Answer:
B, D, E
Step-by-step explanation:
Anything <em>greater </em>than -5 is in the domain.
Answer:
The inequality is 6x ≥ -24
The solution of this inequality is {x : x ∈ R, x ≥ -4} ⇒ [-4, ∞)
Step-by-step explanation:
- In the inequality not more than means ≤
- In the inequality at least means ≥
Let us solve the question
∵ Six times a number x means 6 × x = 6x
∵ At least means ≥
∴ Six times a number x is at least -24 is 6x ≥ -24
∴ The inequality is 6x ≥ -24
Now we will find the solution of the inequality
∵ 6x ≥ -24
→ Divide both sides by 6
∵ ≥
∴ x ≥ -4
∴ The solution of this inequality is {x : x ∈ R, x ≥ -4} ⇒ [-4, ∞)
X = 7
The angles are congruent so you’d do, 4x-5=23 and you’d get x = 7
Answer:
Number 7: Solution U
Number 8: solution
Explanation:
Number 7: Given inequality is
First we simplify the equation and then we find critical points.
Critical points are :
Now we plot the points on number line and find the true and false solution. Please see the attach file fig 1 for number line.
We will check each interval for solution.
Let we take any interval and take any point between the interval and substitute into equation. We get >0 which is greater than 0.
This interval would be false.
Similarly, we will check each interval .
We get solution, U
Number 8: Given inequality is
First we simplify the equation and then we find critical points. Factor numerator and denominator. We get
Critical points are :
Now we plot the points on number line and find the true and false solution. Please see the attach file fig 2 for number line.
We will check each interval for solution.
Let we take any interval and take any point x=0 between the interval and substitute into equation. We get <0 which is less than 0.
This interval would be true.
Similarly, we will check each interval .
We get solution,
Answer: n = 267
Step-by-step explanation: <u>Margin</u> <u>of</u> <u>Error</u> shows the percentage that will differ the result you get from the real population value or, in other words, is the range of values in a confidence interval.
It can be calculated as
margin of error =
in which
z is z-score related to the confidence interval, which is this case is 1.96;
s is standard deviation;
n is the number in a sample;
So, the number of mice must be:
margin of error =
n = 267
<u>For the margin of error with 95% confidence interval be 0.6, it is needed </u><u>267 mice</u><u>.</u>