Evaluate the definite integral
a) Find an anti-derivative
b) Evaluate • f,ª (2ª − 7)*¹112³dx = If needed, round part b to 4 decimal places. ₁*₁ (x² − 7) * 112³ da - = f(x² − 7) * 11x³dx =

It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true

The set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.

Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.

Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.

Learn more about integer on:

https://brainly.com/question/17695139

#SPJ1

Populations tend to accumulate late-acting deleterious mutations through genetic drift, while they accumulate antagonistic-pleiotropic alleles through natural selection, despite both types having late-acting deleterious effects.

Genetic drift, a random process that affects gene frequencies in populations, allows for the accumulation of late-acting deleterious mutations without regard to their fitness consequences. Since drift is not driven by selection, harmful mutations can persist and accumulate over time. In contrast, natural selection acts on antagonistic-pleiotropic alleles, favoring the ones with beneficial effects early in life, even if they have deleterious late-acting effects. This selective pressure promotes the accumulation of alleles that provide immediate fitness advantages but also carry later costs, as long as the overall benefits outweigh the drawbacks.

Learn more about antagonistic-pleiotropic alleles here:

https://brainly.com/question/30077729

#SPJ11

The conditional probabilities of the events are 0.343 and 0.161

Train given that they live in Los Angeles

From the table of values, we have the following readings

P(Train and Live in LA) = 0.12

P(Live in LA) = 0.35

So, the conditional probability is

P = P(Train and Live in LA)/P(Live in LA) =

P = 0.12/0.35

Evaluate

P = 0.343

New York given that they drive a car to work

Here, we have

P(NY and Car) = 0.05

P(Car) = 0.31

So, the conditional probability is

P = P(NY and Car)/P(Car) =

P = 0.05/0.31

Evaluate

P = 0.161

Hence, the probabilities are 0.343 and 0.161

Read more about probabilities at

https://brainly.com/question/251701

#SPJ1

Complete question

A survey was done of commuters in three major cities about how they primarily got to work. The results are shown in the frequency table below. Answer the following conditional probability question.

                             Car         Train        Walk           Total

New York              0.05      0.25           0.10           0.40

Los Angeles          0.18       0.12            0.05          0.35

Chicago                0.08       0.14            0.03          0.25

Total                     0.31         0.51            0.18            1.00

(a) What is the probability that a person picked at random would take a train to work given that they live in Los Angeles

(b) What is the probability that a person picked at random would live in New York given that they drive a car to work

1 solution: (-1,-3)

1) Since we are going to solve these systems graphically, let's begin by setting one pair of t-tables:

b) 2x-y=1, y=-3

2x-y=1 ⇒-y= 1 -2x ⇒ y=2x-1

Now, let's plot those points and trace one increasing line for the first one, and one horizontal line for the constant function y=-3

2) Plotting that system, we can tell the solution is the common point to both equations:

Thus, the answer is (-1,-3)

Answer:

Apply the formula a^2+b^2+2ab=(a+b) ^2 and then multiply 2 with it and then subtract three from it

To determine the energy required to accelerate an 800 kg car from rest to 100 km/h on a level road, we can use the formula for kinetic energy.

Kinetic energy (KE) = 1/2 * mass * velocity^2

First, let's convert the velocity from km/h to m/s since the formula requires the velocity in meters per second. We know that 1 km = 1000 m and 1 hour = 3600 seconds. So, to convert 100 km/h to m/s:
100 km/h * (1000 m/1 km) * (1 h/3600 s) = 27.78 m/s

Now, we can substitute the values into the formula:
KE = 1/2 * 800 kg * (27.78 m/s)^2

Calculating this gives us:
KE = 1/2 * 800 kg * 27.78 m/s * 27.78 m/s = 309,011.2 J

To express this value in kilojoules (kJ), we divide by 1000:
309,011.2 J / 1000 = 309.0112 kJ

Therefore, the energy required to accelerate the 800 kg car from rest to 100 km/h on a level road is approximately 309 kJ.

To know more about  kinetic energy :

https://brainly.com/question/999862

#SPJ11

The value of ∠A and ∠B are both approximately 33.7° to the nearest tenth.

We are given that;

∠C is a right angle,

so sin(∠A) = opposite/hypotenuse = a/c and

cos(∠A) = adjacent/hypotenuse = b/c

Now,

We can use the Pythagorean theorem to find the length of the third side of the triangle:

\(a² + b² = c²\)

where a is the length of the missing side.

we have b = 29 and c = 35.

So we have:

\(a² + 29² = 35²a² + 841 = 1225a² = 384\)

a ≈ 19.6

So the length of the missing side is approximately **19.6** to the nearest tenth.

Now we can use trigonometry to find the angles. We know that sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent.

So we have:

sin(∠A) = a/c

sin(∠A) = 19.6/35

sin(∠A) ≈ 0.56

∠A ≈ 33.7°

cos(∠A) = b/c

cos(∠A) = 29/35

cos(∠A) ≈ 0.83

∠B ≈ 33.7°

Therefore, by pythagoras theorem the answer will be 33.7° to the nearest tenth.

Learn more about Pythagoras theorem;

https://brainly.com/question/343682

#SPJ4

Function y = 3x-x² is not a quadratic function .

Given,

Quadratic function.

Here,

Quadratic equation in standard form :

y = ax² + bx + c

a = coefficient of x² .

b = coefficient of x .

c = constant .

F)

y = (x-1)(x-2)

Further solving to get quadratic equation,

y = x² -3x + 2

It is a quadratic function.

G)

y = x²+2 x-3

The given function is in standard form of quadratic function.

y = ax² + bx + c

It is a quadratic function.

H)

y = 3x-x²

The given function is not a quadratic function .

The function is not in standard form of quadratic function .

y = ax² + bx + c

I)

y = -x²+x(x-3)

The given function is in standard form of quadratic function.

y = ax² + bx + c

Thus function y = 3x-x² is not a quadratic function.

Know more about quadratic function,

https://brainly.com/question/18958913

#SPJ4

To find the difference in price between Luke's original brand of cereal and the super-saving brand, we need to subtract the price of the super-saving brand from the price of Luke's original brand.

The price of Luke's original brand is $11 per box, and the price of the super-saving brand is given by the equation

y = 9x.

To find the price of the super-saving brand, substitute

x = 1 into the equation:

y = 9(1) = $9.  

So, the price of Luke's original brand is $11 and the price of the super-saving brand is $9. To find the difference, subtract $9 from $11: $11 - $9 = $2.  Therefore, the price of a box of Luke's original brand of cereal is $2 more than the price of a box of the super-saving brand.

To calculate how much money Luke saves each month with the change in cereal brand, we need to find the difference in cost between buying 6 boxes of Luke's original brand and 6 boxes of the super-saving brand. The cost of 6 boxes of Luke's original brand is $11 x 6 = $66.  The cost of 6 boxes of the super-saving brand is $9 x 6 = $54. To find the savings, subtract $54 from $66: $66 - $54 = $12. Therefore, Luke saves $12 each month with the change in cereal brand if he buys 6 cereal boxes each month.

To know more about Luke's original brand visit:

https://brainly.com/question/28447852

#SPJ11

An equation is considered linear if it is in the form of y=mx+b where m is the slope of the equation and b is the y-intercept.

There are several properties possessed by linear equations, which are as follows:

Learn more about linear equation at

https://brainly.com/question/11897796

#SPJ1

Answer:

The cost of parking in the garage for 75 minutes is 4.875.

Step-by-step explanation:

The costs of parking h hours is given by the following function:

\(f(h) = 4.5 + 1.5(h-1)\)

Cost of parking 75 minutes.

1 hour is 60 minutes. How many hours are 75 minutes?

1h - 60 min

xh - 75 min

\(60x = 75\)

\(x = \frac{75}{60}\)

\(x = 1.25\)

75 minutes is 1.25 hours. So we have to find f(1.25).

\(f(1.25) = 4.5 + 1.5*(1.25-1) = 4.875\)

The cost of parking in the garage for 75 minutes is 4.875.

Answer:

3:2

Step-by-step explanation:

Triangles ABC and PMN are similar.  This is evident from the marks identifying equal angles.

The ratio of the two longest sides is 20:30, or 2:3.

The ratio of the two shortest sides is 12:18, or 2:3.

Finally, the ratio of the two sides of intermediate length is 16:24, or 2:3.

The scale factor of the alrger triangle to the smaller triangle is 3:2.

The negative trend pattern exists in the given data.

The Given information is as follows: Month 1 2 3 4 5 6 7

Value 23 15 20 12 18 22 15

To find: What type of pattern exists in the data

The pattern that exists in the given data can be determined by creating a graph between month and value. So, the graph will be as follows: Type of pattern: From the above graph, it is evident that there is a Negative trend pattern in the data. Answer: (d) Negative trend pattern.

Conclusion: Thus, the negative trend pattern exists in the given data.

To know more about negative visit

https://brainly.com/question/1929368

#SPJ11

we know that

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y)

so

the rule is

(x,y) -----------> (-x,-y)

Applying the rule of the rotation to the given figure

we have the following coordinates

A(1,5) -----------> A'(-1,-5)

B(4,8) ---------> B'(-4,-8)

C(7,7) --------> C'(-7,-7)

D(7,5) ------> D'(-7,-5)

E(5,3) ------> E'(-5,-3)

using a graphing tool

Draw the image of the rotated figure

see the attached figure

please wait a minute

Answer:

B,C,F

Step-by-step explanation:

That's the answer. Hope that helps.

representing the number on number line a < -1/2

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence.

given that

4(2a+3)<7-2a

firstly solve the equation so now multiply 4 with 2a and 3 .

8a + 12<7-2a

then move -2a to the left side and +12 to right side. then -2a changes to +2a and +12 changes to -12

8a + 2a < - 12 + 7

now add the values on both sides

10a < - 5

now divide the both sides by 10

\( \frac{10}{10} a < - \frac{5}{10} \)

\(a < - \frac{1}{2} \)

so ,

\(a < - \frac{1}{2} \)

Learn more about number line, refer :

https://brainly.com/question/24644930

#SPJ9

The 95% prediction interval for the adjusted distribution volume of a single healthy individual is approximately 12.03 to 76.89.

To calculate a 95% prediction interval for the adjusted distribution volume of a single healthy individual based on the given data, follow these steps:

1. Calculate the mean (µ) and standard deviation (σ) of the sample:
Mean (µ) = (22+39+40+42+43+46+51+57+64+65+68+69+72) / 13 = 578 / 13 = 44.46
Standard deviation (σ) = √(Σ(x-µ)² / (n-1)) = 15.15 (approx.)

2. Find the t-value corresponding to a 95% prediction interval for 12 degrees of freedom (n-1) from a t-distribution table or calculator (e.g., online t-table or calculator). The t-value for 12 degrees of freedom and 95% prediction interval is 2.179 (approx.).

3. Calculate the prediction interval using the following formula:
Prediction interval = µ ± t * σ * √(1 + (1/n))
Prediction interval = 44.46 ± 2.179 * 15.15 * √(1 + (1/13))

4. Compute the final values:
Lower bound: 44.46 - 2.179 * 15.15 * √(1 + (1/13)) = 12.03 (approx.)
Upper bound: 44.46 + 2.179 * 15.15 * √(1 + (1/13)) = 76.89 (approx.)

Know more about adjusted distribution volume here:

https://brainly.com/question/29399152

#SPJ11

Answer:

3rd option

Step-by-step explanation:

∠ 1 and 75° are corresponding angles and are congruent , so

∠ 1 = 75°

Answer:

a) 0.8

b) 0.3

c) 0.9

d) 0.95

Step-by-step explanation:

A probability always adds up to 1. It is between the scale of 0 (never likely) to 1 (very likely).

So:

1 - 0.2 = 0.8

1 - 0.7 = 0.3

1 - 0.1 = 0.9

1 - 0.05 = 0.95

Hope this helped!

The conclusion can be drawn that this is a contradiction since y was assumed to be an irrational number.

The statements are:

x . y = m/n

substituting the values.

a/b . y = m/n

multiplication property of equality.

b/a . a.b . y  = m/n . b/a

simplify.

y = mb/na

The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.

To learn more about rational number check the link below:

https://brainly.com/question/12088221

#SPJ4

Answer:

42 cm^2

Step-by-step explanation:

Base = 21 cm

Height = 4 cm

Area = \(\frac{base\times height}{2}\)

Substitute values into the given equation

\(A = \frac{21\times 4}{2} \\\\A = \frac{84}{2} \\\\A = 42cm^2\)

Given that a conductive coating in micrometers has a density function of 600x-2 for 100 ?m < x < 120 m.

We are to determine the mean and variance of the coating thickness and the average cost of the coating per part.

Step 1: Mean of the coating thickness: Mean μ = ∫xf(x)dx, where f(x) is the probability density function of x.μ = ∫100x(600x-2)dx [120-100]μ = 196.078 μm

Therefore, the mean of the coating thickness is 196.078 μm.Step 2: Variance of the coating thickness: Variance σ² = E(x²) - [E(x)]² where E(x²) and E(x) are the expected values of x² and x respectively(x²) = ∫x²f(x)dx, [120-100]E(x²) = 13,336.40μ²E(x) = ∫xf(x)dx, [120-100]E(x) = 38,422.59μ²σ² = E(x²) - [E(x)]²σ² = 2,193,272.27 μ²

Therefore, the variance of the coating thickness is 2,193,272.27 μ².Step 3: Average cost of the coating per part:We have been given that the cost of the coating is $0.50 per μm of thickness on each part.

Hence, the average cost of the coating per part is:$0.50 x 196.078$ = $98.04

Therefore, the average cost of the coating per part is $98.04.

For more information on average cost visit:

https://brainly.com/question/14415150

#SPJ11

Answer:

terminating decimal maybe :)

Step-by-step explanation:

Answer:

what goes in the blank space: repeating

Step-by-step explanation:

Any rational number (that is, a fraction in the lowest terms) can be written as either a terminating decimal or a repeating decimal.

Answer:

3

Step-by-step explanation:

Answer:

We know that the distributive property says this:

a(b+c) = ab + ac

If we apply this to our case, we can put

3a(2b+c) = 3a * 2b + 3a * c

When we multiply numbers and letters, we should multiply both of them:

3a * 2b + 3a * c = 3*2*a*b + 3*a*c = 6ab +3ac

We can use this when we find a number multiplied by a parenthesis..

Answer:

6ab + 3ac

Step-by-step explanation:

3a(2b) + 3a(c)

6ab + 3ac

Answer: (8,8)

Step-by-step explanation: because, you just need to do the math

The equation of line is y = ( 3/4 )x + 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( 8 , 8 )

Let the second point be Q = Q ( 4 , 5 )

Now , the slope of the line between the two points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 8 ) / ( 4 - 8 )

Slope m = -3/-4

Slope m = 3/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 3/4 ( x - 8 )

On simplifying the equation , we get

y - 8 = ( 3/4 )x - 6

Adding 8 on both sides of the equation , we get

y = ( 3/4 )x + 2

Therefore , the value of A is y = ( 3/4 )x + 2

Hence , the equation of line is y = ( 3/4 )x + 2

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ2