9. Six people arrive at a party (A, B, C, D, E, F). They arrive at different times. In how
many ways can they arrive? Find the probability that A arrives first and F arrives last.

Answer:

I'm sure its x>10

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+7>27

Subtract 7 from both sides

2x+7−7 27−7

2x>20

Divide both sides by 2

2x/2 > 20/2

= x>10

Using Pythagoras theorem, the length of AE in the square  2√2 unit

To find the length of side AE, we have to use use the dimension of BD given.

In the figure given, the length of all sides are equal to one another. This implies that the sides are equidistant to one another.

In a given square, all the sides are equal to one another, but the length of the diagonal is the square root of the sum of two sides

This can be further explained as

BD = AC

Using Pythagoras theorem

BD² = AD² + BA²

4² = x² + x²

16 = 2x²

x² = 8

x = √8

x = 2√2

However, we need to find the length of AE

AE is half the length size of AD

AE = 2√2 / 2

AE = √2

The distance AE = √2

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Answer:

3√3v/3x V

Step-by-step explanation:

d/dt[32/3π, sin (tim), 3√3v/3x, V]

The standard deviation of X is $2.00.

Probability is the likelihood that a specific occurrence will occur. Probabilities can be written as proportions with a 0 to 1 or 0% to 100% range.

Let X be the amount one wins. If the die is 4 or 5, the amount one wins is $1. If the die is 6, the amount one wins is $4. If the die is 1, 2, or 3, the amount is $0. Then, the probability of winning from 1 to 6 is 1/6.

The value of the expected mean (μ) is,

[tex]\begin{aligned}\mu&=\sum X P(X)\\&=1\times \frac{1}{6}+1\times \frac{1}{6}+4\times \frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}\\&=\frac{6}{6}\\&=1\end{aligned}[/tex]

Therefore, the standard deviation (σ)is [tex]\begin{aligned}\sigma&=\frac{\sum(X-\mu^2)}{n}\\&=\frac{(1-1)^2+(1-1)^2+(4-1)^2+(0-1)^2+(0-1)^2+(0-1)^2}{6}\\&=\frac{12}{6}\\&=2\end{aligned}[/tex]

The answer is $2. The correct option is option E.

The complete question is -

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. Use Scenario 6-2. Which of the following is the standard deviation of X? A. $1.00 B. $1.35 C. $1.41 D. $1.78 E. $2.00

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An algorithm is a collection of clear instructions for solving a specific issue in computer programming.

Step 1: Start

Step 2: Declare variables num1, num2 and sum.

Step 3: Read values num1 and num2.

Step 4: Add num1 and num2 and assign the result to sum.

       sum←num1+num2

Step 5: Display sum

Step 6: Stop

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Rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y = [tex]\frac{5}{4}x+1[/tex].

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

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Answer:

k = -4

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}4x - 8y = -3\\2x + ky = 10\end{cases}[/tex]

Rewrite the given equations so that they are in slope-intercept form.

[tex]\begin{aligned}4x-8y&=-3\\4x&=8y-3\\4x+3&=8y\\\dfrac{4x+3}{8}&=y\\y&=\dfrac{1}{2}x+\dfrac{3}{8}\end{aligned}[/tex]

[tex]\begin{aligned}2x+ky&=10\\ky&=-2x+10\\y&=\dfrac{-2x+10}{k}\\y&=-\dfrac{2}{k}x+\dfrac{10}{k}\end{aligned}[/tex]

An inconsistent system of linear equations has no solutions and therefore the lines are parallel.  

Parallel lines have the same slope:

[tex]\implies \dfrac{1}{2}=-\dfrac{2}{k}[/tex]

[tex]\implies \dfrac{1}{2}k=-2[/tex]

[tex]\implies k=-2 \cdot 2[/tex]

[tex]\implies k=-4[/tex]

Answer:

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

Equation in the standard form ax + by = c  has:

Given system:

Compare the slopes of the two lines:

We need them to be equal:

Compare the y-intercepts of the two lines:

We need to confirm they are not same:

Confirmed, so k = -4 is our solution.

Answer:

6 2/3

Step-by-step explanation:

2 1/6 + 4 3/6

6 4/6

6 2/3

Answer: A

Step-by-step explanation:

Because Milwaukee's population is smaller than that of Baltimore, the only correct answer would be one that has the population of Baltimore higher than that of Milwaukee, which is only A

The solution for the variable is that the variable should be greater than 9.375

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Given: the inequality 58x+170 > 42x+320. The unknown variable is x

In word problem, we can write:

When a variable x is multiplied by 58 and then 170 is added. The result is greater than variable x multiplied by 42 with 320 added

Solution for the unknown

58x+170 > 42x+320

58x-42x > 320-170

16x > 150

x > 150/16

x > 9.375

Thus, the solution for the unknown is that the unknown should be greater than 9.375

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Answer:

X=3

Step-by-step explanation:

The percentage of the hotel rooms in the city which were occupied during the convention is 98%.

What is percentage?

A percentage is a piece of a whole expressed as a number between 0 to 100. Nothing is said to be zero percent; everything is said to be 100 percent; half of something is said to be 50 percent; and nothing is zero percent.

You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

As given in the question,

Number of hotel room occupied = 9,800

Number of hotel room unoccupied = 200

Total number of the rooms in city = 9800 + 200

Total number of the rooms in city = 10,000

To calculate the percentage we proceeds as follow:

(9800/10000)100 = 98%

Therefore, the percentage is 98%.

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The probability that 200 or fewer homes were purchased as investment properties is 0.937. This is calculated using the binomial distribution formula, where n = 600, p = 0.31, and x = 200.

1. The binomial distribution formula for calculating the probability of an event occurring is:

P(x) = nCx * p^x * q^(n-x)

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1 - p).

2. In this problem, n = 600, p = 0.31, x = 200, and q = 1 - 0.31 = 0.69.

3. Plugging these values into the formula, we get:

P(x) = 600C200 * 0.31^200 * 0.69^400

4. Solving this equation, we get P(x) = 0.937.

5. Therefore, the probability that 200 or fewer homes were purchased as investment properties is 0.937.

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Answer:

6.64

Step-by-step explanation:

The nearest hundredth is the second digit after the decimal point.

6.6428571 rounded to the nearest hundredth is 6.64

This means that the probability that a doll selected at random will blink and have moving limbs is 0.26.

There is a 50% chance that the outcome will be heads, thus 50 heads are to be expected. When we really attempt it, though, we might instead get 48 heads, 55 heads, or anything else at all, but in most situations, it will be a figure close to 50.

calculation

If B is a set of moveable arms and legs and A is the number of dolls that can blink, then P(A)=0.47, P(B)=0.56, P(A' and B')=0.23,

therefore P(A or B)=1-0.23=0.77, and

P(both blink and moveable limbs)=P(A and B)=0.47+0.56-0.77=0.26.

This means that the probability that a doll selected at random will blink and have moving limbs is 0.26.

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An example of inverse variation is y = 3/x .

What is Inverse Variation ?

Unlike the direct variation, where one quantity varies directly as per changes in another quantity, in the case of inverse variation, the first quantity varies inversely as per another quantity. Hence, the first quantity is inversely proportional to the other.

Let us say, x and y are two variables, then as per inverse variation:

y = k/x

or

xy = k

For example :

If x and y are in an inverse variation and k/3 = 2, and k/x = 3, then find the value of x when y = 2.

Given, k/3 = 2

then, k = 3 x 2 = 6

k/x = 3

So, x = k/3 = 6/3 = 2

Hence, if y = 2, then ;

x = k/y = 6/2 = 3

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A base is a negative number and an exponent is also a negative number is explained in two ways:

(a) if the negative exponent is an even number, then the result will be a positive number.

(b) if the negative exponent is an odd number, then the result will be a negative number.

The required negative exponential formula is

a⁻ᵇ = 1/aᵇ or 1/a⁻ᵇ = aᵇ

Consider two negative numbers '-x' as the base and '-n' as the exponent.

So, the given statement in mathematical form is as below:

⇔ (-x)⁻ⁿ

Then, we can evaluate them in two ways by considering 'n' to be an even and an odd number.

(a) If 'n' is an even number:

from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write

(-x)⁻ⁿ = 1/(-x)ⁿ

Since 'n' is an even number (-x)ⁿ = xⁿ

So, the result will be a positive rational or decimal number.

I.e., (-x)⁻ⁿ = 1/xⁿ

(b) If 'n' is an odd number:

from the exponent formula, a⁻ᵇ = 1/aᵇ, we can write

(-x)⁻ⁿ = 1/(-x)ⁿ

Since 'n' is an odd number (-x)ⁿ = -xⁿ

So, the result will be a negative rational or decimal number.

I.e., (-x)⁻ⁿ = -1/xⁿ

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The  expressions are factors of the polynomial 3x4 - 14x³ 3x²+54x -40 are

Generally, To factor a polynomial using synthetic division, we need to find a factor of the polynomial that can be divided into the leading coefficient and the constant term of the polynomial.

In this case, the leading coefficient is 3 and the constant term is -40. One factor of 3 and -40 is (-4)(10).

The complete factorization of the polynomial is 3x⁴ - 14x³ + 3x² + 54x - 40  gives The remainder is 0, so the other factor is (x - 4)(x + 2)(x - 1)(x + 1).

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If the domain of f(x) = x² - 4 is limited to {-1, 0, 1, 2} the greatest value of the range is 0

The range represents the output values

Using the given expression to solve it can be found that the output values are

for x = -1, f(x) = x² - 4 = -1² - 4 = -3

for x = 0,  f(x) = x² - 4 = 0² - 4 = -4

for x = 1, f(x) = x² - 4 = 1² - 4 = -3

for x = 2, f(x) = x² - 4 = 2² - 4 = 0

The greatest value of the range is 0

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Answer:

6418698

-3485835

2932863

Step-by-step explanation:

The probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched:

No-hitters    probability

     0             0.5944

     1             0.3093

     2             0.0804

     3             0.0139

In this question, we have been given  the probability that a major league pitcher pitches a no-hitter in a game is about 1/1300.

We need to determine the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched.

Here, p = 1/1300

            = 0.0008

q = 1 - p

  = 1 - 1/1300

  = 1299/1300

  = 0.9992

And n = 650

We know that the binomial distribution formula.

P(x) = nCx * p^(x) * q^(n - x)

Using binomial distribution we find required probability.

For x = 0,

P(x = 0) = 650C0 * (1/1300)^0 * (1299/1300)^(650 - 0)

P(x = 0) = 1 * 1 * (0.9992)^650

P(x = 0) = 0.5944

For x = 1,

P(x = 1) = 650C1 * (1/1300)^1 * (1299/1300)^(650 - 1)

P(x = 1) = 650 * (0.0008) * (0.9992)^649

P(x = 1) = 0.52  * 0.5948

P(x = 1) = 0.3093

For x = 2,

P(x = 2) = 650C2 * (1/1300)^2 * (1299/1300)^(650 - 2)

P(x = 2) = 210925 * (0.0008)^2 * (0.9992)^648

P(x = 2) = 0.0804

For x = 3,

P(x = 3) = 650C3 * (1/1300)^3 * (1299/1300)^(650 - 3)

P(x = 3) = 45559800 * (0.0008)^3 * (0.9992)^647

P(x = 3) = 0.0139

Therefore, the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched are 0.5944, 0.3093, 0.0804, and 0.0139 respectively.

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The partial fraction decomposition of the function is x⁴ + 2 / x⁵ + 4x³ = -1/8x + 1/2x³ + 9/8x(x²+4)

Partial fraction decomposition function:

In algebra, When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction.

Given,

Here we have the expression

x⁴ + 2 / x⁵ + 4x³

Here we need to find the partial fraction decomposition function.

In order to solve this, first we have to factorize the denominator, then we get,

=> x⁴ + 2 / x⁵ + 4x³ = (x⁴ + 2) / x³ (x² + 4)

Now,  Partial fraction for each factors is written as,

=> A/x + B/x² + C/x³ + (Dx + E)/ (x² + 4)

Now, we have to  Multiply through by the common denominator of x³ (x² + 4), then we get,

=>  x⁴+2=A (x²(x²+4)) + B(x(x²+4)) + C (x²+4) + (Dx + E)(x³)

When we simplify this one, then we get,

=> x⁴ + 2 =Ax⁴ + 4Ax² + Bx³ + 4Bx + Cx² + 4C + Dx⁴ + Ex³

Group the x-terms and the constant terms

=> x⁴ + 2 =(A +D)x⁴ + (4A + C) x² + (B + E)x³ + 4Bx + 4C

Coefficients of the two polynomials must be equal, so we get equations

A+D=1

B+E=0

4A+C=0

4B=0

4C=2

After solving these equations, we get

A = -1/8, B = 0, C = 1/2, D=9/8, E = 0

Then when we substitute these values in the original fraction,

=> -1/8x + 1/2x³ + 9/8x(x²+4)

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In a rhombus, all sides are the same length, and the opposite angles are equal. The diagonals also bisect each other at 90 degrees.

We know that,

A rhombus has two congruent acute and two congruent obtuse angles.

Here we use the terms  x and y to represent the angles.

where x is the acute angle

The angles total 360 degrees.

So far, we have:

2(x+y) = 360

By dividing both sides by 2 , we get,

x + y = 180

We can assume y is 3 times larger than x,

That is y = 3x

As a result, the equation becomes,

x + 3y = 180

Calculate the total

4x = 180

As a result, the acute angle is 45 degrees.

Hence we proved that y is 3 times larger than x.

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It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

Given that

Ted can remove the trash from a football field in three hours. The same field may be cleared by Jacob in two hours. The scenario can be represented by the equation when they cooperate, where t is the total number of hours needed to clear the field.

We have to find how long will it take ted and jacob to clear the field together.

We know that,

Let the number of hours = t

Ted can clear the field = t/3

Jacob can clear the field = t/2

Together they can clear the field = t/3 + t/2 = 1

3t+2t/6 = 6/6

2t + 3t = 6

5t = 6

t = 6/5

t = 1.2 hours.

Converting

1.2 hours = 1 hour 12 minutes.

Therefore, It will take 1 hour 12 minutes to clear the field together Ted and jacob when Ted can remove the trash from a football field in three hours.

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Yes ,induction can be used to prove the following is true for every nonnegitive integer n.

If P (n) is true, so is P (n + 1) because this argument holds true for any nonnegative integer n, it establishes the second fact required by the induction proof. As a result of the Induction Principle, the predicate P (m) is true for all nonnegative integers, m.

Mathematical induction is a technique for proving the truth of a statement, theorem, or formula for each and every natural number n. This is generalized as the 'Principle of Mathematical Induction,' which we would use to prove any mathematical statement.

For instance, 13 +23 + 33 +..... +n3 = (n(n+1) / 2)

The statement is assumed to be true for all natural number values in this case.

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The distributive property of 25+45 is 25+45 = 5(5+9).

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Say you wish to multiply 5 by the product of 10 plus 3.

When two terms are similar, we often sum the two amounts before multiplying by 5. 5(10 + 3) = 5(13) = 65.

So, the distributive property of 25+45:

25+45 = 5(5+9)

Therefore, the distributive property of 25+45 is 25+45 = 5(5+9).

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Answer:

-7i

Step-by-step explanation:

Sqrt-49 = Sqrt49 *(- 1)

= Sqrt49 * sqrt-1

= ±7 * i

= ±7i

Answer:

All Correct! The corinates on the graph are all graphed in the correct position.

Answer:

Yes, you are correct.

Step-by-step explanation:

Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

If 60% of the population supports massive federal budget cuts.

We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.

So, the probability is, 155 / 250 = 0.62

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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