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Sladkaya [172]
3 years ago
8

Darla measured the length of 4 ants in science class they were 1/2 inch 3/5 inch,1/4 inch and 3/10 inch long.What is the differe

nce between the two shortest ants and the two longest ants?
Mathematics
1 answer:
stiks02 [169]3 years ago
5 0

Convert them to have the same denominator then subtract

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Given the function () = $
elena-s [515]

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is  f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

<h3>The inverse of the function?</h3>

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4


Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through  by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

<h3>Sum of arithmetic series</h3>

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

<h3>The common ratio of the sequence</h3>

Here, we have:

T11  = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2


Read more about sequence at:

brainly.com/question/7882626

#SPJ1

6 0
2 years ago
What the area of the triangle!<br><br><br> need help with these question would mean a lot
zloy xaker [14]
Heyy I don’t think your pictures are loading it just shows grey
3 0
3 years ago
Brian flips a fair coin 3 times. What is the probability of getting exactly 2 tails?
sammy [17]

Answer:

3/8

Step-by-step explanation:

The possible outcomes

TTT TTH THT THH  HHH HHT HTH HTT  = 8 outcomes

There are TTH THT HTT  3 with exactly two tails

P ( exactly 2 tails) = 3/8

7 0
3 years ago
Read 2 more answers
Y+4=2 what is the answer for y
stepladder [879]

Answer:

y = -2

Step-by-step explanation:

y + 4 = 2

y = 2 - 4

y = -2

8 0
3 years ago
Read 2 more answers
Two types of sandwiches were made for a tea party. 55% of the sandwiches were cheese sandwiches and the rest were chicken sandwi
Helen [10]

"To solve this problem, the formula can be used

I = P / T

Where I is the fraction of the sample

P is the amount of the sample

T is the total amount of sample

Since P = 252 chicken sandwiches and I = 0.55

And solve for T

T = 252 / 0.52

T = 458 sandwiches in total"

hope this helps


7 0
3 years ago
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