How many rearrangements of abcd are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either ab or ba.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

(A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.

It is typically a number, but it can also be any expression.

They may also be referred to as parameters if the coefficients are variables in and of themselves.

A coefficient is, in other words, the numerical factor of a term that contains both constants and variables.

For instance, the coefficient in the expression 2x is 2.

So, we have: (a + b)3

Since we have nothing before (a + b)3.

Then the coefficient will be 1 here.

If we have 3 after (a + b) then the coefficient will be 3.

Therefore, (A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.

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Correct question:
What are the coefficients for the binomial expansion of (a + b)3?

a. 1, 4, 6, 4, 1

b. 1,1

c. 1, 2,1

d. 1,3,3, 1

μ1 <= μ2,

 mean score on campus 1 is higher than on campus 2

There is also a competing theory put forth by the researcher, according to which test results are unrelated and the advanced learning program has minimal bearing on students' academic performance. Because the researcher wants to know if the scores are greater or lower than the state average, this is an illustration of a two-sided hypothesis.

 μ1 <= μ2,

 mean score on campus 1 is higher than on campus 2.

Because the researcher wants to know if the scores are greater or lower       than the state average, this is an illustration of a two-sided hypothesis.

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The rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

We have to write a rule for the dilation,

A transformation is termed as an operation that moves, flips, and create a new shape.

Dilation is also a type of transformation that enlarges or reduces any shape or graph of any function, to create a new graph or shape.

The scale factor, k determines how much large or small the dilation figure will be as compared to the previous shape or figure.

So, the rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

Hence, the rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

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Answer:

5/6

Step-by-step explanation:

The results of previous dice rolls don't have any effect on the result the next time the die is rolled.

The relative frequency of getting a 5 on the next roll is 5/6

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency). Conditional relative frequency is relative frequency conditional to some special characteristic.

We are given that a fair die is rolled 25 times. it landed on the number 5 eight times.

We need to find the relative frequency of getting a 5 on the next roll

relative frequency = 5/6

The results of previous dice rolls that have any effect on the result the next time the die is rolled.

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Answer:

Step-by-step explanation:

The amount of something that needs to be bought will be $2,875.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

If there is a 15% increase in the aggregate price level, a consumer who had been looking to purchase something that cost $2,500.

Let 'x' be the amount that needs to pay. Then the amount of something that needs to be bought will be given as,

x = (1 + 15%) of $2,500

x = (1 + 0.15) x $2,500

x = 1.15 x $2,500

x = $2,875

The amount of something that needs to be bought will be $2,875.

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Answer:

The correct answer is 5.672 x 10^3

Step-by-step explanation:

change the exponent for 3.28 x 10^2, and you get 0.328 x 10^3, and then subtract normally, which gets you 5.672 x 10^3

Cartlon's score is 4.5434.

Given that,

Carlton has a z-score 1.74 on the achievement test.

From the z-table we get the value 0.959.

We know the formula for standard deviation,

z = (x - μ) / σ

where x = score, σ = standard deviation, μ =  mean

Now z-score corresponding to 98th percentile is 2.06

substituting the values in the above equations,

2.06 = (x - 0.959) / 1.74

i.e. x - 0.959 = 2.06 * 1.74

                    x = 3.5844 + 0.959

                    x = 4.5434

Therefore carlton's score is 4.5434.

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The inverse of the functions are f⁻¹(x) = 1/2(x + 3), f⁻¹(x) = 1/2√(x + 5) and A⁻¹(r) = 1/2√(r/pi)

Function (a)

This function is given as

f(x)=1/(2x)-3

The function needs to be represented as an equation

So, we have

y = 1/(2x) - 3

Swap the positions of x and y

x = 1/(2y) - 3

So, we have

1/(2y) = x + 3

Take the inverse of both sides

2y = 1/(x + 3)

Divide by 2

y = 1/2(x + 3)

So, the inverse function is

f⁻¹(x) = 1/2(x + 3)

Function (b)

This function is given as

f(x)=4x²-5

The function needs to be represented as an equation

So, we have

y = 4x²-5

Swap the positions of x and y

x = 4y² - 5

So, we have

4y²= x + 5

Divide both sides by 4

y²= 1/4(x + 5)

Take the square roots

y= 1/2√(x + 5)

So, the inverse function is

f⁻¹(x) = 1/2√(x + 5)

Function (c)

This function is given as

A(r) = 4(pi)r²

The function needs to be represented as an equation

So, we have

y = 4(pi)r²

Swap the positions of r and y

r = 4(pi)y²

So, we have

y²= r/(4pi)

Take the square roots

y = 1/2√(r/pi)

So, the inverse function is

A⁻¹(r) = 1/2√(r/pi)

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Each person will pay $516.44.

To split an expense means to divide it into equal parts among the data given.

Over here we have, three friends so we will split the amount among them.

Here, sharing the cost of living means first calculating their total expenses (rent and other costs), which must then be divided among them.

They spend $859.32 on additional expenses in addition to their $690 rent payment.

Their total expenses are rent and other costs.

$690 + $859.32 = $1549.32.

We must now divide the money among the three friends 1554.32/3 =$516.44.

Therefore each individual will pay $516.44.

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The correct answer is the equation of the line is y = [tex]-\frac{2}{3} x - 2[/tex]

Given the equation of the parallel line is 2x + 3y = 3

and the required line passes through the point (3, -4) where x is 3 and y is -4

We can write the given equation  as:

⇒ 3y = 3 - 2x

Dividing both sides by 3

[tex]y = 1 - \frac{2x}{3}[/tex]

On comparing this equation with y= mx+b, thus m = [tex]-\frac{2}{3}[/tex] and the slopes of parallel lines are always equal.

Using the point slope form, we will derive the equation of line

⇒ [tex]y-y_1 =m ( x- x_1)[/tex]

⇒ [tex]y- (-4) = -\frac{2}{3} (x-3)[/tex]

⇒ [tex]y+4= -\frac{2}{3} (x) - \frac{2}{3} (-3)[/tex]

⇒ [tex]y = -\frac{2}{3} (x) +2-4[/tex]

⇒ [tex]y = -\frac{2}{3} (x) - 2[/tex]

Hence, the equation of the required line is [tex]y = -\frac{2}{3} (x) - 2[/tex]

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For six tests, the Bonferroni corrected p value is 120.

Given,

Bonferroni adjustment;-

The Bonferroni technique is an easy procedure that permits the construction of several confidence intervals or comparison statements while maintaining a constant overall confidence coefficient.

Here,

Divide the initial alpha level (often set to 0.05) by the total number of tests to make the adjustment. The result of the calculation is a Bonferroni-corrected p value, which will serve as the new cutoff point for classifying a single test as significant.

So,

6/0.05 = 120

That is,

The Bonferroni corrected p value is 120 for 6 number of tests.

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This is not a simple random sample because not all combinations of 100 toys could have been chosen.

A factory has 20 assembly lines producing a popular toy.

This is not a simple random sample because not all combinations of 100 toys could have been chosen. We know that it will be a random sample if all the 100 toys will ne chosen randomly but in this question not all the 100 toys will be chosen. The answer is No, because not all combinations of 100 toys could have been chosen.

Therefore, quality control staff randomly selected 5 toys from each output, and this is not a simple random sample because not all combinations of 100 toys could have been chosen.

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The estimated age of the archaeological sample  as calculated from the given data is  = 2622.58333 years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 73 % of the 14C remains

then |A1|/|A2|  = 0.73

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.73)= -0.00012t

t = -0.31471/ -0.00012

 = 2622.58333 years

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay.

For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.

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The amount Amy is expected to pay on rent and utilities each year is $15,600. (Option D)

Rent and utilities refer to the amount paid each month for utilization of accommodation and for utility services which are products, services and equipment related to energy, telecommunications, water, and sewerage respectively.

Based on the information provided in the salary analysis table, Amy’s monthly rent and utilities are:

Total = Amy’s Rent + Amy’s Utilities = $1100 + $200 = $1300

As there are 12 months in a year, the yearly total is:

Total = $1300 x 12 = $15,600

Hence, the amount Amy is expected to pay on rent and utilities each year is $15,600.

Note: The question is incomplete. The complete question probably is Amy is analyzing a job offer. How much should she expect to pay on rent and utilities each year? A) $1,300 B) $2,400 C) $13,200 D) $15,600.

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The total number of no votes are 4422.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given:   The ratio of yes votes to no votes is 5 to 6 i.e.

          yes votes /no votes = 5/6

  It means there are total 11 votes ( 5 votes for yes and 6 votes for no)

  which gives

                    no votes/total votes= 6/11---(i)

But in the given question total votes are 8107,

so let us consider there are x votes for no which implies

                       no votes/total votes= x/8107

From (i), we have

                   x/8107 = 6/11

               ⇒ x = 6*8107/11 = 4422.

Then the total number of no votes is 4422.

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NOTE: The question given in the portal is incomplete. Here is the complete question.

Question: The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 8107 total votes, how many no votes were there?

A table can be used to solve equational systems.

A list of particular points from the straight-line graphs is called a table of values. On a graph, the y-values at the points where the lines converge will be the same. We'll be looking for the x-location in the tables where the y-values are equal.

In a table solution, the system's two linear equations are changed with x-values. The solution is established when the same y-value appears in both equations.

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Making an interval estimate for the population mean requires making the following assumptions about the population:

a. The population is thought to have a normal distribution.

b. The central limit theorem is presumptively true.

Given,

Making an interval estimate for the population mean requires making the following assumptions about the population:

a. The population is thought to have a normal distribution.

b. The central limit theorem is presumptively true.

The distribution of a variable's values is described by a normal distribution. There are 50% of the data to the left and 50% to the right of the mean in this probability distribution, which is symmetrical about the mean. The majority of the data are centered around the mean, meaning that they are more likely to occur or be located close to the mean than distant from it. A bell curve will represent the normal distribution's graph form. Mean = mode = median describes a normal distribution.

According to the Central Limit Theorem, when a variable does not follow a normal distribution, repeated random samples from the population will result in sample means that are normally distributed, regardless of the underlying distribution of the sample. This indicates that as the sample size increases, the sampling distribution of the sample means moves closer to a normal distribution.

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Agile promotes innovation, speeds up product delivery, and motivates workers in a world that values technology above everything else

What is enterprise ?

Despite being another word for a for-profit business or organization, the word "enterprise" is most frequently related to entrepreneurial endeavors. Those who are successful in business are frequently referred to as "enterprising." Legal businesses come in a variety of shapes and sizes, but the most popular ones in the US.

Industry goliaths can no longer win by virtue of their size and market power. Today, adapting to a constantly shifting corporate environment and quickly changing client demands requires speed and agility.

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We call this a triple zero, or a zero with multiplicity 3. For zeros with even multiplicities, the graphs touch or are tangent to the x-axis at these x-values

What is the multiplicity of 0 3?

We call this a triple zero, or a zero with multiplicity 3. For zeros with even multiplicities, the graphs touch or are tangent to the x-axis at these x-values. For zeros with odd multiplicities, the graphs cross or intersect the x-axis at these x-values.

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Answer:

[tex]\huge\boxed{\sf 2 \ unit^2}[/tex]

Step-by-step explanation:

Since both base and perpendicular are the same, let's denote both of them by one variable i.e. x

Using Pythagoras Theorem because it is a right-angled triangle.

[tex](Hypotenuse)^2=(Base)^2+(Perp)^2[/tex]

Where,

Base, Perp = x

Hypotenuse = [tex]2\sqrt{2}[/tex]

So,

[tex](2\sqrt{2})^2=(x)^2+(x)^2 \\\\4 \times 2 = x^2+x^2\\\\8 = 2x^2\\\\Divide \ both \ sides \ by \ 2\\\\4 = x^2\\\\Take \ sqrt\\\\2 = x \\\\x = 2[/tex]

So, Base and Perpendicular both equal 2.

[tex]\displaystyle =\frac{1}{2} (Base)(Perp)\\\\= \frac{1}{2} (2)(2)\\\\= 2 \ unit^2\\\\\rule[225]{225}{2}[/tex]

Answer:

2 unit^2

Step-by-step explanation:

a^2 +b^2=c^2 is the formula we use we can turn both a and b to x since they are the same legnth and c is 2√2

X^2+x^2=2√2^2

2x^2=4(2)

2x^2=8

/2.   /2

x^2=4

Square root both sides

x=2

so the base and the height is 2

So we use triangle formula

1/2(2)(2)

1/2(4)

2

The area is 2

Hopes this helps please mark brainliest

Elimination and substitution is one approach to solve linear equation problems.

Put the equations in actually Standard Form as a first step, which really is quite significant. Choose which sort of variable to basically remove in step two, which particularly is quite significant. 3, very further showing how 3 in a basically major way. Multiply the equations and really find the solutions, so 3, fairly further showing how 3, which for all intents and purposes is quite significant. Step 4: Reconnect the plug to particularly locate the particularly second variable, which really shows that for the most part choose which basically variable to kind of remove in step two in a sort of major way.

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The given Fibonacci sequence ,

b)  First term of the Fibonacci sequence is 8.

c) First term = y-x.

Fourth term = x+y

Fifth term = y+30.

What is Fibonacci Sequence?

 A series in which each number is the sum of the two numbers before it is known as the Fibonacci Sequence. We must specify values for the first two terms in order to complete the Fibonacci Sequence. In the Fibanocci sequence we can find next term by adding previous terms.

Here the given Fourth term = 30 and Fifth term = 49.

Here second and third terms are x and y. Let us take first term as a.

We know that the Fibonacci sequence is sum of previous terms.

The sequence are,

=> a , x , y , 30 ,49 ,...

Here Fourth term = 30

=> second term + third term = 30

=> x+y = 30----->1

Now the fifth term is third term + fourth term = 49

=> y+30 =49

=> y =19.

Put y=19 into 1 then,

=> x+19=30

=> x = 30-19 =11

Now third term is first term+second term = third term

=> a+x =y

=> a+11=19

=> a =19-11 =8.

b) First term of the Fibonacci sequence is 8.

c) Third term = first term+second term

=> y = first term +x

=> First term = y-x.

Fourth term = Second term+third term

=>Fourth term = x+y

Fifth term = third term+fourth term

=> Fifth term = y+30.

Therefore the given Fibonacci sequence ,

b)  First term of the Fibonacci sequence is 8.

c) First term = y-x.

Fourth term = x+y

Fifth term = y+30.

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The rate of change of the volume of sphere when is decreasing at a constant rate is found as  3319.16 cm³/min.

For the stated question-

Thus, the volume of sphere is found by the equation.

Volume of sphere V = 4/3 πr³

V =  1611 cm³.

1611 = 4/3 πr³

On solving,

r = 7.27 cm

Rate change of the volume;

dV/dt = 4/3 πr² × 3

dV/dt =  4 πr²

Put r = 7.27 cm and π = 3.14

dV/dt =   4 x 3.14 x 7.27²

dV/dt = 3319.16 cm³/min.

Thus, the rate of change of the volume of sphere when is decreasing at a constant rate is found as  3319.16 cm³/min.

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I don't know the answer but I believe it could be the 3rd one

The solutions of x in the interval [0°, 360°) are 3[tex]\pi[/tex]/4 and 5[tex]\pi[/tex]/4 respectively.

What is a quadrant?

The quadrant is the area that is bounded by the point where the X and Y axes connect.

A plane is split into four sections in the cartesian system, the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.

Given, 2cos x + √2 = 0

       or, 2cos x = -√2

       or, cos x = -√2/2 = -1/√2 = - cos ([tex]\pi /4[/tex] )

As the given cos(x) is negative, then it must lie in quadrants II and III respectively for the given interval  [0°, 360°).

Then, cos x = cos ([tex]\pi[/tex] - [tex]\frac{\pi}{4}[/tex])             and, cos x = cos ([tex]\pi +\frac{\pi }{4}[/tex])

       or, x = 3[tex]\pi[/tex]/4                                 or, x = 5[tex]\pi[/tex]/4

Hence, the required solutions of x are 3[tex]\pi[/tex]/4  and 5[tex]\pi[/tex]/4.

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The upper limit of blood pressure is 123.4.

The lower limit of blood pressure is 116.6..

The applicant's blood pressure limit does not meet the standards limit of blood pressure to qualify for study.

we have given that,

mean , μ = 120

standard deviation , σ = 4

The z - distribution of the 60% is,

P( -z < Z < z ) = 0.60

P( Z < z ) - P( Z < -z ) = 0.60

2× P(Z < z ) - 1 = 0.60

2× P(Z < z ) = 1 + 0.60

P( Z < z ) = 1.60 / 2

P( Z < z ) = 0.80

P( Z < -0.84) = 0.80

z = -0.84 and z = 0.84

let X be the required mean of sample .

Using z - score formula,

X = (z × σ )+ μ

= -0.84 × 4 + 120

= 116.6

and

X = z × σ + μ

= 0.84 × 4 + 120

= 123.4

Hence , Lower blood pressure limit = 116.6

Upper blood pressure limit = 123.4

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Complete question:

To qualify for a medical study, an applicant must have a systolic blood pressure in the 60% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate-value calculations to 2 decimal places. Applicants must have a lower blood pressure limit of 118.48 and an upper blood pressure limit of 124.16 to qualify for the study.

The probability of red on the second spin 1/12. the probability of blue on the second spin 1/18.  the probability of not spinning cyan on either spin is 25/36.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The ratio of favorable outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range.

Probability = Number of Favorable Outcomes / Total Number of

we know the formula of probability;

probability=favorable outcomes/total number of outcomes

so for red:

P(red) = 3/6 = 1/2

so for blue:

P(blue) = 2/6 = 1/3

so for cyan

P(cyan) = 1/6

Now totally;

P( cyan then red) =  1/6 * 1/2 = 1/12

P(cyan then blue) =  1/6 * 1/3 = 1/18

P( no cyan on 2 spins) = (1/2+1/3)* (1/2+1/3) = 5/6 * 5/6 = 25/36

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