What are three elements to calculate simple interest

Answers

Answer 1
Answer: The three elements to calculate simple interest is principal, interest rate, and time. Good luck!

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A rancher needs to enclose two adjacent rectangular​ corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 390 yd of fencing is​ available, find the largest total area that can be enclosed.

Answers

Width  = 55 yards

Length   =  165 yards

Maximized area   =  9075 sq yd

Step-by-step explanation:

Here, the total length of fencing available  =  390 yd

Let L = length of the side parallel to river

W = width of other 3 sides.

So, total fencing L  +  3 W =  390 yd

or, L  = 390 - 3 W

Now, Area of the field  = L x W

= (390 - 3 w) (W)

or, A  =  -3 W² + 330 W

The maximum value of above function is  at W = ((-b)/(2a) ) = (-330)/(2* (-3))  =  55

So, W = 55 yards

Now, L = (390 - 3 (55) ) =  165 yards

Now, maximized area  = L x W

= 55 x 165  = 9075 sq yds

Which of the following integers is in the solution set of │1 – 3x│ < 5 ?I -1
II 1
III 2

Answers

|1-3x| < 5\n\nx=-1\n\n|1-3\cdot(-1)| < 5\n\n|1+3| < 5\n\n|4| < 5\n\n4 < 5-the\ true


x=1\n\n|1-3\cdot1| < 5\n\n|1-3| < 5\n\n|-2| < 5\n\n2 < 5-the\ true


x=2\n\n|1-3\cdot2| < 5\n\n|1-6| < 5\n\n|-5| < 5\n\n5 < 5-the\ false




|1-3x| < 5\n\n1-3x < 5\ \wedge\ 1-3x > -5\n\n-3x < 5-1\ \wedge\ -3x > -5-1\n\n-3x < 4\ /:(-3)\ \wedge\ -3x > -6\ /:(-3)\n\nx > -(4)/(3)\ \wedge\ x < 2\n\nx\in(-(4)/(3);\ 2)\n\nI\ x=-1\in(-(4)/(3);\ 2)\n\nII\ x=1\in(-(4)/(3);\ 2)\n\nIII\ x=2\notin(-(4)/(3);\ 2)

Arthur baked 1 7/12 dozen muffins. Nina baked 1 1/12 dozen muffins. How many dozen muffins did they bake?

Answers

Answer:

Total number of dozen muffins they both bake is 2(8)/(12)    

Step-by-step explanation:

Given : Arthur baked 1(7)/(12) dozen muffins. Nina baked 1(1)/(12) dozen muffins.

We have to find the total number of dozen muffins did they both bake.

To find the total number of dozen muffins did they both bake is equal to number of dozen of muffins Arthur bake and  number of dozen of muffins Nina bake

That is

Mathematically written as ,

Total number of dozen muffins = number of dozen of muffins Arthur bake + number of dozen of muffins Nina bake

Given : Arthur baked 1(7)/(12) dozen muffins

and Nina baked 1(1)/(12) dozen muffins.

Total number of dozen muffins = 1(7)/(12)+1(1)/(12)  

Simplify, we get,

Total number of dozen muffins = 1(19)/(12)+(13)/(12)  

Adding, we get,

Total number of dozen muffins = 1(19+13)/(12)=(32)/(12)  

Thus, Total number of dozen muffins they both bake is 2(8)/(12)    

they baked 2 dozen because each dozen is 12  so one did 17 + another did 11 = 28 and divide it by 12 get. 2 dozens.

The graph of y=4x-11 is translated up 8 units. Which equation represents the translated graph?

Answers

It would be y=4x-3 because -11 show that it went down 11 units. So if it is going to go up 8 units, -11+8 is -3.

Add 1/6+3/4+2/3. Simplify the answer and write it as a mixed number, if possible. A)
1 14/24


B)
1/2


C)
19/12


D)
1 7/12

Answers

To simplify the answer and write it as a mixed number is D)1 7/12

How to Add 1/6+3/4+2/3.

To add the fractions 1/6, 3/4, and 2/3, we need to find a common denominator.

The common denominator for 6, 4, and 3 is 12.

Converting the fractions to have a denominator of 12:

1/6 = 2/12

3/4 = 9/12

2/3 = 8/12

Now we can add the fractions:

2/12 + 9/12 + 8/12 = 19/12

The sum of the fractions is 19/12.

To simplify the answer and write it as a mixed number, we divide the numerator (19) by the denominator (12):

19 ÷ 12 = 1 remainder 7

Therefore, the answer is 1 7/12.

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Find the lowest common denominator for the 3 fractions. It is 12.
Rewrite each fraction with the denominator 12.
1/6 = 2/12
3/4 = 9/12
2/3 = 8/12
2/12 + 9/12 + 8/12 = 19/12
This can be written as the mixed number 1 7/12.
The answer is D) 1 7/12

. For vectors B⃗ =−iˆ−4jˆB→=−i^−4j^ and A⃗ =−3iˆ−2jˆA→=−3i^−2j^ , calculate (a) A⃗ +B⃗ A→+B→ and its magnitude and direction angle, and (b) A⃗ −B⃗ A→−B→ and its magnitude and direction angle.

Answers

(a) A + B: The result is -4i - 6j, with a magnitude of 2√13 and a direction angle of arctan(3/2).

(b) A - B: The result is -2i + 6j, with a magnitude of 2√10 and a direction angle of arctan(-3).

The given vectors are:

B = -i - 4j

A = -3i - 2j

(a) A + B:

To add two vectors,

Simply add their corresponding components.

So, A + B = (-3i - 2j) + (-i - 4j)

Combining the i-components, we get:

-3i - i = -4i.

And combining the j-components, we get:

-2j - 4j = -6j.

Therefore, A + B = -4i - 6j.

To find the magnitude of A + B,

Use the Pythagorean theorem:

|A + B| = √((x^2 + y^2)),

Where x is the magnitude of the i-component and y is the magnitude of the j-component.

In this case,

x = -4 and y = -6,

So: |A + B| = √((-4)^2 + (-6)^2)

|A + B| = 2√13

To find the direction angle of A + B,

Use the arctan function:

θ = arctan(y / x),

Where y is the j-component and x is the i-component.

In this case,

x = -4 and y = -6,

so: θ = arctan(-6 / -4)

θ = arctan(3/2)

Therefore, the magnitude of A + B is 2√13 and the direction angle is arctan(3/2).

(b) A - B:

To subtract two vectors,

Subtract their corresponding components.

So, A - B = (-3i - 2j) - (-i - 4j).

Combining the i-components, we get:

-3i + i = -2i.

And combining the j-components, we get:

-2j - (-4j) = 2j + 4j = 6j.

Therefore, A - B = -2i + 6j.

To find the magnitude of A - B,

Use the Pythagorean theorem:

|A - B| = √((x^2 + y^2)),

Where x is the magnitude of the i-component and y is the magnitude of the j-component.

In this case,

x = -2 and y = 6,

so: |A - B| = √((-2)^2 + 6^2)

|A - B| = 2√10

To find the direction angle of A - B,

Use the arctan function:

θ = arctan(y / x),

Where y is the j-component and x is the i-component.

In this case, x = -2 and y = 6,

so:

θ = arctan(6 / -2)

θ = arctan(-3)

Therefore,

The magnitude of A - B is 2√10 and the direction angle is arctan(-3).

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The complete question is:

For vectors B =−i −4j  and A =−3i −2j ,

Calculate (a) A + B and its magnitude and direction angle, and (b) A − B and its magnitude and direction angle.

The resulting vectors after adding and subtracting vectors A and B are A + B = -4i - 6j with a magnitude of 7.21 and A - B = -2i + 2j with a magnitude of 2.83. The direction angle for the vectors are calculated using arctan of the absolute value of the components' ratios.

For vectors B = -i - 4j and A = -3i - 2j, you first need to add and subtract these vectors component-wise to get the resulting vectors. Addition gives A + B = -i + (-3i) + -4j + (-2j) = -4i - 6j, whereas subtraction gives A - B = -3i - (-i) + -2j - (-4j) = -2i + 2j.

The magnitude of a vector is calculated by the Pythagorean theorem: (magnitude of A+B) = sqrt((-4)^2 + (-6)^2) = 7.21 and (magnitude of A-B) = sqrt((-2)^2 + 2^2) = 2.83.

The direction angle is found using arctan(|Ay / Ax|), but adjustment must be made depending on the quadrant of the resulting vector. In conclusion, (a) A + B = -4i - 6j, |A + B| = 7.21, angle = arctan(6/4), and (b) A - B = -2i + 2j, |A - B|= 2.83, angle = arctan(2/2).

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