completing the square and factoring: x^2+10x=15

The probability that the spinner lands on yellow and the coin toss is heads is 9/20.

To find the probability that the spinner lands on yellow and the coin toss is heads, we need to determine the probability of each event and then multiply them together.

The probability of the spinner landing on yellow is given by the number of yellow sections (18) divided by the total number of sections (20). Therefore, the probability of the spinner landing on yellow is 18/20 or 9/10.

The probability of the coin toss resulting in heads is 1/2 since there are two equally likely outcomes, heads and tails.

To find the probability of both events occurring together, we multiply the individual probabilities:

Probability (Spinner lands on yellow and Coin toss is heads) = Probability (Spinner lands on yellow) * Probability (Coin toss is heads)

= (9/10) * (1/2)

= 9/20

Therefore, nine out of twenty times, the spinner will fall on yellow and the coin will come up heads.

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a) The smallest number of tiles needed to make a square is 3.

b) The smallest number of tiles needed to make a square is 11.

a) To make a square using rectangular tiles that are 12 cm long and 4 cm wide, we need to find the side length of the square that is divisible by both 12 and 4. The smallest common multiple of 12 and 4 is 12, so a square with a side length of 12 cm can be made.

To calculate the number of tiles needed, we divide the side length of the square by the length of each tile. In this case, 12 cm ÷ 4 cm = 3.

Therefore, the smallest number of tiles needed to make a square is 3.

b) To make a square using rectangular tiles that are 11 cm long and 3 cm wide, we need to find the side length of the square that is divisible by both 11 and 3. The smallest common multiple of 11 and 3 is 33, so a square with a side length of 33 cm can be made.

To calculate the number of tiles needed, we divide the side length of the square by the length of each tile. In this case, 33 cm ÷ 3 cm = 11.

Therefore, the smallest number of tiles needed to make a square is 11.

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Answer:

For a polynomial function, if any of its solutions were zero, that would mean that its corresponding factor is zero. Thus, the polynomial would have a factor of zero, which would make the entire polynomial zero. In other words, if there were a solution of zero, that solution would be a root of the polynomial function.

However, a polynomial function can only have a finite number of roots, which is equal to its degree. Therefore, if a polynomial function had a solution of zero, that would mean that it has one more root than its degree, which is impossible. This is because a polynomial function with degree n can have at most n roots.

Therefore, all solutions of a polynomial function must be non-zero, or in other words, the function must have no roots of zero. This ensures that the polynomial function has the correct number of roots, which is equal to its degree.

This argument applies to all polynomial functions, regardless of their degree or coefficients. Therefore, it is a general property of polynomial functions that all of their solutions must be non-zero.

(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 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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o find the percent of those who passed the first test and also passed the second test, we can use the concept of conditional probability.

Given that 32% of the class passed both tests, and 70% of the class passed the first test, we want to determine the percentage of those who passed the first test and also passed the second test.

We can set up the calculation as follows:

Percentage = (Number of students who passed both tests) / (Number of students who passed the first test)

Since 32% of the class passed both tests and 70% of the class passed the first test, we can substitute these values into the equation:

Percentage = (0.32) / (0.70)

Calculating this division, we find:

Percentage ≈ 0.4571

Converting this to a percentage, we get approximately 45.71%.

Therefore, the correct answer is:

D. About 46% (rounded to the nearest percent).

The question is about percentages and the correct answer is that approximately 46% of the students who passed the first test also passed the second one.

The student's question is about the concept of percentages, a basic concept in Mathematics. The problem mentioned is about calculating the percentage of students who passed both tests out of those who passed the first one.

Given that 32% of the entire class passed both tests and that 70% of the class passed the first test, to find the percentage of students who passed the first test and also the second one, one can use the following steps:

Using these steps, you would find out that approximately 46% of the students who passed the first test also passed the second one. Therefore, D. About 46% is the correct answer.

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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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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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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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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.

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 relationship described by the equation 4y = 2x is proportional.

The relationship in the equation 4y = 2x is proportional. By simplifying the equation, we got that y = (1/2)x, which shows that y is directly proportional to x. In a proportional relationship, the ratio of y to x always remains constant.

In this scenerio, the constant of proportionality is 1/2. As x increases or decreases, y also increases or decreases by half of x.

So, the relationship between y and x in this equation is proportional, indicating that changes in x will result in corresponding proportional changes in y.

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The question is:-

Is the relationship described by the equation 4y = 2x proportional or non-proportional?

Answer:

The sum of the interior angles =

(n-2)*180

= (17-2)*180

= 2700°

hope this helps

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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).

In accordance with the exponential model, the current forest area is equal to 2801.149 square kilometers after six years.  

According with statement, the forest area decreases exponentially in time. Then, the exponential model is defined by following model:

n(x) = n' · (1 - r)ˣ

Where:

If we know that n' = 4400 km², r = 0.0725 and x = 6 yr, then the current forest area is:

n(6) = 4400 · (1 - 0.0725)⁶

n(6) = 2801.149

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Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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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 amount of sand that he should purchase for the project is: 2400 cubic feet

The formula for the Volume of a Box is:

V = L * W * H

Where:

L is Length

W is Width

H is height

Now, the volume of the given box is:

V = 12 * 4 * 5

V = 240 cubic feet

Since the number of boxes required is 10, then we say that:

Total Volume = 240 * 10

Total volume = 2400 cubic feet

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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 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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Answer: it is b

Step-by-step explanation:

i worked it out

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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Step-by-step explanation:

2x+1+2=4

2x=4-2-1

2x=4-3

2x=1

DIVIDE BOTH SIDES BY 2

2x/2 = 1/2

x = 1/2

Answer:

2x+1+2=4

2×=4-3

2× =1

2×/2=1/2

× = 1/2

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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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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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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