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3 years ago

(01.02 LC)Simplify negative 3 and 1 over 9 − negative 8 and 1 over 3.

Mathematics

1 answer:

blsea [12.9K]3 years ago

6 0

As we are given with

$-3\frac{1}{9}-(-8\frac{1}{3})\\\\$

we are supposed to simplify this expression. which can be done as below

$\\=-3\frac{1}{9}+8\frac{1}{3}\\\\=\frac{-28}{9}+\frac{25}{3}\\\\=\frac{-28+75}{9}\\\\=-\frac{47}{9}\\$

$=5\frac{2}{9}$

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You have two parents, four grandparents, eight greatgrandparents, and so forth.

Leviafan [203]

A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or $2^{2}$ ancestors.
In the third generation we have 8 ancestors ot $2^{3}$ ancestors.

We can see that each succesive generation has two times more members. The sum is:
$2+4+8+16+...+ 2^{40}$

To calculate number of ancestors we can use formula for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
 $S= a_{1} * \frac{1- r^{n} }{1-r}$
Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements

For this question:
a1 = 2
r = 2
n = 40
 $S= 2* \frac{1- 2^{40} }{1-2} =2 199 023 255 550$

b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years

c.
Total number of people who have ever lived = $10^{10}$
Number of ancestors in 40 generations = $2.2*10^{12}$

The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.

8 0

3 years ago

7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about quadratic equations:

brainly.com/question/27638369

6 0

2 years ago

Read 2 more answers

On a six-question multiple-choice test there are five possible answers for each question, of which one is correct and four are i

gizmo_the_mogwai [7]

Answer:

Step-by-step explanation:

given that on a six-question multiple-choice test there are five possible answers for each question, of which one is correct and four are incorrect

By mere guessing probability for choosing correct answer = p = 0.2

also each question is independent of the other

Hence if X is the number of correct questions then

X is binomial with p = 0.2 and n = 6

a) being correct on three questions,

= $P(X=3) = 0.08192$

(b) being correct on four questions,

= $P(X=4) = 0.01536$

= $P(x=6) = 0.000064$

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3 years ago

56 times a number minus 13 is equal to 6 less than the number.

Eddi Din [679]

Answer:

Step-by-step explanation:

The steps in the photo above

I hope that is useful for you :)

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3 years ago

POLYGON BASICS (GEOMETRY) PLEASE HELP!!

Vesna [10]

Answer:

Polygons are named according to the number of sides and angles they have. The most familiar polygons are the triangle, the rectangle, and the square. A regular polygon is one that has equal sides. Polygons also have diagonals, which are segments that join two vertices and are not sides.

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3 years ago