If x+2 is a factor of x^3+6x^2+kx+10, then if we replace x by -2 in the polynomial x^3-6x^2+kx+10, we must get zero:
x=-2→(-2)^3-6(-2)^2+k(-2)+10=0→
-8-6(4)-2k+10=0→
-8-24-2k+10=0
-2k-22=0
Solving for k. Adding 22 both sides of the equation:
-2k-22+22=0+22
-2k=22
Dividing both sides of the equation by -2:
-2k/(-2)=22/(-2)
k=-11
Answer: k = - 11
Answer:
- -1392.09
- -1744.43
- -1636.41
Step-by-step explanation:
using the given integral
calculate: Δx = (12-0) / 8 = 3/2
Xo = 0, f(x) = 
X1 = 3/2 , X2 = 3, X3 = 9/2, X4 = 6, X5 = 15/2, X6 = 9, X7 = 21/2, X8 = 12
Inputting the given values into the Trapezoid rule, midpoint rule and Simpson's rule to approximate the given integral with the specified value of n = 8
Ok so it's a proportion so this fraction is to this fraction. the smaller rectangle has sides 4 and 12. the larger one has 8 and x. so u set it up 4/12=8/x. the 4 and 8 r both the short sides so u want those on top and 12 and x r long sides so those on bottom. since that is not an answer option u can set it up as 8/4=x/12 because u still keep the variables of the same rectangle from being multipled with each other. so answer #2 is correct
Answer:
Step-by-step explanation:
Given that in an investigation of pregnancy-induced hypertension, one group of women with this disorder was treated with low-dose aspirin, and a second group was given a placebo. A sample consisting of 50 women who received aspirin has mean arterial blood pressure 120mmHg and standard deviation 10mmHg; a sample of 42 women who were given the placebo has mean blood pressure 115mmHg and standard deviation 12mmHg.
Population variances are equal

(two tailed test at 5% significance level)
Here x denotes group I and Y group II
N Mean StDev SE Mean
Sample 1 50 120 10 1.4142
Sample 2 42 115 12 1.8516
Pooled std deviation = 10.9565
df=80
Mean difference= 5
Test statistic t = mean diff/std error =
=2.1803
p value = 0.0318
since p <0.05 we reject H0
b) We find p >0.01 hence at 1% significance level we accept H0
This implies that 99% confidence interval contains mean difference =0