MATHEMATICS HIGH SCHOOL

Sheba opened a retirement account with $36,500. Her account grewat a rate of 7% per year compounded annually. She made no deposits
or withdrawals on the account. At the end of 20 years, what was the
account worth, to the nearest dollar?
(1) $87,600 (3) $141,243
(2) $130,786 (4) $1,483,444,463

Answers

Answer 1
Answer: After 20 years, the account is worth 3) $141,243 rounded to the nearest dollar.

7% interest rate compounded annually means that the interest earned also earns an interest  with the rate of 7%. Thus, the principal is multiplied with 1.07 or 107%.

Y1        36,500.00                         1.07      39,055.00     
Y2        39,055.00                        1.07      41,788.85     
Y3        41,788.85                        1.07      44,714.07     
Y4        44,714.07                        1.07      47,844.05     
Y5        47,844.05                        1.07      51,193.14     
Y6        51,193.14                        1.07      54,776.66     
Y7        54,776.66                        1.07      58,611.02     
Y8        58,611.02                        1.07      62,713.80     
Y9        62,713.80                        1.07      67,103.76     
Y10      67,103.76                        1.07      71,801.02     
Y11      71,801.02                        1.07      76,827.10     
Y12      76,827.10                        1.07      82,204.99     
Y13      82,204.99                        1.07      87,959.34     
Y14      87,959.34                        1.07      94,116.50     
Y15      94,116.50                        1.07    100,704.65   
Y16    100,704.65                        1.07    107,753.98   
Y17    107,753.98                        1.07    115,296.76   
Y18    115,296.76                        1.07    123,367.53   
Y19    123,367.53                        1.07    132,003.26   
Y20    132,003.26                        1.07    141,243.48

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The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). What are the values of j and k?

A company has three operational departments namely weaving, processing and packing with capacity to produce three different types of clothes namely suiting’s, shirting’s and woolens yielding a profit of rupees 2 ,4and 3 per meter respectively.1 meter of suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly 1 meter of shirting requires 4 minutes in weaving ,1 minute in processing and 3 minutes in packing.1 meter of woolen requires 3 minutes in each department .In a week total run time of each department is 60,40 and 80 hours for weaving, processing and packing respectively. Formulate this as LPP and find the solution.

Answers

Answer: Scroll down for solution

Step-by-step explanation: To formulate this problem as a Linear Programming Problem (LPP), we need to define the decision variables, objective function, and constraints.

1. Decision Variables:

Let's denote the number of meters of suiting, shirting, and woolen produced as:

- x1: Number of meters of suiting produced

- x2: Number of meters of shirting produced

- x3: Number of meters of woolen produced

2. Objective Function:

The objective is to maximize the profit, which can be calculated as follows:

Profit = 2x1 + 4x2 + 3x3

3. Constraints:

a) Weaving Department:

The total run time available for weaving is 60 hours per week. The time required to produce 1 meter of suiting, shirting, and woolen in the weaving department is given as 3 minutes, 4 minutes, and 3 minutes, respectively. Since there are 60 minutes in an hour, the constraint for the weaving department can be expressed as:

3x1 + 4x2 + 3x3 ≤ 60

b) Processing Department:

The total run time available for processing is 40 hours per week. The time required to produce 1 meter of suiting, shirting, and woolen in the processing department is given as 2 minutes, 1 minute, and 3 minutes, respectively. The constraint for the processing department can be expressed as:

2x1 + 1x2 + 3x3 ≤ 40

c) Packing Department:

The total run time available for packing is 80 hours per week. The time required to produce 1 meter of suiting, shirting, and woolen in the packing department is given as 1 minute, 3 minutes, and 3 minutes, respectively. The constraint for the packing department can be expressed as:

1x1 + 3x2 + 3x3 ≤ 80

d) Non-negativity constraint:

The number of meters produced cannot be negative, so we have the constraint:

x1, x2, x3 ≥ 0

Now, we have the LPP formulated with the decision variables, objective function, and constraints. To find the solution, we can use a method such as the Simplex method or graphical method to optimize the objective function while satisfying the constraints.

For which equation is x=-1/3 not a solutionA. 7+9x=4
B. 6x-5=7
C. 18+9/x=-9
D. 12x+8=4

Answers

The answer is B.

A. 7+9(-1/3)=4
B. 6(-1/3)-5= (-7)
C. 18+9/(-1/3)= (-9)
D. 12(-1/3)+8=4

Hope this helps

Line m passes through the points (3, 7) and (6, 12) while line n passes through the points (-5, 1) and (-2, 6).Which statement accurately describes the relationship between the two lines?

A. Lines m and n have the same slope so they are parallel.
B. Lines m and n have the same slope so they are perpendicular.
C. Lines m and n have opposite reciprocal slopes so they are perpendicular.
D. Lines m and n have opposite reciprocal slopes so they are parallel.

Answers

HENCE STATEMENT A IS CORRECT.

WHAT IS RELATIONSHIP ?

Finding if and statement given match to asked or not.

How to solve?

A. Lines m and n have the same slope so they are parallel.- true

B. Lines m and n have the same slope so they are perpendicular.- false

C. Lines m and n have opposite reciprocal slopes so they are perpendicular.- false

D. Lines m and n have opposite reciprocal slopes so they are parallel.- false

Learn more about numbers brainly.com/question/25734188

#SPJ2

Answer:

A. Lines m and n have the same slope so they are parallel.

Step-by-step explanation:

I am confused on numbers 25 and 29, the instructions are at the top.

Answers

#25 is fairly simple.  Plug in -4 and 3 into the equation, and the extraneous root will be the one that does not work.
√(12-(-4)) = √(16) = \frac{+}{}4
Extraneous root in this case is positive four since +4≠-4
√(12-3) = √(9) = \frac{+}{}3
In this case it's negative 3, since -3≠3

#29 can be turned into a quadratic equation.
x= √(2x+3)
Square both sides to get
x^(2)=2x+3
Then bring the 2x+3 to the other side, setting the quadratic equal to zero.
x^(2)-2x-3=0
Factor to find that it's equivalent to
(x-3)(x+1)=0
Therefore x is equal to positive 3 and negative 1.  Plug both back into the original equation.  Whichever does not work is the extraneous root, and the answer is the one that does.
x= √(2x+3)
3= √(2(3)+3)
3= √(9)
Extraneous root would be negative 3.

-1= √(2(-1)+3)
-1= √(1)
Extraneous root would be positive 1.

Your answers are positive 3 and negative 1.
Extraneous roots are negative 3 and positive 1.

Suppose a triangle has sides 3, 4, and 6. Which of the following must be true? A. The triangle in question is a right triangle. B. The triangle in question is not a right triangle. C. The triangle in question may or may not be a right triangle.

Answers

We can use the Pythagorean theorem:
c² = a² + b²
In this case:
6² = 3² + 4²
36 = 9 + 16
36 = 25  ( not correct )
This is not a right triangle.
Answer:
B ) The triangle in questionis not a right triangle.

Answer:

not a right triangle

Step-by-step explanation:

I am a little confused: One method you can use to determine whether a triangle is a right triangle, given three side lengths, is to apply the converse of the Pythagorean Theorem. Alternately, you can use trigonometric ratios. Show that the triangle in the diagram is a right triangle by using trigonometric ratios. ( Be sure to show all work/and or reasoning.

Answers

Answer with explanation:

The triangle in the Diagram Described has following measurement:

 Longest Side = 65 units

One side which can be either Perpendicular or base = 63 units

And , other side which can be also, either Perpendicular or base = 16 units

We can prove that the triangle described is right triangle by two ways.

1. Using Converse of Pythagorean Theorem

Square of Longest side = Sum of Squares of other two sides-----(1)

So, Square of Longest Side =  65²=4225

Sum of Square of other two sides = 16² + 63²

                                        = 256 + 3969

                                        =  4225

Statement (1), is valid.

So,Triangle is right angled triangle, right angled at A.

2. using Trigonometric Ratios

Suppose the triangle is right Angled at A.

In Right triangle B AC

tan B=\frac{\text{Perpendicular}}{\text{Base}}\n\ntan B=(16)/(63)\n\ntan C=(63)/(16)\n\n tan(B +C)=(tan B + tan C)/(1-tan B * tanC)\n\ntan (B +C)=((16)/(63)+(63)/(16))/(1-(16)/(63)* (63)/(16))\n\ntan (B +C)=\frac{\text{Any rational number}}{0}\n\ntan (B +C)=\infty\n\nB +C=90^(\circ)\n\n \text{Using the trigonometric Identity},tan(A+B)=(tan A +tan B)/(1-tan A*tan B)

B +C =90°

Also,→ ∠A + ∠B + ∠C=180°≡ (Angle sum property of triangle)

→∠A +90°=180°

→∠A=180° -90°

→∠A=90°

So, triangle is right Angled triangle , Right angled at A.

Hence ,proved.
Trigonometric ratios are sine, cosine, and tangent (opposite side over hypotenuse, adjacent side over hypotenuse, and opposite side over adjacent side, respectively); if you wanted to prove that one of the angles of the triangle is 90º, then the cosine of that angle would be 0, the sine would be 1, and the tangent would be undefined. 
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