Answer:
option: B (
) is correct.
Step-by-step explanation:
We are given the solution set as seen from the graph as:
(-4,2)
1)
On solving the first inequality we have:
On using the method of splitting the middle term we have:
⇒ 
⇒ 
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and 
i.e. x>-2 and x<4
so we have the region as:
(-2,4)
Case 2:
and 
i.e. x<-2 and x>4
Hence, we did not get a common region.
Hence from both the cases we did not get the required region.
Hence, option 1 is incorrect.
2)
We are given the second inequality as:
On using the method of splitting the middle term we have:
⇒ 
⇒ 
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and 
i.e. x>2 and x<-4
Hence, we do not get a common region.
Case 2:
and 
i.e. x<2 and x>-4
Hence the common region is (-4,2) which is same as the given option.
Hence, option B is correct.
3)
On using the method of splitting the middle term we have:
⇒ 
⇒ 
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x>-2 and x>4
Hence, the common region is (4,∞)
Case 2:
and
i.e. x<-2 and x<4
Hence, the common region is: (-∞,-2)
Hence, from both the cases we did not get the desired answer.
Hence, option C is incorrect.
4)
On using the method of splitting the middle term we have:
⇒ 
⇒ 
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x<2 and x<-4
Hence, the common region is: (-∞,-4)
Case 2:
and
i.e. x>2 and x>-4.
Hence, the common region is: (2,∞)
Hence from both the case we do not have the desired region.
Hence, option D is incorrect.
A late assignment is very much like a late payment on a credit card bill. If you lose 10 points for every day that an assignment is late and you have to pay a fee for however many days you forgot to pay the bill, (you are losing money for having to pay an extra fee). If you start the habits of turning in assignments in late. Those habits will be carried with you into adulthood and you will owe a sum of money since you have failed to pay a bill on time. You will lose points for late work and you will lose money for late bills.
The answer is: [C]: -0.7, ⅕, 0.35, ⅔ .
________________________________________
Explanation:
_________________________________________
<span>
Note that in this correct Answer choice "C" given, we have the following arrangement of numbers:
_____________________________________________________
</span>→ -0.7, ⅕, 0.35, ⅔ ;
______________________________________
We are asked to find the "Answer choice" (or, perhaps, "Answer choices?") given that show a set of numbers arranged in order from "least to greatest"; that is, starting with a value that is the smallest number in the arrangement, and sequentially progressing, in order from least to greatest, with the largest (greatest) number in the arrangement appearing as the last number in the arrangement.
______________________
Note the EACH of the 4 (four) answer choices given consists of an arrangement with ONLY one negative number, "- 0.7". Only TWO of the answer choices—Choices "B" and "C"—have an arrangement beginning with the number, "-0.7 "; So we can "rule out" the "Answer choices: [A] and [D]".
________________________
Let us examine: Answer choice: [B]: <span>-0.7, 0.35, ⅕, ⅔ ;
</span>_________________________
Note: The fraction, "⅕" = "2/10"; or, write as: 0.2 .
________________________________________
The fraction, "⅔" = 0.6666667 (that is 0.6666... repeating; so we often see a "final decimal point" rounded to "7" at some point.
___________________________________________
Through experience, one will be able to automatically look at these 2 (two) fractions and immediately know their "decimal equivalents".
____________________________________________
Otherwise, one can determine the "decimal form" of these values on a calculator by division:
_________________________
→ ⅕ = 1/5 = 1 ÷ 5 = 0.2
_________________________
→ ⅔ = 2/3 = 2 ÷ 3 = 0.6666666666666667
___________________________________
For Answer choice: [B], we have:
______________________________
→ -0.7, 0.35, ⅕, ⅔ ;
_________________________
→ So, we can "rewrite" the arrangement of "Answer choice [B]" as:
___________________________________________
→ -0.7, 0.35, 0.2, 0.666666667 ;
________________________________
→ And we can see that "Answer choice: [B]" is INCORRECT; because
"0.2" (that is, "⅕"), is LESS THAN "0.35". So, "0.35" should not come BEFORE "⅕" in the arrangement that applies correctly to the problem.
_______________________________________
Let us examine: Answer choice: [C]: -0.7, ⅕, 0.35, 0.666666667 .
____________________________________________
→ Remember from our previous— and aforementioned—examination of "Answer Choice: [B]" ; that:
____________________________
→ ⅕ = 0.2 ; and:
→ ⅔ = 0.666666667
_______________________
So, given:
____________
→ Answer choice: [C]: -0.7, ⅕, 0.35, ⅔ ;
______________________
→ We can "rewrite" this given "arrangement", substituting our known "decimal values for the fractions:
______________________________
→ Answer choice: [C]: -0.7, 0.2, 0.35, 0.666666667 ;
_________________________________________
→ As mentioned above, this sequence starts with "-0.7", which is the ONLY negative number in the sequence; as such, the next positive number is correct. Nonetheless, "0.2" (or, "(⅕") is the next number in the sequence, and is greater than "-0.7". The next number is "0.35. "0.35" is greater than "⅕" (or, "0.2"). Then next number is "(⅔)" (or, "0.666666667").
"(⅔)"; (or, "0.666666667") is greater than 0.35.
____________________________
This set of numbers: "-0.7, ⅕, 0.35, ⅔" ; is arranged in order from least to greatest; which is "Answer choice: [C]: -0.7, ⅕, 0.35, ⅔" ; the correct answer.
________________________________________________________
Split the second term 7x^2 - 8x - 12 into two terms
7x^2 + 6x - 14x - 12
Factor out common terms in the first two terms, then in the last two terms
x(7x + 6) - 2(7x + 6)
Factor out the common term; 7x + 6
<u>(7x + 6)(x - 2) </u>
Answer:
a) 68.26% probability that a student scores between 350 and 550
b) A score of 638(or higher).
c) The 60th percentile of test scores is 475.3.
d) The middle 30% of the test scores is between 411.5 and 488.5.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a. What is the probability that a student scores between 350 and 550?
This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So
X = 550
has a pvalue of 0.8413
X = 350
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that a student scores between 350 and 550
b. If the upper 3% scholarship, what score must a student receive to get a scholarship?
100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88
A score of 638(or higher).
c. Find the 60th percentile of the test scores.
X when Z has a pvalue of 0.60. So it is X when Z = 0.253
The 60th percentile of test scores is 475.3.
d. Find the middle 30% of the test scores.
50 - (30/2) = 35th percentile
50 + (30/2) = 65th percentile.
35th percentile:
X when Z has a pvalue of 0.35. So X when Z = -0.385.
65th percentile:
X when Z has a pvalue of 0.35. So X when Z = 0.385.
The middle 30% of the test scores is between 411.5 and 488.5.
