Hello :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a <span>≠ 0) is :
</span><span>Δ = b² -4ac
1 ) </span>Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ <span>< 0 : no reals solutions
in this exercice : x² = 5-x
x² +x-5 = 0 .... a =1 b= 1 c=-5
calculate </span>Δ..................................
Answer:
Range = 30 inches
Mid Range = 55 inches
Step-by-step explanation:
Range = largest number - smallest number
70 - 40 = 30 inches
Mid range (largest number + smallest number) / 2
70 + 40 = 110 ÷ 2 = 55
Answer:
hope this help
Step-by-step explanation:
sorry..I send pic instead..hope this help
Answer:
90% confidence interval -> {0.4529, 0.5871}
Step-by-step explanation:
<u>Check conditions for a 1-proportion z-interval:</u>
np>10 -> 150(0.52)>10 -> 78>10 √
n(1-p)>10 -> 150(1-0.52)>10 -> 72>10 √
Random sample √
n>30 √
For a 90% confidence interval, the critical value is z=1.645
The formula for a confidence interval is:
CI = p ± z√[p(1-p)/n]
<u>Given:</u>
p = 78/150 = 0.52
n = 150
z = 1.645
Therefore, the 90% confidence interval is:
CI = 0.52 ± 1.645√[0.52(1-0.52)/150] = {0.4529, 0.5871}
Context: We are 90% confident that the true proportion of all voters who
plan to vote for the incumbent candidate is contained within the interval
Answer:
2πr³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ← r is the radius and h the height
Here h = 2r, hence
V = πr² × 2r = 2πr³