Answer:
we have (a,b,c)=(4,-2,0) and R=4 (radius)
Step-by-step explanation:
since
x²+y²+z²−8x+4y=−4
we have to complete the squares to finish with a equation of the form
(x-a)²+(y-b)²+(z-c)²=R²
that is the equation of a sphere of radius R and centre in (a,b,c)
thus
x²+y²+z²−8x+4y=−4
x²+y²+z²−8x+4y +4 = 0
x²+y²+z²−8x+4y +4 +16-16 =0
(x²−8x + 16) + (y² + 4y + 4 ) + (z²) -16 = 0
(x-4)² + (y+2)² + z² = 16
(x-4)² + (y-(-2))² + (z-0)² = 4²
thus we have a=4 , b= -2 , c= 0 and R=4
Part 1) we have that
volume smaller solid=512 cm³
volume larger solid=2197 cm³
we know that
volume larger solid=[scale factor]³*volume smaller solid
scale factor=∛[volume larger solid/volume smaller solid]
scale factor=∛[2197/512]-----> scale factor=1.625
Part 2)
the ratio of the surface areas is equal to [scale factor]²
1.625²-------> 2.64
Part 3)
surface area smaller solid=960 cm²
then
surface area larger solid=scale factor²*surface area smaller solid
surface area larger solid=[1.625]²*960-----> 2535 cm²
surface area larger solid is 2535 cm²
Answer:
X=26
Step-by-step explanation:
The probability of Erin not having a heart attack according to her family history would be 30%.
The probability of the test predicting correctly is 67%.
Therefore, the probability of the test correctly predicting that Erin will not have a heart attack would be (0.30)(0.67) = 0.201 or 20.1%.
we know that
A number is an inequality solution if the number satisfies the inequality
<u>Part 1)</u> 
rewrite the inequality
The answer Part 1) is the option D 
Because satisfies the inequality
-----> is true
<u>Part 2)</u> 
The answer Part 2) is the option A 
Because satisfies the inequality
-----> is true
<u>Part 3)</u> 
we're going to verify every case
<u>case A)</u> For 
substitute the value of x in the inequality
------> is true
therefore
The number 
is a solution
<u>case B)</u> For 
substitute the value of x in the inequality
------> is not true
therefore
The number 
is not a solution
<u>case C)</u> For 
substitute the value of x in the inequality
------> is not true
therefore
The number 
is not a solution
<u>case D)</u> For 
substitute the value of x in the inequality
------> is not true
therefore
The number 
is not a solution
therefore
The answer Part 3) is the option A
