5 7 Find the general antiderivative of the function f(x) = 4 4 v(5x-3) - 5/2 e^3x + 7/x^2

The absolute maximum value of f(x) = x³ - 6x² + 9x + 6 on [-1, 6] is 84, which occurs at x = 6, and the absolute minimum value is 0, which occurs at x = 3.

To find the absolute maximum and minimum values of the function f(x) = x³ - 6x² + 9x + 6 on the interval [-1, 6], we need to find the critical points of the function and evaluate the function at the endpoints of the interval.

First, we find the derivative of the function

f'(x) = 3x² - 12x + 9

Setting f'(x) = 0 to find the critical points, we get

3x² - 12x + 9 = 0

Dividing both sides by 3, we get

x² - 4x + 3 = 0

Factoring, we get

(x - 1)(x - 3) = 0

So the critical points are x = 1 and x = 3.

Next, we evaluate the function at the endpoints of the interval

f(-1) = (-1)³ - 6(-1)² + 9(-1) + 6 = 2

f(6) = 6³ - 6(6)² + 9(6) + 6 = 84

Now we need to evaluate the function at the critical points

f(1) = 1³ - 6(1)² + 9(1) + 6 = 10

f(3) = 3³ - 6(3)² + 9(3) + 6 = 0

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The given question is incomplete, the complete question is:

Find the absolute maximum and absolute minimum values off on the given interval. (If an answer does not exist, enter DNE.) f(x) = x³ - 6x² + 9x + 6 on [-1, 6]

To find the critical value at 0.05, we need to use the chi-square distribution. Since the null hypothesis (H0) asserts that the variance is less than 6, we can use a one-tailed test with alpha = 0.05.

To calculate the critical value, we need to first find the degrees of freedom (df) which is equal to n-1, where n is the sample size.

In this case, df = 26-1 = 25.

Next, we need to find the chi-square value for a one-tailed test with 25 degrees of freedom and alpha = 0.05.

We can use a chi-square distribution table or a calculator to find this value. Using a calculator, we get: χ² = CHISQ.INV(0.05, 25) = 37.65248

Therefore, the critical value for this test is 37.65248. Any calculated chi-square value greater than this critical value would lead to rejection of the null hypothesis.

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When something decreases by 15.7%, the growth factor is about 1.182 and when something decreases by 0.12%, the growth factor is about 1.00012.

In math, what is the definition of multiplying?

Multiplication is a mathematical process that shows the amount of times a number has been added to itself. It is represented by the multiplication symbols (x) or (*). Division is a mathematical process that shows how many equal amounts add up to a given quantity.

If something decreases by 15.7%, the increase in the factor is 100 / (100 - 15.7) Equals 1.182.

As a result, when something decreases by 15.7%, the growth factor is about 1.182.

When something falls by 0.12%, the expansion factor is 100 / (100 - 0.12) = 1.00012.

As a result, when something decreases by 0.12%, the growth factor is about 1.00012.

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The tanks will be closest to each other at time 11:11 AM and the nearest distance between the tanks is 27.16 km.

Let's assume that the two tanks meet at a point (x, y) at time t.

Using the Pythagorean theorem, the distance between the tanks is:

D(t) = √(50 - 20t)² + (15t)²

To find the time when the tanks are closest, we need to find the minimum value of D(t).

We can do this by taking the derivative of D(t) with respect to t and setting it equal to zero:

dD/dt = (-40(50 - 20t) + 30t) /√(50 - 20t)² + (15t)² = 0

Solving for t, we get:

t = 125/34 hours

125/34 hours = 3.6765 hours

= 3 hours and 41 minutes after 7:30 AM

So the tanks will be closest to each other at approximately 11:11 AM.

To find the nearest distance between the tanks at that time, we can substitute t = 125/34 into the expression for D(t):

D(125/34) = 27.16 km

Hence, the nearest distance between the tanks is approximately 27.16 km.

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The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level is that the true mean score improvement on the outcomes assessment test is equal to or less than 3%.

The null hypothesis is a statement that assumes there is no significant difference or relationship between two variables in a population, or that any observed difference or relationship is due to chance or sampling error. It is usually denoted by "H0" and is used in statistical hypothesis testing to determine whether there is evidence to support an alternative hypothesis.

In the given question,

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level would be:

H0: The true mean score improvement on the outcomes assessment test is equal to or less than 3%.

This hypothesis assumes that there is no significant improvement in the mean score on the outcomes assessment test as a result of the review course. The alternative hypothesis would be:

Ha: The true mean score improvement on the outcomes assessment test is greater than 3%.

This hypothesis assumes that there is a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

To test these hypotheses, we would use a one-tailed t-test with a significance level of 0.05 and calculate the t-value and p-value based on the sample data. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is no evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

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Answer: The answer is

X = 1488/35

Step-by-step explanation:

Answer:

9 or 50/9

Step-by-step explanation:

If we are going of the data 9 of them should have blue eyes.
100/2=50
18/2=9

Based on the information, the data table can be represented as follows:
```

Wins                 No Clear  Winner   Totals
Initiator Loses     18           14             32
Fight                    24          75            99
No Fight              15           104           119
Totals                  57           193          250
```

Here's a breakdown of the data:
1. Initiator Loses:
  - 18 wins
  - 14 no clear winner
  - 32 total outcomes
2. Fight:
  - 24 wins
  - 75 no clear winner
  - 99 total outcomes
3. No Fight:
  - 15 wins
  - 104 no clear winner
  - 119 total outcomes
4. Totals:
  - 57 total wins
  - 193 total no clear winner
  - 250 total outcomes
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The equation that represents how much will be in the account after 7 years is f(x) = 5500 * (1.028)⁷

From the question, we have the following parameters that can be used in our computation:

The equation that represents how much will be in the account after 7 years is represented as

f(x) = P * (1 + r)ˣ

Where

P = 5500

r = 2.8% =

Substitute the known values in the above equation, so, we have the following representation

f(x) = 5500 * (1 + 2.8%)ˣ

Evaluate the sum

f(x) = 5500 * (1.028)ˣ

After 7 years, we have

f(x) = 5500 * (1.028)⁷

Hence, the equation is f(x) = 5500 * (1.028)⁷

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Any normal distribution is approximately 99.7% likely to have data that falls within 3 standard deviations of the mean.

This means that the vast majority of data points in a normal distribution will be clustered around the mean and within a predictable range of values. Standard deviations are a useful tool for understanding the spread of data in a normal distribution and for making predictions about where new data points are likely to fall.

In a normal distribution, approximately 99.7% of the data observed lies within 3 standard deviations of the mean.

The normal distribution, commonly referred to as the Gaussian distribution, is a probability distribution that is frequently used in statistics to characterise real-world phenomena that have a propensity to gather around a central value with a distinctive shape.

With the mean, median, and mode all being equal and situated in the centre of the curve, a normal distribution has a bell-shaped shape and is symmetrical. The distribution's spread is determined by the standard deviation.

A normal distribution is observed in many natural phenomena, including human height, IQ scores, and measurement errors. The central limit theorem further asserts that the distribution of the sum of a large number of independent random variables with finite mean and variance is often normal.

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Orla needs to sample at least 139 people from the population to obtain a 95-percent confidence level estimate of the proportion of people who enjoy the new flavor with a margin of error of 0.07.

To calculate the smallest sample size required, we need to use the formula:

n = (Z^2 * p * q) / E^2

where:

n = sample size
Z = the Z-score for the desired confidence level (95% in this case)
p = estimated proportion of the population who enjoy the new flavor
q = 1 - p
E = margin of error (0.07 in this case)

Since we do not have any information on the estimated proportion p, we will assume a worst-case scenario of p = 0.5 (which means that we have no idea whether the population likes the new flavor or not). Using this value, we can calculate the smallest sample size required as follows:

n = (1.96^2 * 0.5 * 0.5) / 0.07^2
n = 138.2979

We need to round up to the nearest integer, so the smallest sample size required is 139.

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Using Taylor series, the approximation P3(1.2) = 0.77083. Error R3(1.2) < 0.000235. Thus, P3(1.2) - |R3(1.2)| = 0.770599, within 0.001 of f(1.2).

In part C, we found the third-order Taylor polynomial for f about x=1 to be P3(x) = 1 - 1/2(x-1) + 1/8[tex](x-1)^2[/tex]- 1/48[tex](x-1)^3[/tex].

To show that this approximation is within 0.001 of the exact value of f(1.2), we need to estimate the error using the remainder term. The remainder term for the third-order Taylor polynomial is given by R3(x) = f(x) - P3(x) = (1/4!)[tex](x-1)^4[/tex]f⁴(c), where c is some number between 1 and x.

Using the given formula for fⁿ(1), we can compute f⁴(c) = (-1)³(3!)/2⁴ = -3/16. Thus, we have R3(1.2) = (1/4!)[tex](0.2)^4[/tex](-3/16) = -0.000234375.

Since R3(1.2) is negative, we know that P3(1.2) > f(1.2), so our approximation is too high. Therefore, to ensure that our approximation is within 0.001 of the exact value of f(1.2), we need to subtract the error bound from our approximation. That is, we need to use P3(1.2) - |R3(1.2)| as our estimate. Substituting values, we get P3(1.2) - |R3(1.2)| = 0.770833333 - 0.000234375 = 0.770598958.

Since |f(1.2) - P3(1.2)| < |R3(1.2)|, we can conclude that our approximation is within 0.001 of the exact value of f(1.2).

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Answer:

Step-by-step explanation:

A=6s² is your formula

s=1/4  plug this into your cube formula

A=6(1/4)²

  =6(1/16)

  =3/8 in³

Answer:

a)

[tex] \sin(x) - \cos(x) = 0[/tex]

[tex] \sqrt{2} \sin(x - \frac{\pi}{4} ) = 0[/tex]

[tex]x - \frac{\pi}{4} = 0[/tex]

[tex]x = \frac{\pi}{4} \: radians = 45 \: degrees[/tex]

x = 45°

b)

[tex] \sin(x) - \cos(x) = .5[/tex]

[tex] \sqrt{2} \sin(x - \frac{\pi}{4} ) = \frac{1}{2} [/tex]

[tex] \sin(x - \frac{\pi}{4} ) = \frac{ \sqrt{2} }{4} [/tex]

[tex]x - \frac{\pi}{4} = {sin}^{ - 1} \frac{ \sqrt{2} }{4} [/tex]

[tex]x = \frac{\pi}{4} + {sin}^{ - 1} \frac{ \sqrt{2} }{4} =1.15 \: radians = 65.70 \: degrees[/tex]

x = about 65.70°

The linearization l(x) of the function at a is -(x-π/2).

We have, f(x) = cos (x), x =π/22

Now, differentiating on both sides

f'(x) = -sin (x)

At x=π/2

y = f(π/2) = cos (π/2) = cos (90°)= 0

and f'(π/2) = -sin(π/2) = -sin (90°) = -1

Now, The linearization is the tangent line

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

     = 0 + (-1)(x-π/2)

Therefore, the linearization l(x) of the function at a is -(x-π/2)

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For $23, you can rent a computer at the local copy center for approximately 25 minutes and 27 seconds.

A declarative sentence that can be either true or false, but not both, is called a statement.

Let's call the amount of time that can be rented "t" (in minutes).

We know that there is a $9 setup charge and an additional $5.50 for every 10 minutes, so the total cost C (in dollars) can be expressed as:

C = 9 + 5.5 × (t / 10)

We want to find out how much time can be rented for $23, so we can set C equal to 23 and solve for t:

23 = 9 + 5.5 × (t / 10)

Subtracting 9 from both sides, we get:

14 = 5.5 × (t / 10)

Multiplying both sides by 10/5.5, we get:

t = 25.45 minutes

So, for $23, you can rent a computer at the local copy center for approximately 25 minutes and 27 seconds.

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In linear equation, The maximum height reached by the rocket, to the nearest tenth of a foot is 256 feet.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

y=-16t²+ 112t + 60

dy/dt = -16(2t)+ 112

Substitute the value of dy/dt as 0, to get the value of t,

0 = -32t + 112

112  = 32t

t = 3.5

Substitute the value of t in the equation to get the maximum height,

y=-16t²+ 112t + 60

y=-16(3.5²)+ 112(3.5)+60

y = 256 feet

Hence, the maximum height reached by the rocket, to the nearest tenth of a foot is 256 feet.

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Answer:

number 11 is kayaking

Step-by-step explanation:

add all of them up which will give you 100.Then do 360÷100=3.6

3.6×15=54

EASY DUBS

Answer:

(11) The central angle of a sector in a circle graph can be calculated by finding the ratio of the number of campers who chose that activity to the total number of campers, and then multiplying by 360 degrees.

For paddleboarding, the ratio is:

54 (number of campers who chose paddleboarding) / 100 (total number of campers) = 0.54

The central angle for paddleboarding is:

0.54 x 360 degrees = 194.4 degrees

Therefore, paddleboarding does not have a central angle of 54 degrees.

For kayaking, the ratio is:

15 / 100 = 0.15

The central angle for kayaking is:

0.15 x 360 degrees = 54 degrees

Therefore, the answer is Kayaking.

(12) Assuming that the proportion of principals in the exhibit room is representative of the entire conference, we can estimate the number of principals in attendance at the conference as follows:

The proportion of teachers in the exhibit room is 18/70 = 0.2571

The proportion of principals in the exhibit room is 52/70 = 0.7429

If we assume these proportions hold for the entire conference, then we can estimate the number of principals in attendance as:

(0.7429)(750) = 557.175

Therefore, we can predict that there were about 557 principals in attendance at the conference. Answer: There were about 557 principals in attendance.

(13) Out of 225 students, 27 prefer cookies.

To predict the number of cookies the college will need, we can use proportions.

Let x be the total number of students in the college who prefer cookies. Then, we can set up the following proportion:

27/225 = x/4000

Solving for x, we get:

x = (27/225) * 4000

x = 480

Therefore, the best prediction about the number of cookies the college will need is that it will have about 480 students who prefer cookies.

The answer is: The college will have about 480 students who prefer cookies.

(14) bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44, is the correct way to display the given data.

(15) To determine which bus typically has the faster travel time, we need to compare the measures of center (mean and median) for both data sets.

For Bus 47, the median is the middle value when the data is arranged in order, which is 14 minutes. The mean can be found by summing all the travel times and dividing by the total number of students:

(4+6+10+10+12+12+16+16+16+18+22+22+22+28+28) / 15 = 16.13 minutes (rounded to the nearest hundredth)

For Bus 18, the median is the middle value when the data is arranged in order, which is 12 minutes. The mean can be found by summing all the travel times and dividing by the total number of students:

(6+6+8+9+10+10+12+12+14+14+16+16+18+20+22) / 15 = 12.27 minutes (rounded to the nearest hundredth)

Comparing the measures of center, we see that Bus 47 has a higher mean and median, indicating that it typically has a longer travel time than Bus 18. Therefore, the answer is: Bus 18, with a median of 12.

A sequence of transformations maps ∆ABC to ∆A′B′C.

The correct answer that can be used to describe the drop down menu that we have here are:

A sequence of transformations maps ∆ABC to ∆A′B′C.

The sequence of transformations that maps AABC to AABC is a rotation 90º clockwise about the origin followed by a reflection across the line y = x

What is a transformation in mathematics?

This is the term that is used to describe the various ways that the shape of a geometric figure are known to be manipulated. This is done in terms of its position, lines and its point. The original position of the image is what is called the pre image.

The four types of transformation that we have are called the

Therefore, A sequence of transformations maps ∆ABC to ∆A′B′C.

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To find the median, we need to first arrange the data set in order:

13, 14, 19, 24, 44

The median is the middle number, which is 19.

To find the mean, we add up all the numbers and divide by the total number of numbers:

(13 + 14 + 19 + 24 + 44) / 5 = 22

Therefore, the median is 19 and the mean is 22.

~~~Harsha~~~

Answer:

19 and 22

Step-by-step explanation:

To find the median, we need to first put the numbers in order from least to greatest:

13, 14, 19, 24, 44

There are five numbers in the data set, and the middle number is 19. Therefore, the median is 19.

To find the mean, we add up all the numbers and divide by the total number of numbers:

(24 + 14 + 13 + 19 + 44) ÷ 5 = 22

Therefore, the mean is 22.

The prerequisite for a required course is that students must have taken either course A or course B. By the time they are​ juniors, 57​% of the students have taken course​ A, 29% have had course​ B, and 14​% have done both. ​

a) 28% of juniors are not eligible.

​b) The probability that a junior who has taken course A has also taken course B is 24.6%

a) To find the percentage of juniors who are ineligible for the course, we need to find the percentage of juniors who have not taken either course A or course B.
First, we can find the percentage of juniors who have taken both courses:
57% (who have taken course A) + 29% (who have taken course B) - 14% (who have taken both) = 72%
So, 72% of juniors have taken either course A or course B.
To find the percentage of juniors who are ineligible, we can subtract this from 100%:
100% - 72% = 28%
Therefore, 28% of juniors are ineligible for the course.
b) To find the probability that a junior who has taken course A has also taken course B, we need to use the information given about the percentage of students who have taken both courses.
Out of the 57% of juniors who have taken course A, 14% have also taken course B. So, the probability that a junior who has taken course A has also taken course B is:
14% / 57% = 0.246 or 24.6% (rounded to one decimal place)
Therefore, the probability that a junior who has taken course A has also taken course B is 24.6%.

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The result after the evaluation of definite integral is -12 + 4π, under the given condition that  [tex]I = \int\limits^0_4 (2+\sqrt{16} -x^{2})dx[/tex]needs to be  interpreted concerning the known areas.

The given definite integral  [tex]I = \int\limits^0_4 (2+\sqrt{16} -x^{2})dx[/tex]could be placed as the difference between two areas
The area under the curve of the function (2+√16-x²) from x=0 to x=-4
The area of a rectangle with base 4 and height 2.

The area under the curve can be evaluated by finding the area of a quarter circle with radius 4 and subtracting it from the area of a triangle with base 4 and height 2.
The quarter circle has an area of πr²/4 = π(4)²/4 = 4π
The triangle has an area of (1/2)(4)(2) = 4.
Therefore, the area under the curve is 4π - 4.
The area of a rectangle with base 4 and height 2 is simply 8.

Now,
[tex]I = \int\limits^0_4 (2+\sqrt{16} -x^{2})dx[/tex]
= (4π - 4) - 8
= -12 + 4π
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The appropriate appendix table or technology to answer this question would be a chart or graph showing the annual cost of attending private and public colleges.

Technology is the application of scientific knowledge for practical purposes, especially in industry. Technology can be used to create new products, processes, and services, improve existing ones, optimize efficiency, and solve problems. It includes both hardware and software components, such as computers, communication networks, robotics, and artificial intelligence, as well as the knowledge and skills to use these tools. Technology has the potential to improve lives, increase productivity, and enable more efficient use of resources. Despite the potential benefits, technology can also create ethical, legal, and economic challenges.

This would allow for a visual comparison of the data, making it easier to interpret the results. Additionally, a chart or graph would make it easier to identify any trends or patterns in the data.

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Convenience sampling is likely to get the largest number of subjects in the shortest period of time, as it involves selecting individuals who are readily available and willing to participate.

Option b. Convenience sampling is correct.

However, it may not necessarily provide a representative sample and may introduce bias into the results.

Random sampling, on the other hand, is the most reliable method of obtaining a representative sample, but may take longer to recruit participants.

Cluster sampling and network or snowball sampling can also be effective methods for obtaining a large sample, depending on the research question and available resources.

Convenience sampling is correct.

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a)The only value of p for which lim f(x) exists is p = 1.b) The limit of f(x) doesnt exist.

(a)We have given the equation f(x) = 24 – 24 cos(2x) – 48x^2. To find the value of the constant p for which lim f(x) exists, we need to simplify f(x) and check the left and right-hand limits as x approaches 0.

f(x) = 24 – 24 cos(2x) – 48[tex]x^{2}[/tex]

= 24 (1 – cos(2x)) – 48[tex]x^{2}[/tex]

= 48 [tex]sin^{2} x^{}[/tex] – 48[tex]x^{2}[/tex]

Now, as x approaches 0, sin(x) ~ x. So, we can replace [tex]sin^{2} x^{}[/tex] with [tex]x^{2}[/tex] in the above expression.

f(x) = 48 [tex]sin^{2} x[/tex] – 48[tex]x^{2}[/tex]

= 48[tex]x^{2}[/tex] – 48[tex]x^{2}[/tex] = 0

Therefore, the only value of p for which lim f(x) exists is p = 1.

(b) Using p = 1, we have:

lim f(x) = lim [6x sin(6x) + px] / [[tex]x^{3}[/tex]]

= lim [6 sin(6x) + p/[tex]x^{2}[/tex]] / 3[tex]x^{2}[/tex] (Dividing numerator and denominator by [tex]x^{2}[/tex])

= 6 lim sin(6x)/6x + p/3 lim 1/[tex]x^{2}[/tex] (Applying limit rules)

Now, lim sin(6x)/6x = 1 (using the limit definition of derivative)

And lim 1/[tex]x^{2}[/tex] = infinity (as x approaches 0 from both sides)

Therefore, lim f(x) = 6 + infinity = infinity, limit doesn't exist.

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The rate of the area change at the end of 13 seconds is 650π ft2/s.

Given that the radius of the circular ripple increases at a constant rate of 5 ft/s, we can calculate the rate at which the area enclosed by the ripple is increasing. The area of a circle is given by the formula A = πr2, where A is the area and r is the radius.

Since the radius increases at 5 ft/s, after 13 seconds, the radius will be 13 * 5 = 65 ft.

To find the rate of change of the area with respect to time, we can differentiate the area formula with respect to time:

dA/dt = d(πr2)/dt = 2πr(dr/dt)

We are given that dr/dt = 5 ft/s. At the end of 13 seconds, the radius is 65 ft. Plugging these values into the equation, we get:

dA/dt = 2π(65)(5) = 650π ft2/s

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Answer: 2:45

Step-by-step explanation: 90 mins is an hour and 30 mins

The completion of the flowchart proof is given below:

<ABD = <BDC

(alternate angles)

<BAC = <ACD

(alternate angles)

BE= ED

A flowchart proof is a visual representation of an argument or deduction, wherein all of its components are displayed as nodes formed in shapes such as diamonds and rectangles.

Connected by directional arrows to demonstrate the logic behind them, these symbols offer a simple yet effective way to comprehend the intricate complexities associated with any given inference. This method serves to exhibit transparent and thorough methods for deciphering complex proofs.

Alternate angles are two angles that are not next to each other and are created by the intersection of two lines, situated on different sides of the transversal. When the lines are parallel, they have the same distances.

The completion of the flowchart proof is given below:

<ABD = <BDC

(alternate angles)

<BAC = <ACD

(alternate angles)

BE= ED

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Answer:

The answer for

a)35

b)35

Step-by-step explanation:

a)34.9961----->2d.p

=35=to 2.d.p

b)34.9961------>the nearest tenth

=35