Answer:
a) The first inequality is 100 + 55x > 150 + 51x;
b) The final inequality results in x > 12.5
c) Sal's mother will need to use the second phone for at least 13 months.
Step-by-step explanation:
a) Let x represent the number of months.
1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.
2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.
3. For the second phone to be cheaper, we set up the inequality:
150 + 51x < 100 + 55x
which simplifies to
100 + 55x > 150 + 51x
b) Now solve this:
55x - 51x > 150 - 100
4x > 50
so x > 12.5
c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).
Answer:
A. C. E. F.
Which correspond to 2, 3, 5, and 6.
Step-by-step explanation:
Within geometry, exterior angles are defined as those angles formed between any side of a polygon and the extension of an adjacent side, as demonstrated in the diagram.
Observing the figure, angles 2 and 3 arise from a side of the triangle and a line extended from the following side. Likewise, angles 5 and 6 are created similarly. Thus, these four angles are classified as exterior angles.
Seven hundred nineteen thousand, nine hundred twenty-seven
Response:1 and 2
Step-by-step Explanation:
Provided data
Volume required 
For the initial cylinder
For the second cylinder
For the third cylinder
For the fourth cylinder
Thus, cylinders 
and 
meet the requirement as they remain under 
Thus, the average is 72.97
We must deduct the mean from each number and square the result.
(65-72.97)^2= 63.5209
(68-72.97)^2=24.7009
(69-72.97)^2=15.7609
(70-72.97)^2=8.8209
(71-72.97)^2= 3.8809
(72-72.97)^2=0.9409
(90-72.97)^2=290.0209
(95-72.97)^2=485.3209
Next, we sum these new values (also taking their frequencies into account) and compute their average.
Sum the figures
63.5209+(2 •24.7009=49.4018)+(5•15.7609=78.8045)+(8•8.8209=70.5672)+(7•3.8809=27.1663)+(3•0.9409=2.8227)+(2•290.0209=580.0418)+(2•485.3209=970.6418)= 1,842.967
Then divide by the total number to determine the mean
1,842.967/ 30=61.43223333
The standard deviation is the square root of the average which equals
Square root of 61.43223333=7.837871735
Round it to the nearest tenth
The Standard Deviation is 7.8
