MATHEMATICS HIGH SCHOOL

A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK is a different code from BAIK.)The size of the sample space is . The probability that the first three letters of the four-letter code are vowels is?

Answers

Answer 1

Answer:

Answer: The size of the sample is 840.

The probability that the first three letters of the four-letter code are vowels is $=(1)/(35)$

Step-by-step explanation:

Th total number of letters given to form code of 4 letters = 7

Since, the order of the letters in the code matters, which means there is no repetition.

The total number of ways to form the code size = $7*6*5*4=840$

Therefore, The size of the sample is 840.

Since, there are 3 vowels and rest of 4 letters are consonant.

The number of ways to form code such that the first three letters of the four-letter code are vowels = $3*2*1*4=24$

The probability that the first three letters of the four-letter code are vowels is

= $(24)/(840)=(1)/(35)$

Answer 2

Answer:

The probability that the first three letters of the four-letter code are vowels is 1/35 and the size of the sample is 840.

What is the explanation for the above?

Step 1 - Determine the sample size.

It is to be noted that the total number of letters given to form code of 4 letters = 7

Given that the order of the letters in the code matters, which means there is no repetition; hence,

The total number of ways to form the code size = 7 x 6 x 5 x 4 = 840

Thus, the size of the sample is 840.

Step 2 - Solve for the Probability

Given that there are 3 vowels and rest of 4 letters are consonant.

The number of ways to form code such that the first three letters of the four-letter code are vowels

= 3 x 2 x 1 x 4

= 24

Hence, the probability that the first three letters of the four-letter code are vowels is

= 24/840

= 1/35

Learn more about probability at;
brainly.com/question/24756209
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What is the coefficient of the variable in the expression 4 − 3x − 7 + 6?

Answers

Answer:

the coefficient of the variable in the given expression is, -3

Step-by-step explanation:

Coefficient states that a number which is used to multiply a variable.

For example:

here, y is the variable and 4 is the coefficient.

As per the statement:

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Wade's grandmother gave him $100 for his birthday. Wade wants to save his money to buy a new MP3 player that cost $275. Each month, he adds $25 to his MP3 savings. Write an equation in slope-intercept form for x, the number of months that it will take Wade to save $275

Answers

Answer:

The answer is:

275 = 25X + 100

Step-by-step explanation:

1.The equation for the slope- intercept is:

y = mx + b

2. Recognize and value variables

x = number of months

y = the expected range to arrive

m = is the amount Wade earns per month

b = the amount of money saved.

3. Solve the equation for X which is the unknown.

275 - 100 = 25X

175 / 25 = X

X = 7

4. . Show the result

275 = 25(7) + 100

275 = 275

5. Wade will take 7 months to buy your MP3 if he saves 25 for each month.

7 months because after the 100 dollars u add u 25 7 times to get 275

What is the first step of the following division problem?(8x^3 – x^2 + 6x + 7) ÷ (2x – 1)

A. Divide 8x^3 by 2x.
B. Divide 2x by 8x^3.
C. Divide 6x by 2x.
D. Divide 2x by 6x.

Answers

c. divide 6x by 2x, because you have to put the same variables together.

Given AD || GJ. Refer to the figure and provide an appropriate name for BCF and GHF.A. alternate interior angles
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Answers

Answer:

C. Corresponding angles

Step-by-step explanation:

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Which value is the eighth term in the sequence: an= - 1/125 (5^n-1)?-3125
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Answers

Hello,

Answer C

$a_(8)=-(5^(8-1))/(125)=-625$

Explain the derivation behind the derivative of sin(x) i.e. prove f'(sin(x)) = cos(x)How about cos(x) and tan(x)?

Answers

1.

$f'(\sin x) = \lim_(h \to 0) (f(x+h) - f(x))/(h) = \lim_(h \to 0) (\sin(x+h) - \sin(x))/(h) = \n \n = \lim_(h \to 0) (2 \sin( (x+h - x)/(2)) \cdot \cos( (x+h+x)/(2)) )/(h) = \lim_(h \to 0) (2 \sin( (h)/(2)) \cos( (2x+h)/(2) ) )/(h) = \n \n = \lim_(h \to 0) [ (\sin( (h)/(2)) )/( (h)/(2) ) \cdot \cos ((2x+h)/(2)) ] = \lim_(h \to 0) [1 \cdot \cos( (2x+h)/(2) ) ] =$

$= \cos( (2x)/(2)) = \boxed{\cos x}$

2.

$f'(\cos x) = \lim_(h \to 0) (f(x+h) - f(x))/(h) = \lim_(h \to 0) (\cos(x+h) - \cos(x))/(h) = \n \n = \lim_(h \to 0) (-2 \sin ( (x+h+x)/(2)) \cdot \sin ( (x+h-x)/(2)) )/(h) = \lim_(h \to 0) (-2 \sin ( (2x+h)/(2)) \cdot \sin ( (h)/(2)) )/(h) = \n \n = \lim_(h \to 0) (-2 \sin ( (2x+h)/(2)) )/(2) \cdot (sin( (h)/(2)) )/( (h)/(2) ) = \lim_(h \to 0) -\sin( (2x+h)/(2)) \cdot 1 =$

$= -\sin( (2x)/(2)) = \boxed{\sin x }$

3.

$f'(\tan) = \lim_(h \to 0) (f(x+h) - f(x))/(h) = \lim_(h \to 0) (\tan(x+h) - \tan(x))/(h) = \n \n = \lim_(h \to 0) ( (\sin(x+h-x))/(\cos(x+h) \cdot \cos(x)) )/(h) = \lim_(h \to 0) ( (\sin(h))/( (\cos(x+h-x) + \cos(x+h+x))/(2) ) )/(h) =$

$= \lim_(h \to 0) ( (\sin(h))/(\cos(h) + \cos(2x+h)) )/( (1)/(2)h ) = \lim_(h \to 0) (\sin(h))/( (1)/(2)h \cdot [\cos(h) + \cos(2x+h)] ) = \n \n = \lim_(h \to 0) (\sin(h))/(h) \cdot (1)/( (1)/(2) \cdot (\cos(h) + cos(2x+h) ) = 1 \cdot (1)/( (1)/(2) \cdot (1+ cos(2x) ) = (2)/(1 + 2 \cos^(2) - 1 ) = \n \n = (2)/(2 \cos^(2) x) = \boxed{ (1)/(\cos^(2)x) }$

4.

$f'(\cot) = \lim_(h \to 0) (f(x+h) - f(x))/(h) = \lim_(h \to 0) (\cot(x+h) - \cot(x))/(h) = \n \n = \lim_(h \to 0) ( (\sin(x - x - h))/(\sin (x+h) \cdot \sin (h)) )/(h) = \lim_(h \to 0) ( (\sin(-h) )/( (\cos(x+h-x) - \cos(x+h+x))/(2) ) )/(h) =$

$= \lim_(h \to 0) ( (-\sin(h))/(\cos(h) - \cos(2x+h)) )/( (1)/(2)h ) = \lim_(h \to 0) ( - \sin(h))/( (1)/(2)h \cdot [\cos(h) - \cos(2x+h)] ) = \n \n = \lim_(h \to 0) (- \sin (h))/(h) \cdot (1)/( (1)/(2) \cdot [\cos(h) - \cos(2x+h)] ) = -1 \cdot (2)/(1 - cos(2x)) = \n \n = - (2)/(1 -1 + 2 \sin^(2)x) = - (2)/(2 \sin^(2) x) = \boxed{- (1)/(\sin^(2) x) }$

I posted an image instead.

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