Mr. Salinger has 8 packs of seeds. The line plot shows the weight of each pack. Mr. Salinger wants to redistribute the seeds in such a way that each pack weighs the same. What will be the weight of each pack?

The number of different colors that Sam can use for the triangle is given as follows:

60 different colors.

The Fundamental Counting Theorem (also known as the multiplication rule) is a fundamental principle in combinatorics that describes how to count the number of possible outcomes in a sequence of events.

The theorem states that if there are m ways that one event can occur and n ways that a second event can occur, then there are m x n ways that both events can occur.

The parameters for this problem are given as follows:

Hence the number of options is obtained as follows:

5 x 4 x 3 = 60 options.

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a. The probability that all four units are good is 0.2067 (approx),

b. The probability that exactly two units are good is 0.0226 (approx).

Given a shipment of 13 microwave ovens contains four defective units and a vending company purchases four units at random, we need to calculate the probability of the following events:

(a) all four units are good.

(b) exactly two units are good.

(a) What is the probability that all four units are good?

To solve this, we need to use the formula for the probability of an intersection of independent events.

Since the probability of getting a good unit is 9/13, then the probability of getting 4 good units in a row is calculated as follows:

P(All 4 units are good) = P(Good unit) × P(Good unit) × P(Good unit) × P(Good unit) = 9/13 × 9/13 × 9/13 × 9/13 = 47829609/232044048 = 0.2067 (approx)

(b) What is the probability that exactly two units are good?

Here, we need to use the binomial probability formula since the number of good units follows a binomial distribution. We need to find the probability of getting exactly 2 good units, given that we are purchasing 4 units.

P(exactly 2 units are good) = C(4,2) × P(Good unit)² × P(Defective unit)²

= 6 × (9/13)² × (4/13)²

= 52488/2320440

= 0.0226 (approx)

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The roots of the given quadratic equation are x= 4, [tex]\frac{-3}{2}[/tex]

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0The roots of a quadratic equation are found using the quadratic formula. In place of the factorization method, this formula aids in evaluating the quadratic equations' solutions. The quadratic formula aids in identifying the problem's fictitious roots when a quadratic equation lacks actual roots. Shreedhara Acharya's formula is another name for the quadratic formula.

2x² - 5x​ -12 = 0

The Shridharacharya formula or quadratic formula -

[tex]x=\frac{-b\ +-\sqrt{b^2-4ac}}{2a}[/tex]

we have a=2, b=-5 and c=-12

[tex]x=\frac{5+-\sqrt{5^2-4*2*12}}{2*2}\\\\x=\frac{5+-\sqrt{25+96}}{4}\\\\x=\frac{5+\sqrt{121}}{4}\\\\x=\frac{5+-11}{4}\\now, \\x=\frac{5+11}{4}=\frac{16}{4}\\x=4\\x=\frac{5-11}{4}\\x=-6/4\\x=-3/2[/tex]

The mistake in your solution is we have the value of b=-5 so , when we put the value of b in a formula then -5 will be 5.

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f(x) = 3x2 + 4x − 9,  the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This can be written in interval notation as [−9, ∞).

Interval notation is a mathematical notation used to express the range of a variable. It is used to represent intervals on the number line, either on the real line or on the complex plane.

In this case, the domain of f(x) = 3x2 + 4x − 9 is all real numbers. The range of this function is all real numbers greater than or equal to -9. This can be written in interval notation as [−9, ∞).

The function is a quadratic polynomial of the form ax2 + bx + c. The domain of a polynomial function is all real numbers (i.e. any x-value). The range of the function is the set of all y-values that it can produce.

Here the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This means that the minimum y-value that the function can produce is -9. This means that the range of the function is all real numbers greater than or equal to -9.

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Thus, the distance of ladder from the building is found to be 11.53 ft.

Exactly single right angle measure 90 degrees characterises a right triangle.

The hypotenuse of the a right triangle's square is equal to the sum of its other two sides, according to the Pythagorean Theorem. It is written as a²+b²=c² in equation form.

Pythagoras is in the form of;

a²+b²=c²

Let the distance of ladder from the building be 'x'.

Height of ladder from ground h = 6 ft.

Length of ladder l = 13 ft.

Here, using the Pythagorean theorem;

x² + 6² = 13²

x²  = 13² -  6²

x²  = 169 - 36

x²  = 133

x = √133

x = 11.53

Thus,  the distance of ladder from the building is found to be 11.53 ft.

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In option C, we can see that the equation is in vertex form.

What is parabola ?

A parabola is a symmetrical U-shaped curve formed by the graph of a quadratic function. It is a type of conic section that results from the intersection of a cone and a plane that is parallel to one of the sides of the cone. A parabola can also be defined as the set of points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. Parabolas have many applications in physics, engineering, and mathematics, including projectile motion, antenna design, and optimization problems.

According to the question:
The equation that reveals the minimum or maximum value of f(x) without changing the form of the equation is C f(x)=(x-2)²-16.

This equation is in vertex form, which is f(x) = a(x-h)² + k. In this form, the vertex of the parabola is at the point (h, k), and the value of "a" determines whether the parabola opens upwards or downwards.

In option C, we can see that the equation is in vertex form, where the vertex is (2, -16). Therefore, the minimum value of f(x) is -16, which occurs at x=2.

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Answer:

[tex]60n - 97[/tex]

Step-by-step explanation:

[tex]3 - 5( - 3n + 5)3 - 5( - 3n + 5)[/tex]

[tex]3 + (15n - 25)3 + 15n - 25[/tex]

[tex]3 + 45n - 75 + 15n - 25[/tex]

[tex]60n - 97[/tex]

The solution to the system of equations is (x, y) = (2, 1).

A system of equations is a set of two or more equations that are to be solved simultaneously, meaning that the values of the variables that satisfy each equation in the system must be found. The solution to a system of equations is the set of values for the variables that satisfy all the equations in the system.

To solve the system of equations:

8x - 5y = 11 ...(1)

4x - 3y = 5 ...(2)

We can use the elimination method to eliminate one of the variables. We want to eliminate the variable "y", so we need to multiply equation (2) by -5/3, which will give us:

-5/3(4x - 3y) = -5/3(5)

-20x/3 + 5y = -25/3 ...(3)

Now we can add equations (1) and (3) to eliminate "y":

8x - 5y + (-20x/3 + 5y) = 11 - 25/3

Combining like terms, we get:

(24x - 15y - 20x + 15y)/3 = 8/3

Simplifying, we get:

4x/3 = 8/3

Multiplying both sides by 3, we get:

4x = 8

Dividing both sides by 4, we get:

x = 2

Now we can substitute x = 2 into equation (1) or (2) to find y. Let's use equation (1):

8x - 5y = 11

8(2) - 5y = 11

16 - 5y = 11

Subtracting 16 from both sides, we get:

-5y = -5

Dividing both sides by -5, we get:

y = 1

Therefore, the solution to the system of equations is (x, y) = (2, 1).

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Complete question:

Given the system of equation:

8x - 5y = 11

4x - 3y = 5

Find the value of x and y.

Joelle has a total of 32 yards of ribbon in all, the correct option is A.

Let's use x to represent Joelle's total amount of ribbon. We know that 24 yards of the ribbon represent 86% of her total amount of ribbon, which can be expressed as:

24 = 0.86x

We can solve for x by dividing both sides by 0.86:

x = 27.91

The response options are all integers, thus we must round to the closest whole number because of this. Since 0.91 is greater than or equal to 0.5, we round up to 28.

Therefore, Joelle has a total of

x = 27.91 / 0.86

= 32.44 yards of ribbon.

Once again, we round to the nearest whole number, which is 32.

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The complete question is:

To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all?

A 32

B 192

C 300

D 1920​

In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.

In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.

The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.

The values of all the variables associated with this basic feasible solution are:

x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.

Note that these values correspond to the entries in the tableau in the "BV" column.

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The missing tableau is in the image attached below

The measure of angle R in ΔSRT which is drawn inside the circle is 77.5°.

Circle is a two-dimensional shape that is defined as the set of all points that are equidistant from a central point. It is often represented as a round shape with a curved boundary.

Since SR is a diameter of the circle, it follows that angle STR is a right angle (90°). Therefore, we can find the measure of angle SRT using the following equation:

∠SRT + ∠STR = 180°

(2x-23°) + 90° = 180°

2x + 67° = 180°

2x = 180° - 67°

2x = 113°

x = 56.5°

∠TRS = 5x-97°

∠TRS = 5(56.5°)-97°

∠TRS = 192.5°

Finally, we can find the measure of angle SRT:

∠SRT = 180° - ∠STR - ∠TRS

∠SRT = 180° - 90° - 192.5°

∠SRT = -102.5°

Therefore, to find the measure of angle R, we need to add 180° to angle SRT:

∠R = ∠SRT + 180°

∠R = -102.5° + 180°

∠R = 77.5°

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Using the identity sin² 0 + cos² 0 = 1, the value of cos 0 is 0.951 (to the nearest hundredth)

Using the identity sin² 0 + cos² 0 = 1, we can solve for cos 0:

cos² 0 = 1 - sin² 0

cos² 0 = 1 - (-0.31)²

cos² 0 = 1 - 0.0961

cos² 0 = 0.9039

Taking the square root of both sides, we get:

cos 0 ≈ ±0.951

Since 0 is in the interval ³ < 0 < 2π, we know that cos 0 must be positive. Therefore, to the nearest hundredth, cos 0 ≈ 0.95.

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The probability that a randomly selected adult weighs between 120 and 165 lbs is approximately 0.8186.

Since the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs, we can use the standard normal distribution to calculate the probability.

We first need to standardize the values using the formula: z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation.

For x = 120 lbs, z = (120 - 140) / 25 = -0.8, and for x = 165 lbs, z = (165 - 140) / 25 = 1.0. We can then use a calculator to find the probability between -0.8 and 1.0, which is approximately 0.8186.

Thus, the chance of picking an adult at random who weighs between 120 and 165 lbs is roughly 0.8186.

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BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Triangle congruence: Two triangles are said to be congruent if their three corresponding sides and their three corresponding angles are of identical size.

You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another.

Two triangles are congruent if they satisfy all five conditions for congruence.

They include the right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and angle-side-angle (SSS) (RHS).

So, in the given △DAB and △DCB:

AC = AC = Common

∠DAC = ∠BAC = AC is the angle bisector

∠DCA = ∠BCA = AC is the angle bisector

Then, △DAB ≅ △DCB under the ASA congruency rule,

Then, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

Therefore, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)

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Answer:

A = 21 units²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height between parallel sides )

here b = 7 and h = 3 , then

A = 7 × 3 = 21 units²

After 6 weeks, the size of the bacteria is 1600, and after 15 weeks, the size of the bacteria is 12800

Let N₀ be the initial number of bacteria in a population and r be the growth rate of the bacteria.

The doubling time t doubles the population after each time interval t, hence:

Nt = N₀ × 2^(t/t) Nₜ

= N₀ × 2^(t/d)Nt/N₀

= 2^(t/d)ln(Nₜ/N₀)

= (t/d)ln2ln(Nₜ) - ln(N₀)

= (t/d)ln2ln(Nₜ/N₀)

= (t/d)ln2t/d

= ln(Nt/N₀) / ln2

Now, we can calculate the time required for the population to double in size as

t = d × ln2/ln(Nₜ/N₀)

Now, let's substitute the values given and solve:

a) After 6 weeks, t = 3 weeks (since doubling time is 3 weeks)

So, Nₜ/N₀ = 2^(t/d)

= 2^(6/3)

= 2^2 = 4

Nt = N₀ × 4

= 100 × 4

= 400.

After 6 weeks, the size of the bacteria is 400.

b) After 15 weeks,

t = d × ln2/ln(Nₜ/N₀)ₜ

= 3 × ln2/ln(128)

= 3 × 0.9983/7.1554

= 0.4186 weeks

So, Nₜ/N₀ = 2^(t/d)

= 2^(15/3)

= 2^5

= 32Nₜ

= N₀ × 32 = 100 × 32

= 3200

After 15 weeks, the size of the bacteria is 3200.

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Answer: No

Step-by-step explanation:

Because the length of the box is shorter than the length of the club

20in<26in

The width of the box is also shorter than the width of the club

13in<16in

The height of the box is also shorter than the height of the club

11in<16in

But what about putting it at an angle?

So we know  [tex]a^{2} +b^{2} =c^{2}[/tex]

so let's try [tex]20^{2} +13^{2} =x^{2}[/tex]

                               [tex]x^{2}[/tex]=569

                               [tex]x=\sqrt{159}[/tex]

x is near 23.85 in, but 23.85<26. So no.

The probability that it will take at least 5 minutes until the student is served when he enters the restaurant today is 50%.

This is because there is an equal chance that it could take less than 5 minutes or more than 5 minutes until the student is served.

In probability terms, the student's wait time is a random variable with two possible outcomes - wait time less than 5 minutes, or wait time greater than or equal to 5 minutes. Since there is an equal chance of either outcome occurring, the probability of the wait time being greater than or equal to 5 minutes is 50%.

This is also known as the Law of Large Numbers.

To further illustrate this concept, imagine that the student flips a fair coin. The two possible outcomes of the coin toss are heads or tails. Since each outcome has an equal chance of occurring, the probability of either heads or tails is 50%.

In this case, the probability of the student's wait time being at least 5 minutes is the same as the probability of the coin toss being heads or tails, hence making the probability 50% or 0.5.

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To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.

Step 1: Find a common denominator for all the fractions.

Step 2: Convert each fraction to an equivalent fraction with the common denominator.

Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.

Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.

Step 5: Write the fractions in order from least to greatest.

For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.

Step 1: The common denominator for 3, 5, and 8 is 120.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.

1/3 = 40/120

2/5 = 48/120

3/8 = 45/120

Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48

Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.

Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.

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If i have four boxes arranged in a [tex]2 \times 2[/tex] grid, in 6 distinct ways can i place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit

If a student has four boxes arranged in a 2 × 2 grid, the distinct ways to place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit are six in number.

There are two possibilities for which box is left blank, so let's consider them separately:

Case 1: The top left box is left blank. In this case, the other three boxes must contain the digits 1, 2, and 3. There are three choices for what digit goes in the top right box, and then two choices for what digit goes in the bottom left box, and then one choice for what digit goes in the bottom right box.

This gives a total of 3·2·1 = 6 ways to place the digits in the boxes when the top left box is left blank.

Case 2: A different box is left blank. In this case, one of the digits must be left out. There are three choices for which digit is left out, and then three choices for which box is left blank. Once the digit and the blank box have been chosen, the remaining two digits can be placed in the other two boxes in any order, giving 2 ways.

This gives a total of 3·3·2 = 18 ways to place the digits in the boxes when a different box is left blank.

Therefore, the distinct ways to place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit are six in number.

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The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.

We can use the formula for calculating probabilities of combinations:

P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players

Total number of ways to choose 2 DVD players out of 6 is:

C(6,2) = 6! / ([2!] [4!]) = 15

Number of ways to choose 2 non-defective DVD players out of 4 is:

C(4,2) = 4! / ([2!] [2!]) = 6

Therefore, the probability that Cecil chooses 2 non-defective DVD players is:

P(not defective) = 6/15 = 2/5

So the value of P(not defective) is 2/5.

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Yes, we can say the shape of the sampling distribution for the sample mean if we know the population distribution.

However, if we do not know the population distribution, we cannot determine the exact shape of the sampling distribution for the sample mean. In this case, we can make use of the Central Limit Theorem (CLT) to make some assumptions about the shape of the sampling distribution. According to CLT, as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution, provided that the sample size is sufficiently large. Therefore, if the sample size is 19 and the population distribution is unknown, we can assume that the sampling distribution of the sample mean is approximately normal if the sample data is not heavily skewed or contains extreme outliers.

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Answer:$69.99

Step-by-step explanation:

If you start with $100 and spend 3.5% of it every day for 10 days, the amount of money you will have left at the end of the 10 days can be calculated as follows:

Day 1:

Starting with $100

Spending 3.5% of $100 = $3.50

Money left = $100 - $3.50 = $96.50

Day 2:

Starting with $96.50 (money left from Day 1)

Spending 3.5% of $96.50 = $3.38

Money left = $96.50 - $3.38 = $93.12

Day 3:

Starting with $93.12 (money left from Day 2)

Spending 3.5% of $93.12 = $3.26

Money left = $93.12 - $3.26 = $89.86

Continue this process for each of the 10 days, and you will have:

Day 4: $86.72

Day 5: $83.68

Day 6: $80.75

Day 7: $77.92

Day 8: $75.18

Day 9: $72.54

Day 10: $69.99

Therefore, after 10 days of spending 3.5% of $100 every day, you will have $69.99 left.

Answer:

Step-by-step explanation:

69.99

Answer:

Answer and Explanation: The symmetric bell shape of the normal curve implies that the skewness of the distribution of the data is 0, and most of the observation is located at the middle of the distribution. The shape of the normal distribution is not positive and negative skewed, the shape seems to be bell-shaped.

HOPE THIS HELPS!

6(y - 7z) This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.

A factor is an expression or number that evenly divides another expression or number without leaving a remainder.

To factor the expression 6y - 42z, we need to find the greatest common factor (GCF) of the two terms.

The GCF of 6y and 42z is 6, since both terms are divisible by 6. We can factor out the 6 from both terms, leaving:

6(y - 7z)

Notice that the term inside the parentheses (y - 7z) cannot be factored any further, since there is no common factor other than 1. Therefore, the fully factored form of 6y - 42z is:

6(y - 7z)

This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.

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As per the unitary method, Nikhil has 21 pencils and Cortez has 63 pencils.

Let's say Nikhil has x number of pencils. Then, according to the problem, Cortez has three times as many pencils as Nikhil. Therefore, Cortez has 3x number of pencils.

Together, they have a total of 84 pencils. So, we can write an equation based on the number of pencils owned by Nikhil and Cortez as follows:

x + 3x = 84

Simplifying the equation, we get:

4x = 84

Dividing both sides by 4, we get:

x = 21

So, Nikhil has 21 pencils. Using the fact that Cortez has three times as many pencils as Nikhil, we can find out how many pencils Cortez has:

Cortez has 3x = 3(21) = 63 pencils.

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Complete Question:

Lance has three times as many pencils as Nick, and they have 84 pencils together. How many pencils does each of them have?

Answer: 6

Step-by-step explanation:

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The factors of 78 are: 1, 2, 3, 6, 13, 26, 39, 78

Then the greatest common factor is 6.

Heres something you need to learn about the greatest common factor (gcf)

What is the Greatest Common Factor?

The largest number, which is the factor of two or more numbers is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors that are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Let us consider the example given below:

Greatest Common Factor (GCF)

For example – The GCF of 18, 21 is 3. Because the factors of the number 18 and 21 are:

Factors of 18 = 2×9 =2×3×3

Factors of 21 = 3×7

Here, the number 3 is common in both the factors of numbers. Hence, the greatest common factor of 18 and 21 is 3.

Similarly, the GCF of 10, 15 and 25 is 5.

How to Find the Greatest Common Factor?

If we have to find out the GCF of two numbers, we will first list the prime factors of each number. The multiple of common factors of both the numbers results in GCF. If there are no common prime factors, the greatest common factor is 1.

Finding the GCF of a given number set can be easy. However, there are several steps need to be followed to get the correct GCF. In order to find the greatest common factor of two given numbers, you need to find all the factors of both the numbers and then identify the common factors.

Find out the GCF of 18 and 24

Prime factors of 18 – 2×3×3

Prime factors of 24 –2×2×2×3

They have factors 2 and 3 in common so, thus G.C.F of 18 and 24 is 2×3 = 6

Also, try: GCF calculator

GCF and LCM

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Least Common Multiple of two or more numbers is the smallest number (non-zero) that is a multiple of all the numbers.

Factoring Greatest Common Factor

Factor method is used to list out all the prime factors, and you can easily find out the LCM and GCF. Factors are usually the numbers that we multiply together to get another number.

Example- Factors of 12 are 1,2,3,4,6 and 12 because 2×6 =12, 4×3 = 12 or 1×12 = 12. After finding out the factors of two numbers, we need to circle all the numbers that appear in both the list.

Greatest Common Factor Examples

Example 1:

Find the greatest common factor of 18 and 24.

Solution:

First list all the factors of the given numbers.

Factors of 18 = 1, 2, 3, 6, 9 and 18

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

The largest common factor of 18 and 24 is 6.

Thus G.C.F. is 6.

Example 2:

Find the GCF of 8, 18, 28 and 48.

Solution:

Factors are as follows-

Factors of 8 = 1, 2, 4, 8

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 28 = 1, 2, 4, 7, 14, 28

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest common factor of 8, 18, 28, 48 is 2. Because the factors 1 and 2 are found all the factors of numbers. Among these two numbers, the number 2 is the largest numbers. Hence, the GCF of these numbers is 2.

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The dimensions that maximize the enclosed area are L = 41.665 feet and W = 41.665 feet for each corral and the maximum area is 10868.09 square feet.

To find the dimensions that maximize the enclosed area, we need to use optimization techniques. Let's denote the length of each rectangular corral by L and the width by W. We can write the total enclosed area as A = 6LW.

The perimeter of each corral is given by P = 2L + 2W, and we have a total of 6 corrals, so the total length of fencing required is 6P = 12L + 12W.

We are given that we have 1,000 feet of fencing, so we can write 12L + 12W = 1000, or equivalently, L + W = 83.33 (rounded to two decimal places).

We can now use this equation to express one of the variables (say, W) in terms of the other: W = 83.33 - L.

Substituting this expression for W into the formula for the enclosed area, we get A = 6L(83.33 - L) = 499.98L - 6L^2.

To find the value of L that maximizes the area, we need to take the derivative of A with respect to L and set it equal to zero: dA/dL = 499.98 - 12L = 0. Solving for L, we get L = 41.665 (rounded to three decimal places).

Substituting this value back into the expression for W, we get W = 83.33 - L = 41.665.

The maximum area is A = 6LW = 10868.09 square feet (rounded to two decimal places).

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The perimeter of the updated blueprint will be 24 times the sum of the original length and width.

If Ezra wants to multiply the dimensions of the stage by a certain percentage to make the image 12 times larger than the original, he needs to find out what percentage that is.

To do this, he can divide the desired size of the new stage by the original size of the stage, and then multiply by 100 to get the percentage increase. So, if the original blueprint dimensions are x by y, and he wants to make the image 12 times larger, the new dimensions will be 12x by 12y.

To find the percentage increase, he can use the following formula:

Percentage increase = [(new size - original size) / original size] x 100

In this case, the new size is 12 times the original size, so the formula becomes:

Percentage increase = [(12x * 12y - x * y) / (x * y)] x 100

Simplifying this expression gives:

Percentage increase = [(144xy - x * y) / (x * y)] x 100 = 14300%

Therefore, Ezra needs to multiply the dimensions of the stage by 14300% to make the image 12 times larger than the original blueprint.

To find the perimeter of the updated blueprint, he can use the formula for the perimeter of a rectangle, which is: Perimeter = 2(length + width)

In this case, the length and width have been multiplied by 12, so the new perimeter becomes:

Perimeter = 2(12x + 12y) = 24(x + y)

Therefore, the perimeter of the updated blueprint will be 24 times the sum of the original length and width.

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The inverse function is R(L) = (360 - L)/15. It will take 8 weeks to pay loan if student owes $240 and 24 weeks to pay off the whole loan.

A. Let's start by defining the function L(w) as the amount owed w weeks after the student borrows the money. The student borrowed $360 and agreed to pay $15 per week, so the amount owed after w weeks can be calculated as:

L(w) = $360 - $15w

B. To find the inverse of function L, we need to switch the roles of the input and output variables. Let's call the inverse function R, where R(L) is the number of weeks it takes to pay off the loan if the amount owed is L. We can solve the equation from part A for w:

L(w) = $360 - $15w

$15w = $360 - L

w = (360 - L)/15

Therefore, the inverse function R(L) is:

R(L) = (360 - L)/15

This function tells us how many weeks it will take to pay off the loan for a given amount owed. For example, if the student owes $240, we can plug that into the inverse function to find out how many weeks it will take to pay off the loan:

R($240) = (360 - 240)/15 = 8

So it will take 8 weeks to pay off the loan if the student owes $240.

C. To find out how many weeks it will take to pay off the loan, we need to find the value of w when L(w) = 0 (i.e., when the loan is fully paid off). We can set L(w) = 0 and solve for w:

L(w) = $360 - $15w = 0

$15w = $360

w = 24

So it will take 24 weeks to pay off the loan.

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