\(solve : - \\ \\ (19 {}^{2} + 21 {}^{2} ) = {?}\)
​

This expression gives us a present value of approximately $1,376,500.

To calculate the present value of John Doe's winnings, we need to find the present value of each individual payment and then sum them up.

The formula to calculate the present value of an annuity is:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the annual payment, r is the discount rate, and n is the number of periods.

In this case, John Doe will receive $100,000 each year for 30 years, and the discount rate is 6%. Plugging these values into the formula, we get:

PV = $100,000 * (1 - (1 + 0.06)^(-30)) / 0.06

Calculating this expression gives us a present value of approximately $1,376,500.

Therefore, the correct answer is:

c. $1,376,500.

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The height of 70 inches, and location of the wristband as well as the period of 15 seconds gives the function for the height of the wristband as the equation;

The model for the height can be derived from the general form of the sine function as follows;

Maximum point = 70 - 4 = 66 at t = 0

Minimum point = 4

Amplitude, A = (66 - 4) ÷ 2 = 31

D = 4 + 31 = 35

At t = 0, we have;

66 = 31 × sin(B × 0 - C) + 35

31 = 31 × sin(- C)

sin(- C) = 1

C = -π/2

1 minute = 60 seconds

1 second= 1 minute/60

15 seconds = (15/60) minutes

Period = 15 seconds = 15/60 minutes

Period = 2•π/B

Therefore;

15/60 = 2•π/B

1/4 = 2•π/B

B = 2•π/(1/4) = 8•π

y = Height of the function

Let h represent the height of the wristband.

The equation for the height is therefore;

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Answer:45

Step-by-step explanation:

Sin^-1= 5÷7

Answer:

Step-by-step explanation:

Thde y-intercept is the value oy y when x = 0.  The data table tells us the value of y when x=0 is 4.  The ordered pair is (0,4)

The value of ∠GFH=59°, in the given question.

What do you mean by angle?

Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet.

According to the data in the given question,

We have :

∠EFH=127°

∠EFG=(8x-4)°

∠GFH=(5x+14)°

Now, we have to solve the value of ∠GFH,

∠EFG+∠GFH=∠EFH

Putting the values given and solve for x,

(8x-4)°+(5x+14)°=127°

8x°-4°+5x°+14°=127°

13x°+10°=127°

13x°=127°-10°

13x°=117°

x=9

Then, putting the value of x in ∠GFH,

∠GFH=(5x+14)°

=(5(9)+14)°

=(45+14)°

=59°

Therefore, the value of ∠GFH=59°.

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The volume of the object is 48 cubic millimeters (mm³).

A volume question's response is displayed in cubic units. Volume is calculated as follows: volume = length x breadth x height.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. The area included within a three-dimensional object's limits is referred to as its volume.  It is referred to as the object's capability on occasion.

To calculate the volume, you need to multiply the length, width, and height of the object. Assuming the measurements you provided represent the length, width, and height respectively, the volume would be:

Volume = Length × Width × Height

= 4mm, 4mm, and 3mm

= 48 mm³

Therefore, the volume of the object is 48 cubic millimeters (mm³).

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Answer: \(\cos^2 \theta+\sin^2 \theta=1\)

Step-by-step explanation:

This is the Pythagorean identity.

Answer:

If you want a to be greater than 2b, then take any number in the range of real numbers that is greater than 2 times. For example, a=4, 2b=1; a=5, 2b=4.

Step-by-step explanation:

Answer:

v =  sqrt(473)

Step-by-step explanation:

v^2 = u^2 +2as

Let u = 9 a = 7 and s = 28

v^2 = 9^2 +2(7)(28)

v^2 = 81 + 392

v^2 = 473

Take the square root of each side

sqrt(v^2) = sqrt(473)

v =  sqrt(473)

Answer:

<B = 32°

c = 9.43

Step-by-step explanation:

To find the measure of <B, add up the measures of the two angles that you know and subtract from 180°.

58° + 90° = 148°

180° - 148° = 32°

The measure of <B is 32°.

To find the length of side c, use the Pythagorean Theorem.

a² + b² = c²

5² + 8² = c²

25 + 64 = c²

89 = c²

c = √89

c = 9.433981132 ⇒ 9.43 (rounded to two decimal places)

The length of side c = 9.43.

Hope that helps.

Answer:

It's bubbled in so it's C.

Step-by-step explanation:

Why did u ask something that was answered?

Thanks for your time.

(>.<) <3 Kris

The number of ways to select 12 countries from different blocks is 11,415, based on the multiplication principle of counting.

There are 3 ways to select 3 countries from the block of 45. There are 35 ways to select 4 countries from the block of 57. The other 5 countries will come from the remaining block of 91. We are to determine the number of ways 12 countries can be selected to serve on a united nations council if 3 are selected from a block of 45, 4 are from a block of 57, and the others from the remaining 91 countries. Let us apply the Multiplication Principle of Counting to determine the total number of ways:

Multiplication Principle of Counting: The multiplication principle of counting is a counting principle used to determine the total number of possible outcomes of a sequence of events that occur in a particular order.

Suppose an experiment consists of two events E1 and E2 with n1 and n2 possible outcomes respectively. Then the total number of possible outcomes for the two events is given by n1 x n2. Likewise, if an experiment consists of k events, E1, E2, . . . , Ek, with n1, n2, . . . , nk possible outcomes respectively, then the total number of possible outcomes for the k events is given by n1 x n2 x ... x nk.

There are 3 ways to select 3 countries from a block of 45.

There are 35 ways to select 4 countries from a block of 57.

There are 91 ways to select 5 countries from a block of 91.

The total number of ways 12 countries can be selected to serve on a united nations council is given by;

3 ways × 35 ways × 91 ways= 11,415 ways.

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Answer:

Well, 1 is 3.8 The second one is 40,

Step-by-step explanation:

I believe 1 is 3.8, b/c 1.9*2 is 3.8, and the difference between exponents makes 3 zeros, so 2000.

The second one is 40, I confirmed this by doing .0001 to replicate 10 to the negative 4th power

By doing 9.5*.0001*40, I got the 0.038 from 1

Answer:

3.8 × 10-3 is 2,000 times greater than 1.9 × 10-6. It is also 4 times greater than 9.5 x 10-4.

Step-by-step explanation:

I started by doing 0.0000019 x 2000 and got 0.0038. If you move the decimal point 4 over you get 3.8.

EVERYONE ELSE IS WRONG!!! I got this correct on the test after retaking it, the second one is NOT 40 it is 4.

Answer:

15a

Step-by-step explanation:

5a + 10a = 15a

Option (A) :  least: 10 hours; greatest: 14 hours

The function f(x) = sin x has all real numbers in its domain, but its range is

−1 ≤ sin x ≤ 1.

How to solve such range questions?

Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question

Given: d(t) = 2sin(xt) + 12

=  −1 ≤ sin (xt) ≤ 1.

=  −2≤ 2 sin (xt) ≤ 2.

=  10 ≤ 2sin (xt) + 12 ≤ 14

=   10 ≤d(t) ≤ 14

Thus  least: 10 hours; greatest: 14 hours

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The standard deviation of the sample proportion in this situation is approximately 0.0414.

To find the standard deviation of the sample proportion, we need to use the formula:

Standard deviation of sample proportion (σp) = √[(p × (1 - p)) / n]

Where:

p = population proportion (percentage of customers with state minimums for insurance) = 78% = 0.78

n = sample size = 100

Substituting the values into the formula, we have:

σp = √[(0.78 × (1 - 0.78)) / 100]

Calculating the expression within the square root:

σp = √[(0.78 × 0.22) / 100]

= √[0.1716 / 100]

= √0.001716

≈ 0.0414

Therefore, the standard deviation of the sample proportion in this situation is approximately 0.0414.

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Answer:

Step-by-step explanation:

answer is 5

Answer:

x=9

Step-by-step explanation:

both sides are 14 and the other triangle is 7 so 14/7=2 and 18/2=9

Answer:

The angle measures are

x + (x + 30) + 2x = 180

x = 37.5

Step-by-step explanation:

x + (x + 30) + 2x = 180.  (combine x and 2x)

3x + (x + 30) = 180.  (combine 3x and x, 30 cant combine)

4x + 30 = 180.  (subtract 30 from both)

4x = 150.  (divide both sides by 4)

x = 37.5

Hence, the length of the curve defined by the parametric equations x = 4sin^2(t) and y = 4cos^2(t) over the interval 0 ≤ t ≤ 5π is 20π units.

To find the distance traveled by the particle, we need to calculate the length of the curve defined by the parametric equations x = 4sin^2(t) and y = 4cos^2(t) over the given time interval 0 ≤ t ≤ 5π.

We can use the arc length formula to calculate the length of the curve. The arc length formula for a parametric curve defined by x = f(t) and y = g(t) is given by:

L = ∫[a, b] √[f'(t)^2 + g'(t)^2] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t) with respect to t.

Let's start by finding the derivatives of x and y with respect to t:

x = 4sin^2(t)

x' = d/dt(4sin^2(t))

= 8sin(t)cos(t)

= 4sin(2t)

y = 4cos^2(t)

y' = d/dt(4cos^2(t))

= -8cos(t)sin(t)

= -4sin(2t)

Now, let's calculate the length of the curve using the arc length formula:

L = ∫[0, 5π] √[x'(t)^2 + y'(t)^2] dt

= ∫[0, 5π] √[16sin^2(2t) + 16sin^2(2t)] dt

= ∫[0, 5π] √[32sin^2(2t)] dt

= ∫[0, 5π] √[32sin^2(2t)] dt

= ∫[0, 5π] 4√[2sin^2(2t)] dt

= 4∫[0, 5π] √[2sin^2(2t)] dt

= 4∫[0, 5π] √[2(1 - cos^2(2t))] dt

= 4∫[0, 5π] √[2(1 - (1 - 2sin^2(t))^2)] dt

= 4∫[0, 5π] √[2(2sin^4(t))] dt

= 4∫[0, 5π] √[8sin^4(t)] dt

= 4∫[0, 5π] 2sin^2(t) dt

= 8∫[0, 5π] sin^2(t) dt

We can use the trigonometric identity sin^2(t) = (1 - cos(2t))/2 to simplify the integral further:

L = 8∫[0, 5π] sin^2(t) dt

= 8∫[0, 5π] (1 - cos(2t))/2 dt

= 4∫[0, 5π] (1 - cos(2t)) dt

= 4∫[0, 5π] dt - 4∫[0, 5π] cos(2t) dt

The integral of dt over the interval [0, 5π] is simply the length of the interval, which is 5π - 0 = 5π. The integral of cos(2t) over the same interval is zero since the cosine function is periodic with period π.

Therefore, the length of the curve is given by:

L = 4(5π) - 4(0)

= 20π

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Answer:

68688

Step-by-step explanation:

Let's begin by identifying key information given to us:

We are given 8 interior angles & which are listed below:

Reading the value of the protractor, we will get the following angle for KDC = 130 degrees.

Angle DC = 50 degrees (Alternate Interior Angles with LDC)

Angle LDC = 50 degrees (Supplementary Angle with KDC)

Angle DCH = 130 degrees (Alternate Interior Angles KDC)

Angle MEF = 50 degrees (Corresponding Angle with DC)

Angle HEF = 130 degrees (Corresponding Angle with CDH)

Angle EFJ = 50 degrees (Alternate Interior Angles with MEF)

Angle EF = 130 degrees (Supplementary angle with EFJ)

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Trains leave the endpoint of the route every 8 minutes.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given information are,

Time taken by dog to meet the train = 4 minutes,

Time take by train to catch the dog = 12 minutes

Let x is the time when train leaves the route,

Since, the train catches up the dog in 12 minutes, and the dog meets the train in 4 min, so the equation,

12 - x = 4

x = 8

Trains leave the endpoint of the route every 8 minutes.

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Answer:

56

Step-by-step explanation:

The easiest way to solve this is by cross multiplying. We can make an equation to find the answer of this by simply taking a side from each triangle and then the variable and equal side on the other triangle, shown below.

\(let \: \: ? = x\)

\( \frac{7}{49} = \frac{8}{x} \)

Now we solve with cross multiplication

\(7 x = 392 \\ x = 56\)

Now we know the mystery number is 56

Answer:

y = (x+5)/3

Step-by-step explanation:

Isolate y

x = 3y - 5

x + 5 = 3y

(x+5)/3 = y

Answer:

-4x + 19

Step-by-step explanation:

3 + 2(4x + 7) - 12x + 2

3 + 8x + 14 - 12x + 2

-4x + 19

I hope this helps!