For the function below, approximate the area under the curve on the specified interval as directed. (Round your answer to the nearest thousandth. ) f(x) = 8e-x2 on [0, 6] with 3 subintervals of equal width and right endpoints for sample points

Answers

Answer 1

Area under the curve on the specified interval is 0.293

What is Area under the curve?

In order to assess and compare the bioavailability profiles of different medications, the area under the curve, which indicates the overall exposure that the body receives to an active agent, is used.

By performing a definite integral between the two locations, one can determine the area under a curve between two points.

Given,

f(x) = 8e-x2 on [0, 6]

so,

= 2*f(2) + 2*f(4) + 2*f(6)

= 2[f(2) + f(4) + f(6)]

= 2[0.1465 + 0 + 0] (F(4) and F(6) are infinitesimal)

= 0.293

The specified interval's area under the curve is 0.293.

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Related Questions

Write an equation in point slope and slope intercept form of a line that passes through the given point and has the given slope m.(If possible please show work)

Answers

Answer:

Point-Slope: $y+4=-\frac{1}{2}(x+3)$

Slope-Intercept: $y=-\frac{1}{2}x-\frac{11}{2}$

Step-by-step explanation:

The point-slope formula is $y-y_{1}=m(x-x_{1} )$. The slope-intercept formula is $y=mx+b$. Since we are given the point and slope, we can directly plug it into the point-slope formula.

Point-Slope

$y-(-4)=-\frac{1}{2}(x- (-3))$

$y+4=-\frac{1}{2} (x+3)$

To find the slope-intercept form, we can manipulate the point-slope form to get the slope-intercept form.

Slope-Intercept

$y+4=-\frac{1}{2}x-\frac{3}{2}$

$y=-\frac{1}{2}x-\frac{11}{2}$

Answer: Point slope form y+4= -1/2(x+3)

Slope intercept form: y=-1/2x -11/2

Step-by-step explanation:

(-3,-4) : m= -1/2

So we know the slope and to write it in point slope form it will be like ,

y- b = m(x-a) Where b is the y value and a is the x value and m in this case is the slope .

y- (-4) = -1/2 ( x-(-3) which reduces to y+4= -1/2(x+3)

Now to write it in slope intercept form it will be like y=mx+b and we kow htat m is the slope but we do not know b the y-intercept. But using the given coordinates we could plot it into the formula and solve for b.

y = mx +b

We know that y is -4

We know that m is -1/2

we know that x is -3

so -4 = -1/2(-3) + B

-4 = 3/2 + b

-3/2 -3/2

b= -11/2

We know now that the y intercept is -11/2 so we could write it in slope intercept form.

y= -1/2x - 11/2

Liza is designing a calendar as a fund-raising project for Math Class. The cost of printing
is 5000php, plus 150php per calendar. Write an equation in slope-intercept form that
models the total cost of printing the calendars.

Answers

Answer: y = 150x+5000

Step-by-step explanation:

Equation in slope-intercept form:

y= mx+c , where x= independent variable , y= dependent variable, m= slope , c= y-intercept.

Given: The cost of printing is 5000php, plus 150 php per calendar.

If x= Number of calendar and y= Cost of x calendars.

Then, m= 150 , c= 5000

Equation becomes

y = 150x+5000

A doctor sees between 7 and 12 patients each day.

On Mondays and Tuesdays, the appointment times are 15 minutes.

On Wednesdays and Thursdays, they are 30 minutes.

On Fridays, they are one hour long.

The doctor works for no more than 8 hours a day.

Here are some inequalities that represent this situation.

Answers

Answer:

The complete question seems to be:

A doctor sees between 7 and 12 patients each day.

On Mondays and Tuesdays, the appointment times are 15 minutes.

On Wednesdays and Thursdays, they are 30 minutes.

On Fridays, they are one hour long.

The doctor works for no more than 8 hours a day.

Here are some inequalities that represent this situation.

0.25 ≤ y ≤ 1

7 ≤ x ≤ 12

xy ≤ 8

What represents each variable?

7 ≤ x ≤ 12

We know that the doctor sees between 7 and 12 patients each day, and the smallest value of x is 7, and the largest is 12, then x must represent the number of patients that the doctors see in a given day.

0.25 ≤ y ≤ 1

now,

On Mondays and Tuesdays, each appointment is 15 minutes long.

An hour has 60 minutes.

Then 15 minutes = 15/60 hours = 0.25 hours.

On Wednesdays and Thursdays, they are 30 minutes.

30 minutes = 30/60 hours = 0.5 hours.

Then the possible value of the time for each appointment are {0.25, 0.5, 1}

Then the variable y must represent the time that each appointment takes.

xy ≤ 8

We know that:

x = number of patients in a given day.

y = time that the appointment takes in a given day.

x*y = total number of hours that he works in that given day.

and we know that he works, at maximum, 8 hours.

then the inequality xy ≤ 8 has sense.

Amber baked 120 cookies to give to five friends she wants to put the same number of cookies in each bag which of the following can she use to find out how many cookies to put in each bag

Answers

Answer:

she can divide the amount of cookies to friends

Step-by-step explanation:

120/5= 24

Assume that the heights of American women are approximately normally distributed with a mean of 66.5 in. and a standard deviation of 2.5 in. Within what range are the heights of 95% of American women? Please help immediately!!! :(

Answers

I think they should be within 64-69 inches in height.

Graph the parabola Y=x^ +2x -1Plot five points on the parabola the vertex the two points to the left of the vertex the two points to the right of the vertex then click on the graph a function button

Answers

Given the equation of the parabola

$y=x^2+2x-1$

which can be written as

$\begin{gathered} y=x^2+2x+1-1-1 \\ =(x+1)^2-2 \end{gathered}$

Comparing with

$y=a(x-h)^2+k$

gives a = 1, h = -1 and k = -2.

The vertex is (h, k) = (-1, -2).

Whats is the area of the figure? in squares inches

Answers

Please there is no figure shown

Standard automobile license plates in a country display 1 numbers, followed by 3 letters, followed by 3 numbers. How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.)

Answers

The counting principle says that we multiply the number of ways for each of these events together to get the total number of ways to get a license plate. Hence, there are $158184000$ ways to create a license plate.

What is the counting principle?

The fundamental counting principle states that if there are $p$ ways to do one thing and $q$ ways to do another thing, then there are $p$×$q$ ways to do both things.

So,

The number of ways to count the first number are $9$ ways.

The number of ways to count the first letter are $26$ ways

The number of ways to count the next letter are $26$ ways

The number of ways to count the third letter are $26$ ways

The number of ways to count the next number are $10$ ways

The number of ways to count the next number are $10$ ways

The number of ways to count the next number are $10$ ways

So, the total number of ways to get a license plate is:-

$(9).(26).(26).(26).(10).(10).(10)=158184000$.

Hence, there are $158184000$ ways to create a license plate.

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calculate the perimeter

Answers

Answer:

Its 58 centimeters

Step-by-step explanation:

Copy the figure at right. Calculate the measure
of each lettered angle. Explain
how you determined the
measures d and h.

Answers

The angles of each letter are as follows:

∠a = 124°

∠b = 56°

∠c = 56°

∠d = 38°

∠e = 38°

∠f = 76°

∠g = 66°

∠h = 104°

∠k = 76°

∠n = 86°

∠p = 38°

∠a = 180 - 56 = 124°(total angle on a straight line)

∠b = 56°(vertically opposite angles)

∠c = 56°(corresponding angle to ∠b) Note this is possible because there are 2 parallel lines and a transversal.

2∠d + ∠d + 66 = 180 (sum of angles in a triangle)

3∠d = 180 - 66

3∠d = 114

∠d = 114 / 3

∠d = 38°

∠d = ∠e (given)

Therefore,

∠e = 38°

∠d + 66 + ∠f = 180

38 + 66 + ∠f = 180

∠f = 76°

Recall external angle of a triangle is equals to the sum of the opposite angles. Therefore,

∠f + ∠g = ∠d + ∠h

∠f + ∠g = 38 + 104

76 + ∠g = 142

∠g = 66°

∠d is one of the base angles of an isosceles triangle. Therefore base angles of the isosceles triangle are equal. This means the other base angle opposite ∠d in the isosceles triangle is congruent to ∠d.

Therefore,

2∠d + ∠h = 180(sum of angles in a triangle)

76 + ∠h = 180

∠h = 180 - 76

∠h = 104°

∠h + ∠k = 180 (sum of angles on a straight line)

∠k = 76°

∠n = 180 - ∠d - ∠c (angles on a straight line)

∠n = 86°

∠p = 180 - 56 - ∠n (sum of angle in a triangle)

∠p = 38°

Therefore, the angles of the letters are:

∠a = 124°

∠b = 56°

∠c = 56°

∠d = 38°

∠e = 38°

∠f = 76°

∠g = 66°

∠h = 104°

∠k = 76°

∠n = 86°

∠p = 38°

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Help meh rn pleaseeee

Answers

Answer: -8 degrees

Step-by-step explanation: it's -3 + -5 basically

Answer:

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.04 cm. He knows that the population standard deviation is 0.26 cm. Assuming a level of significance of 0.02, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? Step 3 of 3: Draw a conclusion and interpret the decision.

Answers

Assuming a level of significance of 0.02, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?

Step 1: Null and Alternative HypothesisThe null hypothesis (H0): The machine does not need recalibration after testing 196 bolts.The alternative hypothesis (H1): The machine needs recalibration after testing 196 bolts.

Step 2: Determine the level of significance level of significance (α) = 0.02

Step 3: Find the critical valueThe level of significance is 0.02, which indicates that the critical value is zα/2 = ±2.33 using the z-table.

Step 4: Calculate the z-test statistics = (x - μ) / (σ/√n) = (4.04 - 4.00) / (0.26 / √196)z = 4.0

Step 5: Determine the p-values-value = P (Z > 4) ≈ 0Using the p-value approach, if the p-value is less than the level of significance, reject the null hypothesis.

In this case, the p-value is almost 0, indicating that there is a statistically significant difference between the sample mean and the hypothesized population mean of 4.0 cm.

Step 6: Conclusion Since the p-value is less than the level of significance, we can reject the null hypothesis and accept the alternative hypothesis. It implies that the machines need recalibration as there is sufficient evidence to suggest that the bolts' mean length is more significant than the required specification of 4.00 cm.

Therefore, the manufacturer should recalibrate the machine to ensure that the bolts' length is within the required specification.

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Suppose that f(3)=2 and g(-2)=6 explain how f(x) and g(x) cannot be inverse funtions of one another

Answers

If f{g(x)} = g(x) and g{f(x)} = f(x)

That means they cannot be inverse functions of one another.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given that f(3) = 2 and g(-2) = 6.

From the expression, f⁻¹(2) = 3 and g⁻¹(6) = -2

So now we take the composition,

f{g(-2)} = f (6) = y (let)

Then f⁻¹(y) = 6 = g (-2) , which is given.

Now, f{g(-2)} = g (-2).

And similarly g{f(3)} = g (2) = k (let)

g⁻¹(k) = 2 = f (3)

Now, g{f(3)} = f (3)

Therefore, if f{g(x)} = g(x) and g{f(x)} = f(x)

That means they cannot be inverse functions of one another.

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Find the area and perimeter of the square using formula and
the given dimensions.
A square with a side length of 13 meters.

A P = 22 m, A = 129 sq. m

B P = 42 m, A = 159 sq. m

C P = 52 m, A = 169 sq. m

D P = 32 m, A = 189 sq. m

Answers

Answer:

A= l×l

= 13×13

A= 169

P= 4l

= 4×13

= 52

so the answer is C

Pls help me find the answer in the circled question on the image

Answers

The answer is 33/8 or 4 1/8

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction as t increases. Eliminate parameter to find a Cartesian equation of the curve.1) x= 2t-1 y=1/2t+12) x=3t+2 y=2t+33)x=t^3 -3 y=t+2 -3≤t≤3

Answers

The value of y can be written as y=(x+5)/4.

Here our task is not to find the value of x or y but to find the relation between x and y by eliminating the t from both the equations.

Given that,

Curve equations are x= 2t-1 y=1/2t+1

x= 2t-1 and y=1/2t+1

2t = x+1

t = (x+1)/2

substitute t value in y

y = t/2 + 1

y = (x+1/2)/2 + 1

y = x+5/4

you can also write x =4y-5

But generally when we have to draw the graph we will be taking x as input value and y as output value so y can be written as y=(x+5)/4

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Divide: 7 5/6 ÷ 2/3 need help

Answers

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

What is the rental cost? Step by step.

Answers

The rental cost in dollars per square foot is $11,00

What is the rental cost in dollars per square foot?

Cost of renting 1.250 square feet = $13, 750 per month

Rental cost per square foot = Total renting cost / total renting area

= $13, 750 per month / 1.250 square feet

= $11,000

Hence, $11,000 is the rental cost in dollars per square foot.

Answers

Answer:

i cant see

Step-by-step explanation:

the screen is broken :(

Answer:

What the answer chioces?

Step-by-step explanation:

In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (b) What is the probability that a subject would guess more than 20 correct in a series of 36 trials?

Answers

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

How to find the pobability that a subject would guess more than 20 correct in a series of 36 trials

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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expand the following
1. ( m+n)(10m-4n)
2.(6x+y)

Answers

hope it helps....!!!!!

expand the following1. ( m+n)(10m-4n)2.(6x+y)

A container is in the shape of a right rectangular prism. Hayden wants to put a stick in the container.
What is the length in inches of the longest stick that will fit in the container

Answers

Answer:

13 in.

Step-by-step explanation:

First figure out the length of the diagonal of the base.

3²+4²=c²

9+16=c²

25=c²

√25=c

c=5

Now we can figure out the stick using the same method.

5²=12²=c²

25+144=c²

169=c²

√169=c

c=13

Please help quick I need it

Answers

The area of the composite figure is 122.24 units².

How to find the area of a composite figure?

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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Solve for x in the diagram.

Answers

Answer:

x = 20

Step-by-step explanation:

x° + 2x° + (x+10)° = 90°

3x° + x° + 10° = 90°

4x° + 10° = 90°

4x° = 90°-10°

4x° = 80°

x = 80/4

x = 20

Answer:

20°

Step-by-step explanation:

The sum of all three angles combined is 90°. You can see this by the square at the corner. This means that you have to add all of the angles together and set it equal to 90° to solve for x.

x° + 2x° + (x + 10)° = 90°

3x° + (x + 10)° = 90°

4x° + 10° = 90°

4x° = 80°

x = 20°

You want to be able to withdraw $25,000 each year for 30 years. Your account earns 8% interest. a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account?

Answers

Answer:

600

Step-by-step explanation:

suppose that there are 5 children in a gymnastics class. one day, they count the number of steps each persontakes while walking on their hands until they lose balance and come down. the results are: ashley (20),brittany (8), carol (22), darla (26), and erica (24).the mean number of steps these children took whilewalking on their hands is 20 steps.

Answers

The population is the number of children in gymnastic class = 5.

A parameter is the mean number of steps taken by the 5 children.

What is a parameter?

Four parameters, referred to as hybrid or h Parameters, can be used to assess any linear circuit with input and output terminals. These parameters are one measured in ohm, one in mho, and two dimensionless. Hybrid is short for "mixed." These parameters are referred to as hybrid parameters since they have dual dimensions

Here, we have

Given that,

Suppose that there are 5 children in a gymnastics class.

One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.

The mean number of steps these children took while walking on their hands is 20 steps.

We have to find the population and parameters.

The area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class make up the population.

Population = number of children in gymnastic class = 5.

Parameter = mean number of steps taken by the 5 children.

Hence, Population is the number of children in gymnastic class = 5.

A parameter is the mean number of steps taken by the 5 children.

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Find the tangent of J
I
K
√35
√79
Write your answer in simplified, rationalized form. Do not round.

Answers

The calculated value of the tangent of J is tan(J) = √35/√79 or tan(J) = √2765/79

Finding the tangent of J

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

Opposite = √35

Adjacent = √79

The tangent of J is calculated as

tan(J) = Opposite/Adjacent

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

tan(J) = √35/√79

So, we have

tan(J) = √2765/79

Hence, the solution is √2765/79

Answers

Answer:

The ratio of the drag coefficients $\dfrac{F_m}{F_p}$ is approximately 0.0002

Step-by-step explanation:

The given Reynolds number of the model = The Reynolds number of the prototype

The drag coefficient of the model, $c_{m}$ = The drag coefficient of the prototype, $c_{p}$

The medium of the test for the model, $\rho_m$ = The medium of the test for the prototype, $\rho_p$

The drag force is given as follows;

$F_D = C_D \times A \times \dfrac{\rho \cdot V^2}{2}$

We have;

$L_p = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2 \times L_m$

Therefore;

$\dfrac{L_p}{L_m} = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2$

$\dfrac{L_p}{L_m} =\dfrac{17}{1}$

$\therefore \dfrac{L_p}{L_m} = \dfrac{17}{1} =\dfrac{\rho _p}{\rho _p} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_p} \right)^2 = \left(\dfrac{V_p}{V_m} \right)^2$

$\dfrac{17}{1} = \left(\dfrac{V_p}{V_m} \right)^2$

$\dfrac{F_p}{F_m} = \dfrac{c_p \times A_p \times \dfrac{\rho_p \cdot V_p^2}{2}}{c_m \times A_m \times \dfrac{\rho_m \cdot V_m^2}{2}} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}$

$\dfrac{A_m}{A_p} = \left( \dfrac{1}{17} \right)^2$

$\dfrac{F_p}{F_m} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}= \left (\dfrac{17}{1} \right)^2 \times \left( \left\dfrac{17}{1} \right) = 17^3$

$\dfrac{F_m}{F_p} = \left( \left\dfrac{1}{17} \right)^3$= (1/17)^3 ≈ 0.0002

The ratio of the drag coefficients $\dfrac{F_m}{F_p}$ ≈ 0.0002.

For the following question, use the function h = - 16t² + vot + h(0), where h is the height of the object after time t, vo is the initial velocity, and h(0) is the initial height. An object is thrown upward from a height of 880 ft with an initial velocity of 96 ft/ s. How long will it take for the object to reach the ground?