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Oksanka [162]
3 years ago
5

in a multiple choice test there are 10 questions. each question has 5 choices how many ways can they complete the test no two co

nsecutive answers
Mathematics
1 answer:
klio [65]3 years ago
5 0

Answer:

1310720

Step-by-step explanation:

Given,

Total number of questions = 10,

Number of choices = 5,

If there are no two consecutive answers,

That is, if we have options a, b, c, d and e for each question,

Then, a could not be the answer of two consecutive questions,

We could pick 1 out of 5 answers for the first question and then for the remaining 9 questions we have only have 4 choices,

Hence, the total number of ways = 5 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

=5\times 4^9

=1310720

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Answer:

140 inches

Step-by-step explanation:

one decagon has 10 sides

14*10= 140

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I'll. ark brainlyest and give a lot of points for answering this right ​
valina [46]

Answer:

\displaystyle T'(  2,4)

\displaystyle U'( 1,1)

\displaystyle S' ( 3,2)

Step-by-step explanation:

we current vertices of the given triangle

  • \displaystyle T( - 2,4)
  • \displaystyle U( - 1,1)
  • \displaystyle S ( - 3,2)

remember that,

\rm\displaystyle(x,y) \xrightarrow{ \rm reflection \:  over \: y - axis}( -  x,y)

so we obtain:

\rm\displaystyle \: T( - 2,4) \xrightarrow{ \rm reflection \:  over \: y - axis}T'(  2,4)

\rm\displaystyle \: U( - 1,1) \xrightarrow{ \rm reflection \:  over \: y - axis}U' ( 1,1)

\rm\displaystyle S( - 3,2) \xrightarrow{ \rm reflection \:  over \: y - axis}S'( 3,2)

6 0
3 years ago
A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground. How high is the top of
-Dominant- [34]

Answer:

63.6 feet

Step-by-step explanation:

  • sin (45)=\frac{x}{90}
  • x=90 sin (45)
  • x=45\sqrt{2}
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2 years ago
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yaroslaw [1]

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8 0
3 years ago
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters
natita [175]

Answer:

0.0479 = 4.79% probability that fewer than 11 of them will vote

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.

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 combinations 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.

70% of all eligible voters will vote in the next presidential election.

This means that p = 0.7

20 eligible voters were randomly selected from the population of all eligible voters.

This means that n = 20

What is the probability that fewer than 11 of them will vote?

This is:

P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)

In which

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

P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308

P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120

P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039

P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010

P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002

P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0

The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then

P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479

0.0479 = 4.79% probability that fewer than 11 of them will vote

8 0
3 years ago
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