Question #6
Find the value of x
8
09
07
O 10
4
8
15
12

Answer:

Restrictions:

x ≠ -1/5; x ≠ 1

Answer:

[tex] \dfrac{5x - 9}{x - 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{25x^2 - 40x - 9}{5x^2 - 4x - 1} = [/tex]

[tex] = \dfrac{25x^2 - 45x + 5x - 9}{5x^2 - 5x + x - 1} [/tex]

[tex] = \dfrac{5x(5x - 9) + 1(5x - 9)}{5x(x - 1) + 1(x - 1)} [/tex]

[tex] = \dfrac{(5x + 1)(5x - 9)}{(5x + 1)(x - 1)} [/tex]

[tex] = \dfrac{5x - 9}{x - 1} [/tex]

5x + 1 = 0

x = -1/5

x - 1 = 0

x = 1

Restrictions:

x ≠ -1/5; x ≠ 1

Answer:

[tex] \dfrac{5x - 9}{x - 1} [/tex]

Answer:

Width = 7.3 feet

Step-by-step explanation:

Step 1:  Find the scale of the drawing:

Step 2:  Convert feet to inches:

Step 3:  Simplify the fraction:

Thus, the simplified fraction is 23/5952.

Step 4:  Find the actual width of the room:

Step 5:  Simplify the fraction:

Step 6:  Convert inches to feet:

Step 7:  Round to the nearest tenth of a foot:

Rounding to the nearest tenth of a foot, we get **7.3 ft**.

Thus, the actual width of the room is about 7.3 ft.

Answer: it is b

Step-by-step explanation:

i worked it out

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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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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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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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.

We have:

[tex]$\frac{600\text{ cc}}{45\text{ seconds}} = \frac{2000\text{cc}}{x \text{ seconds}}[/tex]

Cross multiplying, we get:

[tex]$600x = 90000$[/tex]

We divide both sides by 600 and get:

[tex]$\frac{600x}{600} = \frac{90000}{600}$[/tex]

[tex]$x=\boxed{150}$[/tex]

It takes 150 seconds (2 minutes and 30 seconds) for the sprayer to disperse 2000 cc of herbicide. Hope this helps!

The HCF of 560 and 729 is 1.

To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.

Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.

Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.

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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 correct answer would be "None of these" since none of the provided options indicate a basic solution.

The solution with a pH of 2 is considered to have basic character. The pH scale measures the acidity or alkalinity of a solution, ranging from 0 to 14. A pH value below 7 indicates acidity, while a pH above 7 indicates alkalinity. Thus, a pH of 2 is highly acidic and not basic.

On the other hand, the pOH scale is the inverse of the pH scale and measures the concentration of hydroxide ions (OH-) in a solution. A higher pOH value indicates a higher concentration of hydroxide ions and a more basic solution. Therefore, a pOH of 13 or 4 would suggest a basic solution.

Considering the given answer choices, neither pOH = 13 nor pOH = 4 is considered to have basic character.

It's important to note that the pOH scale is less commonly used in everyday situations compared to the pH scale when discussing the acidity or basicity of a solution. So, the correct answer is none of these.

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Answer:

To apply the fourth-order Runge-Kutta method, we can use the following steps:

Given:

Initial condition: y = 1 when x = 0

Step size: h = 0.1

We want to find the approximate value of y when x = 1/5.

The fourth-order Runge-Kutta method involves the following steps:

Set up the following equations:

k1 = hf(x, y)

k2 = hf(x + h/2, y + k1/2)

k3 = hf(x + h/2, y + k2/2)

k4 = hf(x + h, y + k3)

Update the values:

y = y + (k1 + 2k2 + 2k3 + k4)/6

x = x + h

Repeat steps 1 and 2 until the desired x-value is reached.

Let's apply these steps to find the approximate value of y when x = 1/5:

Step 1:

x = 0, y = 1

h = 0.1

k1 = 0.1 * f(x, y) = 0.1 * f(0, 1)

k2 = 0.1 * f(x + h/2, y + k1/2) = 0.1 * f(0 + 0.1/2, 1 + k1/2)

k3 = 0.1 * f(x + h/2, y + k2/2) = 0.1 * f(0 + 0.1/2, 1 + k2/2)

k4 = 0.1 * f(x + h, y + k3) = 0.1 * f(0 + 0.1, 1 + k3)

Step 2:

y = y + (k1 + 2k2 + 2k3 + k4)/6

x = x + h

Repeat steps 1 and 2 until x = 1/5.

Performing these calculations step by step will yield the approximate value of y when x = 1/5 using the fourth-order Runge-Kutta method.

Step-by-step explanation:

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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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:

x = 4√2

Step-by-step explanation:

Identifying the triangle in the diagram:

45-45-90 triangle rules:

Finding x:

Since the hypotenuse is 8 units long and, we can find x by setting 8 equal to x√2:

(8 =  x√2) / √2

8/√2 = x

Rationalize the denominator to simplify:

(8/√2) * (√2/√2)

8√2 / 2

4√2

Thus, x = 4√2

The electrostatic force between the two charges is 5,977.68 N.

The electrostatic force between the two charges separated by the given distance is calculated by applying Coulomb's law.

F = kq₁q₂ / r²

where;

The electrostatic force between the two charges is calculated as follows;

F = (9 x 10⁹ x 16.9 x 10⁻⁶ x 60.7 x 10⁻⁶ ) / ( 0.0393 )

F = 5,977.68 N

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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 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?

The linear approximation of √653 is approximately 24.8163.

To find the linear approximation to a function at a given point, we can use the formula:

L(x) = f(a) + f'(a)(x - a)

where L(x) is the linear approximation, f(a) is the value of the function at point a, f'(a) is the derivative of the function at point a, and (x - a) represents the difference between the given point x and the approximation point a.

In this case, we are given f(x) = √3 and we want to approximate √653 using the linear approximation. Let's find the linear approximation first.

Taking the derivative of f(x) = √3, we get:

f'(x) = 1 / (2√3)

Now, let's evaluate the linear approximation at a = 64:

L(x) = √3 + (1 / (2√3))(x - 64)

Substituting x = 653 into the linear approximation equation:

L(653) = √3 + (1 / (2√3))(653 - 64)

L(653) ≈ √3 + (1 / (2√3))(589)

L(653) ≈ √3 + (1 / (2√3))(589)

Calculating this approximation, we get:

L(653) ≈ √3 + (1 / (2√3))(589) ≈ 24.8163

Therefore, the linear approximation of √653 is approximately 24.8163, rounded to 4 decimal places.

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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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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:1.9975

Step-by-step explanation:

The computation of the linear approximation of the given function is shown below:

L(x) = 2 - 1 ÷ 4(x)

As we are looking for √3.9

So here

x = 0.1

So

= 4 - 0.1

= 3.9

Now

L(0.1) = f(3.9) = 2 - (0.1 ÷ 4)

= 1.975

now

substitute the x = 0.01

Then

L(0.01) = f(3.99) = 2 - (0.01 ÷ 4)

= 1.9975

We simply applied the above equations

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:

2/5 = g/80

5g = 160, so g = 32 grams of gold

Answer:

The sum of the interior angles =

(n-2)*180

= (17-2)*180

= 2700°

hope this helps