Answer:
<h2>
11.2≤
12.8 </h2>
Step-by-step explanation:
Confidence interval for the population mean is expressed by the formula;
CI = xbar ± Z(S/√n) where;
xbar is the sample mean = 12.5
Z is the z score at 99% confidence = 2.576
S is the standard deviation = √variance
S = √2.4 = 1.5492
n is the sample size = 25
Substituting the given values into the formula given above,
CI = 12.5 ± 2.576(1.5492/√25)
CI = 12.5 ± 2.576(0.30984)
CI = 12.5 ± 0.7981
CI = (12.5-0.7981, 12.5+0.7981)
CI = (11.2019, 12.7981)
Hence the 99% confidence interval for the population mean is 11.2≤12.8 (to 1 decimal place)
Answer:
D. (-x+5)^2/9+(y-4)^2/4=1 (I assume there was a mistype)
Step-by-step explanation:
The first step is isolating the sine and cosine functions.
x=5-3cos(t)
x + 3cos(t) = 5
3cos(t) = 5 - x
cos(t) = (5 - x)/3
y=4+2sin(t)
y - 4 = 2sin(t)
(y - 4)/2 = sin(t)
Then, square at both sides of the equal sign
cos²(t) = (5 - x)²/3² = (5 - x)²/9
sin²(t) = (y - 4)²/2² = (y - 4)²/4
Recall the trigonometric identity and replace.
cos²(t) + sin²(t) = 1
(5 - x)²/9 + (y - 4)²/4 = 1
Y=kx
-5=k(15)
-5/15=k
-1/3=k
now,
y=-1/5x
3=-1/5x
3×5=-1(x)
15=-1(x)
multiplying both sides by -1,we get
-15=x
Answer:
27
Step-by-step explanation:
15x-31 = 9x+11
6x-31 = 11
6x = 42
x = 7
15x -31 + 9x + 11 + s = 180
15(7) -31 + 9(7) + 11 + s = 180
105 - 31 + 63 + 11 + s = 180
153 + s = 180
s = 27
Answer:
The three unknown angles X, Y , and Z are:
X = 40, Y = 20, and Z = 120
Step-by-step explanation:
Let's name X the measure of the first angle, Y the measure of the second one, and Z that of the third one.
Then we can create the following equations:
X = 2 Y
Z = 100 + Y
and
X + Y + Z = 180
So we use the first equation and the second one to substitute for the variable X and Z in the thrid equation:
2 Y + Y + (100 + Y) = 180
4 Y + 100 = 180
4 Y = 80
Y = 80/4 = 20
Then X = 40, Y = 20, and Z = 120
