<span>The simplest method to do this is with the vector dot
product. Let the vector A = <9i + 5j> with magnitude √106 be the base
diagonal, and B = <5j + 3k> be the diagonal vector on the side, with
magnitude √34. Then cos θ = (A dot B) divided by the product of the magnitudes.
A dot B =30, so
cos θ = 30 / √(34 x 106)</span>
<span> = 0.4997 ==></span>
<span> θ = 49.19° is the
answer</span>
Answer:
Step-by-step explanation:
I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x
f(b) - f(a)
The formula for "average rate of change" is a.r.c. = --------------
b - a
change in function value
This is equivalent to ---------------------------------------
change in x value
For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:
8
------ = 8 units (Section A)
1
Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from
4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is
224 units
----------------- = 224 units (Section B)
1 unit
The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.
This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").
The measure of angle theta is 30 degrees.
This is a 30-60-90 triangle where the short leg is half that of the hypotenuse. The short leg is opposite the smallest angle 30 degrees.
You can use trig to find that
sin(angle) = opposite/hypotenuse
sin(theta) = 5/10
sin(theta) = 0.5
theta = arcsin(0.5)
theta = 30 degrees
We will compare pairwise treatment with the help of t-statistic to find the best treatment.The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesized value relative to its standard error.We need to check if the treatments are effective in curing phobia.
First, we must determine whether there is a relationship between the type of treatment used and the final result (cure or not cure). We may examine this using the Chi-square test of association.In the second phase, we must determine if all therapies are the same or different if the alternative hypothesis—that is, whether there exists any kind of link between therapy and cure—is accepted.
We must perform a One-way ANOVA for the treatments in this case, assuming that all treatments are equal. If the null hypothesis is rejected in this instance, then the treatments differ. then, we go to step three.We will compare pairwise treatment with the help of t-statistic to find the best treatment.
To learn more about t-statistic visit:brainly.com/question/15236063
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