How many Liters of a liquid can be held in a barrel

FIFTY POINTS!! Please help! I'll give brainliest

melomori [17]

Answer:

4851 ways

Step-by-step explanation:

The fish have 3 choices. They can make it above, below, or though the pipe. Keep in mind there are 100 fish total:

group 1 + group 2 + group 3 = 100

If we keep group 3 (the fish that swim below the pipe) constant, say 1, and increment the other two (group 2 starting off at 1) we find 98 possibilities.

98 + 1 + 1 = 100,

97 + 2 + 1 = 100,

96 + 3 + 1 = 100

. . . 98 possibilities

Now we take group 1 as one greater (1 + 1 = 2) and then start incrementing group 2 starting from 1 as done before. So 97 + 2 + 1 = 100. Followed by 96 + 3 + 1, 95 + 4 + 1...97 possibilities

If we continue this pattern, we have 98 + 97 + 96... + 1 total possibilities to partition this school of fish.

98 + 97 + 96... + 1,

Sum = n(n + 1)/2 = 98(98 + 1)/2 = 98(99)/2 = 4851

8 0

3 years ago

1. Create a symbolic form for each of the functions described below.

agasfer [191]

Answer:

a) f(x) = -5/2x +50

b) f(x) = 50·0.90^x

c) f(x) = 8/3x -30

d) f(x) = 10·1.15^x

Step-by-step explanation:

Apparently, you're studying linear and exponential functions. The general form of a linear function in "slope-intercept" form is ...

f(x) = mx + b

where m is the slope (rate of change of output with respect to input), and b is the "output-intercept", the function value for an input of zero.

__

The general form of an exponential function is ...

f(x) = a·(1 +r)^x

where "a" is the "output-intercept", the function value for an input of zero, and r is the fractional change for a unit change in input, x. Here, you're given r as a percentage. It will be positive when output increases with input, and it will be negative when output decreases with input.

__

Using the above function prototypes in the given scenarios, we have ...

a. A linear function with b=50, m=-10/4 = -5/2, so the function is ...

f(x) = -5/2x +50

__

b. An exponential function with a=50, r=-0.10, so the function is ...

f(x) = 50·(1 -0.10)^x

f(x) = 50·0.90^x

__

c. A linear function with b=-30 and m = 16/6 = 8/3, so the function is ...

f(x) = 8/3x -30

__

d. An exponential function with a=10 and r=+0.15, so the function is ...

f(x) = 10·1.15^x

_____

Comment on functions with percentage change

You need to be a little bit careful with percentage change in a function. There are some scenarios where the rate of change in a linear function is described using percentages. For example, one might say that a car depreciates linearly, and has lost 40% of its value in the first 3 years. Then the rate of change is -13.33% of its original value each year.

Percentages are always in relation to some base value. If that base value is changing with each percentage change, the function is exponential. If that base value remains constant, then the function is linear.

4 0

3 years ago

What is the area of a sector with a central angle of pi/3 radians and a diameter of 12.4m

stich3 [128]

Answer:

see explanation

Step-by-step explanation:

The area (A) of the sector of a circle is

A = area of circle × fraction of circle

= πr² × $\frac{\frac{\pi }{3} }{2\pi }$

diameter = 12.4 ⇒ r = 6.2, thus

A = π × 6.2² × $\frac{1}{6}$

= π × 38.44 × $\frac{1}{6}$

= $\frac{38.44\pi }{6}$ ≈ 20.13 m² ( to 2 dec. places )

5 0

3 years ago

Quiz Time..... 2² + 4³ × 4³ ? Use explanation!

Anna71 [15]

(2 x 2) + (4 x 4 x 4) x (4 x 4 x 4) =
4 + 64 x 64 =
4 + 4096 =
4100

8 0

3 years ago

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which algebraic expression is a polynomial with a degree of 4? a: 5x4 b: x5 – 6x4 14x3 x2 c :9x4 – x3 – d:2x4 – 6x4

dybincka [34]

Answer: the option C. c) 9x⁴– x³– ...

Explanation:

1) A polynomial of one variable is an expression of the kind:

$a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0$

2) The order of the polynomial is the highest exponent of the variable, this is n

3) When the expression has one term it is called a monomial, when the expression has two terms it is called a binomial, when the expression has 3 terms it is called a trinomial.

Usually expressions of that kind with two or more terms are referred as polynomial, but one term is referred as monomial.

4) For the given expressions you have:

a) 5x⁴: it is a monomial (one term), which is usually not referred as polynomial properly.

b) x⁵ – 6x⁴ + 14x³ + x²: it is a polynomial with degree 5 (the highest power).

c) 9x⁴– x³– ... : altough the expression is incomplete, assuming that the next terms are monomials with degree less than 4, then this is a polynomial with degree 4, and is the right answer choice.

d) 2x⁴ – 6x⁴: since both terms have the same power, they can be simplified into one term, - 4x⁴, and it is a monomial.

7 0

3 years ago

Read 2 more answers