The tree diagram shows the sample space for tossing a coin three times. Which of these shows all outcomes with exactly 2 heads?

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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The volume of the sphere is 5,575.28 ft³.

The volume of the sphere is calculated by applying the following formula as shown below;

V = ⁴/₃ πr³

where;

The radius of the sphere is calculated as follows;

r = d/2

where;

r = 22 ft / 2

r = 11 ft

The volume of the sphere is calculated as;

V = ⁴/₃ π(11)³

V = 5,575.28 ft³

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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 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: 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 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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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

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 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 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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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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If "∠A" is complementing angle "∠B" and "∠C" is complementing "∠B", then the true statement is (a) ∠A ≅ ∠C, because both the angles have the same measure.

The "Complementary-Angles" are two angles that add up to 90 degrees, which is also known as a right-angle. When two angles are complementary, they are said to complement each other.

Since the angles : ∠A and ∠C are both complementary to ∠B, we can write :

⇒ ∠A + ∠B = 90°,

⇒ ∠B + ∠C = 90°,

Next, We subtract "∠B" from both sides of each equation,
We get;

⇒ ∠A = 90° - ∠B,

⇒ ∠C = 90° - ∠B,

We see that the measure of the angle "A" and angle "C" is same.

Therefore, ∠A and ∠C have the same measure, option (a) is the correct answer.

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The given question is incomplete, the complete question is

If ∠A is a complementary angle of ∠B and ∠C is a complementary angle of ∠B, then which of the following statements is true?

(a) ∠A ≅ ∠C

(b) ∠A ≅ ∠B

(c) ∠A + ∠C ≅ ∠B

(d) ∠B ≅ ∠C

x < -2 is the solution for the given inequality.

To solve the inequality:

-3(x - 3) > 5 - 5x

We can start by using the distributive property and simplifying both sides of the inequality:

-3x + 9 > 5 - 5x

Next, we can add 5x to both sides of the inequality to get the x terms on one side:

2x + 9 > 5

Then, we can subtract 9 from both sides of the inequality to isolate the variable:

2x > -4

Finally, we divide both sides by 2, remembering to reverse the inequality because we are dividing by a negative number (-3):

x < -2

Therefore, the solution to the inequality is x < -2.

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Answer:

[tex]\frac{3}{4} = \frac{6}{8} = \frac{9}{12} = \frac{18}{24} [/tex]

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 total amount spent is $9.50.

We have,

2 1/2 yards of fabric cost 7.00.

3 rolls of ribbon cost 2.50.

So, the total amount of money spend

= Cost of fabric + cost of ribbon

= 7 + 2.50

= $9.50

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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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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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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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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 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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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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A bag of daffodil bulbs costs $12 and a bag of windflower bulbs $8.

Let's use the letters "w" for the price of a bag of windflower bulbs and "d" for the price of a bag of daffodil bulbs.

We may construct the following system of equations based on the above information:

Perry's sales:

w + d = 20 (equation 1)

Darryl's sales:

7w + d = 68 (equation 2)

To solve for w and d, we can use the elimination method. Multiplying equation 1 by -1, we get:

-w - d = -20

Adding this to equation 2, we eliminate d and get:

6w = 48

Dividing both sides by 6, we get:

w = 8

Substituting this value of w into equation 1, we can solve for d:

8 + d = 20

d = 12

Therefore, a bag of windflower bulbs costs $8 and a bag of daffodil bulbs costs $12.

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All city residents who support the arts. Therefore, the option C is the correct answer.

As the city official would lie to know that if public support for increased funding of arts programs. By collecting data the officials show the survey after every 25 persons and ask for their opinion.

They also tend to raise a fund that states the population in the scenario of a city resident that supports the arts.

The population in this scenario is the people surveyed by the city official. The city official is conducting a survey outside a concert hall after a show, which means they are targeting people who have just attended a show. Since the city official is asking every 25th person to exit their opinion about raising funds for the arts, these are the people who are included in the population being surveyed.

Therefore, the option C is the correct answer.

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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

Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.

Since a represents apple and c represents cherry:

We can now go ahead to solve for a and c using a simultaneous equation approach.

From equation (1)

a = 36 - c

Substituting this expression into equation (2), we get:

Therefore, 13 cherry pies were sold. To find the number of apple pies sold, we can substitute this value of c into equation 1:

Therefore, 23 apple pies were sold.

In other words, Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.

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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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