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kicyunya [14]
3 years ago
13

Insert geometric means in each geometric sequence.

Mathematics
1 answer:
Digiron [165]3 years ago
5 0

Answer:

\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}

\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}

81, \underline{27, 9, 3, 1},\dfrac{1}{3}

Step-by-step explanation:

Given the Geometric sequences:

1. ___, 24, ___, ___, 3/64

2. ___, 1/4, 1/2, ___

3. 81, ___, ___, ___, ___, 1/3

To find:

The values in the blanks of the given geometric sequences.

Solution:

First of all, let us learn about the n^{th} term of a geometric sequence.

a_n=ar^{n-1}

Where a is the first term and

r is the common ratio by which each term varies from the previous term.

Considering the first sequence, we are given the second and fifth terms of the sequences.

Applying the above formula:

ar = 24\\ar^4 = \dfrac{3}{64}

Solving the above equation:

r = \dfrac{1}{8}

Therefore, the sequence is:

\underline{192}, 24, \underline{3}, \underline{\dfrac{3}{8}}, \dfrac{3}{64}

Considering the second given sequence:

ar = \dfrac{1}{4}\\ar^2 = \dfrac{1}{2}\\\text{Solving the above equations}, r = 2

Therefore, the sequence is:

\underline{\dfrac{1}8}, \dfrac{1}{4}, \dfrac{1}{2}, \underline{1}

Considering the third sequence:

a = 81\\ar^5=\dfrac{1}{3}\\\Rightarrow r = 3

Therefore, the sequence is:

81, \underline{27, 9, 3, 1},\dfrac{1}{3}

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Answer:

There is not enough evidence to conclude that  average starting salary for clerical employees in the state is less than ​$35,000 per year.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 35,000 dollars per year

Sample mean, \bar{x} = 34,700 dollars per year

Sample size, n = 100

Alpha, α = 0.10

Population standard deviation, σ = 3,500 dollars per year

First, we design the null and the alternate hypothesis

H_{0}: \mu = 35,000\text{ dollars per year}\\H_A: \mu < 35,000\text{ dollars per year}

We use one-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{34700 - 35000}{\frac{3500}{\sqrt{100}} } = -0.8571

Now, z_{critical} \text{ at 0.10 level of significance } = -1.28

Since,  

z_{stat} > z_{critical}

We fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to conclude that  average starting salary for clerical employees in the state is less than ​$35,000 per year.

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3 years ago
The wholesale price for a pillow is $3.50 . A certain department store marks up the wholesale price by 60%. Find the price of th
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Answer:

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Step-by-step explanation:

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Please help it would be much appreciated!!
AlekseyPX

Answer:

a) P) 0.25 = 1/4  both

b) P) 0.75 = 3/4  one

c) P) 0.25  = 1/4  none

Step-by-step explanation:

4 routes to D + H

6 routes to H + S

= D  H   S

     4  | 6

    - 2 | -3

=    2  |  3  = route 1 = 2/4  and route 2 = 3/6

= 1/2 route 1 and 1/2 route 2

Answer a ) = 1/2 x 1/2 = 0.25 = 1/4  = 0.25 probability

Answer b)  = 1- (1/2 x 1/2) = 1- 0.25 = 3/4 = 0.75 probability

Answer c)  = 1/2 x 1/2 = 0.25 = 1/4 = 0.25 probability  

3 0
2 years ago
What is the speed of a horse that runs a distance of 2,592 meters in 144 seconds? ____meters
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Answer: 18 meters/s

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21. Brian wants to purchase a piece of fabric
ella [17]

Brian should purchase Choice C of fabric

<em><u>Solution:</u></em>

Given that Brian wants to purchase a piece of fabric  that is between 49 and 53 inches long

So piece of fabric should be between: 49 and 53 inches

  • Choice A is 4\frac{3}{4} feet long

Let us convert feet to inches

4\frac{3}{4} feet = \frac{4 \times 4 + 3}{4} = \frac{19}{4} feet

Now convert to inches

We know that,

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So this is not correct

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Now convert to inches

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But this choice is greater than given condition that piece of fabric should be between: 49 and 53 inches

So this is not correct

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Now convert to inches

\frac{13}{3} feet = \frac{13}{3} \times 12 inches = 52 inches

So this 52 inches lies between 49 and 53 inches

So Brian should purchase Choice C of fabric

8 0
3 years ago
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