Use the Lagrange Error Bound to give a bound on the error, E₄, when eˣ is ap- proximated by its fourth-degree (n = 4) Taylor polynomial about 0 for 0 ≤ x ≤ 0.9.

If the entrance of the tunnel is modeled by y = -1/18x^2 + 2x - 2 then the height of the tunnel is 16 feet.

The entrance of a tunnel can be modeled by the equation y = -1/18x^2 + 2x - 2, where x and y are measured in feet. To find the height of the tunnel, follow these steps:

1. Determine the vertex of the parabola, which represents the highest point (or the height) of the tunnel.
2. The vertex can be found using the formula: x_vertex = -b / (2a), where a and b are the coefficients in the quadratic equation y = ax^2 + bx + c.

In this case, a = -1/18 and b = 2. So:

x_vertex = -2 / (2 * -1/18) = -2 / (-1/9) = 18

3. Now that we have the x-coordinate of the vertex, we can find the y-coordinate (height) by plugging the x_vertex value into the equation:

y = -1/18(18^2) + 2(18) - 2

4. Calculate the value of y:

y = -1/18(324) + 36 - 2 = -18 + 36 - 2 = 16

So, the height of the tunnel is 16 feet.

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Answer:

the answer is A

Step-by-step explanation:

√3 = Irrational

√12 = Irrational

but if

√3 × √ 12 = √36 = 6 = rational

The original height of the candle was approximately 26 inches. Rounded to the nearest inch, it will be 27 inches.

Formula for the surface area of a cylinder:

S = 2πrh + 2πr^2

where S is the surface area, r is the radius, and h is the height.

The radius is 2 inches and that the surface area after burning half the candle is 176 square inches. Substitute this values in the equation for surface area:

176 = 2π(2)(h/2) + 2π(2)^2

Simplifying:

176 = 2πh + 8π

168 = 2πh

h = 168/(2π)

h ≈ 26.75

So the original height of the candle was approximately 26 inches. Rounded to the nearest inch, the original height is 27 inches.

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After solving the cost function, the cost of each small van is $8,500 and the cost of each large van is $15,000.

Let's use the variables x and y to represent the cost of a small van and a large van, respectively.

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

5x + 2y = 72500

2x + 6y = 107000

We can solve for x and y by using any method of linear equations, such as substitution or elimination. Here, we'll use elimination:

Multiplying the first equation by 3 and the second equation by -1, we get:

15x + 6y = 217500

-2x - 6y = -107000

Adding these two equations, we eliminate the y variable:

13x = 110500

Dividing both sides by 13, we get:

x = 8500

Now we can use this value to find y:

5x + 2y = 72500

5(8500) + 2y = 72500

42500 + 2y = 72500

2y = 30000

y = 15000

Therefore, the cost of each small van is $8,500 and the cost of each large van is $15,000.

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The percent error in measuring if the actual length is 4.1 cm and the measured length is 3.9 cm is 4.88%

The error refers to the estimated difference between the measured and actual measurement of an object. Error is mainly of three types systematic errors, random errors, and negligent errors.

Measured length = 3.9

Actual length = 4.1

Error = actual value - measured value

= 4.1 - 3.9

= 0.2

Error percent is the ratio of error to the actual value multiplied by 100

Error percent = [tex]\frac{0.2}{4.1}[/tex] * 100

= 4.88%

Thus, the error percent in the given question comes out to be 4.88%

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To determine how many biscuit packages, pemmican packages, and butter and cocoa packages are needed per day for one person.

Calculating an individual's daily Caloric food requirements based on calorie intake and percentage of calories from each food group requires several pieces of information. The first is the total daily calorie requirement, which varies based on factors such as age, gender, height, weight, and physical activity level.

The second is the percentage of daily calories that should come from each food group, which is determined by dietary guidelines and varies based on factors such as age and gender. Finally, the calorie content of each food item must be known to determine how much of each food is needed to meet daily calorie and nutrient requirements.

Once these factors are known, it is possible to calculate how many biscuit packages, pemmican packages, and butter and cocoa packages are needed per day for one person. However, without knowing the specific calorie content and nutritional value of each food item, it is impossible to provide a specific answer.

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The probability that a senior drives to school is 0.3 or 30%.

To find the indicated probability using the two-way table, we need to locate the row for "senior" and the column for "drive to school" and then find the corresponding cell.

Let's assume that the two-way table shows the number of students who either drive or take the bus to school based on their grade level. We are interested in finding the probability that a student drives to school given that they are a senior.

So, we locate the row for "senior" and the column for "drive to school". Let's say that the cell in the intersection of these two is labeled "30". This means that there are 30 seniors who drive to school.

Next, we need to find the total number of seniors in the sample. Let's say that the total number of seniors in the sample is 100.

To find the probability that a senior drives to school, we divide the number of seniors who drive to school by the total number of seniors in the sample:

P(drive to school | senior) = 30/100 = 0.3 or 30%

Therefore, the probability that a senior drives to school is 0.3 or 30%.

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Answer:

Step-by-step explanation:

Yes , that is correct. The growth factor for the balance in the account at the end of the year is calculated by adding 1 to the annual interest rate, which is expressed as a decimal, and multiplying the result by the balance. This gives the formula:

Ending balance = Beginning balance * (1 + r)

where r is the annual interest rate as a decimal.

The 95 percent confidence interval for the population mean is $65.59 to $74.41.

To calculate a 95% confidence interval for the population mean, we will use the sample mean, population standard deviation, and sample size provided. The formula for the confidence interval is:

CI = X ± (Z * (σ / √n))

Where:
- X is the sample mean, $70.00
- Z is the Z-score for a 95% confidence interval, 1.96
- σ is the population standard deviation, $17.50
- n is the sample size, 60

CI = $70.00 ± (1.96 * ($17.50 / √60))

Calculate the margin of error:

Margin of Error = 1.96 * ($17.50 / √60) ≈ $4.41

Now, calculate the confidence interval:

Lower Limit = $70.00 - $4.41 ≈ $65.59
Upper Limit = $70.00 + $4.41 ≈ $74.41

So, the 95% confidence interval for the population mean is approximately $65.59 to $74.41.

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A smaller MAD indicates less variability in the data set, while a larger MAD indicates greater variability.

The mean absolute deviation (MAD) is a measure of the variability of a set of data. It measures the average distance between each data point and the mean of the data set.

In this case, the MAD of Mr. Zimmerman's class is 0.46. This means that, on average, each data point in the class is about 0.46 units away from the mean of the data set.

The MAD gives an idea of how spread out the data is from the mean, regardless of whether the data is positively or negatively deviated from the mean.

A smaller MAD indicates less variability in the data set, while a larger MAD indicates greater variability.

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Answer:

The answer is -8

Step-by-step explanation:

Here's a key

()= Do first

/ = Divide

If something is outside the () and there is no symbol then multiply.

Step-by-step explanation:

suppose 2 more variable y and z

On the basis of given data & Using combining-functions, We can say that

a).The function P(x) which represents the price of a ticket can we given by where x represents the number of 0.75 price decreases= ($15 - 0.75x)

b). the function T(x) which represents number of tickets sold on a day

=(180 + 10x)

c). the revenue would be if the magician decides to sell the tickets for

$12 =  $ 2640

The process of composition, in which the result of one function becomes the input of another, allows us to create complex functions from basic ones. A complicated function may occasionally need to be broken down into two or more simpler ones, using the opposite method.

Given that:

Current price of ticket = $15

Average tickets sold per day = 180

Price decrease each time = $0.75

Number of price decreases = x

Total Price decrease = 0.75x

Increase in number of tickets with price decrease each time = 10

Total increase in number of tickets with x times price decrease = 10x

a). Function to represent total price of tickets

P(x) = current price - total price decrease  

      = ($15 - 0.75x)

Function to represent number of tickets T(x)

= average number of tickets+ total increase in tickets

= (180 + 10x)

b)Function to represent total revenue R(x) = total tickets x total price

                                                                      = T(x) . P(x)

                                                                      = (180 + 10x) ($15 - 0.75x)

c)Given that total price of tickets=$12

                                            P(x)=$12

                             ($15 - 0.75x) = $12

                                      - 0.75x  =  $12 - $15

                                       - 0.75x  =  - $3

                                              x = 3 ÷ 0.75

                                              x = 4 times

The number of times price decreased=4

Total tickets sold T(x) =(180 + 10x)

                                  =(180 + 10(4))

                                  =180+40

                                   =220 tickets

Total revenue= T(x) . P(x)

                    = 220 x 12

                    =$2640

Total revenue earned on 220 tickets at $12 is $ 2640

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The maximum value represents (b) the point where most profits are made

Given that the graph is the graph of a company's profit

The maximum value represents (b) the point where most profits are made

Given that the graph is the graph of a company's profit

The x-intercept is when the profit = 0

So

The x-intercept represents (b) the price per pen where no profit is made

This is calculated as

Rate = [f(6) - f(3)]/[6 - 3]

So, we have

Rate = [0 - 120]/[6 - 3]

Rate = -40

The domain of this graph given the situation is (0, 6] because the values do not makes sense beyond those points

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Answer:

179.3

Step-by-step explanation:

Rectangle:

L x W

10 x 14 = 140

Semicircle:

(π · r²) / 2

D = 10, r = 10 ÷ 2 = 5

(3.14 · 5²) / 2 = 39.25

Area of figure = 140 + 39.25 = 179.25 = 179.3 (rounding to tenth)

The height of the feeder is approximately 4 inches.

We can use the formula for the volume of a cone, which is V = (1/3)π[tex]r^{2}[/tex]h, where V is the volume, r is the radius, and h is the height. We know that V = 113.04 and r = 3, so we can solve for h:

113.04 = (1/3)*π*([tex]3^{2}[/tex])h

113.04 = 9πh

h = 113.04 / (9π)

h ≈ 4 inches

The y- intercept of a direct equation is the point where the line crosses the y- axis. It's the value of y when x is equal to 0.   To graph a direct equation, you can  compass the y- intercept on the y- axis, and  also use the  pitch to find other points on the line.

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Answer: 2.704 2.74 4.2 4.27 4.72

Step-by-step explanation:

2/9 as a percentage is approximately 22.2%.

To convert the fraction 2/9 to a percentage, you simply need to divide the numerator (2) by the denominator (9) and then multiply the result by 100.

1. Divide the numerator by the denominator: 2 ÷ 9 ≈ 0.2222
2. Multiply the result by 100: 0.2222 × 100 = 22.22%

Now, to round the answer to one decimal place, we consider the second digit after the decimal point. In this case, it's 2. Since it's less than 5, we can round down.

So, 2/9 as a percentage rounded to one decimal place is approximately 22.2%.

In summary, converting a fraction to a percentage involves dividing the numerator by the denominator and then multiplying the result by 100. Rounding to a specific decimal place helps in presenting the result in a more easily understandable form, especially when dealing with non-integer values.

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Answer:

BE = 17

Step-by-step explanation:

We Know

BC = 12 and CE = 15

Find BE.

We Take

12 + 15 = 27

So, BE = 17

1) The discount percentage is 16.07%.

2) The discounted price of F₁, F₂ is $470,000

3) The amount that Adam had after purchasing F₁, F₂ is $530,000.

The discount percentage is a product of the discount amount divided by the original cost, multiplied by 100.

Price of item F = $280,000

Discounted price = $235,000

Discount amount = $45,000 ($280,000 - $235,000)

Discount rate = 16.07% ($45,000/$280,000 x 100)

Discounted price of F₁, F₂ = $470,000 ($235,000 x 2)

The amount that Adam had before the purchase = $1,000,000

The amount he had after purchasing F₁, F₂ = $530,000 ($1,000,000 - $470,000).

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Answer:

179.3 square units

Step-by-step explanation:

We have to find the area of the rectangle and area of semicircle using the formula and then add the areas.

Area of rectangle:

                  length = 14 units

                   width = 10 units

          [tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

                                             = 14 * 10

                                             = 140 square units

Area of semicircle:

                diameter of semicircle = width of the rectangle

                                                 d =  10 units

                                                 r = d ÷ 2

                                                    = 10 ÷ 2

                                                    = 5 units

                     [tex]\boxed{\text{\bf Area of semicircle = $\dfrac{1}{2}\pi r^2$}}[/tex]

                                                       [tex]\sf = \dfrac{1}{2}*3.14*5*5\\\\ = 39.26\\\\ = 39.3 \ square \ units[/tex]

Area of the figure = area of rectangle +  area of semicircle

                             = 140 + 39.3

                             = 179.3 square units

In order to create a sector with an area of 2 square units, we need to draw a central angle of approximately 24.4 degrees and a radius of approximately 1.49 units.

In order to create a sector with an area of 2 square units, we need to find the radius of the circle and then calculate the central angle that corresponds to an area of 2 square units.

Let's start by using the formula for the area of a circle, which is:

A = πr²

We know that the area of the circle is 7 square units, so we can write:

7 = πr²

Solving for r, we get:

r = √(7/π)

r ≈ 1.49

Now, we can use the formula for the area of a sector, which is:

A = (θ/360)πr²

where θ is the central angle in degrees.

To find the central angle that corresponds to an area of 2 square units, we can write:

2 = (θ/360)π(1.49)²

Solving for θ, we get:

θ ≈ 24.4 degrees

So, to create a sector with an area of 2 square units, we need to draw a central angle of approximately 24.4 degrees and a radius of approximately 1.49 units.

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The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases.

what is exponent ?

In mathematics, an exponent (also known as a power or index) is a number that indicates how many times a given number (the base) must be multiplied by itself.

In the given question,

The given exponential model is:

y = 200(0.80)ˣ

where:

y is the output (dependent variable)

x is the input (independent variable)

To determine whether the model represents exponential growth or decay, we need to examine the base of the exponent, which is 0.80 in this case.

If the base is greater than 1, then the model represents exponential growth, and if the base is between 0 and 1, then the model represents exponential decay.

In this case, the base of the exponent is 0.80, which is between 0 and 1. Therefore, the model represents exponential decay.

The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases. The factor represents the rate of decay per unit of the independent variable, which in this case is 0.80.

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To find the projection of u onto v, we need to use the formula:

projv(u) = (u · v / |v|^2) * v

where u · v is the dot product of u and v, and |v|^2 is the magnitude of v squared.

First, we calculate u · v:

u · v = (-8i - 4j - 2k) · (0i + 2j + 2k) = 0 + (-8*0) + (-4*2) + (-2*2) = -8

Next, we calculate |v|^2:

|v|^2 = (2)^2 + (2)^2 = 8

Now, we can plug these values into the projection formula:

projv(u) = (-8 / 8) * (2j + 2k) = -1j - 1k

So the projection of u onto v is -1j - 1k.

To find the vector component of u orthogonal to v, we can use the formula:

u - projv(u)

We already found projv(u) to be -1j - 1k, so we just need to subtract that from u:

u - projv(u) = (-8i - 4j - 2k) - (-1j - 1k) = -8i - 3j - k

Therefore, the vector component of u orthogonal to v is -8i - 3j - k.
To find the projection of u onto v, we will use the formula:

proj_v(u) = (u•v / ||v||^2) * v

where u = -8i - 4j - 2k, v = 2j + 2k, and • denotes the dot product.

First, calculate the dot product (u•v):

u•v = (-8)(0) + (-4)(2) + (-2)(2) = -8 - 4 = -12

Next, calculate the magnitude squared of v (||v||^2):

||v||^2 = (0^2) + (2^2) + (2^2) = 0 + 4 + 4 = 8

Now, use the formula:

proj_v(u) = (-12 / 8) * v = -1.5 * (2j + 2k) = -3j - 3k

Next, to find the vector component of u orthogonal to v, use the formula:

u_orthogonal = u - proj_v(u)

u_orthogonal = (-8i - 4j - 2k) - (-3j - 3k) = -8i - 1j + 1k

So, the projection of u onto v is -3j - 3k, and the vector component of u orthogonal to v is -8i - 1j + 1k.

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Answer:

x = 15

I think thats what u wanted me to do- I hope it helps though. Middle school is hard.

Step-by-step explanation:

2x/3 + x/5 = 13

Here, we have to two different denominators in the LHS. So in order to solve the equation, we need to have like denominators and hence we find the Least Common Multiple (LCM).

The LCM of the denominators 3 and 5 is 15. Hence, we multiply each term to bring the denominator to 15.

5.(2x/3) + 3.(x/5) = 13

Now we combine the fractions with common denominator.

10x/15 + 3x/15 = 13

(10x + 3x)/15 =13

13x/15 = 13

Now, multiply the numbers and solve

13x = 13 . 15

x = 15 (cancelling 13 from both LHS and RHS)

Answer:

y=1.2x-6.4

Step-by-step explanation:

get slope

y2-y1/x2-x1

6.4 - 4.6/0-(-1.5)

1.8/1.5=1.2

get formula

y-y1=m(x-x1)

y-4.6=1.2(x-1.5)

y-4.6=1.2x-1.8

y-4.6=1.2x-1.8

y=1.2x-6.4

Using the compound interest formula, the interest Brian will earn after 6 years is: $2,347.22.

We can use the formula for compound interest to calculate the interest earned by Brian:

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

where:

A = the amount after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

In this case, P = $9,083, r = 2.90% or 0.029, n = 4 (since interest is compounded quarterly), and t = 6.

So,

A = 9083(1 + 0.029/4)^(4*6)

= $11,430.22

The interest earned will be the difference between the amount after 6 years and the initial investment:

Interest = A - P = $11,430.22 - $9,083 = $2,347.22

Therefore, Brian will earn $2,347.22 in interest after 6 years.

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The monthly installment of the air conditioner is $ 21 and the total amount paid for the air conditioner is $ 1188. She has to pay $ 288 more for buying the air conditioner on hire purchase.

Original cost = $900

Downpayment = 20%

Downpayment = 20% of 90

= 0.20 * 900

=$180

For simple interest,

A = P + P * r * t

where A is the amount

P is the principal

r is the rate of interest

t is the time

Given,

P = Total cost - Downpayment

= 900 - 180

= $720

r = 10%

t = 4 years

A  = 720 + 720 * 0.10 * 4

= $ 1008

Number of months she has to pay = 4 * 12

= 48 months

Monthly installment = 1008 / 48

= $ 21

Total amount paid = Downpayment + Monthly installments

= 180 + 1008

= $ 1188

Money paid more = 1188 - 900

= $ 288

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The p-value for the hypothesis test is approximately 0.000006.

To find the p-value, we follow these steps:

1. State the null hypothesis (H0) and alternative hypothesis (H1):
  H0: p = 0.5
  H1: p > 0.5

2. Calculate the sample proportion (p-hat): p-hat = 120/200 = 0.6

3. Calculate the test statistic (z) using the formula: z = (p-hat - p) / √((p * (1 - p)) / n)
  z = (0.6 - 0.5) / √((0.5 * 0.5) / 200) ≈ 2.683

4. Find the corresponding p-value using a z-table or calculator. The area to the right of the test statistic (2.683) is approximately 0.000006.

Since the p-value (0.000006) is less than the significance level (typically 0.05), we reject the null hypothesis, indicating that the true proportion of apple weights larger than 100 grams is larger than 0.5.

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