The Answer to your question is 8
Answer:
21440
Step-by-step explanation:
<h2>
Simplify:</h2>
Start by multiplying 7x³ by x² and -5.
- 7x⁵ - 35x³ + (8x² - 3)(x² - 5)
Multiply 8x² by x² and -5.
- 7x⁵ - 35x³ + 8x⁴ - 40x² + (-3)(x² - 5)
Multiply -3 by x² and -5.
- 7x⁵ - 35x³ + 8x⁴ - 40x² -3x² + 15
Combine like terms together.
- 7x⁵ - 35x³ + 8x⁴ - 43x² + 15
Rearrange the terms in descending power order.
- 7x⁵ + 8x⁴ - 35x³ - 43x² + 15
<h2>Verify (I): </h2>
Substitute x = 5 into the above polynomial.
- 7(5)⁵ + 8(5)⁴ - 35(5)³ - 43(5)² + 15
Evaluate the exponents first.
- 7(3125) + 8(625) - 35(125) - 43(25) + 15
Multiply the terms together.
- 21875 + 5000 - 4375 - 1075 + 15
Combine the terms together.
This is the answer when substituting x = 5 into the simplified expression.
<h2>
Verify (II):</h2>
Substitute x = 5 into the expression.
- [7(5)³ + 8(5)² - 3][(5)² - 5]
Evaluate the exponents first.
- [7(125) + 8(25) - 3][(25) - 5]
Multiply the terms in the first bracket next.
Evaluate the expressions inside the brackets.
Multiply these two terms together.
This is the answer when substituting x = 5 into the original (unsimplified) expression.
The summation of negative 5 n minus 1, from n equals 3 to 12 can be
expressed as
n = 3/12
substitute the value of n to the equatio
-5n – 1
-5( 3/12 ) -1
-9/4
Answer: No , at 0.05 level of significance , we have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.
Step-by-step explanation:
Let 
denotes the average hours of sleep per night.
As per given , we have
, since 
is left-tailed and population standard deviation is unknown, so the test is a left-tailed t -test.
Also , it is given that ,
Sample size : n= 22
Sample mean : 
Sample standard deviation : s= 1.93
Test statistic : 
i.e. 
For significance level 
and degree of freedom 21 (df=n-1),
Critical t-value for left-tailed test= 
Decision : Since the test statistic value (0.58) > critical value 1.7207, it means we are failed to reject the null hypothesis .
[Note : When 
, then we accept the null hypothesis.]
Conclusion: We have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.
Answer:
x = 30
Step-by-step explanation:
a) The sum of the angles along the line is 180°. That means ...
2x° +90° +x° = 180°
__
b) Subtracting 90° and dividing by 3° gives ...
3x° = 90°
x = 30
