The correct answer between all the choices given is the third
choice or letter C.
Each question has four choices, then the probability to guess a correct answer is
![p= \frac{1}{4}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B1%7D%7B4%7D%20)
and the probability to select incorrect choice is
![q=1-p=1- \frac{1}{4} = \frac{3}{4}](https://tex.z-dn.net/?f=q%3D1-p%3D1-%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20)
.
You have a 5-question multiple-choice test, then n=5. The <span>probability that you will guess exactly three out of five questions correctly is </span>
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</span><span>
![C_n^kp^nq^{n-k}=C_5^3p^3q^{5-3}= \dfrac{5!}{3!\cdot 2!} \left( \dfrac{1}{4} \right)^3\left( \dfrac{3}{4} \right)^2=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2} \cdot \dfrac{9}{1024} =](https://tex.z-dn.net/?f=C_n%5Ekp%5Enq%5E%7Bn-k%7D%3DC_5%5E3p%5E3q%5E%7B5-3%7D%3D%20%5Cdfrac%7B5%21%7D%7B3%21%5Ccdot%202%21%7D%20%5Cleft%28%20%5Cdfrac%7B1%7D%7B4%7D%20%5Cright%29%5E3%5Cleft%28%20%5Cdfrac%7B3%7D%7B4%7D%20%5Cright%29%5E2%3D%5Cdfrac%7B1%5Ccdot%202%5Ccdot%203%5Ccdot%204%5Ccdot%205%7D%7B1%5Ccdot%202%5Ccdot%203%5Ccdot%201%5Ccdot%202%7D%20%5Ccdot%20%5Cdfrac%7B9%7D%7B1024%7D%20%3D)
</span>
![= \dfrac{90}{1024} = \dfrac{45}{512}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B90%7D%7B1024%7D%20%3D%20%5Cdfrac%7B45%7D%7B512%7D%20)
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Answer: hewo, there! your answer is below
x= -5/4
or x= 8
Step-by-step explanation:
step 1: Subtract 27x+40 from both sides.
4x2−(27x+40)=27x+40−(27x+40)
4x2−27x−40=0
Step 2: Factor left side of equation.
(4x+5)(x−8)=0
Step 3: Set factors equal to 0.
4x+5=0 or x−8=0
hope this helps you
have a great Day
Plz makr branilest
Answer:
sinΘ = ![\frac{12}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B13%7D)
Step-by-step explanation:
sinΘ =
=
= ![\frac{12}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B13%7D)