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2 years ago

Find the 9th term of the geometric sequence 729,243,81

Mathematics

2 answers:

dybincka [34]2 years ago

5 0

<h2><u><em>Vote Me Brainliest!</em></u></h2>

Answer:

1/9

Step-by-step explanation:

Using them formula :

Tn=a x r^(n-1)

T9=729 x (1/3)^(9-1)

T9=729 x (1/3)^8

T9=729 x 1/6561

T9=729/6561

T9=1/9

Black_prince [1.1K]2 years ago

3 0

Answer:1/9

Step-by-step explanation:

729,243,81

First term(a)=729

Common ratio(r)=243/729=1/3

Using them formula :

Tn=a x r^(n-1)

T9=729 x (1/3)^(9-1)

T9=729 x (1/3)^8

T9=729 x 1/6561

T9=729/6561

T9=1/9

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A large washer has an outer radius of 10mm and a hole with a diameter of 14mm. What is the area of the top surface of the washer

choli [55]

<h2>Answer:</h2>

The area of the top surface of the washer is: 160.14 square mm.

<h2>Step-by-step explanation:</h2>

The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)

Now, we know that the area of the annulus region is given by:

$Area=\pi (R^2-r^2)$

where R is the outer radius and r is the inner radius.

Here we have:

$R=10\ mm\\\\and\\\\r=7\ mm$

Hence, we have:

$Area\ of\ top\ surface=\pi (10^2-7^2)\\\\i.e.\\\\Area\ of\ top\ surface=\pi (100-49)\\\\i.e.\\\\Area\ of\ top\ surface=\pi\cdot 51\\\\i.e.\\\\Area\ of\ top\ surface=160.14\ mm^2$

4 0

2 years ago

Read 2 more answers

Best Company sells personalized mugs for $18 each plus a fixed fee of $26 for shipping and handling for the entire order. The Cu

Step2247 [10]

26+18m = 14+22m

26 + 18m-22m=14

26-4m=14

-4m=12

m=3

3 mugs

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2 years ago

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A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 squar

Vika [28.1K]

Given:
2 parallelograms with an area of 9 1/3 yd²
height of each parallelogram is 1 1/3 yd

Area of parallelogram = base * height

We need to divide the combined area into two to get each parallelogram's base.

9 1/3 = ((9*3)+1)/3 = 28/3

28/3 ÷ 2 = 28/3 * 1/2 = 28/6 yd² or 4 4/6 yd² ⇒ 4 2/3 yd²

Area of each parallelogram is 4 2/3 yd²

4 2/3 yd² = base * 1 1/3 yd

14/3 yd² ÷ 4/3 yd = base

14/3 yd² x 3/4 yd = base
14*3 / 3*4 = base
42 / 12 = base
3 6/12 yd = base
or 3 1/2 yd = base

a) the base of each parallelogram is 3 1/2 yards
b) we can assume that the two parallelograms form a rectangle.
area of a rectangle is length times width.

length is 3 1/2 yds * 2 = 7 yds
width is 3 1/2 yds

Area of rectangle = 7 yds * 3 1/2 yds
Area = 7 yd * 7/2 yd
Area = 7*7 / 2 yd²
Area = 49 / 2 yd²
Area = 24 1/2 yd²

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2 years ago

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A population has a standard deviation of 80. A random sample of 400 items from this population is selected. The sample mean is d

Helga [31]

Answer:

$ME= 1.8808 * \frac{80}{\sqrt{400}} =7.5232$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =80$ represent the population standard deviation

n=400 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.8808$