Well exercising Ned walked 1/9 of a mile in one 1/2 of an hour at this rate how far will he have traveled after 1 hour

The question provides that the blades of a ceiling fan rotate around a fixed axis and begin to rotate with a constant angular acceleration such that they are rotating at 10 revolutions per second after a certain period of time.

After 60 turns, the fan will be rotating at 15 revolutions per second.

Solution:The given data is:Initial angular speed, ω₁ = 0 (since they start from rest)

Final angular speed, ω₂ = 15 revolutions/sec

Angular acceleration, α = constant

Number of revolutions for the first part, n₁ = 60

Number of revolutions for the second part, n₂ = (total revolutions) - (n₁) = (60 + 10) - 60 = 10 revolutions

Using the formula for the angular velocity, ω = ω₀ + αt

and the formula for the number of revolutions, n = ωt / 2π

We can find out the time required to reach a final speed of 15 rev/s as follows:15 = 0 + αt ⇒ t = 15 / α

The total time required to reach a speed of 15 rev/s would be the sum of the time required to reach a speed of 10 rev/s and the time required to reach 15 rev/s.t = t₁ + t₂ ⇒ t₂ = t - t₁

We can find the value of t₁ from the formula for the number of revolutions during the first part of the motion as follows:n₁ = ω₁t₁ / 2π0 = αt₁² / 2 + ω₁t₁ / 2π ⇒ t₁ = 0

Using the formula for the number of revolutions, we can find the value of t₂ as follows:n₂ = (ω₁t₂ + 1/2 αt₂²) / 2π ⇒ t₂ = 20/α

The value of α can be found by equating the two formulas for t₂ obtained above:

20/α = 15 / α + t₁⇒ α = 100 / 3 rad/s²

We can now substitute this value in the formulas for t and t₂ to find the times required to reach speeds of 10 and 15 rev/s respectively.t₁ = 0 s, t₂ = 60 / 3 = 20 s

Answer: The time required for the blades of the ceiling fan to rotate with a constant angular acceleration before rotating at 10 revolutions per second is 0 seconds and the time required to reach a speed of 15 revolutions per second is 20 seconds.

To know more about acceleration, visit

https://brainly.com/question/2303856

#SPJ11

Paula made a scale drawing of the auditorium, which is a replica of the actual auditorium, but smaller in size. The scale drawing shows measurements of the actual auditorium at a reduced size.

Paula needs to determine the scale used to draw the auditorium. The scale is the ratio of the lengths of the corresponding sides of the actual auditorium and the scale drawing. We can use the following formula to find out the scale of the drawing:

Scale = (Length of the corresponding side of the actual object) / (Length of the corresponding side of the scale drawing)First, we have to convert 56 feet to inches:1 foot = 12 inches56 feet = 56 x 12 = 672 inchesNow, we can find the scale of the drawing as follows:

Now, we can use the scale to determine the length of other parts of the auditorium. For example, if a door in the auditorium is 32 inches long on the drawing, its actual length would be 32 x 8 = 256 inches or 21.3 feet. Therefore, the missing value in the ratio 3 inches : ____ feet is 2.333 feet. (This is obtained by dividing 84 inches by 36 inches, which is equivalent to 3 feet. Then multiplying the result by 3 inches, which gives 7/12 or 0.5833 feet or 7 inches. This can be written as 2.333 feet.)

To know more about drawing visit:

brainly.com/question/23033135

#SPJ11

The 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

To find the 27th term of an arithmetic sequence, we can use the formula:

[tex]\[a_n = a_1 + (n - 1)d\][/tex]

where [tex]\(a_n\)[/tex] represents the [tex]\(n\)[/tex]th term, [tex]\(a_1\)[/tex] is the first term, [tex]\(d\)[/tex] is the common difference, and [tex]\(n\)[/tex] is the term number.

Given that [tex]\(a_1 = -13\)[/tex] and the common difference [tex]\(d = 4\)[/tex], we will simply substitute these values into the given formula:

[tex]\[a_{27} = -13 + (27 - 1) \cdot 4\][/tex]

Simplifying the equation, we have:

[tex]\[a_{27} = -13 + 26 \cdot 4\][/tex]

Calculating the expression, we get:

[tex]\[a_{27} = -13 + 104\][/tex]

Finally, evaluating the sum, we find:

[tex]\[a_{27} = 91\][/tex]

Therefore, the 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

For more questions on arithmetic sequence:

https://brainly.com/question/6561461

#SPJ8

The mean absolute deviation (MAD) of the data set, rounded to the nearest tenth, is 5.4 bags of caramel corn.

To calculate the mean absolute deviation, we first find the mean of the data set by adding up all the values and dividing by the total number of nights: (16 + 23 + 32 + 24 + 19 + 27 + 18) / 7 = 19.7 bags.

Next, we find the absolute deviation for each night by subtracting the mean from each data point and taking the absolute value of the difference: |16 - 19.7| = 3.7, |23 - 19.7| = 3.3, |32 - 19.7| = 12.3, |24 - 19.7| = 4.3, |19 - 19.7| = 0.7, |27 - 19.7| = 7.3, |18 - 19.7| = 1.7.

We then calculate the average of these absolute deviations by adding them up and dividing by the total number of nights: (3.7 + 3.3 + 12.3 + 4.3 + 0.7 + 7.3 + 1.7) / 7 = 5.4 bags.

Therefore, the mean absolute deviation of this data set is 5.4 bags of caramel corn. This value represents the average distance between each data point and the mean, providing an indication of the variability or dispersion in the number of bags sold each night at the concession stand.

Learn more about mean absolute deviation:

https://brainly.com/question/32035745

#SPJ11

Answer:

I believe it's A

Step-by-step explanation:

The value of the given expression is approximately 71.31.

[tex]$$75 - 12(20 ÷ 2.5) ÷ 26$$[/tex]

The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.

So, we follow the Order of Operations to solve this expression.

Firstly, we will evaluate the parentheses:

[tex]$$20 ÷ 2.5 = 8$$[/tex]

Now, the given expression becomes:

[tex]$$75 - 12 × 8 ÷ 26$$[/tex]

Then, we will evaluate multiplication and division in order from left to right.

12 × 8 = 96

So, the given expression becomes:

[tex]$$75 - 96 ÷ 26$$[/tex]

Evaluating division, we get:

[tex]$$75 - 3.6923$$[/tex]

Now, we will add and subtract from left to right.

[tex]75 − 3.6923 ≈ 71.31[/tex]

Therefore, the value of the given expression is approximately 71.31.

So, the required  is approximately 71.31.

To know more about expression visit:

https://brainly.com/question/28170201

#SPJ11

The selling price of the novel would be Rs 375. The bookseller should sell the novel for Rs 375 to earn a profit of 25%. Profit percentage is a measure of the profit earned as a percentage of the cost price.

In this case, the bookseller earns a profit of 25%. To calculate the selling price, we need to determine the profit earned and add it to the cost price.

To find the profit earned, we multiply the cost price by the profit percentage. In this case, the cost price of the novel is given as Rs 300, and the profit percentage is 25%. To calculate the profit, we multiply Rs 300 by (25/100) or 0.25. The result is Rs 75, indicating that the bookseller earns a profit of Rs 75.

To obtain the selling price, we add the profit to the cost price. In this case, the cost price is Rs 300, and the profit is Rs 75. Adding them together, we get Rs 375 as the selling price of the novel.

To calculate the selling price, we need to determine the profit earned by the bookseller and add it to the cost price.

Given:

Profit percentage = 25%

Cost price of the novel = Rs 300

To calculate the profit, we multiply the cost price by the profit percentage:

Profit = 25% of Rs 300 = (25/100) * 300 = Rs 75

The selling price is obtained by adding the profit to the cost price:

Selling price = Cost price + Profit = Rs 300 + Rs 75 = Rs 375.

Therefore, the selling price of the novel is Rs 375.

Learn more about profit here: brainly.com/question/32381738

#SPJ11

The 11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes.

To find out if Jillian will make the cross country team, we must check if she can run 3 1/2 miles in less than 40 minutes. The time required for Jillian to run one mile is found by dividing 40 minutes by 3.5:40 / 3.5 = 11.43Jillian must complete one mile in 11.43 minutes to be eligible for the cross country team.

Since ,11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

to know more about cross country team visit  :

https://brainly.com/question/31578767

#SPJ11

To identify the beverage that consistently yielded the highest profit according to the Smith's BBQ Report, we need to compare the profit margins of liquor, beer, and wine. By analyzing the profit margins over time, we can determine which beverage consistently had the highest margin, indicating the highest profit.

To determine which beverage consistently yielded the highest profit, we need to analyze the data provided in the Smith's BBQ Report. The report likely includes information on the sales and profits generated from liquor, beer, and wine. By comparing the profit margins of each beverage over a period of time, we can identify the one that consistently yielded the highest profit.

1. Analyzing profit margins: To determine the beverage with the highest profit, we examine the profit margins for liquor, beer, and wine. Profit margin is calculated by subtracting the cost of goods sold (COGS) from the revenue and dividing the result by the revenue. By comparing the profit margins of each beverage, we can identify which one consistently had the highest margin.

For example, if the profit margin for beer is consistently higher than that of liquor and wine across different time periods, it suggests that beer consistently yielded the highest profit. The profit margin analysis would provide insights into the beverage that generated the most profit for Smith's BBQ consistently.

Learn more about liquor : brainly.com/question/29628218

#SPJ11

The cost of a carton of milk is a) $0.35.

To find the cost of a carton of milk, we can set up a system of equations based on the given information.

Let's assume the cost of a hamburger is "h" and the cost of a carton of milk is "m".

From the information given, we can create the following equations:

Equation 1: 2h + 1m = 2.85 (from Monday's purchase)

Equation 2: 3h + 2m = 4.45 (from Tuesday's purchase)

We can solve this system of equations to find the value of "m", the cost of a carton of milk.

Multiplying Equation 1 by 2 and Equation 2 by 1, we can eliminate "h" and solve for "m":

4h + 2m = 5.70

3h + 2m = 4.45

Subtracting Equation 2 from Equation 1, we get:

(4h + 2m) - (3h + 2m) = 5.70 - 4.45

h = 1.25

Now, we can substitute the value of "h" back into Equation 1 or Equation 2 to find the value of "m":

2(1.25) + 1m = 2.85

2.50 + m = 2.85

m = 2.85 - 2.50

m = 0.35

Therefore, the cost of a carton of milk is $0.35.

The correct answer is option a) $0.35.

To learn more about cost here:

https://brainly.com/question/28551452

#SPJ4

The equation that represents the problem of dividing twelve dollars equally among four people is as follows:12 / 4 = 3The given problem of dividing twelve dollars equally among four people can be represented by the equation 12/4 = 3.

Here, 12 represents the total amount of money that is being divided and 4 represents the number of people among whom the money is being divided .In this problem, we divide the total amount of money by the number of people to find out how much money each person will get. As there are four people to divide the money among, we divide the total amount of $12 by 4 to get $3 as the share of each person. Therefore, the equation that represents this problem is 12/4 = 3.

Learn more about dividing here:

https://brainly.com/question/14758494

#SPJ11

There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

To calculate the percent change, we'll use the following formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Let's calculate the percent change for each statistic:

1. Number of people living with the disease:

  Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100

                ≈ (-4.3 million / 31.6 million) * 100

                ≈ -0.136 * 100

                ≈ -13.6%

Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

2. Number of deaths from the disease:

  Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100

                ≈ (-1.2 million / 2.4 million) * 100

                ≈ -0.5 * 100

                ≈ -50%

Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

Learn more about Percent change here

https://brainly.com/question/29002135

#SPJ4

The line of best fit is a straight line that best fits the scattered data points on a scatterplot. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

In this particular case, the equation of the line of best fit is y = -6x + 97, where x represents the number of absences and y represents the final grade.

This means that for every additional absence a student has, their final grade is expected to decrease by 6 points. The y-intercept of 97 means that if a student had zero absences, their predicted final grade would be 97.

It is important to note that the line of best fit is a prediction, and not a definitive statement about the relationship between the variables. While it can provide some insight into the relationship between the number of absences and final grade, there may be other factors that are not taken into account by the model.

Additionally, the equation of the line of best fit is only valid within the range of the data used to create the model. Extrapolating beyond this range may not produce accurate predictions.

Overall, the line of best fit is a useful tool for analyzing relationships between variables, but it should be used with caution and in conjunction with other analyses to get a complete understanding of the relationship between variables.

To know more about straight line visit:

https://brainly.com/question/31693341

#SPJ11

Answer

there's 120 members in total

84 not pensioners

Explaination

36÷30% = 120

70% are not pensioners

so 70% × 120 = 84

or you could minus the pensioners from the total 120-36=84

The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.

Given: Triangle ABC is acute with heights AD, BE, and CF.

To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

1. Let the side lengths of triangle ABC be a, b, and c.

2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.

3. The perimeter of triangle ABC is a + b + c.

4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.

5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.

6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

Learn more about triangles on

https://brainly.com/question/17335144

#SPJ4

In calculus, there are different ways to differentiate the tangent to a curve. The first principle is one of the ways to differentiate the tangent to a curve.

Differentiation is the foundation of calculus, and it's used to find rates of change, maxima and minima, and the behavior of functions in general.The first principle of differentiation.

The first principle is the fundamental approach to finding derivatives, which involves finding the limit of the difference quotient, or f(x + h) – f(x) / h as h approaches zero. This difference quotient represents the slope of the line tangent to the curve at the point (x, f(x)).

The first principle formula for differentiation is given by:lim h → 0 [f(x + h) – f(x) / h]To differentiate the tangent to the curve y = 2x² – 5x + 3 at the point where x = 2 using the first principle, we need to find the slope of the line tangent to the curve at x = 2. We start by finding the equation of the tangent line and then calculate its slope using the first principle.To find the equation of the tangent line, we differentiate the given function, y = 2x² – 5x + 3:dy/dx = 4x – 5At x = 2, dy/dx = 4(2) – 5 = 3.

Thus, the slope of the tangent line at x = 2 is 3.

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y – f(2) = m(x – 2)y – (2(2)² – 5(2) + 3) = 3(x – 2)y – 4 = 3x – 6y = 3x – 2

This is the equation of the tangent line to the curve

y = 2x² – 5x + 3

at the point where x = 2. The slope of the tangent line is 3.

To know more about tangent line  visit:

https://brainly.com/question/23416900

#SPJ11

A polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

A polynomial in standard form with a degree of 6 is written as P(x) = a₆x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀, where a₆ ≠ 0 and a₀, a₁, a₂, a₃, a₄, a₅, and a₆ are coefficients.

To ensure that the polynomial has only complex solutions, we need to make sure that all of its roots are complex numbers.

Complex numbers have the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)).

By factoring the polynomial into linear factors, we can ensure that each factor (x - zᵢ) contributes a complex root.

Here, z₁, z₂, z₃, z₄, z₅, and z₆ represent complex numbers.

Since the polynomial has a degree of 6, we need six complex factors to form the polynomial.

The product of these factors will give us the desired polynomial with complex solutions.

Therefore, the polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

Learn more about Polynomial here:

https://brainly.com/question/11355579

#SPJ11

There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.

Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.

Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.

Learn more about proportion here:- brainly.com/question/31548894

#SPJ11

We can use the formula for compound interest: after 7 years, Ed will have approximately $617.

To determine how much money Ed will have after 7 years of investing $500 at an annual interest rate of 3% compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, P = $500, r = 3% (or 0.03), n = 4 (quarterly compounding), and t = 7. Plugging these values into the formula, we can calculate the final amount:

A = 500(1 + 0.03/4)^(4*7)

Simplifying the equation, we get:

A = 500(1.0075)^(28)

Calculating the expression within the parentheses, we find:

A = 500(1.234)

Finally, we can compute the final amount:

A = $617

Therefore, after 7 years, Ed will have approximately $617.


To learn more about rate click here: brainly.com/question/199664

#SPJ11

The surface area of the cuboid is 324 cm2, the volume of the cuboid is 360 cm3. And the Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)

Solution: Length of cuboid = l = 12cmWidth of cuboid = b = 6cmHeight of cuboid = h = 5cmSurface area of cuboid = 2 (lb + bh + lh)

By substituting the given values of l, b and h, we get:

Surface area of cuboid = 2 (12 × 6 + 6 × 5 + 12 × 5) = 2 (72 + 30 + 60) = 2 × 162 = 324 cm2∴ The surface area of the cuboid is 324 cm2.Length of diagonal of cuboid, d =√l2 + b2 + h2By substituting the given values of l, b and h, we get:d =√12² + 6² + 5²=√144 + 36 + 25=√205=14.317 cm (approx)∴

The length of diagonal of the cuboid is 14.317 cm.

Volume of cuboid = lbh

By substituting the given values of l, b and h, we get:

Volume of cuboid = 12 × 6 × 5 = 360 cm3∴

The volume of the cuboid is 360 cm3.

(2b) Calculation of the area of a kite when its sides are 8cm and 6cm, and its vertical diagonal is 5cm.Given, sides of the kite are 8cm and 6cm respectively. Vertical diagonal of kite = 5cmArea of kite = (Product of diagonals)/2By using Pythagoras theorem on a kite, we have:

Horizontal diagonal of kite, d =√(52 + 42)=√41 = 6.403 cm

Area of kite = (Product of diagonals)/2

By substituting the given values of vertical diagonal and horizontal diagonal, we get:

Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)

Surface area of cuboid = 2 (lb + bh + lh)

Length of diagonal of cuboid, d =√l2 + b2 + h2Volume of cuboid = lbh2b) Area of kite = (Product of diagonals)/2.

To know more about Length of cuboid visit :-

https://brainly.com/question/29424737

#SPJ11

The original cost of the curling iron was approximately $90.82.

Jema had a 45% coupon for a new curling iron, which means she was eligible for a discount of 45% on the original cost of the curling iron. The final price she paid after the discount was $49.95. To find out the original cost of the curling iron, we can use the formula:

Original cost = Final price / (1 - Discount rate)

In this case, since the discount rate is 45%, or 0.45 as a decimal, the formula becomes:

Original cost = $49.95 / (1 - 0.45)

Original cost = $49.95 / 0.55

Original cost ≈ $90.82

Therefore, the original cost of the curling iron was approximately $90.82.

This calculation shows that Jema took advantage of a significant discount on the original cost of the curling iron. By using the coupon, she was able to save around $41.87 on the purchase. This demonstrates the importance of looking for discounts and deals when shopping, as they can help save money and get more value for your purchases.

learn more about original cost here

https://brainly.com/question/7568734

#SPJ11

Kent will earn $553.12 in interest from his 18-month CD with an interest rate of 3.25%.

To calculate the interest earned, we can use the formula: Interest = Principal × Rate × Time. In this case, the principal (amount invested) is $8,500, the interest rate is 3.25% (or 0.0325 as a decimal), and the time is 18 months (or 1.5 years). Plugging in these values into the formula, we get: Interest = $8,500 × 0.0325 × 1.5 = $553.12. Therefore, Kent will earn $553.12 in interest from his CD.

It's important to note that the interest rate is typically expressed as an annual rate. In this case, the interest rate is 3.25%, which means that for a full year, Kent would earn 3.25% of the principal amount. However, since the CD term is 18 months (or 1.5 years), we need to adjust the formula accordingly. By multiplying the principal by the interest rate and the time, we can determine the total interest earned over the given period. In this case, the interest earned is $553.12.

Learn more about interest here:

https://brainly.com/question/8100492

#SPJ11

Tommy walks 2 miles to school each morning, and he sees a billboard every 1/5 of a mile.

To find out how many billboards he sees, we can divide the total distance he walks (2 miles) by the distance between each billboard (1/5 of a mile).

Number of billboards = Total distance / Distance between billboards

= 2 miles / (1/5 mile)

= 2 miles * (5/1)

= 10 billboards

Therefore, Tommy sees 10 billboards each morning.

learn more about:- billboards here

https://brainly.com/question/31623835

#SPJ11

To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.

In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.

To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:

3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 - 3 and one-fifth.

Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:

3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 + 3 and one-fifth.

In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.

To learn more about variable click here:

brainly.com/question/15078630

#SPJ11

To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².

The first step is to substitute the given values into the formula:

29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).

Next, we simplify the equation and distribute the terms:

29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).

After combining like terms, we have:

29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.

Combining similar terms further, we get:

29,946 = 34x² + 40x - 6.

Now, we can rearrange the equation and set it equal to zero:

34x² + 40x - 29,946 = 0.

To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a).

By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.

After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.

To know more about area click here

brainly.com/question/13194650

#SPJ11

The solution to the problem is that Omar has 16 apples and 14 bananas. the first row satisfy the condition that Omar has four times as many apples as bananas.

To solve this problem, we are given that Omar has four times as many apples as bananas and a total of 30 pieces of fruit.

Let's represent the number of apples as 'a' and the number of bananas as 'b'.

We know that a + b = 30, as the total number of fruits is 30.

From the given information, we are also told that Omar has four times as many apples as bananas, which can be expressed as a = 4b.

To find the values of 'a' and 'b', we can use the table provided:

Types of Fruit  | a | b | a + b |

-------------------------------

16 apples and 14 bananas

20 apples and 10 bananas

22 apples and 8 bananas

24 apples and 6 bananas

We can observe that in the first row, a = 16 and b = 14. Let's check if these values satisfy the given conditions.

If we add the number of apples and bananas, we get 16 + 14 = 30, which matches the total number of fruits given.

We can also verify that a = 4b: 16 = 4 * 14.

Therefore, the solution to the problem is that Omar has 16 apples and 14 bananas.

It's worth noting that the other rows in the table represent different combinations of apples and bananas that sum up to 30, but only the values in the first row satisfy the condition that Omar has four times as many apples as bananas.

In conclusion, Omar has 16 apples and 14 bananas, as per the given information and by checking the values in the table.

Learn more about solution here

https://brainly.com/question/24644930

#SPJ11

The equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative. Therefore, if p is less than or equal to 0, then there is no real number x such that x^2 = p.

For example, if p = -1, then the equation x^2 = -1 has no real number solutions. This is because the square of any real number is always non-negative. Therefore, there is no real number x such that x^2 = -1.

However, if p is greater than 0, then there are two real number solutions to the equation x^2 = p. These solutions are x = sqrt(p) and x = -sqrt(p).

For example, if p = 4, then the equation x^2 = 4 has two real number solutions. These solutions are x = 2 and x = -2.

In conclusion, the equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative.

The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.

To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.

1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.

Learn more about measurements here:- brainly.com/question/2107310

#SPJ11

The sum of f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3 is 5x^2 + x + 5, while the difference is x^2 + 5x - 1. These results are obtained by adding and subtracting the corresponding terms of the two functions.



To find the sum and difference of the functions f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3, we add and subtract the corresponding terms.

For the sum, we add the like terms: (3x^2 + 2x^2) + (3x - 2x) + (2 + 3) = 5x^2 + x + 5.

For the difference, we subtract the like terms: (3x^2 - 2x^2) + (3x + 2x) + (2 - 3) = x^2 + 5x - 1.

Therefore, the sum of the functions is given by f(x) + g(x) = 5x^2 + x + 5, and the difference of the functions is given by f(x) - g(x) = x^2 + 5x - 1.

To learn more about sum and difference click here

brainly.com/question/29774937

#SPJ11

A catalytic ozone destruction cycle requires no atomic oxygen and it incorporates the photochemical decomposition of ClONO₂ to Cl and NO₃, and photochemical decomposition of the later to NO and O₂. The overall reaction is NO + O₃ → NO₂ + O₂

In the lower stratosphere, a proposed mechanism for ozone destruction in the late spring over northern latitudes begins with the photochemical decomposition of ClONO₂ to Cl and NO₃. This reaction is catalyzed by sunlight in the lower stratosphere. The photodissociation of NO₃ is the next step in the cycle, and it results in the production of NO and O₂.

The NO then reacts with O₃ in the following reaction: NO + O₃ → NO₂ + O₂The NO₂ that is produced then reacts with atomic oxygen to form NO₃, and the cycle starts again with the photodissociation of ClONO₂. The NO that is produced during the reaction between NO₂ and O₃ can also react with atomic oxygen to form NO₂, which can then go on to form NO₃.However, the catalytic cycle that has been proposed requires no atomic oxygen to be present. The NO that is produced during the reaction between NO₂ and O₃ reacts with more O₃ to form NO₃ and O₂: NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂The NO₃ that is produced in this reaction can then go on to react with more O₃, starting the cycle over again. Thus, the overall reaction for the catalytic ozone destruction cycle is:NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂NO₃ + O₃ → NO + 2O₂The cycle continues as long as the necessary reactants are available.

To know more about catalytic ozone destruction  visit :-

https://brainly.com/question/8108051

#SPJ11