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3 years ago

Given

Mathematics

1 answer:

arlik [135]3 years ago

3 0

Answer:

a = 3, b = - 7

Step-by-step explanation:

Substitute x = 2 into the equation and equate to 5, that is

a(2)² + b = 5

4a + b = 5 → (1)

Substitute x = 3 into the equation and equate to 20

a(3)² + b = 20

9a + b = 20 → (2)

Subtract (1) from (2) term by term to eliminate b

(9a - 4a) + (b - b) = (20 - 5), that is

5a = 15 ( divide both sides by 5 )

a = 3

Substitute a = 3 into either of the 2 equations and solve for b

Substituting in (1)

4(3) + b = 5

12 + b = 5 ( subtract 12 from both sides )

b = - 7

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The authors of a paper presented a correlation analysis to investigate the relationship between maximal lactate level x and musc

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Answer:

a) Sample correlation coefficient, r = 0.7411

bi) test statistic, t = 4.102

bii) P-value = 0.000736

Step-by-step explanation:

a) The formula for the sample correlation coefficient is given by the formula:

$r = \frac{S_{xy} }{\sqrt{S_{xx} S_{yy} }} }$

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r = 0.7511

i) formula for the test statistic is given by the formula:

$t = \frac{r\sqrt{n-1} }{\sqrt{1 - r^{2} } }$

sample size, n = 4

$t = \frac{0.7511\sqrt{14-1} }{\sqrt{1 - 0.7511^{2} } }$

t = 4.102

ii) Degree of freedom, df = n -2

df = 14 -2

df = 12

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2 years ago

PLEASE HELP ASAP FOR 10 POINTS!! ❤️

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Answer:

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Step-by-step explanation:

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Answer:

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The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

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The interest is compounded anually, so $n = 1$

$A = P(1 + \frac{r}{n})^{nt}$

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Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

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3 years ago

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