Solve the quadratic equation by using a numeric approach. 0.02x squared + 0.1 x minus 2 = 0 a. x = 2.3 and x = -29.2 c. x = 5.6 and x = -12.2 b. x = 7.8 and x = -12.8 d. x = 1.3 and x = -22.6 Please select the best answer from the choices provided A B C D

The required sample sizes are given as follows:

a) Previous estimate of 0.52: n = 1839.

b) No previous estimate: n = 1842.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of 0.995, so the critical value is z = 2.575.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For an estimate of 0.52, the parameters are given as follows:

[tex]M = 0.03, \pi = 0.52[/tex]

Hence the sample size is obtained as follows:

[tex]0.03 = 2.575\sqrt{\frac{0.52(0.48)}{n}}[/tex]

[tex]0.03\sqrt{n} = 2.575\sqrt{0.52 \times 0.48}[/tex]

[tex]\sqrt{n} = \frac{2.575\sqrt{0.52 \times 0.48}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\right)^2[/tex]

n = 1839.

Without a previous estimate, the sample size is given as follows:

[tex]0.03 = 2.575\sqrt{\frac{0.5(0.4)}{n}}[/tex]

[tex]0.03\sqrt{n} = 2.575\sqrt{0.5 \times 0.5}[/tex]

[tex]\sqrt{n} = \frac{2.575\sqrt{0.5 \times 0.5}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.5}}{0.03}\right)^2[/tex]

n = 1842.

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In the given situation, one snack bar has 14 carbohydrates.

Let's denote the number of carbs in one snack bar as "x".

From the given information, we can set up a system of two equations:

2x + 3y = 73 (where y is the number of carbs in one glass of milk)

4x + 2y = 86

We can then solve for x by using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and subtract it from the second equation:

4x + 2y = 86

(4x + 6y = 146) (2 times the first equation)

-4y = -60

Dividing both sides by -4, we get:

y = 15

Substituting this value of y into the first equation, we can solve for x:

2x + 3y = 73

2x + 3(15) = 73

2x + 45 = 73

2x = 28

x = 14

Therefore, there are 14 carbs in one snack bar.

Step-by-step explanation:

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of carbohydrates in one snack bar.

Now, we can use the given information to set up a system of equations:

2x + 3y = 73 (where y is the number of carbohydrates in one glass of milk)

2y + 4x = 86

We have two equations and two unknowns, so we can solve for x and y using any method we prefer. Here, we will use the substitution method:

Rearrange the first equation to solve for y: y = (73 - 2x)/3

Substitute this expression for y in the second equation: 2((73 - 2x)/3) + 4x = 86

Simplify: (146 - 4x)/3 + 4x = 86

Multiply both sides by 3 to eliminate the fraction: 146 - 4x + 12x = 258

Simplify: 8x = 112

Solve for x: x = 14

Therefore, one snack bar has 14 carbohydrates.

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In the given situation, one snack bar has 14 carbohydrates.

Let's denote the number of carbs in one snack bar as "x".

From the given information, we can set up a system of two equations:

2x + 3y = 73 (where y is the number of carbs in one glass of milk)

4x + 2y = 86

We can then solve for x by using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and subtract it from the second equation:

4x + 2y = 86

(4x + 6y = 146) (2 times the first equation)

-4y = -60

Dividing both sides by -4, we get:

y = 15

Substituting this value of y into the first equation, we can solve for x:

2x + 3y = 73

2x + 3(15) = 73

2x + 45 = 73

2x = 28

x = 14

Therefore, there are 14 carbs in one snack bar.

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of carbohydrates in one snack bar.

Now, we can use the given information to set up a system of equations:

2x + 3y = 73 (where y is the number of carbohydrates in one glass of milk)

2y + 4x = 86

We have two equations and two unknowns, so we can solve for x and y using any method we prefer. Here, we will use the substitution method:

Rearrange the first equation to solve for y: y = (73 - 2x)/3

Substitute this expression for y in the second equation: 2((73 - 2x)/3) + 4x = 86

Simplify: (146 - 4x)/3 + 4x = 86

Multiply both sides by 3 to eliminate the fraction: 146 - 4x + 12x = 258

Simplify: 8x = 112

Solve for x: x = 14

Therefore, one snack bar has 14 carbohydrates.

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Answer:

i hope this helps

Step-by-step explanation:

Answer: the line will go through (0, -3) and for every x value it will go down one

Step-by-step explanation:

Example: (0, -3), (1, -5), (2, -7)

9 is the equivalent value of x from the given triangle.

The angle bisector theorem is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into.

Applying the rule to solve the given question, we will have:

3x-7/12 = 3x +3/18

Cross multiply

12(3x+3) = 18(3x-7)36x + 36 = 54x - 126

Collect the like terms

36x-54x = -126 - 36

-18x = -162

x = 162/18

x = 9

Hence the value of x from the given figure is 9.

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The First and Fifth statement is correct.

A number which can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The Survey of randomly-selected students on a campus of 1,000 students conducted who preferred coffee to tea.

Here, The sample proportion is found to be 59%.

We have to find out which statement is true.

Since, the sample statement is 59% .

Hence, It is on every 100 students, 59 students prefer coffee over tea.

Thus, The first statement is 590 students must prefer coffee to tea is true.

And, Second statement is Less than 590 students must prefer coffee to tea is false .

And, The third statement is More than 590 students must prefer coffee to tea is also false.

And, The fourth statement is,

The sample proportion which must precisely the entire population’s choice is also wrong because we conduct the survey only on students but population contains adults, child and aged peoples so we can't clearly make a conclusion that it is a entire populations choice. So this statement is also false.

And, The fifth statement is the population proportion is not necessarily equal to the sample proportion is true because from the fourth statement it is clear the above survey is only conducted for the college students so it is not equal for population proportion.

Hence, the First and Fifth statement is correct.

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A survey of randomly-selected students on a campus of 1,000 students asked who preferred coffee to tea. The sample proportion is found to be 59%. Which statement is true? 590 students must prefer coffee to tea. Less than 590 students must prefer coffee to tea. More than 590 students must prefer coffee to tea. The sample proportion must precisely represent the entire population’s choice. The population proportion is not necessarily equal to the sample proportion.

Answer:[tex]\frac{1}{8}[/tex]<[tex]\frac{3}{20}[/tex]

Step-by-step explanation:

As a result, after five years, the business makes $102.10 per hour of work performed by men.

The gains that a company makes are its earnings. They are obtained by deducting revenue from cost of products sold, running costs, and taxes. The creation and ongoing running of a company are primarily motivated by the desire to generate profits. Dividend payments to stockholders can then be made with the earnings.

If the factory earned $80 per man-hour of labor when it opened, and each year earns an additional 5% per man-hour, we can calculate the earnings for any given year using the formula:

E = $80 × (1 + r)ⁿ

where E is the earnings per man-hour, r is the annual rate of increase (5% = 0.05), and n is the number of years since the factory opened.

For example, if we want to find the earnings per man-hour after 3 years, we would plug in n=3:

E = $80 × (1 + 0.05)³

E = $80 × 1.157625

E = $92.61

Therefore, after 3 years, the factory earns $92.61 per man-hour of labor.

Similarly, if we want to find the earnings per man-hour after 5 years, we would plug in n=5:

E = $80 × (1 + 0.05)⁵

E = $80 × 1.276282

E = $102.10

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The correct question is:

A factory earned $80 per man-hour of labor when it opened Each year, the factory earns an additional 5% per man-hour

Fοr Marcus's situatiοn the prοbability value is οbtained as οptiοn B: 15%.

Prοbability is a way tο gauge hοw likely sοmething is tο happen. Many things are difficult tο fοrecast with absοlute cοnfidence. Using it, we can οnly make predictiοns abοut the likelihοοd οf an event happening, οr hοw likely it is. Prοbability can range frοm 0 tο 1, with 0 denοting an impοssibility and 1 denοting a certainty.

Tο find the prοbability that all 3 disks selected will be either all red οr all white, we need tο cοunt the number οf times that this οutcοme οccurs in the simulatiοn, and divide by the tοtal number οf pοssible οutcοmes.

Lοοking at the simulatiοn results, we can see that there are 2 times when all 3 disks are red -

There is alsο 1 time when all 3 disks are white -

Sο the tοtal number οf times that all 3 disks are either all red οr all white is 3.

There are a tοtal οf 20 pοssible οutcοmes in the simulatiοn, since there are 3 chοices fοr each οf the 3 selectiοns, and the selectiοns are made with replacement.

Sο, the prοbability οf selecting 3 disks that are all red οr all white is -

3/20 = 0.15 = 15%

Therefοre, the prοbability value is 15%.

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Marcus has a bag of plastic disks that are red (R) or white (W). He performs a simulation by randomly selecting 3 disks from the bag at one time and recording the results. He then puts the disks back in the bag. His results are shown.

RR   WW  WR  RW  WR

R       R      R    W    W

RW   RW  WW  RW  WW

 R      R     W      R      R

WR   RW  RR  RW  WR

W     W    W   W     W

WR   RW  WR  RW  RR

W     W    W     R     R

Based on the simulation, what is the probability that all 3 disks selected will be either all red or all white?

A. 85%

B. 15%

C. 10%

D. 5%

The minute and second equivalent to [tex]13\frac{5}{10}[/tex] minutes is, 13 minutes 30 seconds.

A clock can be thought of as a circle having 12 steps and we know that circle is 360°,

So, the measure of each integer step of a clock is 30°.

We know, 1 minute is equal to 60 seconds.

Converting the mixed fraction into an improper fraction we have,

[tex]13\frac{5}{10} = \frac{135}{10}[/tex] minutes which is equal to,

[tex]\frac{135}{10}\times60[/tex] seconds.

= 810 seconds.

= 60×13 + 30 seconds.

= 13 minutes 30 seconds.

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The amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Given,

The principal amount P = $30,000

The time period t = 40 years

The rate of interest r = 10%

The number of times compounded in a year n = 1

The compound interest formula can be used to calculate the amount at the end of 40 years.

[tex]A = P(1 + \frac{r}{n})^{nt} = 30000(1 + \frac{0.1}{1})^{1*40}[/tex]  = $1,357,777.67

Therefore the amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.

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The highest temperature on record belongs to California's Death Valley which, in 1913, reached a temperature of 134 degrees Fahrenheit, or 56.7 degrees Celsius, Al Jazeera reports.

The highest temperature in India is found in this city, situated at a height of 178 metres in Rajasthan, the country's biggest state. There, 50 degrees Celsius has been recorded as the greatest temperature to date. Extreme weather may be found in the city both in the summer and the winter.

However, according to the India Meteorological Department, the highest temperature ever recorded in India was 51°C (123.8°F) in the town of Phalodi, Rajasthan on May 19, 2016. It's important to note that temperatures can vary greatly depending on the location and time of year.

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The expression of the length of the arc is  4πb⁵

The circle has a radius of 9b³. An arc subtend an angle at the centre of 80b² degrees. Therefore, the expression for the length of the arc can be solved as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 80b² / 360 × 2 × π × 9b³

length of arc = 144b⁵π / 36

Therefore,

length of arc = 4πb⁵

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Using the arithmetic operations it is obtained that Russell ran 4 miles through his neighborhood every day after school.

To solve this problem, we can use the following equation -

total distance = distance per day x number of days

We know that Russell ran 2 miles around the football field before school every day.

Using multiplication,

Therefore, his total distance for the week from running around the football field is -

2 miles/day × 5 days = 10 miles

We also know that Russell ran a longer route through his neighborhood after school every day.

Let's call the distance of this route "x" miles.

Russell ran this route 5 times during the week, so his total distance from running through his neighborhood is -

Use multiplication,

x miles/day × 5 days = 5x miles

Finally, we know that Russell's total distance for the week was 30 miles. We can set up the equation -

Use addition,

10 miles + 5x miles = 30 miles

Simplifying, we get -

5x miles = 20 miles

x = 4 miles

Therefore, the distance value is obtained as 4 miles.

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Answer:

[tex]c+13 > 78[/tex]

Step-by-step explanation:

[tex]c+13 > 78[/tex]

They must collect over 78 coats. They already have 13 so they must either add that to the amount they still need to collect or subtract it from the number they're trying to beat.

The measure of angle ABC in the triangle inscribed in the circle is given as follows:

m < ABC = 84º.

The sum of the measures of the interior angles of a triangle is of 180º.

The internal angles for the triangle are given as follows:

Then the measure of angle ABC is obtained as follows:

m < ABC + 2 x 48 = 180

m < ABC = 180 - 96

m < ABC = 84º.

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By answering the above question, we may infer that Due to the fact that equation we are multiplying a unit of money by a unit of time, the units for this product are dollars.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

$9/hour multiplied by 8 hours results in:

$8 × $9/hour = $72

Due to the fact that we are multiplying a unit of money by a unit of time, the units for this product are dollars.

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The correct answer is f(m)=5230(1.015)m12.

A function is a self-contained block of code that takes inputs, performs specific operations on those inputs, and produces an output. It is a subprogram that performs a specific task, and helps to break down larger programs into smaller, more manageable pieces. Functions are also reusable, meaning that once a function is written, it can be used over and over again in different places in the program.

This function can be used to represent the student enrollment m months after the study began, as it takes into consideration the number of years (t) represented by the number of months (m) and incorporates it into the equation. The equation multiplies the number of months (m) by 12 to convert it into the number of years (t) used in the original equation, f(t)=5230(1.015)t. This ensures that the correct student enrollment is calculated based on the number of months since the study began.

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The area of the painting, frame and painting, frame are 84 square inches, 174 square inches and 90 square inches. respectively.

Length = 10.5 in

Width = 8 in

Area of the painting = Length × Width

= 10.5 in × 8 in

= 84 square inches

Length = 14.5 in

Width = 12 in

Area of the frame and painting = Length × width

= 14.5 in × 12 in

= 174 square inches

Area of the frame = Area of the frame and painting - Area of the painting

= 174 square inches - 84 square inches

= 90 square inches

In conclusion, the areas are 84 square inches, 174 square inches and 90 square inches. respectively.

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Therefore, the prime trinomials are: 5x² + 4x + 4 and 5x² – 8x + 2.

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using the operations of addition, subtraction, and multiplication. Polynomials are widely used in mathematics and other fields to model a wide range of phenomena and processes. In a polynomial, the variables are usually represented by letters such as x, y, or z, while the coefficients are numbers that multiply the variables. The exponents indicate the power to which each variable is raised.

Here,

To determine which trinomials are prime, we need to factor each trinomial and check if it can be factored further into linear factors with integer coefficients. If a trinomial can be factored further, then it is not prime. On the other hand, if a trinomial cannot be factored further, then it is prime.

Let's factor each trinomial and see which ones are prime:

x² + 11x + 18

This trinomial can be factored into (x + 2)(x + 9), so it is not prime.

x²  + 11x + 18

This trinomial can be factored into (x + 2)(x + 9), so it is not prime.

x² – 3x – 2

This trinomial can be factored into (x – 2)(x + 1), so it is not prime.

x²  – 3x – 2

This trinomial can be factored into (x – 2)(x + 1), so it is not prime.

5x² + 4x + 4

This trinomial cannot be factored further, so it is prime.

5x² – 8x + 2

This trinomial cannot be factored further, so it is prime.

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Answer:

10 points

Step-by-step explanation:

· The team was penalized 30 points in 3 plays.

· Suppose the team was penalized an equal number of yards each play.

To find the supposed amount of points for each penalty, find the unit rate.

Total points ÷ Total Plays

30 ÷ 3

10 points

Answer:

No

Step-by-step explanation:

from Pythagoras theorem, if the triangle is right angled square of largest side should be equal to sum of the squares of smaller two sides. the square of largest side is 18^2= 324  

9^2=81 and the last side is 17^2= 289

81+ 289= 370

This triangle is NOT a right triangle.

Values of the variable are as follows:

V = 20

R = 28

X = 48

We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. The part to whole ratio is one, and the part-to-part ratio is another. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

In the questions given,

The ratios of the sides of the first triangle = 36/18

= 2/1 or 2:1

Now in the second triangle, V/10 = 2/1

⇒ V = 20

In the second question in case of the squares,

the ratios of the sides = 13/13 = 1:1

So, the value of R = 28

Now in the last question,

The ratio of the rectangle's sides is 6:2. = 3/1 o 3:1

So, 144/X = 3/1

⇒ X = 144/3

= 48

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Sarah fell behind 3 meters each lap.

What is Total distance?

Whole distance refers to the actual travel distance between the origin and destination locations of the item.

If Sarah was 15 meters behind Anna when Anna finished the race, and they both ran the same distance, we can divide the total distance by the number of laps they ran to find the distance they ran per lap:

Total distance = 5 laps

Distance per lap = total distance / number of laps = 5 laps / 1 = 5

So Sarah and Anna each ran 5 meters per lap. If Sarah fell behind the same number of meters during each lap, we can use a negative integer to describe the distance she fell behind each lap. The distance she fell behind each lap is:

-3 meters (since 3 meters + 3 meters + 3 meters + 3 meters + 3 meters = 15 meters, which is the distance by which she was behind when Anna finished the race).

Therefore, Sarah fell behind 3 meters each lap.

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Answer:

1 = 36

2. = 32

3 = 10

4.= 21

5. = 14

6 =7456200

Step-by-step explanation:

The decimal calculation for Arturo's is 18.97, Bonnie's is 20.51, Courtney's is 31.42, Dawson's is 35.00.

Measurement is the process of assigning a numerical value to a physical quantity, such as length, weight, temperature, or time. Measurements are used to quantify and compare different aspects of the world around us, and they play a crucial role in many areas of science, engineering, and everyday life.

Measurements can be made using a variety of tools and techniques, ranging from simple rulers and scales to sophisticated scientific instruments. The accuracy and precision of a measurement depend on many factors, including the quality of the measuring instrument, the skill of the person making the measurement, and the conditions under which the measurement is taken.

In order for measurements to be meaningful and useful, they must be expressed in units that are well-defined and universally accepted. The International System of Units (SI) is the most widely used system of units in the world, and it is based on seven fundamental units of measurement, including the meter for length, the kilogram for mass, the second for time, and the kelvin for temperature.

Student           Measurement (yards)    Decimal Calculation

Arturo           6√28                            18.97

Bonnie           8√17                            20.51

Courtney   10π                            31.42

Dawson           3.5√100                    35.00

To calculate the decimals, we can use a calculator to evaluate the square roots and π, and then multiply by the given constant factor, and round the result to the nearest hundredth yard.

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The complete question is:

Answer:

Step-by-step explanation:

Area of semi circle is 1/2 (πr²)

1/2 (3.14×6²)

56.52 unit²

The translation that occurred to the segment is: B. The segment was shifted to the right four units and up five units.

Translation is a transformation in which an object is moved without being rotated, resized or distorted. It involves sliding the object a certain distance in a certain direction, while maintaining its shape and size. The resulting image of the object is congruent to the original object, meaning that they have the same size and shape.

To find the translation that occurred to the segment, we need to calculate the distance between point A and its image A' and the direction in which the translation occurred.

The distance between A and A' is given by:

√((7-3)² + (2-(-3))²) = √(16 + 25) = √(41)

So the segment was translated by a distance of √(41).

To find the direction of the translation, we can subtract the coordinates of A from the coordinates of A':

(A'x - Ax, A'y - Ay) = (7-3, 2-(-3)) = (4, 5)

So the segment was shifted to the right four units and up five units.

Therefore, the correct answer is B. The segment was shifted to the right four units and up five units.

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Answer:

89.974

Step-by-step explanation: