 7".

less than icon. (greater than or equal to) and two other comparison characters (less than or equal to). Think of the symbol as something like a crocodile's mouth, with numbers representing small fish on either side.

Alligators always prefer to eat more fish. The higher the number, the more the crocodile's mouth opens.

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Answer: x = -7

Step-by-step explanation:

7(x + 4) = -21

x + 4 = -3

x = -7

Answer:

-7 because -7 + 4 is -3 and 7 x -3 is -21

Step-by-step explanation:

The equation which represents the number of the team 't' participated in the water balloon contest is equal to 12t = 48 and number of teams are 4.

Let us consider 't' represents the number of teams participated in the water  balloon contest.

Total number of water balloons given by Javier to each team is equal to 12

Total number water balloons distributed by the Javier is equal to 48.

The equation which represents the number of the team in the water balloon contest is given by :

12t = 48

Number of teams participated in contest are:

⇒ t = 48 / 12

⇒ t = 4

Therefore, the equation represents the number of teams in the balloon  contest is equal to 12t = 48 and number of teams are 4.

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The mode of this set of numbers is 1,the median of this set of numbers is 1.

Mean: To find the mean of this set of 5 numbers, we first add them together and divide by the number of measurements. 0 + 7 + 1 + 1 + 4 = 13. 13 divided by 5 (the number of measurements) is 2.6. Therefore, the mean of this set of numbers is 2.6.

Median: To find the median of this set of 5 numbers, we first need to arrange them in order from least to greatest. 0, 1, 1, 4, 7. The median is the middle number, so it is 1. Therefore, the median of this set of numbers is 1.

Mode: To find the mode of this set of 5 numbers, we need to look for the number that appears most often. In this set, the number 1 appears twice while the rest of the numbers appear only once. Therefore, the mode of this set of numbers is 1.

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For the system of equations x - 2y = 4 and y = 4 - x, the solution is (4, 0) Trevor is correct. So Option B is correct

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

the system of equations,

x - 2y = 4

And y = 4 - x,

x - 2y =  4

-x - y  = -4     (multiply the equation by -1)

  -3y  = 0

     y  = 0

x - 0 = 4

x   = 4

Hence, the solution of system is (4, 0)

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Answer:

She drinks 4.8 ounces of water per hour

Step-by-step explanation:

We know

Yasmin drank 3/4 of an 8-ounce glass of water in 1 1/4 hours

3/4 of 8 ounce = 6 ounces

1 1/4 = 5/4 = 1.25 hours

How much can she drink per hour?

6 divided by 1.25 = 4.8 ounces of water per hour

So, she drinks 4.8 ounces of water per hour.

A 32-bit signed number expressed in the hexadecimal number is 0xFFFFFFFB.

For negative number is represented by 2's complement. It is 1's complement +1.

0000-> Hex digit 0

0001-> Hex digit 1

0010-> Hex digit 2

0011-> Hex digit 3

0100-> Hex digit 4

0101-> Hex digit 5

0110-> Hex digit 6

0111-> Hex digit 7

1000-> Hex digit 8

1001-> Hex digit 9

1010-> Hex digit A

1011-> Hex digit B

1100-> Hex digit C

1101-> Hex digit D

1110-> Hex digit E

1111-> Hex digit F

32-bit number is 00000000000000000000000000000101. Its 1's complement is 11111111111111111111111111111010

2's complement is 11111111111111111111111111111010+1 =11111111111111111111111111111011

for hexadecimal, we group 4 binary bits

11111111111111111111111111111010= 1111 1111 1111 1111 1111 1111 1111 1010

hexadecimal value of 1111 is F

hexadecimal value of 1111 is F

hexadecimal value of 1111 is F

hexadecimal value of 1111 is F

hexadecimal value of 1111 is F

hexadecimal value of 1111 is F

hexadecimal value of 1111 is F

hexadecimal value of 1011 is B

Therefore, the hexadecimal number is 0xFFFFFFFB.

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Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.

What is binary ?

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".

An irreflexive closure is a mathematical concept that refers to the creation of a new binary relation from a given binary relation by adding the property of irreflexivity. A binary relation is irreflexive if it does not relate any element to itself. The irreflexive closure of a binary relation is the smallest irreflexive relation that contains it.

In other words, the irreflexive closure of a binary relation is a modified version of the original relation where no element is related to itself. The process of finding the irreflexive closure involves removing all self-referential relationships and adding new relationships to preserve the original relationships between elements.

Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.

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The linear function rule that models the cost of 'y' of a package containing 'x' number of comic books is y = x + 6.50.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A poster and 5 comic books cost $11.50 and a poster and 10 comic books cost $16.50.

slope(m) = (16.50 - 11.50)/(10 - 5).

slope(m) = 5/5.

slope(m) = 1.

16.50 = 10(1) + b.

b = 6.50.

y = x + 6.50.

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Answer:

-12x + 28

Step-by-step explanation:

To do this question we have to expand the brackets and collect like terms

1) Expand brackets

2) Collect like terms

TOP TIP:

Be careful with the operations for example if we were to say that -4 × -7 = -28 our answer would be wrong!

The rules for the operations is that if a - and a + are multiplied the answer will always be -.

If the operations are a - and - the answer will always be +

Plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3) on graph as below.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given linear equation is y= -1.5x.

Substitute, x=0, 1, 2, 3, 4, 5, .......

So, y=0, -1.5, -3, -4.5, -6.0, ....

Plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3)

Therefore, plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3) on graph as below.

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"Your question is incomplete, probably the complete question/missing part is:"

Graph linear equations y= -1.5x.

Cardinality of the power set of the given set = 64

Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.

Example set:

{1,2,3}

All the possible subsets of this set:

{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}

The power set of the above set is written as:

P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })

Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.

Cardinality of the power set of a given set is expressed by a formula:

where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.

Hence in the given case, we have  n = 6.

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The cost of 96 hotdogs from Value Market would be $94.04.

The cost of 96 hotdogs from Sammy's Bulk Store would be $75.84.

The better buy for bottled water would be from Value Market.

Value Market is a store that offers products at low prices, usually with a focus on basic household items, food and drink.

a) The cost of 96 hotdogs from Value Market would be 96 × $0.99 = $94.04.

b) The cost of 96 hotdogs from Sammy's Bulk Store would be 96 × $0.79 = $75.84.

c) The better buy for bottled water would be from Value Market. Value Market offers bottled water for $0.69 per bottle while Sammy's Bulk Store offers bottled water for $0.89 per bottle. Therefore, buying bottled water from Value Market would result in a lower cost for 96 bottles, which would be $0.69 × 96 = $66.24, compared to $0.89 × 96 = $83.84 from Sammy's Bulk Store.

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Answer:

x=40

Step-by-step explanation:

The Samole variance for the given data is 0.

The variance is mean squared difference between each data point and the center of the distribution measured by the mean.

The given data is 5,10,7,12,0,20,15,22,8,2.

We know that, Variance = [tex]\frac{\sum( {\bar x-x} )}{Number of observations }[/tex]

Here, [tex]\bar x[/tex] = (5+10+7+12+0+20+15+22+8+2)/10

= 101/10

= 10.1

Now, variance = [(10.1-5)+(10.1-10)+(10.1-7)+(10.1-12)+(10.1-0)+(10.1-20)+(10.1-15)+(10.1-22)+(10.1-8)+(10.1-2)]/10

= 0/10

= 0

Therefore, the Samole variance for the given data is 0.

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Answer:

Q10:  a = 1    (Choice D)

Q11.   2b = -10 (Choice A)

Step-by-step explanation:

The given equation is

[tex]2x + y = 7[/tex]

We can rewrite this equation with y on the left side and other terms on the right:

Subtract [tex]2x[/tex] from either side:

[tex]2x + y - 2x = 7 - 2x\\\\y = 7 - 2x\;\;\cdots \cdots(1)\\[/tex]

Q10

The value of [tex]y = a[/tex]  corresponds to an [tex]x[/tex] vlaue of [tex]6[/tex]

Plug in [tex]x = 3[/tex] into the equation [tex](1)[/tex] :

[tex]a = 7-2(3)\\\\a = 7 - 6\\\\a = 1\\\\[/tex]                    ANSWER

Q11
We can find b using the same technique as Q10
[tex]b = 7 - 2(6)\\\\b = 7-12\\\\b = -5\\\\[/tex]

Therefore
[tex]2b = 2(-5) = -10[/tex]             ANSWER

Answer:

4/7

Step-by-step explanation:

The solution to the expression is -328000

From the question, we have the following parameters that can be used in our computation:

calculate -8000 * 41 in long division​

The above expression is a product expression

This means that it cannot be evaluated using long division

When the expression is evaluated. we have

-8000 * 41 = -328000

Hence, the solution is -41000

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