To calculate h evaluate inside the square root before taking the square root
h = √(7² - 3.5²) = √(49 - 12.25) = √36.75 = 6.06 ( to 2 dec. places)
<u>We'll assume the quadratic equation has real coefficients</u>
Answer:
<em>The other solution is x=1-8</em><em>i</em><em>.</em>
Step-by-step explanation:
<u>The Complex Conjugate Root Theorem</u>
if P(x) is a polynomial in x with <em>real coefficients</em>, and a + bi is a root of P(x) with a and b real numbers, then its complex conjugate a − bi is also a root of P(x).
The question does not specify if the quadratic equation has real coefficients, but we will assume that.
Given x=1+8i is one solution of the equation, the complex conjugate root theorem guarantees that the other solution must be x=1-8i.
Answer:
5.2 in
Step-by-step explanation:
An equilateral triangle is a triangle with 3 equal sides
Divide the equilateral triangle into two congruent triangles and use Pythagoras theorem to find the height
The Pythagoras theorem : a² + b² = c²
where a = height
b = base = 6 in / 2 = 3 in
c = hypotenuse = 6 in
6² = 3² + h²
h = 36 - 9 = 27
√27 = 5.196 inch
to the nearest tenth = 5.2 in
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Answer:
E: None of the above
Step-by-step explanation:
Hello!
The objective is to find out how much time it takes people to commute to work.
Two samples where taken and two hypothesis tests where made:
One:
Sample mean 71 min; p-value: 0.03
Two:
Sample mean 72 min; p-value: 0.06
You have to choose from the options, a possible pair of hypotheses used for these two tests.
The parameter of the study is the population mean μ.
In the statistic hypotheses, the parameters are given either a known population value or a suspected value. So all options including sample values are wrong.
As said before the objective of the survey is to "determine how much time people spend commuting to work" in other words, whether or not the population mean is equal to a certain value.
H₀: μ = μ₀
H₁: μ = μ₀
Where μ₀ represents the theoretical value of the population mean. As you can say the hypotheses pair is two-tailed, not one-tailed.
Then the correct answer is E: None of the above
I hope this helps!
