40)
6 cm
4 cm
12 cm
Find the volume of the rectangular prism.
will

$42 is the amount Zahra will save each year

How to find how much Zahra will save every year?

Given that:

Zahra does 1 load of wash per day

Hot wash & warm rinse = 71 cents per load

Warm wash & cold rinse = 25 cents per load

Right now three-fourths of all her laundry is done with the hotter water

Right now:

cost of hot wash in a year = 0.71 x 3/4 x 365 = $194.3625

cost of warm wash in a year = 0.25 x 1/4 x 365 = $22.8125

Total cost =  $194.3625 + $22.8125 = $217.175

After the cut:

cost of hot wash in a year = 0.71 x 1/2 x 365 = $129.575

cost of warm wash in a year = 0.25 x 1/2 x 365 = $45.625

Total cost =  $129.575 + $45.625 = $175.2

Savings = Total cost of right now - Total cost after the cut

Savings = $217.175 - $175.2 = $41.975 = $42

Note: we have 365 days in a year

Therefore, Zahra will save $42 every year. Option b. is the answer

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The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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The value of the definite integral cos(πt/2) dt 0 is -2/π.

We can start by using the substitution

u = πt/2.

Then

du/dt = π/2 and calculus

dt = 2/π du.

Also, when

t = 0, u = 0 and when

t = 9, u = 9π/2.

Substituting these in the integral, we get:

∫₀⁹ cos(πt/2) dt = \(\int\limit ^{(9\pi /2)}\) cos u (2/π) du = (2/π) \([sin(u)]\theta^(9\pi /2)\)

Using the periodicity of the sine function, we can simplify this expression as:

(2/π) [sin(9π/2) - sin(0)] = (2/π) [-1 - 0] = -2/π

Therefore, the value of the definite integral is -2/π.

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So the question is asking us to find the definite integral of the function cos(πt/2) between the limits of 0 and 1. An integral is a mathematical tool used to find the area under a curve between two points. In this case, we need to evaluate the area under the curve of cos(πt/2) between t=0 and t=1.

To solve this, we can use the formula for the definite integral:

∫[a,b]f(x)dx = [F(x)] from a to b
Where F(x) is the antiderivative of f(x). In this case, the antiderivative of cos(πt/2) is 2/π sin(πt/2). So plugging in the limits of integration, we get:

∫[0,1]cos(πt/2)dt = [2/π sin(πt/2)] from 0 to 1
Evaluating this, we get:

[2/π sin(π/2)] - [2/π sin(0)]

Simplifying:

[2/π] - 0 = 2/π

So the definite integral of cos(πt/2) between 0 and 1 is 2/π.
To evaluate the definite integral of cos(πt/2) from 0 to 1, follow these steps:

1. Find the antiderivative of cos(πt/2) concerning t. To do this, apply the chain rule for integration: ∫cos(πt/2) dt = (2/π)sin(πt/2) + C, where C is the constant of integration.

2. Now, apply the definite integral limits 0 to 1: [(2/π)sin(πt/2)] from 0 to 1.

3. Plug in the upper limit (1) and subtract the value with the lower limit (0): [(2/π)sin(π(1)/2)] - [(2/π)sin(π(0)/2)].

4. Simplify: (2/π)(sin(π/2)) - (2/π)(sin(0)).

5. Evaluate the sine values: (2/π)(1) - (2/π)(0) = 2/π.

So, the definite integral of cos(πt/2) from 0 to 1 is 2/π.

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Answer:

133

Step-by-step explanation:

If you need an explanation please tell me.

Answer: This means that Mark spent more on dining out last month than what he had budgeted, and the difference was greater than 20 dollars.

Mark had set aside a specific amount of money each month for dining out expenses. However, last month he exceeded that amount and spent more than what he had budgeted. The difference between the amount he planned to spend and what he actually spent was negative and greater than 20 dollars, indicating that he overspent by more than 20 dollars. This implies that the cost of dining out was higher than expected, and Mark spent more money on it than he had originally intended to.

Step-by-step explanation:

Answer:

140

Explanation: cause -180 + 40 = -140 (but absolute value is 140)

Answer:

equal to 1

Step-by-step explanation:

I believe this is the answer. Also I see that ur new. Well welcome to Brainly.

Answer:

S > R + Q

Step-by-step explanation:

Locations:

P = 0.30

Q = 1.10

R = 2.80

S = 4.40

Statements:

A. P + Q > R

B. P > S - Q

C. S > R + Q

Find the correct statement:

P + Q > R

0.30 + 1.10 > 2.80

1.40 > 2.80

This statement is incorrect

P > S - Q

0.30 > 4.40 - 1.10

0.30 > 3.30

This statement is incorrect

S > R + Q

4.40 > 2.80 + 1.10

4.40 > 3.90

This statement is correct

Therefore, the correct statement is S > R + Q

Hope this helps!

The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.

Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.

Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:

Sphere 1 produces the greatest electric field at point P since it is the closest to it.

Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.

Sphere 3 produces the smallest electric field at point P since it is the farthest from it.

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The length of Raj's piece of string is 12x units.

To determine the length of Raj's piece of string, we need to find Kiki's third-longest piece.

Looking at the line plot or list of lengths provided, we can identify the third-longest length of Kiki's pieces.

Let's assume Kiki's third-longest piece has a length of x units.

According to the problem, Raj's piece of string is 12 times as long as Kiki's third-longest piece.

Therefore, the length of Raj's piece of string would be 12 × x units.

We can only express it as 12x units, where x represents the length of Kiki's third-longest piece.

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When defining inverse trigonometric functions, we need to ensure that the function is one-to-one within a certain interval:  the choices that could be used to define the inverse of the given trigonometric functions are (c) and (d).

This means that each output corresponds to only one input. The standard way to define the inverse trigonometric functions involves restricting the domain of the original function.

In the given choices, we can check if the restrictions would allow us to define the inverse of the given trigonometric functions.

a) Restricting f(x) = sin x to [π, 2π) would not work for defining the inverse of sin x, because sin x is not one-to-one within this interval. For example, sin(π/2) = sin(3π/2) = 1, which violates the one-to-one condition for the inverse function.

b) Restricting f(x) = cos x to [π, 2π) would also not work for defining the inverse of cos x, because cos x is not one-to-one within this interval. For example, cos(π) = cos(2π) = -1, which violates the one-to-one condition for the inverse function.

c) Restricting f(x) = tan x to (π, 2π) would work for defining the inverse of tan x, because tan x is one-to-one within this interval. This restriction excludes the vertical asymptotes at π/2 and 3π/2, where the function is not defined.

d) Restricting f(x) = cot x to (π, 2π) would also work for defining the inverse of cot x, because cot x is one-to-one within this interval. This restriction excludes the vertical asymptotes at 0 and π, where the function is not defined.

Therefore, the choices that could be used to define the inverse of the given trigonometric functions are (c) and (d).

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The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

15 ×6 ÷2

mmmmaaaaaattttthhhh

Answer:

90

Step-by-step explanation:

Just multiply the 15 and the 6

Answer:

67

Step-by-step explanation:

1. Find the common difference of the arithmetic sequence

2. Find the 3rd term of the arithmetic sequence using the arithmetic sequence formula

⭐What is an arithmetic sequence?

1. Substitute the first term into the arithmetic sequence formula

\(a_n = a_1 + d(n-1)\)

\(a_n = 40+d(n-1)\)

2. Substitute the 7th term into the equation to solve for d

\(a_7 = 40+d(7-1)\\a_7 = 40+d(6)\)

\(a_7 = 40 + 6d\\121 = 40 + 6d\)

\(81 = 6d\) . . . . . . . subtract 40 from both sides of the equation

\(13.5 = d\) . . . . . . divide both sides by 6 to isolate d

3. Substitute d back into our original equation

\(a_n = 40 +13.5(n-1)\)

4. Solve for the third term by substituting 3 for n

\(a_n = 40+13.5(n-1)\\a_3 = 40+13.5(3-1)\\a_3 = 40+13.5(2)\\a_3 = 40 + 27\\\)

∴ \(a_3 = 67\)

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Paula will use 20 oz of sauce and 80 oz of cheese to make 5 pizzas.

We can use the rate of use of pizza sauce and cheese to determine how much of each ingredient Paula will use to make 5 pizzas.

From the information provided, we can see that for every 4 oz of sauce, Paula uses 16 oz of cheese. We can use this ratio to determine the amount of sauce and cheese used for any number of pizzas.

To make 5 pizzas, Paula will use 4 x 5 = 20 oz of sauce and 16 x 5 = 80 oz of cheese.

So, Paula will use 20 oz of sauce and 80 oz of cheese to make 5 pizzas.

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SOLUTION:

Case: Interpreting slopes from linear equations

Method:

V(x) = 20.6 + 2.2x

Compared to

y = mx + b

Where m is the slope and it is being interpreted as the rise for every single run on the line graph.

As it applies,

V(x) = 20.6 + 2.2x

m = 2.2 thousand ie. 2200

It is interpreted as the amount the value increases by each month.

Final answer:

The value of this investment is increasing at a rate of $2200 each month

20 raise the power 7

Step-by-step explanation:

Which clearly means 20 × itself 7 times

Answer:

y= 3x + 1

Step-by-step explanation:solve for y

subtract 3x from the left  which leaves -y= -3x -1

then you have to take flip the signs or divide by -1  so it comes out to y=3x + 1

Answer:

y = 3x + 1

Step-by-step explanation:

Slope Intercept form is written out as the following:

y = mx + b

In order to convert "3x - y = -1", we first subtract 3x from both sides, giving us:

-y = -3x - 1

Since we have "-y", we multiply -1 on both sides.

-1(-y) = -1(-3x - 1)

Multiplying two negatives makes a positive, hence when we multiply -1 on both sides, it becomes this:

y = 3x + 1

So converting to the Slope Intercept form ends up being "y = 3x + 1"

The net force on a vehicle is directly proportional to its acceleration and mass, according to Newton's Second Law of Motion. Therefore, we can use the equation F = ma, where F is the net force, m is the mass of the vehicle, and a is the acceleration.

We know that the net force on the vehicle is 1800 and its acceleration is 1.5. Substituting these values into the equation, we get:
1800 = m × 1.5

To solve for m, we need to isolate it on one side of the equation. Dividing both sides by 1.5, we get:

m = 1800 ÷ 1.5

m = 1200

Therefore, the mass of the vehicle is 1200 kilograms to the nearest kilogram

Net force = mass × acceleration

In this case, the net force on the vehicle is 1800 N (Newtons), and it is accelerating at a rate of 1.5 m/s² (meters per second squared). We can rearrange the formula to solve for mass:

Mass = net force ÷ acceleration

Now, plug in the given values:

Mass = 1800 N ÷ 1.5 m/s²

Mass ≈ 1200 kg

To the nearest kilogram, the mass of the vehicle is approximately 1200 kg.

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There are 720 different choices if order matters and there are 120 different choices if order does not matter.

a) If order matters,

The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).

So the total number of choices is:

10 x 9 x 8 = 720

Therefore, there are 720 different choices if order matters.

b) If order does not matter,

We need to divide the number of choices by the number of ways the three numbers can be arranged.

Since there are 3 numbers, they can be arranged in 3! = 6 ways.

So the number of choices when order does not matter is:

(10 x 9 x 8) / 6 = 120

Therefore, there are 120 different choices if order does not matter.

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The most appropriate choice for permutation and combination will be given by

Number of sequences obtained by drawing three balls = 8000

Number of sequences obtained by drawing four balls = 16000

What is permutation and combination?

When there is a case of ordering, the number of arrangements that can be made in a set is called permutation

When there is no case of ordering, the number of arrangements that can be made in a set is called combination.

Here,

For three balls

Total number of balls = 20

Number of balls drawn = 3

This problem is same as the problem for drawing of r balls from n balls with replacement

So number of choices for first place = 20

Number of choices for second place = 20

Number of choices for third place = 20

Total number of sequences obtained = \(20 \times 20 \times 20\)

                                                              = 8000

For four balls

So number of choices for first place = 20

Number of choices for second place = 20

Number of choices for third place = 20

Number of choices for fourth place = 20

Total number of sequences obtained = \(20 \times 20 \times 20 \times 20\)

                                                              = 16000

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The product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

WHAT IS BOX METHOD ?

The box method, also known as the grid method, is a visual method used to multiply two numbers or two binomials. It involves creating a grid or box and filling it in with the products of the digits in each row and column. The method works for both single-digit and multi-digit numbers.

To use the box method for multiplying two numbers, we draw a box with two rows and two columns. We write one number along the top row and the other number along the left column. Then, we multiply the digits in each row and column and write the products in the corresponding cell of the box. Finally, we add the numbers in each cell of the box to get the product of the two numbers.

The box method can be used to multiply two binomials, such as (4x + 7) and (3x - 8). To use the box method, we draw a box with four cells, and we write the two binomials along the top and left sides of the box, like this:

     |  4x  |  7

-------------------

 3x  |      |

-------------------

    |      |

Then, we fill in the four cells of the box by multiplying the corresponding terms. For example, the top-left cell is filled by multiplying 4x and 3x, which gives 12x². The other cells are filled in a similar way:

     |  4x  |  7

-------------------

 3x  | 12x² | 28x

-------------------

    | -21x | -56

Next, we combine the terms in each row and column of the box, and write the final answer as the sum of these terms:

12x² + 28x - 21x - 56

Simplifying this expression gives:

12x² + 7x - 56

Therefore, the product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

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The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The bn subsequence is defined as the subsequence of the (n)n sequence, whose terms don't have 9 in their decimal notation.

This means that if n has a 9, then bn is not equal to n. Thus, it is a sequence of integers from which all terms that have a 9 are removed. For instance, b1 = 1, b2 = 2, b3 = 3, b4 = 4, b5 = 5, b6 = 6, b7 = 7, b8 = 8, b9 = 10, b10 = 11, b11 = 12, b12 = 13, b13 = 14, b14 = 15,

and so on. Note that b9 = 10 since 9 has a 9 in its decimal notation and is removed. It is necessary to determine whether the following series converge or diverge:∑[infinity]n=1an where an=1bn, and (bn)n is the subsequence of (n)n whose terms do not have a 9 in their decimal notation.

The ratio test can be used to solve the question that we have:∑[infinity]n=1an where an=1bn.

Let's evaluate the limit:lim n→∞ |an+1/an| = lim n→∞ |bn/bn+1|.If the limit is less than 1, then the series converges. Otherwise, it diverges.

There is an inverse relationship between an and bn. That is, as an increases, bn decreases, and vice versa.

Furthermore, if bn = n, then an = 1/n. To demonstrate that the ratio of bn to bn+1 approaches 1, we may construct a lower bound.

To achieve this, we must identify an integer N such that for any n >= N, bn+1 <= bn + 1. If we can accomplish this, we'll see that bn/bn+1 approaches 1 as n approaches infinity. We'll utilize N = 10 in this case. Then we can demonstrate that for all n >= 10, bn+1 <= bn + 1.

Furthermore, we have:lim n→∞ |bn+1/bn| = 1. As a result, the series diverges since the limit equals 1. Therefore, the following series diverges or is infinite.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

The ordered pair (-5, -4) does not satisfy both equations simultaneously, it is not a solution to the system.

To check whether the ordered pair (-5, -4) is a solution of the system of equations:

1) 3x - y = -11

2) 2x - 2y = -3

We substitute x = -5 and y = -4 into both equations and check if the equations hold true.

For equation 1:

3(-5) - (-4) = -11

-15 + 4 = -11

-11 = -11

The equation is satisfied.

For equation 2:

2(-5) - 2(-4) = -3

-10 + 8 = -3

-2 = -3

The equation is not satisfied.

The ordered pair (-5, -4) does not satisfy both equations simultaneously, it is not a solution to the system.

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Answer:

135 degrees

Step-by-step explanation:

Answer:

135. isosceles triangles have two equal sides/angles. <CBD is 135, from adding 70 and 65.

the Answer is 22 if that helpes :)