How is solving an equation with the variable on both sides of the equation the same as and different from solving an
equation with the variable on one side of the equation?

It will cost $186.30 to run the resistance heater for 30 days with the given conditions.

Given data:

Power consumed by the resistance heater = 4.5 kW

Running time = 6 hours/day

Period of running = 30 days

Cost of electricity = Average price in Massachusetts

To calculate the total energy consumption during this time period,

we use the formula below:

Energy = Power × Time

Energy consumed in 6 hours

= 4.5 kW × 6 hours

= 27 kWh/day

Total energy consumed in 30 days

= 27 kWh/day × 30 days

= 810 kWh

To calculate the cost of running the resistance heater, we use the formula below:

Cost = Energy × Cost per unit of electricity

Cost of electricity per unit in Massachusetts is assumed to be $0.23/kWh

Cost of running the resistance heater

= 810 kWh × $0.23/kWh

= $186.30

Therefore, it will cost $186.30 to run the resistance heater for 30 days with the given conditions.

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Answer:

Step-by-step explanation:

Answer:

(-4,0)

ignore this line

The correct answer is 0.00544 m^3.

To calculate the volume of a cylindrical steel bar, we need to use the formula:

Volume = π * (radius^2) * height

Given that the diameter of the round steel bar is 76 mm, we can calculate the radius by dividing the diameter by 2:

Radius = diameter / 2 = 76 mm / 2 = 38 mm = 0.038 m

The length of the steel bar is given as 1.2 m.

Now we can substitute these values into the formula:

Volume = π * (0.038^2) * 1.2

Volume = 3.14159 * (0.038^2) * 1.2

Volume ≈ 0.005439632 m^3

Rounded to four decimal places, the volume of the 1.2 m long steel bar is approximately 0.0054 m^3.

Therefore, the correct answer is 0.00544 m^3.

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Answer:

Below

Step-by-step explanation:

6.5 x 10^-9   is the same as  65 x 10^-10    now you can add them together (since the exponents are the same ) to get

69.6 x 10 ^-10  which is   6.96 x 10^-9

press menu and select option,press 2 to select to a polynomial degree of 2,select the number that matches the inequality u are about to solve and lastly input the values of coefficient of x into the expression and press equal to sign on the calculator

A relationship between two expressions or values that are not equal to each other is called 'inequality. '

Inequality can be greater than >, less than < , great than or equal to ≥ , less than or equal to ≤.

like other equations, inequality can be solved on a calculator. This process shows how inequality can be solved on a calculator. For example if 3x²+4x+5≥0 is to be solved on a calculator, the following steps are to be taken

Step 1 : press menu and select option B( inequality option)

Step2 : press 2 to select to a polynomial degree of 2

step 3 : select the number that matches the inequality u are about to solve

step 4: input the values of coefficient of x into the expression

step 5 : press the equal to sign on the calculator.

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The theoretical probability of selecting a red marble from the bag is approximately 0.33.

To find the theoretical probability of selecting a red marble from the bag, we need to divide the number of favorable outcomes (number of red marbles) by the total number of possible outcomes (total number of marbles).

The bag contains a total of 3 blue + 5 red + 7 yellow = 15 marbles.

The number of red marbles is 5.

Therefore, the theoretical probability of selecting a red marble is:

p(red) = 5/15

Simplifying this fraction, we get:

p(red) = 1/3 ≈ 0.33 (rounded to the nearest hundredth)

So, the theoretical probability of selecting a red marble from the bag is approximately 0.33.

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Answer:

8/9 divided by 3/4 is equivalent to 16/18 divided by 6/8

Step-by-step explanation:

Just multiplied the numerator and denominator of both fractions by 2.

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 definite integral given is 2e1/x5 x6 dx.

To solve this integral, we need to use integration by parts. We will use u = 2e1/x5 and dv = x6 dx. Using integration by parts, we have:

∫ udv = uv - ∫vdu

Therefore, we have:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) ∫e1/x5 dx

We can solve this last integral by using the substitution x5 = u. Doing so, we have:

∫ e1/x5 dx = (1/5) ∫ eudu

Using integration by parts, we have:

∫ eu du = eu u - ∫ ueu du

Therefore, we have:

∫ e1/x5 dx = (1/5) [eu u - ∫ ueu du] = (1/5) [eu u - u2 eu/2]

Substituting x5 = u, we have:

∫ e1/x5 dx = (1/5) [ex5 x5 - x10 ex5/2]

Finally, we can substitute this result into the original integral and get the answer:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) [(1/5) [ex5 x5 - x10 ex5/2]]

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Answer:

Okay, where's the question?

The formula is weight of object = mass x gravity

if you punch the numbers in the formula correctly the mass in kg is 875.634 kg x 9.8 m/s =  8,581.2132

The number of ways to select 3 pages in ascending index order depends on the total number of pages available.

To find the number of ways to select 3 pages in ascending index order, we can use the concept of combinations . In combinatorics, selecting objects in a specific order is often referred to as permutations. However, since the order does not matter in this case, we need to consider combinations instead.

The number of ways to select 3 pages in ascending index order can be calculated using the combination formula. Since we are selecting from a set of pages, without replacement and order doesn't matter, we can use the formula C(n, k) = n! / (k!  (n-k)!), where n is the total number of pages and k is the number of pages we want to select.

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The solution to the given system of equation is 17 1/2

Fractions are ratio of two integers. Given the expression below;

28 / 1 3/5

Convert mixed fraction to improper fraction

28/(8/5)

28 * 5/8

14 * 5/4

7 * 5/2

35/2

Hence the solution to the given system of equation is 17 1/2

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Based on the arithmetic sequence with the first term −5 and the common difference 4 is 660, we could find m = 20.

To find the sum of the first m terms of an arithmetic sequence, we can use the formula:

sum = (m/2)(2a + (m-1)d),

where a is the first term,

d is the common difference,

and m is the number of terms.

In this case, we are given a = −5, d = 4, and sum = 660. We can plug these values into the formula and solve for m:
660 = (m/2)(2(-5) + (m-1)(4))
660 = (m/2)(-10 + 4m - 4)
660 = (m/2)(4m - 14)
1320 = m(4m - 14)
0 = 4m^2 - 14m - 1320

Now we can use the quadratic formula to solve for m:
m = (-b ± √(b^2 - 4ac))/(2a)
m = (-(−14) ± √((−14)^2 - 4(4)(-1320)))/(2(4))
m = (14 ± √(196 + 21120))/8
m = (14 ± √21316)/8
m = (14 ± 146)/8

Now we have two possible values for m:
m = (14 + 146)/8 = 160/8 = 20
m = (14 - 146)/8 = -132/8 = -16.5

Since m must be a positive integer, we can conclude that m = 20. Therefore, the sum of the first 20 terms of the arithmetic sequence is 660.

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Answer:

1/4 c. + 2 tbsp.

Step-by-step explanation:

3/4 c. = 12 tbsp.

12 / 2 = 6

6 tbsp. = 1/4 c. + 2 tbsp.

Answer:

answer 9x

Step-by-step explanation:

The future superannuation fund balance, considering a current balance of $45,000, annual contributions of $17,500, a 5.5% annual return, and a 40-year investment period, is estimated to be around $764,831.

To calculate the future superannuation fund balance at retirement, you can use the compound interest formula:

Future Balance = Current Balance × (1 + Annual Return Rate)^(Number of Years of Investment)

In this case, the current balance is $45,000, the annual return rate is 5.5% (or 0.055), and the number of years of investment is 40. The annual contributions of $17,500 can be treated as additional contributions each year.Using the formula, the future balance at retirement can be calculated as:Future Balance = ($45,000 + $17,500) × (1 + 0.055)^40

Simplifying the calculation, the future balance at retirement is approximately $764,831.46. So, the estimated superannuation fund balance at retirement for this person would be around $764,831.

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Answer:

J''(- 3, 3 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x )

Thus J(1, 1 ) → J'(- 1, 1 )

Under a dilatation with scale factor 3, multiply each of the coordinates of J' by 3, that is

J'' = (3(- 1), 3(1)) = (- 3, 3 )

Both M and S in sexagesimal notation = 3600D.

Here converting 'D' into minutes.

We know that a degree is made up of 60 minutes.

so multiply D with 60 we get

⇒ D x 60 = M

Now convert 'M' into seconds.

Again, there are 60 seconds in a minute,

so multiply M with 60 we get,

⇒ M x 60 = S

Simplify this equation by substituting D x 60 for M,

⇒D x 60 x 60 = S

Simplifying further, we get,

⇒ 3600D = S

Hence, 3600D is equal to both M and S in sexagesimal notation.

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Answer:

1.a

2.c

3.d

4.b

Step-by-step explanation:

Answer:

14.88

A = \(\frac{h_bb}{2}\)

    = 4.8 × 6.2 / 2

     = 14.88

Answer:

60.25 then 34.5

Step-by-step explanation:

Answer:

60.75 and 119.25

Step-by-step explanation:

Answer:

$35

Step-by-step explanation:

Monday: $15

Tuesday: $10

15+10=35

$35 total

Answer:

-25

Step-by-step explanation:

The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.

We can use the formula for the volume of a cone, which is:

Volume = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:

13.4 = (1/3)π(3.2)²h

Multiplying both sides by 3 and dividing by π(3.2)², we get:

h = 3 × 13.4 / π(3.2)²

h ≈ 2.5 m

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Answer:

the rate of change is 2 percent per exam

Step-by-step explanation:

Answer:

The rate of change is 2 percent per exam.

Step-by-step explanation:

:)

sin⁻¹(sin((5π/4))) = -π/4

sin⁻¹(sin(2π/3)) = 2π/3

cos⁻¹(cos(-7π/4)) = π/4

cos⁻¹(cos(π/6)) = π/6

The inverse sine function, sin⁻¹(x), gives the angle whose sine is equal to x. Similarly, the inverse cosine function, cos⁻¹(x), gives the angle whose cosine is equal to x.

In the first expression, sin⁻¹(sin((5π/4))), the sine of 5π/4 is -1/√2, which is equivalent to -π/4 when considering the range of -π/2 ≤ θ ≤ π.

In the second expression, sin⁻¹(sin(2π/3)), the sine of 2π/3 is √3/2. Since 2π/3 is within the range of -π/2 ≤ θ ≤ π, the answer is 2π/3.

In the third expression, cos⁻¹(cos(-7π/4)), the cosine of -7π/4 is -1/√2, which is equivalent to π/4 within the range of 0 ≤ θ ≤ π.

In the fourth expression, cos⁻¹(cos(π/6)), the cosine of π/6 is √3/2. Since π/6 is within the range of 0 ≤ θ ≤ π/2, the answer is π/6.

Hence, the evaluated expressions are -π/4, 2π/3, π/4, and π/6, respectively.


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