25.
What is the height of a box if the width is x + 1, the length is x + 3, and the volume is x3 + 6x2 + 11x + 6? (Hint: Recall
that V= (wh.)
Ox+2
none of the answer choices
O-x-2
O x-2
-x+2
0

The derivative of y with respect to x is:

[tex]dy/dx = -4x / (1 - x^4)[/tex]

The chain rule and the quotient rule must be utilized in order to determine the derivative of y with respect to x.:

First, we can rewrite y as follows:

[tex]y = ln[(1 - x^2)/(1 + x^2)][/tex]

Let's define two functions:

[tex]u = 1 - x^2[/tex]

[tex]v = 1 + x^2[/tex]

Then, y can be rewritten in terms of u and v as:

y = ln(u/v)

Now, we can use the chain rule to find the derivative of y with respect to u and v, respectively:

[tex]dy/du = 1/u\\dy/dv = -1/v[/tex]

Using the quotient rule, we can find the derivative of y with respect to x:

[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)[/tex]

[tex]du/dx = -2x\\dv/dx = 2x[/tex]

Substituting in the values we get:

[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)\\= (1/u) * (-2x) + (-1/v) * (2x)\\= -2x/(1 - x^2) - 2x/(1 + x^2)\\= -4x / (1 - x^4)[/tex]

Therefore, the derivative of y with respect to x is:

[tex]dy/dx = -4x / (1 - x^4)[/tex]

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Answer:

-1.82

Step-by-step explanation:

It won't let me write the explanation for some reason. I'll put it in the comments below

Answer:

Plot the points on the graphing calculator, and then determine the linear regression equation: y = -.7222x + 7.2111

The closest equation is A.

Rick is more likely to select a large egg. Jens probability for a large egg is87.5 ricks is 90.7

Probability is a fundamental concept that gauges the plausibility of an event taking place. It is expressed numerically within the range of 0 to 1, with values corresponding to complete impossibility and absolute certainty respectively.

When probability values take on an exact midpoint value such as 0.5, they indicate equal probabilities for both possible outcomes. Experts use probability models before making significant decisions in fields such as science, engineering, finance, and speculative markets like gambling.

The study of these apprehension methods and their application form the foundation of probability theory, which helps analyze chance events' rules and guidelines.

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The time it would take for the trains to pass each other, would be 58.54 minutes.

The trains were initially 200 km apart and so we need to find the time till they pass each other, with the speeds they are currently going at.

To find this time, we first need to find the combined speeds of the trains to be :

= 96 + 109

= 205 km / h

With the combined speed, the time till they pass each other would be:

= Distance between trains / Combined speed

= 200 / 205

= 58. 54 minutes

= 0. 98 hours

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The time it would take for the trains to pass each other, would be 58.54 minutes.

The trains were initially 200 km apart and so we need to find the time till they pass each other, with the speeds they are currently going at.

To find this time, we first need to find the combined speeds of the trains to be :

= 96 + 109

= 205 km / h

With the combined speed, the time till they pass each other would be:

= Distance between trains / Combined speed

= 200 / 205

= 58. 54 minutes

= 0. 98 hours

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Answer:

∠AGB or ∠EGD.

Step-by-step explanation:

∠AGB & ∠EGD make a straight line with ∠BGD which means they're supplementary.

Answer: ∠BGA

Step-by-step explanation:

Starting Angle: ∠BGD

Supplement: ∠BGA

Answer:

12 is the answer

Step by step explanation

to get answer move all terms not containing x to the right side of the equation

Answer:

Yes, 222 is an outlier

Step-by-step explanation:

{222, 346, 346, 435, 435, 505, 667, 667, 667, 779, 844}

Q1 = 435

Q3 = 667

IQR = Q3 - Q1 = 232

222 is below Q1 - 1.5*IQR (104)

Answer:

the maximal height is 14.75 units of distance.

Step-by-step explanation:

We want to find the maximum height of the function

h(t) = -16*t^2 + 24*t + 5

In order to find the maximum, we need to find the value of t where the derivate of h(t) is equal to zero, then we evaluate our original function in that time.

The derivate of h(t) (or the vertical velocity) is:

h'(t) = 2*(-16)*t + 24 = -32*t + 24

we want to find the value of such:

0 = -32*t +24

32*t = 24

t = 24/32 = 0.75

Now we evaluate our height function in that value.

h(0.75) = -16*0.75^2 + 25*0.75 + 5 = 14.75 units

linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating.

By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.

What is Equation?
An equation is a mathematical statement that states the equality of two expressions. It is made up of two parts—the left side and the right side—that are separated by an equal sign (=). The left side of an equation is made up of terms, which are numbers and/or variables, and the right side is made up of a single number or variable. Equations are used to solve for unknown values in mathematics, science, and engineering.

The best predicted price of a diamond with a weight of 1.6 carats can be found by using a linear regression equation. This equation uses the paired carat weight (x) and the price (y) data to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the carat weight increases. The equation can then be used to calculate the predicted price of a diamond with a weight of 1.6 carats.

The best predicted price of a diamond with a color rating of 3 can be found by using the paired color (x) and the price (y) data. Using the data, a linear regression equation can be used to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the color rating increases. The equation can then be used to calculate the predicted price of a diamond with a color rating of 3.

In conclusion, linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating. By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.

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Answer:

y = 2x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = 2 and y- intercept c = 1 , then

y = 2x + 1 ← equation of line

The cost of the materials for the cheapest container is when width = 1.5 m

Given data ,

Let's use "w" metres to represent the rectangular storage container's width. The length would be "2w" metres since the base's length is twice as long as its width.

The container's height is indicated by the letter "h" metres.

Volume is determined by the following formula:

20 = (2w)(w)(h) 20 = 2w²h

The equation may be rearranged to represent "h" in terms of "w":

h = 20 / (2w²)

The container's "w" and "h" surface area is the next item to discuss. The surface area would be made up of the base and the four sides as the container has an open top.

We are given that the cost of material for the base is $20 per square meter and the cost of material for the sides is $3 per square meter

Cost of base material = 20 x 2w² = 40w² dollars

Cost of side material = 3 x 4wh = 12wh dollars

Total cost of material = Cost of base material + Cost of side material = 40w² + 12wh dollars

Now we can substitute the expression for "h" that we derived earlier:

Total cost of material = 40w^2 + 12w(20 / (2w²)) = 40w² + 120 / w

To find the value of "w" that minimizes the cost of material, we can take the derivative of the total cost of material with respect to "w" and set it equal to zero, then solve for "w":

d/dw (40w² + 120 / w) = 0

80w - 120 / w² = 0

On multiplying by w² on both sides , we get

80w = 120

Divide by 80 on both sides , we get

w = 3/4 m

Hence , the width of the rectangular box is w = 1.5 meter

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Answer:

the Indian cricket team played 13 matches after the first two weeks.

Step-by-step explanation:

Let's assume that the Indian cricket team played x matches after the first two weeks.

We know that the team won 50% of the matches played in the first two weeks. So, out of the 6 matches played in the first two weeks, they won 0.5*6 = 3 matches.

We also know that at the end of the series, their success rate was 75%. This means that out of the total number of matches played in the entire series, they won 75% of them. Let's say the total number of matches played in the series is y. Then, we can write:

Number of matches won = 0.5*6 + x (matches won in the first two weeks + matches won after the first two weeks)

Total number of matches played = 6 + x (matches played in the first two weeks + matches played after the first two weeks)

According to the given information, the success rate at the end of the series was 75%. So we can write:

Number of matches won / Total number of matches played = 75/100

Substituting the values, we get:

(0.5*6 + x) / (6 + x) = 75/100

Simplifying this equation, we get:

12 + 4x = 25 + 3x

x = 13

Therefore, the Indian cricket team played 13 matches after the first two weeks.

Answer:

width*2 +length *2

Step-by-step explanation:

Answer:

The best measure of central tendency to use in a set of data depends on the characteristics of the data and the specific objective of the analysis. Let's examine the given data set: 12, 8, 15, 45, 7, 13.

Mean: The mean, also known as the average, is calculated by summing up all the values in the data set and dividing by the total number of values. The mean is sensitive to extreme values and can be influenced by outliers. In this case, the mean is calculated as (12 + 8 + 15 + 45 + 7 + 13) / 6 = 100 / 6 ≈ 16.67.

Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. The median is not affected by extreme values and is a good measure to use when there are outliers or when the data is not symmetrically distributed. In this case, when the data set is arranged in ascending order, the median is 13, as it is the middle value.

Mode: The mode is the value that appears most frequently in a data set. It is a useful measure when we want to identify the most common value in the data set. In this case, the mode is not applicable as there are no repeated values in the data set.

Based on the characteristics of the given data set, the median is a good measure to use as it is not affected by extreme values and provides a central value that represents the middle of the data set. The mean may be influenced by the outlier value of 45, and the mode is not applicable in this case. So, the best measure of central tendency to use in this data set would be the median.

The 95% confidence interval for the mean time for all players is given as follows:

Between 7.14 minutes and 10.74 minutes.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 10 - 1 = 9 df, is t = 2.2622.

Inserting the data-set into a calculator, the parameters are given as follows:

[tex]\overline{x} = 8.94, s = 2.52, n = 10[/tex]

Then the lower bound of the interval is given as follows:

8.94 - 2.2622 x 2.52/sqrt(10) = 7.14 minutes.

The upper bound of the interval is given as follows:

8.94 + 2.2622 x 2.52/sqrt(10) = 10.74 minutes.

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The order of a matrix is 2 x 5.

We have,

The order of a matrix is in the form of:

= number of rows x number of columns

Now,

The given matrix has 2 rows.

The given matrix has 5 columns.

Now,

= number of rows x number of columns

= 2 x 5

Thus,

The order of a matrix is 2 x 5.

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Answer: C. 1.87 deaths per 100,000 people

Step-by-step explanation:

To find the fatality rate, we need to divide the number of traffic fatalities by the total population and then multiply by 100,000.

Fatality rate = (Number of traffic fatalities / Total population) x 100,000

Plugging in the values given in the question:

Fatality rate = (19,261 / 103,000,000) x 100,000 = 1.87 deaths per 100,000 people.

Therefore, the correct option is C.

The equations that represent both scenarios are x + y > 100 and 2x + 5y ≥ 350

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

Let x represents the loaves of bread sold, and y represents the loaves of yeast bread sold.

She needs to sell over 100 loaves of bread, hence:

x + y > 100

Also, she needs to make at least $350, hence:

2x + 5y ≥ 350

Plotting both equations gives the graph attached.

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Answers:

a) The equation is  y = 196(0.77)^x

b) The chart is shown below

c) The graph is shown below

================================================

Explanation:

Part (a)

One template of an exponential equation is y = ab^x

In this case

If 23% of the audience leaves, then 77% remains. This is another way to see where b = 0.77 comes from. Exponential decay will have 0 < b < 1.

Therefore, the equation is y = 196(0.77)^x

Other equations are possible.

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

Part (b)

I'll be using LibreOffice spreadsheet to make the table. Any spreadsheet software will do.

Type x into cell A1

Type 0 and 1 into cells A2 and A3 in that order.

Select cells A2 and A3. Pull down the small marker at the bottom right corner. Pull this marker down to cell A12 to get values 2 through 10 (which will be in cells A4 to A12).

Now move to cell B1. Type in y = 196(0.77)^x in this cell.

In cell B2, type in "=ROUND(196*(0.77)^A2)" without quotes. As you can probably guess, the ROUND function will round to the nearest whole number. The calculation 196*(0.77)^A2 computes the result of y = 196*0.77^x when plugging x = 0 which is in cell A2.

Do not forget about the equal sign up front.

After cell B2 is filled in, hit enter. Then pull down the smaller marker at the bottom right corner to cell B12. A bunch of whole numbers should fill in cells B3 to B12

This is what you should get for your table

[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{y} = 196(0.77)^{\text{x}}\\\cline{1-2}0 & 196\\\cline{1-2}1 & 151\\\cline{1-2}2 & 116\\\cline{1-2}3 & 89\\\cline{1-2}4 & 69\\\cline{1-2}5 & 53\\\cline{1-2}6 & 41\\\cline{1-2}7 & 31\\\cline{1-2}8 & 24\\\cline{1-2}9 & 19\\\cline{1-2}10 & 14\\\cline{1-2}\end{array}[/tex]

x = week number

y = viewer count (approximate)

Example calculation:

Plug in x = 5 to get y = 196*0.77^5 = 53.05297 approximately which rounds to y = 53. Therefore, we estimate there would be about 53 people in the audience for week 5.

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

Part (c)

You could use a spreadsheet to make the graph, but I find GeoGebra is more friendly for graphing. But we'll be using the data we just made in the spreadsheet.

Select cells A2 through B12. This is the 11 row by 2 column block of x,y data pairs. Do not select the headers at the top.

Copy that data and paste it into GeoGebra's spreadsheet mode.

Then select that same block of data in GeoGebra. Right-click to go to "create" then to "list of points". It will do as it describes. Eleven points will show up in the graph window. Resize and adjust the window if needed.

I'm using the following window parameters

The graph is shown in the screenshot below.

Answer:

[tex]\textsf{a.} \quad \textsf{Equation:} \;\;\;y=196(0.77)^x[/tex]

b.  See below.

c.  See attachment.

Step-by-step explanation:

We can model the given situation using an exponential decay equation since the weekly change in audience is a constant percentage change.

[tex]\boxed{y=a(1-r)^x}[/tex]

where:

Given the movie started with an audience of 196 people viewing, a = 196.

Given the movie loses 23% of its audience each week, r = 0.23.

As the movie loses a constant percentage of its audience each week, let x be the number of weeks.

Substitute the values of a and r into the formula and simplify:

[tex]y=196(1-0.23)^x[/tex]

[tex]y=196(0.77)^x[/tex]

Therefore, the equation that models the given scenario is:

[tex]\boxed{y=196(1-0.23)^x}[/tex]

Create a table for the first ten weeks by substituting the values of x from zero through 10 into the equation. Round each number to the nearest whole number.

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}$Weeks$\;x&$Audience$\;y\\\cline{1-2}\vphantom{\dfrac12}0&196\\\cline{1-2}\vphantom{\dfrac12}1&151\\\cline{1-2}\vphantom{\dfrac12}2&116\\\cline{1-2}\vphantom{\dfrac12}3&89\\\cline{1-2}\vphantom{\dfrac12}4&69\\\cline{1-2}\vphantom{\dfrac12}5&53\\\cline{1-2}\vphantom{\dfrac12}6&41\\\cline{1-2}\vphantom{\dfrac12}7&31\\\cline{1-2}\vphantom{\dfrac12}8&24\\\cline{1-2}\vphantom{\dfrac12}9&19\\\cline{1-2}\vphantom{\dfrac12}10&14\\\cline{1-2}\end{array}[/tex]

The graph of the function is an exponential decay curve, which starts at (0, 196) and approaches zero as x approaches infinity.

The x-axis represents the number of weeks and the y-axis represents the audience size.

Use a scale of x : y = 1 : 10.

Plot the points from the table and draw a smooth curve through them that approaches zero as x approaches infinity.

We define ln(x)=int[(1 , x)(1/t)dt], then (ln(x))’=1/x . Define e^x as the inverse of ln(x) .

Then lim [ln(1+x)/x] =lim 1/(1+x) =1 as x approaches to 0 (using the Hp rule). Let ln(1+y)=x then y=e^x-1 and lim[ln(1+y)/y]=lim[x/e^x-1]=1 as x approaches to 0. then limit[(e^h-1)/h]=1 as h approaches to 0 . We have

lim[(5e^x-5e^(x+h))/3h]=(5/3)lim[(e^x-(e^x)(e^h))/h]=(5/3)e^xlim[(1-e^h))/h]=

-(5/3)e^xlim[(e^h-1))/h]=-(5/3)e^x as h approaches to 0.

Answer:

Step-by-step explanation:

Factoring a square root means that you are finding the closest numbers that multiply together. The easiest square roots are ones that factor directly into squares, such as √100, but more complicated ones involve several square roots, such as √225. Here are the steps to finding the square root using factoring:

   1. Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. For √100, the factors would be √(10 x 10). The factors of √225 would be √(25 x 9).

   2. Separate the factors into their own square roots. Because both factors of √100 are 10, the square root of 100 is 10. For √225, you would separate the factors under their own square root signs, so the formula would be √25 x √9.

  3.  Solve for the individual squares. Next, you would find the squares of each of the individual factors. √25 = 5 and √9 = 3. The remaining formula will look like 5 x 3.

   4. Finish solving the equation. Now that you know what the simplified squares are, you will find that 5 x 3 = 15. So, √225 = 15.

Hope that helps!

Answer: ∠FGE

Step-by-step explanation:

Congruent: Have the same angle measure

Starting Angle: ∠BGC
Angle Of Congruence: ∠FGE

The length of the segment CD given the length of BE is 42 inches

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

Using the proportional ratio from the triangle, we have

CD = 1.5 * BE

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

CD = 1.5 * 28

Evaluate

CD = 42

HEnce, the lengtth is 42 inches

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An equation is y = -12/3 when x = 3, y = -4.

What is equation?

An equation is a mathematical statement that indicates that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find the value of unknown variables that satisfy the given conditions.

If x and y vary inversely, it means that as x increases, y decreases and vice versa. We can write this relationship as:

x × y = k

where k is a constant of proportionality. To find the value of k, we can use the given information.

When x = 3, y = -4:

3 × (-4) = k

k = -12

Now we can substitute k into the equation to get:

x × y = -12

This is the equation relating x and y. To find y when x = 3:

3 × y = -12

y = -12/3

Therefore, when x = 3, y = -12/3.

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An equation is y = -12/3 when x = 3, y = -4.

What is equation?

An equation is a mathematical statement that indicates that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find the value of unknown variables that satisfy the given conditions.

If x and y vary inversely, it means that as x increases, y decreases and vice versa. We can write this relationship as:

x × y = k

where k is a constant of proportionality. To find the value of k, we can use the given information.

When x = 3, y = -4:

3 × (-4) = k

k = -12

Now we can substitute k into the equation to get:

x × y = -12

This is the equation relating x and y. To find y when x = 3:

3 × y = -12

y = -12/3

Therefore, when x = 3, y = -12/3.

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