write 9/8 in atleast 3 different ways as a sum of fractions

We can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

If there are integers s and t such that as + bt = 15, then we can conclude that gcd(a, b) divides 15. This is known as Bézout's identity, which states that for any two integers a and b, there exist integers s and t such that as + bt = gcd(a, b).

To see why this is true, consider the set of all linear combinations of a and b, that is, the set {ax + by : x, y are integers}. This set contains all multiples of gcd(a, b) since gcd(a, b) divides both a and b.

Therefore, gcd(a, b) is the smallest positive integer that can be expressed as a linear combination of a and b.

Now, if as + bt = 15, then 15 is a linear combination of a and b, which means that gcd(a, b) divides 15.

Conversely, if gcd(a, b) divides 15, then we can find integers s and t such that as + bt = gcd(a, b), and we can scale this equation to obtain as' + bt' = 15, where s' = (15/gcd(a, b))s and t' = (15/gcd(a, b))t.

Therefore, we can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

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Answer:

Multiply the first equation by 5 and the second equation by 2. Then add.

Multiply the first equation by 2 and the second equation by 5, then subtract.

Step-by-step explanation:

Given

\(- 2x + 5y = -15\)

\(5x + 2y = -6\)

Required

Steps to solve using elimination method

From the list of given options, option 2 and 3 are correct

This is shown below

Option 2

Multiply the first equation by 5

\(5(- 2x + 5y = -15)\)

\(-10x + 25y = -75\)

Multiply the second equation by 2.

\(2(5x + 2y = -6)\)

\(10x + 4y = -12\)

Add

\((-10x + 25y = -75) + (10x + 4y = -12)\)

\(-10x + 10x + 25y +4y = -75 - 12\)

\(29y = -87\)

Notice that x has been eliminated

Option 3

Multiply the first equation by 2

\(2(- 2x + 5y = -15)\)

\(-4x + 10y = -30\)

Multiply the second equation by 5

\(5(5x + 2y = -6)\)

\(25x + 10y = -30\)

Subtract.

\((-4x + 10y = -30) - (25x + 10y = -30)\)

\(-4x + 25x + 10y - 10y= -30 +30\)

\(21x = 0\)

Notice that y has been eliminated

Answer:

How many solutions does the system have?

✔ exactly one

The solution to the system is

(

⇒ 0,

⇒ -3).

Step-by-step explanation:

the next two parts

Answer:

her

Step-by-step explanation:

In the balance sheet, mortgage notes payable are reported as a long-term liability only.

Mortgage notes payable represent the amount owed by a company for a mortgage loan. These loans are typically long-term obligations that are expected to be repaid over an extended period, often several years. Therefore, mortgage notes payable are classified as long-term liabilities in the balance sheet.

Current liabilities are obligations that are expected to be settled within a short period, usually one year or less. Since mortgage notes payable typically have a longer repayment term, they do not meet the criteria to be classified as current liabilities.

By reporting mortgage notes payable as a long-term liability, the balance sheet provides a clear distinction between the company's short-term and long-term obligations, helping stakeholders understand the company's financial position and obligations over different time horizons.

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The complete statement is -

"Even though the triangles are all different sizes, the decimal values for each ratio are same."

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is that -

"Even though the triangles are all different sizes, the decimal values for each ratio are ​_____."

We can write the complete statement as -

"Even though the triangles are all different sizes, the decimal values for each ratio are same."

Therefore, the complete statement is -

"Even though the triangles are all different sizes, the decimal values for each ratio are same."

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Answer:

\(x=3.5\)

Step-by-step explanation:

Notice that CD bisects Angle C.

Then by the Angle Bisector Theorem, we can write the following proportion:

\(\frac{6}{4.2}=\frac{5}{x}\)

Now, we can solve for x. Cross multiply:

\(5(4.2)=6(x)\)

Multiply:

\(21=6x\)

Divide both sides by 6:

\(x=21/6=7/2=3.5\)

Hence, the vale of x is 3.5.  

Answer:

4.2

Step-by-step explanation:

Each equation is in slope-intercept form will be y = -2x+3 and y=3x-7 respectively.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.

Given equations;

2x+y=3

-2y=14-6x

Equation 2 in the slope-intercept form can be written as;

y= 3x-7

Equation 1 in the slope-intercept form can be written as;

y= -2x+3

Hence,each equation is in slope-intercept form will be y = -2x+3 and y=3x-7 respectively.

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Answer:

y=-2x+3, y=3x+-7 How do the slopes and y–intercepts of the two equations compare? The slopes and the y-intercepts are different.They system represents lines that Intersect at one point Exactly one solution

Step-by-step explanation:

edge 2022

Answer:

Maria chose C. 2682

Step-by-step explanation:

Answer:

140÷440(you can write it as a fraction)

=0.318181882

=0.32

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Answer:

A. 400*45.2=400*45+400*0.2=18000+80=18080

B. 14.9*100=15*100-0.1*100=1500-1=1490

C. 76.2*200=76*200+0.2*200=15200+4=15204

Step-by-step explanation:

The length of the rectangle with a perimeter of 24 inches and a width of 7 inches is 5 inches.

The perimeter of a rectangle is given by the formula: P = 2l + 2w where P is the perimeter, l is the length, and w is the width. We know that the perimeter of the rectangle is 24 inches and the width is 7 inches.

Substituting the given values in the formula for the perimeter of the rectangle, we have:

24 = 2l + 2 × 7

Simplifying, 24 = 2l + 14

Subtracting 14 from both sides, we get:

10 = 2l

Dividing both sides by 2, we get: l = 5

Therefore, the length of the rectangle is 5 inches.

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The probability that the five selected individuals are of the same sex is 0.252.

To calculate the probability, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes: The total number of ways to select 5 individuals out of 20 is given by the combination formula, which is denoted as C(20, 5) and is equal to 15504.

Number of favorable outcomes: We need to consider two cases: selecting 5 women or selecting 5 men.

Case 1: Selecting 5 women: The number of ways to select 5 women out of 10 is given by C(10, 5), which is equal to 252.

Case 2: Selecting 5 men: The number of ways to select 5 men out of 10 is also C(10, 5), which is equal to 252.

Therefore, the total number of favorable outcomes is 252 + 252 = 504.

Probability: The probability of selecting 5 individuals of the same sex is the ratio of favorable outcomes to total outcomes. So, the probability is 504/15504 = 0.0325.

The probability that the five individuals selected at random are of the same sex is 0.0325, which is equivalent to approximately 0.252 when expressed as a fraction.

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The number of different fruit salads that can be made using up to three  different fruits is 41

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

For each possible number of fruits (1, 2, or 3), we can count the number of ways to choose that many fruits from the available options and then sum up the results

To make a fruit salad with one fruit, we can choose any of the six available fruits. There are 6 ways to do this

To make a fruit salad with two fruits, we can choose any two fruits from the six available options. This can be done using the combination formula

C(6,2) = 6! / (2! x (6-2)!) = 15

So, there are 15 ways to make a fruit salad with two fruits

And , To make a fruit salad with three fruits, we can choose any three fruits from the six available options. This can be done using the combination formula:

C(6,3) = 6! / (3! x (6-3)!) = 20

So , the total number of ways A = 6 + 15 + 20

A = 41 ways

Hence , the different fruit salads is A = 41

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9514 1404 393

Answer:

  x = 38.2

Step-by-step explanation:

Each of the functions of x represents the measure of an angle in the triangle. You write an equation for x by using what you know about the relationships of angles in a triangle: their sum is 180°.

  (2x) +(x -18) +(2x +7) = 180

  5x -11 = 180 . . . . . . . collect terms

  5x = 191 . . . . . . . . . . add 11

  x = 38.2 . . . . . . . . . divide by 5

The level of measurement for the variable size of soft drinks and popcorn combos that come in sizes that are small, medium, large, and jumbo sold by a movie theater concession stand is "ordinal level of measurement."Explanation:The four primary levels of measurement are nominal, ordinal, interval, and ratio.

The nominal level of measurement is the lowest, and the ratio level of measurement is the highest. The level of measurement for the variable size of soft drinks and popcorn combos sold by a movie theater concession stand is ordinal.The variable size of soft drinks and popcorn combos that come in sizes that are small, medium, large, and jumbo sold by a movie theater concession stand is measured using an ordinal scale

. It indicates that the variable's levels are ranked in a specific order or sequence. The sizes can be ranked as small, medium, large, and jumbo, with jumbo being the highest level of measurement. The difference between each level of the ordinal level of measurement is undefined, which means that the difference between small, medium, large, and jumbo cannot be established using the ordinal level of measurement. Therefore, the variable size of soft drinks and popcorn combos is measured at an ordinal level of measurement.

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Answer:

x-2y=7

Step-by-step explanation:

Explanation:

There are 8 letters in the word "GEOMETRY".

Use the nPr permutation formula with n = 8 and r = 7 and you'll find that 8P7 = 40320.

Or you can compute it like this 8*7*6*5*4*3*2 = 40320

This would be the answer if we could tell the E's apart.

However, we cannot tell the E's apart, so we have to divide by 2 to correct for the double-counting.

There are 40320/2 = 20160 different seven letter combinations possible.

Answer:

The median is 17 and the mode is 19

Step-by-step explanation:

Answer

g(x) = 2ˣ⁺² or 2^(x + 2)

Explanation

When a function f(x) is translated horizontally along the x-axis by a units, the new function is represented as

f(x + a) when the translation is by a units to the left.

f(x - a) when the translation is by a units to the right.

Looking at the coordinates of the points given on f(x) and g(x), we can see that g(x) is just f(x) translate 2 units to the left.

Hence, if f(x) = 2ˣ

g(x) = f(x + 2) = 2ˣ⁺² or 2^(x + 2)

Hope this Helps!!!

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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a) The probability that all 3 of your answers are incorrect is 27/64.

b) The probability that all 3 of your answers are correct is 1/64.

c) The probability that exactly 1 of your answers are correct is 9/16.

(a) The probability of guessing the incorrect answer for a single question is 3/4. Since each question is independent of the others, the probability of guessing all 3 questions incorrectly is:

(3/4) x (3/4) x (3/4) = 27/64

(b) Similarly, the probability of guessing all 3 questions correctly is:

(1/4) x (1/4) x (1/4) = 1/64

(c) To calculate the probability that exactly 1 of your answers are correct, we need to consider all possible ways in which this could happen. There are three questions and each question has four possible answers, so there are a total of 4 x 4 x 4 = 64 possible ways to answer all three questions.

The number of ways to answer exactly one question correctly is:

3 x (1/4) x (3/4) x (3/4) = 27/64

(We are multiplying by 3 because there are three ways to choose which question to answer correctly.)

Similarly, the number of ways to answer exactly two questions correctly is:

3 x (1/4) x (1/4) x (3/4) = 9/64

(The factor of 3 comes from the three ways to choose which questions to answer correctly.)

Finally, the number of ways to answer all three questions incorrectly is:

(3/4) x (3/4) x (3/4) = 27/64

So the probability of answering exactly one question correctly is:

27/64 + 9/64 = 36/64 = 9/16

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Answer:

12/8

Step-by-step explanation:

To find a reciprocal of a fraction, just flip the numbers upside down or invert it.    

In other words, swap the numerator over the denominator to get the reciprocal.

Example: 3/4 → 4/3

Have a great day and stay safe!

Answer:

5

Step-by-step explanation:

The opposite of -5 is 5. You find this opposite by switching the negative sign to a positive sign.

Answer:

5

Step-by-step explanation:

Just take away the sign or add the sign from the number to get a integer. There you go it's just that easy️‍ enjoy good day

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Answer:

Yes, it is!!!

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The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

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The difference between the greatest and least amount of cupcake flavors is 0. 75

From the information given, we have that:

1/ 4 of cupcakes = chocolates

0. 2 of cupcakes = vanilla

Remaining = strawberry

Let the total number of cupcakes be 1

Strawberry = 1 - chocolates - vanilla

Strawberry = 1- 0. 25 - 0. 2

Strawberry  = 1 - 0. 05

Strawberry = 0. 95

The difference between the greatest and least amount of cupcake flavors

= Strawberry cupcakes - Vanilla cupcakes

= 0. 95 - 0. 2

= 0. 75

Thus, the difference between the greatest and least amount of cupcake flavors is 0. 75

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a) The mean can be calculated by adding all values and then divide by the total number of values:

b) The median is the middle value in the list of numbers, then you have to order the numbers as follows: 0, 0, 1, 3, 6.

c) The mode is the value that occurs most often, as you have a 0 value twice, then

d) To calculate the sample variance you can use this formula

The sample standard deviation is the square root of sample variance, then

The condition that is not met is that the sample size must be large enough to assume that the sample proportions are normally distributed.

Number is a mathematical object used to count, measure, and label. It is one of the fundamental building blocks of mathematics and is essential for any kind of calculation or measurement. Number is an abstract concept that is used in many different ways, from counting objects to expressing complex mathematical systems. Numbers can be used to represent anything from a single item to the entire universe. Numbers are also used to represent abstract ideas such as time, money, and probability.

With a sample size of only 25, it is not possible to assume that the sample proportions follow a normal distribution. As such, calculating a confidence interval for the population proportion of bags with too much salt is not possible.

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Complete questions as follows-
sapling a quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. of the bags inspected, 3 had too much salt. which of the conditions for calculating a confidence interval for the population proportion of bags with too much salt is not met?