How much simple interest is earned on $1,272 deposited in a bank for  20 years at 3% annual interest rate?

Answer:

Step-by-step explanation:

as an educated guess i would choose the third choice for the second question

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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The amount of tax that Derek paid on his car is given as follows:

$749.85.

The amount of tax is obtained applying the proportions in the context of this problem.

The total cost is of $4999, with a GST tax rate of 15%, hence the amount of tax paid is obtained multiplying the total cost of $4999 by the equivalent decimal of the percentage, which is of 15/100 = 0.15, hence:

0.15 x 4999 = $749.85.

Meaning that $749.85 is the amount of GST that was included in the purchase of the car.

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Answer:

No, because not all corresponding angles are congruent.

Step-by-step explanation:

In order for two triangles to be similar you must have that you know at least 2 corresponding angles are congruent which would also imply the third set of angles are also congruent. You can also tell if two triangles are similar based on their corresponding sides being proportional. Without even checking the proportionally part of corresponding sides, I see the 3 angles in the first triangle do not have the same measurement as the one in the second triangle. Therefore, the triangles cannot possibly by similar.

Hope this helped you love.

the answer is two :D

Answer:

4/8= 2/4=1/2= 50%

Step-by-step explanation:

4 out of the 8 new cars have a fuel efficiency of less than 27 mpg. that is is 50%

Answer:2

Step-by-step explanation:

goggle

Answer:

5 divided by 2 = 2.5

Step-by-step explanation:

Answer:

if I'm correct it would be 200

Step-by-step explanation:

0.20 x 200 = 40

Answer:

Step-by-step explanation:

20% off means the 20% was taken away from the original price which will have us remaining with 80%

80% = 40

100% (original price) = 100% x 40

                                           80%

=$ 50.00

Answer:

$15

Step-by-step explanation:

Answer

Use division, how many times will 14 go into 210?

210÷14=15

$15

Or you can also multiply 15x14=210

Answer:

\(\boxed{AC = 2.3}\)

Step-by-step explanation:

AD = BD  (CD bisects AB means that it divides the line into two equal parts)

So,

AD = BD = AB/2

So,

AD = 3/2

AD = 1.5

Now, Finding AC using Pythagorean Theorem:

\(c^2 = a^2+b^2\)

Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)

\(AC^2= (1.5)^2+(\sqrt{3} )^2\)

\(AC^2 = 2.25 + 3\)

\(AC^2 = 5.25\)

Taking sqrt on both sides

\(AC = 2.3\)

Answer:

\(\boxed{2.29}\)

Step-by-step explanation:

The length of AB is 3 units.

The length of CD is \(\sqrt{3}\) units.

D is the mid-point of points A and B.

AD is half of AB.

\(\frac{3}{2} =1.5\)

Apply Pythagorean theorem to solve for length of AC.

\(c=\sqrt{a^2 +b^2 }\)

The hypotenuse is length AC.

\(c=\sqrt{1.5^2 +(\sqrt{3}) ^2 }\)

\(c=\sqrt{2.25+3 }\)

\(c=\sqrt{5.25}\)

\(c= 2.291288...\)

Step-by-step explanation:

The primary goal of a debate is for students to generate effective critical thinking into primary issues in the given topic.

Answer:

20

Step-by-step explanation:

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

J

Step-by-step explanation:

If you look closely, you can see the slope line is decreasing which means all the positive slopes are automatically wrong, and second the first point the line intersects with the graph is 6 down which means the answer is -6

Answer: The final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Explanation: We have to use contour integration to evaluate the integral cos20 -do, [. a²+6²-2abcose where b> a > 0.

Let \(f(z) = cos(20 - z) / [a² + b² - 2abcos(z - 6)] .\)

The denominator in the integral looks like\(cos(z - 6) = Re(e^(i(z-6)) ).\)

Therefore, we have \(cos(20 - z) = Re(e^(i(20 - z)))\)

Thus, we can write the integral as follows: `I = ∮ |z|=1 f(z) dz `

By Cauchy's Residue Theorem, the integral of f(z) over any closed curve in the complex plane is equal to `2πi` times the sum of residues of f(z) at its poles within the curve.

If we use the parametrization \(`z = 6 + b/a + re^(it)`\) with `0 <= t <= 2π`, then the integral becomes:

\(`I = -i ∫ 0^{2π} dt (a² + b² - 2abcos(t) ) / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`\)

This integral can be computed using the residue theorem. If we define

\(`g(z) = 1 / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`,\)

then the residue of g(z) at `z = 6 + b/a + i(asin((r/a)sin(t-θ))` is given by:

\(`Res(g, z) = lim_{z->6+b/a+i(asin((r/a)sin(t-θ)))} (z - (6 + b/a + i(asin((r/a)sin(t-θ))))) g(z) / [a² + b² - 2abcos(t)]`\)

We can compute this residue using L'Hopital's Rule.

After some algebraic manipulation, we can show that the residue is:\(`Res(g, z) = -1 / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Hence, by the residue theorem, we have: \(`I = -2πi / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Therefore, the final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

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Answer:

Step-by-step explanation:

4x + 1 + 9x -3 = 180

13x + 1 - 3 = 180

13x -2 = 180

13x = 180 + 2

13x = 182

x = 182 : 13

x = 14

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

check

4 × 14 + 1 + 9 × 14 - 3 = 180              (remember PEMDAS)

56 + 1 + 126 - 3 = 180

180 = 180

the answer is good

From the given coordinate points the quadrilateral formed is square.

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

The given coordinates are Q(4, 5), U(12, 14), A(20, 5), D(12, -4).

Using distance formula Distance = √[(x₂-x₁)²+(y₂-y₁)²].

Here,

QU= √[(12-4)²+(14-5)²]

= √8²+9²

= √145

= 12.04 units

UA= √[(20-12)²+(5-14)²]

= √8²+(-9)²

= 12.04 units

AD= √[(12-20)²+(-4-9)²]

= √(-8)²+(-9)²

= 12.04 units

DQ= √[(12-4)²+(-4-5)²]

= √8²+(-9)²

= 12.04 units

All the sides are equal.

Using slope formula,

Slope of QU

(14-5)/(12-4)

= 9/8

Slope of UA

= (5-14)/(20-12)

= -9/8

Slope of AD

= (-4-5)/(12-20)

= 9/8

Slope of DQ

= (-4-5)/(12-4)

= -9/8

Slope of sides are perpendicular

Therefore, from the given coordinate points the quadrilateral formed is square.

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The value of x in the equation \(\frac{x}{2} = \frac{x^2}{x - 2}\) are x = 0 and x = -2

The expression is given as:

\(\frac{x}{2} = \frac{x^2}{x - 2}\)

Cross multiply

\(x(x - 2) =2 * x^2\)

Open the bracket

\(x^2 - 2x =2x^2\)

Collect like terms

\(- 2x =2x^2 - x^2\)

Evaluate the like terms

\(- 2x =x^2\)

Rewrite as:

\(x^2 + 2x =0\)

Factor out x

x(x + 2)  =0

Expand

x = 0 or x + 2 = 0

Solve for x

x = 0 or x = -2

Hence, the value of x are x = 0 and x = -2

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Answer:

  c = 0

Step-by-step explanation:

You want the value of c such that point (c, 4) is on the line with slope 1 through point (-7, -3).

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

The line with slope 1 through point (-7, -3) has equation ...

  y +3 = 1(x +7)

  y = x +4 . . . . . . . subtract 3 and simplify

The value of x when y=4 can be found using this equation.

  4 = x +4

  0 = x . . . . . . . subtract 4

The value of c is 0.

Sequence of P1, P2, and P3 are 6 8 6

Needs matrix = Claim matrix - Allocation matrix

R1 R2 R3 R1 R2 R3

P1 0 1 2 P1 -1 -1 1

P2 2 0 0 P2 2 2 0

P3 0 0 2 P3 0 0 -2

Resource vector = Sum of Allocation matrix - Available vector

R1 R2 R3

6 7 5

Available vector = Resource vector - Sum of Allocation matrix

R1 R2 R3

3 4 2

According to the Banker's algorithm

Then, the available vector becomes:

R1 R2 R3

4 5 3

P2's needs satisfied Hence, P2 selected for execution.

R1 R2 R3

6 8 4

P3's needs satisfied. Hence, P3 selected for execution.

R1 R2 R3

6 8 6

So, we have a safe sequence of P1, P2, and P3.

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a. Using the calculated z-score, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

b. The appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

(a) To find the probability that a randomly chosen bolt has a width between 941 and 957 mm, we can use the z-score formula and the standard normal distribution.

First, let's calculate the z-scores for the given values using the formula:

z = (x - μ) / σ

where:

For x = 941:

z₁ = (941 - 952) / 10 = -1.1

For x = 957:

z₂ = (957 - 952) / 10 = 0.5

Next, we need to find the probabilities corresponding to these z-scores using a standard normal distribution table or a calculator.

Using the standard normal distribution table, we find:

P(z < -1.1) ≈ 0.135

P(z < 0.5) ≈ 0.691

Since we want the probability of the width falling between 941 and 957, we subtract the two probabilities:

P(941 < x < 957) = P(-1.1 < z < 0.5) = P(z < 0.5) - P(z < -1.1) ≈ 0.691 - 0.135 = 0.5558

Therefore, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

(b) To find the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749, we need to find the z-score corresponding to this probability.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a cumulative probability of 0.8749 is approximately 1.15.

Now, we can use the z-score formula to find the value of C:

z = (x - μ) / σ

Substituting the known values:

1.15 = (C - 952) / 10

Solving for C:

C - 952 = 1.15 * 10

C - 952 = 11.5

C ≈ 963.5

Therefore, the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

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Answer:

112 square inches

Step-by-step explanation:

Area of a triangle is B*h/2

14 x 16 = 224

224/2 = 112

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

\(36-\frac{a}{4}\)

To set up an integral that represents the length of a curve over the interval 5 ≤ t ≤ 9, we need the parametric equations of the curve.

Let's assume the curve is described by the equations x = f(t) and y = g(t), where f(t) and g(t) represent the x-coordinate and y-coordinate of the curve, respectively.

The length of the curve can be approximated by breaking it into small line segments and summing their lengths. As the line segments become infinitely small, the approximation approaches the exact length of the curve.

The length of a small line segment between two points (x₁, y₁) and (x₂, y₂) can be calculated using the distance formula:

\(d = √[(x₂ - x₁)² + (y₂ - y₁)²]\)

We can apply this formula to each successive pair of points on the curve to calculate the length of each line segment. The integral that represents the length of the curve is then obtained by summing these lengths over the interval of interest.

Mathematically, the length of the curve over the interval 5 ≤ t ≤ 9 can be represented by the integral:

L = ∫[5 to 9] √[(dx/dt)² + (dy/dt)²] dt

Where dx/dt and dy/dt represent the derivatives of x and y with respect to t, respectively.

It's important to note that the specific form of the parametric equations f(t) and g(t) would be required to evaluate this integral.

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Answer:

£8400

Step-by-step explanation:

Answer:

-12.6

Step-by-step explanation:

its decreasing that eliminates 3 and 4

and the decrease is bigger than 1.6 so that eliminates 2

making the obvious answer number 1

Answer:

a

Step-by-step explanation:

Answer:

\(18.03\)

Step-by-step explanation:

Formula: \(a^{2}+b^{2}=c^{2}\)

\(15^{2}+10^{2}=x^{2}\)

\(225+100=x^{2}\)

\(x^{2}=325\)

\(x = 5\sqrt{13}=18.03\)