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Sveta_85 [38]
3 years ago
13

If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of g

etting at least 1 correct? if a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing?
Mathematics
1 answer:
QveST [7]3 years ago
4 0
There is a 1/5 chance of getting each question correct.  The probability of getting <em>at least</em> 1 correct is written as such:
<em>P</em>(<em>X</em> ≥ 1) = 1 - <em>P</em>(<em>X</em> = 0) 
This is because the only other option than getting at least one correct is to get nothing correct.
Since there is a 1/5 chance of getting each question correct, there is a 4/5 chance of getting each question wrong:
1 - <em>P</em>(<em>X</em> = 0) = 1 - (4/5)^10 (since there are 10 questions, with a 4/5 chance of missing each one)
= 1 - 0.1073741824 ≈ 0.8926 = 89.26% chance of getting at least one question correct.  Given this probability, it is reasonable to expect to pass by guessing.
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Answer: range= 26, variance= 80 and standard deviation= 8.94

Step-by-step explanation:

Range = highest - lowest

Range = 146 - 120

Range= 26

Let m be mean

M=mean=sum/n

Mean=(120+134+146+127+138+133) / 6

M=798/6

M=133

The standard deviation sample formula:

S.D = sqrt( Summation of |x-m|^2 / n-1)

Let start finding:

|x-m|^2

For 1st: |120-133|^2=169

For 2nd: |134-133|^2=1

For 3rd: |146-133|^2=169

For 4th: |127-133|^2=36

For 5th: |138-133|^2=25

For 6th: |133-133|^2=0

Summation of |x-m|^2 = 400

The standard deviation formula is :

S.D = sqrt( Summation of |x-m|^2 / n-1)

S.D= sqrt(400 / 5)

S.D=sqrt(80)

S.D= 8.94

Variance = (Summation of |x-m|^2 / n-1)

Variance= 400/5

Variance= 80

3 0
3 years ago
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AVprozaik [17]
35.45 rounded to the nearest whole number would be 35.
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3 years ago
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How do I solve polynomials
spin [16.1K]

Answer:

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

Also they can have one or more terms, but not an infinite number of terms.

These are polynomials:

3x

x − 2

−6y2 − ( 79)x

3xyz + 3xy2z − 0.1xz − 200y + 0.5

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5

(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)

 

These are not polynomials

3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)

2/(x+2) is not, because dividing by a variable is not allowed

1/x is not either

√x is not, because the exponent is "½" (see fractional exponents)

 

But these are allowed:

x/2 is allowed, because you can divide by a constant

also 3x/8 for the same reason

√2 is allowed, because it is a constant (= 1.4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

monomial, binomial, trinomial

Variables

Polynomials can have no variable at all

Example: 21 is a polynomial. It has just one term, which is a constant.

Or one variable

Example: x4 − 2x2 + x   has three terms, but only one variable (x)

Or two or more variables

Example: xy4 − 5x2z   has two terms, and three variables (x, y and z)

What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.

For example we know that:

If you add polynomials you get a polynomial

If you multiply polynomials you get a polynomial

So you can do lots of additions and multiplications, and still have a polynomial as the result.

Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.

Example: x4−2x2+x

x^4-2x^2+x  

See how nice and

smooth the curve is?

You can also divide polynomials (but the result may not be a polynomial).

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

4x3-x-3 The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

Example: Put this in Standard Form: 3x2 − 7 + 4x3 + x6

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x6 + 4x3 + 3x2 − 7

You don't have to use Standard Form, but it helps.

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Write the first six terms of the sequence.
butalik [34]

Step-by-step explanation:

1st term = -n²+6

= -(1)²+6

= -1+6

=5

2nd term = -(2)²+6

= -4+6 = 2

3rd term= -(3)²+6

=-9+6 = -3

4th term= -(4)²+6

= -16+6 = -10

5th term = -(5)²+6 = -25+6 = -19

6th term = -(6)²+6 = -36+6 = -30

5,2, -3,-10,-19, -30

optionB

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A dog buried 18 bones in his backyard. On Monday, he dug up 1/2 of his bones. On Tuesday, he dug up another 1/3 of his bones. Ho
Korolek [52]

Answer:

3

Step-by-step explanation:

A dog buried 18 bones

On Monday he dug up 1/2 of the bones

On Tuesday he dug up 1/3 of the bones

= 1/2 × 18

= 9

= 1/3×18

= 6

Therefore the remaining bones still buried in the ground can be calculated as follows

= 9+6

= 15

= 18-15

= 3

Hence 3 bones are still buried in the ground

5 0
2 years ago
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