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Jlenok [28]
3 years ago
6

Srinivasa Ramanujan, the great East Indian mathematician, was invited to Cambridge University in England in 1914 by the English

mathematician G. H. Hardy. One day Ramanujan was ill in the hospital, and Hardy came to visit him. Hardy remarked that he had come in taxicab #1729, and said that he thought that this was an entirely uninteresting number. Ramanujan instantly replied, "Oh no! 1,729 is the smallest number that can be written as the sum of two cubes in two different ways."
The table below shows two patterns of numbers. The pattern in the top row represents the counting numbers. The pattern in the second row consists of the cubes of the counting numbers.

Which two pairs of numbers have cubes that add up to 1,729? Because there are two pairs of numbers to find, you should select a total of four numbers from the list below.

A. 8
B. 7
C. 12
D. 11
E. 10
F. 9
G. 1
H. 2
I. 3
J. 4
K. 5
L. 6
Mathematics
2 answers:
ale4655 [162]3 years ago
6 0

Answer:

1,10,9,12 for APEX

Step-by-step explanation:


kotegsom [21]3 years ago
3 0
(12,1):12³+1³=1728+1=1729
(10,9): 10³+9³=1000+729=1729
☺☺☺☺
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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen
noname [10]

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

n = 5, p = 0.93

Calculate P(at least one valve opens).

This is P(X \geq 1)

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

P(X = 0) + P(X \geq 1) = 1

P(X \geq 1) = 1 - P(X = 0)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807

Finally

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193

There is a 99.99998% probability that at least one valve opens.

5 0
3 years ago
Read 2 more answers
Which algebraic expression is equivalent to the expression below? 25/4(5x-4/5)+29
andre [41]

Notice* No options are provided, so I will solve the expression.

Answer:

\frac{125x+96}{4}

Step-by-step explanation:

Step 1: Simplify \frac{4}{5}

Step 2: Rewriting the whole as an Equivalent Fraction

 Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

5x = 5x/1 = 5x * 5/5

<em>Equivalent fraction</em> : The fraction thus generated looks different but has the same value as the whole

<em>Common denominator </em>: The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

dding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5x • 5 - (4)     25x - 4

--------------    =    ---------

5                        5  

Step 3: Simplify 25/4

Rewriting the whole as an Equivalent Fraction :

Adding a whole to a fraction

Rewrite the whole as a fraction using  4  as the denominator :

29 = 29/1 = 29 * 4/4

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

5 • (25x-4) + 29 • 4     125x + 96

---------------------------  =     -----------

4                                             4    

Final result :

 125x + 96

 —————————

     4    

___________

Terms and topics:

  • Dividing exponents
  • Polynomial roots
  • Nonlinear equations
  • Equations which are reducible to quadratic
  • Reducing fractions to lowest terms
7 0
2 years ago
How do you sketch a graph of a function?
Illusion [34]

The graph of a function can be sketched by plotting points.

First and foremost, it is to be determined if the function is odd/even or periodic. Next, we find the x and y intercepts. To sketch a graph of a function, one can start by plotting a few points that lie on the graph using the coordinates given by the function. For example, if the function is y = x², then points (0, 0), (1, 1), and (2, 4) can be plotted by substituting the values of x into the function to find the corresponding values of y.

Subsequent to this, one can connect the points with a smooth curve to form the graph of function. If the function is a straight line, the graph will be a straight line. If the function is quadratic, the graph will be a parabola. The graph may take on a more complicated shape for more complex functions.

Read more about the graph of a function on:

brainly.com/question/26857518

#SPJ4

4 0
1 year ago
Please help me with the question please ASAP ASAP please ASAP help please please ASAP ASAP please ASAP help
musickatia [10]

Answer:

omg someone help asap!1

Step-by-step explanation:

3 0
3 years ago
Della bought a tree sampling that was 2 1/4 feet tall. During the first year, it grew 1 1/6 feet. After two years, it was 5 feet
Pani-rosa [81]

Answer:

tree sampling: 2 1/4ft

through 1 year grown: 1 1/6ft

after two years growing: 5ft

1 1/6 coverted into a decimal is 0.16

0.16 x 32 = 5.12 (5)

not sure if this is right, but hope it helps

6 0
3 years ago
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