How many ways can four guests sit in a row of six chairs so that the leftmost chair is used and the rightmost chair is empty?

The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

A) [tex]x^{-2}+15x-3[/tex]

Here, the exponent of x is -2. So, the expression is not a polynomial.

B) [tex]-x^3+5x^2+7\sqrt{x} -1[/tex]

Here, the power of one of the term is 1/2. So, the expression is not a polynomial.

C) [tex]\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex]

Here, the power of one of the term is -2. So, the expression is not a polynomial.

D) 5.3x²+3x-2

Here, the power of each term is positive integer. So, the expression is a polynomial.

E) [tex]4x^4-10[/tex]

Here, the power of each term is positive integer. So, the expression is a polynomial.

The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.

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If angle ∠4 = 29 degrees, then

The m∠4 = 29 degrees

Part 1

The angles on a straight line add up to 180 degrees.

∠4 + ∠1 = 180

29 + ∠1 = 1180

∠1 = 180-29

= 151 degrees

Part 2

The angles on a straight line add up to 180 degrees.

∠1 + ∠2 = 180

151 + ∠2 = 180

∠2 = 180-151

= 29 degrees

Part 3

The angles on a straight line add up to 180 degrees.

∠2 + ∠3 = 180

29 +  ∠3 = 180

∠3 = 180-29

= 151 degrees

Hence, If  angle ∠4 = 29 degrees, then

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To solve this expression we have to add 2 to both sides of the equation:

So, the correct option is: B: 5.5

The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2

The equation is given as

4(3m + 1) − 2m = −16

Open the brackets in the above equation

So, we have

12m + 4 − 2m = −16

Collect the like terms in the above equation

So, we have the following equation

12m − 2m = −16 -4

Evaluate the like terms in the above equation

So, we have the following equation

10m = −20

Divide both sides by 10

m = -2

Hence, the soluton is m = -2

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Answer: (52,72) (52 adults and 72 children)

Step-by-step explanation:

1) Create 2 formulas that show the information show above, 2.5x+2y=274 showing how the x is how many adults paid for a ticket and y is how many children paid for a ticket. The second formula being x+y=124 meaning the combination of children and adults equal 124 people.

2) Take those formulas and input them into a graph as shown in the picture (Graph 1)

3) Find the common point shown on the graph (should be the middle grey dot if on Desmos as shown (Graph 2)

4) The common point is (52, 72)

And if you plug these numbers in by replacing the x's and y's i shown in step 1 they bring an output of 274 and 124

Hope this helps :)

The solution of system of equation is x = 2 and y = 7. We should multiply first equation with 2 so that when we add the two equations, we csystem of equation an eliminate the variable y.

What is system of equation?

Two or more equations that share variables are said to be .

For instance, consider two equations where x and y are shared:

x + y = 6

3x + y = 2

We might be able to solve equations that have the same number of variables. Where the lines intersect in this case is the answer (1,5)

Given system of equation:

5x + 3y = 41,

3x - 6y = 9

Lets multiply the first equation with 2, we get

10x + 6y = 82

Adding these equation with second given equation we get,

10x +6y +(3x - 6y) = 82 + 9

13x = 91

x = 91/13

x = 7

putting the value of x in any one equation

3(7) -6y = 9

y = 2

Therefore, the x and y in the given system of equation are 7 and 2 respectively.

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Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.

A = L * B

Hence the width B may be found from

1400 = 56 * B

B = 1400/56

B = 25 feet

b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,

the total cost to fence the backyard will be

= $10 * 2(56 + 25)

= $1,620

Answer:

A

Step-by-step explanation:

ax + by = c  Subtract ax from both sides

by = -ax + c  Divide all the way through by b

[tex]\frac{by}{b}[/tex] = [tex]\frac{-a}{b}[/tex] x + [tex]\frac{c}{b}[/tex]

y = - [tex]\frac{a}{b}[/tex] x +[tex]\frac{c}{b}[/tex]

Answer:

  y = -3x +6

Step-by-step explanation:

You want to solve the equation 6x +2y = 12 for y.

We can isolate the y-term by subtracting 6x from both sides.

  6x -6x +2y = -6x +12

  2y = -6x +12 . . . . . . . . . . simplify

Then we can get y by itself by dividing both sides by 2:

  2y/2 = -6x/2 +12/2

  y = -3x +6 . . . . . . . . . . . simplify

The expression for y is  y = -3x +6.

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Answer:

(x + 3)² + (y - 6)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 3, 6 ) and r = 3 , then

(x - (- 3 )² + (y - 6)² = 3² , that is

(x + 3)² + (y - 6)² = 9

Solution

For this case we can do the following:

tan x = 35/30

And we can solve for x and we got:

And rounded to the nearest degree is:

49º

Answer:

1. Fact that all individuals are created equal and are endowed by their creator with certain unalienable rights is a clear statement in the Declaration of Independence.

2. Aim of having a government is to safeguard these rights,  the people have the right and the duty to alter, abolish, or over through that government.

3. The Decoration of Independence lists the grievances that the government has failed to resolve and reconcile with the colonies.

4. The decree was made to become an autonomous nation and the motives for asserting independence are listed in the grievances.

Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation

The reasonable domain and range are 0 ≤ x ≤ 15 and 0 ≤ y ≤ 360 and the domain is continuous

From the question, we have

Gallon gas tank = 15 gallons

This means that the domain is from 0 to 15

This can be represented as 0 ≤ x ≤ 15

For the range, we have

0 * 24 ≤ y ≤ 15 * 24

Evaluate

0 ≤ y ≤ 360

This means that

Range: 0 ≤ y ≤ 360

Lastly, the domain of the situation is continuous

This is so because the gas in the tank can take decimal values

Take for instance, the gas tank can be 13.79 gallons full

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Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

Hello there!

If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:

1  2  3  4  5  6  7  8  9  10  11  12

When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.

In this example: What is the probability of picking an even number?

Ask yourself: What are we trying to find?

We are trying to find the probability of even numbers.

Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?

The bag consists of: 1  2  3  4  5  6  7 8  9  10  11  12

Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.

Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.

Finally, think about: What is the total amount of samples in this bag?

We know that there are 12 balls, so 12 would be the total amount.

To conclude, we can find 6 even numbers in a bag of 12 balls;

Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].

We know that each bow cost $5.25.

We also know that the woman spent a total of $84.

Lets call x the number of bows she bought.

Then, we can write:

The woman bought 16 bows.

‘B’ had a better college entrance exam score due to the higher value of Z-Score.

The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.

[tex]Z=\frac{(observation-mean)}{standard deviation}[/tex]

By putting the values as given in the question,We get,

A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.

B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.

Thus ‘B’ had a better score.

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The approximate volume of the pyramid when it's 75% full is 303.75 inches³.

The volume of a square base pyramid can be represented as follows:

volume of the square base pyramid = 1 / 3 Bh

where

Therefore, the square bas pyramid has a base side of 9 inches and height of 15 inches. Let's find the volume when it's 75% full.

B = 9² = 81 inches²

h = 15 inches

Therefore,

volume of the square base pyramid = 1 / 3 × 81 × 15

volume of the square base pyramid = 81 × 5

volume of the square base pyramid = 405 inches³

Therefore, when it's 75% full

volume  = 75% of 405

volume = 75 / 100 × 405

volume = 30375 / 100

volume = 303.75 inches³

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The increase in the national debt from 2005 to 2015 using scientific notation is 1.3176 × 10^13.

Scientific notation simply means a way of expressing numbers that are either too large or too small.

The U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015 and in September 29,

2005, the national debt was 4.974 x 10^12 dollars.

The increase will be the difference between the two notations. This will be:

= 1.815 x 10^13 - 4.974 x 10^12

= 1.3176 × 10^13

The increase is 1.3176 × 10^13.

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The required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.

As of the given condition,
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29, 2005, the national debt was 4.974 x 10^12 dollars.

Here,
The required increase in the debt is evaluated as the arithmetic difference of the debt in the years 2015 and 2005.

So.
Increase in debt = 1.815 × 10¹³ - 0.4974 × 10¹³ = 1.3176 × 10¹³

Thus, the required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.

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SOLUTION

From the question

Cross multiplying you have that

Hence, the answer is 70

The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0 and the definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)".

A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x². Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Here,

f(x)=2x²-x³

g(x)=-x²

f(x)/g(x)=(2x²-x³)/-x²

=x²(2-x)/-x²

f(x)/g(x)=x-2

The definition of function defines "function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)". The value of f(x)/g(x)=x-2 for f(x)=x²-x³ + x² and g(x) = -x² and where x # 0.

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Answer:

In both cases we get the same answer: the sum of the first 100 positive even numbers is 10,100.

Step-by-step explanation:

2 + 4 + 6 + 8 + ....+ 198 + 200 =

= (2 + 200) + (4 + 1998) + ... + (100 + 102) = 50*202 = 10,100

The exponential model A=64.5e^0.02t describes the population, A of a country in millions, t years after 2003. The population of the country will be 108 million in

we have the expression

A=64.5e^0.02t

For A=108

substitute

108=64.5e^0.02t

108/64.5=e^0.02t

Apply ln both sides

ln(108/64.5)=ln(e^0.02t)

ln(108/64.5)=0.02t(ln(e))

ln(108/64.5)=0.02t

solve for t

t=ln(108/64.5)/0.02

t=26 years

therefore

2003+26=2029

answer is

Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.

As given in the question,

Given equation :

|x – 55| = 4.2

To determine the maximum and minimum speed in miles per hour from the given equation we have,

x-55 = 4.2 or x-55 =-4.2

Add 55 both the side of the equation,

x-55 +55 =4.2+55  or x-55+55 = -4.2 +55

x =59.2 or x = 50.8

Maximum speed is 59.2 determine by equation x-55 = 4.2

Minimum speed is 50.8 determine by equation x-55 = -4.2

Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to

x -55 =4.2.

The complete question is:

On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?

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the unit price for 1 lb of turky is $0.99

The cost of 14 lb of turkey = $13.86

let the cost of 1 lb of turkey = y

The unit price is the cost for 1lb of turkey:

14 lb = 13.86

1 lb = y

cross multiply:

14(y) = 1(13.86)

14y = 13.86

divide both sides by 14:

14y/14 = 13.86/14

y = 0.99

Hence, the unit price for 1 lb of turky is $0.99

The problem states that "three increased by a quotient", this implies that the three is separated from the quotient, therefore, we need to create the equation in the following manner:

The correct answer is "b".

Answer:

157 cups

Step-by-step explanation:

First, convert in to cm

83.375 in  * 2.54   Cm/in = 211.77 cm

Each cup adds 1.3 cm to the (9.2 - 1.3 cm) base     (Base is 7.9)

211.77  =  7.9  + 1.3  x          X is the number of cups

         X = 156.9 = ~ 157 cups