By using the e- definition of limits, prove that lim,- (2.x2 – 1 + 1) = 7. 2 0

1.- I'll write the inequality as an equation

y = x

2.- I'll asign values to x to get y

x y

-2 -2

-1 -1

0 0

1 1

2 2

3.- I'll sketch the line, hold on

4.- Join the points and shade the area

The red line must be dash but the solution is the dash line and the green area.

Becuase the inequality is y < x, the sign "<" means below the line (shade the area below the line)

If the sign would be ">" it would mean shade the area over the line

The measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees

What are isosceles triangles?

Isosceles triangles are triangles that have two sides equal in measurement.

Main Body:

From the given diagram;

∠BAC = 18 degrees

∠BDC = 48 degrees

Required angle  : ∠ABD

From the diagram, ∠DAB = ∠BAC = 18 degrees

Also, ∠ADC + ∠ACD + ∠DAC = 180

Since triangles ACD is isosceles, hence ∠ADC = ∠ACD. The expression above becomes

∠ADC + ∠ADC + ∠DAC = 180

2∠ADC + ∠DAC = 180

2∠ADC  = 180 - 36

2∠ADC = 144

∠ADC = 144/2

∠ADC = 72 degrees

This means that ∠ADB = 72 - ∠BDC

∠ADB = 72 - 48

∠ADB = 24 degrees

Get the required angle ABD

From triangle ADB, ∠ABD + ∠ADB + ∠DAB = 180

∠ABD + 24 + 18 = 180

∠ABD + 42 = 180

∠ABD = 180 - 42

∠ABD = 138 degrees

Hence the measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees.

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The measure of ∠RST(angle S)  can be found using the external angle theorem and the measure of ∠RST is 49 degrees.

It states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle

Therefore,

∠SRT + ∠RST = 128°

let

∠RST = x

Therefore,

79 + x = 128

subtract 79 from both sides of the equation

79 - 79 + x = 128 - 79

x = 49°

Therefore,

∠RST = 49°

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This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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Answer::

Explanation:

Let the number of lasagna cupcakes made = x

Let the number of Gorgonzola onion tarts made = y

0. It takes ,10 minutes, to assemble each pan of lasagna cupcakes.

1. It takes ,15 minutes, to roll out the Gorgonzola onion tarts and fill each pan.

2. She has a maximum of ,2 hours (120 minutes), to assemble the appetizers.

These translate to the inequality:

0. Each pan of lasagna cupcakes takes 20 minutes to bake.

1. Each pan of Gorgonzola tarts takes 6 minutes to bake.

2. She has 60 minutes to bake the appetizers.

These translate to the inequality:

Since she must bake either lasagna cupcakes or Gorgonzola tarts, we have that:

So the system of inequalities is:

The graph that bests represents this scenario is:

There appears to be a positive correlation between shoe size and grade point average in Professor Walker's class, suggesting that students with larger shoe sizes tend to have higher GPAs.

The observation made by Professor Walker suggests a relationship between shoe size and grade point average. A positive correlation means that as one variable (shoe size) increases, the other variable (GPA) also tends to increase. In this case, the observation indicates that students with larger shoe sizes tend to have higher GPAs. However, it is important to note that correlation does not imply causation.

It is possible that the observed relationship is coincidental or influenced by other factors. Factors such as age, gender, or socioeconomic status could be associated with both shoe size and academic performance, leading to a spurious correlation. To establish a definitive causal relationship, further research and analysis would be required to account for confounding variables and determine the underlying mechanisms, if any, between shoe size and GPA.

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Answer:

84+(x+9)=180

Step-by-step explanation:

84º+(x+9)º = 180º, so x+93 = 180, so x=87. Hope this helps!

$25,000 of Geoffrey's income is subject to the net investment income tax.

The net investment income tax applies to certain types of income, including rental real estate income, and is calculated based on an individual's modified adjusted gross income (MAGI) and filing status. In the case of Geoffrey, his rental real estate income of $25,000 is subject to the net investment income tax.

To calculate the net investment income tax, we need to determine Geoffrey's MAGI. His total income for the year consists of $25,000 in rental real estate income and $180,000 in wages, totaling $205,000. Since he has no adjustments to income, his MAGI is equal to his total income of $205,000.

Therefore, the amount of Geoffrey's income subject to the net investment income tax is $25,000.

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The sample variance formula is: (sum of squared differences between each data point and the sample mean) divided by (sample size minus one).

The sample variance formula is a statistical calculation used to measure the variability of a set of data values in a sample. Variance is a measure of how spread out a set of data is, and it provides a measure of the average deviation of the individual data points from the sample mean.

The sample variance formula is calculated by taking the sum of the squared differences between each data point and the sample mean, and dividing that value by the sample size minus one. The resulting value provides a measure of how much the data points vary from the mean of the sample, and is an important tool for assessing the reliability and validity of statistical results.

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Answer: AI:EF

Step-by-step explanation:

Answer:

D. ) AI:EF

Step-by-step explanation:

PLATO

Answer:

Step-by-step explanation:

1) correct

2) correct

3) 51-8b

4) 5(a+b)

5) (x+y)/3

Answer:

y= 3x - 5

Step-by-step explanation:

coordinates given: (4,7) & (1, -2)

to find m (slope) = rise/run = (y2-y1) /(x2-x1)

= ( -2-7) / (1 - 4)

= -9/-3

= 3

therefore, y=3x + b

to find b:

taken coordinate: (4,7)

y=3x + b

7=3 (4) + b

7= 12 + b

7-12 = b

-5 = b

(*the value of b will be same even if we take the other coordinate)

therefore, y = 3x -5

The limit definition of the derivative of a function y=f(x) is the rate of change of y with respect to x, represented by the symbol dy/dx.

The derivative of a function y=f(x) is a measure of how much the function y changes as x changes. It is represented by the symbol dy/dx and can be calculated using the limit definition.

The limit definition states that the derivative of a function at a point x is equal to the limit of the ratio of the change in y to the change in x as the change in x approaches 0.

This is represented mathematically as: dy/dx = lim(h->0) (f(x+h) - f(x)) / h.

This definition is the foundation for the whole Calculus, it is a powerful tool for solving problems in physics, engineering, economics and many other fields.

It also allows for mathematical analysis of many complex functions and helps in understanding the properties of functions such as increasing and decreasing, maxima and minima, concavity and inflection points.

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The value of x from the given condition is 34. Therefore, option B is the correct answer.

Given that, m∠C = (3x + 1)° and m∠D = (2x + 9)°.

Consecutive angles lie along the transversal, both angles will always be on one side of the transversal, and they'll either both be inside the parallel lines or outside the parallel lines (interior or exterior angles, respectively). Consecutive angles are always supplementary if the transversal crosses parallel lines.

Since, consecutive angles are always supplementary, we get

(3x + 1)°+(2x + 9)° =180°

⇒ 5x+10=180

⇒ 5x=170

⇒ x=34

The value of x from the given condition is 34. Therefore, option B is the correct answer.

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Answer:

nth term = 10 + (n - 1)-3

Step-by-step explanation:

a) 10, 7, 4, 1

First term,a = 10

Common difference,d = 7 - 10 = -3

nth term = a + (n - 1)d

nth term = 10 + (n - 1)-3

b 6, 4, 2,0

First term,a = 6

Common difference,d = 4 - 6 = -2

nth term = a + (n - 1)d

nth term = 6 + (n - 1)-2

c) 9,4 -1,-6

First term,a = 9

Common difference,d = 4 - 9 = -5

nth term = a + (n - 1)d

nth term = 9 + (n - 1)-5

d) 2.5, 2. 1.5, 1

First term,a = 2.5

Common difference,d = 2 - 2.5 = -0.5

nth term = a + (n - 1)d

nth term = 2.5 + (n - 1)-0.5

The expression 2 + (negative 20) + 8 can be simplified by adding the numbers in any order, since addition is commutative. One way to do this is to add the positive and negative numbers separately, and then combine the results. For example:2 + (negative 20) + 8 = (2 + 8) + (negative 20) = 10 + (negative 20) = negative 10The simplified expression is negative 10. This means that the scuba diver is 10 meters below sea level.

Step-by-step explanation:

The volume of a cube is

\(a {}^{3} \)

where a is the side length,

Note: If you want to remember this formula, know that a cube is basically a bunch of squares stacked on one another vertically and horizontally

The area of a square with side length a, is

\( {a}^{2} \)

If we multiply that by the height of the cube, which is a.

\( {a}^{2} \times a = {a}^{3} \)

That is the easy way to derive the formula of the volume of a cube.

Back on track, we know the volume so we must solve for a.

1.

\(125 = {a}^{3} \)

Assuming you took algebra, to isolate the variable a, we must undo it being raised to the third power.

To do this, we take the cube root of both sides

\( \sqrt[3]{125} = \sqrt[3]{a {}^{3} } \)

The cube root of 125 is 5 so

\(5 = a\)

5 cm

2.

\(8 = {a}^{3} \)

\( \sqrt[3]{8} = \sqrt[3]{ {a}^{3} } \)

\(2 = a\)

2 ft

3.

\(343 = {a}^{3} \)

\(a = 7\)

7 yd

4.

\(1000 = a {}^{3} \)

\(10 = a\)

10 mm

5.

\(1728 = {a}^{3} \)

\(a = 12\)

12 in. or 1 ft

6.

\(1 = {a}^{3} \)

\(a = 1\)

1 m

Answer:

A cube can be seen as a square that has been 'stretched'. We know that all four sides of a square are equal, thus, the sides of the faces of a cube are also equal.

In order to find the volume of a cube, the formula we apply is length x width x height (lwh).

Since all the sides are the same, another formula for the volume of the cube can be written as volume = x^3 in which x stands for the length of each side. When plugging in the formula:

1) V = 125 cm^3

   125 = x^3

   ∛125 = x

    5 = x

When finding the cube root, you can use a calculator or fingure out the answer yourself by multiplying any number by itself three times.

2) 8 = x^3

   ∛8 = x

      2 = x

3) 343 = x^3

 ∛343 = x

        7 = x

4) 1000 = x^3

 ∛1000 = x

         10 = x

5) 1728 = x^3

  ∛1728 = x

    12 = x

6) 1 = x^3

   ∛1 = x

      1 = x

Make sure to include the appropriate unit for each answer

Answer:

Step-by-step explanation:

The

average rate of change

of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the

secant line

connecting the 2 points.

To calculate the average rate of change between the 2 points use.

∣

∣

∣

∣

∣

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

a

a

f

(

b

)

−

f

(

a

)

b

−

a

a

a

∣

∣

∣

−−−−−−−−−−−−−−−

f

(

9

)

=

9

2

−

6

(

9

)

+

8

=

35

and

f

(

4

)

=

4

2

−

6

(

4

)

+

8

=

0

The average rate of change between (4 ,0) and (9 ,35) is

35

−

0

9

−

4

=

35

5

=

7

This means that the average of all the slopes of lines tangent to the graph of f(x) between (4 ,0) and (9 ,35) is 7.

Answer:

1/3^2

Im trying to earn my brainliest..so if you don't mind :)

Answer:

C what grade are u in that's ez

Here to solve the probability of this sum, it is difficult to say that the probability without no information.

(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.

(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.

A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.

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Answer:

b because if u read it makes the most sence

Step-by-step explanation:

Answer:

c or b

Step-by-step explanation:

To determine the number of observations needed in the sample to estimate a population mean with a sampling distribution error SE=0.24 and a 95% confidence interval, we can use the formula:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (for a 95% confidence level, Z ≈ 1.96)

σ = standard deviation of the population (given as approximately 7.9)

E = sampling distribution error (given as 0.24)

Plugging in the values, we have:

n = (1.96 * 7.9 / 0.24)²

Calculating this expression, we find:

n ≈ 45.564

Since we cannot have a fraction of an observation, we round up to the nearest whole number. Therefore, the number of observations that would have to be included in the sample is 46.

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Answer:

1 dimension

Step-by-step explanation:

ouo

Answer:

1 dimension.

Step-by-step explanation:

Lines have one dimension, polygons have two dimensions, solids have three dimensions. Lines only have the dimension length. Polygons have the dimensions length and width. Solids have the dimensions length, width, and height.

Answer:

red

Step-by-step explanation:

Is the chair with the most amount of chairs meaning the more amount the more percent you'll to get chosen

The answer is 15.To determine the number of different homes that can be built, we need to consider the different combinations of interior plans and home exteriors.

Given that there are three different interior plans and five different home exteriors, we can use the multiplication principle to find the total number of combinations. Multiplying 3 by 5 gives us 15 unique combinations.Let's break it down: For each of the three interior plans, we have five options for the home exterior. This means that for the first interior plan, we can pair it with any of the five home exteriors. Similarly, for the second interior plan, we can also pair it with any of the five home exteriors, and the same applies to the third interior plan.

Using the multiplication principle, we multiply the number of options for each choice together to find the total number of combinations. In this case, it is 3 (interior plans) multiplied by 5 (home exteriors), which equals 15. Therefore, the developer can build 15 different homes by combining the three interior plans with the five home exteriors. In conclusion, the answer is 15.

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Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

Answer:

x=-3

Step-by-step explanation:

Because its straight, on the x-axis, and on -3.

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

Explanation:

This green line goes through -3 on the x axis. Every point on this line has the same x coordinate and that x coordinate is x = -3. For instance, the two points (-3,5) and (-3,2) are on this green line. The equation of this line is x = -3 to indicate that x must be -3, but y can be anything you want. So that's why the y term doesn't even show up here. We cannot write the equation into slope intercept form. The slope of any vertical line is undefined.

Answer:

less than a mile is the answer