-1
A line's y-intercept is 0, and its slope is
20
What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Submit

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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Answer:

7π over 3

Step-by-step explanation:

Convert from degrees to radians using the ratio π over 180.

The Binary Search Tree is as follows:

                                                   E

                                            /            \

                                         S                T

                                        /                    \

                                      I                       W

                                   /                            \

                                A                               M

                              /                                    \

                             C                                     G

                              \

                                D

The set of letters is {I, D, S, A, E, T, C, G, M, W} and len (I, D, S, A, a) = 5

Binary Search Tree:The binary search tree based on the alphabetical ordering of the letters is:

post-order sequence is: C, D, A, G, M, I, W, T, S, E.

To draw the binary search tree for the given post-order sequence, follow the steps below:

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You have to include a question or a link to thw question so qe could solve it.

Answer:

the answer is option A

PLEASE MARK ME AS BRAINLY

Step-by-step explanation:

The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer:

A) x = -4

Step-by-step explanation:

\(3x-2\left(6-x\right)=7x+2\left(5+x\right)-6\\\\\mathrm{Expand\:}3x-2\left(6-x\right):\quad 5x-12\\\\\mathrm{Expand\:}7x+2\left(5+x\right)-6:\quad 9x+4\\5x-12=9x+4\\\\\mathrm{Add\:}12\mathrm{\:to\:both\:sides}\\5x-12+12=9x+4+12\\\\Simplify\\5x=9x+16\\\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\5x-9x=9x+16-9x\\\\Simplify\\-4x=16\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\frac{-4x}{-4}=\frac{16}{-4}\\\\Simplify\\x=-4\)

To pay off a loan of $49,000 at an annual interest rate of 9% compounded monthly, with monthly payments of $400, it will take approximately 12.9 years.

To determine the time it takes to pay off the loan, we can use the formula for the number of periods (n) in the compound interest formula. In this case, the loan amount is $49,000, the monthly payment is $400, and the monthly interest rate is 9% divided by 12 (0.09/12 = 0.0075). We can use the following formula:

\(n = -log(1 - (r * P) / A) / log(1 + r)\)

where r is the monthly interest rate, P is the monthly payment, and A is the loan amount.

Plugging in the values, we have:

\(n = -log(1 - (0.0075 * 49000) / 400) / log(1 + 0.0075)\)

Calculating this expression, we find that n is approximately 12.9 years. Therefore, it will take approximately 12.9 years to pay off the loan with monthly payments of $400, rounded to one decimal place.

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Given:

A TV with a cash price of $245.00 and a down payment of $4.90.

So, the amount financed =

So, the answer will be option D. $240.10

Answer:

A sample proportion of approximately 0.524 would be so "extreme" in the positive direction that it would be higher than 95% of the sample proportion's we could see from such surveys.

Step-by-step explanation:

To determine the sample proportion that would be higher than 95% of the sample proportion's we could see from such surveys, we can use the normal approximation for p.

Given that we assume the true proportion p = 0.5 and we want to find an extreme value in the positive direction, we can calculate the z-score corresponding to the 95th percentile (z = 1.645).

Using the formula for the z-score:

z = (sample proportion - normal approximation) / sqrt(normal approximation * (1 - normal approximation) / n)

Plugging in the values:

1.645 = (sample proportion - 0.5) / sqrt(0.5 * (1 - 0.5) / 1000)

Now we can solve for sample proportion:

1.645 * sqrt(0.5 * (1 - 0.5) / 1000) = sample proportion - 0.5

sample proportion = 1.645 * sqrt(0.5 * (1 - 0.5) / 1000) + 0.5

Calculating the value:

sample proportion ≈ 0.524

Therefore, a sample proportion of approximately 0.524 would be so "extreme" in the positive direction that it would be higher than 95% of the sample proportion's we could see from such surveys.

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Answer:

12

Step-by-step explanation:

1/2x = 6

x = 12

Answer:

x=12

Step-by-step explanation:

half of 12 is 6. 6-2=4

Answer:

this is som A sorry if you can't read it

Answer:

D

Step-by-step explanation:

{(-2,1)(2,7)} that's my answer

Answer:

9.25

Step-by-step explanation:

15.75 minus 6.50 then you get 9.25

The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.

acc to our question-

hence,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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4 square units will be the area of the largest rectangle.

Given,

First, let's build a rectangle ABCD, where A is the point at the bottom right corner and B,C, and D are the points designated in accordance with A.

Now,

Let A = (p, 0)

B = (-p, 0)

C = (-p, 3 - p²)

D = (p, 3 - p²)

Then the area of rectangle is given as: BA×AD

= 2p × 3 - p²

A = 6p - 2p³

Taking the derivative with respect to p, we have

A' = 6 - 6p²

Now,

A' =0

⇒ 6 - 6p² = 0

⇒ 6p² = 6

⇒ p² = 1

Since, we have to find the greater area, therefore we will take p = 1.

Now, substituting the value of p in (A), we have

Greater area = A= 6 - 2 x 1 = 4 square units

Therefore,

The  area of the largest rectangle should be 4 square units.

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Question is incomplete. Completed question is given below;

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x2?

Answer:

1/2

Step-by-step explanation:

Answer:

y=1/2x-8

Step-by-step explanation:

any variable b(-8) would be fine as long as the slope m(1/2) is the same

Main Answer:The volume is \(\pi\)/6.

Supporting Question and Answer:

How can we determine the volume using the slicing method when the slices are semicircles perpendicular to the x-axis?

To determine the volume using the slicing method with semicircular slices perpendicular to the x-axis, we need to integrate the areas of the infinitesimally thin slices over the range of x-values. The radius of each semicircle depends on the x-coordinate, and we can use the formula for the area of a semicircle to calculate the area of each slice. By integrating the areas over the given range, we can obtain the total volume of the solid.

Body of the Solution:To find the volume using the slicing method, we need to integrate the areas of the infinitesimally thin slices perpendicular to the x-axis.

In this case, the slices perpendicular to the x-axis are semicircles. The radius of each semicircle depends on the x-coordinate.

Let's denote the variable of integration as x and consider a slice at a specific value of x. The corresponding semicircle's radius is given by r = 1 - x (since the triangle's height is 1 and decreases linearly with x).

The area of a semicircle is given by A = (1/2) * \(\pi\) * r^2.

Integrating the area over the range of x from 0 to 1, we get:

V = ∫[0,1] A dx = ∫[0,1] (1/2) * \(\pi\) * (1 - x)^2 dx

Simplifying and evaluating the integral, we get:

V = (\(\pi\)/2) * ∫[0,1] (1 - 2x + x^2) dx = (\(\pi\)/2) * [x - x^2/2 + x^3/3] |[0,1] = (\(\pi\)/2) * [1 - 1/2 + 1/3] = (\(\pi\)/2) * [2/6] = \(\pi\)/6

Final Answer:Therefore, the volume of the solid bounded by the triangle and the semicircles is π/6, rounded to two decimal places.

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The volume off the given triangle is π/6.

How can we determine the volume using the slicing method when the slices are semicircles perpendicular to the x-axis?

To determine the volume using the slicing method with semicircular slices perpendicular to the x-axis, we need to integrate the areas of the infinitesimally thin slices over the range of x-values. The radius of each semicircle depends on the x-coordinate, and we can use the formula for the area of a semicircle to calculate the area of each slice. By integrating the areas over the given range, we can obtain the total volume of the solid.

To find the volume using the slicing method, we need to integrate the areas of the infinitesimally thin slices perpendicular to the x-axis.

In this case, the slices perpendicular to the x-axis are semicircles. The radius of each semicircle depends on the x-coordinate.

Let's denote the variable of integration as x and consider a slice at a specific value of x. The corresponding semicircle's radius is given by r = 1 - x (since the triangle's height is 1 and decreases linearly with x).

The area of a semicircle is given by A = (1/2) *  * r^2.

Integrating the area over the range of x from 0 to 1, we get:

V = ∫[0,1] A dx = ∫[0,1] (1/2) *  * (1 - x)^2 dx

Simplifying and evaluating the integral, we get:

V = (/2) * ∫[0,1] (1 - 2x + x^2) dx = (/2) * [x - x^2/2 + x^3/3] |[0,1] = (/2) * [1 - 1/2 + 1/3] = (/2) * [2/6] = /6

Final Answer:Therefore, the volume of the solid bounded by the triangle and the semicircles is π/6, rounded to two decimal places.

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Answer:

A: The cube of a number less than the square root of the number.

Step-by-step explanation:

None

Answer:

55mph

Step-by-step explanation:

there 1.62 km in each mile

With the volume of water poured at rate 8 m³/minute, when the height of water is 5 meters, the water will be rising at rate 0.23 m/minute.

Let:

r = radius of water at an instant

h = level of water at an instant

Then,  due to similarity property:

r/h =  4/6 = 2/3

Or,

r = 2/3 . h

The volume of the poured water is:

V = 1/3. πr².h

Substitute r = 2/3 . h into the formula:

V = 1/3. π(2/3. h)².h

V = 4/27. πh³

Take the derivative with respect to t:

dV/dt = 4/27 . 3πh² . dh/dt

dV/dt = 4/9 . πh² . dh/dt

Substitute: dV/dt = 8 m³/minute and h = 5 m:

8 = 4/9 .  π .5² . dh/dt

dh/dt = 0.23 m/minute.

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So, the maximum value of the function || Bx|| subject to the constraint is e. 9

The function we want to maximize is ||Bx||, where B is the given matrix and x is a vector with \(||x||^2 = 1\). We can rewrite this as:

\(||Bx||^2 = (Bx)^(T) (Bx) = x^{(T)} B^{(T)} B x\)

Since B is a 2x2 matrix, \(B^{(T)}B\) is also a 2x2 matrix:

\(B^{(T)} B = [4 0]\)

[0 9]

Thus, we can write:

\(||Bx||^2 = x^{(T)} B^{(T)} B x = [x1 x2] [4 0; 0 9] [x1; x2] = 4x1^2 + 9x2^2\)

So, we need to maximize the function\(4x1^2 + 9x2^2\) subject to the constraint \(x1^2 + x2^2 = 1.\)

We can use Lagrange multipliers to solve this problem. The Lagrangian function is:

\(L(x1, x2, \lambda) = 4x1^2 + 9x2^2 - \lambda(x1^2 + x2^2 - 1)\)

The partial derivatives are:

∂L/∂x1 = 8x1 - 2λx1 = 0

∂L/∂x2 = 18x2 - 2λx2 = 0

\(\partial L/\partial \lambda = -(x1^2 + x2^2 - 1) = 0\)

From the first two equations, we can see that x1 = 4λ and x2 = 9λ. Substituting these into the third equation, we get:

\(x1^2 + x2^2 = (4\lambda)^2 + (9\lambda)^2 = 1\)

Solving for λ, we get:

λ = ±1/√(97)

We can plug these values of λ into x1 and x2 to get two possible vectors:

x1 = 4λ = ±4/√(97)

x2 = 9λ = ±9/√(97)

We need to find the maximum value of ||Bx||, which is:

||Bx|| = ||[2 0; 0 -3] [x1; x2]|| = ||[2x1; -3x2]|| = 2|x1| + 3|x2|

Plugging in the values of x1 and x2, we get:

||Bx|| = 2|4/√(97)| + 3|9/√(97)| = 38/√(97)

Therefore, the answer is not one of the options given.

However, the closest option is e. 9, which is approximately equal to 38/4.12. So, the closest answer is e. 9.

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Answer:

a) 10n -6

b) -5n +105

c) 7f + 1

d) -11n +48

Step-by-step explanation:

for an example let's take a) 4, 14, 24, 34

term value:

14 - 4 = 10 (coefficient)

term number:

4 = 34

4×10=40

34 - 40 = -6

coefficient and constant

therefore v = 10n -6

lol are you a Bhutanese?

The nine fundamental solutions to the differential equation are:
Y1 = e^(3t)(cos(2t) + 2i*sin(2t))    Y2 = e^(3t)(cos(2t) - 2i*sin(2t))    Y3 = t^3    Y4 = t^4    Y5 = t^3*e^(-3t)    Y6 = t^4*e^(-3t)
Y7 = e^(-3t)    Y8 = t*e^(-3t)    Y9 = t^2*e^(-3t)

To find the nine fundamental solutions to the given 9th order, linear, homogeneous, constant coefficient differential equation, we need to consider the roots of the characteristic equation, which factors as follows:

(r2 + 2r + 5)(r3)(r + 3)4 = 0

The roots of the characteristic equation are:

r1 = -1 + 2i
r2 = -1 - 2i
r3 = 0 (with multiplicity 3)
r4 = -3 (with multiplicity 4)

To find the fundamental solutions, we need to use the following formulas:

If a root of the characteristic equation is complex and non-repeated (i.e., of the form a + bi), then the corresponding fundamental solution is:
y = e^(at)(c1*cos(bt) + c2*sin(bt))

If a root of the characteristic equation is real and non-repeated, then the corresponding fundamental solution is:
y = e^(rt)

If a root of the characteristic equation is real and repeated (i.e., of the form r with multiplicity k), then the corresponding fundamental solutions are:
y1 = e^(rt)
y2 = t*e^(rt)
y3 = t^2*e^(rt)
...
yk = t^(k-1)*e^(rt)

Using these formulas, we can find the nine fundamental solutions as follows:
y1 = e^(3t)(cos(2t) + 2i*sin(2t))
y2 = e^(3t)(cos(2t) - 2i*sin(2t))
y3 = t^3*e^(0t) = t^3
y4 = t^4*e^(0t) = t^4
y5 = t^3*e^(-3t)
y6 = t^4*e^(-3t)
y7 = e^(-3t)
y8 = t*e^(-3t)
y9 = t^2*e^(-3t)

So the nine fundamental solutions to the differential equation are:
Y1 = e^(3t)(cos(2t) + 2i*sin(2t))
Y2 = e^(3t)(cos(2t) - 2i*sin(2t))
Y3 = t^3
Y4 = t^4
Y5 = t^3*e^(-3t)
Y6 = t^4*e^(-3t)
Y7 = e^(-3t)
Y8 = t*e^(-3t)
Y9 = t^2*e^(-3t)

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Answer:

To determine if there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit, we need to see if the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is constant.

On the first day, the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is 20°C / 68°F = 5/17.

On the second day, the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is 10°C / 50°F = 1/5.

Since the ratio of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is different on the two days, there is not a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.

Step-by-step explanation:

Since both data points satisfy the proportional relationship equation, we can conclude that there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.

To determine if there is a proportional relationship between the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F), we can check if the data points given for both temperatures satisfy the proportional relationship equation:

°F = (9/5) * °C + 32

Let's calculate the proportional relationship using the given data points:

1. First data point: 68°F and 20°C

  °F = (9/5) * 20 + 32

  °F = 36 + 32

  °F = 68

  The first data point (68°F and 20°C) satisfies the proportional relationship equation.

2. Second data point: 50°F and 10°C

  °F = (9/5) * 10 + 32

  °F = 18 + 32

  °F = 50

The second data point (50°F and 10°C) also satisfies the proportional relationship equation.

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The approximate distance from y to y’ in the given triangle x y z reflected over its hypotenuse to form kite x y z y is  9.2 units.

The value of angle X in ΔXYZ is calculated as follows;

tanx = 12/5

tanx = 2.4

x = tan⁻¹(.24)

x = 67.38⁰

The height from vertex Y to horizontal line XZ is calculated as follows;

sinx = h/5

h = 5(sinx)

h = 5(sin67.38)

h = 4.62

YY' = 4.62 + 4.62 = 9.24 units

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Answer:

A ✔️

Step-by-step explanation:

"4.6"