Change to vertex form, with step by step. Thanks

From greatest to least5.25, 1, 3/4 (or 0.75), -5/2 (or -2.5), -8.345

To sort these numbers from largest to smallest, we must establish a consistent format for swift comparison.

Among the various numbers included are whole figures, fractions and decimals, causing us to mix them uniformly first so that they match— in decimals.

-5/2 = -2.5

5.25 = 5.25 (no alteration required)

1 = 1.0 (to simplify analysis, only adding decimal points)

3/4 = 0.75

-8.345 = -8.345 (essentially unchanged)

At this point, we can effortlessly contrast and compare the numbers.

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For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: A. function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics and Geometry, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1 and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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Answer:

There are 300 students at East High School.

Step-by-step explanation:

East High School has 1/10 as many students as West High School, which means that the number of students at East High School is equal to 1/10 of the number of students at West High School.

To find out how many students are at East High School, we can multiply the number of students at West High School by 1/10:

East High School = West High School x 1/10East High School = 3000 x 1/10East High School = 300

Therefore, there are 300 students at East High School.

Answer:

East High School has 1/10 × 3,000 = 300 students.

The coefficients a, b, and c in the 12th term of the expanded form are 312, 64, and 11, respectively.

The 12th term is 312(64x^3)(y^11) or 19968x^3y^11.

We would use the binomial theorem formula

Σ [n! / (k!(n - k)!) * a^(n - k) * b^k] for k = 0 to n.

For our calculation, we have affirmed that n equals 14 whereas a and b are equivalent to 4x and y respectively.

Our objective parameter is set to the twelfth term where k holds the value of 11 (as k begins counting from zero).

Thus substituting these values in the binomial equation, it follows:

(4x + y)^14 = Σ [14! / (k!(14 - k)!) * (4x)^(14 - k) * y^k] from k= 0 to 14.

From this derivation, the number we had sought becomes calculable by assigning value k equals 11:

Term_12 = 14! / (11!(14 - 11)!) * (4x)^(14 - 11) * y^11.

The above simplifies after that further leading to:

Term_12 = 14!/(11! × 3!) × (4x)^3×y^11\

Term_12=(14 × 13 × 12)/(3 × 2 × 1) × (4x)^3 × y^11

which leads to, after computation:

Term_12= 2 ×13 × 12×64x^3y^11

Immediately from our results, the constant values a, b, and c have become clear:

a = 2 × 13 × 12 which reduces to 312

b = 64

c = 11

Thus note that for term 12: 'a' is equal to 312; 'b' is represented by 64 while 'c' stands for 11.

Simplification of this value would lead to expressing the twelfth term as 19968 x^3 y^11.

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Given the expression (4x + y)^14, find the coefficients a, b, and c in the 12th term of the expanded form

Answer: A. 102

Step-by-step explanation:

1,125 divided by 11 is 102.2727... so only 102 full goodie bags can be made.

The value of the expressions are;

a. 4n - 8

b. 64

c. 18

d. 5(n + 3)

Algebraic expressions are described as expressions that consists of terms, constants, coefficients, factors and variables.

They are also identified to consist of mathematical operations which includes;

Using the distributive property, we have;

a. 4(n - 2)

expand the bracket, we get;

4n - 8

b. . 8(2+6)

8(8)

expand the bracket

64

c. 6•8-6•5

48 - 30

Subtract

18

d. 5n+15

factorize the expression

5(n + 3)

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The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

We have,

Equation of circle: x²+ y² – 2x – 8 = 0

The standard equation of a circle is

x² + y² + 2gx + 2fy + C= 0

where Centre is (-g, -f)

and, radius = √g²+f²-C

from given equation the center is

2gx = -2x

x= -1

and,  2fy = 0

f = 0

So, the Centre = (-(-1), 0) = (1, 0)

Now, r = radius = √g²+f²-C

r= √1²+0²-(-8)

r=√9

r = 3 units

Hence, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The quadratic regression equation for the data is given as follows:

y = 2.4x² - 14.4x + 46.8.

To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.

The points for this problem are taken from the table, as follows:

(1, 35), (2, 27), (3, 24), (4, 28), (5, 33).

Inserting these points into a calculator, the equation is given as follows:

y = 2.4x² - 14.4x + 46.8.

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The values AB² + BC² ≠ AC², triangle ABC is not a right triangle.

A mathematical notion known as the Pythagorean theorem explains how a right triangle's sides relate to one another. It asserts that the square of the hypotenuse's (the triangle's longest side) length equals the product of the squares of the other two sides (the adjacent and opposite sides).

To find the length of AB, we use the distance formula:

AB = √[(x2 - x1)² + (y2 - y1)²]

AB = √[(1 - (-9))² + ((-1) - (-3))²]

AB = √[10² + 2²]

AB = √104

To find the length of BC, we use the distance formula:

BC = √[(x2 - x1)² + (y2 - y1)²]

BC = √[(-3 - 1)² + ((-7) - (-1))²]

BC = √[(-4)² + (-6)²]

BC = √52

To find the length of AC, we use the distance formula:

AC = √[(x₂ - x₁)² + (y₂ - y₁)²]

AC = √[(-3 - (-9))² + ((-7) - (-3))²]

AC = √[6² + (-4)²]

AC = √52

Using the Pythagorean Theorem, we can determine if triangle ABC is a right triangle. If a triangle is a right triangle, then the sum of the squares of the lengths of the two shorter sides will equal the square of the length of the longest side. So, we need to check if:

AB² + BC² = AC²

(√104)² + (√52)² = (√52)²

104 + 52 = 52

156 ≠ 52

Since AB² + BC² ≠ AC², triangle ABC is not a right triangle.

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If a  sports ball has a diameter of 11cm then the volume of the ball is 696.5 cubic centimeters

The volume of a sphere can be calculated using the formula:

V = (4/3)πr³

where V is the volume of the sphere, r is the radius of the sphere, and π is a constant equal to approximately 3.14159.

Since the diameter of the sports ball is given as 11 cm, we can find the radius by dividing the diameter by 2:

r = 11 cm / 2 = 5.5 cm

Now we can substitute this value of r into the formula and calculate the volume:

V = (4/3)π(5.5 cm)³

V = (4/3)π(166.375 cm³)

V = 696.5 cm³

Therefore, the volume of the sports ball is 696.5 cubic centimeters (cm³).

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The perimeter of the quadrilateral is  b + 2c - 2 inches

To determine the value of the perimeter, we need to know the properties of a quadrilateral.

These properties includes;

The perimeter of a quadrilateral is expressed as;

Perimeter = A + B + C + D

add the values of the sides

Substitute the values, we have;

Perimeter = b + c + b - 2 + c - b

collect the like terms

Perimeter = b + 2c - 2

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The value of x in the equation  27=−5x+3 is -24/5

The given equation is 27=−5x+3

We have to find the value of x

Subtract 3 from both sides

27-3=-5x

24=-5x

Divide both sides by 5

x=-24/5

Hence, the value of x in the equation  27=−5x+3 is -24/5

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The required fraction of the number of trees in a full row that is the number of trees in the extra row is 6/10.

Number of full rows = 8450 trees / 125 trees/row = 67.6 rows

Since Emiliano cannot plant a fraction of a row, the number of full rows he plants is 67.

To find the number of trees in the extra row, we need to subtract the number of trees in the full rows from the total number of trees:

Number of trees in the extra row = 8450 trees - (125 trees/row × 67 rows) = 75 trees

Therefore, Emiliano plants 67 full rows and an extra row with 75 trees.

To find the fraction of the number of trees in a full row that is the number of trees in the extra row, we need to divide the number of trees in the extra row by the number of trees in a full row:

Fraction of the number of trees in a full row that is the number of trees in the extra row = 55 trees / 125 trees/row = 0.6 or 60/100 or 6/10

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The statement that is not true is (c) The measure of ∠R is the same as ∠N.

We have,

From the question, we have the following parameters that can be used in our computation:

The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1).

The coordinates of ΔUNA are U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).

Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)

This is a rigid transformation

And so, the side lengths and the corresponding angle measures are equal

However, angles R and N are not corresponding angles

So, the false statement is (c) The measure of ∠R is the same as ∠N.

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The only solution to the equation is cos(x) = 5/7.

We have,

cos²(x) + sin²(x) = 1:

Substituting.

7cos²(x) - 26 = 7(1 - sin²(x)) - 26

= 7 - 7sin²(x) - 26

= -19 - 7sin²(x)

Now,

-19 - 7sin²(x) = -20sin(x) - 7

We can simplify this equation by moving all the terms to one side:

7sin^2(x) - 20sin(x) - 12 = 0

We can solve this quadratic equation using the quadratic formula:

sin(x) = [20 ± √(20² - 4(7)(-12))] / (2(7))

sin(x) = [20 ± √(784)] / 14

sin(x) = (10 ± 28) / 14

sin(x) = 2/7 or sin(x) = -2.

However, we should check whether each solution is valid by substituting it back into the original equation and ensuring that both sides are equal.

So,

If sin(x) = 2/7,

7cos²(x) - 26 = -20 (2/7) - 7

7cos²(x) = -10/7

But since cos²(x) is always non-negative, there is no real solution to this equation.

If sin(x) = -2,

7cos²(x) - 26 = -20 (-2) - 7

7cos²(x) = 25

Taking the square root of both sides, we get:

cos(x) = ±5/7

The two solutions to the original equation are:

sin(x) = -2 and cos(x) = 5/7

or

sin(x) = -2 and cos(x) = -5/7

However, we should note that there is no real number whose sine is equal to -2, so there is no real solution to the equation.

Therefore, the only solution is:

cos(x) = 5/7

Thus,

The only solution is cos(x) = 5/7.

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After 20 years, the initial investment of $650 will have grown to $2,386.10

Now, let's consider the problem at hand: a $650 investment at 6.5% interest compounded continuously for 20 years. To calculate the final amount of the investment, we can use the formula:

A = P[tex]e^{rt}[/tex]

where A is the final amount, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time (in years).

Plugging in the values given in the problem, we get:

A = 650 x [tex]e^{0.065 \times 20}[/tex]

Simplifying this expression, we get:

A = 650 x [tex]e^{1.3}[/tex]

Using a calculator, we can find that  [tex]e^{1.3}[/tex] is approximately 3.6693. Therefore, the final amount of the investment is:

A = 650 x 3.6693

A = $2,386.10

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The level of significance based on the information will be:

a. F = 4.11, with 3 df between and 30 df within - < 0.05

b. F = 1.12, with 5 df between and 83 df within - > 0.05

c. F = 2.28, with 4 df between and 42 df within - > 0.05

The likelihood of rejecting the null hypothesis when it is true, or the alpha level, is used in statistical tests to evaluate statistical significance.

The significance level, or alpha, for this example is set at 0.05 (5%). This was accurately illustrated above

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The error in this derivation in step 3 will be cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).

The trigonometric identities are given as,

sin²x + cos²x = 1

cos 2x = cos²x - sin²x

A 2-column table with 4 rows.

Column 1                      Column 2

    1                      cos 2x = cos²x – sin²x

   2                                  = cos²x – (1 – cos²x)

   3                                  = cos²x – 1 – cos²x

   4                                  = 2 cos²x – 1

The error in this derivation in step 3 will be cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).

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Answer:

,-3

A magic square is a square grid where the numbers in each row, column, and diagonal add up to the same total. In this case, we have 8 numbers to fill in a 3x3 grid, so we'll start with the number in the middle cell, which must be 1 to balance the negative numbers around it:

|- - -|

|- 1 -|

|- - -|

Now let's fill in the other cells one at a time, following the rule that each row, column, and diagonal must add up to the same total (which we'll call S):

|-2 - -|

|- 1 -|

|- - -|

We can't put -3 in the top left corner, since that would leave us with two negative numbers in the top row. Instead, we'll put -3 in the bottom right corner:

|-2 - -|

|- 1 -|

|- -3 -|

Now we need to find a number to put in the top row that will make it add up to S. The sum of the top row so far is -2, and we need it to be S/3, since there are 3 cells in the row. So we need to find a number x that satisfies:

-2 + x = S/3

Multiplying by 3 and adding 2 to both sides, we get:

3x = S + 6

So the number we need to put in the top row is (S+6)/3. We'll call this number y:

|-2 y -|

|- 1 -|

|- -3 -|

Now let's find a number to put in the bottom row. The sum of the bottom row so far is -3, and we need it to be S/3. So we need to find a number z that satisfies:

-3 + z = S/3

Multiplying by 3 and adding 3 to both sides, we get:

3z = S + 9

So the number we need to put in the bottom row is (S+9)/3. We'll call this number w:

|-2 y -|

|- 1 -|

|w -3 z|

Finally, let's find a number to put in the top right corner. The sum of the diagonal from top right to bottom left is -2+1-z, which must be equal to S. So we have:

S = -2 + 1 - z

Simplifying, we get:

S = -1 - z

Since we know that the sum of each row is S, we can add up the numbers in the top row and subtract that from S to get:

S -2 - y = -1 - z

Simplifying, we get:

S = z - y + 1

Now we can substitute in expressions for S, y, and z to get an equation for w:

(z + 6)/3 - 2 - (S+6)/3 = -3(z + 9)/3 + 1

Multiplying by 3 to clear the fractions, we get:

z + 6 - 2(S+6) = -3z - 24 + 3

Simplifying, we get:

2S = 2z - 27

So the value of w must satisfy:

(w + 9)/3 + (S+9)/3 = -3z - 24 + 1

Multiplying by 3 to clear the fractions, we get:

w + 9 + S + 9 = -9z - 69

Substituting in expressions for S and z, we get:

w + 9 + (z - y + 1) + 9 = -9z - 69

Simplifying, we get:

w = -10z - 88

Now we can plug in values for z

This is an incomplete question, I think the question will be

A sandwich shop employee named Lucy takes 2.5 minutes to make a sandwich. If she continues at the same rate, how long will it take her to make 10 sandwiches? Write the answer in minutes.

it will take Lucy 25 minutes to make 10 sandwiches if she continues at the same rate.

If Lucy takes 2.5 minutes to make a sandwich, then to find out how much time it would take for her to make 10 sandwiches, we simply multiply the time taken for one sandwich (2.5 minutes) by the number of sandwiches required (10).

10 x 2.5 = 25 minutes

Therefore, if she continues to work at the same rate of making one sandwich in 2.5 minutes, she will be able to make 10 sandwiches in 25 minutes.

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Her rate loss in pounds per week is given as follows:

3.75 pounds per week.

Her rate loss in pounds per week is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate loss is given by the division of the loss by the number of weeks.

The parameters are given as follows:

Hence the rate loss is given as follows:

r = 60/16

r = 3.75 pounds per week.

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The solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.

The given inequality is x³-5x²+10>0.

Solve for x by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: −1.26354284<x<1.75564007 or x>4.50790277

Interval Notation:(−1.26354284,1.75564007)∪(4.50790277,∞)

Therefore, the solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.

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Answer:

plein-air. Is the correct answer

Claude Monet's Impression: Sunrise (1872) is considered a plein-air painting because it was completed out-of-doors.

Applying the inscribed angle theorem, the measure of angle STU in the circle is: 29°.

When an inscribed angle intercepts an arc in a circle, the measure of the inscribed angle is always half of the measure of the arc it intercepts, based on the inscribed angle theorem.

Angle STU is an inscribed angle that intercepts arc SU in the given circle, therefore:

(5x - 16) = 1/2(12x - 50)

Solve for x:

2(5x - 16) = 12x - 50

10x - 32 = 12x - 50

10x - 12x = 32 - 50

-2x = -18

x = 9

m∡STU = (5x - 16) = 5(9) - 16

m∡STU = 29°

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The standard deviation of the sum S = I + O is [tex]$1,508.48[/tex]. The Option C is correct.

In order to calculate standard deviation of the sum S = I + O on the information given from the question, we can use this formula: "SD(S) = sqrt[SD(I)^2 + SD(O)^2 + 2Cov(I,O)]".

Details:

SD(I) & SD(O) means standard deviations of in-state and out-of-state tuition.

Cov(I,O) means covariance between the two variables.

The two variables I and O are independent

Their covariance is zero

Now, we can solve the S.D. using the formula. The SD(S):

= sqrt[SD(I)^2 + SD(O)^2]

= sqrt[(1003.25)^2 + (1126.50)^2]

= sqrt[1006510.5625 + 1269002.25]

= sqrt[2275512.8125]

= 1508.48029901

= $1508.48

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The probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.

To pass the quiz with a minimum passing grade of 60%, a person needs to answer at least 12 questions correctly out of the 20 total questions.

If a person is making random guesses for all of the answers, the probability of guessing one question correctly is 1/4, since there are 4 possible answers for each question. The probability of guessing one question incorrectly is 3/4.

Using the binomial probability formula, we can find the probability of passing the quiz by correctly guessing at least 12 questions:

P(X >= 12) = 1 - P(X < 12)

where X is the number of questions answered correctly.

P(X < 12) = sum of the probabilities of getting 0, 1, 2, ..., or 11 questions correct:

P(X < 12) = C(20,0)(1/4)⁰(3/4)²⁰ + C(20,1)(1/4)¹(3/4)¹⁹ + ... + C(20,11)(1/4)¹¹(3/4)⁹

where C(20,0), C(20,1), ..., C(20,11) are the binomial coefficients.

We can use a calculator or a computer to evaluate this sum of probabilities, or we can use a normal approximation to the binomial distribution if we assume that np = 20(1/4) = 5 and n x (1-p) = 20 x (3/4) = 15 are both greater than 10.

Using the normal approximation, we can find the mean and standard deviation of the binomial distribution:

mean = np = 20(1/4) = 5

Standard deviation = √(np(1-p)) = √(20*(1/4) x (3/4)) = √(15/2) = 1.94 (rounded to 2 decimal places)

Then, we can standardize the distribution by subtracting the mean and dividing by the standard deviation:

z = (12 - 5) / 1.94 = 3.61 (rounded to 2 decimal places)

Using a standard normal distribution table or a calculator, we can find the probability of getting a z-score greater than 3.61:

P(Z > 3.61) = 0.0002 (rounded to 4 decimal places)

Therefore, the probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.

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The number of children, parents, and Grandparents that were in attendance are:

First, we should come up with equations that relate the number of children, parents, and Grandparents, given the information we know. The equations would have C for children, P for parents, and G for grandparents.

Total number of people:

C + P + G = 400

Parents to grandparents:

P = 2G

Children to parents:

C = P + 50

Substituting gives:

( P + 50 ) + P + ( P / 2 ) = 400

P + 50 + P + P / 2 = 400

(5 / 2) P + 50 = 400

(5 / 2 )P = 350

P = 140 parents

The children would be:

C = P + 50

= 140 + 50

= 190 children

The grandparents:

G = P/2

= 140/2

= 70 grandparents

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