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2 years ago

Calculate the missing terms of the geometric sequence 2048,?,?,?,8

Mathematics

1 answer:

Setler [38]2 years ago

4 0

Answer: 2048, 512, 128, 32, 8

Step-by-step explanation:

Recognize 2048 is 2^11, as all hackers know

1024 is 2^10 :-). Also 8 is 2^3.

So this problem is exactly similar to filling in the geometric sequence starting at 10^11 = 100,000,000,000, with three intermediate values ending with 10^3 = 1000.

(100,000,000,000) = 10^11

1,000,000,000 = 10^9

10,000,000 = 10^7

100,000, = 10^5

(1,000) = 10^3

Or, it is exactly similar to filling in the arithmetic series 11, a, b, c, 3. That one is (11), 9, 7, 5, (3), where we subtract 2 each time.

$A_0 = 11$

$A_{n+1} = A_{n} - 2$

The answer is (2048), 512, 128, 32, (8) where we divide by 2^2 each time. Or (2^11), 2^9, 2^7, 2^5, (2^3).

$G_0 = 2^{11}=512$

$G_{n+1} = G_{n} / 2^2$

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In the diagram of circle O, what is the measure of abc? 34° 45° 68° 73°

Lady_Fox [76]

Answer:

A. $m\angle ABC=34^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle ABC.

First of all, we will find measure of major arc AC by subtracting 146 from 360 degrees.

$\text{Measure of arc AC}=360^{\circ}-146^{\circ}$

$\text{Measure of arc AC}=214^{\circ}$

Now, we will use tangent-tangent angle theorem to solve for ABC.

Tangent-Tangent angle theorem states that angle formed by two tangents outside a circle is half the difference of intercepted arcs.

$m\angle ABC=\frac{214^{\circ}-146^{\circ}}{2}$

$m\angle ABC=\frac{68^{\circ}}{2}$

$m\angle ABC=34^{\circ}$

Therefore, the measure of angle ABC is 34 degrees and option A is the correct choice.

5 0

2 years ago

Read 2 more answers

A clothing store is analyzing merchandise prices to help make decisions on what to charge for clothing on clearance. The store o

Aleks [24]

The variable is Quantitative, has Interval level of measurement.

Variables which can be quantified & expressed numerically are Quantitative variables. Eg : as given , price

Variables which cant be qualified & expressed numerically are Qualitative variables. Eg : level of honesty, loyalty etc

Nominal & Ordinal are qualitative variables : signifying yes or no to a category (like men or women) , or ranks (x better than y) respectively. So price level is not such categorical & ordinal ratio.

Quantitative ratio variables are with reference to time , or are in forms of rate (like speed , growth per year). So, price level is not such ratio variable also.

Price is a quantitative variable, in which the ranking, its difference can be calculated. This is characteristic of a <u>Quantitative Interval Variable</u>.

4 0

2 years ago

Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5? The differ

tamaranim1 [39]

<span>Let be A =a3b +9a2b2-4ab5, and B=a3b-3a2b2+ab5,so the difference can be defined as A - B =a3b +9a2b2-4ab5 -(a3b-3a2b2+ab5), when there is negative sign in front of the parathesis, all the inside signs must change: that is as follow: A- B= a3b +9a2b2-4ab5 - a3b + 3a2b2 - ab5= a3b-a3b +9a2b2+3a2b2-4ab5- ab5= 12a2b2 -5ab5, the fist term has 2+2=4, as a degree,the second term has 1 +5 =6, so the true answer : The difference is a binomial with a degree of 6</span>

6 0

2 years ago

Read 2 more answers

Jada is making lasagna and pizzas for a party recipe calls for 1 1/4 cups and she uses 1/2 she doubled her recipe and made 5 piz

grigory [225]

This question is not correctly written

Complete Question

Jada is making lasagna and pizzas for a large party. Her lasagna recipe calls for 1 1/4 cups of tomato paste, and her pizza recipe uses 1/2 cup of tomato paste per pizza. She will double her lasagna recipe and make 5 pizzas. Write and evaluate an expression for how many 3/4- cup cans of tomato paste she will need in all.

Answer:

The evaluate and for how many 3/4-cup cans of tomato she need in all is 20/3

Step-by-step explanation:

Step 1

From the question, we are told that:

1 single lasgna recipe uses: 1 1/4 cups of tomato paste = 5/4 cups

If she doubles her recipe, the number of cups of tomato paste =

2 × 5/4 cups of tomato paste

= 10/ 4 = 5/2 cups of tomato pastes

Step 2

From the question, we are told that:

1 Pizza recipe = 1/2 cup of tomato pastes

5 Pizza =

5 × 1/2 cup of tomato paste

= 5/2 cups of tomato paste

Steps 3

The total number of cups of tomato paste Jada will use in making double lasagna and 5 pizzas is calculated as

= 5/2 + 5/2

= (5 + 5)/ 2

= 10/2

= 5 cups.

Step 4

We are asked to evaluate how many 3/4 -cup cans of tomato she need in all.

This means we should find how many 3/4 - cup cans can be found in the total number of cups of tomato paste that Jada used.

Total number of cups that Jada used = 5 cups of tomato paste

The number of 3/4-cup cans in 5 cups is calculated as:

5 ÷ (3/4)

= 5 × 4/3

= 20/3

Therefore, the evaluate and for how many 3/4-cup cans of tomato she need in all is 20/3

8 0

2 years ago

Suppose a certain airline uses passenger seats that are 16.2 inches wide. Assume that adult men have hip breadths that are norma

Pachacha [2.7K]

Answer:

Each adult male has a 5.05% probability of having a hip width greater than 16.2 inches.

There is a 0.01% probability that the 110 adult men will have an average hip width greater than 16.2 inches.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem

Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. This means that $\mu = 14.4, \sigma = 1.1$ .

What is the probability that any one of those adult male will have a hip width greater than 16.2 inches?

For each one of these adult males, the probability that they have a hip width greater than 16.2 inches is 1 subtracted by the pvalue of Z when X = 16.2. So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16.2 - 14.4}{1.1}$