Which set of rational numbers is correctly ordered from least to greatest?
-0.5 -0.4 -0.3

1) Disprove the following statement by giving a counterexample: "For all integers m and n, if 2m + n is odd then m and n are both odd."

Counterexample: Let m = 2 and n = 1. Then 2m + n = 5, which is odd, but m = 2 is even

2) Starting point: "Let x be a real number such that x > 1."

Conclusion to be shown: "Then x^2 > x."

3) The statement " The difference of any two odd integer is even" is true because we can prove by assuming that a and b are odd integers, and then show that their difference (a - b) is even.

1) Counterexample to "For all integers m and n, if 2m + n is odd then m and n are both odd":

Let m = 2 and n = 1. Then 2m + n = 5, which is odd, but m = 2 is even, so the statement is false.

Starting point: "Assume that for all integers m and n, if 2m + n is odd, then m and n are both odd."

Conclusion to be shown: "The assumption is false, as there exists a counterexample where m is even and 2m + n is odd."

2) The statement "For all real number x, if x > 1 then x^2 > x" is true.

Starting point: "Let x be a real number such that x > 1."

Conclusion to be shown: "Then x^2 > x."

To prove this, we can start by factoring x^2 - x as x(x-1). Since x is greater than 1, both factors are positive. Therefore, x(x-1) is positive, which implies that x^2 - x is positive. This proves that x^2 > x when x > 1.

3) The statement "The difference of any two odd integers is even" is true.

Starting point: "Let a and b be odd integers."

Conclusion to be shown: "Then a - b is an even integer."

Since a and b are odd, they can be expressed as a = 2m + 1 and b = 2n + 1, where m and n are integers. Then, a - b = (2m + 1) - (2n + 1) = 2m - 2n = 2(m - n), which is even since it is a multiple of 2. Therefore, the difference of any two odd integers is even.

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The mathematical mistake that Riley made is that:
"She used the wrong common denominator." (Option A)

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

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Answer:

She used the wrong common denominator.

Step-by-step explanation:

Answer:

15days

Step-by-step explanation:

number of days Barry work = 20

If Malaysia is 25% efficient

Number of days less than Barry = 25% of 20

Number of days less than Barry = 0.25 * 20

Number of days less than Barry = 5

Number of days worked by Malaysia = 20 - 5

Number of days worked by Malaysia = 15days

Answer:  195 inches.

Step-by-step explanation:

Given: Sam is building a model of an antique car.

The scale of his model to the actual car is 1:10.

⇒Scale factor = \(\dfrac1{10}\)

Since,  Length of actual figure = (Length of model ) ÷ Scale factor.

If length of model of car = 19.5 inches.

Then, the length of the actual car = \(19.5\div\dfrac{1}{10}=19.5\times10=195\text{ inches}\)

Hence, the length of the actual car  = 195 inches.

Answer:

a. 3/40

b. 37/40

c. 2/39

d. 37/39

e. 3/39

h. 36/39

k. 1/260

m. 37/520

n. 37/520

w. 111/130

Step-by-step explanation:

First person:

a. 3/40

b. 37/40

_____

Second person:

left-handed branch of tree diagram: since the first person was left-handed, it means there is one less left-handed person, and one less person for the total

c. 2/39

d. 37/39

not left-handed branch of tree diagram: since the first person wasn't left-handed, there are still 3 left-handed people, and there is one less person for the total.

e. 3/39

h. 36/39

_____

for the final probabilities, just multiply along the tree branches:

k = a × c = 1/260

m = a × d = 37/520

n = b × e = 37/520

w = b × h = 111/130

Answer:

x = 82°

y = 8°

Step-by-step explanation:

\(x + 98 = 180 \\ x = 180 - 98 \\ x = 82\)

\(y + x = 90 \\ y + 82 = 90 \\ y = 90 - 82 \\ y = 8\)

Answer:

\(y^{-2}\)

Step-by-step explanation:

there is a rule that says

\((x^a)^b=x^{ab}\)

so in our case

\((y^{\frac{-1}{2} })^4=y^{\frac{-4}{2} }=y^{-2}\)

so that's our answer

\(y^{-2}\)

Answer:

y^-2 or 1/y²

Step-by-step explanation:

y^-1/2 * 4

y^-4/2

y^-2

The solution cannot be written as a ratio of two integers, the solution is irrational

The formula calculating the area of a square is given as

A = L^2

Given the parameters

A = 150

Substitute

150 = L^2

l = √150
L= √25 * 6

L =5√6

Since the solution cannot be written as a ratio of two integers, the solution is irrational

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The minimum cost to meet the minimum requirements is $1280.

To determine the minimum cost, we need to calculate the number of platters required to meet the minimum requirements for each item (hamburgers, hot dogs, and chicken wings) and then multiply it by the cost of each platter.

Let's calculate the number of platters required for each item:

For hamburgers:

80 hamburgers / 1 burger per platter = 80 platters

For hot dogs:

95 hot dogs / 1 hot dog per platter = 95 platters

For chicken wings:

380 chicken wings / 5 chicken wings per platter = 76 platters

Now, let's calculate the cost:

For Platter A:

80 platters * $16 per platter = $1280

For Platter B:

95 platters * $20 per platter = $1900

The minimum cost would be the lower of the two costs, which is $1280. Therefore, the minimum cost to meet the minimum requirements is $1280.

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Complete Question:

The Very Possible Foods Company makes vegan versions of hamburgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of 1 burger, 3 hot dogs, and 5 chicken wings, which costs $16. Platter B consists of 2 burgers, 1 hot dog, and 8 chicken wings, which costs $20.

A barbecue organizer requires 80 hamburgers, 95 hot dogs, and 380 chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?

The solution of the equation is x = 6±2√11.

What is a quadratic equation?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Here, we have

Given: x² - 12x = 8

Now, we factorize the given equation and find the solution.

x² - 12x = 8

x² - 12x - 8 = 0

We apply here the quadratic formula.

= (-b ±√b²-4ac)/2

= (12 ±√12²-4×1×(-8))/2

= (12±√144+32)/2

= (12±√176)/2

= (12±4√11)/2

= 6±2√11

Hence, the solution of the equation x² - 12x = 8 is 6±2√11.

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The correct statement that compares the value of the 6 in 26.495 and 17.64 is the value of the 6 in 26.495 is 10 times the value of the 6 in 17.64. Therefore, the correct option is D.

This is because the value of a digit is determined by its place in the number. In 26.495, the 6 is in the tenths place, which means it represents 6/10 or 0.6. In 17.64, the 6 is in the hundredths place, which means it represents 6/100 or 0.06. Therefore, the value of the 6 in 26.495 is 0.6 and the value of the 6 in 17.64 is 0.06.

To compare these values, we can divide the value of the 6 in 26.495 by the value of the 6 in 17.64. This gives us 0.6/0.06 = 10. Therefore, the value of the 6 in 26.495 is 10 times greater than the value of the 6 in 17.64 which corresponds to option D.

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Angle ∠C and angle ∠E are supplementary angles. Then the correct option is B.

The sum of the supplementary angle is 180 degrees.

The sum of two acute angles will be less than 180 degrees.

Similarly, the sum of two obtuse angles is more than 180 degrees.

The addition of angle ∠C and angle ∠E is calculated as,

∠C + ∠E = 61° + 119°

∠C + ∠E = 180°

The addition of angle ∠C and angle ∠E is 180°. Thus, the correct option is B.

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Answer: its 0 right or is it supposed to be a face or sumthin

Step-by-step explanation:

If triangle ABC is a right triangle and

A half circle has 180 degrees, so the sum of \(\begin{gathered} 90\text{ + (}x\text{-12)}+x\text{ = 180 } \\ x\text{ - 12 + x = 180 - 90 } \\ 2x\text{ - 12 = 90} \\ 2x\text{ = 90 + 12} \\ 2x\text{ = 102} \\ x=\text{ 102/2 } \\ x=\text{ 51º} \end{gathered}\)So, if x= 51º, then m

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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The solution for the system of equations is (-19,55).

As given the equations in the question

y = –3x – 2

Simplify the above

y + 3x = -2

5x + 2y = 15

Multiply y + 3x = -2 by 2 and subtracted from 5x + 2y = 15.

2y - 2y + 5x -6x = 15 + 4

-x = 19

x = -19

Putting the value of x in the equation y + 3x = -2.

y + 3 × - 19 = -2

y - 57 = -2

y = -2 + 57

y = 55

Therefore the solution for a system of equations is (-19,55).

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Answer:

96 students attend chess club after school on Wednesday's.

Step-by-step explanation:

To solve this problem, simply multiply 800 x 0.12.

    800 x 0.12 = 96

I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer Brainliest. It would help a lot. Have a great day!

Answer:

\(\huge\boxed{\text{96 students}}\)

Step-by-step explanation:

In order to find how many students stay back for Chess Club, we want to find 12% of 800.

To do this, we can set up a percentage proportion.

\(\frac{12}{100} = \frac{x}{800}\)

We can now solve for x by cross multiplying.

\(800 \cdot 12 = 9600\\9600 \div 100 = 96\)

So, 96 students attend Chess Club on Wednesdays.

Hope this helped!

Answer:

10E+3 <92

10(e:6) or any number

10(6)=60+3=63 <92

Step-by-step explanation:

Answer:

10e + 3 < 92

Step-by-step explanation:

Any number times ten plus three is less than 92. Like e = 3, which would be 10(3)+3, or 33. Any number that would make the statement true can be used in the place of e.

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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The Effective Annual Rate (EAR) for the given nominal annual interest rates with different compounding periods are 12.55% for quarterly, 7.23% for monthly, 17.47% for daily and 12.75% for continuous compounding.

a. The Effective Annual Rate (EAR) for 12% compounded quarterly is 12.55%. To calculate this, we use the formula EAR = (1 + r/n)^n - 1, where r is the nominal annual interest rate and n is the number of times interest is compounded in a year. Plugging in the values, we get EAR = (1 + 0.12/4)^4 - 1 = 0.1255 or 12.55%.

b. The Effective Annual Rate (EAR) for 7% compounded monthly is 7.23%. To calculate this, we use the same formula as before. Plugging in the values, we get EAR = (1 + 0.07/12)^12 - 1 = 0.0723 or 7.23%.

c. The Effective Annual Rate (EAR) for 16% compounded daily is 17.47%. To calculate this, we use the same formula as before. Plugging in the values, we get EAR = (1 + 0.16/365)^365 - 1 = 0.1747 or 17.47%.

d. The Effective Annual Rate (EAR) for 12% with continuous compounding is 12.75%. To calculate this, we use the formula EAR = e^r - 1, where e is the mathematical constant approximately equal to 2.71828 and r is the nominal annual interest rate. Plugging in the values, we get EAR = e^(0.12) - 1 = 0.1275 or 12.75%.

In summary, we can say that the Effective Annual Rate (EAR) for the given nominal annual interest rates with different compounding periods are 12.55% for quarterly, 7.23% for monthly, 17.47% for daily and 12.75% for continuous compounding. The EAR takes into account the effect of compounding on the nominal interest rate, providing a more accurate representation of the true cost of borrowing or the true return on an investment.

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Answer:

a = √c² - b²

Step-by-step explanation:

The process...

Answer:

216 pancakes every 9 hours

Step-by-step explanation:

9/3 = 3

72 x 3 = 216

Answer: p = - 5.8

Step-by-step explanation:

0.7p - 0.2p = -9.57 + 6.67

0.5p = -2.9

p =  \(\frac{-2.9}{0.5}\)

p = - 5.8

please give me a brainliest answer

Answer:

$2.90 %Step-by-step explanation:

because if you round it it would be close to 90 and if you mutiply 2 x 2 =4 x 89

Answer: £450

Step-by-step explanation:

If they bought 2 tickets, they could get an extra ticket for free. As there are three of them, they would buy 2 tickets, get one for free and then buy another ticket to make it four.

In that case they would have only paid for 3 tickets.

The total cost of 3 tickets is:

= 600 * 3

= £1,800

The 4 of them would therefore have to pay:

= 1,800 / 4

= £450

Answer:

127

Step-by-step explanation:

quick math

Answer:

34?

Step-by-step explanation: