Answer:
x < - 4
Step-by-step explanation:
-5x + 12 > 32
- 12 > - 12
-5x > 20
-5x/-5 < 20/-5
x < - 4
Add all the chips to find the total amount.
7 + 9 + 3 + 6 = 25 chips
Since there are 6 blue chips (6/25), that's the probability of just getting once.
When you pick a blue chip and it doesn't get replaced, then that means there is one fewer blue chip and one fewer from the total amount.
5/24
Multiply both probabilities.
6/25 * 5/24 = 30/600
Simplify.
30/600 → 1/20
Therefore, the answer is B
Best of Luck!
Answer: B) No; the remainder is 234, so (x+3) is not a factor.
===============================================================
Explanation:
We'll use the remainder theorem. That theorem says if we divide p(x) over (x-k), then the remainder is p(k). A special case of this theorem says that if we get 0 as the remainder, then (x-k) is a factor of p(x).
We're dividing f(x) over (x+3) which means that k = -3. Think of x+3 as x-(-3) so you can match it up with the form x-k.
To find the remainder of f(x)/(x+3), we need to compute f(-3).
Plug x = -3 into the f(x) function to get...
f(x) = 4x^3 + 11x^2 - 75x + 18
f(-3) = 4(-3)^3 + 11(-3)^2 - 75(-3) + 18
f(-3) = 234
The remainder is 234, which is isn't zero, so (x+3) is not a factor of f(x).
the shape of christina’s garden is a rectangle
and trapezoid. The rectangle has a dimensions of 4 units by 2 units. The trapezoid
upper base is 8 units and the lower base is 4 units and the height is 2 units
Area of the garden = area rectangle + area
trapezoid
A = (LW) + 0.5( base1 + base2)(h)
A = ( 4 x 2) + 0.5 ( 8 + 4) (2)
A = 20 sq units
Number of carrots = 20 sq units x 15 carrots/
sq units
<span>= 300 carrots</span>
Either the question is wrong or it is must be "for all positive integers number" . Because for real number there are examples where it is not true . For example x = 1/2 it gives 0 which is a even number . For all positive integers the statement is true by following proof :
<span>f(x) = 2x-1 </span>
<span>f(x)%2 = (2x-1)%2 = (2x-1+2)%2 = (2x+1)%2 = ((2*(x%2))%2 + 1)%2 </span>
<span>now x%2 is either 1 or 0 </span>
<span>for x%2 = 1 </span>
f(x)%2 = ((2*(1))%2 +1)%2 = (2%2+1)%2 = 1
for x%2 = 0
f(x)%2 = ((2*(0))%2 + 1)%2 = (0+1)%2 = 1
So in all cases f(x)%2 = 1 so f(x) must be odd for all positive integers
Here is another proof by mathematical induction :
<span>let x = 1 be base condition then </span>
<span>f(1) = 1 so it is true for that </span>
<span>Lets assume f(x) is odd </span>
then f(x+1) = 2(x+1)-1
f(x+1) = 2x+2-1
f(x+1) = 2x+1
<span>f(x+1) = 2x-1 + 2 </span>
<span>f(x+1) = f(x) + 2 </span>
<span>f(x) = odd </span>
<span>so f(x) + 2 must be odd.</span>