in the given figure decide when line 1 and line 2 are parrelel or not​

The dimensions of the garden are not the same as they were when using the scale of 1 cm : 8 m.

Dimension is a measure of spatial extent. It can refer to either physical size or abstract concepts such as magnitude, capacity, or scope. For example, two-dimensional refers to an object that has length and width, while three-dimensional refers to an object that has length, width, and depth. Dimension is an important concept in mathematics, particularly in geometry and topology, as it allows us to classify and measure the size and shape of objects. In physics, dimension is used to describe the properties of space-time, including length, width, height, and time. Dimension is also used in many other fields, including art, architecture, engineering, and psychology.

Using a scale of 1 cm : 16 m, the dimensions of the garden would be 64 cm by 96 cm.
This is double the dimensions of the garden when using a scale of 1 cm : 8 m, which was 32 cm by 48 cm.
Therefore, the dimensions of the garden are not the same as they were when using the scale of 1 cm : 8 m.

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The function f·g(-7) is approximately equal to -55/7.

Given are two functions, f(x) = x²+6 and g(x) = (x+8)/x, we need to find f·g(-7),

To find the value of f·g(-7), we need to first evaluate the functions f(x) and g(x), and then multiply them together at x = -7.

Given:

f(x) = x² + 6

g(x) = (x + 8) / x

Let's evaluate f(-7):

f(-7) = (-7)² + 6

= 49 + 6

= 55

Now, let's evaluate g(-7):

g(-7) = (-7 + 8) / (-7)

= 1 / (-7)

= -1/7

Finally, we can calculate f·g(-7) by multiplying the values we found:

f·g(-7) = f(-7) · g(-7)

= 55 · (-1/7)

= -55/7

Therefore, f·g(-7) is approximately equal to -55/7.

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The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

x² + 5x + 4 = 0

We have given:

x² + 5x + 4 = 0

Comparing the equation with the standard form.

a = 1, b = 5 and c = 4

Substituting it in the formula

D = 5² - 4 × 1 + 4

By further calculation

D = 25 - 16

D = 9,

The quadratic roots are real and distinct

Therefore, the value of b² - 4ac is 9.

Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

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12 Cups of sugar will Quinn need to make 16 pies.

In the given question,

Quinn is baking sweet potato pies.

The table shows the ratio of cups of sugar to number of pies.

Number of Pies = 3                          5                            9

Cups of Sugar   = 1 and one half     2 and one half      4 and one half

We have to find the cups of sugar Quinn will need to make 16 pies.

From the given table we know that,

To make 3 sweet potato pies Quinn needed 1 and one half of cup. We can write it as

3 sweet potato pies = 1 1/2 Cups of sugar..................Equation 1

To make 5 sweet potato pies Quinn needed 2 and one half of cup. We can write it as

5 sweet potato pies = 2 1/2 Cups of sugar..................Equation 2

To make 9 sweet potato pies Quinn needed 4 and one half of cup. We can write it as

9 sweet potato pies = 4 1/2 Cups of sugar..................Equation 3

Since we have to find the cup of sugar needs for making 16 pies.

So as given we can see that when we add Equation 1 and 2.

We get

3 sweet potato pies + 5 sweet potato pies = 1 1/2 Cups of sugar + 4 1/2 Cups of sugar

(3+5) sweet potato pies = (1 1/2 + 4 1/2) Cups of sugar

Firstly we simplify the mixed fraction in fraction

We can convert 1 1/2 in fraction by multiplying 1 by 2 then add the result of multiplication of 1 and 2 by 1.

So we get 1 1/2 = 3/2

Now we convert 4 1/2 is in fraction. We can convert 4 1/2 in fraction by multiplying 4 by 2 then add the result of multiplication of 4 and 2 by 1.

So we get 4 1/2 = 9/2.

So 8 sweet potato pies = (3/2 + 9/2) Cups of sugar

8 sweet potato pies = (3+9)/2 Cups of sugar

8 sweet potato pies = 12/2 Cups of sugar

8 sweet potato pies = 6 Cups of sugar...................Equation 4

Multiply Equation 4 by 2

8×2 sweet potato pies = 6×2 Cups of sugar

16 sweet potato pies = 12 Cups of sugar

Hence, 12 Cups of sugar will Quinn need to make 16 pies.

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It will take 3.2 hours to travel 385.00 kilometers at 75.00 miles per hour

From the question, the speed at which you are traveling is 75.00 miles per hour. To determine how long it will take you to travel 385.00 kilometers,

First, we will convert 385.00 kilometers to miles

1 kilometer = 0.621371 miles

∴ 385.00 kilometer = 385 × 0.621371 miles

385.00 kilometer ≅ 239.228 miles

Now, to determine how long it will take to travel a distance of 239.228 miles at a speed of 75.00 miles per hour

From the formula

\(Speed = \frac{Distance }{Time}\)

∴ \(Time = \frac{Distance}{Speed}\)

But, Distance = 239.228 miles and Speed = 75.00 miles per hour

∴ \(Time = \frac{239.228}{75.00}\)

Time = 3.2 hours

Hence, it will take 3.2 hours to travel 385.00 kilometers at 75.00 miles per hour

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Answer:   B.x^3+4x^2-19x+14 is correct

Step-by-step explanation:

(x + 7)(x2 – 3x + 2)

Multiplying both

x^3-3x^2+2x+7x^2-21x+14

x^3+4x^2-19x+14

After expanding the given equation, the equivalent expression is found to be \(x^3 + 4x^2 -19x +14\)

The correct answer is B

Given expression:

\((x + 7)(x^2 - 3x + 2)\)

To find:

The given expression can be expanded as follows;

\((x + 7)(x^2 - 3x + 2)\\\\remove \ the \ bracket \ by \ multiplying \ through \ with \ "x" \ and \ "7"\\\\x(x^2 - 3x + 2) + 7(x^2 - 3x + 2)\\\\x^3 - 3x^2 + 2x + 7x^2 - 21x+ 14\\\\simplify \ further \ by \ collecting \ similar \ terms \ together\\\\x^3 + (-3x^2 + 7x^2)+ (2x-21x) + 14\\\\x^3 + 4x^2 - 19x+ 14\)

Thus, the equivalent expression of the given equation is \(x^3 + 4x^2 -19x +14\)

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Answer:

its A

Step-by-step explanation: i guessed

Answer:

-35.148

I don't know if you need to round the answer or not

Step-by-step explanation:

Hello there!

\(\sf \longmapsto 1.12 \: \times ( - 2.9)\)

This is a arithmetic expression.We need to find the result of it.

\(\sf \longmapsto12.12 \times ( - 2.9)\)

As (-) * (+) equals to (+),

The new Arithmetic expression will be :-

\(\sf \longmapsto - (12.12 \: \times 2 . 9)\)

Then, Simply multiply :-

\(\sf \longmapsto - (35 .148)\)

Remove the parenthesis:-

\(\sf \longmapsto - 35.148\)

On Converting -35.148 to fraction :-

\(\sf \longmapsto \: - \dfrac{8787}{250} \)

On Mixed fraction:-

\(\sf \longmapsto \: - 35\dfrac{37}{250} \)

______________________________________

Henceforth the answer of the arithmetic expression is :-

\( \boxed{\bf \: - 35.148 \: (approx.)}\)

In Alternate Form:-

\(\boxed{\bigg\{\bf \: - \dfrac{8787}{250} , - 35\dfrac{37}{250}\bigg\}} \)

________________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

Given that x follows a binomial distribution with parameters n = 12 and p = 0.15, we can use the following formulas to find the expected value E(x) and variance Var(x):

E(x) = n * p

Var(x) = n * p * (1 - p)

Substituting n = 12 and p = 0.15, we get:

E(x) = 12 * 0.15 = 1.8

Var(x) = 12 * 0.15 * (1 - 0.15) = 1.53

Therefore, the expected value of x is E(x) = 1.8, and the variance of x is Var(x) = 1.53.

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The rate of bacterial population increase is related to the size of the current population. If there were initially 4,000 people present, there will be 8,000 people present in 60 minutes. The number of bacteria will reach 63,000 after 4 hours.

1. There are 4000 bacteria in the initial population.

2. The number of bacteria doubles to 8000 after 60 minutes.

3. There are 16000 bacteria after two hours.

4. There are 32000 bacteria after three hours.

5. There are 63000 bacteria after 4 hours.

A particular kind of virulent bacteria's rate of growth in a culture is being investigated. It has been noted that the bacterial population's growth rate is related to the quantity present. It is possible to compute that 63,000 bacteria will be present after 4 hours if the starting population of 4000 bacteria quadrupled during the first 60 minutes. The original population can be multiplied by 2 every hour to determine this. The population will double to 8,000 after the first hour. By the end of the second hour, there will be 16,000 people living there. The population will double to 32,000 after the third hour. By the end of the fourth hour, there will be 63,000 people living there. Consequently, there will be 63,000 germs total in the environment after 4 hours. As the population of the bacteria in the culture doubles every hour, this demonstrates their exponential growth rate.

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The correct antiderivative for dy/dx - 1/x^2+1 is option D, In(x^2+1)+C.

The term "anti" in antiderivative refers to the opposite operation of differentiation, which means finding the function whose derivative is given.

The given function's derivative is dy/dx - 1/x^2+1, and option D represents the antiderivative of this function.

Option A is incorrect because it does not have the -1/x^2+1 term, option B is incorrect because it has a 2x term instead of -1/x^2+1, and option C is incorrect because its derivative is 1/(x^2+1) instead of dy/dx - 1/x^2+1.

Hence the antiderivative for dy/dx - 1/x^2+1 is  In(x^2+1)+C.

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The lower limit for the 95%confidence interval for the given mean and standard deviation is equal to 39.03.

As given in the question,

Sample size 'n' = 60

Mean 'μ' = $40.80

Standard deviation 'σ' = $7.00

Using z-score table of normal distribution

z-value for 95%confidence interval = 1.96

Formula used

Confidence interval

= μ ± ( z-value × σ ) /√n

= 40.80 ±  (1.96 × 7)/√60

= 40.80 ± (13.72 /7.75)

= 40.80 ±1.770

Lower limit of the confidence interval is equal to :

40.80 - 1.770 = 39.03

Upper limit of the confidence interval is equal to :

40.80 + 1.770 = 42.57

Therefore, the lower limit for the 95% confidence interval is equal to 39.03.

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The investor's rate of return is given as follows:

A. -2.5%.

The rate of return is obtained applying the proportions in the context of the problem.

An investor purchased 100 shares of stock in a company for $20 per share, hence the total cost of the purchase was of:

20 x 100 = $2000.

One year later, the investor sold all the shares for $1,950, hence the return was of:

1950 - 2000 = -$50.

Then the rate of return is calculated as follows:

-50/2000 = -2.5%.

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Answer:

the possible amounts that he will spend is $29-$15=$14

The probability that a student chosen randomly from the class is a male who does not have an A is 0.52

The given parameters are:

The probability that a student chosen randomly from the class is a male who does not have an A is calculated as:

P = 13/25

Evaluate

P = 0.52

Hence, the probability is 0.52

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False

A p-value of 0.09 does not suggest a statistically significant result leading to a decision to reject the null hypothesis if the Type I error rate (α level) is 0.05. In hypothesis testing, the p-value is compared to the significance level (α) to make a decision.

If the p-value is less than or equal to the significance level (p ≤ α), typically set at 0.05, it suggests strong evidence against the null hypothesis, and we reject the null hypothesis. Conversely, if the p-value is greater than the significance level (p > α), it suggests weak evidence against the null hypothesis, and we fail to reject the null hypothesis.

In this case, with a p-value of 0.09 and a significance level of 0.05, the p-value is greater than the significance level. Therefore, we would fail to reject the null hypothesis. The result is not statistically significant at the chosen significance level of 0.05, and we do not have sufficient evidence to conclude a significant effect or relationship.

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Answer :

is approximately 100 cm ²

Step -by-step explanation

\(r \: = 10 \\ l \: = 21.81 \\ T.S.A \: of a \: cone\: = \pi \times r(r + l)\)

\( \frac{22}{7} \times 10(10 + 21.81) \\ \frac{22}{7} \times 10(31.81) \\ \frac{22}{7} \times 318.1\)

\( \frac{22}{7} \times 318.1 \\ = 999.7 \\ = 100 {cm}^{2} \)

Answer:

Width: 81 m

Length: 93 m

Area: 7,533 m

Perimeter: 348 m

Answer:

93 m is the length of the rectangular garden.

Step-by-step explanation:

Answer:

IH

Hope this helps!

Based on the given data, the professors' grading procedures have different variances. To determine if the difference is statistically significant at the 2% level of significance, we can use a two-sample F-test. The F-statistic is calculated by dividing the larger variance by the smaller variance. In this case, the F-statistic is 2.97. Using a critical value of 5.05, we can reject the null hypothesis that the variances are equal. Thus, the decision is that there is a statistically significant difference in the variance of the professors' grading procedures.

In statistics, variance is a measure of the spread of a distribution. When comparing two variances, we can use a two-sample F-test to determine if they are statistically different. The F-statistic is calculated by dividing the larger variance by the smaller variance. If the calculated F-value is greater than the critical value, we reject the null hypothesis that the variances are equal.

In this case, the professors' grading procedures have different variances, with Professor 1 having a larger variance than Professor 2. Using a two-sample F-test, we determined that the difference in variances is statistically significant at the 2% level of significance. This means that there is strong evidence to suggest that the professors' grading procedures differ in their spread of grades.

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The property of real numbers illustrated by each equation depends on the specific equation. However, some common properties of real numbers include the commutative property, associative property, distributive property, identity property, and inverse property.

The property of real numbers illustrated by each equation depends on the specific equation. However, there are several properties of real numbers that can be applied to equations:

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Answer:

Start with the parent function y=1/x^2

Add 3 to x in the denominator, because the graph is shifted left 3.

Add 1 to the fraction, because the graph is shifted up 1 unit

Step-by-step explanation:It is the answer 100% on assignment

Answer:

Associative property

Step-by-step explanation:

The given property is:

A + (B +  C) = (A + B) + C

which is called "associative property of addition".

Hence, this property is used in the given expression which is "rearranging the parenthesis does not affect the result."

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

x=9

Step-by-step explanation:

AIA's are supplementary 15x+45=180

180-45=130

130/15 = 9

Answer:

This is not a right triangle(No)

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

If you use Pythagorean Theorem, you can determine whether or not these measurements make a right triangle. The hypotanuse is always the longest side, or c, in this equation.

a^2+b^2=c^2

14^2+23^2=25^2

196+529=625

725=625

Obviously, this set of measurements do not make a right triangle. Hope this helped!

The minimum stopping distance is 800 ft.

Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.

Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.

Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(4x+10y=-140\implies 10y=-4x-140\implies y=\cfrac{-4x-140}{10} \\\\\\ y=\cfrac{-4x}{10}-\cfrac{140}{10}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-14\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies {\Large \begin{array}{llll} \cfrac{5}{2} \end{array}}}}\)

The company's upgrade in production machinery, which allows for real-time transmission of data about the fit tolerance for assembled parts of each unit produced, represents an increase in the timeliness and efficiency of data transmission.

Prior to the upgrade, data about the fit tolerance for assembled parts was transmitted at the end of a production run.

This means that the information regarding the quality and precision of the assembled parts was collected and transmitted after the entire production process was completed.

However, with the upgrade in production machinery, the company now has the capability to transmit this data in real-time as the measures are taken during the production process.

The upgrade represents an increase in the timeliness and efficiency of data transmission.

By transmitting the data in real-time, the company can immediately identify any deviations or issues in the fit tolerance of the assembled parts.

This allows for timely interventions and adjustments to be made during the production process, reducing the likelihood of producing defective or substandard units.

Real-time data transmission also enables the company to have a more accurate and up-to-date understanding of the quality of each unit produced. This information can be used for immediate feedback, quality control purposes, and process improvements.

Overall, the upgrade in production machinery enhances the company's ability to monitor and control the fit tolerance of assembled parts, leading to improved production efficiency and product quality.

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You have a total of 3 bills ( 2 one dollar and 1 five dollar)

There are two chances out of the three of getting a one dollar bill.

This is written as 2/3 probability

Answer: 2/3