Answer:the total number of horses in the herd is 36
Step-by-step explanation:
Let x represent the total number of horses in the herd.
One fourth of the herd of horses was seen in the forest. This means that the number of horses that was seen in the forest would be
1/4 × x = x/4
Twice the square root of the herd had gone to the mountain slopes. This means that the number of horses that had gone to the mountain slopes would be
2 × √x = 2√x
Three times five horses remained on the riverbank. This means that the number that remained would be
3 × 5 = 15
Therefore
x/4 + 2√x + 15 = x
x - x/4 - 15 = 2√x
(4x - x - 60)/4 = 2√x
(3x - 60)/4 = 2√x
Cross multiplying,
3x - 60 = 8√x
Squaring both sides of the equation, it becomes
(3x - 60)(3x - 60) = 64x
9x² - 180x - 180x + 3600 = 64x
9x² - 360x - 64x + 3600 = 0
9x² - 424x + 3600 = 0
Applying the quadratic equation
x = (- b ±√b² - 4ac)/2a
x = ( - - 424 ± √-424² - 4(9 × 3600)/2 × 9
x = (424 ± √179776 - 129600)/18
x = (424 ±√50176)/18
x = (424 + 224)/18 or
x = (424 - 224)/18
x = 36 or x = 11.11
the number of horses must be whole number. Therefore, the number of horses is 36
Answer:
1/7776.
Step-by-step explanation:
The probability of rolling a six in 1 throw = 1/6.
Rolling a 6 5 times in a row = (1/6)^5
= 1/7776.
The probability is multiplied because each roll is independent from other rolls.
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.
https://www.coolmath4kids.com/math-help/fractions/adding-and-subtracting-fractions-different-denominators
For example:
1/2 + 1/3
We need to find something called the least common denominator (LCD)... It's really just the LCM of our denominators, 2 and 3.
The LCM of 2 and 3 is 6. So, our LCD 6.
We need to make this our new denominator...
Change the 1/2:
1 x 3 over 2 x 3 = 3/6
Change the 1/3:
1/2 + 1/3 = 3/6 + 2/6
Now we can do it!
(3+2)/6 = 5/6
2³ and 3²
2² and 3³
lowest powers of each common factor is gcf
2² · 3²
Answer:
Step-by-step explanation:
Given
Required
Determine the 6th term
This is calculated as:
Where
Substitute , and
