Function 1:
f(x) = -x² + 8(x-15)f(x) = -x² <span>+ 8x - 120
Function 2:
</span>f(x) = -x² + 4x+1
Taking derivative will find the highest point of the parabola, since the slope of the parabola at its maximum is 0, and the derivative will allow us to find that.
Function 1 derivative: -2x + 8 ⇒ -2x + 8 = 0 ⇒ - 2x = -8 ⇒ x = -8/-2 = 4
Function 2 derivative: -2x+4 ⇒ -2x + 4 = 0 ⇒ -2x = -4 ⇒ x = -4/-2 ⇒ x= 2
Function 1: f(x) = -x² <span>+ 8x - 120 ; x = 4
f(4) = -4</span>² + 8(4) - 120 = 16 + 32 - 120 = -72
<span>
Function 2: </span>f(x) = -x²<span> + 4x+1 ; x = 2
</span>f(2) = -2² + 4(2) + 1 = 4 + 8 + 1 = 13
Function 2 has the larger maximum.
Answer:
1 pair of socks cost $6.99
Step-by-step explanation:
$27.96 divided by 4 = $6.99
Hope I helped :)
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Answer:
216 gallon
Step-by-step explanation:
We are given that
Milk in gallon probability week
200 3/30 3
205 4/30 4
210 6/30 6
215 5/30 5
220 4/30 4
225 3/30 3
230 2/30 2
235 2/30 2
240 1/30 1
Total weeks=30
We have to find the average number of gallons of milk consumed per week
The average number of gallons of milk consumed per week
=Total number of gallons of milk/total weeks
Using the formula
The average number of gallons of milk consumed per week
=
=
=
gallons/week
Hence, the average number of gallons of milk consumed per week= 216 gallon
Answer:
a) 4/17
b) 1/12
c) 3/34
d) 3/34
Step-by-step explanation:
a) The probability of choosing the first nickel is 9/(9 + 6 + 3) (because there are 9 nickels to choose from and a total of 9 + 6 + 3 = 18 coins to choose from) = 9/18 = 1/2. The probability of choosing the second nickel is 8/17 (because there's no replacement, we have 9 - 1 = 8 nickels remaining to choose from and 18 - 1 = 17 total coins). Multiply these together: (1/2) * (8/17) = 8/34 = 4/17
b) The probability of choosing a nickel is 9/18 (just like above) = 1/2. The probability of choosing a dime is 3/18 (because there are 3 dimes and since there IS replacement, we still have 18 total coins to choose from). Multiplying these, we get: (1/2) * (3/18) = 3/36 = 1/12
c) The probability of choosing a nickel is 9/18 = 1/2. The probability of choosing a dime after that is 3/17 (because there are 3 dimes to choose from, but since there's NO replacement, there are only 18 - 1 = 17 total coins). Multiplying these, we get: (1/2) * (3/17) = 3/34
d) The probability of choosing a penny is 6/18 (because there are 6 pennies) = 1/3. The probability of choosing a nickel next is 9/17 (because there is NO replacement, there are 18 - 1 = 17 total coins remaining). The probability of choosing a second nickel is 8/16 = 1/2 (because there are 17 - 1 = 16 total coins and 9 - 1 = 8 nickels left). Multiplying these, we get: (1/3) * (9/17) * (1/2) = 9/102 = 3/34
Hope this helps!
Answer:
2 x
x 5
or 90
Step-by-step explanation: