help! i need help on this :(

Answer:

Roots = (1, 0) and (-5, 0)

Vertex = (-2, -9)

Two additional points = (-4, -5) and (0, -5)

Step-by-step explanation:

The given equation y = x² + 4x - 5 is a quadratic equation with a positive leading coefficient. Therefore, the shape of the curve is a parabola that opens upwards.

The roots of a quadratic equation are the x-values that satisfy the equation y = 0. They are the points at which the curve crosses the x-axis.

To calculate the roots of the given equation, set it to zero and solve for x.

[tex]\begin{aligned}x^2+4x-5&=0\\x^2+5x-x-5&=0\\x(x+5)-1(x+5)&=0\\(x-1)(x+5)&=0\\\\\implies x-1&=0 \implies x=1\\\implies x+5&=0 \implies x=-5\end{aligned}[/tex]

Therefore, the roots of the equation are (1, 0) and (-5, 0).

The x-value of the vertex of a quadratic function in the form ax² + bx + c is -b/2a.

For the given equation y = x² + 4x - 5, a = 1 and b = 4.

To find the x-value of the vertex, substitute these values into the formula:

[tex]x_{\sf vertex}=\dfrac{-b}{2a}=\dfrac{-4}{2(1)}=-2[/tex]

To find the y-value of the vertex, substitute the x-value of the vertex into the given equation:

[tex]y_{\sf vertex}=(-2)^2+4(-2)-5=-9[/tex]

Therefore, the vertex is (-2, -9).

To find two other points on the curve, substitute two values of x into the equation.

[tex]\begin{aligned}x=-4 \implies y&=(-4)^2+4(-4)-5\\&=16-16-5\\&=0-5\\&=-5\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies y&=(0)^2+4(0)-5\\&=0+0-5\\&=0-5\\&=-5\end{aligned}[/tex]

The axis of symmetry of a quadratic equation is the vertical line that divides the parabola into two mirror images. The x-value of the vertex is the axis of symmetry. Therefore, the axis of symmetry is x = -2.

To graph the given equation:

(1) Area of triangle = 6in²

Area of rectangle of first kind=18in²

Area of rectangle of second kind= 30in²

(2) 90in²

(3) 0 as it is 2-D body

Surface area refers to the total area that covers the surface of a three-dimensional object, including all of its faces, sides, and any other surfaces that are exposed. It is measured in square units, such as square meters or square feet, and is calculated by adding up the areas of each individual surface of the object. The surface area is a fundamental property used to describe the physical characteristics of an object, and it is important in many different fields, including mathematics, physics, and engineering.

Volume is a measure of the amount of space that a substance or object occupies, typically in cubic units such as liters or cubic meters. It is commonly used to describe the size or amount of a liquid, gas, or solid.

(1) Area of triangle = 6in²

Area of rectangle of first kind=18in²

Area of rectangle of second kind= 30in²

(2) The surface area of entire figure =( 6×2+18+2×30)in²

= 90in²

(3) Volume is =0 as it is a 2-D body

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B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.

The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.

They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.

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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.

B. save time in arriving at solutions to problems . The correct answer is:

Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.

One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.

However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.

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Answer:

-5d + 5.5 < 17

-5d < 11.5

d > -2.3

A is the correct solution.

Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,

To solve this problem, we can use the formula for permutations, which is:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).

Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:

52P52 = 52! / (52 - 52)! = 52!

Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.

Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.

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Therefore, the equation for which g = 5 is not the solution is 4g = 20.

An equation is a mathematical statement that shows the equality between two expressions or values. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations can be used to solve problems or to describe relationships between quantities. They are commonly written in the form of "expression 1 = expression 2" or "expression 1 - expression 2 = 0", where the goal is to find the value(s) of the variable(s) that make the equation true.

To check for which equation g = 5 is not the solution, we can substitute g = 5 into each equation and see which ones result in a false statement.

[tex]8g = 40[/tex]

Substituting g = 5 gives: 8(5) = 40, which is true. Therefore, g = 5 is a solution to this equation.

4g = 20

Substituting g = 5 gives: 4(5) = 20, which is false. Therefore, g = 5 is not a solution to this equation.

g - 2 = 3

Substituting g = 5 gives: 5 - 2 = 3, which is true. Therefore, g = 5 is not a solution to this equation.

2g = 25

Substituting g = 5 gives: 2(5) = 25, which is false. Therefore, g = 5 is not a solution to this equation.

Therefore, the equation for which g = 5 is not the solution is 4g = 20.

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Answer:

To find the circumference of a circle with diameter 25cm, we can use the formula:

Circumference = π × Diameter

where π (pi) is a mathematical constant approximately equal to 3.14159.

Substituting the diameter of 25cm, we get:

Circumference = π × 25cm

= 3.14159 × 25cm

= 78.53975cm

Therefore, the circumference of the circle with diameter 25cm is approximately 78.54cm.

To find the circumference of a circle with diameter 2.5cm, we can again use the same formula:

Circumference = π × Diameter

Substituting the diameter of 2.5cm, we get:

Circumference = π × 2.5cm

= 3.14159 × 2.5cm

= 7.85398cm

Therefore, the circumference of the circle with diameter 2.5cm is approximately 7.85cm.

a. The probability of getting 3 on both dice is 1/36.

b. The probability of each sample point is 1/36.

c. The probability of getting a sum of 7 is 6/36 or 1/6.

d. The probability of getting at least one 5 is 11/36.

e. The probability of getting a sum of 10 or more is 6/36 or 1/6.

a. The sample space for tossing two fair dice can be listed as follows:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

b. Since the dice are fair, each outcome is equally likely.

Therefore, the probability of each sample point is 1/36.

a. The event of getting 3 on both dice can only happen in one way, that is, (3,3).

Therefore, the probability of getting 3 on both dice is 1/36.

b. For the sum of the numbers to be even, either both dice must be odd or both must be even.

There are 3 odd numbers (1, 3, 5) and 3 even numbers (2, 4, 6) on a die. Thus, there are 3 x 3 = 9 ways to get an even sum.

The probability of getting an even sum is therefore 9/36 or 1/4.

c. To get a sum of 7, the following combinations are possible: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Therefore, there are 6 ways to get a sum of 7.

Thus, the probability of getting a sum of 7 is 6/36 or 1/6.

d. To get at least one 5, we can either get a 5 on the first die or the second die or both.

There are two ways to get a 5 on one die and one way to get a 5 on both dice.

Thus, the probability of getting at least one 5 is 11/36.

e. There are several ways to get a sum of 10 or more: (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6).

Therefore, there are 6 ways to get a sum of 10 or more.

Thus, the probability of getting a sum of 10 or more is 6/36 or 1/6.

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The expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm is approximately 7.67.

What is the frequency?

The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

To find the expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm, we need to calculate the expected frequency for that cell using the formula:

Expected frequency = (row total * column total) / grand total

For this particular cell, the row total is 16 (from the table) and the column total is 23.

The grand total is 48 (also from the table). So, we can calculate the expected frequency as:

Expected frequency = (16 * 23) / 48 = 7.67

Rounding this to the nearest hundredth, we get the expected count as 7.67.

Therefore, the expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm is approximately 7.67.

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Answer:

6 examinations

Step-by-step explanation:

We Know

A doctor can complete 3 examinations in 2 hours.

How many examinations can the doctor complete in 4 hours?

We see

4 hours is 2 hours times 2

We take

3 x 2 = 6 examinations

So, the doctor can complete 6 exams in 4 hours.

The domain of  the composition function fog(x) when f(x)= √6x and g(x)= 1/ (x-6) is equal to  (-∞, 6) U (6, ∞).

Function f(x) = √6x

And g(x)= 1/ (x-6

Composition function fog is ,

fog(x) = f(g(x))

Domain of fog(x),

First, find the domain of g(x),

Here,

g(x) = 1/(x-6)

The denominator of g(x) cannot be equal to zero,

So we must exclude x = 6 from the domain of g(x).

The domain of g(x) is equal to ,

domain of g(x) = {x | x ≠ 6}

The range of g(x) is,

As x approaches 6 from the left, g(x) approaches negative infinity,

And as x approaches 6 from the right, g(x) approaches positive infinity.

Range of g(x) = (-∞, 0) U (0, ∞)

Now, the domain of fog(x),

fog(x)

= f(g(x))

= √6g(x)

=√ 6 (1 /(x - 6 ) )

Square root sign must be non-negative.

Since the range of g(x) does not include zero,

Exclude the part of the range that is less than zero.

The domain of fog(x) is,

domain of fog(x)

= {x | g(x) > 0}

= {x | x < 6} U {x | x > 6}

The domain of fog(x) consists of all real numbers except x = 6.

Therefore, the domain of fog(x) is (-∞, 6) U (6, ∞).

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The above question is incomplete, the complete question is :

Given f(x)= √6x and g(x)= 1/ (x-6) Which value is in the domain of fog.

Three distances that are equivalent to 1/2 mile are:

880 yards

1,609.34 meters

2,640 feet

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.

Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.

He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.

We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:

6x ≥ 480

Dividing both sides by 6, we get:

x ≥ 80

This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

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The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.

Hence, the correct option is B.

In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.

IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.

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In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).

The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.

The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)

Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).

Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).

The point (2,5) will change to if it is reflected across the line y=x (5,2).

Therefore, the correct option is 1. (-2, 5).

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Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.

Given data:

Area of triangle = 1/2* base * height

Ratios:

area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)

area of larger triangle / area of smaller triangle = B*H / b*h

area of larger triangle / area of smaller triangle = 10*5 / 5*2

area of larger triangle / area of smaller triangle = 50 / 10

area of larger triangle / area of smaller triangle = 5/ 1 = 5:1

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

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Complete question:

what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.

Dimension of  larger triangle: base B = 10 cm, Height H = 5 cm.

Dimension of  smaller triangle : base b = 5 cm, Height H = 2 cm.

The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.

To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.

Using the formula, we get:

V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3

Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.

Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99

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suppose that x is a normal random variable with a mean of 5. if p{x > 9} = .2, So, the approximate variance of the normal random variable X is 22.66.

To find the variance of a normal random variable X with mean 5 and given P(X > 9) = 0.2, we will follow these steps:

1. Recognize that X follows a normal distribution: X ~ N(μ, σ²), where μ = 5 and σ² is the variance we want to find.

2. Convert the probability statement P(X > 9) = 0.2 to a standard normal distribution (Z) by finding the corresponding Z-score:
  Z = (X - μ) / σ

3. Look up the Z-score that corresponds to the given probability (0.2) in a standard normal (Z) table. Since the table typically gives P(Z < z), we'll find P(Z < z) = 1 - 0.2 = 0.8. The corresponding Z-score is approximately 0.84.

4. Plug in the known values and solve for σ:
  0.84 = (9 - 5) / σ
  σ ≈ 4 / 0.84
  σ ≈ 4.76

5. Finally, find the variance, which is σ²:
  σ² ≈ 4.76²
  σ² ≈ 22.66

So, the approximate variance of the normal random variable X is 22.66.

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The approximate variance of the normal random variable X is the square of the standard deviation:

Var(X) ≈ [tex](4.76)^2[/tex] ≈ 22.65 (rounded to two decimal places).

To approximate the variance of the normal random variable X with a mean of 5, given that P(X > 9) = 0.2, we can use the z-score and standard normal distribution.

First, we calculate the z-score using the standard normal distribution formula:

z = (X - μ) / σ

where X is the value of interest (in this case, 9), μ is the mean (5), and σ is the standard deviation.

Plugging in the values, we get:

z = (9 - 5) / σ = 4 / σ

Next, we use the standard normal distribution table or a calculator to find the z-score that corresponds to a cumulative probability of 0.2. Let's assume that z = -0.84.

Now, we can use the z-score formula to solve for the standard deviation σ:

-0.84 = 4 / σ

Cross-multiplying, we get:

-0.84σ = 4

Dividing both sides by -0.84, we get:

σ ≈ 4 / -0.84 ≈ -4.76

Since the standard deviation cannot be negative, we discard the negative value and take the absolute value, resulting in:

σ ≈ 4.76

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If the three babies consume 50 liters of milk in 20 days, then 4 babies will consume 83 liters of milk in 25 days.

We can start by using the given information to calculate the daily milk consumption rate per baby. The total milk consumed over 20 days by the three babies is 50 liters. Therefore, the daily milk consumption rate per baby is:

Daily milk consumption rate per baby = 50 liters / (3 babies x 20 days) = 0.83 liters per day per baby

If we add another baby, the total number of babies becomes 4. We want to find out how much milk they will consume in 25 days. Total milk required for 4 babies in 25 days = (number of babies) x (daily milk consumption rate per baby) x (number of days)

Substituting the given values, we get:

Total milk required = 4 x 0.83 liters per day per baby x 25 days

Total milk required = 83 liters

As a result, if three babies drink 50 liters of milk in 20 days, four babies will drink 83 liters of milk in 25 days.

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Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.

Given data:

fraction of crate brought by friend = 1/2

Total number of ice buckets = 6

Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets

Fraction of crate in each bucket = (1/2) / 6

Fraction of crate in each bucket =  1 / (2*6)

Fraction of crate in each bucket = 1/12

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

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The unit price for the first bag is $2.12 per kilogram and the unit price for the second bag is $2.09 per kilogram.

To find the unit price, we need to divide the total cost by the weight of the bag.

For the first bag

Unit price = Total cost / Weight

Unit price = $15.84 / 7.48 kg

Unit price = $2.12/kg

Therefore, the unit price for the first bag is $2.12 per kilogram.

For the second bag

Unit price = Total cost / Weight

Substitute the values in the equation

Unit price = $16.58 / 7.94 kg

Unit price = $2.09/kg

Therefore, the unit price for the second bag is $2.09 per kilogram.

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Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

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To determine the contribution of predictor X7 to a multiple linear regression model with p predictors and n observations, the partial F-test can be used to calculate the partial F-statistic for X7. This partial F-statistic is related to the t-test calculated for X7 in the same model, as the square of the t-statistic for X7 is equal to the partial F-statistic for X7.

To calculate the partial F-statistic for X7, you first fit the full model with all p predictors and record the residual sum of squares (RSS). Then, you fit a reduced model without X7 and record the residual sum of squares for this model (RSSr). The partial F-statistic for X7 is calculated as (RSSr - RSS) / q / RSS, where q is the number of predictors in the reduced model (excluding X7). This statistic follows an F distribution with 1 numerator degree of freedom and q denominator degrees of freedom.

The partial F-statistic is related to the t-test calculated for X7 in the same model because the square of the t-statistic for X7 is equal to the partial F-statistic for X7. Specifically, t^2 = partial F, where t is the t-statistic for the coefficient of X7 in the full model.

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--The complete question is, Suppose you have a multiple linear regression model with p predictors and n observations. Using the partial F-test, you want to determine the contribution of a particular predictor, say X7, to the model. How do you calculate the partial F-statistic for X7 and how is it related to the t-test calculated for X7 in the same model?--

There are 216 possible outcomes for each trial of rolling three standard dice.

In probability theory, an outcome is defined as the result of a single experiment or trial. The total number of outcomes in a trial can be determined by the multiplication principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m x n ways to do both.

In this case, Michelle is rolling three standard dice simultaneously, which means that there are six possible outcomes for each die. Therefore, the total number of outcomes for a single trial is calculated by multiplying the number of outcomes for each die. Using the multiplication principle, we get:

Number of outcomes for each die = 6

Total number of outcomes for a single trial = 6 x 6 x 6 = 216

It is important to note that not all outcomes are equally likely, and the probability of getting a specific outcome can be calculated by dividing the number of favorable outcomes by the total number of outcomes.

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The ounces of  beeswax needed by Leah to make 15 more small candles is equal to 49.95 ounces.

Let us consider 'x' be the ounces of beeswax required by Leah to make 15 candles.

To make 6 small candles, Leah uses 20 ounces of beeswax.

So, to make one small candle,

Ounces of beeswax used by Leah ,

= 20 ounces / 6 candles

= 3.33 ounces/candle (rounded to two decimal places)

To make 15 more small candles,

Ounces of beeswax Leah will need is equals to,

⇒ x = 15 candles x 3.33 ounces/candle

⇒ x = 49.95 ounces (rounded to two decimal places)

Therefore, Leah needs 49.95 ounces of beeswax to make 15 more small candles.

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