A number is in expanded form: (9 x 10) + (6 x 1) + (2 x 1/100) + (3 x 1000) What is the number is standard form?

Answer:

The answer is 33.75 per hour

Step-by-step explanation:

Divide 135 by 4

Acceleration  = 10.0 m/s²

Given information:

x1 = 257.76 m;

t1 = 4.30 s

x2 = 308.07 m;

t2 = 4.80 s

x3 = 363.04 m;

t3 = 5.30 s

We have to calculate the acceleration of the airplane at t2 = 4.80 s.

So, the formula for acceleration is: a = (v - u) / (t - t0) where, v = final velocity, u = initial velocity, t = final time, t0 = initial time.

Let's calculate the velocity at time t2. We can use the following formula for that: v = u + at (where v is the final velocity). We assume the acceleration to be constant.

Therefore, acceleration of the airplane is: a = (v - u) / (t - t0)

Solving the above formula, we get: v = u + a (t - t0)

Substituting the given values, we get: v2 = v1 + a (t2 - t1)............. (1)

v1 = v0 + a (t1 - t0)............. (2)

Subtracting (2) from (1), we get: v2 - v1 = a (t2 - t1) - a (t1 - t0)

Solving the above equation for acceleration a, we get: a = (v2 - v1) / (t2 - t1)

Therefore, acceleration of the airplane at t2 = 4.80 s is: a = (v2 - v1) / (t2 - t1)

a = ((308.07 - 257.76) / (4.80 - 4.30))

a = 10.0 m/s²

Therefore, the acceleration of the airplane at t2 = 4.80 s is 10.0 m/s².

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Answer:

x = 79

Step-by-step explanation:

Angles in a triangle add up to equal 180

That being said we can calculate the missing angle by subtracting the measures of the known  angles from 180

So, x = 180 - 54 - 47 = 79

Hence x = 79

The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.

To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get \(x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0\). Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.

To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =\(x^r = x^((1 +\)i√3)/2) = x^(1/2) *\(x^(i√3/2\)). Using the binomial series expansion and Euler's formula, we can write \(x^(1/2) and x^(i√3/2)\) as infinite series.

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Answer:

4

Step-by-step explanation:

Four people will play basketball, so 10 - 4 = 6.

Half as many people will play baseball, and half of 4 is 2, so 6 -2 = 4.

The rest will play soccer, which is 4.

The effective rate per quarter for an annual interest rate of 9% compounded quarterly is approximately 9.37%.

To find the effective rate per quarter when the annual interest rate is 9% compounded quarterly, we can use the formula for the effective interest rate:

Effective Rate = (1 + (Annual Rate / Number of Periods))^Number of Periods - 1

In this case:

Annual Rate = 9%

Number of Periods = 4 (since it's compounded quarterly)

Plugging in these values into the formula:

Effective Rate = \((1 + (0.09 / 4))^4 - 1\)

Calculating this equation will give us the effective rate per quarter:

Effective Rate = \((1 + 0.0225)^4 - 1\)

Effective Rate ≈ 0.0937 or 9.37% (rounded to two decimal places)

Therefore, the effective rate per quarter for an annual interest rate of 9% compounded quarterly is approximately 9.37%.

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The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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Answer: A rain gauge measures the amount of rainfall based off of the amount collected in the cylinder.

Step-by-step explanation: A rain gauge is really just a cylinder that catches rain. If an inch collects in the cylinder, it means an inch of rain has fallen. It's that simple. Most standard rain gauges have a wide funnel leading into the cylinder and are calibrated so that one-tenth of an inch of rain measures one inch when it collects inside.

Answer:

30ft

Step-by-step explanation:

Don't worry I just know

Answer:

The 9 in the thousands place equals a thousand (9,000) and the place to the right equals a hundred (900).

Step-by-step explanation:

Answer:

Step-by-step explanation:

9000 - 900

= 8100

Answer:

for a c6 parallel  b is e14

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. The range of G is the set of possible values that G can take. G represents the distribution over the number of girls chosen, so G can take any value between 0 and 2, inclusive. That is, the range of G is {0, 1, 2}.

b. To give the distribution over the random variable G, we need to determine the probability of each possible value of G.

Let's consider each possible value of G in turn:

If no girls are chosen (G=0), then both representatives must be boys. The probability of choosing a boy on the first draw is 3/10, and the probability of choosing another boy on the second draw is 2/9 (since there are only 2 boys left). Therefore, the probability of G=0 is (3/10) * (2/9) = 1/15.

If one girl is chosen (G=1), then one representative must be a girl and the other must be a boy. There are two ways this can happen: either the girl is chosen first and then the boy, or the boy is chosen first and then the girl. The probability of choosing a girl on the first draw is 7/10, and the probability of choosing a boy on the second draw is 3/9 (since there are 3 boys left). The probability of choosing a boy on the first draw is 3/10, and the probability of choosing a girl on the second draw is 7/9 (since there are 7 girls left). Therefore, the probability of G=1 is (7/10) * (3/9) + (3/10) * (7/9) = 14/45.

If two girls are chosen (G=2), then both representatives must be girls. The probability of choosing a girl on the first draw is 7/10, and the probability of choosing another girl on the second draw is 6/9 (since there are 6 girls left). Therefore, the probability of G=2 is (7/10) * (6/9) = 7/15.

Therefore, the distribution over the random variable G is:

G=0 with probability 1/15

G=1 with probability 14/45

G=2 with probability 7/15

Answer:

2 19/5

Step-by-step explanation:

4 7/9 ÷ 1 7/12

start by turning them into improper fraction by multiplying the denominator to the whole number and adding the product to the numerator , you will get :

42/9 ÷ 17/12

42/9 * 12/17 ( reciprocal )

42/3 * 4/17 (9 and 12 can be cut smaller because both are in 3's table)

= 172/51

turn this into mixed fraction by -

Divide the numerator by the denominator.

Write down the whole number answer

Then write down any remainder above the denominator

you will get = 2 19/5

4 7/9 divided by 1 7/12 will be 3 1/57.

The first thing to do is to change the mixed fraction to improper fraction and this will be:

= 4 7/9 ÷ 1 7/12

= 43/9 ÷ 19/12

Then we change the division sign to multiplication and this will be:

= 43/9 × 12/19

We then reduce to lowest term

= 43/9 × 12/19

= 43/3 × 4/19

= 172/57

= 3 1/57

In conclusion, 4 7/9 divided by 1 7/12 is 3 1/57.

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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 surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions.

Surface area=6(3.4)^2=69.36 square feet

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

A 3D object's surface area is the entire area that all of its faces cover. For instance, if we need to calculate how much paint is required to paint a cube, we can use the cube's surface area. determine how much paint is needed to paint it. It is consistently expressed in square units.

As a refresher, the surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions.

Surface area=6(3.4)^2=69.36 square feet

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The rate at which the water level is rising when it is 5 meters high is approximately 0.477 m/min

The volume of a conical tank:
V = (1/3)πr^2h
where V is the volume of the tank, r is the radius, and h is the height.
Differentiating both sides with respect to time, we get:
dV/dt = (1/3)π(2rh dr/dt + r^2 dh/dt)
Where dV/dt is the rate at which the volume is changing (in m^3/min), and dr/dt and dh/dt are the rates at which the radius and height are changing, respectively.
We know that water is pouring into the tank at a rate of 6m^3/min, so we can substitute this value for dV/dt. We also know that the height of the water level is rising, so dh/dt is what we need to find. Finally, we know that when the water level is 5 meters high, the radius of the water surface can be found using similar triangles:
r/h = 4/10
r = (4/10)h = 0.4h
Now we can substitute all of these values into the formula and solve for dh/dt:
6 = (1/3)π(2(0.4h)(dh/dt) + (0.4h)^2 dh/dt)
6 = (1/3)π(0.8h + 0.16h^2) dh/dt
dh/dt = 6 / [(1/3)π(0.8h + 0.16h^2)]
When the water level is 5 meters high, h = 5, so:

dh/dt = 6 / [(1/3)π(0.8(5) + 0.16(5)^2)]

dh/dt = 0.477m/min

Therefore, the rate at which the water level rises when it is 5 meters high is approximately 0.477 m/min.

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Cindy's average tax rate is approximately 13.59%.

To calculate Cindy's average tax rate, we divide the total tax paid by her taxable income and then multiply by 100 to express it as a percentage.

Average tax rate = (Total tax paid / Taxable income) * 100

In this case, Cindy's taxable income is $65,500, and she has calculated that she will owe $8,902 in taxes.

Average tax rate = (8,902 / 65,500) * 100

Average tax rate ≈ 13.59%

Therefore, Cindy's average tax rate is approximately 13.59%.

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Cindy is projecting her earnings to be $90,000, a taxable income of $65,500, and has calculated that she will owe $8,902. Her average tax rate is 13.60%.

How to find the average tax rate?

The average tax rate is determined by dividing the total tax paid by the total income earned. The average tax rate is calculated by dividing the total amount of tax paid by the total taxable income.

Average Tax Rate = Total Tax Paid / Taxable Income Cindy's

The average tax rate can be found as follows:

Average tax rate = (Total tax paid ÷ Taxable income) × 100%

Average tax rate = ($8,902 ÷ $65,500) × 100%

Average tax rate = 0.135994 × 100% ≈ 13.60%

Therefore, Cindy's average tax rate is 13.60%.

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Area. The amount of space covered by a two-dimensional object; the amount of carpet you'd need to cover a floor would depend on the floor's area.

Perimeter. The distance around a two-dimensional object; the amount of fence you'd need to surround your yard equals the perimeter of your yard. (The perimeter of a circular object is called the circumference.

Volume. The amount of three-dimensional space inside an object; the amount of liquid inside a soda can represents the can's volume.

Surface area. Measures the amount of "skin" needed to cover a three-dimensional object, neglecting its thickness; the amount of siding you'd need to completely cover a house represents the surface area of that house's walls.

Description Formula Variables

Area of a rectangle A = l · w l = length, w = width

Perimeter of a rectangle P = 2(l + w) l = length, w = width

Area of a circle A = r2 r = radius of circle

Circumference of a circle C = 2r r = radius of circle

Volume of a rectangular solid V = l · w · h l = length, w = width, h = height

Volume of a cylinder V = r2h r = radius; h = height

Surface area of a cube SA = 6l2 l = length of side

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Answer:

-3

Step-by-step explanation:

1-7           -6

------ =   -------- =    -3

0--2          2

The most general antiderivative for the given function `\(5e^(x) + 6 dx` is `5e^(x) + 6x + C`\).

To find the most general antiderivative for the function \(`5e^(x) + 6 dx`,\) we can integrate each term separately using the power rule and the constant multiple rule of integration.The general antiderivative is given by:∫(5e^(x) + 6) dx = ∫5e^(x) dx + ∫6 dxNow, we know that ∫a dx = ax + C, where "a" is a constant and "C" is the constant of integration. Therefore,∫(5e^(x) + 6) dx = ∫5e^(x) dx + ∫6 dx= 5∫e^(x) dx + 6∫1 dx= 5e^(x) + 6x + CThus, the most general antiderivative for the given function `5e^(x) + 6 dx` is `5e^(x) + 6x + C`.Final Answer:

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If there are 1,000 phones in total and 100 of them have between 200 and 249 songs while 600 of them have between 150 and 199 songs, then there are more phones with between 150 and 199 songs.

We cannot determine whether there are more phones that have between 200 and 249 songs stored on them than have between 150 and 199 songs without additional information.

For example, if there are 1,000 phones in total and 500 of them have between 200 and 249 songs while 200 of them have between 150 and 199 songs, then there are more phones with between 200 and 249 songs. However, if there are 1,000 phones in total and 100 of them have between 200 and 249 songs while 600 of them have between 150 and 199 songs, then there are more phones with between 150 and 199 songs.

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The decimal approximation for cot(235°36') is approximately -0.9503.

To find the decimal approximation for cot(235°36'), we first need to convert the angle to degrees.

The given angle is 235°36'. We can convert this to decimal degrees by adding the fraction of minutes to the degree value. There are 60 minutes in a degree, so we divide 36 by 60 to convert it to a fraction of a degree:

36 / 60 = 0.6 degrees

Now, we can add this fraction to the degree value:

235 + 0.6 = 235.6 degrees

The cotangent function is the reciprocal of the tangent function. To find the cotangent of an angle, we can use the following formula:

cot(x) = 1 / tan(x)

Since we want to find cot(235.6°), we can find tan(235.6°) first and then take the reciprocal.

Using a scientific calculator or software, we can find

tan(235.6°) ≈ -1.0529

Now, we can take the reciprocal to find cot(235.6°):

cot(235.6°) ≈ 1 / (-1.0529) ≈ -0.9503

Therefore, the decimal approximation for cot(235°36') is approximately -0.9503.

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The phase margin of the system is approximately 7.38 degrees.

To find the phase margin, we first need to find the closed-loop transfer function of the system. For a unity feedback system, the closed-loop transfer function is given by:

T(s) = G(s) / (1 + G(s))

where G(s) is the forward path transfer function.

Substituting G(s) into the equation above, we get:

T(s) = 100 (s + 2) s(s + 1)(s + 4) / [s(s + 1)(s + 4) + 100 (s + 2)]

Simplifying the expression above, we get:

T(s) = 100 (s + 2) / [s(s + 1)(s + 4) + 100 (s + 2)]

To find the phase margin, we need to find the frequency at which the phase of the closed-loop transfer function is -180 degrees. We can do this by setting the denominator of the closed-loop transfer function equal to zero and solving for the frequency. This frequency is known as the phase crossover frequency.

Setting the denominator of the closed-loop transfer function equal to zero, we get:

s(s + 1)(s + 4) + 100 (s + 2) = 0

Expanding the equation above, we get:

s^3 + 5s^2 + 4s + 200 = 0

Using a numerical method or a graphical method, we can find that the phase crossover frequency is approximately 2.02 rad/s.

To find the phase margin, we need to evaluate the phase of the closed-loop transfer function at the frequency of 2.02 rad/s. We can do this by substituting s = j2.02 into the closed-loop transfer function and computing the phase angle.

Substituting s = j2.02 into the closed-loop transfer function, we get:

T(j2.02) = 100 (j2.02 + 2) / [j2.02(j2.02 + 1)(j2.02 + 4) + 100 (j2.02 + 2)]

Taking the complex conjugate of the denominator and multiplying the numerator and denominator by the complex conjugate of the denominator, we get:

T(j2.02) = [100 (j2.02 + 2)] / [|j2.02|^2 (j2.02 + 1)(j2.02 + 4) + 100 (j2.02 + 2)] × e^jθ

where θ is the phase angle.

Computing the magnitude and phase angle of the closed-loop transfer function at the frequency of 2.02 rad/s using a calculator or software, we get:

|T(j2.02)| = 0.2806

θ = -172.62 degrees

The phase margin is then given by:

PM = 180 degrees + θ

PM = 180 degrees - 172.62 degrees

PM = 7.38 degrees

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The given question is incomplete, the complete question is:

For the unity feedback system, the forward path transfer function is: G(s) = 100 (s + 2) s(s + 1)(s + 4) . find the phase margin.

Answer:

2

Step-by-step explanation:

2(z)+2 = 4

2z = 2 x 2 = 4

The probability that the child must wait at least 9 minutes on a given morning is approximately 0.2231.

Let X be the waiting time at the bus stop. We know that X is exponentially distributed with mean 6 minutes. Therefore, the probability density function (PDF) of X is given by:

f(x) = 1/6 * e^(-x/6) for x >= 0

To find the probability that the child must wait at least 9 minutes, we need to calculate the following probability:

P(X >= 9) = integral of f(x) from 9 to infinity

= integral from 9 to infinity of (1/6 * e^(-x/6)) dx

Using integration by substitution, let u = x/6, du = 1/6 dx, so that:

P(X >= 9) = integral from 3/2 to infinity of e^(-u) du

= [e^(-u)] evaluated from 3/2 to infinity

= e^(-3/2)

≈ 0.2231

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If you select 25 in the Top Values list, Access displays the top 25 records in the query results.

Queries are excellent tools in Microsoft Excel to show information from related tables in a single result set, as the results that you pull from queries aren’t limited to a single table.

The way to create a simple query using the wizard is as follows;

Now, If you select 25 in the top values list, access displays the top 25 records in the query results.

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Juan should accept projects with a profitability index greater than 1.0. In this case, neither Project A nor Project B has a profitability index greater than 1.0.

To determine which project or projects Juan should accept based on the profitability index rule, we need to calculate the profitability index for both projects.

The profitability index is calculated by dividing the present value of cash inflows by the initial investment:

Profitability Index = Present Value of Cash Inflows / Initial Investment

For Project A:

Initial Investment = $72,500

Discount Rate = 10%

Year 1 Cash Flow = $18,700 / (1 + 0.10)¹  = $17,000

Year 2 Cash Flow = $46,300 / (1 + 0.10)²  = $38,000

Year 3 Cash Flow = $12,200 / (1 + 0.10)³  = $8,000

Present Value of Cash Inflows = $17,000 + $38,000 + $8,000 = $63,000

Profitability Index for Project A = $63,000 / $72,500 = 0.869

For Project B:

Initial Investment = $72,500

Discount Rate = 12%

Year 1 Cash Flow = $10,600 / (1 + 0.12)¹ = $9,464

Year 2 Cash Flow = $15,800 / (1 + 0.12)² = $11,821

Year 3 Cash Flow = $67,900 / (1 + 0.12)³ = $47,044

Present Value of Cash Inflows = $9,464 + $11,821 + $47,044 = $68,329

Profitability Index for Project B = $68,329 / $72,500 = 0.942

Based on the profitability index rule, Juan should accept projects with a profitability index greater than 1.0. In this case, neither Project A nor Project B has a profitability index greater than 1.0.

Therefore, the answer is:

C. Accept either A or B, but not both.

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