Hahshxnxjennshsne did. D d d s s d d d

Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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The height of the cliff is approximately 269 feet.

We will be using the tangent function to find the height of the cliff.
Draw a right triangle with the rowboat at one corner, the cliff's base as the adjacent side, and the cliff's height as the opposite side.

The angle of elevation (73.8 degrees) is between the rowboat and the cliff's base.
We are given the adjacent side (75 feet) and we need to find the opposite side (height of the cliff).

To do this, we will use the tangent function:
tan(angle) = opposite side / adjacent side
Plug in the given values:
tan(73.8) = height / 75
Solve for the height:
height = tan(73.8) * 75
Calculate the value:
height ≈ 269.4 feet
Round the height to the nearest foot:
height ≈ 269 feet.

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To find the alternating series error bound, we need to use the formula: |Error| ≤ |Next Term|, The next term in the series is (-1)^4+1 * 1/(4*4) = 1/16.



So the error bound is:

|Error| ≤ 1/16

Now we need to find which of the answer choices is less than or equal to 1/16.

Checking each one:

a. 3/23 > 1/16
b. 5/32 = 0.15625 ≤ 1/16
c. 1/4 > 1/16
d. 3/8 > 1/16

Therefore, the answer is b. 5/32.
Hi! To answer your question, let's first define the terms "partial sum" and "convergent series":

- A partial sum is the sum of a finite number of terms in a sequence or series.
- A convergent series is a series whose sum approaches a finite limit as the number of terms increases.

Now, for the given convergent series ∑n=3 to ∞ (−1)^(n+1) * (2n), we're asked to approximate its value using a partial sum with three terms. This means we need to find the sum from n=3 to n=5:

S_3 = (−1)^4 * (2*3) + (−1)^5 * (2*4) + (−1)^6 * (2*5)
S_3 = 6 - 8 + 10

To find the alternating series error bound, we use the next term in the series, n=6:

Error bound = |a_(n+1)| = |(−1)^7 * (2*6)| = |−12|

Now, let's find the correct answer from the options provided:

a. 3/2
b. 5/32
c. 1/4
d. 3/8

None of these options match our calculated error bound of |-12|. Please double-check the options or provide additional context to clarify the question.

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If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

\(t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}\)

The sum of these times must be equal to the total time of the trip, therefore:

\(t_{stage1} + t_{stage2} = 5\)

\(\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10\)

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

To get rid of a fraction in an equation, you need to multiply both sides of the equation by the reciprocal of the fraction.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To get rid of a fraction in an equation, you need to multiply both sides of the equation by the reciprocal of the fraction.

For example, if you have the equation:

1/3x = 4

To get rid of the fraction 1/3, you can multiply both sides of the equation by its reciprocal, which is 3/1 (or just 3):

(3/1) * (1/3)x = (3/1) * 4

Simplifying, we get:

x = 12

So the solution to the original equation is x = 12.

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Answer: She had left 54% of the money which is $1620.

Step-by-step explanation:

40% of $3000 = $1200

15% of $1200 = $180

$3000 - ($1200 + $180)

$3000 - $1380 = $1620

$1620 is the money she had left.

$1620 is 54% of $3000

She had 54% left of the money.

Hope that helped~!

Answer:

It should be A.

Step-by-step explanation:

rate 1:459.7

rate2:424.2

rate3:433.4

The function that satisfies the differential equation y′ = -2 with initial condition y(0) = -8 is y = -2x - 8.

To solve the differential equation y′ = -2 with initial condition y(0) = -8, we need to find the function y(x) that satisfies both the differential equation and the initial condition.

We can start by integrating both sides of the differential equation with respect to x:

∫y′ dx = ∫(-2) dx

y = -2x + C

where C is a constant of integration.

To find the value of C, we can use the initial condition y(0) = -8:

y(0) = -2(0) + C = C = -8

So the solution to the differential equation with initial condition is:

y = -2x - 8

Therefore, the function that satisfies the differential equation y′ = -2 with initial condition y(0) = -8 is y = -2x - 8.

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x + 54 + 5x = 90°

6x = 90 - 54

6x = 36

x = 36/6 = 6

value for x is 6

Answer:

\(\frac{1}{3^{6}}\)

Step-by-step explanation:

\(\frac{3^{-7}}{3^{-1}} \\\\\frac{1}{3^{-1+7}} \\\\\frac{1}{3^{6}}\)

Hope this helps!

The lengths of line segments are -

NO = √100 = 10 units

OP = √25 = 5 units

PQ = √100 = 10 units

QN = √25 = 5 units

The slopes of the line segment are -

m (NO) = (-6/8) = -3/4

m(OP) = (4/3) = 4/3

m(PQ) = (6/-8) = -3/4

m(QN) = (4/3) = 4/3

The distance (d) and slope (m) can be calculated using the formulas -

(d)² = (x₂ - x₁)² + (y₂ - y₁)²

m = (y₂ - y₁)/(x₂ - x₁)

Given are the coordinates of four points of a Quadrilateral as

follows → N(-8, 3)  O(0, -3)  P(3, 1)  Q(-5, 7).

PART 1 → Finding lengths

In order to calculate the length of each segment, we will use the distance formula given by -

(d)² = (x₂ - x₁)² + (y₂ - y₁)²

The length of line segment NO will be →

(NO)² = (0 + 8)² + (- 6)² = 64 + 36 = 100

NO = √100 = 10 units

The length of line segment OP will be →

(OP)² = (3)² + (4)² = 25

OP = √25 = 5 units

The length of line segment PQ will be →

(PQ)² = (-8)² + (6)² = 64 + 36 = 100

PQ = √100 = 10 units

The length of line segment QN will be →

(QN)² = (-8+5)² + (-4)² = 25

QN = √25 = 5 units

PART 2 → Finding Slopes

The slope can be calculated using the following formula -

m = (y₂ - y₁)/(x₂ - x₁)

The coordinates are → N(-8, 3)  O(0, -3)  P(3, 1)  Q(-5, 7).

The slope of NO will be →

m (NO) = (-6/8) = -3/4

The slope of OP will be →

m(OP) = (4/3) = 4/3

The slope of PQ will be →

m(PQ) = (6/-8) = -3/4

The slope of QN will be →

m(QN) = (4/3) = 4/3

Therefore -

The lengths of line segments are -

NO = √100 = 10 units

OP = √25 = 5 units

PQ = √100 = 10 units

QN = √25 = 5 units

The slopes of the line segment are -

m (NO) = (-6/8) = -3/4

m(OP) = (4/3) = 4/3

m(PQ) = (6/-8) = -3/4

m(QN) = (4/3) = 4/3

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Answer:

AB = 4 BC = 2 AC= 2√5

Step-by-step explanation:

Hope this helps!

Answer:

12

Step-by-step explanation:

24/3 (divide each side by 3)

8/1

8 hats per day

96 hats divided by 8 = 12/1

12 days

The  total distance it flies, rounded to the nearest mile is: d. 1,692 miles .

First distance= 550 miles (given)

Second distance=483 miles (given)

Now let find the third distance

Let x represent the third distance

Hence:

x/sin79 = 550/sin55

x= 659.1

Now let calculate the total distance

Total distance=550+483+659.1

Total distance= 1692.1

Total distance= 1692 miles (rounded)

Therefore the correct option is d.

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Answer:

Yes

Step-by-step explanation:

To check, the squared values of the two smaller lengths must equal the squared value of the biggest length (Pythagorean Theorem)

40² + 75² = 85²

1600 + 5625 = or ≠ 7225

7225 = 7225

It is equivalent so it is correct.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Step-by-step explanation:

\(\tt{ 6(4c-2) }\)

\(\tt{ 24c-12 }\)

Check the picture below.

The solution is, the length of the base is 36 cm.

Here, we have,

given that,

The height and base of a triangle are in the ratio 1 : 3 respectively.

if the area of the triangle is 216cm²,

let, the length of the base is 3x

so, we get, The height = x

now, we know that,

area = 1/2 * base * height

so, we have,

216 = 1/2 * x* 3x

or, 432 = 3x^2

or, x^2 = 144

or, x = 12

Hence, The solution is, the length of the base is 36 cm.

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we have the expression

Group terms

factor (c+1)

Simplify

Answer:

A

Step-by-step explanation:

The measure of the angle is 48 degrees and the triangle BCD is isosceles.

What is a Circle?

A circle is a round-shaped figure with all the points on one plane, the distance between the center and all the points on the circumference is the same.

Thre arc mBC inscribes angle BDC

According to the theorem, the angle made by the arc on the center is double that made at the circumference.

mBDC = (1/2) * mBC

mBDC = (1/2) * 118 = 59°

It is also known from the secant theorem that, the angle made by the two secants is equal to half of the angle inscribing the arc.

mA = (1/2) * (mBC - mDE)

35 = (1/2) * (118 - mDE)

70 = 118 - mDE

The measure of DE = 48°

The sum of all the arcs in a circle is 360°

So,

mBC + mCD + mDE + mBE = 360

mCD = 360 - 118 - 48 - 76 = 118°

The angle CBD is inscribed by the arc mCD

mCBD = (1/2) * mCD = (1/2) * 118 = 59°

The angles CBD and BDC are equal, so the triangle is isosceles.

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Answer:

(C) 496

Step-by-step explanation:

area = 100 yd × 372 yd = 37,200 yd²

37,200 yd² / 75 yd² = 496

Answer: (C) 496

Answer:

16000

Step-by-step explanation:

Simply add the two roughly in your head and round up or down to nearest thousand

The diagonal of the given brick using the Pythagorean Theorem is 5√2.

So, let the diagonal be 'x'.

Pythagorean formula: x² = b² + h²

Now,

Therefore, the diagonal of the given brick using the Pythagorean Theorem is 5√2.

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Answer:(-5/2)^3=-125/8

-5/3^2= -5/9

Step-by-step explanation:

Answer:

A square or cube....

Step-by-step explanation:

Who keep spamming random questions????

To find f−1(a) when f(x) = 3x3 + 4 sin x + 4 cos x, and a = 4, we can solve for x by rearranging the equation.

Start with the equation f(x) = 3x3 + 4 sin x + 4 cos x the isolate the x term by subtracting 4 cos x and 4 sin x from both sides: 3x3 = f(x) - 4 cos x - 4 sin x . Subtract 4 from both sides: 3x3 = f(x) - 4 cos x - 4 sin x - 4
Divide both sides by 3: x3 = (f(x) - 4 cos x - 4 sin x - 4) / 3
Take the cube root of both sides: x = (f(x) - 4 cos x - 4 sin x - 4)1/3 / 31/3

Plug in a = 4 for f(x): x = (4 - 4 cos x - 4 sin x - 4)1/3 / 31/3

Then Solve for x.

We can use the trigonometric identity sin2x + cos2x = 1 to simplify the equation in step 6 to x = (4 - 8 - 4)1/3 / 31/3. Then, after dividing by 31/3, the equation simplifies to x = (-4)1/3.

Therefore, f−1(a) = (−4)1/3 when a = 4 and f(x) = 3x3 + 4 sin x + 4 cos x.

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Answer:

B

Step-by-step explanation:

it's right

Answer:

B. 90

Step-by-step explanation:

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer:

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