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3 years ago

Find the area of a circle with a radius of 6 centimeters. Round to the nearest tenth

Mathematics

1 answer:

coldgirl [10]3 years ago

8 0

Answer: 113.1 cm^2

Step-by-step explanation: The formula to find the area of a circle is 3.14r^2. R stands for radius which is 6 in this case so just plug that in for R. 3.14(6)^2=113.1

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What are the factors of -30 and the sum of 4?

Alex787 [66]

Answer:

Answer: 30 = 1 x 30, 2 x 15, 3 x 10, or 5 x 6. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Prime factorization: 30 = 2 x 3 x 5.

Step-by-step explanation:

Still stuck? Get 1-on-1 help from an expert tutor now.

4 0

2 years ago

Read 2 more answers

A back contains 120 marbles some are red and the rest are black They are 19 red marbles for every black marble How many red marb

egoroff_w [7]

Answer:

6.3 ?

Step-by-step explanation:

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2 years ago

How much would $500 invested at 6% interest compounded monthly be worth after 4 years? Round your answer to the nearest cent

Rama09 [41]

1) Compound interest formula:
$A = P(1+ \frac{r}{n}) ^{nt}$ **<span>
**A = amount, P = principal amount, r = rate, n = # of times interest is compunded every year, t = time(in years)
2) Plug numbers in
</span> $A = (500)(1+ \frac{0.06}{12}) ^{(12)(4)}$
3) Solve
A = 635.24458054

Hope this helped! Good Luck!

7 0

3 years ago

3. A new process has been developed for applying pho toresist to 125-mm silicon wafers used in manufac turing integrated circu

dlinn [17]

Answer:

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

The null hypothesis is rejected

The 99% confidence level is $13.3930 < \mu < 13.3994$

Step-by-step explanation:

From the question we are told that

The sample size is n = 10

The population mean is $\mu = 13.4 000 \ angstroms$

The level of significance is $\alpha = 0.05$

The sample data is

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

$\= x = \frac{13.3987+ 13.3957\cdots +13.4002 }{10}$

=> $\= x = 13.3962$

Generally the sample standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }$

=> $\sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 + (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2 }{10} }$

=> $\sigma =0.0039$

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{13.3962 - 13.4000}{\frac{0.0039}{\sqrt{10} } }$

=> $z = 3.08$

Generally the p-value is mathematically represented as

$p-value = 2P( z > 3.08)$

From the z-table $P(z > 3.08)= 0.001035$

$p-value = 2* 0.001035$

$p-value = 0.00207$

So from the obtained value we see that

$p-value < \alpha$

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is 99% then the level of significance is

$\alpha = (100 -99)\%$

=> $\alpha = 0.01$

Generally from the normal distribution table critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 2.58 * \frac{0.0039}{\sqrt{10} }$

=> $E = 0.00318$

Generally the 99% confidence interval is mathematically represented as

$13.3962 - 0.00318 < \mu < 13.3962 + 0.00318$

=> $13.3930 < \mu < 13.3994$

7 0

3 years ago

Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and c= 81,000 km. Assume the cen

elena-14-01-66 [18.8K]

Answer:

$\frac{x^2}{55000^2} - \frac{y^2}{59464^2} =1$

Step-by-step explanation:

the transverse axis is horizontal.

so its a horizontal hyperbola

Center is the origin so center is (0,0)

Equation of horizontal hyperbola is

$\frac{x^2}{a^2} - \frac{y^2}{b^2} =1$

Given a= 55000 and c= 81000

c^2 = a^2 + b^2

81000^2 = 55000^2 + b^2

subtract 55000^2 on both sides

b = sqrt(81000^2 - 55000^2)= 59464.27

now plug in the values

$\frac{x^2}{55000^2} - \frac{y^2}{59464^2} =1$

7 0

2 years ago