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Brums [2.3K]
3 years ago
12

Mathematics Inclined Week #1: Difficult Category

Mathematics
1 answer:
Whitepunk [10]3 years ago
4 0
Let n=1. Then the statement says

1(1!)=1
(1+1)!-1=2!-1=2-1=1

so it holds for the base case.

Assume it holds for n=k, i.e. that

1(1!)+2(2!)+3(3!)+\cdots+k(k!)=(k+1)!-1

and use this to show it holds for n=k+1. You have

1(1!)+2(2!)+\cdots+k(k!)+(k+1)(k+1)!=(k+1)!-1+(k+1)(k+1)!
=(k+1)!(1+k+1)-1
=(k+1)!(k+2)-1
=(k+2)!-1

which is what you needed to show, so the statement is true.
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Which equation best represents a trend line for the scatter plot?
kvasek [131]
Y = (-3/7)x + 4

Looking at the graph, you can see the trend line plotted. And conveniently, there are a couple of points on the trend line that are indicated. Those points being (0,4) and (7,1). The equation of a line in slope intercept form is:y = ax+b

Looking at the points available, the point (0,4) already gives us the y intercept since x is equal to 0. So our equation becomes:
y = ax + 4

Now we need to determine a which is the slope. The slope is the change in y divided by the change in x. So let's do that
(1-4)/(7-0) = -3/7

And now our equation becomes:
y = (-3/7)x + 4

And given formatting issues, the first option available is the correct one.
3 0
3 years ago
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How do you get the answer to 4x+10=-26
s2008m [1.1K]
4x = -36  Subtract 10 from both sides
x = -9  Divide by 4 on both sides
6 0
3 years ago
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Identify the equation that translates y=ln(x) five units down.
kari74 [83]

We are given equation: y=ln(x) .

And translation is 5 units down.

We know the rule of transformation f(x) = y + k, if k is greater than 0 it would move up or if k is less than 0, it would move down.

For the given translation 5 unit down, 5 should be less than 0.

Number less than 0 are negative numbers.

So, we need to add -5 in the given function to ln(x).

So, we would get the final equation for five units down as

y =ln(x) - 5.

6 0
3 years ago
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A bag contains 20 slips of paper Individually numbered. If a slip of paper and a letter in the word PENNSYLVANIA is chosen at ra
Soloha48 [4]

Answer:

P(M4\ n\ V) = 2.083\%

Step-by-step explanation:

Given

Paper = 20 slips

Word: PENNSYLVANIA

Required

Determine P(Multiple of 4 and V)

The sample size of the 20 slips is:

n(S) = 20

The outcomes of multiples of 4 is:

M4= \{4,8,12,16,20\}

n(M4) = 5

So, the probability of multiples of 4 is:

Pr(M4) = \frac{5}{20}

Pr(M4) = \frac{1}{4}

The sample size of PENNSYLVANIA is:

n(S) = 12

The outcome of V is:

n(V) = 1

So, the probability of V is:

P(V) = \frac{1}{12}

So, the required probability is: P(Multiple of 4 and V)

P(M4\ n\ V) = P(M4) * P(V)

P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}

P(M4\ n\ V) = \frac{1}{48}

P(M4\ n\ V) = 0.02083

Express as percentage

P(M4\ n\ V) = 0.02083 * 100\%

P(M4\ n\ V) = 2.083\%

4 0
3 years ago
What is the value of i 97 – i?<br> –i<br> 0<br> –2i<br> i Superscript 96
Valentin [98]

<em>The question is not clearly readable, but I'm assuming the expression which makes more sense, so you can have a clue</em>

Answer:

i^{97}-i=0

Step-by-step explanation:

<u>Powers of The Imaginary Unit</u>

The imaginary unit i is defined as

i=\sqrt{-1}

The first powers of i are

i^0=1

i^1=i

i^2=(\sqrt{-1})^2=-1

i^3=i.i^2=-i

i^4=i^2.i^2=1

And so on the cycle repeats every four numbers. To find the value of i^{96} we can find the remainder of 96/4=0. So i^{96}=i^0=1

The given expression is

i^{97}-i

Factoring

i(i^{96}-1)

Since i^{96}=1

=i(1-1)=0

The required value is 0

6 0
3 years ago
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