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Rasek [7]
2 years ago
11

If a geometric sequence has a1 = 256 and a8 = 512, find the exact value of the common ratio ????.

Mathematics
1 answer:
marusya05 [52]2 years ago
7 0

Answer:r=1.104

Step-by-step explanation:

Given

First term a_1=256

a_8=512

Also a_8 can also be written in

a_8=ar^7

where r=common difference

512=256r^7

2=r^7

r=\left ( 2\right )^{\frac{1}{7}}

r=1.104

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Two angles are complementary. the measure of ∠abc is x° and the measure of ∠dbc is (3x + 10)°. what is the value of x? enter you
Marta_Voda [28]
This problem can be expressed through the equation:
x+3x+10= 90

To solve it we subtract 10 on both sides
→x+3x=80
Add x and 3x
→4x=80
And divide each side by 4
→x=80/4
→x=20

ANSWER:
20
8 0
2 years ago
The diagram shows a scale drawing of a playground. In the scale drawing the playground has a length of 16 cm and a width of 8 cm
kicyunya [14]

Answer:

3 m : 4 cm, 3 m/4 cm, 3 m to 4 cm

Step-by-step explanation:

The actual playground will have an area of 72 m², and have one side be double the other, because the scale drawing does so too.

We can make a system of equations: l * w = 72, l = 2w

Substitute: 2w * w = 72

Simplify: 2 * w² = 72

Divide: w² = 36

Square root: <em>w = 6 m</em> (no negatives due to distances always > 0)

Substitute: l = 2 * 6 m

Simplify: <em>l = 12 m</em>

This means that the relations of one side is <em>6 m : 8 cm</em>. That can be simplified to 3 m : 4 cm.

8 0
2 years ago
Riya’s height is 150 cm while her brother is 160 cm tall. If Riya
Lemur [1.5K]
Riya’s BMI is 20 which means she is a normal weight. Her brother’s BMI is 18.7, which is low but is still a normal weight. So yes, their heights are proportioned to their weights.
5 0
2 years ago
Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Us
grigory [225]

Answer:

The confidence interval on this case is given by:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

\bar X = \frac{62.532+76.478}{2}= 69.505

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

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".  

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".

\bar X represent the sample mean  

\mu population mean (variable of interest)  

\sigma represent the population standard deviation  

n represent the sample size  

Assuming the X follows a normal distribution  

X \sim N(\mu, \sigma)

The confidence interval on this case is given by:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

\bar X = \frac{62.532+76.478}{2}= 69.505

So then the mean for this case is 69.505

5 0
2 years ago
How many integers $n$ satisfy the inequality $3n^2 - 4 \le 44$?
FromTheMoon [43]

Answer:

7 integers

Step-by-step explanation:

The inequality to solve is  3n^2-4

We can do algebra and solve this:

3n^2-4

If we solve 3n^2-48=0, we will get the intercepts. So:

3n^2-48=0\\3(n^2-16)=0\\n^2-16=0\\n^2=16\\n=4,-4

<em>Since, the inequality is less than, the solution set is all numbers between -4 and 4. So</em>

<em>-4 < n < 4</em>

<em />

<em>*note: -4 and 4 is NOT included, so the integers in the range are:</em>

<em>-3, -2, -1, 0, 1 , 2, 3</em>

<em>Which is </em><em>7 integers.</em>

8 0
2 years ago
Read 2 more answers
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