The tables represent two linear functions in a system. A 2 column table with 5 rows. The first column, x, has the entries, negat
2 answers:
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Answer:
V = 34,13*π cubic units
Step-by-step explanation: See Annex
We find the common points of the two curves, solving the system of equations:
y² = 2*x x = 2*y ⇒ y = x/2
(x/2)² = 2*x
x²/4 = 2*x
x = 2*4 x = 8 and y = 8/2 y = 4
Then point P ( 8 ; 4 )
The other point Q is Q ( 0; 0)
From these two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.
Now with the help of geogebra we have: In the annex segment ABCD is dy then
V = π *∫₀⁴ (R² - r² ) *dy = π *∫₀⁴ (2*y)² - (y²/2)² dy = π * ∫₀⁴ [(4y²) - y⁴/4 ] dy
V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴
V = π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )
V = π * [256/3 - 51,20]
V = 34,13*π cubic units
Answer:
Each fudge cookie has 80 calories.
Each lemon cream has 65 calories.
Step-by-step explanation:
We will let represent the calories in lemon creams and
represent the calories in fudge cookies.
Two lemon creams and four fudge cookies together have 450 calories. So, we can write the following equation:
And four lemon creams plus two fudge cookies together have 420 calories. So, we can write the following equation:
We now have a system of equations. We can solve this by elimination.
For the first equation, we can multiply both sides by -2. This way, the will cancel when we add the two equations together.
So, the first equation becomes:
Add this to the second equation. Hence:
Simplify:
Divide both sides by -6. Hence:
So, there are 80 calories in one cookie.
We can use the first equation again to find the amount of calories in one cream. We have:
Substituting 80 for yields:
Then it follows that:
So, there are 65 calories in each lemon cream.
Answer:
<em>The 9th percentile of X is 44.96</em>
Step-by-step explanation:
<u>Percentiles for a Normal Distribution</u>
The standard normal distribution can be used for computing percentiles. For example, the median is the 50th percentile being the center value, the first quartile is the 25th percentile, and so on.
To compute percentiles of a normal distribution we can use the formula
Where is the mean,
is the standard deviation of the variable X, and z is the z-score value from the standard tables
The value of X can also be directly obtained from digital tables included in math packages and tools like Excel.
The Excel NORM.INV Function calculates the inverse of the cumulative Normal Distribution Function for a given value of p, and
.
We'll use the values
NORM.INV(0.09,53,6) results in 44.96 which means the 9th percentile of X is 44.96
We could have used the standard normal distribution, which only needs the value of p
That is the value of z, we now apply the formula
We get the very same result as before