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3 years ago

The decimal equivalent of 5/3 is a repeating decimal

Mathematics

1 answer:

Klio2033 [76]3 years ago

3 0

Answer:

1.6666666666666666

Step-by-step explanation:

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Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

Step-by-step explanation:

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

Step-by-step explanation:

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

Step-by-step explanation:

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

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2 years ago

The value of x is . I cant find any answers on this

GenaCL600 [577]

The angle that is next to 9x should be 180 - 9x because it is a straight angle.

Since there are 180 degrees in an angle we can add up the values to 180 and solve for x.

180- 9x + 5x + 9 + x = 180
-3x = -9
x = 3

Hope this helped!

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What is the selling price of a set of scrubs if the markup is 80% of the cost, and the cost is $37.99?

attashe74 [19]

Answer:

Discount = Original Price x Discount %/100

Discount = 37.99 × 80/100

Discount = 37.99 x 0.8

You save = $30.39

Final Price = Original Price - Discount

Final Price = 37.99 - 30.392

Final Price = $7.60

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Danelle and Jim Baraja have obtained a $70,000 mortgage loan at an annual interest rate of 6.00 for years. What is the monthly p

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Total Paid:$147,060.36
Monthly payment $408.50
Total Interest Paid $77,060.36
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2 years ago

What are the slope and y-intercept -3x-8y=10

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The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

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The decimal equivalent of 5/3 is a repeating decimal​

The decimal equivalent of 5/3 is a repeating decimal