What is the slope of a line that passes thru -14,13) and 7,0)

Rena spent 6 days reading her book completing the same fraction of the book each day if she had a total of 8/9 of her book after

Artyom0805 [142]

Answer:

The fraction of the book that Rena read every day is $\frac{4}{27}$

Step-by-step explanation:

Rena spent 6 days reading her book completing the same fraction of the book every day and you want to know the fraction of the book she read each day. Knowing that Rena had a total of 8/9 of her book read after 6 days, then you simply divide the total amount of the book read during those days by 6, the number of days:

$\frac{8}{9}$ ÷6

To divide a fraction by a whole number, you must convert the whole number into a fraction, finding the reciprocal of that fraction, and multiply it by the first fraction. That is, you must find the reciprocal of the number that is after the division symbol; and then you multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol). Remember that to find the reciprocal of a number, you simply have to change the numerator and denominator of the number.

Since 6 can be considered to be a fraction equal to $\frac{6}{1}$ , by inverting the number, then you get $\frac{1}{6}$

Then:

$\frac{8}{9}$ ÷6= $\frac{8}{9} *\frac{1}{6}$

Now you multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final solution.

$\frac{8}{9}$ ÷6= $\frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}$

Finally, simplifying the fraction:

$\frac{8}{9}$ ÷6= $\frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}=\frac{4}{27}$

So:

$\frac{8}{9}$ ÷6= $\frac{4}{27}$

The fraction of the book that Rena read every day is $\frac{4}{27}$

3 0

3 years ago

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

3 years ago

Y = -x+5y=−x+5y, equals, minus, x, plus, 5

Serga [27]

The answer is D
Hope this hel

6 0

3 years ago

A fruit juice company includes 1.872 ounces of orange juice in a 6.65-ounce bottle of a mixed fruit

BigorU [14]

Answer:

4.778 ounces

Step-by-step explanation:

Given that:

Ounces of orange juice in mixed fruit juice = 1.872

Ounces of mixed fruit juice = 6.65 ounces

Ounces of Mixed fruit juice that is not orange juice :

(Ounces of mixed fruit juice - Ounces of orange juice)

(6.65 - 1.872) ounces

= 4.778 ounces

6 0

2 years ago

Evaluate the expression three squared times five cubed.

Margaret [11]

Answer:

The expression is equivalent to 1,125

Step-by-step explanation:

Arithmetic Expressions

It's given the word expression: "three squared times five cubed". It can be written in math form as:

$3^2\times 5^3$

Expanding the powers:

$3^2\times 5^3=3*3*5*5*5 = 1,125$

The expression is equivalent to 1,125

7 0

3 years ago