What two numbers has a sum of 9 and a product of 30

The change in electrical potential when moving along the x-axis from x = 5.0 m to x = 1.0 m. The result depends on the values of A, B, and C, which are given as 1.5 V/m^(-3), 0.45 V/m^(-2), and -15 V/m^(-1) respectively.

To calculate the change in electrical potential, we need to integrate the electric field along the path of motion. In this case, we are moving along the x-axis, so only the x-component of the electric field is relevant.

The electric potential difference (ΔV) between two points A and B is given by the formula:

ΔV = ∫ E · dl

where E is the electric field and dl is an infinitesimal displacement along the path of motion. Since we are only concerned with the x-component of the electric field, the integral simplifies to:

ΔV = ∫ (Ax^2 + Bz) dx

Integrating with respect to x from x = 5.0 m to x = 1.0 m, we can find the change in electrical potential.

ΔV = ∫ (Ax^2 + Bz) dx = ∫ (1.5x^2 + Bz) dx

Evaluating the integral, we get the change in electrical potential when moving along the x-axis from x = 5.0 m to x = 1.0 m in the given electric field.

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Answer:

prime number between 1 to7

The description of set P is the set of prime numbers less than or equal to 7 and the rule is {x | x is a prime number less than or equal to 7}

The set P is given as:

P = {2,3,5,7}

Note that the numbers are prime numbers.

This means that the description of set P is the set of prime numbers less than or equal to 7

The rule form of the set would be:

P = {x | x is a prime number less than or equal to 7}

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The number of divisors counted twice is equal to the number of positive integers that have the form \($2^a\cdot 3^b\cdot 5^c$\) for some nonnegative integers a, b, and c such that and \(0 \le c \le 5\). There are \(11\cdot 11\cdot 6 = 726\) such divisors.

We will first find the prime factorization of each of the given numbers: \(\begin{align*}12^{12} &= (2^2\cdot 3)^{12} = 2^{24} \cdot 3^{12}, \10^{10} &= 2^{10} \cdot 5^{10}, \15^{15} &= (3\cdot 5)^{15} = 3^{15}\cdot 5^{15}.\end{align*}\)

For a positive integer n to be a divisor of at least one of these numbers, it must contain some combination of the prime factors 2, 3, and 5.

Any divisor of \(12^{12}\) must have the form \(2^a\cdot 3^b\)for some nonnegative integers a and b such that \(0 \le a \le 24\) and \(0 \le b \le 12.\) Therefore, there are \(25\cdot 13 = 325\)possible divisors of \(12^{12}.\)

Similarly, any divisor of \($10^{10}$\)must have the form\($2^a\cdot 5^b$\)for some nonnegative integers a and b such that \($0 \le a \le 10$\) and \($0 \le b \le 10$\). Therefore, there are \($11\cdot 11 = 121$\)possible divisors of\($10^{10}$.\)

Finally, any divisor of \($15^{15}$\)must have the form for some nonnegative integers a and b such that \($0 \le a \le 15$\) and \($0 \le b \le 15$\). Therefore, there are \($16\cdot 16 = 256$\) possible divisors of \($15^{15}$\).

We want to count the total number of positive integers that are divisors of at least one of these numbers. Notice that we have counted some divisors twice (for example, \($2^1 \cdot 3^1$\)is a divisor of both \($12^{12}$\) and\($10^{10}$)\), so we need to subtract the number of divisors that we have counted twice. Similarly, we have counted some divisors three times, so we need to add the number of divisors that we have counted three times. We have not counted any divisor four or more times, so we do not need to consider those cases.

The number of divisors counted twice is equal to the number of positive integers that have the form \($2^a\cdot 3^b\cdot 5^c$\) for some nonnegative integers a, b, and c such that \($0 \le a \le 10$\), \($0 \le b \le 5$\), and \($0 \le c \le 10$\). There are \($11\cdot 6\cdot 11 = 726$\) such divisors (we chose the exponents for 2, 3, and 5 separately).

Finally, the number of divisors counted three times is equal to the number of positive integers that

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Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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Answer: the first one is C.) The graphs are reflected across the y-axis

the second one is A.) The graphs are the same

Step-by-step explanation:

The graphs are reflected across the y-axis.

Here we have the two functions:

You can remember that for a given function f(x), a reflection over the y-axis is written as:

g(x) = f(-x).

So if we have:

f(x) = 3^x

The reflection over the y-axis gives:

g(x) = 3^(-x).

So we can conclude that the relation between the graphs is that these are reflected across the y-axis.

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The shape of a cross section that is perpendicular to the base of a triangular prism is a triangle.

A triangular prism is a three-dimensional shape with two parallel triangular bases and three rectangular faces connecting them.

When a cross-section is taken that is perpendicular to one of the bases, the shape of the cross-section is the same as the shape of that base, which is a triangle.

The base of the triangle will be the base of the triangular prism, and the height of the triangle will be the height of the triangular prism.

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The 3x3 matrix representing the composite 2D transformation of translating by (5,9) and then rotating 45° about the origin using homogeneous coordinates is: [ cos(45°) -sin(45°) 5  sin(45°) cos(45°) 9  0 0 1 ]

To find the matrix that represents the composite transformation, we first need to construct the individual transformation matrices for translation and rotation.

Translation Matrix:

The translation matrix for translating by (5,9) is:

[ 1 0 5

0 1 9

0 0 1 ]

Rotation Matrix:

The rotation matrix for rotating 45° about the origin is:

[ cos(45°) -sin(45°) 0

sin(45°) cos(45°) 0

0 0 1 ]

To obtain the composite transformation matrix, we multiply the translation matrix by the rotation matrix. Matrix multiplication is performed by multiplying corresponding elements and summing them up.

The resulting composite transformation matrix, accounting for translation and rotation, is:

[ cos(45°) -sin(45°) 5

sin(45°) cos(45°) 9

0 0 1 ]

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The probability that the next customer to enter the shop will order a cookie is given as follows:

31/60.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in which a cookie is ordered are given as follows:

Hence the probability is obtained as follows:

3/4 x 1/3 + 2/5 x 2/3 = 1/4 + 4/15 = 15/60 + 16/60 = 31/60.

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The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Thus, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

The complete question is:

In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9.

Approximate the height of the mountain. (Round your answer to one decimal place.)

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The population of students in Baltimore will be 4329 in 5 years.

Exponential growth is a function that shows an increase within a population that occurs at the same rate over time.

Given that, the current student population of Baltimore is 2000, the population increases at a rate of 16.7% each year.

We need to find the student population in 5 years

To find the same, we will use, exponential growth model for the future population P(x) where x is in years, is given by,

A = P(1+r)ⁿ

Where,

A = final population

P = initial population

r = rate, n =time

A = 2000(1+0.167)⁵

A = 2000(1.167)⁵

A = 4328.967

A ≈ 4329

Hence, the population of students in Baltimore will be 4329 in 5 years.

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the approximate arc length traced out by the endpoint of the vector-valued function f(t) = tcos(t)i + tsin(t)j over the interval [0, 2π] is approximately 10.6706 units.

What is arc?

An arc is a curved segment of a circle or any curved line. It is formed by connecting two points on the curve, and the arc itself lies on the circumference of a circle or the curved line.

To find the arc length traced out by the endpoint of the vector-valued function f(t) = tcos(t)i + tsin(t)j over a specific interval, we can use the arc length formula for a vector-valued function.

The arc length formula for a vector-valued function r(t) = xi + yj + zk over an interval [a, b] is given by:

\(L = \int[a, b] \sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) dt\)

In this case, our vector-valued function is f(t) = tcos(t)i + tsin(t)j, where x = tcos(t), y = tsin(t), and z = 0 (since there is no z-component in the function).

Therefore, we need to calculate the derivatives dx/dt, dy/dt, and dz/dt to substitute them into the arc length formula.

dx/dt = cos(t) - tsin(t)

dy/dt = sin(t) + tcos(t)

dz/dt = 0 (since z = 0)

Now, let's compute the arc length over the interval [a, b] using the arc length formula:

\(L = \int[a, b] \sqrt((cos(t) - tsin(t))^2 + (sin(t) + tcos(t))^2 + 0^2) dt\\\\= \int[a, b] \sqrt(cos^2(t) - 2tcos(t)sin(t) + t^2sin^2(t) + sin^2(t) + 2tcos(t)sin(t) + t^2cos^2(t)) dt\\\\= \int[a, b] \sqrt(1 + t^2) dt\)

Since the interval is given as [0, 2π], we will substitute a = 0 and b = 2π into the integral:

\(L = \int[0, 2\pi] \sqrt(1 + t^2) dt\)

Using numerical software or calculators, the approximate value of the integral is found to be approximately 10.6706.

Therefore, the approximate arc length traced out by the endpoint of the vector-valued function f(t) = tcos(t)i + tsin(t)j over the interval [0, 2π] is approximately 10.6706 units.

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Answer:

20 carros

Step-by-step explanation:

Dado que un automóvil tiene cuatro neumáticos, multipliqué la C por 4

M es para motocicletas. ya que las motos tienen 2 neumáticos. Multipliqué M por 2

de hecho, la respuesta está en la imagen de arriba

Using the law of tangents, the angle of the person’s eyes to the top of the building is approximately 36.87 degrees.

Angle  isc figure that can be described as the amount of rotation between two straight line not planes and angles is measured in degree with the full circle being 360°.

This can be calculated by setting up the following equation:

tan(angle) = 80 ft / (200 ft - 4 ft)

Solving for the angle, we get:

angle = tan-1(80 ft / 196 ft)

angle = tan-1(0.408163265)

angle = 36.87 degrees (to the nearest hundredth of a degree).

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Answer:

To find the surface area of a cylinder you need a specific formula.

The formula to finding the surface area is

\(A=2\pi rh+2\pi r^2\)

2 x pi x 7 + 2 x pi x 4 squared

144.513262065 would be the specific answer.

Answer:

A group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the survey are shown below:

60 students like building snowmen

10 students like building snowmen but do not like skiing

80 students like skiing

50 students do not like building snowmen

Make a two-way table to represent the data and use the table to answer the following questions.

To Find:

Part A: What percentage of the total students surveyed like both building snowmen and skiing? Show your work. (5 points)

Part B: What is the probability that a student who does not like building snowmen also does not like skiing? Explain your answer. (5 points)

Solution:

Before proceeding further let us solve it by drawing a Venn diagram, drawing a universal set that is a rectangular box and inside that draw two sets that are circle intersecting each other, name the two circles as Sn and Sk for snowmen and skiing respectively,

using the given data fill all the values in the Venn diagram

The total number of students surveyed are 160.

(A) The number of students who liked both building snowmen and skiing is 50 and the total number of students is 160, finding the percentage we have,

Hence, the percentage of students who liked both building snowmen and skiing is 31.25%.

(B) The no of students who don't like anything is 20 and the total no of students is 160, finding the probability we have,

Hence, the probability that students don't like doing any of the activities is 0.125.

Step-by-step explanation:

sorry for long answer...lol...

Answer:

20 yards

Step-by-step explanation:

94-10-12-22-30=20

Given:

It can be written as follows.

Dividing 5.44 by 6.8, we get

Hence the quotient is

Answer:

x = 7

Step-by-step explanation:

(3x-1)/12 = 15/9

27x-9 = 15x12 = 180

27x = 189

x = 7

Answer:

\(3 \frac{3}{4}\)

Step-by-step explanation:

We have a right rectangular prism and the question is asking for the volume.

Look for the formula of volume :

V = LWH

L being length

W being width

H being height

The formula is basically saying to multiply all sides together, so let's do as so.

\(2*1\frac{1}{4} * 1\frac{1}{2}\)

= \(3 \frac{3}{4}\)

Answer:

c

Step-by-step explanation:

Answer:

1 − 2 cos x

Step-by-step explanation:

y' = 2 sin x

y = C − 2 cos x

1 = C − 2 cos(π/2)

1 = C

y = 1 − 2 cos x

(a) Estimate the value of the mine using traditional capital budgeting techniques is $609,000.0. (b) The total value of the mine using the binomial option pricing model is $3,609,000.0. (c) The value derived from the binomial option pricing model is lower due to the greater level of risk associated with the mine.

a. Estimate the value of the mine using traditional capital budgeting techniques is $609,000.0.

b. Estimate the value of the mine based upon an option pricing model.

Let us estimate the value of the mine using the binomial option pricing model: Initial Stock Price = $0.85

Strike Price = $0.40

u = 1.25d = 0.80

Rf = 7%

Time to expiration = 25 years

Number of time periods = 25

Size of time period = 1 year

25th-Step Terminal Stock Price = $6.75

There are 26,830 possible terminal stock price paths.

Average terminal stock price = $8.24 (2,134 paths)26,830-$0.0000 (25,389)$0.0117 (825)$0.0260 (126)$0.0443 (45)$0.0668 (24)$0.0935 (11)$0.1243 (4)$0.1591 (1)$0.1980 (1)

Average = $0.0609

The option value is therefore $0.0609*10,000,000 = $609,000.0

The total value of the mine using the binomial option pricing model is $3,609,000.0.

c. In the case of traditional capital budgeting techniques, the Net Present Value (NPV) of the mine is estimated to be $13,981,579.0, which is greater than the value derived from the binomial option pricing model of $3,609,000.0. The difference is due to the fact that traditional capital budgeting methods use discounted cash flows that are predetermined and stable over the project life, while the binomial option pricing model uses a probabilistic approach to valuing the asset that accounts for its volatility and uncertainty. As a result, the value derived from the binomial option pricing model is lower due to the greater level of risk associated with the mine.

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Answer:

  b = 44

Step-by-step explanation:

We can complete the square(s) to put the equation in standard form. Then we can find the value of b that makes the radius be 7 units.

__

  x^2 +y^2 -4x +2y = b . . . . . given

  (x^2 -4x) +(y^2 +2y) = b . . . . group by variable

  (x^2 -4x +4) +(y^2 +2y +1) = b + 4 + 1 . . . . complete the squares

  (x -2)^2 +(y +1)^2 = b +5 = 7^2 = 49 . . . . . write as squares, show radius

  b = 49 -5 = 44 . . . . subtract 5

The value of b to make the radius 7 is 44.

_____

The standard form of the equation for a circle is ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . center (h, k), radius r

Answer:

16404.2 feet

Step-by-step explanation:

1 in = 2.54 cm

1 km = 100000 cm

5 km = 100000*5 = 500000

1 feet = 12 in

500000 cm = 500000/2.54 = 196850.39 in  

196850.39 in = 196850.36 / 12 = 16404.2 feet

Answer:

\(\frac{x+3}{x}\)

Step-by-step explanation:

Factorise numerator and denominator

x² - 9 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 9

= x² - 3² = (x - 3)(x + 3)

x² - 3x ← factor out x from each term

= x(x - 3)

Then

\(\frac{x^2-9}{x^2-3x}\)

= \(\frac{(x-3)(x+3)}{x(x-3)}\) ← cancel common factor (x - 3) on numerator/denominator

= \(\frac{x+3}{x}\)

Answer:

1:3

Step-by-step explanation:

3:12 is the amount of shaded circles to all circles, 8:2 is basically the same thing as 3:12 and 9:3 is the amount of shaded circles to the amount of non-shaded circles.  1:3 wouldn't work because it is not the right ratio.

Answer:

\(60 \textdegree \)

Skills needed: Geometry

Step-by-step explanation:

1) We are given a regular triangle.

A regular triangle is the same as an equilateral triangle. This means that:

--> All sides are of equal length (congruent)

--> All angles are of same measure (congruent)

-------------------------------------------------------------------------------------------------------------Another thing to remember is that the sum of all angles in a triangle is 180 DEGREES.

------------------------------------------------------------------------------------------------------------- 2) Let's make an equation:

Let's make one of the angles a variable: \(y\)

ALL the angles of the triangle will have a measure of "\(y\)", which means that each of the angles equals \(y\).

---> Sum of all angles (IN VARIABLE TERMS): \(y+y+y=3y\) (1y+1y+1y = 3y)

ALSO:

- Sum of all angles is 180. This can be the right side of the equation.

\(3y = 180\) is our equation based on all the information above.

We want to then isolate \("y"\), so we have to divide by 3.

\(3y \div 3=180 \div 3\)

\(3y \div 3=y, 180 \div 3 = 60\) (doing both division problems)

This means that: \(y=60\)

60 should be the answer.

Answer:

x = 47.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta  = adj / hyp

cos x = 8.8 / 13

Take the inverse cos of each side

cos ^-1 ( cos x) = cos ^-1( 8.8 /13)

x = cos ^-1( 8.8 /13)

x =47.39633319

Rounding to the nearest tenth

x =47.4

Answer:

36.9 degrees

Step-by-step explanation:

using SOHCAHTOA we can see that we need to use cos because the sides that are given are the adjacent side and the hypotenuse so u have to divide the adjacent by the hypotenuse which is 8.8/13 and you should get 0.8 after you round to the nearest tenth and then you use your calculator to do cos^-1 (0.8) and you get 36.9 after you round to the nearest tenth of a degree

The probability of this is (1/6) x (3/6) or 1/12. So, the total probability is 3/36 + 1/12, which simplifies to 1/6.

To find the probability that the sum of two numbers rolled is greater than 3, given that the sum is not greater than 5, we need to first find the probability of the sum being less than or equal to 5. This can be done by finding the probability of rolling a 2, 3, 4 or 5 on the two dice. This probability is 4/36 or 1/9. Now, to find the probability that the sum is greater than 3, given that the sum is not greater than 5, we need to use Bayes' theorem. This gives us (probability of sum>3 and sum<=5)/ (probability of sum<=5), which is (2/36)/(4/36) or 1/2.

The probability that one of the numbers is a 6 and the sum of the two numbers is an odd number can be found by considering the cases where the other number is odd or even. If the other number is odd, then the sum will be even and the probability is 3/36. If the other number is even, then the sum will be odd only if the other number is 1, 3 or 5.

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