Answer: x < 2
<u>Step-by-step explanation:</u>
2x + 1 < 5
Subtract 1 from both sides:
2x < 4
Divide both sides by 2:
x < 2 <em>(x is less than 2)</em>
Graph: ←-------o -2
Interval Notation: (-∞, -2)
Answer:
The parabola is translated down 2 units.
Step-by-step explanation:
You have the parabola f(x) = 2x² – 5x + 3
To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:
f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 <u><em>Expresion A</em></u>
The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.
- If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
- If p> 0 and q <0, the parabola shifts p units to the right and q units down.
- If p <0 and q> 0, the parabola shifts p units to the left and q units up.
- If p <0 and q <0, the parabola shifts p units to the left and q units down.
In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.
This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.
In conclusion, <u><em>the parabola is translated down 2 units.</em></u>
Answer:
a.) Total amount spent on gasoline and oil = $ ( 3.95g + 4.45c )
b.) Total amount spent by Maria = $ 74.02
Step-by-step explanation:
As given,
Cost of gasoline = $ 3.95 gallon
Cost of oil per can = $ 4.45
Also given,
Maria bought g gallons of gasoline and c cans of oil
⇒ Total cost of g gallons of gasoline = g×3.95 = $3.95g
Total cost of c cans of oil = c×4.45 = $4.45c
Now,
a.)
Total amount spent on gasoline and oil = $ ( 3.95g + 4.45c )
b.)
As given ,
Maria buy gasoline , g = 8.6 gallons
Maria buy cans of oil , c = 6
So,
Total amount spent = $ 3.95(8.6) + 4.45(9)
= $ 33.97 + 40.05 = $ 74.02
⇒Total amount spent by Maria = $ 74.02
Answer:
0.0062
Step-by-step explanation:
Let X be the diagnosed blood sugar level.
Probability of committing a Type II error = Probability of failing to detect the disease when the person has the disease = Probability that the diagnosed blood sugar level is less than or equal to 125 =

![= P[Z\le (125 - 150)/10]](https://tex.z-dn.net/?f=%3D%20P%5BZ%5Cle%20%28125%20-%20150%29%2F10%5D)
![=P[Z \le -2.5]](https://tex.z-dn.net/?f=%3DP%5BZ%20%5Cle%20-2.5%5D)
= 0.0062
Answer:
40 minutes
Step-by-step explanation:
You can simply make 200/5 = 40 5 minute calls per month.
This works because every call is a 5-minute call. So then we just have to find how many times we can make a 5-minute call up to 200 minutes. We already have an operation for this: Division. This acts as the opposite of multiplication and speeds our process up.