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Sindrei [870]
3 years ago
10

Write the first five terms of the geometric sequence with the given 1st term and the common ratio.

Mathematics
1 answer:
siniylev [52]3 years ago
6 0

Answer:

  • 1/2, 1/4, 1/8, 1/16, 1/32

Step-by-step explanation:

<u>Given GP with:</u>

  • a_1= 1/2, r = 1/2

<u>The equation for nth term is:</u>

  • a_n=a_1*r^{n-1}

<u>Find the first 5 terms:</u>

  • a_1=1/2\\a_2=1/2*1/2=1/4\\a_3=1/2*(1/2)^2=1/8\\a_4=1/2*(1/2)^3=1/16\\a_5=1/2*(1/2)^4=1/32
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HELP ASAP PLEASE <br> Find the area of the figure.
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Answer:

39.82

Step-by-step explanation:

to find the entire area of the figure, you'll have to split it up into two parts:

   a. triangle

   b. semi-circle

therefore, the formula for the area of a triangle is 1/2(base)(height). in simpler terms, it means to multiply 1/2 by the base and the height. in this case, multiply 1/2 x 5 x 12, which gives you 60/2, which ultimately gives you 30.

to find the area of the semi circle, use the area formula for a circle and divide the area by 2. the formula is: πr^{2}. so, plug in your lengths. this gives you, π(5)^2. divide this by two. you should get an answer of 9.82

finally, add your two areas (30+9.82), which equals 39.82

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Step-by-step explanation:

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Using a sequencing method called "RNAseq," a researcher determines the level of FOXP2 expression
Wewaii [24]

The Z-score is 2.306 to three decimal places. However, the Z-test statistic value shows that it is greater than the Z-critical value, so we reject the null hypothesis \mathbf{H_o}

<h3>What is the Z-score of a test statistic?</h3>

A z-score is a measurement of how often standard deviations the score obtained from a z-test is beyond or under the mean population.

From the given data information, let us find the mean and the standard deviation.

\mathbf{Mean (\bar  x) = \dfrac{1154+5998+1007+...3987+4187+887}{10}}

\mathbf{Mean (\bar  x) = \dfrac{24256}{10}}

Mean (x) = 2425.6

The hypothesis testing can be computed as:

\mathbf{H_o: \mu = 2425.6}

\mathbf{H_1: \mu \ne 2425.6}

The standard deviation (σ) is:

\mathbf{=\mathbf{ \sqrt{\dfrac{(1154-2425.6)^2+....+(887-2425.6)^2}{10-1}}}}

\mathbf{= \sqrt{3199489}}

= 1788.71

Now, the Z-test statistic is determined using the formula:

\mathbf{|Z| = |\dfrac{\bar x - \mu }{\sigma}| }

\mathbf{|Z| = |\dfrac{2425.6 -6550 }{1788.71}| }

\mathbf{|Z| = |-2.3058|  }

Z ≅ 2.306  

Therefore, at a 0.05 level of significance, the Z-critical value is 2.306. However, since the Z-test statistic value shows that it is greater than the Z-critical value, so we reject the null hypothesis \mathbf{H_o}

The complete question is given as:

Using a sequencing method called "RNAseq," a researcher determines the level of FOXP2 expression in 10 different samples of lung tissue, and obtains these data:

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Scientist has previously determined that FOXP2 is expressed in brain tissue at a level of 6,550. Calculate the Z-score associated with a test to see if the average expression of FOXP in her lung tissue samples is different from the levels she measured from brain tissue.

Learn more about calculating the Z-score of a test statistics here:

brainly.com/question/15569214

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2 years ago
a senator wishes to estimate the proportion of united states voters who favor new road construction. what size sample should be
Nitella [24]

The  size of the sample should be obtained at 2401 in order to be 95% confident

Given that:

Margi of error, ME=0.02

Population proportion, p=0.50

To Find: The size of the sample that should be obtained in order to be 95% confident

Let the size of the sample be n

Using formula,

n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401

Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident

Learn more about Population proportion here brainly.com/question/15703406

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8 0
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