a dice game involves rolling 2 dice. if you roll a 2,3,4,10,11 or a 12 you win $5.00. if you roll a 5,6,7,8 or 9 you lose $5.00. how would you setup the problem to determine the expected value you win (or lose) per game?

Without a visual of the tree diagram mentioned in the problem, it is difficult to provide an exact answer. However, we can use the fundamental counting principle to determine the number of possible combinations.

If there are, for example, 4 colors of balloons and 5 types of toys, then the number of different combinations a child may receive would be:

4 (number of colors) x 5 (number of types of toys) = 20

Therefore, the child may receive 20 different combinations of one color of balloon and one type of toy. However, this number may vary depending on the actual number of colors and types of toys available.

Answer:

x = (3 ± sqrt(-47)) / 2.

Step-by-step explanation:

If x - 6 is a factor of f(x), then we know that (x - 6) must divide evenly into f(x), which means that there is another factor of f(x) that we can find by polynomial long division or synthetic division.

Using synthetic division:

We start by writing the coefficients of f(x) in order:

1 3 -22 24

We then write the factor (x - 6) to the left of the coefficients, and draw a line:

6 | 1 3 -22 24

We bring down the first coefficient: 1

1 3 -22 24

1

We multiply 6 by the first coefficient and write the result under the second coefficient: 1

6 | 1 3 -22 24

-6

-3

If x - 6 is a factor of f(x), then we know that (x - 6) must divide evenly into f(x), which means that there is another factor of f(x) that we can find by polynomial long division or synthetic division.

Using synthetic division:

We start by writing the coefficients of f(x) in order:

1 3 -22 24

We then write the factor (x - 6) to the left of the coefficients, and draw a line:

6 | 1 3 -22 24

We bring down the first coefficient:

Copy code

1

6 | 1 3 -22 24

1

We multiply 6 by the first coefficient and write the result under the second coefficient:

Copy code

1

6 | 1 3 -22 24

-6

Copy code

 -3

We add the second and third coefficients to get -19, then multiply by 6 and write the result under the third coefficient:

1

6 | 1 3 -22 24

-6

-3

42

66

We add the last two numbers to get 90. This means that we can write f(x) as:

f(x) = (x - 6)(x² - 3x + 14)

To find the zeros of f(x), we need to solve the equation (x - 6)(x² - 3x + 14) = 0.

The first factor gives us x = 6.

To solve the quadratic factor, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -3, and c = 14. Substituting these values into the formula, we get:

x = (3 ± sqrt(3² - 4(1)(14))) / 2(1)

x = (3 ± sqrt(-47)) / 2

Since the square root of a negative number is not a real number, the quadratic factor does not have any real zeros.

Therefore, the zeros of f(x) are x = 6, and the complex numbers x = (3 ± sqrt(-47)) / 2.

Answer:

it is 5.4 kilometers from White Beach across the lake to the Lodge.

Step-by-step explanation:

Based on the information provided, we can calculate the distance from White Beach across the lake to the lodge by adding the distances from Canoeville to White Beach and from Canoeville to the lodge.

Distance from Canoeville to White Beach: 2.4 km

Distance from Canoeville to the Lodge: 3.0 km

Total distance from White Beach across the lake to the Lodge:

2.4 km + 3.0 km = 5.4 km

So, it is 5.4 kilometers from White Beach across the lake to the Lodge.

Answer:

Step-by-step explanation:

the sum of the internal angles of a regular or irregular pentagon is 540°, we remove the known angles and we will have the answer

540 - 110 - 110 - 120 - 120 =

80°

Answer:

I believe the answer is C. (x + 6)2 + (y − 4)2 = 4

Step-by-step explanation:

Hope this helps :)
Please let me know if its incorrect

Note that the TOTAL amount deducted from Hope's latest paycheck is $315.21

If you examine the paycheck it clearly states under current deductions, that 315.21 was deducted form hopes paycheck.

A paycheck is a written document (a cheque) provided by an employer to pay an employee for services done. It is sometimes spelled paycheque, pay check, or pay cheque.

Employers withhold (or deduct) a portion of their employees' wages to meet payroll and income taxes. A portion of a paycheck may also be removed or withdrawn to pay for retirement or health benefits.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

What was the TOTAL amount deducted from Hope's latest paycheck?

answer choices

$90.00

$284.79

$315.21

$600.00

A coin is biased so that the probability a head comes up when it is flipped is 0.6. Therefore, we can expect to get 6 heads when a biased coin with a probability of 0.6 for heads is flipped 10 times.

To find the expected number of heads when a biased coin is flipped 10 times, we can use the formula:

Expected number of heads = Probability of getting a head × Number of times the coin is flipped

In this case, the probability of getting a head is 0.6 and the coin is flipped 10 times. So the expected number of heads is:
Expected number of heads = probability of getting a head x number of times flipped

Expected number of heads = 0.6 x 10

Expected number of heads = 6

Therefore, the expected number of heads when the coin is flipped 10 times is 6.

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The data distribution is skewed and the mean of the emails is less than the median number of emails.

The median is 22 and the mean is 20.2.

The mean can be found by adding up the number of emails and dividing it by the number of days :
= ( 15 + 16 + 18 + 19 + 22 + 22 + 22 + 22 + 23 + 23 ) / 10

= 20. 2

The median is the number in the middle. As there are 10 numbers, the median would be:

= (Position 5 + Position 6) / 2

= ( 22 + 22 )  / 2

= 22

The mean is less than the median.

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The required coefficient on x² is 2, so the answer is 2. Option B is correct.

We can start by assuming that the quadratic function has the form:

y = ax² + bx + c

where a, b, and c are unknown coefficients to be determined. We can use the three given points on the graph to set up a system of three equations in three unknowns:

7 = a(1)² + b(1) + c

16 = a(2)² + b(2) + c

29 = a(3)² + b(3) + c

Simplifying each equation, we get:

a + b + c = 7

4a + 2b + c = 16

9a + 3b + c = 29

We can solve this system of equations using any method of our choice, such as elimination or substitution. One possible approach is to subtract equation 1 from equation 2 and equation 2 from equation 3, which gives:

a + b + c = 7

3a + b = 9

5a + b = 13

a = 2; b = 3; c = 2

Therefore, the equation for the quadratic function in standard form is:

y = 2x² + 3x + 2

The coefficient on x² is 2, so the answer is 2.

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The probability that the length of time between charges will be between 40 and 70 hours is 0.656.

To solve this problem, we need to standardize the values of 40 and 70 using the given mean and standard deviation, and then use the standard normal distribution table to find the probability.

Standardizing 40: z = (x - mu) / sigma z = (40- 50)/15 z = -2/3

Standardizing 70: z = (x-mu) / sigma z = (70- 50)/15 z 4/3

Now we look up the probabilities associated

with the standardized values -2/3 and 4/3 in the

standard normal distribution table.

Using the table, we find that the probability of z being less than -2/3 is 0.2525 and the probability of z being less than 4/3 is 0.9082.

So the probability of the length of time being between 40 and 70 hours can be found by subtracting the probability of z being less than -2/3 from the probability of z being less than 4/3:

P(40 < x <70) = P(-2/3 <z < 4/3) = P(z < 4/3) - P(z< -2/3)

P(40 < x < 70) = 0.9082-0.2525 P(40 < x <70) = 0.6557

Therefore, the probability that the length of time between charges will be between 40 and 70 hours is approximately 0.656, which is closest to option B.

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The closure property for subtraction holds for integers, but not necessarily for whole numbers.

Closure property is an important concept in mathematics. It refers to the property of a set of numbers to produce a result within the same set when a mathematical operation is performed on any two numbers in that set.

Whole numbers are a subset of integers and include only non-negative numbers, whereas integers include both positive and negative numbers along with zero.

When we subtract two whole numbers, the result may not always be a whole number. For instance, if we subtract 3 from 2, the result is -1, which is not a whole number. This is why Karim concluded that whole numbers are not closed under subtraction.

On the other hand, when we subtract two integers, the result will always be an integer. For example, if we subtract 3 from 2, the result is -1, which is an integer. This is why Ali concluded that integers are closed under subtraction.

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The mean is 89, the median is 89, the mode is 89, and the range is 22.

The mean is 72.6, the median is 76, there is no mode, and the range is 25.

The mean is 60.5, the median is 57.5, there is no mode, and the range is 55.

The mean, median, mode, and range of the given data are calculated as follows:

Mean = sum of values/ number of values

The median is the middle score when the scores are arranged in order from lowest to highest

Mode is the number that occurs most

The range is the difference between the largest and smallest values

1. Mean = (98 + 89 + 76 + 93 + 89) / 5

Mean = 89

76, 89, 89, 93, 98

The median is 89.

The mode is also 89.

Range = 98 - 76

Range = 22

2. Mean = (59 + 63 + 84 + 76 + 81) / 5

Mean = 72.6

Median: 59, 63, 76, 81, 84

The median is 76.

There is no mode for this set of score

Range = 84 - 59

Range = 25

3. Mean = (36 + 48 + 67 + 91) / 4

Mean = 60.5

Median: 36, 48, 67, 91

Median = (48 + 67) / 2

Median = 57.5

The data has no mode

Range = 91 - 36

Range = 55

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The number of elements in power set A where A = { x: x² + 3 < 2, x ∈R }  is equal to  n[P(A)] = 1.

The set A represented as ,

A = { x: x² + 3 < 2, x ∈R }

First, we need to determine the set of values that satisfy the inequality

x² + 3 < 2.

Subtracting 3 from both sides of the inequality gives us,

⇒ x² < -1

However, this inequality has no real solutions, since the square of any real number is always non-negative.

This implies,

The set A is empty,  A = {}.

The power set of the empty set contains only the empty set itself,

so P(A) = {{}}.

This implies, the number of elements in P(A) denoted as n[P(A)] is 1.

Therefore, the number of elements in power set A is equal to  n[P(A)] = 1.

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Answer:

------------------------------

Use the formula for compound interest :

Where:

In this problem, we have:

Now, let's plug these values into the formula:

After 6 years, Lex will have approximately $1780.77 in his savings account.

Answer:

Since complete angle B (<DBA) is = <DBC + <CBA

<DBA = 20° + 30°

<DBA = 50°

Hence complete angle B is 50°

Answer: 63 minutes

Step-by-step explanation:

Use proportions:

8/84 = 6/x

Cross multiply to get:

8x = 504

Simplify by dividing by 8 on both sides.

x = 63.

The unit for force is the Newton (N). The equation for gravitational force is given by Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

where: F is the gravitational force (in Newtons, N) G is the gravitational constant (approximately 6.674 × 10^-11 N·m²/kg²) m1 and m2 are the masses of the two objects (in kilograms, kg) r is the distance between the centers of the masses (in meters, m)

Gravitational force decreases as you move away from Earth because the force is inversely proportional to the square of the distance (r^2) between the objects. If the radius between the centers (r) were to be cut in half, the gravitational force would increase by a factor of 4, since the force is inversely proportional to the square of the distance.

So if r becomes (1/2)r, the force would be inversely proportional to (1/4)r^2, leading to a 4 times increase in force.

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Is the relation a function and explain your reasoning: B. The relation is not a function because the output value Walking has different input values, and the same with No walk.

In Mathematics, 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 input value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the output value on the y-coordinate of a cartesian coordinate.

Based on the table, we can logically deduce that the relation does not represent a function because each of its input value (domain) has more than one dependent value (range) i.e Walked and No Walk.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Part(1)

The measure of the angle will be 45°.

Part(2),

The formula for the shadow is,

6² + x² = 16²

A basic mathematical theorem relating to the lengths of a right-angled triangle's sides is known as the Pythagorean theorem. According to this rule, the square of the length of the hypotenuse (the side that faces the right angle) in any right-angled triangle equals the sum of the squares of the lengths of the other two sides.

Part(1),

To find the angle x, we can use the inverse tangent function. Let's call the length of Joel's shadow "s". Then we have:

tan(x) = opposite/adjacent = 16/s

Taking the inverse tangent of both sides, we get:

x = tan⁻¹(16/s)

We know that Joel's height is 6 ft, so the hypotenuse of the right triangle formed by Joel and his shadow is:

= √(6² + s²)

Now we can use the Pythagorean Theorem to solve for s. Rearranging the formula for h, we have:

s = √(h² - 6²)

Substituting the value of h with the expression above, we get:

s = √((√(6² + s²))² - 6²)

Simplifying this expression, we get a quadratic equation in terms of s:

s² - 256 = 0

Solving for s, we get:

s = ±16

Since s represents the length of the shadow, it must be positive. Therefore, s = 16 ft.

Substituting s into the equation for x, we get:

x = tan⁻¹(16/16) = tan⁻¹(1) = 45°

So the measure of the angle x is 45 degrees.

Part(2),

The formula for a shadow can be written as,

6² + x² = 16²

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Answer: A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 can be expressed in the following form:

f(x) = 7x^5 + ... + ... + ... + ... + 6

Step-by-step explanation: Since the polynomial has a degree of 5, it will have 6 terms in total, including the constant term. However, the other coefficients are unknown, so we need more information to determine them. For example, we could be given additional roots or points on the curve.

Without any further information, the polynomial can only be expressed in this general form.

To solve the equation 2y − 2.3 = 4.1  for y, we can use algebraic manipulation.

In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:

                                 2y - 2.3 = 4.1

                     +2.3                          +2.3

                                   2y = 6.4

Now, we divide both sides by 2 to isolate y:

                                 2y = 6.4

                            ÷2               ÷2

                                  y = 3.2

So, the solution to this equation is  y = 3.2

----------------------------------------------------------------------------------------------------------

We need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.

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- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.

- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.

- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.

a) Etsuko's maximum speed is 4.19 m/s.

b) Bachico is traveling 1.61 times faster than Etsuko.

c) The maximum distance from the pole to the outer ring of horses is 3.56 meters.

d) The time between consecutive "yays" is 7.5 seconds.

Let's call the maximum speed of the carousel V. Then, the circumference of the circular path traveled by the outermost ring of horses is:

C = 2πr, where r is the distance between the pole and the outermost ring of horses.

The time it takes for the carousel to complete one revolution is:

T = C/V

We can use the information given in the problem to set up an equation for the total time it takes for the siblings to pass their mother 17 times:

T = T₁ + 16T₂ = 6 minutes = 360 seconds

So, the time it takes for Etsuko's horse to complete one revolution is:

T₁ = C₁/V

The distance that Etsuko's horse travels between consecutive passes of the mother is equal to the difference in the distances traveled by the innermost and middle rings of horses during one revolution, which is:

Δd = 2.41 - 1.5 = 0.91

So, the time it takes for the carousel to complete one revolution between subsequent passes of the mother is:

Solving for V, we get:

V = 4.19 m/s

Therefore, Etsuko's maximum speed is 4.19 m/s.

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The probability of not getting red is 87.5%.

Hence, The correct option is C.

We know that;

Probability = Number of favorable outcomes / Number of samples

Given that;

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red .

You only have one of eight (1/8) evenly divided orange sections.

The rest is not red,

P = (1 - 1/8

P =  7/8

P = 0.875

P = 87.5%

Therefore, spinning once will yield 7/8 odds of not landing on red are,

⇒ 0.875 or 87.5%.

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The volume of the smaller solid is 292 in³ under the condition that two similar solids have surface areas of 45 in² and 80 in². The volume of the larger solid is 320 in³.

Given the two solids are similar, so their corresponding sides are proportional. Let us consider them calling  the ratio of the corresponding sides k.  The ratio regarding their surface areas is k² and the ratio of their volumes is k³.

Let us consider  the volume of the smaller solid V. It is given the surface area of the smaller solid is 45 in² and that of the larger solid is 80 in²

k² = 80/45 = 8/9

k = √(8/9)

= 0.94 (approx.)

It is given the volume of the larger solid is 320 in³.

k³ = 320/V

0.94³ = 320/V

V = 320/(0.94³)

= 292 in³ (approx.)

The volume of the smaller solid is 292 in³.

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Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148. We may answer this question by using the definition of logrithmic.

Mathematical operations that relate to a number's logarithm are known as logarithmic functions. The power that a given basis must be increased in order to obtain a particular number is known as the logarithm of the number.

Although 10 (also known as the common logarithm) is the base that is most frequently used, logarithms can be calculated in relation to any positive base higher than 1. If the base is 10, the logarithm of such an integer x with regard to a base b is written by log(base b)(x), or just log(x).

We can compress the given logarithm via the logarithmic identity log(base a)(bc) = c * log(base a)(b):

Sqrt(3.5.11) = Log((3.5.11)(1/2), 9) = Log((3.5.11)*(1/2), 9) = (1/2) * Log (3.5.11, 9)

We must now calculate that logarithm of 9 in base 3.5.11. This can be changed to a log with a more recognisable column, such as base 10 or base e, using the change-of-base formula. Using the base 10 scale

3.5.11, 9) = 9)/log (3.5.11)

We can calculate this using a calculator:

log(9) = 0.9542 (reduced to 4 decimal places)

log(3.5.11) = log(3) + log(5) + log(11) = 0.4771, 0.6978, and 1.0414, respectively, yielding 2.2174. (rounded to 4 decimal places)

Therefore:

sqrt(3.5.11),9 = (1/2) log(3.5.11,9) = (1/2) log(9)/log(3.5.11)) = (1/2) log(0.9542/2.2174) = 0.2148 log(3.5.11,9) = (1/2) log(3.5.11, 9) = (1/2) 

Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148.

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The expanded form of the logarithm is:

log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)

What is logarithm?

A logarithm is a mathematical function that tells us what exponent is needed to produce a given number, when that number is expressed as a power of a fixed base. In other words, logarithms tell us how many times we need to multiply the base by itself to get the desired number.

We can use the property of logarithms that says:

log base b (a * c) = log base b (a) + log base b (c)

to expand the logarithm.

Therefore, we have:

log base 9 √(3.5.11) = log base 9 √(3 * 5 * 11)

= log base 9 (3) + log base 9 (5) + log base 9 (11)

So, the expanded form of the logarithm is:

log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)

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The solution is : the velocity of the person on the walk way with respect to the observers on the ground is D 1.7 m/s.

Here, we have,

In order to find the velocity of the person on the walk way with respect to the person on the ground we have to apply relative velocity concept.

Consider the observer on the ground as B and the person walking on the pathway as A.

The relative velocity is the velocity that the body A would appear to an observer on the body B and vice versa.

Mathematically speaking the relative velocity is the vector difference between the velocities of two bodies.

Relative velocity = Velocity of Body A- Velocity of Body B.

Velocity of the person walking on the walkway (A)= 1.5 m/s.(given)

Velocity of the observer on the ground (B)= -0.2 m/s(given).

Relative velocity of object A with respect to B = 1.5 - (-0.2)= 1.7 m/s.

Thus the velocity of the person on the walk way with respect to the observers on the ground is 1.7 m/s.

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complete question:

A person is strolling along a moving walkway at a constant velocity of +1.00 m/s with respect tot he walkway, which moves at a constant velocity of +0.50 m/s with respect to the ground. An observer on the ground is walking at a constant velocity of -0.2 m/s. what is the velocity of the person on the walk way with respect to the observers on the ground?

A - 0.7 m/s

B + 1.3 m/s

C - 0.3 m/s

D + 1.7 ms

Yes (-3,-2) is true.

No (1,6) is false

No (0,4)  is false

To determine if an ordered pair is a point of intersection between the line and the parabola, we need to check if the coordinates satisfy both equations.

(-3, -2)

y = 2x + 4 => -2

= 2(-3) + 4 => -2 = -2 (True)

y = x² + 4x + 1 => -2

= (-3)² + 4(-3) + 1 => -2 = -2 (True)

Answer: Yes

(1, 6)

y = 2x + 4 => 6

= 2(1) + 4 => 6 = 6 (True)

y = x² + 4x + 1 => 6

= (1)² + 4(1) + 1 => 6 ≠ 6 (False)

Answer: No

(0, 4)

y = 2x + 4 => 4

= 2(0) + 4 => 4 = 4 (True)

y = x² + 4x + 1 => 4

= (0)² + 4(0) + 1 => 4 ≠ 1 (False)

Answer: No

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The ratio of the area of triangle XBY to the area of triangle ABC is 9/25. The height of XBY with respect to BY is 24/7, and the height of ABC with respect to BC is 40/7.

To find the ratio of the area of triangle XBY to the area of triangle ABC, we need to first find the heights of both triangles with respect to base BC.

Let's use the formula for the area of a triangle

Area = 1/2 * base * height

For triangle ABC, the base is BC, which has length 5, and let h₁ be the height of triangle ABC with respect to BC.

Area of ABC = 1/2 * 5 * h₁

For triangle XBY, the base is BY, which has length 3, and let h₂ be the height of triangle XBY with respect to BY.

Area of XBY = 1/2 * 3 * h₂

Since the triangles share the same base, we can use the following proportion to find the ratio of their heights

h₁/h₂ = BC/BY

h₁/h₂ = 5/3

We can solve for h₂

h₂ = (3/5)h1

Now, we need to find h1. We can use the fact that the area of triangle ABC is equal to the sum of the areas of triangles ABY and BCY.

Area of ABC = Area of ABY + Area of BCY

1/2 * 5 * h₁ = 1/2 * 3 * (3+h2) + 1/2 * 2 3/2 * (2 3/2 - h₂)

Simplifying the above equation and substituting h₂ = (3/5)h1, we get

5h₁ = 3(3 + 8/5 h₁) + 3h₁/5

Solving for h1, we get

h₁ = 40/7

Substituting h₁ = 40/7 and h₂ = (3/5)h₁ = 24/7 into the formulas for the areas of the triangles, we get

Area of ABC = 1/2 * 5 * 40/7 = 100/7

Area of XBY = 1/2 * 3 * 24/7 = 36/7

Therefore, the ratio of the area of triangle XBY to the area of triangle ABC is

Area of XBY / Area of ABC = (36/7) / (100/7) = 9/25

Hence, the required ratio is 9/25.

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The equation is given as n = c + 2

The plant grows c inches in the first week.

The plant grows n inches in the second week.

mаthеmаticаlly, the equаtion requires that wea rea to to show thе relаtionship between thе growth in thе first wееk (c) and thе growth in thе seсond wееk (n).

thе growth in thе seсond wееk (n) is said to be  2 inсhes more than thе growth in thе first wееk (c) from the given question.

The equation would be

n = c + 2

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The volume of the silo is 3612.56 cubic feet, under the condition that sphere in the top of the silo is a hemisphere with a radius of 12 feet.

Here, we have to implement the formula for deriving the volume of hemisphere,
The volume of a hemisphere with radius 12 feet can be calculated using the formula for the volume of a hemisphere which is (2/3)πr³
here r = radius of the hemisphere.

Staging r=12 feet in the formula
(2/3)π(12 feet)³
= (2/3)π(1728 cubic feet)
= 1152π cubic feet
≈ 3612.56 cubic feet

Then, the volume of the silo is approximately 3612.56 cubic feet.

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