Raphael bowled 4 games and had a mean score of 130. He then bowled two more games with scores of 180-230. What was his mean score for all 6 games? F 90

G 155

H 180

J 185

The probability that Cecilia, Annie, and Kimi are the first 3 gymnasts to perform, in any order, is 1 out of 6,720.

The probability of Cecilia, Annie, and Kimi being the first 3 gymnasts to perform, in any order, can be calculated using the concept of permutations. Since the order of the three gymnasts doesn't matter, we can consider all possible arrangements of the three names.
To find the total number of possible arrangements, we use the formula for permutations of n objects taken r at a time, which is n! / (n-r)!

In this case, n = 3 (the number of gymnasts) and r = 3 (the number of positions to be filled).
Using the formula, we get:
3! / (3-3)! = 3! / 0! = 3! = 3 x 2 x 1 = 6
Therefore, there are 6 possible arrangements for the first 3 gymnasts to perform.

Since we want Cecilia, Annie, and Kimi to be the first 3 gymnasts, we count the number of arrangements where they are in the first 3 positions.
The number of favorable arrangements is 3! because there are 3 gymnasts to be placed in 3 positions, and the order matters in this case.
Therefore, the probability is the number of favorable arrangements divided by the total number of possible arrangements:
P = 3! / 3! = 1
So, the probability that Cecilia, Annie, and Kimi are the first 3 gymnasts to perform, in any order, is 1.

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To find the probability that Cecilia, Annie, and Kimi are the first 3 gymnasts to perform in any order, we need to determine the total number of possible orders and the number of favorable outcomes.

The total number of possible orders can be calculated using the concept of permutations.

Since there are 3 gymnasts, there are 3! (3 factorial) ways to arrange them in order,

which equals 3 x 2 x 1 = 6 possible orders.

To calculate the number of favorable outcomes where Cecilia, Annie, and Kimi are the first 3 gymnasts to perform,

we need to consider that there are 3 positions available for Cecilia, 2 positions remaining for Annie, and 1 position left for Kimi.

This can be calculated using the formula 3 x 2 x 1 = 6.

Therefore, the number of favorable outcomes is 6.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 6 / 6

Simplifying, we find that the probability is 1.

So, the probability that Cecilia, Annie, and Kimi are the first 3 gymnasts to perform, in any order, is 1 or 100%.

This means that it is guaranteed that they will be the first three gymnasts to perform,

regardless of the order in which they are chosen.

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The dean's statement that the average class size is 20 is technically correct, but it can be misleading because most students are in classes with much larger numbers of students.

According to the statement by the dean of Blotchville University, the average class size is 20, which means the average number of students in a class is 20.

Now, let's consider that every student at Blotchville University takes only one course per semester. Given that the total number of students enrolled at Blotchville University is 150, we can calculate the total number of classes.

The formula to calculate the total number of classes is:

Total number of classes = Total number of students / Average number of students in a class

Substituting the values, we have:

Total number of classes = 150 / 20 = 7.5

Since we cannot have a fraction of a class, we round up the value to the nearest whole number. Therefore, the total number of classes is 8.

Hence, the dean's statement that the average class size is 20 is technically correct, but it can be misleading because most students are in classes with much larger numbers of students.

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The simplified value of the expression is 51.45. To simplify the expression, we need to follow the order of operations, which is also known as PEMDAS.

This stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

1. Start by evaluating the expression inside the parentheses: 2 - 6 = -4.
2. Next, square the result: [tex](-4)^2[/tex]= 16.
3. Then, add 5 to the result: 16 + 5 = 21.
4. Now, we can divide the sum of 5.5 and 4.3 by 4: (5.5 + 4.3)/4 = 9.8/4 = 2.45.
5. Finally, multiply the result from step 4 by the result from step 3: 2.45 * 21 = 51.45.

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The given expression: (5.5 + 4.3) / (4 * (2 - 6)^2) + 5, is simplified using the BODMAS rule, which states that mathematical operations should be performed in the order of Brackets, Orders or Indices, Division and Multiplication, and Addition and Subtraction. Following this rule, the simplified answer to the expression is (9.8 / 64) + 5.

In Mathematics, one of the fundamental principles we operate on is the order of operations, also known as

BODMAS/BIDMAS

(Brackets, Orders or Indices, Division and Multiplication, and Addition and Subtraction). Using this principle, the given expression: (5.5 + 4.3) / (4 * (2 - 6)^2) + 5, can be simplified step by step as follows:

So, the simplified answer to the expression is (9.8 / 64) + 5.

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The predictive amount when n=5 is approximately -103.76.

To find the predictive amount when n=5, we can use the equation for a linear regression line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using the given values. The formula for calculating the slope is m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2).

Using the given values, we can calculate the slope:
m = (5*470 - 210*470) / (5*5300 - (210)^2)
 = (2350 - 98700) / (26500 - 44100)
 = -96350 / -17600
 ≈ 5.48

Next, let's find the y-intercept (b). The formula is b = (Σy - mΣx) / n.

Using the given values, we can calculate the y-intercept:
b = (470 - 5.48*210) / 5
 = (470 - 1150.8) / 5
 = -680.8 / 5
 ≈ -136.16

Now we have the equation for the linear regression line: y = 5.48x - 136.16.

To find the predictive amount when n=5, we substitute x=5 into the equation:
y = 5.48*5 - 136.16
 ≈ -103.76

Therefore, the predictive amount when n=5 is approximately -103.76.

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Betsy should invest $20,000 in B-rated bonds and $30,000 in a certificate of deposit (CD) to realize exactly $5,000 in interest per year.

To determine how much money Betsy should invest in each option, we can set up a system of equations based on the given information.

Let's assume Betsy invests x dollars in B-rated bonds and y dollars in a CD.

According to the problem, the total amount of money Betsy has to invest is $50,000. Therefore, we have our first equation:

x + y = 50,000

The interest earned from the B-rated bonds is calculated as 15% of the amount invested, while the interest from the CD is 7% of the amount invested. Since Betsy requires $5,000 in interest per year, we can set up our second equation:

0.15x + 0.07y = 5,000

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

From the first equation, we can express x in terms of y:

x = 50,000 - y

Substituting this expression for x in the second equation, we get:

0.15(50,000 - y) + 0.07y = 5,000

Simplifying the equation:

7,500 - 0.15y + 0.07y = 5,000

7,500 - 0.08y = 5,000

-0.08y = -2,500

Dividing both sides by -0.08:

y = 31,250

Substituting this value of y back into the first equation:

x + 31,250 = 50,000

x = 50,000 - 31,250

x = 18,750

Therefore, Betsy should invest $18,750 in B-rated bonds and $31,250 in a CD to realize exactly $5,000 in interest per year.

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Using Sine rule of Trigonometry, the value of the missing side, c is 28.7

To solve for the missing sides, c, we use the sine rule : The sine rule is related using the formula:

c/ sinC = a / SinA

substituting the values into the formula:

C/sin60° = 14/Sin25

cross multiply

c * sin25 = sin60 * 14

c = (sin60 * 14) / sin25

c = 28.68

Therefore, the value of the side c in the question given is 28.7

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The atoms of distinct elements in a modeling kit can be differentiated by their atomic number, atomic mass, electron configuration, valence electrons, and chemical reactivity. These characteristics help identify and understand the unique properties and behavior of each element.

The atoms of distinct elements in a modeling kit can be identified by several characteristics beyond color. Here are some differences you can expect between the atoms of different elements:

1. Atomic number: Each element has a unique atomic number, which corresponds to the number of protons in the nucleus of its atoms. For example, hydrogen has an atomic number of 1, while helium has an atomic number of 2.

2. Atomic mass: Elements can have different atomic masses, which is the sum of protons and neutrons in the nucleus. For instance, carbon-12 and carbon-14 have different atomic masses but are both isotopes of carbon.

3. Electron configuration: The arrangement of electrons in an atom's electron shells differs between elements. For instance, oxygen has 8 electrons and its electron configuration is 2-6, while nitrogen has 7 electrons and its electron configuration is 2-5.

4. Valence electrons: The number of valence electrons, which are the electrons in the outermost shell, varies among elements. Valence electrons determine an element's chemical properties. For example, carbon has 4 valence electrons, while oxygen has 6 valence electrons.

5. Chemical reactivity: Different elements exhibit varying degrees of reactivity due to the number and arrangement of their electrons. For example, alkali metals like sodium and potassium are highly reactive, while noble gases like helium and neon are inert.
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Acc0rding to the given statement the points of intersection between the circle and line are (2, 1) and (-2, -1).

To find the point(s) of intersection between the circle and line, we can substitute the equation of the line into the equation of the circle.
Given:
Circle equation: x² + y² = 5
Line equation: y = (1/2)x
Substituting y = (1/2)x into the circle equation, we have:
x² + (1/2)x² = 5
Combining like terms, we get:
(5/4)x² = 5
Dividing both sides by (5/4), we obtain:
x² = 4
Taking the square root of both sides, we find:
x = ±2
Now, substituting these x-values into the line equation, we can find the corresponding y-values:
When x = 2, y = (1/2)(2) = 1
When x = -2, y = (1/2)(-2) = -1
Therefore, the points of intersection between the circle and line are (2, 1) and (-2, -1).

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The two given equations intersect at the points (-2, -1) and (2, 1). This solution is accurate and provides step-by-step explanations to help understand the process. It is important to note that the number of intersection points may vary depending on the equations given.

To find the points of intersection between the given circle and line, let's substitute the equation of the line into the equation of the circle.

First, we have the equation of the circle:
x^2 + y^2 = 5

And the equation of the line:
y = (1/2)x

To find the intersection points, we substitute (1/2)x for y in the equation of the circle:
x^2 + (1/2)x^2 = 5

Combining like terms, we have:
(5/4)x^2 = 5

Dividing both sides by (5/4), we get:
x^2 = 4

Taking the square root of both sides, we have:
x = ±2

Now, substitute these x-values back into the equation of the line to find the corresponding y-values.

For x = 2:
y = (1/2)(2) = 1

For x = -2:
y = (1/2)(-2) = -1

Therefore, the points of intersection are: (-2, -1) and (2, 1).

In conclusion, the two given equations intersect at the points (-2, -1) and (2, 1).

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11 quarts is approximately equal to 11 * 946.35 = 10,410 mL.

To convert 11 quarts to milliliters, we can use the conversion factor that 1 quart is approximately equal to 946.35 milliliters. Therefore, 11 quarts is approximately equal to 11 * 946.35 = 10,410 mL.

11 quarts is approximately equal to 10,404.88 milliliters.

To convert quarts to milliliters, we need to consider the conversion factor that 1 quart is equal to 946.352946 milliliters. By multiplying 11 quarts by the conversion factor, we get:

11 quarts * 946.352946 milliliters/quart = 10,409.882406 milliliters.

Rounded to the nearest hundredth, 11 quarts is approximately equal to 10,404.88 milliliters.

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The electrical supply house that has 7532 feet of 12-2/g wire will have 3605 more feet than 3927 feet of 12-3/g wire.

To determine the difference, we need to subtract the length of the 12-3/g wire from the length of the 12-2/g wire.

So, the calculation would be:
7532 feet (12-2/g wire) - 3927 feet (12-3/g wire) = 3605 feet

Therefore, there are 3605 more feet of 12-2/g wire than 12-3/g wire.

The two types of electrical wire used here are:
a. 12-2/g wire: This indicates a type of electrical wire with a gauge of 12 and two conductors (wires) plus a ground wire (g). The gauge of the wire determines its thickness, and in this case, it is 12.
b. 12-3/g wire: This refers to another type of electrical wire with a gauge of 12 as well, but it has three conductors (wires) and a ground wire (g). The additional conductor makes it suitable for circuits that require an extra wire, such as those involving switches or three-way lighting.

Understanding these wire specifications is essential when working with electrical systems, as it helps ensure the correct type and gauge of wire are used for different applications.

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The distance of 2.1 kilometers is approximately equal to 2296.79 yards.

The 2.1km is approximately equal to 1.305 miles.

To convert kilometers to yards, we need to know the conversion factor between the two units. The conversion factor for kilometers to yards is 1 kilometer = 1093.6133 yards.

Therefore, to convert 2.1 kilometers to yards, we can use the following calculation:

2.1 km * 1093.6133 yd/km = 2296.78823 yards

Rounding this value to a reasonable number of decimal places, we get:

2.1 km ≈ 2296.79 yards

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The extended ring R[a], obtained by adjoining an element a to a ring R, is indeed a ring isomorphic to R. This is demonstrated by showing that R[a] satisfies the properties of a ring and by constructing an isomorphism between R[a] and R.

To prove that adjoining an element a to a ring R gives a ring isomorphic to R, we need to show that the extended ring R[a] satisfies the definition of a ring and that there exists an isomorphism between R[a] and R.

First, let's define the extended ring R[a]. The elements of R[a] are represented as polynomials in a with coefficients from R. An element in R[a] can be written as:

R[a] = {r₀ + r₁a + r₂a² + ... + rₙaⁿ | r₀, r₁, r₂, ..., rₙ ∈ R}

where n is a non-negative integer and r₀, r₁, r₂, ..., rₙ are coefficients from R.

Now, let's prove the two main properties of a ring for R[a]:

Closure under addition and multiplication:

For any two elements (polynomials) p = r₀ + r₁a + r₂a² + ... + rₙaⁿ and q = s₀ + s₁a + s₂a² + ... + sₘaᵐ in R[a], the sum p + q and product p * q are also elements of R[a]. This can be proven by applying the distributive property and associativity of addition and multiplication.

Existence of additive and multiplicative identities:

The additive identity in R[a] is the polynomial 0, and the multiplicative identity is the polynomial 1. These identities satisfy the properties of an additive and multiplicative identity, respectively, when added or multiplied with any element in R[a].

Next, we need to show that there exists an isomorphism between R[a] and R, which means there is a bijective map that preserves the ring structure.

Consider the function φ: R[a] → R defined as φ(r₀ + r₁a + r₂a² + ... + rₙaⁿ) = r₀. This function maps each polynomial in R[a] to its constant term.

We can prove that φ is an isomorphism by verifying the following:

a) φ preserves addition: φ(p + q) = φ(p) + φ(q) for any p, q in R[a].

b) φ preserves multiplication: φ(p * q) = φ(p) * φ(q) for any p, q in R[a].

c) φ is bijective: φ is both injective and surjective.

The proofs for these properties involve applying the distributive property and associativity of addition and multiplication, and considering the coefficients of the polynomials.

Hence, we have shown that adjoining an element a to a ring R gives a ring isomorphic to R, denoted as R[a] ∼ R.

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The solution to the system of equations is x = -3,

y = 0, and

z = -2.

To solve the system of equations by substitution, we can substitute the value of x from the third equation into the other two equations.

3x + y - 2z = 22

x + 5y + z = 4

x = -3z

Substituting the value of x from equation 3 into equations 1 and 2, we get:

3(-3z) + y - 2z = 22

-9z + y - 2z = 22

-11z + y = 22

(-3z) + 5y + z = 4

-2z + 5y = 4

Now we have a system of two equations with two variables:

-11z + y = 22 and

-2z + 5y = 4.

By solving these equations, we find that z = -2, y = 0.

Substituting these values back into equation 3, we get:

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

Therefore, the solution to the system of equations is x = 6, y = 0, z = -2.

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To find the value of g^(-1) o g(2), we need to determine the input value that would produce an output of 2 when fed into the function g(x).

Let's begin by finding the inverse function of g(x). We can start by replacing g(x) with y in the equation and then solving for x.

Given:

g(3x - 2) = 7x - 15

Replacing g(x) with y:

y = 7x - 15

Now, let's solve for x in terms of y:

y = 7x - 15

y + 15 = 7x

x = (y + 15) / 7

Therefore, the inverse function g^(-1)(x) is:

g^(-1)(x) = (x + 15) / 7

Now we can find g^(-1) o g(2) by plugging g(2) into g^(-1)(x):

g^(-1) o g(2) = g^(-1)(g(2))

= g^(-1)(7(2) - 15)

= g^(-1)(14 - 15)

= g^(-1)(-1)

Plugging -1 into g^(-1)(x):

g^(-1)(-1) = (-1 + 15) / 7

= 14 / 7

= 2

Therefore, the value of g^(-1) o g(2) is indeed 2.

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It will take 12 hours to fill the tank if both pipes are open

A water tank can be filled by an inlet pipe in 8 hours.

It takes 3 times as long for the outlet pipe to empty the tank.

How long will it take to fill the tank if both pipes are open

The inlet pipe fills the tank in 8 hours.

The outlet pipe empties the tank in 3 times the inlet pipe or 24 hours.

Thus, the effective filling rate is 1/8 - 1/24 or 1/12 which means the tank can be filled by both pipes working together in 12 hours.

Hence, It will take 12 hours to fill the tank if both pipes are open.

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The solution to the equation 7w + 2 = 3w + 94 is w = 23.

To solve the equation 7w + 2 = 3w + 94, we'll begin by isolating the variable w on one side of the equation.

Subtracting 3w from both sides of the equation yields:

7w - 3w + 2 = 3w - 3w + 94

This simplifies to:

4w + 2 = 94

Next, we'll isolate the term with w by subtracting 2 from both sides of the equation:

4w + 2 - 2 = 94 - 2

This simplifies to:

4w = 92

To solve for w, we'll divide both sides of the equation by 4:

4w/4 = 92/4

This simplifies to:

w = 23

To check our answer, we substitute the value of w back into the original equation:

7w + 2 = 3w + 94

Substituting w = 23 gives us:

7(23) + 2 = 3(23) + 94

This simplifies to:

161 + 2 = 69 + 94

Which further simplifies to:

163 = 163

Since both sides of the equation are equal, we can conclude that w = 23 is the solution to the equation.

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Matthew will be responsible for fulfilling the loan agreement and ensuring the remaining balance is paid off.

If Joel stops paying his half of the loan and Matthew cannot locate him, the loan will still need to be repaid. In this case, Matthew will be solely responsible for making the monthly payments of $150 to pay off the remaining balance of $2,300.

Since Joel dropped out of college and took off with the boat and trailer, it is possible that Matthew might face difficulties in locating him to resolve the situation. However, from a legal standpoint, Matthew's obligation to repay the loan remains unchanged. It is advisable for Matthew to contact the lender and explain the situation, providing any relevant information about Joel's whereabouts if available.

The lender may be able to offer alternative solutions, such as adjusting the payment plan or pursuing legal action against Joel.

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To solve the equation (x+3i)(x-3i) = 34, we expand the left side using the FOIL method and simplify the expression. Setting it equal to 34, we solve for x by subtracting 9 from both sides and taking the square root. The solutions are x = 5 and x = -5.

To solve the equation (x+3i)(x-3i) = 34, we can use the FOIL method.

First, let's apply the FOIL method to expand the left side of the equation:
(x+3i)(x-3i) = x*x + x*(-3i) + 3i*x + 3i*(-3i)
           = [tex]x^2[/tex] - 3ix + 3ix - [tex]9i^2[/tex]
           =[tex]x^2 - 9i^2[/tex]

Since [tex]i^2[/tex] is equal to -1, we can simplify the equation further:
[tex]x^2 - 9i^2[/tex] =[tex]x^2[/tex] - 9(-1)
           = [tex]x^2[/tex] + 9

Now, we can set this expression equal to 34 and solve for x:
[tex]x^2[/tex] + 9 = 34

Subtracting 9 from both sides:
[tex]x^2[/tex] = 34 - 9
[tex]x^2[/tex] = 25

Taking the square root of both sides (remembering to consider both positive and negative roots):
x = ±√25
x = ±5

So, the solutions to the equation (x+3i)(x-3i) = 34 are x = 5 and x = -5.

To solve the equation (x+3i)(x-3i) = 34, we can use the FOIL method to expand the left side of the equation. By applying this method, we obtain[tex]x^2 - 9i^2[/tex]. Since [tex]i^2[/tex] is equal to -1, we can simplify this expression further to [tex]x^2[/tex] + 9. Setting this equal to 34, we subtract 9 from both sides and solve for x. Taking the square root of both sides and considering both positive and negative roots, we find that x can equal 5 or -5. Thus, these are the solutions to the equation.

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The simplified expression √16 ⋅ √25 is equal to 20.

To simplify the expression √16 ⋅ √25, we can simplify each square root individually and then multiply the results.

First, let's simplify √16. The square root of 16 is 4 since 4 multiplied by itself equals 16.

Next, let's simplify √25. The square root of 25 is 5 since 5 multiplied by itself equals 25.

Now, we can multiply the simplified square roots together:

√16 ⋅ √25 = 4 ⋅ 5

Multiplying 4 and 5 gives us:

4 ⋅ 5 = 20

Therefore, the simplified expression √16 ⋅ √25 is equal to 20.

In summary, √16 ⋅ √25 simplifies to 20.

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The probability that a randomly selected student in the course has received an A or B is 0.65 or 65%

To find the probability that a randomly selected student in the course has received an A or B, we can use conditional probability based on the given information.

Let's denote the event of doing homework regularly as A, and the event of getting a grade of A or B as B.

We know that P(A) = 0.8, which represents the probability of a student doing homework regularly.

We also know that P(B|A) = 0.75, which represents the probability of getting a grade of A or B given that the student does homework regularly.

Similarly, P(B|A') = 0.25, which represents the probability of getting a grade of A or B given that the student does not do homework regularly.

We can now calculate the probability of getting an A or B using the law of total probability:

P(B) = P(A) * P(B|A) + P(A') * P(B|A')

= 0.8 * 0.75 + 0.2 * 0.25

= 0.6 + 0.05

= 0.65

The probability that a randomly selected student in the course has received an A or B is 0.65 or 65%.

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To start an indirect proof of the statement "AB ≅ CD," the assumption you would make is that "AB and CD are not congruent."

To start an indirect proof of the statement "AB ≅ CD," we assume the opposite of the desired conclusion, which is that "AB and CD are not congruent."

Assume that AB and CD are not congruent: AB ≇ CD.

Next, we proceed with the steps to arrive at a contradiction.

Use the definition of congruent segments: If two segments are congruent, then they have the same length.

If AB and CD are not congruent, then they have different lengths.

Use the Transitive Property of Equality: If two quantities are equal to a third quantity, then they are equal to each other.

If AB has a different length than CD, then AB cannot be equal to CD.

This contradicts our assumption that AB and CD are not congruent.

Since our assumption leads to a contradiction, we can conclude that the statement "AB ≅ CD" is true.

Therefore, the assumption made to start an indirect proof of the statement "AB ≅ CD" is that "AB and CD are not congruent."

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The simplified form of ³√a¹²b¹⁵ is a⁴b⁵. To simplify, divide the exponents inside the radical by the index of 3.

The simplified form of the radical expression ³√a¹²b¹⁵ is a⁴b⁵.

1. To simplify the given radical expression, we need to divide the exponents inside the radical by the index, which in this case is 3.
2. Dividing 12 by 3 gives us 4, and dividing 15 by 3 gives us 5.
3. Therefore, the simplified form of ³√a¹²b¹⁵ is a⁴b⁵.

The simplified form of ³√a¹²b¹⁵ is a⁴b⁵. To simplify, divide the exponents inside the radical by the index of 3.

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The given expression is ³√a¹²b¹⁵. To simplify this radical expression, we need to find perfect cube factors of the variables under the cube root. The simplified form of ³√a¹²b¹⁵ is a¹²b¹⁵.

Let's break down the given expression:

³√a¹²b¹⁵

To simplify, we can rewrite a¹² as (a³)⁴ and b¹⁵ as (b³)⁵. Now the expression becomes:

³√(a³)⁴(b³)⁵

Using the property of exponents, we can bring the powers outside the cube root:

(a³)⁴ = a¹²
(b³)⁵ = b¹⁵

Now the expression simplifies to:

³√a¹²b¹⁵ = a¹²b¹⁵

So, the simplified form of ³√a¹²b¹⁵ is a¹²b¹⁵.

In this case, there are no perfect cube factors, so the expression cannot be simplified further.

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To calculate the number of acres in a parcel measuring 110 yards by 220 yards, we can use the formula:

Area (in square yards) = length (in yards) * width (in yards) So, the area of the parcel would be:

110 yards * 220 yards = 24,200 square yards

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

1 acre = 4,840 square yards

Dividing the area of the parcel by the conversion factor:

24,200 square yards / 4,840 square yards per acre = 5 acres

Therefore, the parcel measuring 110 yards by 220 yards contains 5 acres.

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The parcel measuring 110 yards by 220 yards contains 5 acres.

The given parcel measures 110 yards by 220 yards. To find out how many acres it contains, we need to convert the measurements to acres.

First, let's convert the length and width from yards to feet. There are 3 feet in a yard, so the length becomes 330 feet (110 yards * 3 feet/yard) and the width becomes 660 feet (220 yards * 3 feet/yard).

Next, we convert the length and width from feet to acres. There are 43,560 square feet in an acre.

To find the total area of the parcel in square feet, we multiply the length by the width: 330 feet * 660 feet = 217,800 square feet.

Finally, we divide the total area in square feet by 43,560 to convert it to acres: 217,800 square feet / 43,560 square feet/acre = 5 acres.

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Answer:

t = - 65

Step-by-step explanation:

- [tex]\frac{t}{13}[/tex] - 2 = 3 ( add 2 to both sides )

- [tex]\frac{t}{13}[/tex] = 5 ( multiply both sides by 13 to clear the fraction )

- t = 65 ( multiply both sides by - 1 )

t = - 65

To identify the constant sum for the ellipse, we need to find the distance between the foci of the ellipse. The constant sum for an ellipse is equal to the sum of the distances from any point on the ellipse to each of the foci.

Given that the foci of the ellipse are f1(9, 0) and f2(11, 6), and the point (1, 6) is on the ellipse, we can calculate the distances from the point (1, 6) to each of the foci. Using the distance formula, the distance from (1, 6) to f1(9, 0) is:
√[(9 - 1)^2 + (0 - 6)^2] = √[(8)^2 + (-6)^2] = √[64 + 36] = √100 = 10

Similarly, the distance from (1, 6) to f2(11, 6) is:
√[(11 - 1)^2 + (6 - 6)^2] = √[(10)^2 + (0)^2] = √[100 + 0] = √100 = 10

The constant sum for the ellipse is the sum of these two distances, which is 10 + 10 = 20.

Therefore, the constant sum for the ellipse is 20.

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The 97% confidence interval for the mean germination time is (13.065, 18.535) (option a).

To find the 97% confidence interval for the mean germination time based on the provided data, we can calculate the interval using the t-distribution since the sample size is small (n = 10) and the population standard deviation is unknown.

Using statistical software or a t-distribution table, the critical value for a 97% confidence level with 10 degrees of freedom is approximately 2.821.

Calculating the sample mean and sample standard deviation from the given data:

Sample mean ([tex]\bar x[/tex]) = (18 + 12 + 20 + 17 + 14 + 15 + 13 + 11 + 21 + 17) / 10 = 15.8

Sample standard deviation (s) = √[(Σ(xᵢ - [tex]\bar x[/tex])²) / (n - 1)] = √[(6.2² + (-3.8)² + 4.2² + 1.2² + (-1.8)² + (-0.8)² + (-2.8)² + (-4.8)² + 5.2² + 1.2²) / 9] = 4.652

Now we can calculate the confidence interval:

Confidence Interval = sample mean ± (critical value * (sample standard deviation / √(sample size)))

Confidence Interval = 15.8 ± (2.821 * (4.652 / √10))

Confidence Interval ≈ (13.065, 18.535)

Therefore, the correct option for the 97% confidence interval for the mean germination time is A. (13.065, 18.535).

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The complete question is:

Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. Assume that the population germination time is normally distributed. Find the 97% confidence interval for the mean germination time.

18, 12, 20, 17, 14, 15, 13, 11, 21 and 17

A. (13.065, 18.535)

B. (13.063, 18.537)

C. (13.550, 21.050)

D. (12.347, 19.253)

E. (14.396, 19.204)

The area of one face of the cube is 42 1/4 square inches.

To find the area of one face of the cube, we need to divide the total surface area of the cube by the number of faces it has.

A cube has 6 faces, so if the total surface area of the cube is 253 1/2 square inches, we can divide it by 6 to find the area of one face.

253 1/2 square inches ÷ 6 = 42 1/4 square inches.

Therefore, the area of one face of the cube is 42 1/4 square inches.

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The taxi and takeoff time for commercial jets, represented by the random variable x, is assumed to follow an approximately normal distribution with a mean of 8 minutes and a standard deviation of 3.3 minutes.

Based on the given information, we have a random variable x representing the taxi and takeoff time for commercial jets. The distribution of taxi and takeoff times is assumed to be approximately normal.

We are provided with the following parameters:

Mean (μ) = 8 minutes

Standard deviation (σ) = 3.3 minutes

Since the distribution is assumed to be normal, we can use the properties of the normal distribution to answer various questions.

Probability: We can calculate the probability of certain events or ranges of values using the normal distribution. For example, we can find the probability that a jet's taxi and takeoff time is less than a specific value or falls within a certain range.

Percentiles: We can determine the value at a given percentile. For instance, we can find the taxi and takeoff time that corresponds to the 75th percentile.

Z-scores: We can calculate the z-score, which measures the number of standard deviations a value is away from the mean. It helps in comparing different values within the distribution.

Confidence intervals: We can construct confidence intervals to estimate the range in which the true mean of the taxi and takeoff time lies with a certain level of confidence.

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The value of "m" represents the length of side G F in the kite F G H K. The value of "m" is 3.5. Given that sides G F and F K are congruent, we can conclude that their lengths are equal.

We are given that the length of side G H is 5 m 1 and the length of side H K is 3 m 7.

To find the value of "m," we need to find the length of side G F.

Since G F and F K are congruent, we can set up an equation:

5 m 1 = 3 m 7

To solve for "m," we need to subtract 3 m from both sides of the equation:

5 m - 3 m = 3 m - 3 m + 7

This simplifies to:

2 m = 7

Now, we can solve for "m" by dividing both sides of the equation by 2:

m = 7 ÷ 2

m = 3.5

Therefore, the value of "m" is 3.5.

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The [tex]$n^{th}$[/tex] term of the given sequence is [tex]$$a_n = (-1)^{n+1} \frac{n}{n+4}$$[/tex]

The given sequence is  

[tex]$$-\frac{1}{5}, \frac{2}{6}, -\frac{3}{7}, \frac{4}{8}, \dots$$[/tex]

The problem is to find the first 5 terms and the [tex]$n^{th}$[/tex] term of the given sequence.

Step-by-step explanation: The given sequence is

[tex]$$-\frac{1}{5}, \frac{2}{6}, -\frac{3}{7}, \frac{4}{8}, \dots$$[/tex]

To find the first 5 terms of the given sequence, we will plug in the values of n one by one.

We have the sequence formula,

[tex]$$a_n = (-1)^{n+1} \frac{n}{n+4}$$[/tex]

When n = 1,

[tex]$$a_1 = (-1)^{1+1} \frac{1}{1+4} = -\frac{1}{5}$$[/tex]

When n = 2,

[tex]$$a_2 = (-1)^{2+1} \frac{2}{2+4} = \frac{2}{6} = \frac{1}{3}$$[/tex]

When n = 3,

[tex]$$a_3 = (-1)^{3+1} \frac{3}{3+4} = -\frac{3}{7}$$[/tex]

When n = 4,

[tex]$$a_4 = (-1)^{4+1} \frac{4}{4+4} = \frac{4}{8} = \frac{1}{2}$$[/tex]

When n = 5,

[tex]$$a_5 = (-1)^{5+1} \frac{5}{5+4} = -\frac{5}{9}$$[/tex]

Thus, the first 5 terms of the given sequence are [tex]$$-\frac{1}{5}, \frac{1}{3}, -\frac{3}{7}, \frac{1}{2}, -\frac{5}{9}$$[/tex]

Now, to find the [tex]$n^{th}$[/tex] term of the given sequence, we will use the sequence formula.

[tex]$$a_n = (-1)^{n+1} \frac{n}{n+4}$$[/tex]

Thus, the [tex]$n^{th}$[/tex] term of the given sequence is [tex]$$a_n = (-1)^{n+1} \frac{n}{n+4}$$[/tex]

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