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2 years ago

9

Translate the sentence into an inequality. Twice the difference of a number and 6 is at most – 29. Use the variable w for the un

known number.

2 answers:

rusak2 [61]2 years ago

5 0

Answer:

2w+6> -29

Step-by-step explanation:

basically 2w+6 is less than or equal to -29. sorry I dont have the actual sign for less than or equal to. So just put a line under the arrow.

____ [38]2 years ago

3 0

Answer:2w-6<-29

Step-by-step explanation:

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Helppp? dont guess. pleaseeeee

N76 [4]

Answer:

12/100

Step-by-step explanation:

7 0

2 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution 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.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

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

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

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

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

So

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

How do I solve this finding the first four of the sequence?

nexus9112 [7]

Answer:

- 7, - 3, 1, 5

Step-by-step explanation:

Using the recursive rule and a₁ = - 7, then

a₂ = a₁ + 4 = - 7 + 4 = - 3

a₃ = a₂ + 4 = - 3 + 4 = 1

a₄ = a₃ + 4 = 1 + 4 = 5

The first four terms are - 7, - 3, 1, 5

4 0

3 years ago

I need help with algebra 2 pleasee

Aleonysh [2.5K]

Answer:

$x=\pm \sqrt{21}/7$

Step-by-step explanation:

We can add 9 to both sides of the equation to get $21x^2=9$ .

We can divide both sides of the equation by 21 to get $x^2=9/21$ .

We take the square root of both sides of the equation to get $x=\pm \sqrt{9/21}$ .

However, that isn't in the form we need.

We know that $\sqrt{9/21}=\sqrt{9}/\sqrt{21}=3/\sqrt{21}=3\sqrt{21}/(\sqrt{21}*\sqrt{21})=3\sqrt{21}/21=\sqrt{21}/7$

so the answer is really $x=\pm \sqrt{21}/7$ and we're done!

5 0

3 years ago

Please help me asap..

Andreyy89

Answer:

I think the answer iss ( -∞ , -1] ∪ ( -1/2, +)

Step-by-step explanation:

(ﾉ◕ヮ◕)ﾉ*:・ﾟ✧ ✧ﾟ・: *¯\_(ツ)_/¯

6 0

3 years ago