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3 years ago

What is the common ratio of the sequence below 2/3, 1/6, 1/24,1/96

Mathematics

1 answer:

Olegator [25]3 years ago

4 0

Answer:

As we proved, the common ratio of the sequence is 1/4.

Step-by-step explanation:

Let's find the common ratio of the sequence, this way:

A. What number modifies 2/3 into 1/6?

1/6 ÷ 2/3 =

1/6 * 3/2 = (flipping the reciprocal when we change from division to multiplication)

3/12 = 1/4

B. What number modifies 1/6 into 1/24?

1/24 ÷ 1/6 =

1/24 * 6/1 = (flipping the reciprocal when we change from division to multiplication)

6/24 = 1/4

C. What number modifies 1/24 into 1/96?

1/96 ÷ 1/24 =

1/96 * 24/1 = (flipping the reciprocal when we change from division to multiplication)

24/96 = 1/4

As we proved, the common ratio of the sequence is 1/4.

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620,000 rounded to the ten thousand

Trava [24]

Youre answer would be 620,000 hope this helps!!!

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3 years ago

The data in the table represents a company’s profit based on the number of items produced

frutty [35]

Answer:

(A) y= -1.026x^2 + 1016.402x - 162075

Step-by-step explanation:

Here is the options to the question

Which equation best represents the data?

A) y= -1.026x^2 + 1016.402x - 162075

B) y= -1.036x^2 + 1024.771x - 163710

C) y= 298.214x - 66317.667

D) y= 196.2x – 18710

(A) y= -1.026x^2 + 1016.402x - 162075

The data above represents the company's profit based on number of items produced.

To get the equation which best represents the data, we have to substitute the value of x into the given equations

By substituting x=100 in first equation, we have:

y = -1.02x² + 1016.402x – 162075

y = -1.026(100)² + 1016.402(100) – 162075

y = -70500

Option A satisfies.

Using the second equation

When x = 100

y = -1.036x^2 + 1024.771x - 163710

y = -1.036(100)² + 1024.771(100) - 163710

y = -10360 + 102477.1 – 163710

y = -71592.9

Option B doesn’t satisfies

We can also replace the various values of x in the equations to check whether or not they satisfy.

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3 years ago

this is step three of mathematical induction can somebody help me solve the rest, you only work on the left side to make it equa

kvv77 [185]

Answer:

Step 1(Base step) − It proves that a statement is true for the initial value. Step 2(Inductive step) − It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n+1)th iteration ( or number n+1).

Step-by-step explanation:

3 0

3 years ago

Piravena must make a trip from A to B then from B to C, then from C to A. Each of these three parts of the trip is made entirely

anyanavicka [17]

Answer:

a) Cost of flying from A to B = $425

b) Total distance travelled by Piravena during the complete trip = 7,500 km

c) To minimize cost and arrive at the final cost given, she must have travelled by bus from B to C and then travelled by taking an airplane from C to A.

Step-by-step explanation:

The complete question is presented in the attached image to this question.

Full Question

a) To begin her trip she flew from A to B. Determine the cost of flying from A to B.

b) Determine the distance she travels for her complete trip.

c) Piravena chose the least expensive way to travel between cities and her total cost was $1012.50. Given that she flew from A to B, determine her method of transportation from B to C and her method of transportation from C to A.

Solution

a) The distance from A to B is given as 3250 km.

To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometer.

So, to fly 3250 km, she will pay

100 + (0.10×3250) = $425

b) For her complete journey, she is to make a trip from A to B then from B to C, then from C to A.

Her complete distance travelled = AB + BC + CA

But it is given that the three cities form a right angled triangle as given in the question with AB serving as the hypotenuse side.

Pythagoras theorem gives that the square of the hypotenuse side is equal to the sum of the respective squares of the other two sides

AB² = BC² + CA²

3250² = BC² + 3000²

BC² = 3250² - 3000² = 1,562,500

BC = √1,562,500 = 1,250 km

Total distance covered by Piravena during the entire trip = AB + BC + CA = 3250 + 1250 + 3000 = 7,500 km

c) Her total cost of travel = $1012.50

But she definitely flew from A to B at a cost of $425

This means she spent (1012.50 - 425) on the rest of the journey, that is, $587.5

Note that to travel by bus, it is $0.15 per kilometre and to travel by airplane is $100 + $0.10 per kilometre. Indicating that the airplane saves cost on long distance travels while the bus saves cost on short distance travels.

To confirm this, we calculate the two options (bus or airplane) for each route.

If she travels B to C by bus, cost = 0.15 × 1250 = $187.5

If she travels B to C by airplane, cost = 100 + (0.10×1250) = $225

Hence, the bus obviously minimizes cost here.

If she travels from C to A by bus, cost = 0.15 × 3000 = $450

If she travels from C to A by airplane, cost = 100 + (0.10×3000) = $400

Here, travelling by airplane minimizes the cost.

So, if we confirm now that she travelled from B to C by bus and then from C to A by airplane, total cost = 187.5 + 400 = $587.5

which is the remaining part of her total cost is she minimized expenses!

Hope this Helps!!!

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3 years ago

if 1 000 bottles of an award-winning wine are to be packed in special gift boxes which can hold six bottles each, calculate how

Anuta_ua [19.1K]

Step-by-step explanation:

Introduction:

This section basically dedicated to the classification of the antennas which are used in different wavelength.

Wire Antennas:

Wire antennas are familiar to the layman because they are seen virtually everywhere on automobiles, buildings, ships, aircraft, spacecraft, and so on.

There are various shapes of wire antennas such as a straight wire (dipole), loop, and helix which are shown in Figure 1.3.

Loop antennas need not only be circular.

They may take the form of a rectangle, square, ellipse, or any other configuration.

The circular loop is the most common because of its simplicity in construction

Aperture Antennas

Aperture antennas may be more familiar to the layman today than in the past because of the increasing demand for more sophisticated forms of antennas and the utilization of higher frequencies.

Some forms of aperture antennas are shown in Figure 1.4.

Antennas of this type are very useful for aircraft and spacecraft applications, because they can be very conveniently flush-mounted on the skin of the aircraft or spacecraft. In addition, they can be covered with a dielectric material to protect them from hazardous conditions of the environment.

Microstrip Antennas

Microstrip antennas became very popular in the 1970s primarily for spaceborne applications.

Today they are used for government and commercial applications. These antennas consist of a metallic patch on a grounded substrate.

The microstrip antennas are low profile, comformable to planar and nonplanar surfaces, simple and inexpensive to fabricate using modern printed-circuit technology, mechanically robust when mounted on rigid surfaces, compatible with MMIC designs, and very versatile in terms of resonant frequency, polarization, pattern, and impedance.

These antennas can be mounted on the surface of high-performance aircraft, spacecraft, satellites, missiles, cars, and even handheld mobile telephones

Array Antennas

Many applications require radiation characteristics that may not be achievable by a single element. It may, however, be possible that an aggregate of radiating elements

in an electrical and geometrical arrangement (an array) will result inthe desiredradiation characteristics.

The arrangement of the array may be such that the radiation from the elements adds up to give a radiationmaximum ina particular directionor directions, minimum in others, or otherwise as desired.

Typical examples of arrays are shownin Figure 1.6.

Usually the term array is reserved for an arrangement in which the individual radiators are separate as shown in Figures 1.6(a/c).

However the same term is also used to describe an assembly of radiators mounted on a continuous structure, showninFigure 1.6(d).

6 0

2 years ago

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