The process of completing the square is done for f(x) = x^2 +10x + 21 to be changed into a vertex form..which step shows Three steps toward this process? why did you pick your answer ?

Answer: $18.6

Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off

The heat of formation of HC₂H₃O₂ can be found using thermochemical data given. The heat of formation is energy released or absorbed in the formation of compound from its elements in their most stable states.

To calculate the heat of formation for acetic acid (HC₂H₃O₂), the following thermochemical data can be used:

- Heat of formation of carbon (C) = -394.36 kJ/mol

- Heat of formation of hydrogen (H) = +218.79 kJ/mol

- Heat of formation of oxygen (O) = -249.21 kJ/mol

The equation for the heat of formation of acetic acid is as follows:

HF(HC₂H₃O₂) = 2 x (heat of formation of hydrogen) + 1 x (heat of formation of carbon) + 3 x (heat of formation of oxygen)

Plugging in the values, we get:

HF(HC₂H₃O₂)= 2 x 218.79 + 1 x -394.36 + 3 x -249.21

Therefore, the heat of formation of acetic acid is -824.93 kJ/mol.

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The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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Answer:

\(\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}\) Whatever this number may be

Step-by-step explanation:

The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus

\(6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0\)

We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:

\(6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94\)

Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:

\((-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})\)

At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual \(\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}\), whatever abomination of a number it might become:

\(\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}\)

At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.

Answer:

3.38

Step-by-step explanation:

first do the multiplication

2×0.81

= 1.62

then the subtraction

5- 1.62= 3.38

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer:

y=-x-2

Step-by-step explanation:

The slope is negative 1 and the y intercept is -2

Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.

The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.

1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.

A

1   4

2   8

3   9

4   5

5   2

6   7

7   7

8   5

9   8

2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.

3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.

4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.

5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.

Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.

In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.

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Answer:

Step-by-step explanation:

x = (0.5,0)

y= (0,-3)

slope = 2

Answer

Taking all the clues given, one by one, and formulating the correct top 10, we have

1) Gateway Arch in St. Tim, Missouri.

2) San Jacinto Monument in La Porte, Texas.

3) Washington Monument in Washington, DC.

4) Perry's Victory and International Peace Memorial in Put-in-Bay, Ohio.

5) Jefferson Davis Memorial in Fairview, Kentucky.

6) Bennington Battle Monument in Bennington, Vermont.

7) Soldiers and Sailors Monument in Indianapolis, Indiana.

8) Pilgrim Monument in Cape Cod, Provincetown, Massachusetts.

9) Bunker Hill Monument in Boston, Massachusetts.

10) High Point Monument in High Point, New Jersey.

The sum of slip is 9 small coffee order, then sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

A hat contains 4 slips of paper labeled as 3,3,6 and 8. One slip is selected randomly and without replacing, another one is selected. The number on the slips are added together.

The probability of getting a sum of 6 (3+3) is,

\(P_(3,3)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(3,3)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(3,3)=\dfrac{2}{12}\\P_(3,3)=\dfrac{1}{6}\)

The probability of getting the sum of 9 (6+3) or (3+6) is,

\(P_(3,6)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,6)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,6)=\dfrac{4}{12}\\P_(3,6)=\dfrac{1}{3}\)

The probability of getting the sum of 9 (6+3) or (3+6) is,

\(P_(3,8)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,8)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,8)=\dfrac{4}{12}\\P_(3,8)=\dfrac{1}{3}\)

The probability of getting a sum of 6 (3+3) is,

\(P_(6,8)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(6,8)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(6,8)=\dfrac{2}{12}\\P_(6,8)=\dfrac{1}{6}\)

There are three size of coffee to order:

Thus, when the sum of slip is 9 small coffee order, if sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.

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Answer:

21.6 $ / h

Step-by-step explanation:

Since it is a raise you'll calculate by multiplying the $ / h by (1 + % / 100)

In this case 1 + % / 100 = 1 + 20 / 100 = 1 + 0.20 = 1.20

1.20 * 18 = 21.6 $ / h

NB.:

If it was a decrease by 20 % => 1 - 20 / 100 = 1 - 0.20 = 0.80

You would multiply the $ by 0.80.

Answer: serbia

Step-by-step explanation:

a) There are 2400 animals on the farm.

b) The number of sheep on the farm is 700.

c) The percentage of rabbits in relation to the total number of animals is 37.5%.

d) The angle that represents the number of pigs is 75 degrees.

a) To determine the total number of animals on the farm, we add up the number of rabbits, sheep, cattle, and pigs:

Total number of animals = 900 (rabbits) + 700 (sheep) + 300 (cattle) + 500 (pigs) = 2400 animals.

b) The number of sheep on the farm is given as 700.

c) To calculate the percentage of rabbits in relation to the total number of animals, we divide the number of rabbits by the total number of animals and multiply by 100:

Percentage of rabbits = (900 / 2400) * 100 = 37.5%.

d) To calculate the angle that represents the number of pigs, we need to find the proportion of the total number of animals that pigs make up, and then convert it to an angle on the pie chart.

Proportion of pigs = 500 / 2400 = 0.2083.

To find the angle in degrees, we multiply the proportion by 360 degrees:

Angle representing pigs = 0.2083 * 360 = 75 degrees.

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Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.

The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.

The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.

Step-by-step explanation:

Therefore, the expected value can be calculated as follows:

(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)

= $0.073

The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.

Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.

References:

Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.

"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Answer:

All of them have intersections with each other, so we can't really say anything from that. But only -3x + 10 has a y-intercept higher than y=0.

So let's just say -3x+10 is different.

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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The approximate population in 2016 is 91, 604 population

The exponential equation representing the statement is \(P=P_0e^t\)

Substituting into the formula will give:

If by 2012 the population had increased to 81,000, then:

81000 =  56000e^12k

81000/56000 = e^12k

1.4464 = e^12k

ln1.4464 = 12k

0.3691 = 12k

k = 0.3690/12

k = 0.03076

Get the prediction of the population in 2016.

\(P = 56000e^{16(0.03076)}\\P=56000e^{0.49213}\\P = 56000(1.6357)\\P = 91,603.70\)

Hence the approximate population in 2016 is 91, 604 population

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The length of FG is approximately 15.3 cm.

To calculate the length of FG using Pythagoras' theorem, we need to find the length of the hypotenuse (FG) of a right triangle. Let's denote the length of FG as x.

According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

\(FG^2 = GH^2 + FH^2\)

Given that GH = 8 cm and FH = 13 cm, we can substitute these values into the equation:

\(x^2 = 8^2 + 13^2\)

\(x^2 = 64 + 169\)

\(x^2\) = 233

To find x, we take the square root of both sides:

x = √233 ≈ 15.26 cm (rounded to 1 decimal place)

Therefore, the length of FG is approximately 15.3 cm.

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Answer:

\(\Large \boxed{\sf 17 \ and \ 18}\)

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

\((x) \times (x+1) =306\)

Solve for x.

Expand brackets.

\(x^2 +x =306\)

Subtract 306 from both sides.

\(x^2 +x -306=306-306\)

\(x^2 +x -306=0\)

Factor left side of the equation.

\((x-17)(x+18)=0\)

Set factors equal to 0.

\(x-17=0\)

\(x=17\)

\(x+18=0\)

\(x=-18\)

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

\((17)+1\)

\(18\)

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

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TYSM!

Answer:

zeros are ±2

Step-by-step explanation:

y = x² - 4

this can be factored into (x+2)(x-2)

if you then set each factor equal to zero you will get zeros of ±2

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

5 mph

Step-by-sep explanation:

To find of out the difference between the speed of the two drivers in miles per hour (not in miles per minute), first, calculate the unit rate or speed of driver 1 using the graph, and driver 2 using the table given.

Unit rate/speed = distance travelled/time = y/x.

Speed of Driver 1/unit rate:

The graph shows 1.5 miles (y) is travelled in 2 minutes (x).

Convert the 2 minutes to hour, you will have:

\( \frac{2}{60} = \frac{1}{30} hr \)

Speed in mph = \( \frac{y}{x} = \frac{1.5}{\frac{1}{30}} = 1.5*\frac{30}{1} = 45 \)

Speed of Driver 1 in mph = 45 mph

Speed of Driver 2/unit rate:

The table shows 2.5 miles (y) is travelled in 3 minutes (x).

Convert the 3 minutes to hour, you will have:

\( \frac{3}{60} = \frac{1}{20} hr \)

Speed in mph = \( \frac{y}{x} = \frac{2.5}{\frac{1}{20}} = 2.5*\frac{20}{1} = 50 \)

Speed of Driver 2 in mph = 50 mph

Difference between the speed of the two drivers = 50 - 45 = 5 mph

Answer:

20° and 70°

Step-by-step explanation:

complimentary angle sum to 90°

let x be the compliment then the angle is 3x + 10 , so

x + 3x + 10 = 90 , that is

4x + 10 = 90 ( subtract 10 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

3x + 10 = 3(20) + 10 = 60 + 10 = 70

the 2 angle measures are 20° and 70°

\( \sf \hookrightarrow \: {(BC)}^{2} + {(AC)}^{2} = {(AB)}^{2} \)

\( \sf \hookrightarrow \: {a}^{2} + {b}^{2} = {c}^{2} \)

\( \sf \hookrightarrow \: {a}^{2} + {(1.98)}^{2} = {(4.63)}^{2} \)

\( \sf \hookrightarrow \: {a}^{2} + (1.98 \times 1.98)= (4.63 \times 4.63) \)

\( \sf \hookrightarrow \: {a}^{2} + (3.9204)= (21.4369)\)

\( \sf \hookrightarrow \: {a}^{2}= (21.4369) - (3.9204)\)

\( \sf \hookrightarrow \: {a}^{2}= 17.5165\)

\( \sf \hookrightarrow \: a= \sqrt{ 17.5165}\)

\( \sf \hookrightarrow \: a= 4.18. Approx\)

Answer: To solve the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

The length of the hypotenuse is c = 4.63.

One of the legs is b = 1.98.

Using the Pythagorean theorem, we can find the length of the other leg, which we'll label as a:

a^2 + b^2 = c^2

a^2 + (1.98)^2 = (4.63)^2

a^2 + 3.9204 = 21.4369

a^2 = 21.4369 - 3.9204

a^2 = 17.5165

Taking the square root of both sides, we find:

a ≈ √17.5165

a ≈ 4.1833

So, the length of the other leg (side a) is approximately 4.1833.

Therefore, the sides of the right triangle are approximately:

Side a ≈ 4.1833

Side b = 1.98

Side c = 4.63

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2