Evaluate the following indefinite integral. ∫x6ex−7x5​/x6dx ∫x6ex−7x5​/x6dx=___

The number of the 1(3/4) inch blocks will be 34 out of the 5 feet of stock.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 1 3/4-inch long machine bolt blanks can be cut from a 5-foot length of the stock. The number of the blocks will be calculated as below:-

Number = 5 foot / ( 1(3/4)

Number = 60 / ( 7/4)

Number = 34.2

Therefore, the number of the 1(3/4) inch blocks will be 34.

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Answer:

n is a neutron , the symbol n stands for neutron

Step-by-step explanation:

63000 = 6.3 x 10n

63000 / 6.3 = 10n (Divide by 6.3)

10000 = 10n

10000 / 10 = 10n / 10 (Divide both sides by 10)

n = 1000

6.3 x 10(1000) = 63000 (Check!)

In a right-skewed distribution, the correct answer is: a. The mean tends to be greater than the median.

In a right-skewed distribution, the tail of the distribution is longer on the right side, indicating that there are a few extreme values that pull the overall distribution towards the right. As a result, the mean is typically influenced by these extreme values and tends to be greater than the median.

The median represents the middle value in a distribution when the data points are arranged in order. Since the right-skewed distribution has a longer tail on the right side, the median is less affected by the extreme values and tends to be closer to the values in the bulk of the distribution.

Therefore, option a is the correct answer: In a right-skewed distribution, the mean tends to be greater than the median.

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Answer:

Division!

Step-by-step explanation:

(1/6) ÷ (3/7)

(1/6)(7/3)

= 7 / 18

Answer:

90°, 62.8° and 27.2°

Step-by-step explanation:

180 = 5x + 133

47 = 5x

9.4= x

2 * 9.4 + 44 = 62.8°

3 * 9.4 - 1 = 27.2°

Answer:

C i think very sorry if im wrong i can't really read it

Step-by-step explanation:

Answer:

6(x)

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

x represents a number, it is also called a variable.

If there is 2 of x, it would be represented like this: 2x

If there is 1 of x, it would be represented like this: x

The z score for a data value of 45 if the mean of a set of data is 59 and the standard deviation is 13.9. is -1.00719424.

A data point's z-score indicates how many standard deviations it is from the population mean. Any raw data value on a normal distribution can yield a z-score.

When a z-score is calculated, a raw data value is transformed into a standardized score on a standardized normal distribution. Since z-scores are expressed in terms of standard deviations, they enable you to compare data from various samples.

A high z-score indicates that the data value is above average. A negative z-score indicates that something is below average.

A z-score table can be used to determine the proportion of the population that falls above or below any given z-score.

The z-score is given by z = (x-μ)/σ

where x is the data value, μ is the mean and σ is the standard deviation.

μ = 59, σ = 13.9 and x = 45

Putting these values in the formula of z.

We get,

\(z = \frac{45 - 59}{13.9} = -1.00719424\)

Hence, the z score is -1.00719424.

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Answer:

  a) 5

Step-by-step explanation:

The shortest distance between Henry and Claire will be found when Henry lives on a straight line between Saul and Claire.

__

Henry must live at least 20-14 = 6 miles from Claire. It is not possible for the distance to be 5 miles.

To achieve the least area, create two separate square enclosures, each with a side length of 25 m. For the greatest area, make one enclosure with a side length of 49 m and another with a side length of 1 m.

To determine the plans for the least and greatest areas using 200 m of fencing, we'll consider two cases: one square enclosure and two square enclosures.

Case 1: One square enclosure
Perimeter = 200 m
Since the perimeter of a square is 4 * side length (s), we have:
200 = 4 * s
s = 50 m

Area of one square enclosure = s^2 = 50^2 = 2500 m^2

Case 2: Two square enclosures
Let s1 and s2 be the side lengths of the two square enclosures.
Perimeter = 200 m
4 * (s1 + s2) = 200
s1 + s2 = 50
Since the area of a square is side length squared, we have:
Area = s1^2 + s2^2

To minimize the area, make the side lengths equal:
s1 = s2 = 25 m
Minimum area = 2 * (25^2) = 2 * 625 = 1250 m^2

To maximize the area, make one side length as large as possible while keeping the perimeter constraint:
s1 = 49 m, s2 = 1 m
Maximum area = 49^2 + 1^2 = 2401 + 1 = 2402 m^2

Therefore, to achieve the least area, create two separate square enclosures, each with a side length of 25 m. For the greatest area, make one enclosure with a side length of 49 m and another with a side length of 1 m.

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The solution to the initial value problem y'=2y^2, y(0)=y0 will have a vertical asymptote at t=3 and a t-interval of existence\((-∞, 3)\) for y0 = -1/6.

To find the solution of the initial value problem\(y'=2y^2, y(0)=y0\), we can use separation of variables and integrate both sides to get:

\(∫1/y^2 dy = ∫2 dt\)

This simplifies to:

\(-y^-1 = 2t + C\)
Where C is the constant of integration. Solving for y, we get:

y = -1/(2t + C)

To find the value(s) of y0 that will result in a vertical asymptote at t=3, we need to set C=6. This is because the denominator of y becomes 0 when 2t + C = 0, or when t = -C/2. Therefore, we want t=3 to be equal to -C/2, or C=-6.

Substituting C=-6 into our expression for y, we get:

y = -1/(2t - 6)

This function has a vertical asymptote at t=3, since the denominator becomes 0 when 2t - 6 = 0, or when t=3.

To find the interval of existence of this solution, we need to check when the denominator of y becomes 0 again. This happens when 2t - 6 = 0, or when t=3. Therefore, the interval of existence of the solution is (-∞, 3) or t < 3.

In summary, the solution to the initial value problem \(y'=2y^2, y(0)=y0\) will have a vertical asymptote at t=3 and a t-interval of existence \((-∞, 3)\) for y0 = -1/6.

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From the given options, it appears that option C, \( X = (\bar{A} \cdot \bar{B}) + (B \cdot C) \), best describes the action of the circuit based on the logical operations performed.

To determine which of the given Boolean equations describes the action of the circuit, let's analyze each equation step by step.

A. \( X = (\overline{A \cdot B}) + (B \cdot C) \)

In this equation, \( X \) is the output of the circuit. The first term, \( (\overline{A \cdot B}) \), represents the negation of the logical AND operation between \( A \) and \( B \). The second term, \( (B \cdot C) \), represents the logical AND operation between \( B \) and \( C \). The two terms are then summed using the logical OR operation.

B. \( X = (A \cdot B) \cdot (B + C) \)

In this equation, \( X \) is the output of the circuit. The first term, \( (A \cdot B) \), represents the logical AND operation between \( A \) and \( B \). The second term, \( (B + C) \), represents the logical OR operation between \( B \) and \( C \). The two terms are then multiplied using the logical AND operation.

C. \( X = (\bar{A} \cdot \bar{B}) + (B \cdot C) \)

In this equation, \( X \) is the output of the circuit. The first term, \( (\bar{A} \cdot \bar{B}) \), represents the negation of \( A \) ANDed with the negation of \( B \). The second term, \( (B \cdot C) \), represents the logical AND operation between \( B \) and \( C \). The two terms are then summed using the logical OR operation.

It's important to note that without additional context or a specific circuit diagram, we can't definitively determine the correct equation for the circuit. The given equations represent different logic configurations, and the correct equation would depend on the specific circuit design and desired behavior.

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Answer:

14cm

Step-by-step explanation:

All side lengths in a cube will be 7 as the properties of a cube are such that all the side lengths are the same.

Think of the longest line in a cube as a hypotenuse on a triangle.

\(7^{2} + 7^{2} = c^{2}\)

49 + 49 = \(c^{2}\)

\(c^{2}\) = 98

c = \(\sqrt{98}\)

\((\sqrt{98})^{2} + (\sqrt{98} )^{2}\) = \(c^{2}\)

\(c^{2}\) = 98 + 98

\(c^{2}\) = 196

c = \(\sqrt{196}\)

c = 14

The longest line in a cube that has a side length of 7cm is 14cm.

Answer:

what we are trying to prove

Step-by-step explanation:

The answer will be 5.9°Fahrenheit

Answer:

y = 3/4x + 2

Step-by-step explanation:

Not sure if you wrote your answer choices incorrectly, but if B is y=3/4x + 2 then the answer is B

a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

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Answer:

width = 5cm

Step-by-step explanation:

hope it helps

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

Define Angle ?

In mathematics, an angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex.

a. The angle 0 is measured from the positive x-axis in a counterclockwise direction. In the Cartesian coordinate system, the positive x-axis lies on the right side of the coordinate plane. Since the angle 0 starts from this position, it falls within the 1st quadrant. The 1st quadrant is the region where both x and y coordinates are positive.

b. The reference angle is the positive acute angle between the terminal side of an angle and the x-axis. Since the angle 0 lies entirely on the positive x-axis, the terminal side coincides with the x-axis. In this case, the reference angle for 0 radians is 0 radians itself. The reference angle is always positive and its value is less than or equal to π/2 radians (90 degrees).

c. To find the point where 0 intersects the unit circle, we consider the trigonometric functions cosine and sine. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.

For angle 0, the cosine function gives the x-coordinate on the unit circle, and the sine function gives the y-coordinate. Since 0 lies on the positive x-axis, the x-coordinate is 1 (cos(0) = 1), and the y-coordinate is 0 (sin(0) = 0). Therefore, the point of intersection with the unit circle for angle 0 is (1, 0).

In summary, angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

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sa paanong paraan nagiging instrumento

Answer:

Steps below

Step-by-step explanation:

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After evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the main trigonometric identities.

We must apply the sine rule and the cosine rule to the non-right-angled triangles.

So, we have the function:

tan (15π - 2t)

Now, evaluate as follows:

(15π - 2t)

Rewrite using trigonometric identities:

- sin(2t)/cos(2t)

Rewrite using trigonometric identities:

- tan(2t)

Therefore, after evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

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The 20th percentile is 20,

The 25th percentile is 22.50.

The 65th percentile is 28.

The 75th percentile is 29.

Given values:

27, 25, 20, 15, 30, 34, 28, and 25.

n = 8

sorting the data gives:

15, 20, 25, 25, 27, 28, 30, and 34.

= 20/100 * 8

= 1.6 ≈ 2

1.6 is rounded to 2, the second value is in the sorted data set is 20 hence the 20th percentile is 20

= 25/100 * 8

= 2

Since 2 is an integer, the mean of the 2nd and the 3rd values in the sorted data set gives the 25th percentile.

( 20 + 25 ) / 2 = 22.5

hence the 25th percentile is 22.50

= 65/100 * 8

= 5.2 ≈ 6

5.6 is rounded to 6, the sixth value is in the sorted data set is 28 hence the 65th percentile is 28

= 75/100 * 8

= 6

Since 6 is an integer, the mean of the 6th and the 7th values in the sorted data set gives the 75th percentile.

( 28 + 30 ) / 2 = 29

hence the 75th percentile is 29

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Answer:

20-24

Step-by-step explanation:

you can see that when you find the middle of the total data the data set left is in the 20-24 category

hope this helps! :)

A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.

A normal number is a number that can be communicated as the proportion of two whole numbers, where the denominator isn't equivalent to nothing. This implies that a normal number can be written in the structure p/q, where p and q are numbers and q isn't equivalent to nothing.

For instance, 3/4, 7/2, and - 5/6 are instances of normal numbers. Be that as it may, numbers like pi (π) and the square foundation of 2 (√2) are not objective, since they can't be communicated as a proportion of two numbers.

Normal numbers are significant in math, as they structure a subset of the genuine numbers and can be utilized to address amounts in a wide range of settings, like portions, proportions, and probabilities. They are additionally utilized broadly in polynomial math, where they structure the reason for tackling conditions and controlling articulations.

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Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E

Given data:

S = initial amount = $54

D = the number of days

C = the cost per day = $6

E: the ending amount = $18

Amelia started with S=$54 and spent C=$6 each day at camp.

Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:

C x D = 6D

Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:

S - (C x D) = E

Substituting the values in the equation we get:

54 - 6D = 18

54 - 18 = 6D

36 = 6D

D = 6

Therefore, Amelia was at camp for 6 days.

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Answer:

Step-by-step explanation:

Comment

n = the discriminant  of the quadratic equation. That is n = √(b^2 - 4ac)

a = 1

b = -3

c = 1

n = √(9 - 4(1*1)) = √5

Answer n = √5

Answer:

A. 25%

B. Candidate B

C. 60% of voters chose Candidate A and Candidate C

Step-by-step explanation:

Answer:

Main can buy 8 tickets.

Step-by-step explanation:

Use the equation total amount ÷ cost of each ticket

Input your information: $36 ÷ $4.50

The equation adds up to 8.

So therefore, Main can buy 8 tickets.