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2 years ago

What is the sum of the first 47 terms of the sequence? -215, -201, -187, -173, ...

Mathematics

1 answer:

Andru [333]2 years ago

6 0

Answer:

5029

Step-by-step explanation:

There is a common difference between consecutive terms, that is

d = - 201 - (- 215) = - 187 - (- 201) = - 173 - (- 187) = 14

This indicates the sequence is arithmetic with sum to n term

= [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 215 and d = 14 , then

= [ (2 × - 215) + (46 × 14) ]

= 23.5 (- 430 + 644)

= 23.5 × 214

= 5029

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Find the derivative of f(x) = 12x^2 + 8x at x = 9.

zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

$(f+g)'=f'+g'$ Sum rule.

$(cf)'=cf'$ Constant multiple rule.

$(x^n)'=nx^{n-1}$ Power rule.

$(x)'=1$ Slope of y=x is 1.

$f(x)=12x^2+8x$

$f'(x)=(12x^2+8x)'$

$f'(x)=(12x^2)'+(8x)'$ by sum rule.

$f'(x)=12(x^2)+8(x)'$ by constant multiple rule.

$f'(x)=12(2x)+8(1)$ by power rule.

$f'(x)=24x+8$

Now we need to find the derivative function evaluated at x=9.

$f'(9)=24(9)+8$

$f'(9)=216+8$

$f'(9)=224$

In case you wanted to use the formal definition of derivative:

$f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

Or the formal definition evaluated at x=a:

$f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$

Let's use that a=9.

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

We need to find f(9+h) and f(9):

$f(9+h)=12(9+h)^2+8(9+h)$

$f(9+h)=12(9+h)(9+h)+72+8h$

$f(9+h)=12(81+18h+h^2)+72+8h$

(used foil or the formula (x+a)(x+a)=x^2+2ax+a^2)

$f(9+h)=972+216h+12h^2+72+8h$

Combine like terms:

$f(9+h)=1044+224h+12h^2$

$f(9)=12(9)^2+8(9)$

$f(9)=12(81)+72$

$f(9)=972+72$

$f(9)=1044$

Ok now back to our definition:

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

$f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}$

Simplify by doing 1044-1044:

$f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}$

Each term has a factor of h so divide top and bottom by h:

$f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}$

$f'(9)=\lim_{h \rightarrow 0}(224+12h)$

$f'(9)=224+12(0)$

$f'(9)=224+0$

$f'(9)=224$

8 0

3 years ago

The United States Marine Corps is reviewing its orders for uniforms because it has a surplus of uniforms for tall men recruits a

Vlad [161]

Answer:

$69.7 -2.58 \frac{2.8}{\sqrt{772}}=69.44$

$69.7 +2.58 \frac{2.8}{\sqrt{772}}=69.96$

And we can conclude that the true mean for the heights of mens between the ages of 18 to 24 is between 69.44 and 69.7 inches.

Step-by-step explanation:

For this case we have the following sample size n =772 from men recruits between the ages of 18 to 24

$\bar X= 69.7$ represent the sample mean for the heigth

$\sigma=2.8$ represent the population standard deviation

We want to construct a confidence interval for the true mean and we can use the following formula:

$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

The confidence level is 0.99 or 99%o then the significance level is $0.01$ and $\alpha/2 =0.005$ and if we find for a critical value in the normal tandar ddistirbution who accumulates 0.005 of the area on each tail we got:

$z_{\alpha/2}= 2.58$

And replacing we got:

$69.7 -2.58 \frac{2.8}{\sqrt{772}}=69.44$

$69.7 +2.58 \frac{2.8}{\sqrt{772}}=69.96$

And we can conclude that the true mean for the heights of mens between the ages of 18 to 24 is between 69.44 and 69.7 inches.

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3 years ago

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At a local fitness center, members pay a $20 membership fee and $3 for each aerobics class. nonmembers pay $5 for each aerobics

Nostrana [21]

3 classes for nonmembers and 5 classes for members

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3 years ago

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Timothy drove his race car 10% farther using the gasoline from Smith's Station compared to gasoline from Jack's Station. After T

Fiesta28 [93]

Answer:

528

Step-by-step explanation:

x = 480

1.1 x = 480 * 1.1

480 + 48 = 528

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3 years ago

A forester measured 28 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard

JulsSmile [24]

Answer:

a) Attachment

b) 6 to 14.8 in

c) 2.5%

Step-by-step explanation:

Given:

- The mean is u = 10.4 in

- The standard deviation s.d = 4.4

- Sample size n = 28

Find:

- Choose the correct Normal model for tree diameters. A. B. C.

- What size would you expect the central 68% of all tree diameters to be?Using the 68-95-99.7 rule, the central 68% of the tree diameters are between ____ inches and _____ inches.

- About what percent of the trees should have diameters below 1.6 inches?

Solution:

- The central 68% lies within two s.d from mean.

10.4 + 1*4.4 = 14.8

10.4 - 1*4.4 = 6

Hence, the central 68% are between 6 and 14.8 inches.

- The central 95% lies within two s.d from mean.

10.4 + 2*4.4 = 19.2

10.4 - 2*4.4 = 1.6

- The central 95% are between 1.6 and 19.2 inches.

- Hence, P ( X < 1.6) = (1 - 0.95)/2 = 0.025 or 2.5%

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3 years ago

What is the sum of the first 47 terms of the sequence? -215, -201, -187, -173, ...​

What is the sum of the first 47 terms of the sequence? -215, -201, -187, -173, ...