As a candle burns, its wick gets smaller over time. When first purchased, the wick is 150 mm in length. After 50 minutes, the wick is only 110 mm in length. Find the slope you would use in a linear model of mm per minute. 3 points Construct an equation that models the length of the wick over this time period. Your answer should be in the proper form using correct letters and numbers with no spaces. 2 points Use your linear model to predict the how many minutes it would take to have 74 mm remaining. 3 points

We want to find a number that is multiple of all the denominators of the fractions we have. For example, in the cases:

we have two denominators: 5 and 3

And for

we have 3 and 12

2/5 + 1/3:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

5 x 3 = 15

then,

and

then we have that

1/3 + 3/12:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

3 x 12 = 36

then

1/3 + 3/12:

We can find the denominator by finding the multiples of both denominators:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We find some the numbers that both multiples share:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We choose the first common multiple, and this is the common denominator. In this case it is 12. Since

3 x 4 = 12, then

The dimensions and area of Sergio's garden are 5 yards and 25 square yards respectively

The given parameters are

Perimeter = 20 yards

For the rectangle to have the greatest are, the rectangle must be a square

So, the dimension is

Length = Perimeter/4

This gives

Length = 20/4

Evaluate

Length = 5

The area of Sergio's garden is

Area = 5 * 5

Evaluate

Area= 25

Hence, the dimensions and area of Sergio's garden are 5 yards and 25 square yards respectively

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The given

system of equations

is:

5x + y = 10   ... (1)

x + (1/5)y = 2   ... (2)

To solve this system, we can use the method of

elimination

. Let's multiply equation (2) by 5 to eliminate the fraction:

5(x + (1/5)y) = 5(2)

5x + y = 10   ... (3)

Comparing equations (1) and (3), we can see that they are identical. This means that equation (3) is just a multiple of equation (1), and therefore the two equations are dependent. The system does not have a unique solution; instead, it has

infinitely many solutions.

To see this, we can rewrite equation (1) as:

y = 10 - 5x

Now, we can substitute this expression for y into either equation (1) or (2). Let's substitute it into equation (1):

5x + (10 - 5x) = 10

10 = 10

As we can see, this equation is always true, regardless of the value of x. This means that for any real value of x, the equation is satisfied. Therefore, the solution set is {x | x is any real number}.

In summary, the given system of equations is

dependent

and has infinitely many solutions. The solution set is {x | x is any real number}.

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The statement "the standard deviation is equal to the square of the variance" is False.

In statistics, both the standard deviation and the variance are measures of variability or dispersion within a dataset.

However, they are distinct measures and not equal to each other.

The variance (σ²) is the average of the squared deviations from the mean.

It is calculated by summing the squared differences between each data point and the mean, and then dividing by the total number of data points. The variance is expressed in squared units of the original data.

On the other hand, the standard deviation (σ) is the square root of the variance.

It represents the average amount of deviation or dispersion of data points from the mean.

By taking the square root of the variance, the standard deviation is expressed in the same units as the original data, making it more interpretable and easier to compare across different datasets.

In summary, the standard deviation is not equal to the square of the variance. Rather, it is the square root of the variance.

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Based on the information provided, the perimeter of the real playground is 80 meters.

To begin, let's start by identifying the length and width in the drawing. For this, you measure the sides using a ruler. According to this, the measures are:

Length = 5 cm

Widht = 3 cm

Now, let's convert these measures to the real ones considering 1 centimeter is 500 centimeters:

5 cm x 500 cm = 2500 cm  = 25 m

3 cm x 500 cm = 1500 cm  = 15 m

Now, let's find the perimeter:

25 meters + 15 meters + 25 meters + 15 meters = 80 meters

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Answer:

cost = 56 + 8t, where t is the number of hours worked for.

for 4 hours of work, cost = 56 + 8 x 4 = $88

Step-by-step explanation:

It is not a triangle.

Does given feet is a triangle or not?

The Triangle Inequality theorem states that in a triangle, , where  and  are shorter side lengths and  is the longest side length.

Given that  5+9<15, the given side lengths do not compose a valid triangle.

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Answer:

d = 53.33333

Step-by-step explanation:

Solve for d on calculator

Answer:

pleas help me asap please!!!!!!

pleas help me asap please!!!!!!

Step-by-step explanation:

pleas help me asap please!!!!!!

We want to see which ones of the given equations are true equations. Here we will see that the only true equation is the second one:

54 ÷ 6 + 3² = 4 + 4²

We define a true equation as an equation where the thing at the left is equal to the thing on the right, so we need to check that for all the given equations.

1) 62 − 22 = 4 + 7⋅22

We just solve each side, we will get:

40 = 158

This is not a true equation.

2) 54 ÷ 6 + 3² = 4 + 4²

   9 + 9 = 4 + 16

   18 = 18

This is a true equation.

3) 8042 = 10 − 22 − 1

Clearly, this is not a true equation.

4) 19 − 2⋅5 = 9⋅73 −9

   19 - 10 = 657 - 9

           9 = 648

This is not a true equation.

Then the only true equation is the second one:

54 ÷ 6 + 3² = 4 + 4²

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Step-by-step explanation:

here is the answer babe. Feel free to ask for more

Answer:  - 1.

Step-by-step explanation:

\(\frac{\dfrac{x+y}{x-y} }{\dfrac{y+x}{y-x} } =\dfrac{x+y}{x-y} \div \dfrac{y+x}{y-x}\\\\{\: \: \: \: \: \: \: \: \: \: \: \: \: } = \dfrac{x+y}{x-y} \times \dfrac{y-x}{y+x}\\\\{\: \: \: \: \: \: \: \: \: \: \: \: \: } = \dfrac{x+y}{x-y} \times \dfrac{-(x-y)}{x+y}\\\\{\: \: \: \: \: \: \: \: \: \: \: \: \: } = \dfrac{-(x+y)(x-y)}{(x-y)(x+y)} \\\\{\: \: \: \: \: \: \: \: \: \: \: \: \: } = -1\)

The standard error of the mean is approximately 0.79 (rounded to two decimal places).

Define standard error ?

The standard error is a statistical term that measures the variability of a sample mean or an estimate of a population parameter from its true value. It is the standard deviation of the sampling distribution of the mean. In simpler terms, the standard error measures how much the sample mean varies from the true population mean. A smaller standard error indicates that the sample mean is more likely to be representative of the population mean, while a larger standard error suggests that the sample mean may not be as reliable.

The formula for the standard error of the mean is:

\(SE = \frac{\sigma }{\sqrt{n}}\)

Where σ is the population standard deviation and n is the sample size.

Substituting the given values:

\(SE =\frac{5}{\sqrt{40}}\)

SE ≈ 0.79

Therefore, the standard error of the mean is approximately 0.79 (rounded to two decimal places).

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the expression to a single logarithm using the properties of logarithms log(x) + log(z^3) - log(y^(1/2))
We can use the properties of logarithms to condense the expression. Firstly, we can use the rule that says log(a) - log(b) = log(a/b). Applying this rule to the first two terms gives us log(x/y^(1/2)). Next, we can use the rule that says nlog(a) = log(a^n).

Applying this rule to the last term gives us log(z^3). Finally, we can use the rule that says log(a) + log(b) = log(ab) to combine the first and last terms, giving us log(xz^3/y^(1/2)).
Therefore, the condensed expression using the properties of logarithms is log(xz^3/y^(1/2)).
 The condensed expression is log(x * z^3 / y^(1/2)).

To condense the given expression using properties of logarithms, we need to apply the following rules:

1. log(a) - log(b) = log(a/b)
2. log(a^n) = n * log(a)

So, let's apply these rules to the given expression:

log(x) - (1/2)log(y) + 3log(z)

First, apply rule 2:

log(x) - log(y^(1/2)) + log(z^3)

Next, apply rule 1:

log(x * z^3 / y^(1/2))

The expression log(x) - (1/2)log(y) + 3log(z) can be condensed to a single logarithm as log(x * z^3 / y^(1/2)).

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Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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The magnetic field in tesla at a point midway between the wires is (e) 20 x 10^(-4).

To find the magnetic field at a point midway between two parallel wires carrying currents, we can use Ampere's Law.

Ampere's Law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop. In the case of two parallel wires, the magnetic field at a point between them is the sum of the magnetic fields generated by each wire.

The formula for the magnetic field due to a straight wire is given by:

B = (μ₀ * I) / (2π * r)

Where:

B is the magnetic field,

μ₀ is the permeability of free space (4π × 10^(-7) T*m/A),

I is the current, and

r is the distance from the wire.

For the wire carrying a current of 8.0A, the magnetic field at the midpoint between the wires is:

B₁ = (4π × 10^(-7) * 8.0) / (2π * 0.002)

  = 2 × 10^(-4) T

For the wire carrying a current of 12A, the magnetic field at the midpoint between the wires is:

B₂ = (4π × 10^(-7) * 12) / (2π * 0.002)

  = 3 × 10^(-4) T

To find the total magnetic field at the midpoint, we sum the magnetic fields due to each wire:

B_total = B₁ + B₂

        = 2 × 10^(-4) T + 3 × 10^(-4) T

        = 5 × 10^(-4) T

Therefore, the magnetic field at a point midway between the wires is 5 × 10^(-4) T.

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Answer:

Step-by-step explanation:

(6). y = \(\frac{1}{3}\) x + 2 [ linear function ]

(7). y = 4 [ horizontal line, linear function ]

(8). x = 2 [ vertical line, not a function ]

A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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Answer:

\(w=\frac{3}{2} ,-1\)

Step-by-step explanation:

\(3|4w-1|-5=10\\\\3|4w-1|=10+5\\\\3|4w-1|=15\\\\|4w-1|=5\\\\\)

here we have two cases

the number that give an absolute value of 5 are 5 and -5

so we have

\(4w-1=5\\\\4w=5+1\\\\4w=6\\\\w=\frac{3}{2}\)

and the other case

\(4w-1=-5\\\\4w=-5+1\\\\4w=-4\\\\w=-1\)

Gianna has a budget of $760 for purchasing biking gear and outfits. She spends $356.46 on a new bicycle, $20.72 on a pair of bike gloves, and $10.01 each on two bicycle reflectors. She plans to buy biking outfits for $45.35 each with the remaining money she has.

The total cost of the items Gianna has already purchased is $397.20. Therefore, the amount of money she has left to spend on biking outfits is $760 - $356.46 - $397.20 = $6.34. Since each biking outfit costs $45.35, Gianna can only afford to buy 1 biking outfit with the remaining money. The amount of money she will have left after purchasing the outfit will be $6.34 - $45.35 = -$39.01, which means she has overspent and will need to either return an item or pay the extra amount out of pocket.

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Complete question:

Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.

She buys a new bicycle for $356.46.

She buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72.

She plans to spend some or all of the money she has left to buy new biking outfits for $45.35 each.

Write and solve an inequality which can be used to determine, the number of outfits Gianna can purchase while staying within her budget.

Since S satisfies both defining properties of an ideal in R, we can conclude that S is indeed an ideal in R.

To prove that the subset S = {λ1r1 +···+ λnrn | λ1,...,λn ∈ R} is an ideal in R, we need to show that it satisfies the two defining properties of an ideal:

1. S is a subgroup of R under addition.
2. S is closed under multiplication by elements of R.

First, let's show that S is a subgroup of R under addition.

- Closure under addition: Let x,y ∈ S, so that x = λ1r1 + ··· + λnrn and y = μ1r1 + ··· + μnrn for some λi,μi ∈ R. Then their sum is x + y = (λ1 + μ1)r1 + ··· + (λn + μn)rn, which is in S since each coefficient is still in R.

- Additive inverse: Let x ∈ S, so that x = λ1r1 + ··· + λnrn for some λi ∈ R. Then its additive inverse is -x = (-λ1)r1 + ··· + (-λn)rn, which is also in S since each coefficient is still in R.

Therefore, S is a subgroup of R under addition.

Next, let's show that S is closed under multiplication by elements of R.

- Closure under left multiplication: Let r ∈ R and x ∈ S, so that x = λ1r1 + ··· + λnrn for some λi ∈ R. Then their product is rx = (rλ1)r1 + ··· + (rλn)rn, which is in S since each coefficient is still in R.

- Closure under right multiplication: This follows from the distributive property of multiplication over addition.

Therefore, S is closed under multiplication by elements of R.

Since S satisfies both defining properties of an ideal in R, we can conclude that S is indeed an ideal in R.

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Answer:

45 rand

Step-by-step explanation:

3 large pizzas is 10 ×3=R30

5 small drinks is 1.50×5=R7.50

tip of R7.50

add all

30+7.50+7.50

=45

Answer:

3x+12/10 simplified is =3x+ 6 /5

Step-by-step explanation:

x+2 /x^2 +6x +8=  7x3+8x2+2 x2

The given rational expression, (5y + 15)/(3y + 9), can be simplified by factoring out the common factor and canceling out common terms.

To simplify the expression, we can factor out the common factor of 5 from the numerator and 3 from the denominator. This yields (5(y + 3))/(3(y + 3)). Now, we can cancel out the common factor of (y + 3) in both the numerator and denominator. This results in the simplified expression of 5/3. Therefore, the rational expression (5y + 15)/(3y + 9) simplifies to 5/3.

In summary, the given rational expression simplifies to 5/3 after factoring out the common terms and canceling out the common factor.

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Answer:

linear

Step-by-step explanation:

y is always 1 behind x

Answer:

A

Step-by-step explanation:

he goes up 3, and goes back 5 so 3-5=-2 but bases in the context, it's just 2 miles

Answer:

A.2 miles

Step-by-step explanation:

3 - 5 = -2

He is 2 miles from his starting point.

A.2 miles

An arithmetic succession, is defined by constant sums or substractions. A geometric succession, is defined by constant products. In this case, we can define this succession as a product

It means this succession is geometric.

Answer:

25º

Step-by-step explanation:

110+45=155

180-155=25

The amount of money paid for the rope in dollars per inch is 0.025 $/in.

Based on the information provided above, we can logically deduce that the store bought 300 feet of nylon rope.

Conversion:

1 feet = 12 inches.

300 feet × 12 inches/feet = 3600 inches.

Therefore, we now know that this store bought 3600 inches of nylon rope.

Furthermore, this store sold 40 inches of nylon rope for $1.60. Thus, we can calculate the selling unit price of nylon rope in dollars per inch as follows;

Selling unit price = $1.60/(40 in.)

Selling unit price = $0.04/in.

At a price of $0.04 per inch, we have:

Selling Price =3600 inches × $0.04/in.

Selling Price = $144

Therefore, since the profit was $54 for selling all of the nylon rope;

Cost price = Selling price - profit

Cost price = $144 - $54

Cost price = $90

The cost in dollars per inch is given by;

Cost in dollars per inch = ($90)/(3600 in.)

Cost in dollars per inch = 0.025 $/in.

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Answer:

x = 27/16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

x + 5/9x = 2(3 - x)

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 21/8 does indeed equal 21/8.

∴ x = 27/16 is a solution to the equation.