Mathematics, 08.01.2020 06:31 tchou8306

Acode 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 . the probability that the first three letters of the four-letter code are vowels .

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Answer from: sipstick9411

$\dfrac{27}{343}$

Step-by-step explanation:

we are given 7 alphabets out of which we need to choose 4 alphabets in order to make a code of 4 letters.

Hence the size of the sample space is: 7^4

since we have to fill in 4 places with the help of these 7 letters.

so in first place we can select one out of any 7 letters, similarly for the second place as it is not mentioned that repetition is not allowed and the same can be done for third and fourth place.

Hence size of sample space is: $7\times7\times7\times7=7^4$

Now the probability of an event is given by:

Probability=(Number of favourable outcomes)/(Total number of outcomes)

Hence here the total number of outcomes= 7^4

Total number of favourable outcomes=outcomes that the first three letters are vowels= $3\times3\times3\times7$ (since in the first place we have three choices for a vowel{A,I,0} similarly for second and third place and in the fourth place any one of the 7 letters could come)

Hence the probability(P) that the first three letters of the four-letter code are vowels is given by:

$P=\dfrac{3\times3\times3\times7}{7\times7\times7\times7}=\dfrac{3\times3\times3}{7\times7\times7}=\dfrac{27}{343}$

Hence, the Probability is: $\dfrac{27}{343}$

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

the answer is 489

step-by-step explanation:

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