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SashulF [63]
3 years ago
15

Write the explicit formula for the

Mathematics
1 answer:
Phoenix [80]3 years ago
7 0

Answer:

a_n=-10n+150

Step-by-step explanation:

This is consider a linear pattern (arithmetic pattern).

We know this because it is either going up or down by the same number each time. It's going down by 10 in this case.

So -10 is the slope of this linear pattern.

The equation for a linear pattern is:

y=mx+b

where x represents the position the term is in

and

where y represents the actual term

and

where m is the slope

So we have y=-10x+b.

(x,y)

(term position in sequence, actual term)

(1,140)

(2,130)

(3,120)

(4,110)

We can find b by using a number with it's position in the sequence (that is plug in one of your points above).

y=-10x+b

140=-10(1)+b

140=-10+b

150=b (after adding 10 on both sides)

The explicit equation for the sequence is y=-10x+150.

They probably prefer you to write: a_n=-10n+150 instead.

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Let X be an exponential random variable with parameter 2. Find the CDF of X . Express your answer in terms of x using standard n
erastovalidia [21]

Answer:

F(x,\lambda) = 1-e^{2x}     for      x\geq0

and   F(x,\lambda) = 0    for   x

Step-by-step explanation:

Remember that the CDF of an exponental random variable is given by

F(x,\lambda) = \left \{ {{1-e^{\lambda x}  \ \  \ \ \  x\geq 0} \atop {0}  \ \ \ \ \ \  \ \ \ \ \ x

where   \lambda   is the parameter.  In this case    \lambda =  2  so, for this case

F(x,\lambda) = \left \{ {{1-e^{2x}  \ \  \ \ \  x\geq 0} \atop {0}  \ \ \ \ \ \  \ \ \ \ \ x

7 0
3 years ago
What the perimeter of 2m 10cm and 45cm of a rectangle
telo118 [61]

You only told us the length of 3 sides, and from those 3,
we can already see that it's not a rectangle.  (If you take
any 3 sides of a rectangle, two of them must be the same
length.)

So we have no way to tell the length of the 4th side, or to
add up the lengths of all 4 sides to get the perimeter.
It could be many different things.

The only thing we know for sure is that the perimeter must be
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The special at a local pizza place says you can choose any 3 toppings from a list of 5. How many possible combinations are there
Mars2501 [29]
Will there are 3 toppings and 5 all together and you add 3 & 5 = 8 so that makes 3/8 i think !
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There are 32 people who voted for Petra for class president.This represents 1/2 of the people who voted. How many people voted i
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$13,168is invested, part at 13%and the rest at
Kryger [21]

Answer: the amount invested at 13% is $9748

the amount invested at 5% is $3420

Step-by-step explanation:

Let x represent the amount invested at 13%.

Let y represent the amount invested at 5%.

$13,168 is invested, part at 13 % and the rest at 5%. This means that

x + y = 13168

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 5%,

P = y

R = 5%

T = 1 year

I = (x × 5 × 1)/100 = 0.05y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

5% by $1438.24, it means that

0.13x - 0.05y = 1438.24 - - -- - - - - -1

Substituting x = 13168 - y into equation 1, it becomes

0.13(13168 - y) - 0.05y = 1438.24

1711.84 - 0.13y - 0.05y = 1438.24

- 0.13y - 0.05y = 1438.24 - 1711.84

- 0.08y = - 273.6

y = - 273.6/- 0.08

y = 3420

x = 13168 - y = 13168 - 3420

x = 9748

7 0
3 years ago
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