Answer:
x is in the range [-1,4]
Step-by-step explanation:
I haven't worked with absolute value inequalities in awhile, but let's take a wack at this.
We are given the following inequality:
| 2x - 3 | <= 5
This implies two possible cases:
[1] -5 <= 2x -3
Or
[2] 2x - 3 <= 5
So let's solve x for both of these cases:
[1] -5 <= 2x - 3
-2 <= 2x
-1 <= x
[2] 2x - 3 <= 5
2x <= 8
x <= 4
So from these cases, we can say the following is true:
x >= -1 and x <= 4
Thus, we can write this in the form
-1 <= x <= 4
Or in interval notation:
{ x is element of reals | -1 <= x <= 4}
Also written as
x is in the range [-1,4]
Where the closed brackets represent 1 and 4 as possible answers whereas parenthesis would imply they were not.
Cheers.
Answer:
1499
5
(Decimal: 299.8)
Step-by-step explanation: =
300
1
−
20
100
=
300
1
+
−20
100
=
300
1
+
−1
5
=
1500
5
+
−1
5
=
1500+−1
5
Answer:
B
Step-by-step explanation:
First calculate BD using sine ratio in Δ BCD and the exact value
sin60° = 
, thus
sin60° = 
= 
= 
= ( cross- multiply )
2BD = 12
( divide both sides by 2 )
BD = 6
-----------------------------------------------------------
Calculate AD using the tangent ratio in Δ ABD and the exact value
tan30° = 
, thus
tan30° = 
= 
= 
= ( cross- multiply )
AD = 6 ( divide both sides by )
AD = 6 → B
Answer:
Step-by-step explanation:
The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 34 minutes. This is the null hypothesis. It is written as
H0 : µ ≤ 34
The alternative hypothesis would be
Ha : µ > 34
This is a right tailed test because of the greater then symbol in the alternative hypothesis. Since the p value for the test was found to be 0.0281281, if we use a significant level of 0.05, then the conclusion would be
Reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the average time spent on the deliveries does exceed 34 minutes.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Mean (m) = 72
Standard deviation (sd) = 10
Grading cutoff policy:
bottom 5% receive F
next 15% receive D
next 35% receive C
next 30% receive B
A) Give the cutoffs for the grades in this course in terms of standardized scores.
Standardized score for grade cutoff:
Locating the Zscore for the proportions on the z table :
Bottom 5% = 0.05 ; corresponding Zscore = - 1.645
next 15% receive D = (5 +15)% 0.20 ; corresponding Zscore = - 0.84
next 35% receive C = (20+35)% = 0.55 ; corresponding Zscore = 0.13
next 30% receive B = (55 + 30)% = 0.85 ; Corresponding Zscore = 1.04
B) Give the cutoffs in terms of actual total scores.
Recall:
Zscore = (x - m) /sd ; where x = actual score
x = sd*z + m
For F:
10*(-1.645) + 72 = 55.55
For D:
10*(-0.84) + 72 = 63.6
For C:
10*(0.13) + 72 = 73.3
For B:
10*(1.04) + 72 = 82.4
C) Do you think that this method of assigning grades is a good one?
Yes, it is good in terms of expressing scores around the mean such that score below are negative and those above are positive. However, it is a little bit ambiguous.
