Answer:
1) Radius of the cone = 9.5 cm
2) BA = 90.25 π cm²
3) SA = 384.7 π cm²
Step-by-step explanation:
1) Radius of the cone = 9.5 cm
2) Base Area of the cone =
BA = (π)(9.5)²
BA = 90.25 π cm²
3) Surface Area of Cone =
SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)
SA = 9.5π(9.5 + 31)
SA = 9.5π(40.5)
SA = 384.7 π cm²
Answer:
(a) The 29th percentile for the number of chocolate chips in a bag is 1198.65.
(b) The number of chocolate chips in a bag that make up the middle 95% of bags are [1146, 1380].
(c) The inter-quartile range of the number of chocolate chips in a bag of chocolate chip cookies is 157.83.
Step-by-step explanation:
Let the random variable <em>X</em> represent the number of chocolate chips in a bag of chocolate chip cookies.
The random variable <em>X</em> is normally distributed with mean, <em>μ </em>= 1263 and a standard deviation, <em>σ </em>= 117.
(a)
Compute the 29th percentile for the number of chocolate chips in a bag as follows:
P (X < x) = 0.29
⇒ P (Z < z) = 0.29
The value of <em>z</em> for the above probability is, <em>z</em> = -0.55.
Compute the value of <em>x</em> as follows:
Thus, the 29th percentile for the number of chocolate chips in a bag is 1198.65.
(b)
According to the Empirical rule 95% of the normally distributed data lies within 2 standard deviations of the mean.
P (μ - σ < X < μ + σ) = 0.95
P (1263 - 117 < X < 1263 + 117) = 0.95
P (1146 < X < 1380) = 0.95
Thus, the number of chocolate chips in a bag that make up the middle 95% of bags are [1146, 1380].
(c)
The inter-quartile range of the normal distribution is:
IQR = 1.349 <em>σ</em>
Compute the inter-quartile range of the number of chocolate chips in a bag of chocolate chip cookies as follows:
IQR = 1.349 <em>σ</em>
= 1.349 × 117
= 157.833
Thus, the inter-quartile range of the number of chocolate chips in a bag of chocolate chip cookies is 157.83.
Answer:
The value of r=
The value of x=
Step-by-step explanation:
Given that,
A)
Now,
8(2r-2)=9(7r+10)
16r-16=63r+90
-16-90=63r-16r
-(16+90)=47r
-106=47r
r=
B)
Now,
5(x+5)=9[3(x-2)-1]
5x+25=9[3x-6-1]
5x+25=9[3x-7]
5x+25=27x-63
25+63=27x+5x
83=32x
x=