Write the expression using only positive exponents. Assume no denominator equals zero.
(-3x^4 y^(-7) )^(-3)
Please show work

The required number of revolution for small gear is 2

The given figure is a  circle,

Then,

Radius of big circle = 7

radius of small circle = 3

Since we know that perimeter of circle = 2πr

Therefore,

Perimeter of big circle = 2x7x(22/7)

                                     =  44 square units

Perimeter of small circle = 2x3x(22/7)

                                     =  18.84 square units

Now the umber of revolution for small gear to complete a single revolution of the larger gear = 44/18.84 = 2.33 ≈ 2

Hence, number of revolution = 2.

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From the convergence test, the radius of Convergence, R for the series [tex]\sum_{n = 1}^{\infty} \frac{n(x - 2)^n}{n^3} \\ [/tex] is equals to 1.

The radius of convergence of a power series is defined as the distance from the center to the nearest point where the series converges. In this problem, we have to determining the interval of convergence we'll use the series ratio test. We have an infinite series is [tex]\sum_{n =1}^{\infty}\frac{n(x - 2)^n}{n^3}\\ [/tex]

Consider the nth and (n+1)th terms of series, [tex]U_n = \sum_{n = 1}^{\infty} \frac{(x - 2)^n}{n²} \\ [/tex]

[tex]U_{n + 1} = \sum_{n = 1}^{\infty} \frac{(x - 2)^{n+1}}{{(n+1)}^2} \\ [/tex]

Using the radius of convergence formula,

[tex]\lim_{n → \infty} \frac{ U_{n + 1} }{U_n} = \lim_{n→\infty} \frac{ \frac{(x - 2)^{n+1}}{(n+ 1)^2} }{\frac{(x - 2)^n}{n²} } \\ [/tex]

[tex]= \lim_{n →\infty} \frac{(x - 2)^{n+1}}{{(n+ 1)}^2} × \frac{n²} {(x - 2)^n} \\ [/tex]

[tex]= \lim_{n → \infty} \frac{(x - 2)n²} {(n+ 1)²} \\ [/tex]

[tex]= \lim_{n → \infty} \frac{(x - 2)} {(1+ \frac{1}{n})²} \\ [/tex]

= x - 2

By D'alembert ratio test [tex]\sum_{n = 1}^{\infty} U_n \\ [/tex], converges for all |x - 2| < 1, therefore R = 1 and interval of convergence is -1 < x- 2 < 1

⇔ 1 < x < 3 ⇔ x∈(1,3), so interval is (1,3).

Hence, required value is R = 1.

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Complete question:

find the radius of convergence, r, of the series [tex]\sum_{n =1}^{\infty}\frac{n(x - 2)^n}{n^3}\\ [/tex].

The fraction of the shape that is shaded is determined as 3/10.

The fraction of the shape that is shaded is the ratio of the shaded area to the total area of the shape.

The area of the shaded shape is calculated as follows;

Area = ¹/₂ x base x height

Let the height of the figure = h

Area = ¹/₂ x 12 mm x h

Area = 6h

The area of the trapezoid is calculated as follows;

Area = ¹/₂ (sum of parallel sides ) x height

Area = ¹/₂ ( 28 mm + 12 mm ) x h

Area = ¹/₂ (40 mm ) x h

Area = 20h

The fraction of the shape that is shaded is calculated as follows;

= 6h / 20h

= 6/20

= 3/10

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Answer:A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

This ultimately implies that, any polygon with three (3) lengths of sides is a triangle.

In Geometry, there are three (3) main types of triangle based on the length of their sides and these are;

Equilateral triangle.

Scalene triangle.

Isosceles triangle.

An isosceles triangle has two (2) congruent sides that are equal in length and two (2) equal angles while the third side has a different length.

Step-by-step explanation:

Answer:

630

Step-by-step explanation:

if it takes 1 hour for it to fill up by 70 ft³

then after 9 hours it is full.

9 X 70 = 630 ft³

a)There are 15,120 agent arrangements where order is important.b)The number of agent arrangements where order is not important is 1.

(a) When order is important, we are looking for the number of permutations. To calculate the number of agent arrangements for the 5 new customers, we use the formula:

nPr = n! / (n-r)!

where n is the number of agents (9), r is the number of customers (5), and ! represents the factorial.

9P5 = 9! / (9-5)!
= 9! / 4!
= 15,120

There are 15,120 agent arrangements where order is important.

(b) When order is not important, we are looking for the number of combinations. In this case, since each customer must be assigned an agent, there's only one way to distribute the agents, as all customers will receive service regardless of agent order. Therefore, the number of agent arrangements where order is not important is 1.

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Answer:

20

Step-by-step explanation:

h (x) = - 2x + 12

h (-4) = - 2(-4) + 12

        = 8 + 12

h (-4) = 20

The required sample size (total) to reject the claim of men in the age group 20-30 averaging the same height in inches in the U.S. and the Netherlands, assuming both populations have a population standard deviation of 4, would be 1456.

To calculate the required sample size, we need to use the formula for sample size calculation in two-sample t-tests, which takes into account the desired level of significance, power, effect size, and population standard deviation. In this case, we want to be 99% confident (i.e., 1% level of significance) and have 90% power, which corresponds to a z-value of 2.33 and a t-value of 1.645. The effect size is 0.5/4 = 0.125, and plugging these values into the formula, we get a required sample size of 1456. This means that if we take a sample of 728 men from each population and find a difference of 0.5 inches or more between their means, we can reject the claim with 99% confidence and 90% power.

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The determinant of the matrix (3a-1b2at) is -288.

Now let's move on to solving the given problem. We are given that the determinant of matrix a is 1, and the determinant of matrix b is -4. We need to calculate the determinant of the matrix (3a-1b2at).

We can start by using the properties of determinants to simplify the expression. The determinant of a product of matrices is equal to the product of their determinants, i.e., det(AB) = det(A) det(B). Using this property, we can write:

[tex]det(3_{(a-1)}b_2a_t) = det(3a) det(-1b) det(2at)[/tex]

Since the determinant of -1b is -1 times the determinant of b, we can simplify further:

[tex]det(3_{a-1}b_2a_t) = det(3a) (-1) det(b) det(2at)[/tex]

Now we can substitute the values given in the problem: det(a) = 1 and det(b) = -4. We also know that det(at) = det(a), since the determinant of the transpose of a matrix is the same as the determinant of the original matrix. Therefore:

det(3a-1b2at) = det(3a) (-1) det(b) det(2a)t

= 3³ det(a) (-1) (-4) 2³ det(a)

= -288 det(a)²

= -288

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A 1992 study of bull terriers found the following: (i) 50% of the studied bull terriers are white. (ii) 11% of the studied bull terriers are deaf. (iii) 20% of the white bull terriers are deaf. The probability that a randomly chosen bull terrier is white and deaf is 0.1, or 10%.

To find the probability that a randomly chosen bull terrier is white and deaf, we can use the given information from the study:
(i) 50% of the studied bull terriers are white (P(White) = 0.5)
(iii) 20% of the white bull terriers are deaf (P(Deaf|White) = 0.2)
Now, we can apply the conditional probability formula to find the probability of a bull terrier being both white and deaf:
P(White and Deaf) = P(Deaf|White) * P(White)
P(White and Deaf) = 0.2 * 0.5
P(White and Deaf) = 0.1

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The given matrix is not square, so it does not have eigenvalues or eigenvectors. The concept of eigenvalues and eigenvectors only applies to square matrices.

For a given square matrix A, if there exists a non-zero vector v and a scalar λ such that Av = λv, then λ is an eigenvalue of A and v is an eigenvector of A corresponding to λ.

In the given problem, the matrix is not square. Therefore, the concept of eigenvalues and eigenvectors does not apply.

If we assume that the given matrix is a typo, and it is actually a 2x2 matrix, then we can find the eigenvalues and eigenvectors as follows:

Let A be the given matrix, and then the characteristic polynomial of A is given by det(A-λI), where I is the identity matrix and det() is the determinant function. Solving the characteristic equation, we get the eigenvalues of A as λ1 = 4 + 5i and λ2 = 4 - 5i.

To find the corresponding eigenvectors, we solve the system of linear equations (A-λI)x=0, where λ is each eigenvalue. For λ1 = 4 + 5i, we get the eigenvector v1 = [2 + i, 1]^T, and for λ2 = 4 - 5i, we get the eigenvector v2 = [2 - i, 1]^T.

Therefore, if the given matrix is actually a 2x2 matrix, the eigenvalues are λ1 = 4 + 5i and λ2 = 4 - 5i, and the corresponding eigenvectors are v1 = [2 + i, 1]^T and v2 = [2 - i, 1]^T.

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The area of the region bounded by the curve r = e^(θ/2) and the sector π ≤ θ ≤ 3π/2 can be found by integrating the equation for the area of a sector and subtracting the area of the triangle formed by the origin and the two points where the curve intersects the sector.

The resulting integral is: A = (1/2)∫π^(3π/2) (e^(θ/2))^2 dθ - (1/2)(e^(π/2))^2 - (1/2)(e^(3π/2))^2Simplifying and evaluating the integral and the two triangle areas gives:  A = 2(e^3/2 - e^π/2) ≈ 7.737 Therefore, the area of the region bounded by the curve r = e^(θ/2) and the sector π ≤ θ ≤ 3π/2 is approximately 7.737 units^2.

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Thus,  the crash rate on the road last year was 21.8 crashes per million vehicles.

To calculate the crash rate on the road last year, we need to use the formula:
Crash Rate = (Number of Crashes / Exposure) x 1,000,000

Where exposure is the measure of traffic volume and can be represented by the two-way Average Annual Daily Traffic (AADT) in this case.

The given two-way AADT for the road section is 755 vehicles per day.

To convert this to total annual traffic volume, we need to multiply it by 365 days:

Total Annual Traffic Volume = 755 vehicles/day x 365 days/year = 275,575 vehicles/year

Now we can calculate the crash rate:
Crash Rate = (6 crashes / 275,575 vehicles) x 1,000,000 = 21.8 crashes per million vehicles

Therefore, the crash rate on the road last year was 21.8 crashes per million vehicles. This means that for every million vehicles that traveled on this road section, there were 21.8 crashes. It's important to note that crash rates are useful measures of safety because they account for exposure to risk, which is influenced by traffic volume.

A higher traffic volume means more exposure to risk, so the crash rate provides a fair comparison of safety between different roads.

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The general solution of the differential equation
y''(t) = 28e^(4t)sin(6t) is y(t) = c1e^(4t)sin(6t) + c2e^(4t)cos(6t).

To find the general solution of the differential equation
y''(t) = 28e^(4t)sin(6t), we can solve the homogeneous equation y''(t) = 0 and then find a particular solution for the non-homogeneous equation.

The homogeneous equation is y''(t) = 0, which has the general solution y(t) = c1 + c2t, where c1 and c2 are arbitrary constants.

To find a particular solution for the non-homogeneous equation, we can use the method of undetermined coefficients. Since the non-homogeneous term is of the form e^(4t)sin(6t), we can assume a particular solution of the form y_p(t) = Ate^(4t)sin(6t) + Bte^(4t)cos(6t). After taking the first and second derivatives, we can substitute them back into the original equation and solve for the coefficients A and B.
We obtain A = -7/200 and B = 3/100.

Therefore, the general solution of the differential equation
y''(t) = 28e^(4t)sin(6t) is y(t) = c1e^(4t)sin(6t) + c2e^(4t)cos(6t) - (7/200)te^(4t)sin(6t) + (3/100)te^(4t)cos(6t), where c1 and c2 are arbitrary constants.

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The correct factor of both terms of the expression 2d - 10 is,

⇒ 2

Since, A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

We have to given that;

An expression is,

⇒ 2d - 10

Since, There are two terms in expression which are 2d and - 10.

And,

2d = 2 × d

- 10 = - 2 × 5

Therefore, The correct factor of both terms of the expression 2d - 10 is,

⇒ 2

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If the universal set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} then (A ∪ B) ∩ C = {1, 3, 5}, A' U B = {0, 2, 4, 6, 7, 8, 9} and  (A ∩ C)' = {0, 2, 4, 6, 7, 8, 9}.

The universal set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

To find (A ∪ B) ∩ C, we first need to find A ∪ B and then find the intersection with C.

A ∪ B is the set of all elements that are in A or B, so:

A ∪ B = {1, 2, 3, 4, 5, 6, 8}

Now we need to find the intersection of A ∪ B and C:

(A ∪ B) ∩ C = {1, 3, 5}

Therefore, (A ∪ B) ∩ C = {1, 3, 5}.

b. A' is the complement of A, which means it is the set of all elements in U that are not in A.

A' = {0, 6, 7, 8, 9}

A' U B is the set of all elements that are in A' or B, so:

A' U B = {0, 2, 4, 6, 7, 8, 9}

Therefore, A' U B = {0, 2, 4, 6, 7, 8, 9}.

c. A ∩ C is the set of all elements that are in both A and C:

A ∩ C = {1, 3, 5}

(A ∩ C)' is the complement of A ∩ C, which means it is the set of all elements in U that are not in A ∩ C:

(A ∩ C)' = {0, 2, 4, 6, 7, 8, 9}

Therefore, (A ∩ C)' = {0, 2, 4, 6, 7, 8, 9}.

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As t approaches infinity, the exponential term (1-e^(-rt)) approaches 1, so the velocity of the skydiver approaches -a(1-1) = -a(0) = 0. Therefore, the answer is (A) 0. The exact value of b is (E) -ln(0.3) / 10.

To determine the exact value of b, we can use the given information and plug in the values into the equation v(t) = -a(1-e^(-bt)). We know that v(10) = 70, so we can substitute those values and solve for b:

70 = -a(1-e^(-10b))
-70/a = 1-e^(-10b)
e^(-10b) = 1 - 70/a
-10b = ln(1-70/a)
b = -ln(1-70/a)/10

So the exact value of b is (B) -ln(1-70/a)/10.

To answer your question, let's first correct the function: v(t) = a(1 - e^(-bt)), where v(t) is the velocity of the skydiver at time t, and a and b are positive constants.

3. To find the skydiver's velocity as t approaches infinity (t -> ∞), analyze the limit of the function:

lim (t->∞) a(1 - e^(-bt))

As t approaches infinity, the term e^(-bt) approaches 0, because the exponent becomes increasingly negative. Therefore, the function approaches:

a(1 - 0) = a

The skydiver's velocity approaches (D) a.

4. Given that a = 100 and the skydiver's velocity is 70 feet per second after 10 seconds, we can find the exact value of b. Plug these values into the function:

70 = 100(1 - e^(-10b))

Now, solve for b:

0.7 = 1 - e^(-10b)
e^(-10b) = 0.3
-10b = ln(0.3)
b = -ln(0.3) / 10

The exact value of b is (E) -ln(0.3) / 10.

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I think the area is 398.48m²

Answer: $11

Step-by-step explanation:

88/8 = 11

Answer = No Solution

Answer:

[tex] log(30) + log( \frac{x}{2} ) = log(60) [/tex]

[tex] log(30( \frac{x}{2} ) ) = log(60) [/tex]

[tex]30( \frac{x}{2} ) = 60[/tex]

[tex] \frac{x}{2} = 2[/tex]

[tex]x = 4[/tex]

The solution of the equation for f is given as follows:

f = (P + 8)/16.

The equation for the perimeter of the triangle in this problem is given as follows:

2(3f-7) + 2(5f+3) = P.

The first step in solving for f is applying the distributive property at the left side of the equality, hence:

6f - 14 + 10f + 6 = P

Then the solution is obtained combining the like terms, then isolating the variable f, as follows:

16f - 8 = P

f = (P + 8)/16.

Meaning that the second option is the correct option in the context of this problem.

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The values of a and b for the function f(x) = (4x+b)/(ax+7) to have x=5 as a vertical asymptote and y=6 as a horizontal asymptote are a=1/6 and b=24.

For the function to have x=5 as a vertical asymptote, the denominator ax+7 must approach 0 as x approaches 5. This means that a must be equal to 1/6 to make ax+7 equal to 0 when x=5.

For the function to have y=6 as a horizontal asymptote, the limit of f(x) as x approaches infinity should be equal to 6. Therefore, we can use the fact that f(x) approaches b/a as x approaches infinity.

If we set b/a = 6, we can solve for b to get b = 6a.

Substituting the value of a we found earlier, we get b = 4.

Therefore, the values of a and b that satisfy the conditions are a=1/6 and b=24.

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Answer:4

Step-by-step explanation:

because A is actually 6,3 while B is 6,7 A to get 7 is 4 time

hope that helps u girl !!

Vector equation with parameter t for the line through the origin and the point (4,13,-10) is:

r(t) = t<4, 13, -10>

To find the vector equation with parameter t for the line through the origin and the point (4,13,-10), we first need to find the direction vector of the line. The direction vector is the vector that starts at the origin and ends at the point (4,13,-10). We can find this vector by subtracting the coordinates of the origin from the coordinates of the point:

<4, 13, -10> - <0, 0, 0> = <4, 13, -10>

This vector represents the direction of the line. To get the vector equation with parameter t, we just need to multiply this direction vector by t and add it to the position vector of the origin, which is <0,0,0>. This gives us the equation:

r(t) = t<4, 13, -10>

where r(t) is the position vector of any point on the line for a given value of t. We can see that when t=0, r(t) = <0,0,0>, which is the position vector of the origin. When t=1, r(t) = <4, 13, -10>, which is the position vector of the point (4,13,-10). Therefore, this equation represents the line passing through the origin and the point (4,13,-10).

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The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

In Mathematics and Geometry, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

According to the Linear Pair Postulate which states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair, we have:

m∠5 + m∠6 =180°.

As a general rule in geometry, the sum of all the angles that are formed by a triangle is equal to 180º and this gives:

m∠2 + m∠3 + m∠5 = 180°.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The value of m by using the Law of Cosines is 586.72​

We are given that;

In triangle whose side are 13in and 20in angle between those lines is 93degree.

Now,

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds:

c^2=a^2+b^2−2abcosC

We want to find c, which is the same as m. So we plug in the given values into the equation and solve for c:

c^2=13^2+20^2−2(13)(20)cos93

c^2=169+400−520cos93

c^2=569−520(−0.0523)

c^2=586.72

c=586.72​

Therefore, by law of cosines the answer will be 586.72​.

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(a) If a is finite, then we know exactly how many elements are in a. For example, if a = {1, 2, 3}, then we know that a has three elements. In this case, we can tell exactly how big a is.

(b) If a is countably infinite, then we know that a has the same cardinality (size) as the set of natural numbers.

This means that we can put the elements of an in a one-to-one correspondence with the natural numbers.

For example, if a = {2, 4, 6, ...}, then we can list the elements of an as a_1 = 2, a_2 = 4, a_3 = 6, and so on. In this case, we can tell how big a is, but it's an infinite size.

(c) If a is uncountable, then we know that a is larger than the set of natural numbers. This means that we cannot put the elements of an in a one-to-one correspondence with the natural numbers.

For example, if a is the set of all real numbers between 0 and 1 (excluding 0 and 1 themselves), then there are uncountably many elements in a. In this case, we can't tell exactly how big a is, but we know that it's larger than the set of natural numbers.

(d) Finally, if we don't have any information about a, then we can't tell how big a is. It's possible that a could be finite, countably infinite, uncountable, or even something else entirely.

Without more information, we simply can't say for sure.

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Note that the standard deviation for the distribution is 1.32 (Option B)

The mean of the distribution can be calculated like this

μ = Σ (x * p(x))

μ =    (1 x 0.02) + (2 x 0.17) + (3 x 0.29) + (4 x 0.27) + (5 x  0.15) + (6 x 0.07)  + (7 x 0.03)

μ = 3.58

The variance can be calculated as:

σ² = Σ( x - μ)² * p ( x) )

= (1 - 3.58)² x 0.02 + (2 - 3.58)² x 0.17 + (3 - 3.58)² x 0.29 + (4 - 3.58)² x 0.27 + (  5 - 3.58)² x 0.15 + (6 - 3.58)² x 0.07 + (7 - 3.58)² x 0.03

σ² = 1.766

The standard deviation can be calculated as the square root of the variance so

σ = √1.766

= 1.32890932723

σ ≈ 1.33

Therefore, the closest answer choice is (b) 1.32.

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The probability of drawing exactly two pairs from a deck of cards containing four aces, four kings, four queens, and four jacks is approximately 0.3623 or about 36.23%.

To have exactly two pairs in a five-card hand, we need two cards of one rank, two cards of another rank, and one card of a different rank.

The number of ways to choose two ranks out of four for the pairs is (4 choose 2) = 6.

For each pair, we can choose two cards out of four in (4 choose 2) = 6 ways.

Finally, we can choose one card from the remaining 44 cards in (44 choose 1) ways.

Therefore, the number of ways to get exactly two pairs is:

6 x 6 x (44 choose 1) = 1584.

The total number of ways to draw five cards out of 16 is (16 choose 5) = 4368.

Therefore, the probability of drawing exactly two pairs is:

P(exactly two pairs) = (number of ways to get exactly two pairs) / (total number of ways to draw five cards)

= 1584 / 4368

= 0.3623 (rounded to four decimal places).

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