Which corectly renames 7/8 and 5/6 using a common denominator

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Answer:

I'm pretty sure it's Distributive property

Step-by-step explanation:

I think this because on the outsides of the parenthesis you can distribute the 2 to the other numbers.

Answer:

P(x) = 35,900 + 2,800(x-1)

Step-by-step explanation:

P(x)

P(1) = $35,900

P(4) = $44,300

Difference in profits

P(4) - P(1)

= P(3)

= $44,300 - $35,900

= $8,400

Rate of change per year = $8,400 / 3

= $2,800 per year

The linear equation

P(x) = 35,900 + 2,800(x-1)

Where

x = number of years

The cost of a paperback book (P) is $5 and the cost of a hardcover book (H) is $7.50.

Let's denote the cost of a paperback book as "P" and the cost of a hardcover book as "H". We can set up a system of equations based on the given information:

Equation 1: 2P + 2H = 25

Nate buys two paperbacks (2P) and two hardcovers (2H) for a total of $25.

Equation 2: 3P + H = 22.50

Tia buys three paperbacks (3P) and one hardcover (H) for a total of $22.50.

Now, we can solve this system of equations to find the values of P and H. By rearranging Equation 1, we get:

2P = 25 - 2H

P = (25 - 2H)/2

Substituting this value of P into Equation 2, we have:

3((25 - 2H)/2) + H = 22.50

Simplifying the equation, we get:

37.5 - 3H + H = 22.50

-2H = 22.50 - 37.50

-2H = -15

H = -15/(-2)

H = 7.50

Substituting this value of H back into Equation 1, we can find P:

2P + 2(7.50) = 25

2P + 15 = 25

2P = 10

P = 5

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The price of a paperback book is $5, and the price of a hardcover book is $7.50.

Let's denote the price of a paperback book as "P" and the price of a hardcover book as "H".

Nate buys two paperbacks and two hardcovers for $25:

Equation 1: 2P + 2H = 25

Tia buys three paperbacks and one hardcover for $22.50:

Equation 2: 3P + 1H = 22.50

We can solve this system of equations using any method, such as substitution or elimination. Here, we'll use the substitution method.

2P + 2H = 25

2H = 25 - 2P

H = (25 - 2P)/2

H = 12.5 - P

Now, substitute this expression for H into Equation 2:

3P + 1H = 22.50

3P + 1(12.5 - P) = 22.50

3P + 12.5 - P = 22.50

2P + 12.5 = 22.50

2P = 22.50 - 12.5

2P = 10

P = 10/2

P = 5

Now that we have the value of P, we can substitute it back into Equation 1 to find H:

2P + 2H = 25

2(5) + 2H = 25

10 + 2H = 25

2H = 25 - 10

2H = 15

H = 15/2

H = 7.5

Therefore, the price of a paperback book (P) is $5, and the price of a hardcover book (H) is $7.50.

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In the given scenario, the value "1672" represents the number of car owners in a country.

A parameter is a characteristic or measure that describes a population, while a statistic is a characteristic or measure that describes a sample.

Since the study was conducted on all 1672 car owners in the country, the value "1672" represents the entire population and is therefore a parameter. It describes the total number of car owners in the country as a whole.

In summary, the value "1672" is a parameter in this context, as it represents a characteristic of the entire population of car owners in the country.

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The measure of both angles is 60 and 180 degrees respectively.

In a literal sense, corresponding means pairwise angles. Like the right corner angles of two triangles etc. But usually, we take them as:

For two similar figures, the pair-by-pair similar angles of those two similar figures are called corresponding angles. They are of the same measurement.

Given that angle a is corresponding to angle b the measure of angle b is 2x+60 and the measure of angle a is x.

Since both the angles are equal then;

Angle A = Angle B

x = 2x + 60

Solving for x;

2x - x = -60

x = -60

Therefore, the measure of both angles is 60 and 180 degrees.

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Answer:

216

Step-by-step explanation:

Split the image into geometric shapes, and then calculate the area of each shape, then add them all up to get your grand total of 216

Answer:

39

Step-by-step explanation:

5x-20=2x+10 (opposite sides of parallelogram are equal)

5x-2x=10+20

3x=30

x=30/3

x=10

Now putting the value of x in 4x-1, we get

(4×10)-1

= 40-1

= 39

Answer:

She deposits $17.00 each week

Step-by-step explanation:

You multiply 85 times 0.2 which gives you 17.

Answer:

60

Step-by-step explanation:

Answer:

pretty sure its B the degree is the biggest number of exonent and the leading coefficient is the number in front of the x that is the biggest. u can look up the graph for end behavior.

Step-by-step explanation:

The probability that the molecules will have a total energy of 6 kJ is 1/9 or approximately 0.111.

To find the probability that the two indistinguishable molecules will have a total energy of 6 kJ, we need to consider all the possible energy level combinations they can occupy.
There are a total of 3 possible energy levels for each molecule, which means there are 3 x 3 = 9 possible energy level combinations for the two molecules. We can list these combinations as follows:
- 1 kJ + 1 kJ = 2 kJ
- 1 kJ + 2 kJ = 3 kJ
- 1 kJ + 3 kJ = 4 kJ
- 2 kJ + 1 kJ = 3 kJ
- 2 kJ + 2 kJ = 4 kJ
- 2 kJ + 3 kJ = 5 kJ
- 3 kJ + 1 kJ = 4 kJ
- 3 kJ + 2 kJ = 5 kJ
- 3 kJ + 3 kJ = 6 kJ
Out of these 9 possible combinations, only one combination has a total energy of 6 kJ, which is the last one in the list. Therefore, the probability that the probability will have a total energy of 6 kJ is 1/9 or approximately 0.111.
This calculation is based on the assumption that each energy level is equally likely to be occupied by each molecule. If there are any other factors that affect the probability of probability each energy level, the calculation may be different.

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The multiplier for the given economy is 4.

The multiplier represents the magnification effect of an initial change in autonomous spending on the overall output of an economy. It is calculated using the formula 1 / (1 - MPC), where MPC is the marginal propensity to consume.

In this case, the MPC is given as 0.75, which means that for every additional dollar of income, individuals spend 75 cents. The multiplier is calculated as 1 / (1 - 0.75) = 4.

The multiplier of 4 indicates that a change in autonomous spending, such as investment or consumption, will have a four times larger impact on the overall output of the economy. In other words, for every dollar increase in autonomous spending, the total output of the economy will increase by four dollars.

In this scenario, since the intended investment is $130, the total increase in output would be 4 * $130 = $520. Therefore, the multiplier effect amplifies the initial change in autonomous spending and leads to a larger increase in output in the economy.

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Answer:

The answer is a

Step-by-step explanation:

As per the daily mean, the peak power load when max is possible to calculate with a computer or calculator.

The highest outdoor temperature and the mean daily peak power load for a sample of 6 days are provided in the table. However, it is impossible to estimate the peak power load when the highest temperature is 84 without more details. The presented data only reflects a sample of 6 days, which may not be typical of the full population, and the connection between peak power load and maximum temperature may not be linear. Furthermore, using the provided data to conduct any calculations is impossible without access to a computer or calculator.

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The slope is \(\frac{3}{4}\)

What is slope ?

 A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not. Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

here the given two pints are

\((x_1,y_1)=(-2,4)\\(x_2,y_2)=(6,10)\)

Now using slope formula,

slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

=> slope m = \(\frac{10-4}{6+2}\)

=> slope m = \(\frac{6}{8}\)

=> slope m = \(\frac{3}{4}\)

Therefore the slope is \(\frac{3}{4}\).

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\(f+44^{\circ}\) and \(71^{\circ}\) are opposite angles.

Therefore

\(f+44^{\circ}=71^{\circ}\\f=27^{\circ}\)

27°

Using information about angles, we can create an equation to solve for f.

Verticle Angles

There is a special angle relationship known as vertical angles. Vertical angles are opposite angles made by interesting lines. The left angle  (made up of f and 44°) and the right angle (71°) are vertical angles. We know this because they are opposite each other and formed by the same interesting lines. Verticle angles are always congruent. This means that their measurements are equal.

Solving for f

We can use the information above to create an equation. Since we know that the left and right angles are congruent, we can set the equal to each other.

Now, we can subtract 44 from both sides and solve for f.

So, angle f must equal 27°.

Answer:

£10.1

Step-by-step explanation:

Highest exchange rate=1.3401

Lowest exchange rate=1.3199

The money Khan would have received more if he exchanged currencies at the highest rate compared to the lowest rate=500*(1.3401-1.3199)=£10.1

Answer:

20

Step-by-step explanation:

- Combine multiplied terms into a single fraction

- Eliminate redundant parentheses

- Multiply all terms by the same value to eliminate fraction denominators

The expression that represent the number of seat in the theatre is 27 × n.

A theatre has 27 rows with n seats in each row. Therefore, the expression that shows the number of seats in the entire theatre can be represented as follows:

An algebraic expression  is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication, division etc.

Hence, the theatre has 27 rows with n seat in each row.

Therefore,

number of seats in the theatre = 27 × n

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The missing side of the given triangle is 5 units.

Given, a right angled triangle with height and base 3 and 4 respectively.

So, Height = 3 units and Base = 4 units

Let the hypotenuse or the missing side be h,

On applying the Pythagoras Theorem, we get

h² = (Height)² + (Base)²

h² = 3² + 4²

h² = 9 + 16

h² = 25

h = √25

h = 5

Hence, the missing side of the given triangle is 5 units.

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Answer: 6 units

Step-by-step explanation:

I know that in a triangle, there's two angles that have equal measures, then the sides opposite to them are equal in length. Thus, the length of side AB is 6 units.

Answer:

AB = 38.64 m

Step-by-step explanation:

\( \cos \: 75 \degree = \frac{10}{x} \\ \\ x = \frac{10}{ \cos \: 75 \degree } \\ \\ x = 38.637033052 \\ \\ x \approx \: 38.64\)

AB = 38.64 m

Answer: Let's assume that it takes Pam x minutes to give a haircut and y minutes to color hair.

From the information given, we can create two equations:

2x + y = 83 (Pam gave 2 haircuts and colored the hair of 1 client in 83 minutes)

1x + 3y = 164 (Pam gave 1 haircut and colored the hair of 3 clients in 164 minutes)

To solve for x and y, we can use elimination method or substitution method. Let's use substitution method.

From the first equation, we can solve for y in terms of x:

y = 83 - 2x

Substituting this into the second equation, we get:

1x + 3(83 - 2x) = 164

Simplifying and solving for x, we get:

x = 30

Substituting this value of x into either of the two equations, we can solve for y:

2(30) + y = 83

y = 23

Therefore, it takes Pam 30 minutes to give a haircut and 23 minutes to color hair.

Step-by-step explanation:

Answer:

1. 4x+3x were added together because they are like terms

2. We subtracted 5 from both sides of the equation

3. We divide both sides of the equation by seven

Step-by-step explanation:

I hope this is what you were looking for... Good luck!

Answer:

100

Step-by-step explanation:

40 +40=80 (both bottom angles)

180-80=100

All of 4x+8 is under a cube root sign.

=====================================================

Work Shown:

To find the inverse, we swap x and y, then solve for y.

\(y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\\)

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

Side note:

If \(f(x) = \frac{1}{4}x^3 - 2\) and \(g(x) = \sqrt[3]{4x+8}\), then \(f(g(x)) = x\) and \(g(f(x)) = x\)for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.

The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.

Although the question does not specify the options, but I have specified my answer as follows:

Given:

The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.

Account Opening Charges: $10

Starting amount: $d

The total amount in the account: $m

Let us say the depositor deposits an amount $k for 'i' number of months

Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.

I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.

The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time

⇒m=d-10+k×i

This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.

Therefore, the following equation is m=d-10+k×i.

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The greatest common divisor for all eight digit integer is 10001

How to find greatest common divisor?

The greatest positive number that is a common factor of both the positive integers (a, b) is what is known as the greatest common divisor for a set of positive integers (a, b) (a, b). Since 1 is always the least positive integer that any two numbers have in common, the GCD of any two integers is never negative or zero. The two numbers' greatest common divisor can be found in one of two ways:

The common divisors are discovered

Utilizing Euclid's algorithm

Any number written in the form of abcdabcd can we written as

(abcd * 10000) + abcd

abcd ( 10000 + 1)

abcd ( 10001)

∴ The greatest common divisor of all eight- digit number is 10001

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