Complete the equation. Hint: Think about how we can fill in each circle below to help us find an equivalent fraction. � 6 = 4 8 6 p ​ = 8 4 ​ start fraction, p, divided by, 6, end fraction, equals, start fraction, 4, divided by, 8, end fraction � = p=p, equals circle with 6 of 12 equal parts shaded. same-sized circle with 4 equal parts.

Here is your answer.

A tank contains 5832 litres of water.

Total amount of water in tank = 5832 litres.

Each day one-third of the water in the tank is removed and not replaced.

Since one third of the water is removed for six days.

1st day = 1/3rd of 5832 litres is removed

[tex] = \dfrac{5832}{3} = 1944[/tex]

Amount of water left = 5832 - 1944 = 3888 litres

2nd day = 1/3rd of 3888 litres is removed

[tex] = \dfrac{3888}{3} = 1296 [/tex]

Amount of water left = 3888 - 1296 = 2592 litres

3rd day = 1/3rd of 2592 litres is removed

[tex] = \dfrac{2592}{3} = 864 [/tex]

Amount of water left = 2592 - 864 = 1728 litres

4th day = 1/3rd of 1728 litres is removed

[tex] = \dfrac{1728}{3} = 576 [/tex]

Amount of water left = 1728 - 576 = 1152 litres

5th day = 1/3rrd of 1152 litres is removed

[tex] = \dfrac{1152}{3} =384 [/tex]

Amount of water left = 1152 - 384 = 768 litres

6th day = 1/3rrd of 768 litres is removed

[tex] = \dfrac{768}{3} = 256 [/tex]

Amount of water left = 1768 - 256 = 512 litres

So, 512 litres water remains in the tank at the end of 6 days

Answer:

To determine the formula of g in terms of f, we would need more information about the specific transformation or relationship between f and g. Unfortunately, you mentioned that there is a graph showing f as a solid blue line and g as a dotted red line, but without additional details about the graph or the transformation, it is not possible to provide the formula of g in terms of f.

If you can provide further information about the relationship between f and g or any specific points or characteristics of the graph, I would be happy to assist you in finding the formula of g in terms of f.

Step-by-step explanation:

The masses between the Earth and the Moon found using the Newton's law of universal gravitation, whereby the gravitational force between them is 1.682 × 10²⁶ N, and the mass of the Moon is about 7.1 × 10²² kg, is about 411,144.67 meters'

The Newton's law of universal gravitation indicates that formula for finding the gravitational force F between two objects, can be expressed as follows;

F = G·(m₁·m₂)/d²

Where;

F = The gravitational force

G = The gravitational constant

m₁ and m₂ are the mass of the two objects

d = The distance between them

Where

F = 1.682 × 10²⁶ N·m²·kg⁻²

G = 6.67430 × 10⁻¹¹ N·m²·kg⁻²

m₁ = 6 × 10²⁴ kg

m₂ = 7.1 × 10²² kg

Plugging in the above values into the Newton's law of universal gravitation, we get;

1.682 × 10²⁶ = 6.67430 × 10⁻¹¹ × (6 × 10²⁴ × 7.1 × 10²²)/d²

d² = 6.67430 × 10⁻¹¹ × (6 × 10²⁴ × 7.1 × 10²²)/1.682 × 10²⁶ ≈ 169039940547

d ≈ √(169039940547) ≈ 411144.67

The distance between the Earth and the Moon, found using the specified masses is about 411144.67 meters.

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answer/explanation:

hope this helps

The graphical solution of the linear program is (A, B ) = (100, 80).

The graphical solution of the linear program is determined by creating a plot of function A and graph of function B, and determine the point the point of intersection of the lines.

The given function of the linear program;

1A ≤ 100

1B ≤ 80

2A + 4B ≤ 440

The expression can be simplified further as;

2A + 4B ≤ 440

divide both sides of the equation by 2;

2A/2 + 4B/2 ≤ 440/2

A + 2B ≤ 220

From the graph of A and B plotted, the solution of the graph is obtained at the intersection of line A and line B, indicated by the red line.

(A, B ) = (100, 80).

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The median is a measure of central tendency in a data set. It represents the middle value when the data is arranged in ascending or descending order.

For an odd number of data points, the median is simply the value that falls exactly in the middle of the ordered list. For example, if we have the data set [1, 3, 5, 7, 9], the median is 5 because it is the value at the center.

However, when the number of data points is even, there is no single middle value. In this case, the median is calculated by taking the average of the two middle values. For example, if we have the data set [2, 4, 6, 8], the two middle values are 4 and 6. The median is then (4 + 6) / 2 = 5.

So, in summary:

For an odd number of data points, the median is the value in the middle of the ordered list.

For an even number of data points, the median is the average of the two middle values.

Answer:

Approximately 116.465 seconds after the chute opens.

Step-by-step explanation:

To find the number of seconds after the chute opens when the skydiver will first be less than 100 feet in altitude, we need to set up and solve the equation H(x) < 100.

Given that H(x) = 3000 - 24.9x represents the altitude of the skydiver at time x seconds after the chute opens, we can rewrite the equation as follows:

3000 - 24.9x < 100

Now, we can solve this inequality to find the value of x:

3000 - 24.9x < 100

-24.9x < 100 - 3000

-24.9x < -2900

To isolate x, we divide both sides of the inequality by -24.9. However, we need to flip the inequality sign since we are dividing by a negative number:

x > (-2900) / (-24.9)

x > 116.465

Therefore, the skydiver will first be less than 100 feet in altitude after approximately 116.465 seconds after the chute opens.

The new vertices after multiplying by 3 are:

A'(0, 0), B'(-12, 0), and C'(-6, 12).

To find the new coordinates of each vertex after multiplying by 3, we simply multiply the x-coordinate and y-coordinate of each vertex by 3.

Given the original vertices:

A(0, 0), B(-4, 0), and C(-2, 4)

After multiplying each coordinate by 3, we get:

[tex]A'(0 \times 3, 0 \times 3) = A'(0, 0)\\B'(-4 \times 3, 0 \times 3) = B'(-12, 0)\\C'(-2 \times 3, 4 \times 3) = C'(-6, 12)[/tex]

This means that each vertex has been scaled by a factor of 3. The x-coordinates are multiplied by 3, resulting in a horizontal stretching or compression, while the y-coordinates are also multiplied by 3, resulting in a vertical stretching or compression.

In this case, the points have been scaled up by a factor of 3, making the triangle larger.

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(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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The left-hand side of the equation is equal to the right-hand side, confirming that x = -1 is the correct solution.by using algebric operation.

To solve the equation -3x - 1/4 = 1/4x + 3, we'll follow the steps below:

1. Combine like terms:

  -3x - 1/4 = 1/4x + 3

2. Get rid of fractions by multiplying the entire equation by the least common denominator (LCD), which is 4:

  4(-3x - 1/4) = 4(1/4x + 3)

  Simplifying:

  -12x - 1 = x + 12

3. Move all the terms with x to one side and the constant terms to the other side:

  -12x - x = 12 + 1

  Simplifying:

  -13x = 13

4. Divide both sides by -13 to isolate x:

  x = 13 / -13

  Simplifying:

  x = -1

Therefore, the solution to the equation is x = -1.

In the given equation, x = -1 satisfies the equation and makes both sides equal. By substituting x = -1 back into the equation, we can verify the solution:

-3(-1) - 1/4 = 1/4(-1) + 3

3 - 1/4 = -1/4 + 3

12/4 - 1/4 = -1/4 + 12/4

11/4 = 11/4

The left-hand side of the equation is equal to the right-hand side, confirming that x = -1 is the correct solution.

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Answer:

Step-by-step explanation:

In general, the assumption of an equal likelihood of boys and girls is a simplification used in certain statistical models or probability calculations. It is based on the idea that the probability of having a boy or a girl is roughly 50% for any given birth. This assumption works well for large populations and over a long period of time, where the random processes involved in determining the sex of a child tend to balance out.

However, in specific situations or smaller sample sizes, the assumption of an equal likelihood of boys and girls may not hold true. There can be biological, genetic, or environmental factors that influence the probability of having a boy or a girl. Some examples where the sample space for the variable "sex" may contradict the assumption include:

Genetic disorders or chromosomal abnormalities: Certain genetic conditions can affect the probability of having a boy or a girl. For instance, in some cases of sex-linked genetic disorders, the probability of having a particular sex may be significantly higher or lower than 50%.

Biased sample selection: If the sample of individuals considered is not randomly selected, but rather influenced by some external factors, the assumption of an equal likelihood may be invalid. For example, if the sample consists only of families who have a strong preference for having a specific sex, the observed distribution may deviate from an equal probability.

Cultural or social factors: Societal or cultural preferences, practices, or interventions can impact the distribution of sex. In some cultures, there may be a strong preference for having boys over girls, leading to a biased sample space.

It is essential to consider these factors and the specific context when analyzing the distribution of sex in a sample space. It is also worth noting that the assumption of equal probability is a simplification and may not reflect the complex reality of biological and social influences on sex ratios.

The assumption that the distribution of sex in humans can be modeled as a coin flip means that boys and girls are equally likely (50%-50%). If the sample space from your document shows different probabilities (eg. 70% boys, 30% girls), it contradicts this assumption, illustrating the occurrence of boys and girls is not equally likely.

The distribution used to model the sex of humans as being just as likely to be a boy as a girl is like a coin flip, with a probability of 0.5 for each outcome. If the sample space in the attached document contradicts this assumption, it must have different probabilities for boys and girls

For instance, imagine we have a sample space where boys are 70% and girls are 30%. This shows a bias towards boys, and therefore, it would not be accurately modeled by a coin flip. An accurate model would have to represent the different probabilities.

Therefore, the coin flip model, which assumes equal probabilities, wouldn't be appropriate to use because the sample space shows that the occurrence of boys and girls is not equally likely.

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The system of equations:

x - y = 2

2x² - 3y² = 15

Has two solutions, which are (9, 7) and (3, 1)

Here we want to solve the system of equations:

x - y = 2

2x² - 3y² = 15

To solve the system of equations we can use substitution or elimination method. Let's use the substitution method in this case:

Step 1: Solve Equation A for x in terms of y:

x = 2 + y

Step 2: Substitute the value of x from Step 1 into Equation B:

2(2 + y)² - 3y² = 15

Step 3: Expand and simplify the equation:

2(4 + 4y + y²) - 3y² = 15

8 + 8y + 2y² - 3y² = 15

8 + 8y - y² = 15

Step 4: Rearrange the equation to bring all terms to one side:

y² - 8y + 7 = 0

Step 5: Factorize the quadratic equation:

(y - 7)(y - 1) = 0

This gives two possible values for y:

y = 7 (Solution 1)

y = 1 (Solution 2)

Step 6: Substitute the values of y back into Equation A to find the corresponding values of x:

For y = 7:

x = 2 + 7 = 9 (Solution 1: x = 9, y = 7)

For y = 1:

x = 2 + 1 = 3 (Solution 2: x = 3, y = 1)

The system of equations has two solutions: (x = 9, y = 7) and (x = 3, y = 1)

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The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

The five more known rotation rules are given as follows:

The original coordinates for this problem are given as follows:

A(0,0), B(5,2), C(5,-5), D(0,-3).

Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

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The die was rolled 20 times, so the total number of possible outcomes is 20.

The die landed on 5 a total of 4 times, so the probability that a die will land on 5 is 4/20 = 0.2 or 20%.

The die landed on 1 a total of 5 times, so the probability that a die will land on 1 is 5/20 = 0.25 or 25%.

If a probability is unlikely, then the probability is less than 0.5 or 50%. This is because the probability of an event ranges from 0 (impossible) to 1 (certain), so any probability less than 0.5 means that the event is less likely to happen than not.

Based on the information, there are 25 cars with good brakes and good tires.

Total cars = 50

Cars with faulty brakes = 10

Cars with faulty tires = 15

Cars with faulty brakes and good tires = 2

Let's calculate the number of cars with good brakes and good tires:

Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires

= 10 + 15 - 2

= 25

Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires

= 50 - 25

= 25

Therefore, there are 25 cars with good brakes and good tires.

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An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

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The solution to the system of equation is dependent and x = 20, y = -15 and z = -3

x+y+ z= 2

3x+4y- z=3

3x + 4y -2z = 6

Multiply (1) by -1 and subtract (1) from (2) to eliminate z

-x - y - z = -2

3x+4y- z=3

4x + 5y = 5

Then multiply (2) by 2 and subtract (3) from it to eliminate z

6x + 8y - 2z = 6

3x + 4y -2z = 6

3x + 4y = 0

4x + 5y = 5

3x + 4y = 0

Multiply 4x + 5y = 5 and 3x + 4y = 0 by 3 and 4 respectively

12x + 15y = 15

12x + 16y = 0

Subtract

16y - 15y = 0 - 15

y = -15

Substitute y = 15 into

12x + 16y = 0

12x + 16(-15) = 0

12x - 240 = 0

12x = 240

divide both sides by 12

x = 20

From (1)

x+y+ z= 2

20 + (-15) + z = 2

20 - 15 + z = 2

5 + z = 2

z = 2 - 5

z = -3

Therefore, x = 20, y = -15 and z = -3.

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Answer:

In the situation described where we have a part-to-whole ratio of 2:5, it means that for every 2 parts of something, there are 5 parts in total. In other words, if we were to divide the whole into equal parts, the specific part we are interested in would make up 2 out of every 5 parts. This ratio provides a relative comparison between the specific part and the entire whole, indicating that the part occupies a smaller portion compared to the whole.

Step-by-step explanation:

Let's assume the original mass of the saline water (salt water) is x grams. According to the given information, the mass ratio of salt to water is initially 1:10.

This means the mass of salt in the saline water is (1/11) * x grams, and the mass of water is (10/11) * x grams.

After adding 22 grams of salt, the mass ratio of salt to water becomes 2:9.

This means the mass of salt is now (2/11) * (x + 22) grams, and the mass of water is (9/11) * (x + 22) grams.

Since the mass of salt remains the same in both scenarios, we can set up an equation:

(1/11) * x = (2/11) * (x + 22)

Simplifying the equation:

x = 2 * (x + 22)

x = 2x + 44

x - 2x = 44

-x = 44

x = -44 (disregard this negative value)

Since the value of x is negative, it is not a valid solution in this context.

It seems there may be an error or inconsistency in the given information or calculations. Please double-check the values and ratios provided to ensure accuracy.

Answer:

Step-by-step explanation:

You want the equation representing the relation between Children's tickets and Senior tickets, and the solution to the problem if ...

The augmented matrix for the problem, and its solution, are shown in the attachment.

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Answer:

If the flammable limit of carbon monoxide is 12.5, and it is five times greater than the flammable limit of acetylene, we can calculate the flammable limit of acetylene as follows:

Flammable limit of acetylene = Flammable limit of carbon monoxide / 5

Flammable limit of acetylene = 12.5 / 5

Flammable limit of acetylene = 2.5

Therefore, the flammable limit of acetylene would be 2.5.

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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The principal amount of the loan is  $5200 with a simple interest charged on it at an annual rate of 10.2%. The amount of interest she paid on the loan is $662.  The number of months she took to pay the total loan would be 15 months.

Formula used,

Interest = Principal amount × Rate of interest × Time ---- (1)

S.I.=P×R×T

Given that:

P = $5200, R= 10.2% , S.I.= $663

On putting the values in equation (1) we get,

663 = 5200 ×0.102×T

Simplifying the above equation, we obtain,

663= 530.4× T

T = 663÷530.4

T= 1.25 years

For time taken in months, we have to multiply the time by 12 months :

T = 1.25×12

T= 15 months

Time= 15 months

Hence, the loan was taken for a period of 15 months.

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The measure of angle ABC is 23.5°

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the center.

Some of the theorem if arc angle relationships are;

The central angle of an arc is the central angle subtended by the arc.

The measure of an arc is the measure of its central angle.

The angle at the centre is twice the angle at the circumference.

Therefore;

angle ABC = 1/2 × arc ADC

= 1/2 × 47

= 23.5°

therefore angle ABC = 23.5°

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______________________________________

We can factor 8x^2+22x+5 by grouping.

First, we need to find two numbers whose product is 8*5=40 and whose sum is 22. These numbers are 2 and 20.

Next, we rewrite the middle term 22x as 2x+20x.

8x^2 + 2x + 20x + 5

Now we group the first two terms and the last two terms together.

2x(4x+1) + 5(4x+1)

We can see that both terms have a common factor of (4x+1), so we can factor it out.

(2x+5)(4x+1)

Therefore, the factorization of 8x^2+22x+5 is (2x+5)(4x+1).

From the graph the correct option is: The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

A one-to-one function is a function where each element in the domain is paired with a unique element in the range. In other words, no two different x-values can have the same y-value.

Looking at the graph, we can see that between the y-values of 0 and 2, there are multiple x-values. For example, when y = 1, there are two corresponding x-values: x = 3 and x = 4. This violates the condition of a one-to-one function.

The graph does not represent a one-to-one function because there are multiple x-values associated with certain y-values, specifically between 0 and 2. It is important to note that a one-to-one function requires each x-value to have only one corresponding y-value, and vice versa, which is not the case in this graph.

The correct option is: The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

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Answer:

To find the solutions for (A) AnB, (B) Buc, and (C) AnBnc, we need to first understand the notations used.

AnB represents the intersection of sets A and B, which is the set of elements that are present in both A and B.

Buc represents the union of sets B and C, which is the set of elements that are present in either B or C or both.

AnBnc represents the intersection of sets A and B complement, also known as the relative complement of B in U. This is the set of elements that are present in A but not in B.

Now, let's find the solutions for each of the given problems:

(A) AnB:

A = {1, 2, 3, 7, 8}

B = {3, 4, 5, 7, 9}

AnB = {3, 7}

Therefore, the solution for (A) AnB is {3, 7}.

(B) Buc:

B = {3, 4, 5, 7, 9}

C = {1, 3, 5, 6, 10}

Buc = {1, 3, 4, 5, 6, 7, 9, 10}

Therefore, the solution for (B) Buc is {1, 3, 4, 5, 6, 7, 9, 10}.

(C) AnBnc:

A = {1, 2, 3, 7, 8}

B = {3, 4, 5, 7, 9}

B complement = {1, 2, 6, 8, 10}

AnBnc = {1, 2, 6, 8}

Therefore, the solution for (C) AnBnc is {1, 2, 6, 8}.

The scale factor from shape A to shape B is determined as 0.75.

The value of the missing length x in shape B is 5.25 cm.

The size by which the shape is enlarged or reduced is called as its scale factor.

Scale factor from shape A to shape B is calculated as;

Scale factor =   3/4 = 9/12 = 0.75

The value of the missing length x in shape B is calculated by applying the principle of similar triangles as follows;

the given lengths of shape A and shape B;

A = 4 cm and 7 cm

B = 3 cm and x cm

The value of the missing length x in shape B is calculated as;

x/3 = 7/4

x = (3 x 7/4)

x = 5.25 cm

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Answer:

385 envelopes will be needed.

Step-by-step explanation:

y = the total number of envelopes needed.

x =  the number of months

y = 5x + 325

y = 5(12) + 325

y = 60 + 325

y = 385

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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