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2 years ago

Find the sum. Homework: 9.4 arithmetic series

Mathematics

1 answer:

RUDIKE [14]2 years ago

5 0

Answer:

Step-by-step explanation:

a1 = 3(1) - 7 = - 4

a2 = 3(2) - 7 = -1

d = a2 - a1

d = -1 - (-4)

d = -1 + 4

d = 3

a60 = 3(60) - 7

a60 = 180 - 7

a60 = 173

n = 60

Sum = (a1 + a60) * n / 2

Sum = (-4 + 173) * 60/2

Sum = (169)*30

Sum = 5070

==================

Just to check, we'll use the second summation formula

d = 3

n = 60

a1 = -4

Sum = (2*a1 + (n - 1)*d )*n / 2

Sum = (2*(-4) + (60 -1)*3)* 60/2

Sum = (-8 + 59*3) * 30

Sum = (177 - 8)*30

Sum = 169 * 30

Sum = 5070

Same answer.

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Maggie and her friends are each able to recruit a certain number of people each year to sample a product. The number of people p

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A function assigns the values. The number of people that were recruited in year 6 is 192.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given that the number of people per year is represented by the function $f(t)=3(2)^t$ .

In the given function, t represents the number of years.

Now, the number of people that were recruited in year 6 can be calculated by putting the value of t as 6 in the given function,

$f(t)=3(2)^t$

f(6) = 3(2)⁶

= 3(64)

= 192

Hence, the number of people that were recruited in year 6 is 192.

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1 year ago

Help answer question 3

Rufina [12.5K]

Answer:

The answer is the first one. Inside the absolute value symbols it is negative but absolute value answers are always positive. Instead of -30 the answer is 30.

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3 years ago

An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a num

gavmur [86]

Answer:

Step-by-step explanation:

An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money?

To solve this problem, we will simply write 1,00,000 in base 2.

2^17 gives 131072, 2^16 gives 65536.

So, the first gift is 65536, we then need to repeat this process for 34,464 ((100,000-65536 = 34,464), to get all gifts in succession.

6 gifts in all: one each of $32, $128, $512, $1024, $32768, and $65536.

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2 years ago

(1 point) There were 23.7 million licensed drivers in California in 2009 and 22.76 million in 2004. Find a formula for the numbe

Salsk061 [2.6K]

Answer:

N(t) = 0.188t + 22.76

Step-by-step explanation:

Number of licensed drivers in 2004 = 22.76 million

Number of licensed drivers in 2009 = 23.7 million

Number of licensed drivers, N as a function of t since year 2004 ;

General form of a linear function :

y = mx + c

c = intercept ; m = slope

Intercept c = value of y ; when x = 0

Here, population after uerssmmx,

Hence,

In 2004 ;

22.76 = mx + c

x = 0

22.76 = c

Number in 2009

x = number of yesrs after 2004 ; x = 2000 - 2004 = 5years

We can find the slope :

y = m*5 + 22.76

y = 23.7 in 2009

23.7 = 5m + 22.76

23.7 - 22.76 = 5m

m = 0.94 / 5

m = 0.188

Hence, the linear function can be written as :

N(t) = 0.188t + 22.76

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3 years ago

the midpoint of a horizontal line segment is at x=1 if the length of the line segment is 10.5. what absolute value equation coul

egoroff_w [7]

Answer: -4.25 ≤ x ≤ 6.25

Step-by-step explanation:

The midpoint of a segment is located at the same distance of each of the endpoints of the segment.

The midpoint is at x = 1.

The length of the segment is 10.5, if we divide it by two we have:

10.5/2 = 5.25

Now, if we want the endpoints to be at the same distance of the midpoint, then the endpoints will be:

Xmax = midpoint + 5.25

Xmin = midpoint - 5.25

Then the extremes are:

Xmax = 1 + 5.25 = 6.25

Xmin = 1 - 5.25 = -4.25

Then this segment can be written as:

Xmin ≤ x ≤ Xmax

-4.25 ≤ x ≤ 6.25

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3 years ago