F(x) = 2x + 3 and g(x) = -4x - 27 find the intersection

Answer:

a) See below.

b) $911 billion

c) See below.

Step-by-step explanation:

Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.

It estimates the slope and y-intercept of a straight line that minimizes the overall distance between the observed data points and the predicted values. The linear regression equation is y = ax + b.

The association between year and amount of disposable income is indicated by the linear regression equation y = ax + b.

The value of a is the slope of the linear regression line, and represents the average rate of change in disposable income per year. As a = 14.0545, it means that the disposable income increases by approximately $14.0545 billion dollars each year.  

As the value of r (correlation coefficient) is very close to +1, it indicates a very strong positive linear correlation between the year and disposable income. This suggests that as the years progress, the disposable income tends to increase.

Linear regression equation:

[tex]\boxed{y=14.05454545x-27198}[/tex]

To predict the amount of disposable income for the year 2000, we can substitute x = 2000 into the linear regression equation:

[tex]y = 14.05454545 \cdot 2000 - 27198[/tex]

[tex]y=28109.0909...-27198[/tex]

[tex]y=911.0909...[/tex]

[tex]y=911[/tex]

Therefore, the predicted amount of disposable income for the year 2000 is approximately $911 billion.

The predicted value of $911 billion for the year 2000 is significantly lower than the actual value of $8128 billion. This implies that the model is not accurately capturing the increasing trend in disposable income over time, leading to an underestimation of the income level in 2000. This suggests that the model may have limitations or inaccuracies when extrapolating beyond the range of the provided data. It indicates the need for caution and further analysis when using the model to make predictions outside of the given timeframe.

Answer:

There are 40 tables.

Step-by-step explanation:

Since we know that there are 9 times as many chairs, then there are tables, all we have to do is divide the number of chairs by 9, and we get the answer 40.

The equation of the line perpendicular to  y = 2 / 3 x - 4 and passes through (6, -2) is y = - 3 / 2x + 7.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

The slopes of perpendicular lines are negative reciprocals of one another.

Therefore, the slope of the line perpendicular to y = 2 / 3 x - 4 is - 3 / 2.

Hence, let's find the line as its passes through (6, -2).

Therefore,

y = - 3 / 2 x + b

-2 = - 3 / 2(6) + b

-2  = -9 + b

b = -2 + 9

b = 7

Therefore, the equation of the line is y = - 3 / 2x + 7.

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Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

Answer:

Step-by-step explanation:

Surface area of a cone = surface area of a circle = pi r^2

250 = pi r^2

[tex]r = \sqrt{ \frac{250}{2} } = 5 \sqrt{5} \: cm[/tex]

Because the height (h) of the cone is double the length of its radius

Then

h = 2r

[tex]h \: = 2 \times 5 \sqrt{5} = 10 \sqrt{5} = 22.36 \: cm[/tex]

The errors in the proposed statement to prove by contradiction that 3·√2 - 7 is an irrational number, is the option;

Proving by contradiction is an indirect method of proving a fact or a reductio ad absurdum, which is a method of proving a statement by the assumption that the opposite of the statement is true, then showing that a contradiction is obtained from the assumption.

The definition of rational numbers are numbers that can be expressed in the form a/b, where a and b are integers

The assumption that 3·√2 - 7 is a rational number indicates that we get;

3·√2 - 7 = a/b, where a and b are integers

Therefore, the error in the method used to prove that 3·√2 - 7 is an irrational number is the option; To apply the definition of rational, a and b must be integers. This is so as the value 3·√2 - 7 is a real number, which is also an irrational number, thereby contradicting the supposition.

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Part A: Approximately 50% of newborn babies weigh more than 3000 grams. Part B: Approximately 84.13% of newborn babies weigh more than 2000 grams. Part C: Approximately 84.13% of newborn babies weigh less than 4000 grams. Part D: Approximately 68% of newborn babies weigh between 2000 and 4000 grams. Part E: The range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.

1: Calculate the Z-scores for the given weights using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For Part A:

Z = (3000 - 3000) / 500 = 0

Using the Z-table, we find that the percentage of babies weighing more than 3000 grams is approximately 50%.

For Part B:

Z = (2000 - 3000) / 500 = -2

Using the Z-table, we find that the percentage of babies weighing more than 2000 grams is approximately 97.72%. Since we want the percentage of babies weighing more than 2000 grams, we subtract this value from 100% to get approximately 2.28%.

For Part C:

Z = (4000 - 3000) / 500 = 2

Using the Z-table, we find that the percentage of babies weighing less than 4000 grams is approximately 97.72%.

For Part D:

To find the percentage of babies weighing between 2000 and 4000 grams, we subtract the percentage of babies weighing more than 2000 grams from the percentage of babies weighing less than 4000 grams.

Approximately 97.72% - 2.28% = 95.44%

For Part E:

Since the Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, we need to find the weights that correspond to the boundaries of this range.

The lower boundary would be the mean minus one standard deviation: 3000 - 500 = 2500 grams.

The upper boundary would be the mean plus one standard deviation: 3000 + 500 = 3500 grams.

Therefore, the range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.

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The correct statement about rectangles is:

1. All rectangles are parallelograms.

2. Parallelograms have exactly 1 pair of parallel sides.

3. So, all rectangles have exactly 1 pair of parallel sides.

A rectangle is a type of parallelogram that has additional properties. By definition, a rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are parallel. Since all four sides of a rectangle are right angles, it follows that a rectangle has exactly 1 pair of parallel sides.

Option 1 states that only some rectangles are parallelograms, which is incorrect. All rectangles are parallelograms because they have opposite sides that are parallel.

Option 2 states that parallelograms have 2 pairs of parallel sides, which is also incorrect. Parallelograms have exactly 2 pairs of parallel sides, not 4. A rectangle is a special type of parallelogram that has additional properties such as all angles being right angles.

Option 3 states that only some rectangles have 2 pairs of parallel sides, which is incorrect. All rectangles have exactly 1 pair of parallel sides, not 2. Having 2 pairs of parallel sides would make a shape a parallelogram, not a rectangle.

Therefore, the correct statement is that all rectangles are parallelograms and have exactly 1 pair of parallel sides. 1,2,3 are correct.

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The correct total weight of the bags of granola is 8 1/4 pounds.

One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.

In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.

To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:

2 + 2 + 3 = 7 (sum of whole numbers)

1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)

Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.

By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.

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The probable question may be:

Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.

what is one thing that you could do to Roberto's Reasoning

The expression to estimate the number of containers of salsa needed is: 48 × 3 × 9. none of the option is correct.

To estimate how many containers of salsa are needed for all the tables in one day, we need to consider the total number of tables and the number of salsa containers required for each table.

Given that there are 48 tables and each table has 3 different types of salsa, we can estimate the total number of containers needed by multiplying the number of tables by the number of salsa types.

However, we also need to account for the fact that there are 9 different sets of customers throughout the day. Each set of customers will use all the tables, so we need to multiply the estimated number of containers by the number of sets of customers to get an accurate estimation for the day.

Let's analyze the options provided:

A) 50 × 9: This option assumes there are 50 tables, which is incorrect based on the given information.

B) 16 × 3 × 9: This option assumes there are 16 tables, which is incorrect based on the given information.

C) 50 × 3 × 10: This option assumes there are 50 tables and 10 different sets of customers. Although the number of tables is incorrect, this option accounts for the number of salsa types and the number of sets of customers. However, it does not accurately represent the given scenario.

D) 40 × 5 × 5: This option assumes there are 40 tables and 5 different sets of customers. It also considers the number of salsa types. However, it does not accurately represent the given scenario as the number of tables is incorrect.

None of the options provided accurately represent the given scenario. The correct expression to estimate the number of containers of salsa needed for all the tables in one day would be:48 × 3 × 9

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The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

To draw the 6th term, represent it visually within the context of the pattern or sequence from which it is derived.

To draw the 6th term, we need to understand the context or pattern from which the term is derived.

Drawing the term usually involves representing the elements or characteristics of the pattern in a visual form.

Without specific information about the pattern, we can provide a general approach to drawing the 6th term.

Identify the Pattern:

Determine the sequence or pattern from which the 6th term is derived.

It could be a numerical sequence, a geometric pattern, or any other pattern.

For example, if the pattern is a number sequence of multiples of 3, the first few terms would be 3, 6, 9, 12, 15, and so on.

Visualize the Pattern: Based on the identified pattern, visualize how the elements change or progress from term to term.

This could involve drawing a diagram, a graph, or any visual representation that captures the pattern.

Consider using a coordinate grid, a number line, or any other suitable visual aid.

Locate the 6th Term:

Use the information from the pattern and the visualization to determine the specific position or value of the 6th term.

In our example of multiples of 3, the 6th term would be 18.

Draw the 6th Term: Finally, represent the 6th term in your chosen visual form.

This could mean marking the position on a number line, plotting a point on a graph, or incorporating the value into a diagram.

Note that the specific method of drawing the 6th term will depend on the nature of the pattern and the context in which it is given.

Providing more details about the pattern would allow for a more accurate and specific visual representation of the 6th term.

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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The option that shows the missing angles in the triangle is:

Option C: m∠1 < m∠4

We know that the sum of angles in a triangle is 180 degrees.

Therefore looking at the given triangle, we can say that:

m∠1 + m∠2 + m∠3 = 180°

We also know that the sum of angles on a straight line is 180 degrees and as such we can say that:

m∠3 +  m∠4 = 180°

By substitution we can say that:

m∠4 = m∠1 + m∠2

Thus:

m∠1 < m∠4

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The missing options are:

m∠1 > m∠4

m∠2 > m∠4

m∠1 < m∠4

m∠3 = m∠4

We can conclude that point A is located at the origin (0, 0).

There is only one possible location for point A is at the origin.

Let's revisit the given information to determine the possible location of point A.

Point C has the same y-coordinate as point B.

This means that the y-coordinate of point C is equal to the y-coordinate of point B.

The distance between point B and point C is equal to the distance between point C and the y-axis.

Let's assume the distance between point B and point C is represented by "d".

According to the information given, the distance between point C and the y-axis is also "d".

Point A has the same x-coordinate as point C.

This implies that the x-coordinate of point A is equal to the x-coordinate of point C.

The distance between point A and point C is twice the distance between point B and point C.

Let's assume the distance between point B and point C is represented by "d".

According to the information given, the distance between point A and point C is 2d.

Based on this information, we can analyze the relationships between the points:

Since the distance between point B and point C is equal to the distance between point C and the y-axis, we can infer that point B lies on the y-axis.

The x-coordinate of point B is 0.

As point C has the same y-coordinate as point B, the y-coordinate of point C is also determined to be the same as the y-coordinate of point B.

Since point A has the same x-coordinate as point C, the x-coordinate of point A will also be 0.

The distance between point A and point C is twice the distance between point B and point C.

As the distance between point B and point C is "d", the distance between point A and point C is 2d.

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Angle "a" in the given isosceles triangle is 40 degrees.

To find the size of angle "a" in the isosceles triangle with a 40-degree angle, we can use the properties of isosceles triangles. In an isosceles triangle, the two equal sides are opposite the two equal angles.

Since the given angle is 40 degrees, we know that the other two angles in the triangle are also equal. Let's call these angles "b" and "c." Therefore, we have:

b = c

Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:

40 + b + c = 180

Since b = c, we can rewrite the equation as:

40 + b + b = 180

Combining like terms, we have:

2b + 40 = 180

Subtracting 40 from both sides, we get:

2b = 140

Dividing both sides by 2, we find:

b = 70

Therefore, both angles "b" and "c" are 70 degrees.

Now, we can find angle "a" by subtracting the sum of angles "b" and "c" from 180 degrees:

a = 180 - (b + c)

= 180 - (70 + 70)

= 180 - 140

= 40

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To find an equation for the temperature, D, in terms of t, we can use the properties of a sinusoidal function to model the temperature variation over the day.

Given:

High temperature: 80 degrees

Low temperature occurs at 5 AM (t = 5)

t is the number of hours since midnight

Let's assume a sinusoidal function of the form:

D = A * sin(B * t + C) + Dc

where:

A represents the amplitude (half the difference between the high and low temperatures)

B represents the frequency (how many cycles occur over a 24-hour period)

C represents the phase shift (how much the function is shifted horizontally)

Dc represents the vertical shift (the average temperature throughout the day)

We can determine the values of A, B, C, and Dc based on the given information.

Amplitude (A):

The amplitude is half the difference between the high and low temperatures:

A = (80 - 50) / 2

= 30 / 2

= 15 degrees

Frequency (B):

Since we want the temperature to complete one cycle over a 24-hour period, the frequency can be calculated as:

B = 2π / 24

Phase Shift (C):

Since the low temperature occurs at 5 AM (t = 5), the function should be shifted horizontally by 5 hours. To convert this to radians, we multiply by (2π / 24):

C = 5 * (2π / 24)

Vertical Shift (Dc):

The average temperature throughout the day is the midpoint between the high and low temperatures:

Dc = (80 + 50) / 2

= 130 / 2

= 65 degrees

Now we can put all the values together to obtain the equation for the temperature, D, in terms of t:

D = 15 * sin((2π / 24) * t + (5 * 2π / 24)) + 65

Simplifying further:

D = 15 * sin((π / 12) * t + (π / 12)) + 65

Therefore, the equation for the temperature, D, in terms of t is:

D = 15 * sin((π / 12) * t + (π / 12)) + 65.