You wish to invest $500. You are going to earn 5% simple interest. How much interest will you earn?

The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.

A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.

To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.

B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.

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Answer:

  1 13/20

Step-by-step explanation:

You want the total of distances walked to be the length of the hike:

  2 1/10 + 1 1/4 + (left to walk) = 5

Then the amount left to walk is the difference ...

  left to walk = 5 - 2 1/10 - 1 1/4

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You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.

  5 - 2 1/10 - 1 1/4

  = (5 -2 -1/10) - 1 1/4

  = 2 9/10 - 1 1/4

  = (2 -1) + (9/10 -1/4)

  = 1 + (9/10 -1/4)

  = 1 + (18/20 - 5/20)

  = 1 13/20 . . . miles left to walk

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Using a calculator:

  5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20

The value of x in the equation given is 8

Using the equations given for our Calculation;

Take the L.C.M of 8 and x ; which is 8x

(7x - 8) / 8x = 3/4

Now we cross multiply;

4(7x - 8) = 3 * 8x

open the bracket

28x - 32 = 24x

28x - 24x = 32

4x = 32

x = 8

Hence, the value of x = 8

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Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.

By being congruent, the corresponding angles and sides are equal.

Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].

By using [tex]\angle A = \angle F[/tex]

So, [tex]100^\circ = \angle 1[/tex]

Therefore, the measure of angle 1 is 100 degrees.

So, Option B is the correct answer.

Answer: The Work done to move the object is  [tex]=23.15 \text { foot pounds }[/tex]

Step-by-step explanation:

Given;

Force F=3 [tex]l b s[/tex]

Vectors of F= (3,-1)

Moves object to a distance=9 [tex]f t s[/tex]

Let A and B be the displacements Vectors

A= (0,-5)

B= (6,-2)

To Find:

Work done in foot-pounds

Solution:

Work done [tex]W=F \times D[/tex]

Direction of force vector= (3,-1)  (i, j)  

                                        =3i-j

Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]

                                 [tex]=\sqrt{9+1}[/tex]

Force vector=(Force/Unit Vector)Direction of  force vectors

                   F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]

Direction of motion vector= (B-A)  

                                          = (6,-2)-(0,-5) x i,j)

                                          =(6-0),(-2-5) x (i, j)

                                          =(6,-7) x (i, j)

                                          =6i-7j

Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]

                                   [tex]=\sqrt{36+49}[/tex]

                                   [tex]=\sqrt{85}[/tex]

Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)

                        [tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]

Workdone [tex]W=F \times D[/tex]

                  [tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]

                  [tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j)  \times(6i-7j)][/tex]

                  [tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]

                  [tex]= [0.94867 \times 0.97619] \times [18+7][/tex]

                  [tex]=23.15 \text { foot pounds }[/tex]

Result:

   Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]

Answer:

[tex]W = 25.617\,lbf\cdot ft[/tex]

Step-by-step explanation:

The work done to move the object is:

[tex]W = F \cdot s \cdot \cos \alpha[/tex]

The angle of the force with respect to change in the position vector is:

[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]

[tex]\alpha \approx 18.415^{\textdegree}[/tex]

The magnitude of the work done is:

[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]

[tex]W = 25.617\,lbf\cdot ft[/tex]

Answer:

Nick's car can travel 384 miles using a full tank of gas.

Step-by-step explanation:

Answer:

$800,000 because she will need to save for 20 years times $40,000

Step-by-step explanation:

Silvia wants to retire at 65 and live on $40,000 a year.

She wants to live till 85 and retire at 65 years.

So, number of years to save = [tex]85 -65= 20[/tex]

And she needs to save [tex]40000\times20=800000[/tex]

Hence, she must save 800,000.

Answer:

1.)- B. 5/12

2)- A. 7/9

Step-by-step explanation:

Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.

To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:

C(n, k) = n! / [k! * (n - k)!]

where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.

Applying this to the given problem, we have:

C(7, 5) = 7! / [5! * (7 - 5)!]

This simplifies to:

C(7, 5) = (7 * 6) / (2 * 1)

Therefore, C(7, 5) = 21.

There are 21 different 5-person committees that can be formed from 7 students.