An item is regularly priced at $65 . It is now priced at a discount of 80% off the regular price. What is the price now?

What are the first and last terms of this geometric series

ANSWER

E. 10 and 640

EXPLANATION

The given series is

$\sum_{i=1}^45 \times 2^{2i-1}$

To find the first term of the series we substitute i=1 to get,

$a_1 = 5 \times {2}^{2 \times 1 - 1}$

$a_1 = 5 \times {2}^{ 1} = 10$

For the last term of the series, we substitute i=4 to obtain,

$a_4 = 5 \times {2}^{2 \times 4 - 1}$

$a_4 = 5 \times {2}^{7}$

This implies that,

$a_4 = 5 \times 128 = 640$

Therefore the correct answer is E

7 0

2 years ago

The total global area of crops has increased from 44.2 million to

alexira [117]

Answer:

311%

Step-by-step explanation:

The percentage change is calculated as ...

percent change = ((new value) -(old value))/(old value) × 100%

Filling in the numbers, we have ...

percent change = (181.5 -44.2)/44.2 × 100% ≈ 311%

The global area increased by 311% over the interval.

7 0

2 years ago

Write the linear equation that gives the rule for this table.

Maksim231197 [3]

to get the equation of any straight line all we need is two points, well, let's just grab them from the table.

hmmm let's use (-49 , -39) and hmmm say (67 , 77)

$(\stackrel{x_1}{-49}~,~\stackrel{y_1}{-39})\qquad (\stackrel{x_2}{67}~,~\stackrel{y_2}{77}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{77}-\stackrel{y1}{(-39)}}}{\underset{run} {\underset{x_2}{67}-\underset{x_1}{(-49)}}}\implies \cfrac{77+39}{67+49}\implies \cfrac{116}{116}\implies 1$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-39)}=\stackrel{m}{1}(x-\stackrel{x_1}{(-49)}) \\\\\\ y+39=1(x+49)\implies y+39=x+49\implies y=x+10$

8 0

2 years ago

Put the steps in correct order to prove that if x is irrational, then 1/x is irrational using contraposition.

SOVA2 [1]

Answer:

The correct order is:

a

c

d

b

Step-by-step explanation:

First, let's write 1/x in a convenient way for us:

a) Substitute 1/x = p/q, to obtain x = 1/(1/x) = 1/(p/q) = q/p.

Now we assume that 1/x is rational (we want to prove that this implies that x will be also rational and because we know that x is irrational assuming that 1/x is rational will lead to an incongruence), then:

c. If 1/x is rational, then 1/x = p/q for some integers p and q with q ≠ 0. Observe that p is not 0 either, because 1/x is not 0.

Now we know that we can write x as a quotient of two integers, we need to imply that, then the next one is:

d) Observe that x is the quotient of two integers with the denominator nonzero.

And that is the definition of rational, then we end with:

b) Hence x is rational.

Which is what we wanted to get.

5 0

2 years ago

1. Find the missing values in the equations.

anastassius [24]

Answer:

a. ? = 12

b. ? = -4

c. ? = 4

d. ? = -3

e. ? = -3

Step-by-step explanation:

6 0

2 years ago

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