Answer:0.849185
Step-by-step explanation:
Binomial probability formula we will use:
where,
The computation of the probability will be :
![$P(x \leq 2 ; 5,0.3)=P(x=0 ; 5,0.3)+P(x=1 ; 5,0.3)+P(x=2 ; 5,0.3)+P(x=3 ; 5,0.3)$\\$=\left[\frac{5 !}{5 !(5-0) !}(0.3)^{0}(1-0.3)^{5-0}\right]+\left[\frac{5 !}{5 !(5-1) !}(0.3)^{1}(1-0.3)^{5-1}\right]$$+\left[\frac{5 !}{5 !(5-2) !}(0.3)^{2}(1-0.3)^{5-2}\right]$$++\left[\frac{5 !}{5 !(5-3) !}(0.3)^{3}(1-0.3)^{5-3}\right]$$++\left[\frac{5 !}{5 !(5-4) !}(0.3)^{4}(1-0.3)^{5-4}\right]$\\$=0.1681+0.3601+0.3087+0.006615+0.00567$\\$\Rightarrow 0.849185$](https://tex.z-dn.net/?f=%24P%28x%20%5Cleq%202%20%3B%205%2C0.3%29%3DP%28x%3D0%20%3B%205%2C0.3%29%2BP%28x%3D1%20%3B%205%2C0.3%29%2BP%28x%3D2%20%3B%205%2C0.3%29%2BP%28x%3D3%20%3B%205%2C0.3%29%24%5C%5C%24%3D%5Cleft%5B%5Cfrac%7B5%20%21%7D%7B5%20%21%285-0%29%20%21%7D%280.3%29%5E%7B0%7D%281-0.3%29%5E%7B5-0%7D%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B5%20%21%7D%7B5%20%21%285-1%29%20%21%7D%280.3%29%5E%7B1%7D%281-0.3%29%5E%7B5-1%7D%5Cright%5D%24%24%2B%5Cleft%5B%5Cfrac%7B5%20%21%7D%7B5%20%21%285-2%29%20%21%7D%280.3%29%5E%7B2%7D%281-0.3%29%5E%7B5-2%7D%5Cright%5D%24%24%2B%2B%5Cleft%5B%5Cfrac%7B5%20%21%7D%7B5%20%21%285-3%29%20%21%7D%280.3%29%5E%7B3%7D%281-0.3%29%5E%7B5-3%7D%5Cright%5D%24%24%2B%2B%5Cleft%5B%5Cfrac%7B5%20%21%7D%7B5%20%21%285-4%29%20%21%7D%280.3%29%5E%7B4%7D%281-0.3%29%5E%7B5-4%7D%5Cright%5D%24%5C%5C%24%3D0.1681%2B0.3601%2B0.3087%2B0.006615%2B0.00567%24%5C%5C%24%5CRightarrow%200.849185%24)
The probability that at most 4 are accepted = 0.849185
Answer:
AC = 5 cm
BD = 12.5 cm (3 sf) [or 2 × root 39]
BE = 6.93 cm (3 sf) [or 4 × root 3]
Step-by-step explanation:
CE = 8cm [CE is radius of circle]
AC + 3 = 8
<u>A</u><u>C</u><u> </u><u>=</u><u> </u><u>5</u><u> </u><u>c</u><u>m</u>
BC = 8cm [BC is a radius of circle]
(AC)^2 + (AB)^2 = (BC)^2 [Pythagoras theorem]
25 + (AB)^2 = 64
AB = 6.2450 cm (5 sf) [or root 39]
BD = 2(BA)
= 2(6.2450)
<u>B</u><u>D</u><u> </u><u>=</u><u> </u><u>1</u><u>2</u><u>.</u><u>5</u><u> </u><u>c</u><u>m</u><u> </u><u>(</u><u>3</u><u> </u><u>s</u><u>f</u><u>)</u><u> </u><u>[</u><u>o</u><u>r</u><u> </u><u>2</u><u> </u><u>×</u><u> </u><u>r</u><u>o</u><u>o</u><u>t</u><u> </u><u>3</u><u>9</u><u>]</u>
(BA)^2 + (AE)^2 = (BE)^2 [Pythagoras theorem]
39 + 9 = (BE)^2
<u>B</u><u>E</u><u> </u><u>=</u><u> </u><u>6</u><u>.</u><u>9</u><u>3</u><u> </u><u>c</u><u>m</u><u> </u><u>(</u><u>3</u><u> </u><u>s</u><u>f</u><u>)</u><u> </u><u>[</u><u>o</u><u>r</u><u> </u><u>4</u><u> </u><u>×</u><u> </u><u>r</u><u>o</u><u>o</u><u>t</u><u> </u><u>3</u><u>]</u>
Answer: 3y +2
Step-by-step explanation:
0.5(30) = 0.25(x). Divide each side by 0.25.
60 = x.
1/4 of 60 = 1/2 of 30
