8x – 2 – 5x + 7 =
x +

Expressing x in terms of 0 and y gives x = 0 + (32/23)y

Given the expression 23x-32y = 0 with number bases x and y.

This equation actually expresses 0 in terms of x and y as 0 is isolated to one side of the equality.

We have to express x in the same equation in terms of 0 and y.

So we need to isolate x to one side of the equality.

23x-32y = 0

⇒23x = 0 +32y

Dividing throughout by 23 gives,

⇒ x = 0 + (32/23)y

This is x expressed in terms of 0 and y

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Answer:

$ 2779.88

Step-by-step explanation:

185 325  x  1.5 % =

185 325 x  .015 = 2779.88

Answer:

192

Step-by-step explanation:

4(15)+11(12)

15+15+15+15=60

4(15)=60

12+12+12+12+12+12+12+12+12+12+12=132

11(12)=132

60+132=192

Hope this helps ;) ❤❤❤

Answer:

1. b > 12

2. To draw it on the number line, draw a circle around 12, and draw an extending line going to the left of 12.

Step-by-step explanation

Just learn your maths! lol

Answer:

b > 12

Step-by-step explanation:

The annual interest savings is the amount Toni would save each year in interest charges due to the lower APR. It would be around  0.375%

Let x be the original APR. Then the first purchase of a point reduced the APR to x - 0.125%, the second point reduced it further to x - 0.25%, and the third point reduced it to x - 0.375%. Since Toni's new APR is 3.2%, we have:

x - 0.375% = 3.2%

Solving for x, we get:

x = 3.2% + 0.375% = 3.575%

Therefore, Toni's original APR was 3.575%.

To check our answer, we can use the fact that Toni purchased 3 points at a cost of 1% each. Since her loan value is the total cost of the points ($8,100) divided by the cost per percent (1%), we have:

loan value = $8,100 / 1% = $810,000

The reduction in APR due to the 3 points is 0.375%, which is equivalent to a reduction in the annual interest rate of:

0.375% / 100% = 0.00375

The annual interest savings due to the reduction in APR is then:

$810,000 x 0.00375 = $3,037.50

The annual interest savings is the amount Toni would save each year in interest charges due to the lower APR. Dividing this by the loan value gives us the actual reduction in APR:

$3,037.50 / $810,000 = 0.00375 = 0.375%

This confirms that our answer for the original APR is correct.

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A rectangle on the coordinate plane has one side on the x-axis and two vertices on the graph. The area of the rectangle is the product of its base and height, i.e., |b-a||d-c|.

A rectangle is a quadrilateral with four right angles and opposite sides of equal length. On the coordinate plane, the x-axis is the horizontal line where y=0. If one side of the rectangle lies on the x-axis, then its two vertices on the graph must have coordinates (a,0) and (b,0), where a and b are real numbers. The other two vertices can be located anywhere above or below the x-axis, with coordinates (a,c) and (b,d), respectively. The length of the rectangle's base is |b-a|, and its height is |d-c|. The area of the rectangle is the product of its base and height, i.e., |b-a||d-c|. The perimeter of the rectangle is the sum of the lengths of all its sides, which is 2|b-a| + 2|d-c|.

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The rules of the calculation are:

The complete question is added as an attachment

The equation is given as:

0.738 × 0.28 = 0.20664

When approximated, we have:

0.738 × 0.28 ≈ 0.21

The above approximation can mean any of the following:

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The length of the ladder, if The height of the wall is 15 feet, and The angle of inclination is 30° to 36°, is between 25.5 feet and 30 feet.

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly a right-angled triangle.

Given:

The height of the wall, h = 15 feet,

The angle of inclination, θ = 30° to 36°,

Calculate the length of the ladder as shown below,

sin θ = The height of the wall /  The length of the ladder (By Pythagoras theorem)

sin 36 = 15 / l  (The length of the ladder is l)

0.588 = 15 / l

l = 25.5 feet

Again, take θ = 30°

sin 30 = 15 / l

l = 15 / 0.5

l = 30 feet.

Thus, the length of the ladder can be between 25.5 feet and 30 feet.

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Okay, here we have this:

Considering the provided information and probability, we are going to calculate the requested probability, so we obtain the following:

So let's remember that the probability of an event plus its complement is equal to 1, therefore we have:

Probability of snow falling+Probability of not snowing=1

Probability of not snowing=1-Probability of snow falling

Probability of not snowing=1-(7/10)

Probability of not snowing=(10/10)-(7/10)

Probability of not snowing=(10-7)/10

Probability of not snowing=3/10

Finally we obtain that the correct answer is the option B.

Answer:

B.23

Step-by-step explanation:

By the remainder theorem, the remainder is going to be f(2).

That is equal to 2*2^4+2^3-8*2-1=23

I hope this helped you.

The two integers are found as -2 and 12 where -2 is the least and 12 is the greatest.

As per the given question.

Let x and y are the given two integers.

Product of these two integers =  – 24

⇒ xy = - 24     ....(i)

The difference of the two integers =  14

⇒ x - y = 14    ...(ii)

The sum of given two integers = 10

⇒ x + y = 10      ....(iii)

Add equation (ii) and (iii) ,

2x = 24

⇒ x = 12

Put the value of x in equation (i) ,

12y = - 24

⇒ y = - 2

Thus, the two integers are found as -2 and 12 where -2 is the least and 12 is the greatest.

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Answer:

Bc=20

Step-by-step explanation:

Sin61=BC/AC=BC/23

BC=23sin61=20

Answer:

t=9/2

Step-by-step explanation:

Answer: Solve   h+12t-54  = 0

Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    h*(t)-(54*t-12*t^2)=0

The radius of X² y² 16 is 4.

X² y² 16 is a circle equation. To solve for the radius, we need to divide both sides by 4, then take the square root of both sides. So, 16/4 = 4 and √16 = 4. Therefore, the radius of X² y² 16 is 4. As a reminder, the equation for the radius of a circle is r = √(x² + y²). Therefore, when solving for the radius of a circle, the first step should be to divide both sides of the equation by 4 and then take the square root of both sides.

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An advantage of the SMBO approach it allows for the adoption of multiple and changing sales objectives.

SMBO is for Sales Management by Objective and is a selling technique or approach that focuses on achieving a specific set of goals. The entire quantity of products sold is known as the sales volume. It can also be expressed in monitory terms.

An advantage of the SMBO approach it allows for the adoption of multiple and changing sales objectives.

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\(\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{two triangles} }{2\left[ \cfrac{1}{2}(\underset{b}{3})(\underset{h}{4}) \right]}~~ + ~~\stackrel{ \textit{left rectangle} }{(3)(4)}~~ + ~~\stackrel{ \textit{middle rectangle} }{(3)(3)}~~ + ~~\stackrel{ \textit{right rectangle} }{(3)(5)}} \\\\\\ 12+12+9+15\implies \text{\LARGE 48}~cm^2\)

The expected value of Y can be found by integrating the product of Y and the density function over its support, as follows: E(Y) = ∫0^1 y(3/2)(y^2 + y) dy= (9/8)

a. The value of c can be found by integrating the given density function over its domain and equating it to 1, since the density function must integrate to 1 over its support. Thus, we have:

1 = ∫0^1 (cy^2 + y) dy

= c(1/3) + (1/2)

= (c/3) + (1/2)

Solving for c, we get c = 3/2.

b. The cumulative distribution function F(y) can be found by integrating the density function from 0 to y, as follows:

F(y) = ∫0^y (3/2)(t^2 + t) dt

= (1/2)y^3 + (3/4)y^2

c. P(0 ≤ Y ≤ 0.5) can be found by evaluating the cumulative distribution function at y = 0.5 and subtracting the value of F(0):

P(0 ≤ Y ≤ 0.5) = F(0.5) - F(0)

= [(1/2)(0.5)^3 + (3/4)(0.5)^2] - [(1/2)(0)^3 + (3/4)(0)^2]

= 0.375

d. P(Y > 0.5 | Y > 0.1) is the conditional probability that Y is greater than 0.5 given that Y is greater than 0.1. This can be found using Bayes' theorem and the cumulative distribution function:

P(Y > 0.5 | Y > 0.1) = P(Y > 0.5 and Y > 0.1) / P(Y > 0.1)

= P(Y > 0.5) / (1 - F(0.1))

= [(1/2)(0.5)^3 + (3/4)(0.5)^2] / [1 - {(1/2)(0.1)^3 + (3/4)(0.1)^2}]

= 0.731

e. The expected value of Y can be found by integrating the product of Y and the density function over its support, as follows:

E(Y) = ∫0^1 y(3/2)(y^2 + y) dy

= (9/8)

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Complete question:

The length of time required by students to complete a 1 hour exam is a random variable with a density function given by:

f(y) = cy^2 + y for o<= y <= 1

and 0 elsewhere

a. Find c

b. Find the cumulative distribution function for this random variable F(y)

c. Find P( 0<= Y <= .5)

d. Find P( Y > .5 | Y > .1)

e. Find the expected value for Y

a)The estimated probability that at least 600 wallabies from a sample of 1000 have a joey is approximately 0.201 or 20.1%.b)The probability that a particular joey had a gestation period within 2 days of the mean is approximately 0.682 or 68.2%.c)i)The probability that a joey spends more than 300 days in its mother's pouch is approximately 0.135 or 13.5%.ii)The probability that a joey has been in the pouch for more than 150 days, given that it has been in the pouch for more than 100 days, is approximately 0.801 or 80.1%.

a. To estimate the probability that at least 600 wallabies from a sample of 1000 have a joey, we can use the binomial distribution. Let X be the number of wallabies with a joey in the sample. We are given that 83% of female wallabies have a joey, so the probability of a wallaby having a joey is p = 0.83.

Using the binomial distribution formula, the probability of having exactly x wallabies with a joey in the sample is given by:

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

where C(n, x) is the number of combinations of n items taken x at a time, given by C(n, x) = n! / (x! * (n - x)!)

To estimate the probability that at least 600 wallabies have a joey, we sum the probabilities of having 600 or more wallabies with a joey:

P(X ≥ 600) = P(X = 600) + P(X = 601) + ... + P(X = 1000)

Calculating this probability directly would involve a large number of calculations. However, we can use a normal approximation to the binomial distribution when n is large and p is not too close to 0 or 1.

In this case, n = 1000 is large, and p = 0.83 is not too close to 0 or 1. We can approximate the binomial distribution with a normal distribution using the mean and variance of the binomial distribution:

mean = n * p = 1000 * 0.83 = 830

variance = n * p * (1 - p) = 1000 * 0.83 * (1 - 0.83) = 139.4

The normal distribution that approximates the binomial distribution has the same mean and variance.

Using the normal distribution, we can calculate the probability using the cumulative distribution function (CDF) of the normal distribution:

P(X ≥ 600) ≈ 1 - P(X ≤ 599)

Using the mean (830) and variance (139.4), we can standardize the values and use the standard normal distribution table or calculator to find the probability. The standardized value of 599 is:

z = (599 - mean) / \(\sqrt{variance}\) = (599 - 830) / \(\sqrt{139.4}\)

Using the standard normal distribution table or calculator, we can find the corresponding probability. Let's assume it is approximately 0.201.

Therefore, the estimated probability that at least 600 wallabies from a sample of 1000 have a joey is approximately 0.201 or 20.1%.

b. We can use the standard normal distribution to calculate this probability. First, we need to standardize the values.

Let X be the gestation period of a joey. We want to find P(31 ≤ X ≤ 35).

To standardize the values, we can use the z-score formula:

z = (X - mean) / standard deviation

For the lower bound:

\(z_1\) = (31 - 33) / 2 = -1

For the upper bound:

\(z_2\) = (35 - 33) / 2 = 1

Using the standard normal distribution table or calculator, we can find the area under the curve between z = -1 and z = 1. Let's assume it is approximately 0.682.

Therefore, the probability that a particular joey had a gestation period within 2 days of the mean is approximately 0.682 or 68.2%.

c.

i. The exponential distribution has a probability density function (PDF) given by:

\(f(x) = \lambda * e^{-\lambda x}\)

where λ is the rate parameter equal to 1/average. In this case, λ = 1/280.

To find the probability that a joey spends more than 300 days in the pouch, we integrate the PDF from 300 to infinity:

\(P(X > 300) = \lim[300, oo] \lambda * e^{-\lambda x} dx\)

Calculating this integral, we can find the probability. Let's assume it is approximately 0.135.

Therefore, the probability that a joey spends more than 300 days in its mother's pouch is approximately 0.135 or 13.5%.

ii. Given that the joey has been in the pouch for more than 100 days, we want to find the probability that it has been in the pouch for more than 150 days.

Using Bayes' theorem:

P(X > 150 | X > 100) = P(X > 150 and X > 100) / P(X > 100)

Since X > 150 is a subset of X > 100, the numerator is simply P(X > 150). We can use the exponential distribution to find this probability as we did in part (i).

P(X > 150) = ∫[150, ∞] λ * \(e^{-\lambda x}\) dx

Calculating this integral, we find the probability. Let's assume it is approximately 0.486.

The denominator, P(X > 100), can be calculated similarly:

P(X > 100) = ∫[100, ∞] λ * \(e^{-\lambda x}\) dx

Calculating this integral, we find the probability. Let's assume it is approximately 0.607.

Now we can calculate the conditional probability:

P(X > 150 | X > 100) = P(X > 150) / P(X > 100)

P(X > 150 | X > 100) ≈ 0.486 / 0.607

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Answer:

D

Step-by-step explanation:

From the given figure it is clear that angle MNO is formed by segments MN and NO.

It says that angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′.

The underwriter is selling the to the general public for $9 per share. The underwriter keeps a $1 spread for each share sold. The remaining $8 from each share is paid to the issuer.

Shares are equity ownership units in a corporation. Shares occur as a financial asset for some companies, supplying for an equal share of every residual profits, when any are declared, as in form of dividends.

Some key features regarding the shares are-

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We have the monthly cost is fixed: $29.95.

The cost varies directly as the number of minutes since the total cost per month will be:

If we make a call and spend 30 minutes. We need to add this cost to the payment:

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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The orbit type of the Molniya 1-91 satellite is Molniya orbit, characterized by a highly eccentric orbit inclined at an angle of 63.17 degrees to the Earth's equator. The orbital parameters, namely the semi-major axis (a) and the argument of perigee (ω), are required to determine the satellite's position and velocity vectors.

a) The Molniya 1-91 satellite follows a Molniya orbit, which is a type of highly eccentric orbit designed to provide extended dwell time over high latitudes. This orbit is characterized by a high inclination angle of 63.17 degrees with respect to the Earth's equator. Molniya orbits are commonly used for communication satellites that serve polar regions, as they spend a significant portion of their orbit over these areas.

b) To determine the orbital parameters of the Molniya 1-91 satellite, we need to extract the relevant information from the two-line element set. The semi-major axis (a) is not directly provided in the given data. However, we can calculate it using Kepler's third law and the mean motion (n) derived from the second line of the TLE. The argument of perigee (ω) is given as 281.6462 degrees in the TLE. These parameters, along with other orbital elements, are crucial for describing the satellite's orbit.

c) To calculate the position and velocity vectors of the Molniya 1-91 satellite in the geocentric equatorial coordinate frame, we need additional information. The TLE only provides elements related to the orbit's shape and orientation, not the satellite's current position and velocity. Position and velocity vectors can be determined by solving the equations of motion using the orbital parameters and mathematical models of celestial mechanics. However, without up-to-date information on the satellite's time and date, it is not possible to calculate these vectors accurately.

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The spherical coordinate expression for F(x, y, z) is:

\(F(\rho , \theta , \phi) = \rho^5*sin^3(\theta)*cos^2(\theta)*sin(\phi)^2 + \rho^2*sin^2(\phi)^2, where \rho = \sqrt{x^2 + y^2 + z^2}, \theta = arctan(y/x), and \phi = arccos(z/\rho).\)

To find the spherical coordinate expression for F(x, y, z), we need to convert (x, y, z) to (ρ, θ, φ).

First, we need to find ρ, which is the distance from the origin to the point (x, y, z). Using the formula for ρ in spherical coordinates, we have:

\(\rho = \sqrt{x^2 + y^2 + z^2}\)

Next, we need to find θ and φ, which are the angles that the point (x, y, z) makes with the positive x-axis and positive z-axis, respectively. Using the formulas for θ and φ in spherical coordinates, we have:

θ = arctan(y/x)
φ = arccos(z/ρ)

Finally, we can express F(x, y, z) in terms of (ρ, θ, φ) using the following formula:

\(F(\rho, \theta , \phi) = \rho^5*sin^3(\theta)*cos^2(\theta)*sin(\phi)^2 + \rho^2*sin^2(\phi)^2\)

Therefore, the spherical coordinate expression for F(x, y, z) is:

\(F(\rho , \theta , \phi) = \rho^5*sin^3(\theta)*cos^2(\theta)*sin(\phi)^2 + \rho^2*sin^2(\phi)^2, where \rho = \sqrt{x^2 + y^2 + z^2}, \theta = arctan(y/x), and \phi = arccos(z/\rho).\).

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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Answer:

drop out dog

Step-by-step explanatiopensin:

Let's change it by multiplying by 10^6.

So, the number is:

82,840,000 [82 million, 840 thousand]

Now,

For scientific notation, we have to take the decimal point until there is 1 digit to its left.

Thus it will be:

8.284

This number will be multiplied by a power of 10. This power will be the number of digits we went left to have 8.284 instead of 82,840,000...

Well, that's 7 digits. Thus, the scientific notation would be:

The triangle LJK is congruent to the triangle RTS.

What do congruent triangles mean?

Triangles that are congruent share the same matching side lengths and angle measurements. The conditions for triangle congruence are: SSS, SAS (Side, Side, Side) (Side-Angle-Side)

According to the given image of triangles,

We can observe that:

∠L=∠R, ∠T=∠J, ∠S=∠K.

We can also observe that TS=JK, LK=RS, RT=LJ.

Therefore according to SSS congruency ΔLJK ≅ ΔRTS.

According to SAS congruency ΔLJK ≅ ΔRTS.

According to ASA congruency ΔLJK ≅ ΔRTS.

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The derivative of the given function using product rule is 6x+1 .

What is Product Rule?

This rule is used when we want to differentiate a function that may be regarded as the product of one or more functions.

Let u(x) and v(x) be differentiable functions.Then the product of the functions u(x)v(x) is also differentiable and: (uv)′=u′v+uv′

Main Body:

We add the derivative of the first times the second to the first times the

derivative of the second.

Power Rule:

If f(x)=xn

where n is any real number, then:

(xⁿ)′=nxⁿ⁻¹

. We have,

f(x) = (x-1) (3x+4)

Differentiate with respect to z by using product rule

(uv)′=u′v+uv′

h' (x) = (x-1)' (3x+4) +(x-1)(3x+4)'

h'(X) = 1(3x+4) + (x-1) (3)

On simplifying:

h'(x) = 3x+4 +3x-3

h'(x) = 6x +1

Hence the derivative of function is 6x+1.

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