how do i do this?

270 calories in 3 serving 450 calories in 5 severing?

We have obtained a series expansion for the integral 1/(1+x^4).

To obtain a series expansion for the integral of 1/(1+x^4), we can use the method of partial fractions to express the integrand as a sum of simpler fractions. First, we note that the denominator of the integrand can be factored as (1+x^2)(1-x^2i)(1+x^2i), where i is the imaginary unit. Thus, we can write:

1/(1+x^4) = A/(1+x^2) + B/(1-x^2i) + C/(1+x^2i)

To solve for A, B, and C, we can multiply both sides of the equation by the common denominator (1+x^2)(1-x^2i)(1+x^2i) and then equate the coefficients of the terms on both sides. This gives us a system of equations:

A(1-x^2i)(1+x^2i) + B(1+x^2)(1+x^2i) + C(1+x^2)(1-x^2i) = 1

Solving this system of equations, we obtain:

A = 1/4

B = -i/4

C = i/4

Thus, we can write:

1/(1+x^4) = 1/4(1+x^2) - i/4(1-x^2i) + i/4(1+x^2i)

We can now integrate each term using the power series expansion for 1/(1+x^2):

1/(1+x^2) = 1 - x^2 + x^4 - x^6 + ...

Integrating each term and simplifying, we obtain:

∫ 1/(1+x^4) dx = 1/4 arctan(x) + 1/8 ln(1+x^2) + i/8 ln(1-x^2i) - i/8 ln(1+x^2i) + C

where C is the constant of integration.

Therefore, we have obtained a series expansion for the integral 1/(1+x^4).

Learn more about integral here

https://brainly.com/question/30094386

#SPJ11

The interval of t-values such that c(t) = (cos t, sin t) traces the upper half of the unit circle (in the counter-clockwise direction) is [0, pi].

To see why this is the case, recall that the unit circle is given by the equation x^2 + y^2 = 1, where (x,y) are the coordinates of a point on the circle. The upper half of the unit circle corresponds to the set of points (x,y) where y is positive or zero. We want to find the values of t for which c(t) lies on the upper half of the unit circle.

Using the definition of c(t), we have c(t) = (cos t, sin t). The y-coordinate of c(t) is sin t, so we want, sin t to be positive or zero. Since sin t is positive in the first and second quadrants of the unit circle, and zero at t = 0 and t = pi, we have that c(t) traces the upper half of the unit circle when t is in the interval [0, pi].

To see that c(t) traces the upper half of the unit circle in the counter-clockwise direction, note that as t increases from 0 to pi, c(t) moves counterclockwise around the unit circle, starting at (1,0) and ending at (-1,0). Thus, the interval [0, pi] corresponds to one-half of a full counterclockwise rotation around the unit circle, which is exactly the upper half of the circle.

To learn about T-distribution, visit:

https://brainly.com/question/16994704

#SPJ11

Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

The quadrant that the graph will not go through is the second quadrant.

The reason is that the slope is positive and there was a translation 6 units down

The quadrants are named in anticlockwise direction starting from the first which has x - positive and y - positive

The graph of y = 2x/3 is a graph with positive slope, moving through the third and first quadrant.

y = 2x/3 - 6 means a translation 6 units down and this pushed the line to get to the fourth quadrant

Hence the remaining quadrant that is untouched is the second quadrant

The graph is attached

learn more about graphs here:

https://brainly.com/question/25184007

#SPJ1

Answer:

Square root of 16 is rational beacuse Square root of 16=4 Whlie the others are Irational.

Step-by-step explanation:

Answer:

Step-by-step explanation: squarefoot of 16 is rational cause 16=4

The additional variable used to determine the values of the original variables in the ordered pair of a system of equations whose solution is an infinite number of solution is called a parameter.

A parameter is an unknown variable that is not included in the original equations of a system of equations.

In algebra, a system of equations is a collection of two or more equations involving the same set of variables. The solution to a system of equations is the point or points at which the equations are true. A system of equations can have a unique solution, no solution, or an infinite number of solutions.

When a system of equations has an infinite number of solutions, it means that the equations are dependent on each other. This means that one of the equations can be expressed in terms of the other equation. The solution to the system of equations is then written in terms of the parameter, which is the variable that is not included in the original equations.

To know more about parameter: https://brainly.com/question/28249912

#SPJ11

Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.

a) The value of x is 155.56 mm (rounded to two decimal places).

b) The value of R is 4.44 mm (rounded to two decimal places).

c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:

UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)

The Lower Control Limit (LCL) for the diameter is calculated as:

LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)

d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:

UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)

The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.

e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:

UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)

LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)

Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.

Learn more about diameter here:

https://brainly.com/question/32968193

#SPJ11

The complete question is:

What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5

Answer:

36

Step-by-step explanation:

= 24/6+2^3*4

= 24/6+8*4

= 4+8*4

= 4+32

= 36

Answer:

\(\displaystyle m=\frac{-2}{11}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-7, 0)

Point (4, -2)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

36.99 or 37 rounded, 184.99 x .20 gets you the answer, basic maths

Triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.

In triangle ADT and EDT, we get that:

AD = DE (given)

AT = ET (given)

DT = DT (common)

So, ΔADT ≅ Δ EDT (SSS congruency rule)

In triangle BLG and PFX, we get that:

BL = PF (given)

BG = PX (given)

∠ B = ∠ P (given)

So, ΔBLG ≅ Δ PFX (SAS congruency rule)

Therefore, we get that, triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.

Learn more about congruency here:

https://brainly.com/question/1675117

#SPJ1

Answer:

iPhone 8+ (2017) 736 × 414 1920 × 1080 16:9 3× 5.5″ 401 PPI

Step-by-step explanation:

a. Dimensions of the screen

The dimensions of the screen are height = 2.7 in and width = 4.8 in

Since the aspect ratio is the ratio of width, w to height, h of the iPhone 8 and it is 16:9, we have that

w/h = 16/9

w = 16h/9

Also, the diagonal length, d = 5.5 inches.

Since the iPhone 8 screen is a rectangle, the diagonal length d is gotten from pythagoras' theorem.

So, d = √(w² + h²)

Since w = 16h/9

d = √(w² + h²)

d = √((16h/9)² + h²)

d = h√((16/9)² + 1²)

d = h√(256/81 + 1)

d = h√[(256 + 81)/81]

d = h√[337/81]

d = h√4.16

d = 2.04h

Making h subject of the formula, we have

h = d/2.04

h = 5.5/2.04

h = 2.7 in

So, w = 16h/9

w = 16 × 2.7 in/9

w = 43.2 in/9

w = 4.8 in

So, the dimensions of the screen are height = 2.7 in and width = 4.8 in

b. Number of pixels per inch

The number of pixels per inch (PPI) is 400 pixels per inch

To find the number per inch, we need to find the total number of pixels on the screen which is 1080 by 1920 = 2073600 pixels.

The area of the screen is A = wh

= 4.8 in × 2.7 in

= 12.96 in²

So, the number of pixels per square inch (PPI²) is 2073600 pixels/12.96 in² = 160000 pixels/in².

So, pixels per inch(PPI) = √160000 pixels/in²

= 400 pixels per inch

So, the number of pixels per inch (PPI) is 400 pixels per inch

Learn more about dimensions of screen here:

https://brainly.com/question/9006934

Answer:

Step-by-step explanation:

Let p be the number of pennies and n be the number of nickels. As you have $8.80 in total (given that pennies are worth $0.01 and nickels are worth $0.05)

0.01p + 0.05n = 8.80

You also know that there are twice as many nickels than pennies (or alternatively, there are 2 nickels for every penny).

n = 2p

You can substitute this value of n into the first equation

0.01p + 0.05n = 8.80

0.01p + 0.05(2p) = 8.80

0.01p + 0.10p = 8.80 (multiplying out the brackets)

0.11p = 8.80 (collecting the p's)

p = 80

Putting this back into the second equation

n = 2p

n = 2(80) = 160

So there are 160 nickels and 80 pennies.

You can put this back into the first equation to check it.

0.01p + 0.05n = 8.80

0.01(80) + 0.05(160) = 0.80 + 8 =8.80

The probability that at least one washing machine breaks down in the first year of operation is approximately 0.9814 or 98.14%.

To find the probability that at least one washing machine breaks down in the first year of operation, we can use the complement rule and subtract the probability of none of the machines breaking down from 1.

Given that 15% of washing machines break down, and 32 machines are purchased by the laundromat, we can calculate the probability using the binomial distribution.

The probability that a single washing machine breaks down in the first year is 15% or 0.15. Since each machine operates independently, we can treat the breakdown of each machine as a Bernoulli trial.

Let's define success as a machine breaking down and failure as a machine not breaking down. The probability of success is 0.15, and the probability of failure is 1 - 0.15 = 0.85.

To find the probability that none of the machines break down, we use the binomial distribution formula:

P(X = k) = C(n, k) * \(p^k\) * \((1 - p)^{n - k}\)

In this case, we want to calculate the probability that k = 0, i.e., none of the machines break down. The formula becomes:

P(X = 0) = C(32, 0) * \(0.15^0\)* \(0.85^{32}\)

Now, to find the probability that at least one machine breaks down, we subtract the probability of none breaking down from 1:

P(at least one breakdown) = 1 - P(X = 0)

By plugging in the values and performing the calculations, we can find the probability that at least one washing machine breaks down in the first year of operation for the laundromat.

P(X = 0) = C(32, 0) * \(0.15^0\)* \(0.85^{32}\)

= 1 * 1 * \(0.85^{32}\)

≈ 0.0186

P(at least one breakdown) = 1 - P(X = 0)

= 1 - 0.0186

≈ 0.9814

Therefore, the probability that at least one washing machine breaks down in the first year of operation is approximately 0.9814 or 98.14%.

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

The number 175 in Annie's equation represents the cost per hour per semester for classwork.

This means that for every additional hour of classwork a college student takes per semester, their fee increases by $175. It is important to note that this cost does not include the cost for housing, which is represented by the constant term of the equation, 3375. Therefore, the equation allows us to calculate the total fee a college student would pay for a semester based on the number of hours of classwork they take and the cost per hour.

More on cost: https://brainly.com/question/24013499

#SPJ11

Answer:

There are 6 sandwich choices.

Step-by-step explanation:

2*3=6

Answer:

374 feet^2

Step-by-step explanation:

Surface area:

area of cross section x 2 = 110feet^2

area of tope x 2 = 264 feet^2

sum / Surface area: 374 feet^2

Answer:

the first equation

Step-by-step explanation:

if you input the values of x in the first equation, you will get the value of y

Answer:

y = 3x

Step-by-step explanation:

Hope this helps

Answer:

2 and 1

Step-by-step explanation:

5 could only go in 16 2 Times and 11 could only go in 17 1 time

The probability that there will be exactly two roommate pairs made up of a backcourt and a frontcourt player is approximately 0.0222 or 2.22%.

Probability = 1 / 45 ≈ 0.0222 (rounded to four decimal places)

To solve this problem, we can break it down into steps:

Step 1: Calculate the total number of possible roommate pairs.

The total number of players in the team is 10. To form roommate pairs, we need to select 2 players at a time from the 10 players. We can use the combination formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of players and k is the number of players selected at a time.

In this case, n = 10 and k = 2. Plugging these values into the formula, we get:

C(10, 2) = 10! / (2!(10-2)!) = 45

So, there are 45 possible roommate pairs.

Step 2: Calculate the number of possible roommate pairs consisting of a backcourt and a frontcourt player.

The team has 6 frontcourt players and 4 backcourt players. To form a roommate pair consisting of one backcourt and one frontcourt player, we need to select 1 player from the backcourt and 1 player from the frontcourt.

The number of possible pairs between a backcourt and a frontcourt player can be calculated as:

Number of pairs = Number of backcourt players × Number of frontcourt players = 4 × 6 = 24

Step 3: Calculate the probability of having exactly two roommate pairs made up of a backcourt and a frontcourt player.

The probability is calculated by dividing the number of favorable outcomes (two roommate pairs with backcourt and frontcourt players) by the total number of possible outcomes (all possible roommate pairs).

Probability = Number of favorable outcomes / Total number of possible outcomes

Number of favorable outcomes = 1 (since we want exactly two roommate pairs)

Total number of possible outcomes = 45 (as calculated in step 1)

Probability = 1 / 45 ≈ 0.0222 (rounded to four decimal places)

Therefore, the probability that there will be exactly two roommate pairs made up of a backcourt and a frontcourt player is approximately 0.0222 or 2.22%.

To know more about the word possible, visit:

https://brainly.com/question/17878579

#SPJ11

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

Learn more about Standard Deviation here :

https://brainly.com/question/23907081

#SPJ1

The number of  minutes it would  take for 9 team members to paint a 3600 square foot wall is 90 minutes.

First step is to find  the  man-minutes

Man - minutes =12 × 45

Man-minutes = 540

Second step is to find the  sq/ft per man/min

2400/540 = 4.44 sq / ft per man-minutes

Now let find the  minutes it would take paint a 3600 square foot wall

let m represent the number of min for 9 men to do 3600 sq/ft

3600/4.44 = 810 man-min

so,

9m = 810

Divide both side by 9m

m = 810/9

m = 90 minutes

Therefore the number of minutes is 90 minutes.

Learn more about number of minutes here: https://brainly.com/question/14154286

#SPJ1

Answer:

D

Step-by-step explanation:

#1

\(\sf \longmapsto3x-4y=11\)

\(\sf \longmapsto3x−4y+4y=11+4y\)

\(\sf \longmapsto3x=4y+11\)

\(\sf \longmapsto \frac{3x}{3} = \frac{4y + 11}{3} \)

\(\sf \longmapsto{x} = \frac{4}{3} y + \frac{11}{3} \)

#2

\(\sf \longmapsto3x+2y=2\)

\(\sf \longmapsto3x+2y+−2y=2+−2y\)

\(\sf \longmapsto3x=−2y+2\)

\(\sf \longmapsto \frac{3x}{3} = \frac{ - 2y + 2}{3} \)

\(\sf \longmapsto \: x = \frac{ - 2}{3} y + \frac{2}{3} \)

Answer: Here you go!

Answer:

A mile is longer

Step-by-step explanation: