elves really love candy canes. they eat 2 a day how many candy canes do they eat throughout the entire year

\(\huge\boxed{\text{$74$ girls}}\ \huge\boxed{\text{$106$ boys}}\)

Hey there! This situation can be modeled and solved using a system of equations. We'll use \(b\) to represent the number of boys and \(g\) to represent the number of girls.

\(\displaystyle{\left \{ {{b+g&=180} \atop {b&=g+32} \right.}\)

Since we know what \(b\) equals, we can substitute it into the first equation.

\(\begin{aligned}b+g&=180\\(g+32)+g&=180&&\smash{\Big|}&&\text{Substitute.}\\2g+32&=180&&\smash{\Big|}&&\text{Combine like terms.}\\2g&=148&&\smash{\Big|}&&\text{Subtract $32$ from both sides.}\\g&=74&&\smash{\Big|}&&\text{Divide both sides by $2$.}\end{aligned}\)

Now that we know the number of girls, use the second equation to get the number of boys.

\(\begin{aligned}b&=g+32\\&=74+32&&\smash{\Big|}&&\text{Substitute.}\\&=106&&\smash{\Big|}&&\text{Add.}\end{aligned}\)

To represent the cost, in cents, of mailing a letter weighing between 0 and 3 ounces using a piecewise-defined function, we can break it down into different weight intervals and calculate the cost for each interval.

Here's the piecewise-defined function P(x):

P(x) =

37 for 0 ≤ x ≤ 1

37 + 26(x - 1) for 1 < x ≤ 2

37 + 26(2 - 1) + 26(x - 2) for 2 < x ≤ 3

For weights between 0 and 1 ounce (inclusive), the cost is a constant 37 cents.

For weights between 1 and 2 ounces (exclusive), the cost is 37 cents for the first ounce plus an additional 26 cents for each additional ounce or fraction of an ounce.

For weights between 2 and 3 ounces (inclusive), the cost is 37 cents for the first ounce, 26 cents for the second ounce, and an additional 26 cents for each additional ounce or fraction of an ounce.

Note that the upper and lower bounds of each interval are inclusive, except for the upper bound of the previous interval, ensuring that there are no gaps or overlaps in the weight ranges.

Please keep in mind that this function is specific to the given cost structure and weight intervals stated in the problem.

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Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.

Answer:

m =1

Step-by-step explanation:

Y2 - Y1. 6-0. 6

m = ------------ = ---------- = ----- = 1

X2 - X1. 0-(-6). 6

Answer:

2x/5=9/15

2x=9/3

x=1.5

Based on evidence from the passage, the most likely inference is that plastic makes life convenient, but its uses have so many cons that its use should be reduced. The answer is option B

The pair of examples that best demonstrate why the use of plastic is a divisive topic is Plastic has advantages and Plastic is difficult to recycle efficiently. The answer is option (B)

Plastic makes life convenient, but its uses have so many cons that its use should be reduced is the most likely inference based on the evidence from the passage. It is tough to recycle due to low value when recycled, especially for single-use and convenience items like packaging and water bottles. Most of the plastic produced is not recycled and either ends up in landfills or as pollution in the environment.

The example: Plastic has advantages and the example: Plastic is difficult to recycle efficiently best demonstrates why the use of plastic is a divisive topic. Although plastic has numerous advantages, including making life convenient, it has a variety of drawbacks. Most of the plastic produced is not recycled, but rather ends up in landfills or as pollution in the environment.

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Background:

"As much as" means that two quantities are being compared and is a keyword for division.

Procedure:

Answer: 2

the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

We know that odd consecutive numbers means the difference between the numbers will be 2

So, let the first odd number be x

Second number will be = x + 2

Third number will be = x + 2 + 2 = x + 4

Now, we are given that, the sum of these odd integers is 153

So, we get the equation as:

x + x + 2 + x + 4 = 153

3 x + 6 = 153

3 x = 153 - 6

3 x = 147

x = 147 / 3

x = 49

Largest integer = x + 4 = 49 + 4 = 53

Therefore, we get that, the value of largest integer when the sum of 3 consecutive odd integers is 153 is 53.

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(a) A total of 66 students were surveyed

(b) Those who are Math majors and not biology majors were 7

(c) Those who were neither math nor biology majors were 47

(d) Those who majored in both math and biology were 4

Answer:5/2/320=900

Step-by-step explanation:

Answer:

z > -108.5

Step-by-step explanation:

1. z/7+19>3.5

Subtract 19 from both sides

2. Z/7 > -15.5

Multiply both sides by 7

3. Z > -108.5

Abilities and altitudes are two individual differences that are generally reliable indicators of the likelihood of system error.

The ability of an individual to effectively use a system is a reliable indicator of the likelihood of system errors. People who are less experienced and less knowledgeable about the system are more likely to make mistakes, which can lead to system errors.

In addition, an individual's attitude towards the system can also have an effect. People who are more anxious or frustrated while using the system may make more errors due to a lack of concentration or incorrect assumptions.

Finally, an individual's susceptibility to stress can also play a role in how likely they are to make mistakes while using the system as stress can lead to a lack of focus and poor decision-making. Knowing these two human individual differences can help to predict the likelihood of system errors and help to reduce the risk of them occurring.

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Answer:

1/2 or 0.5

Step-by-step explanation:

since 7 out of 14 shirts sold were green, the probability would be 7/14. but since you need to simplify, it will be 1/2 or 0.5

Answer:

1/2

Step-by-step explanation:

Since there are a total of 14 t shirts and 7 of them were green, the experimental probability that the next one is also green is 7/14=1/2. Hope this  helps!

The probability will be b) 4/(52 13)

In a standard deck, there are four suits (hearts, diamonds, clubs, and spades), each containing 13 cards. To find the probability of obtaining a bridge hand with all 13 cards of the same suit, we need to determine the number of favorable outcomes (hands with all 13 cards of the same suit) and divide it by the total number of possible outcomes (all possible bridge hands).

Calculate the number of favorable outcomes

There are four suits, so for each suit, we can choose 13 cards out of 13 in that suit. Therefore, there is only one favorable outcome for each suit.

Calculate the total number of possible outcomes

To determine the total number of possible bridge hands, we need to calculate the number of ways to choose 13 cards out of 52. This can be represented as "52 choose 13" or (52 13) using the combination formula.

Calculate the probability

The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Since there is one favorable outcome for each suit and a total of 4 suits, the probability is 4 divided by the total number of possible outcomes.

Therefore, the probability that a bridge hand will contain all 13 cards of the same suit is 4/(52 13).

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The reason why some data mining algorithms require that variables are standardized to zero mean and standard deviation of 1.0 is because it helps to normalize the data and make it more comparable across different variables.

Standardizing the data helps to remove the impact of the scale of the variables on the analysis, allowing for more accurate comparisons and correlations between variables. By doing this, it ensures that no one variable has an undue influence on the results of the analysis. Standard deviation is a statistical measure that is used to measure the amount of variability or dispersion in a dataset. When data is standardized, it allows for a more accurate assessment of the relationship between variables and can improve the accuracy of the analysis. Overall, standardizing variables is a crucial step in the data mining process, as it helps to ensure that the results of the analysis are reliable and accurate.

The reason some data mining algorithms require variables to be standardized (or normalized) to a zero mean and a standard deviation of 1.0 is to ensure consistent and comparable scales for all variables involved. Standardizing variables helps in improving the performance and accuracy of the algorithms.

When variables have different scales or units, it can be challenging for algorithms to interpret their relative importance accurately. By transforming variables to have a zero mean and a standard deviation of 1.0, the algorithms can more effectively process and analyze the data. This standardization process is particularly important for distance-based and gradient-based algorithms, where scale differences can significantly impact the results.

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Answer:

y₂ = 3

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - \(\frac{3}{4}\)

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (7, - 6) and (x₂, y₂ ) = (- 5, y₂ )

m = \(\frac{y_{2}+6 }{-5-7}\) , that is

\(\frac{y_{2}+6 }{-12}\) = - \(\frac{3}{4}\) ( cross- multiply )

4(y₂ + 6) = 36 ( divide both sides by 4 )

y₂ + 6 = 9 ( subtract 6 from both sides )

y₂ = 3

Answer:

x = -∛115

Step-by-step explanation:

x^3 - (-115) = 0

= x^3 + 115

Factoring

(a+b) • (a^2-ab+b^2) =

   a^3-a^2b+ab^2+ba^2-b^2a+b^3 =

   a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=

   a^3+0+0+b^3=

   a^3+b^3

(115 isn't a cube.)

Polynomial roots

P: -1, -5, -23, -115, 1, 5, 23, 115

Q: 1

P/Q: -1, -5, -23, -115, 1, 5, 23, 115

Divisor(s): None

In these sets of data, there are no rational roots shown.

Step-by-step explanation(part 2):

x^3 + 115 = 0

x^3 = -115

x  =  ∛-115

Negative numbers will always have real cube roots.

∛ -115 = ∛ -1 × 115  = ∛ -1 × ∛ 115 = (-1) × ∛ 115

Therefore,

x = -∛115

The simplified expressions are 2^-2 and 60^6

Expression (a)

We have:

2^3 * 2^-5

Apply the product law of indices

2^3 * 2^-5 = 2^(3 - 5)

Evaluate the difference

2^3 * 2^-5 = 2^-2

Expression (b)

We have:

(60^2)^3

Apply the power law of indices

(60^2)^3 = 60^(2 * 3)

Evaluate the product

(60^2)^3 = 60^6

Hence, the simplified expressions are 2^-2 and 60^6

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The distance between the two given points coordinates is; Option C: √85

Formula for the distance between two coordinates is;

d = √((x₂ - x₁)² + (y₂ - y₁)²)

We are given the coordinates as;

(-2, 3) and (5, -3). Thus;

d = √((-2 - 5)² + (-3 - 3)²)

d = √(49 + 36)

d = √85

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Answer:

24002

Step-by-step explanation:

2,592.1856 divided by 0.108

= 24001.7185185

= 24002 (rounded to the nearest whole number)

Hope this helped!

Answer:

\(\huge\boxed{\sf -2}\)

Step-by-step explanation:

\(\sf h(x) = -2x-10\\\\Put \ x = -4\\\\h(-4) = -2(-4) -10\\\\h(-4) = 8-10\\\\\boxed{\sf h(-4) = -2}\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

Step-by-step explanation:

An equation in point-slope form of the line passing through point P(x₁, y₁) with slope m:   y - y₁ = m(x - x₁)

m = -2

P(-3, 6)  ⇒   x₁ = -3,  y₁ = 6

y - 6 = -2(x - (-3))

y - 6 = -2(x + 3)  ←    point-slope form

y - 6 = -2x - 6        {add 6 to both sides}

y = - 2x                 ←    slope-intercept form {intercept=0}

In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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Thus, the cost of the triangular lot land is approximately $81,940 found using Heron's formula.

To determine the cost of the triangular lot, you first need to calculate its area and then convert it to acres.

Given the three sides of the triangle (470 yards, 860 yards, and 1130 yards), you can use Heron's formula to find the area.

Heron's formula for the area of a triangle with sides a, b, and c is:
Area = √(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter, calculated as:
s = (a + b + c) / 2

In this case, a = 470 yards, b = 860 yards, and c = 1130 yards.

Therefore, the semi-perimeter, s, is:

s = (470 + 860 + 1130) / 2 = 1230 yards

Now, plug the values into Heron's formula to calculate the area:

Area = √(1230 * (1230 - 470) * (1230 - 860) * (1230 - 1130))
Area ≈ 198,342.77 square yards

To convert square yards to acres, use the conversion factor:

1 acre = 4,840 square yards
So, the area in acres is:

198,342.77 square yards * (1 acre / 4,840 square yards) ≈ 40.97 acres

Finally, multiply the area in acres by the price per acre to find the cost:
Cost = 40.97 acres * $2000 per acre ≈ $81,940

The cost of the land is approximately $81,940.

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Given:

The inequality is

\(-3(2x - 5) < 5(2 - x)\)

To find:

The correct representations of the given inequality.

Solution:

We have,

\(-3(2x - 5) < 5(2 - x)\)

Using distributive property, we get

\(-3(2x)-3(-5) < 5(2)+5(-x)\)

\(-6x+15 < 10-5x\)

Therefore, the correct option is C.

Isolate variable terms.

\(15-10 < 6x-5x\)

\(5 < x\)

It means, the value of x is greater than 5.

Since 5 is not included in the solution set, therefore, there is an open circle at 5.

So, the graphical represents of the solution is a A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Therefore, the correct option is D.

Answer:

Choice B: Carbon would not be recycled and added to soil, interrupting the cycle.

Step-by-step explanation:

Without the help of decomposers, the ones who break the dead organisms down, the carbon would be locked inside the dead organism. Then carbon wouldn't be able to get recycled through the air. The only way it could be released would be through combustion.

|2s| = 2|s| can be proven by induction. For the base case, if s is empty, then 2s is also empty, and both sides are 0.

We will prove by induction that for any finite set s, |2s| = 2|s|.

Base case: When s is empty, |s| = 0. Thus, |2s| = |∅| = 0, and 2|s| = 2 * 0 = 0. So the equation holds for the base case.

Inductive step: Assume that for a finite set s with |s| = k, |2s| = 2|s|. We will prove that the equation holds for s' = s ∪ {x}, where x is an arbitrary element not in s.

|2s'| = |2(s ∪ {x})| = |(2s) ∪ (2{x})| = |2s| + |2{x}| (by the union property) = 2|s| + 2 (since |2{x}| = 2) = 2(|s| + 1) = 2|s'|.

By the principle of mathematical induction, the equation holds for all finite sets s.

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The depth of trail mix box that is shaped like a rectangular prism must be 2.4 inches.

We are going to use the formula for determining volume to work out the depth of the rectangular prism.

The volume of a rectangular prism is given by the formula:

V = l × w × h

where:

V = the volume

l = the length

w = the width

h = the height.

Given:

w = 7.5 inches

h = 9 inches

V = 162 cubic inches

Now, we are to find the value of d, the depth of the box, which corresponds to the length of the rectangular prism.

Substituting the values into the formula for volume:

162 = d × 7.5 × 9

Simplifying the right-hand side:

162 = 67.5d

Dividing both sides by 67.5, we get:

d = 162 ÷ 67.5

d = 2.4 inches

Therefore, the depth of the box shaped as rectangular prism = 2.4 inches.

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The probability that the product of any two distinct members of the set is a multiple of 196 is 0.2857.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

If two distinct members of the set { 2, 4, 12, 14, 21, 28, 98 } are randomly selected and multiplied, then the total number of possible outcomes is:

7C2 = 21

Counting all the possible pairs of numbers whose product is a multiple of 196, there are 6 possible ways.

(98 x 4) , (98 x 12) , (98 x 14) , (98 x 28) , (28 x 14) , (28 x 21)

Solve for the probability.

p = 6 / 21 = 0.2857

Therefore, the probability is 0.2857.

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Answer:

A. y= -3x - 1

that's the answer of you substitute the figures in x into where x can be located in A