Explanation:
Sum of all angles= 180 degrees
So,
3x + 75= 180
3x= 180 - 75
3x= 105
x= 105/3
x= 35
Answer= 35 degrees
First, factor the expression on the top. What two numbers add to get 8 and multiply to 15? 5 and 3! so the top expression factors to (x+3)(x+5). You can cancel the x+3 from the denominator and end up with x+5. Make sense?
X+10=15
Isolate x by subtracting 10 from both sides
x+10-10=15-10
x=5
Final answer: B
Check by plugging the value in
5+10=15
True
Answer:
The 95% confidence interval for the mean is between 0.985g/cm² and 1.047 g/cm².
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the mean subtracted by M. So it is 1.016 - 0.0310 = 0.985 g/cm²
The upper end of the interval is the mean added to M. So it is 1.016 + 0.0310 = 1.047 g/cm²
The 95% confidence interval for the mean is between 0.985g/cm² and 1.047 g/cm².
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real irrational roots
• If b² - 4ac > 0 and a perfect square then 2 real rational roots
• If b² - 4ac = 0 then 1 real double root
• If b² - 4ac < 0 then 2 complex roots
Given
x² + 3x - 7 = 0 ← in standard form
with a = 1, b = 3, c = - 7 , then
b² - 4ac
= 3² - (4 × 1 × - 7) = 9 + 28 = 37
Since b² - 4ac > 0 then 2 real irrational roots
