can you give me some examples in how to solve for X​

For a quadratic function, f( x) = -( x + 4)(x-1), the computed value of following,

a) value of f(2) is equals to -6.

b) The value of f(0) is equals to 4.

c) The value of derivative of f(x) at x = -2, f'(-2) is equals to 1.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. The standard form of quadratic function is f(x) = ax² + bx + c, where a, b, and c are numbers with a ≠ 0.

We have a quadratic function, f(x) defined as

f( x) = -( x + 4)(x-1) --(1)

this function is present in one variable x.

Now, the value of function can be determined by different inputs.

a) At x = 2, substitute it in the equation (1),

f(2) = -( 2+ 4)(2 - 1)

= -( 6) (1)

= -6

b) Similarly, f(0) = -(0 + 4)( 0 -1 )

= -4(-1)

= 4

c) Rewrite the function, f(x) as f(x) = - x² - 3x + 4

To determine the derivative of f(x), differentiating the function with respect to x

f'(x) = - 2x - 3

At x = -2, f'(-2) = -2(-2) -3

= 4 - 3

= 1

Hence, required value is 1.

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Complete question:

Consider the quadratic function: f(x) = -(x+4)(x-1) compute the following

a) f( 2)

b) f(o)

c) f'(-2)

(I think I already got the answers for a, b, and c, but I wouldn't mind clarification, thank you!)

The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300

Answer:

V = 1980cm^2

Step-by-step explanation:

Volume of rectangle = LxWxH

V = 34 x 6 x 6

V = 1224cm^2

Volume of triangle = (BxHxL)/2

B = 34 - 16 = 18cm

H = 20 - 6 = 14cm

L = 6

V = (18x14x6)/2

V = (18x14x6)/2

V=1512/2 = 756cm^2

1224 + 756 = 1980cm^2

Answer:

Rational numbers are the numbers which are integers and fractions

Irrational numbers are the numbers whose expression as a fraction is not possible

Examples of Rational Number

1/9 – Both numerator and denominator are integers.

7 – Can be expressed as 7/1, wherein 7 is the quotient of integers 7 and 1.

√16 – As the square root can be simplified to 4, which is the quotient of fraction 4/1

0.5 – Can be written as 5/10 or 1/2 and all terminating decimals are rational.

0.3333333333 – All recurring decimals are rational.

Examples of Irrational Number

√2 – √2 cannot be simplified and so, it is irrational.

√7/5 – The given number is a fraction, but it is not the only criteria to be called as the rational number. Both numerator and denominator need to integers and √7 is not an integer. Hence, the given number is irrational.

3/0 – Fraction with denominator zero, is irrational.

π – As the decimal value of π is never-ending, never-repeating and never shows any pattern. Therefore, the value of pi is not exactly equal to any fraction. The number 22/7 is just and approximation.

0.3131131113 – The decimals are neither terminating nor recurring. So it cannot be expressed as a quotient of a fraction.

Answer:

Step-by-step explanation:

\((1/5k)^2=1/5^2*k^2\)

\(1/25*k^2=\frac{k^2}{25}\)

Answer:  \(\frac{1}{25}k^2\)

This is equivalent to \(\frac{k^2}{25}\)

In decimal form, this is equivalent to 0.04k^2

==================================

Work Shown:

We have the two pieces 1/5 and k, all in the parenthesis being squared.

Square each piece

So overall, we end up with the answer \(\frac{1}{25}k^2\) which is equivalent to saying \(\frac{k^2}{25}\)

In decimal form, this is 0.04k^2 because 1/25 = 0.04

We would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g by using properties of the normal distribution.

To find the range in which you would expect to find the middle 68% of amounts of nicotine in these cigarettes, we can use the properties of the normal distribution.

Given:
Mean (μ) = 0.946 g
Standard deviation (σ) = 0.289 g

For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, we can expect the middle 68% of amounts of nicotine to fall within the range:

μ ± σ

Substituting the given values:

0.946 ± 0.289

To calculate the range, we have:

Lower bound = 0.946 - 0.289 ≈ 0.657 g
Upper bound = 0.946 + 0.289 ≈ 1.235 g

Therefore, we can expect to find the middle 68% of amounts of nicotine in these cigarettes to be between approximately 0.657 g and 1.235 g.

Now, if we were to draw samples of size 41 from this population, the standard deviation of the sample mean (also known as the standard error) can be calculated as:

Standard error (SE) = σ / √n

where σ is the population standard deviation and n is the sample size.

Substituting the given values:

SE = 0.289 / √41 ≈ 0.045 g

To find the range in which we would expect to find the middle 68% of the sample means, we multiply the standard error by 1 to capture approximately 68% of the data, giving us:

Lower bound = μ - SE ≈ 0.946 - 0.045 ≈ 0.901 g
Upper bound = μ + SE ≈ 0.946 + 0.045 ≈ 0.991 g

Therefore, we would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g.

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The geometric model that gives the most accurate and precise description of the Earth's surface, but is only occasionally used in mapping, is the geoid.

The geoid is a three-dimensional representation of the Earth's shape, which approximates mean sea level across the globe. It takes into account the irregularities and variations in the Earth's gravitational field, providing a more accurate depiction of the true shape of the Earth.

While the geoid offers the most accurate and precise model for the Earth's surface, it is less commonly used in mapping due to its complex nature and the challenges associated with its implementation. Instead, simpler models like the ellipsoid or the spherical models (such as WGS84) are often used for practical mapping purposes.

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a) A(t) = 450 * (1/2)^(t/4.8)

b) The asymptote is y = 0, representing the limit the substance approaches.

c) Instantaneous rate of change when 50g remains is (ln(1/2)) * 50,

a) The equation to model the amount of grams of the substance remaining, A, after t hours can be represented by the exponential decay formula:

A(t) = A₀ * (1/2)^(t/h)

Where:

A(t) is the amount of grams remaining after t hours,

A₀ is the initial amount of grams (450 grams in this case),

t is the time in hours, and

h is the half-life of the substance (4.8 hours in this case).

Therefore, the equation is:

A(t) = 450 * (1/2)^(t/4.8)

b) The equation of the asymptote for this function is y = 0. The asymptote represents the limit that the amount of the substance approaches as time goes to infinity. In this case, as time passes, the substance continuously decays, approaching zero grams. So, the asymptote at y = 0 is a realistic part of the mathematical model for this scenario.

c) To determine the instantaneous rate of change when 50 grams of the substance remains, we need to find the derivative of the function A(t) with respect to t and evaluate it at A(t) = 50.

A'(t) = (ln(1/2)) * (450 * (1/2)^(t/4.8))

At A(t) = 50:

A'(t) = (ln(1/2)) * (450 * (1/2)^(t/4.8)) = (ln(1/2)) * 50

The value of (ln(1/2)) * 50 represents the instantaneous rate of change when 50 grams of the substance remains. In this context, it represents the rate at which the substance is decaying at that particular moment.

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Answer:

The correct option is;

Low

Step-by-step explanation:

Given that the P-value of the linear correlation = 0.001, we have that the P-value is a demonstration that a linear correlation that has a value in the range of the given correlation is ,most arguably very low

From the z-table, a P-value of 0.001 corresponds to a z-value of -3.09, we have that in a normal distribution since 95% of the scores have a z-score of between -2 and 2, the z-score of -3.09 is very distant from the mean and having a low value, whereby the P-value shows that the likelihood of finding another linear correlation that is as far from the mean as the given correlation  is very low.

The solution to the equation 4x + 17 = 23 is x = 3/2.

It should be noted that to solve this equation, we need to isolate the variable x on one side of the equation.

First, we can subtract 17 from both sides of the equation:

4x + 17 - 17 = 23 - 17

Simplifying the left side of the equation:

4x = 6

Next, we can divide both sides of the equation by 4:

4x/4 = 6/4

Simplifying:

x = 3/2

Therefore, the solution to the equation 4x + 17 = 23 is x = 3/2.

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A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

To find out how many ounces of fruit juice are in a 20-ounce smoothie from Blender Splendor, given that 40% of the smoothie is fruit juice, follow these steps:

1. Convert the percentage to a decimal: 40% = 0.40
2. Multiply the total ounces of the smoothie by the decimal: 20 ounces * 0.40 = 8 ounces

Your answer: A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.

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According to the information, we can infer that the histograms indicate that female students tend to have a higher frequency of studying times compared to male students during the week prior to their AP tests.

By comparing the histograms, we can observe that the frequency of studying times for female students is generally higher across all time intervals compared to male students. Female students have a higher frequency in each category, indicating that they spend more time studying than male students during the week before the AP tests.

To further analyze the distributions, we can also consider the measures of center and variation. The measures of center, such as the mean or median, would provide insights into the typical studying time for each group. Additionally, measures of variation, such as the standard deviation or interquartile range, would indicate the spread or variability of studying times within each group.

Accoding to the above, based on the provided frequency distributions, it can be concluded that female students tend to dedicate more time to studying during the week prior to their AP tests compared to male students.

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The biconditional statement is a polygon has four sides if and only if it is a quadrilateral. Option C

A biconditional statement is defined as a statement that combines both an converse and conditional statement.

It is written in the "if and only if" from.

It is a statement that states a condition depends on another being and vice versa.

From the statement given;

"if a polygon has four sides, then it is a quadrilateral

The biconditional statement is ;

Polygon has four sides if and only if it is a quadrilateral.

Thus, the biconditional statement is a polygon has four sides if and only if it is a quadrilateral. Option C

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Faults are planar features in rocks where the two sides move past each other due to tectonic forces. However, not all planar features in rocks are faults, as there are other types of planar features that do not involve movement. A planar feature that does not involve movement is called a joint.

A planar feature refers to a surface or boundary within a rock that has a relatively consistent orientation or direction. These features can be caused by a variety of geological processes, such as deformation, metamorphism, or sedimentation. Some examples of planar features in rocks include bedding planes, foliation, and cleavage.

A fault, in particular, is a type of planar feature that forms when tectonic forces cause two sides of a rock to move past each other. This movement can be horizontal, vertical, or a combination of both. Faults can range in size from small fractures in the rock to large features that extend for kilometers. They are a common feature in regions where tectonic forces are actively shaping the Earth's crust, such as along plate boundaries or in areas with active volcanism.

On the other hand, a planar feature that does not involve movement is called a joint. Joints are fractures in rocks that do not result in any significant displacement of the rock on either side of the fracture. They can be caused by a variety of factors, such as cooling and contraction of magma or shrinkage of sediments. Joints can be important in geology because they can influence the way that rocks weather and erode over time.

In summary, a planar feature refers to a surface or boundary within a rock that has a relatively consistent orientation or direction. While faults are a type of planar feature that involves movement between two sides of a rock, joints are planar features that do not involve any significant displacement of the rock on either side of the fracture. Understanding these different planar features is important in geology, as they can provide insight into the geological history of a region and can be used to predict future geological activity.

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The vertex and range of the function is option C. Vertex : (2, 0) and Range : {y | 0 ≤ y < ∞}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The input values of a function is called the domain and the output values of the function is called range.

Here the input values are .........,-2, -1, 0, 1, 2, 3, ........

And the output values are .......,4, 3, 2, 1, 0, 1, 2, 3, 4, .....

Output values are the numbers from 0 to infinity.

So Range is {y | 0 ≤ y < ∞}

Vertex of a function is the peak point, whether it may be the maximum or the minimum point.

Here, a minimum point of the function is at x = 2 where the value of the function is 0.

So, the vertex is (2, 0), since the function is actually a parabola.

Hence the correct option is C.

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The net worth expected to be in 2020 is approximately $72,562 (to the nearest dollar).

To find the net worth expected in 2020, we need to integrate the rate of change of net worth, which is given as w'(t) = 7500 - 5t.

Let's integrate w'(t) with respect to t:

∫ (7500 - 5t) dt

Integrating, we get:

7500t - (5/2)t² + C

Where C is the constant of integration.

Now, we can use the given information to solve for C.

The net worth in 2015 was $35,125, which means when t = 0, w(t) = 35,125.

Substituting the values into the equation:

7500(0) - (5/2)(0)² + C = 35,125

0 - 0 + C = 35,125

C = 35,125

Now, we can rewrite the equation as:

w(t) = 7500t - (5/2)t² + 35,125

To find the net worth expected in 2020 (t = 2020 - 2015 = 5), we substitute t = 5 into the equation:

w(5) = 7500(5) - (5/2)(5)² + 35,125

w(5) = 37,500 - (5/2)(25) + 35,125

w(5) = 37,500 - 62.5 + 35,125

w(5) ≈ 72,562.5

Therefore, the net worth expected to be in 2020 is approximately $72,562 (to the nearest dollar).

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Answer:

(3z) - 2

Step-by-step explanation:

Let's see an example:

(4x) - 6

This translates into 6 less than 4 times x

So... 2 less than 3 times z =

(3z) - 2

Answer:

Step-by-step explanation:

That would be "3z - 2:" 2 less than 3 times z.

The mode of the sample can be larger, smaller or equal to the mode of the population, but must not be equal to the mean of the population or 500.

The mode of a sample is the value that occurs most often in the sample. The mode of a population is the value that occurs most often in the population. In a random sample, the mode of the sample can be larger, smaller or equal to the mode of the population. This is because the sample is a subset of the population and the values in the sample may not be the same as the values in the population.

The formula for calculating the mode of a sample is:

Mode = Number of times the most frequent value appears / Total number of values

For example, in a sample of 50 items from a population of 500, the mode of the sample could be equal to the mode of the population, if the most frequent value in the sample appears the same number of times as it does in the population. However, if the most frequent value in the sample appears more or less times than it does in the population, then the mode of the sample will not be equal to the mode of the population.

The mode of the sample must not be equal to the mean of the population, since the sample is a subset of the population and the values in the sample may not be the same as the values in the population. Furthermore, the mode of the sample must not be 500, since the sample is not the entire population.

The mode of the sample can be larger, smaller or equal to the mode of the population, but must not be equal to the mean of the population or 500.

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Answer:

5/6

Step-by-step explanation:

1/3 x 1/5 = 8/15 then add to 3/10 and you get 5/6 simplifed

The sum of 1/3, 1/5, and 3/10 is 5/6.

Based on the given conditions, formulate 1/3 + 1/5 +3/10

To estimate the common denominator and note the numerators above the common denominator, then we get

10 + 6 + 9/30

Calculate the sum or difference in the above equation, we get

10 + 6 + 9/30 = 25/30

Decrease the fraction to the lower term by canceling the greatest common factor, we get

25/30 = 5/6

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Answer:

A

Step-by-step explanation:

Answer: i believe its 3.2 cups per cake

Step-by-step explanation:

9.6 / 3 = 3.2

Answer:

-1.5

that should be it

We have the standard deviation for the population, which means that the z-distribution is used to solve this question.

Doing this, we get that:

The 95% confidence interval for the population mean, in minutes, is (23, 26.5).

Sample mean:

The sample mean is the sum of all observations divided by the number of observations. We have that:

Thus, the sample mean is:

\(\overline{x} = \frac{10\times15 + 18\times30 + 12\times25}{10 + 18 + 12} = 24.75\)

Confidence interval:

We have to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a p-value of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96\frac{5.64}{\sqrt{40}} = 1.75\)

The lower end of the interval is the sample mean subtracted by M. So it is 24.75 - 1.75 = 23 minutes

The upper end of the interval is the sample mean added to M. So it is 24.75 + 1.75 = 26.5 minutes

The 95% confidence interval for the population mean, in minutes, is (23, 26.5).

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The slope is the change in y over the change in x.

The first number in the parentheses is the x value, the second number is the y value.

Slope = (0-3) / (4-0)

Slope = -3/4

The y intercept is the y value when x is 0.

The given point (0,3) has x as 0, so the y intercept would be 3

Answers: slope = -3/4, y intercept = 3

Answer:

y intercept = 3 slope = -3/4

Step-by-step explanation:

I did this on edganuity :)

Answer:

a = 3 b = 5 c = 14 d = 34 e = 30

Step-by-step explanation:

The number of times larger is solved by the exponents

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

From the laws of exponents , mᵃ×mᵇ = mᵃ⁺ᵇ

a)

3⁴ = 3 x 3³

So , it is 3 times larger

b)

5³ = 5 x 5²

So , it is 5 times larger

c)

7¹⁰ = 7² x 7⁸

So , it is 7² or 49 times larger

d)

17⁶ = 17² x 17¹⁴

So , it is 17² or 289 times larger

e)

5¹⁰ = 5⁶ x 5⁴

So , it is 5⁶ times larger

Hence , the exponents are solved

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