The appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.
In this question,
The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data.
The Independent samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.
The independent sample t-test is a useful statistical method of hypothesis testing when an organization wants to determine whether there is a statistical difference between two categories, groups, or items and, furthermore, if there is a statistical difference, whether that difference is significant.
From the definition, the independent sample t-test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.
Hence we can conclude that the appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.
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Use the function, f(x)=50(1.02)^x to identify if it's growth or decay & the percentage of the growth or decay.
The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.
What is the growth rate in the function?The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
In this case, the function is given as:
f(x)=50(1.02)^x
It should be noted 1 + 2% = 1.02 which us the value in the parentheses.
In conclusion, the growth rate is 2%.
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HELPPPP (x-y)^3-(y-x)^2
Answer:
(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²
2x²-4yx+2y²
(y-x)(y-x)= y²-yx-yx+x²
y²-2yx+x²
-(y²-2yx+x²) = -y²+2yx-x²
2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²
or
(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³
Please help me solve this, random answers will be removed
Answer:
m∠B ≈ 70.8°
Step-by-step explanation:
The Law of Cosines relates three sides of a triangle and the angle opposite one of them.
SetupThe law of cosines tells you ...
b² = a² +c² -2ac·cos(B)
Solving for angle B, we get ...
B = arccos((a² +c² -b²)/(2ac))
where 'a' and 'c' are the sides adjacent to the angle of interest. We want angle B, so we can fill this formula as follows:
B = arccos((13² +11² -14²)/(2·13·11))
SolutionB = arccos(94/286)
B ≈ 70.812°
__
Additional comment
Another angle can be found using the Law of Sines.
A = arcsin(sin(70.812°)×13/14) ≈ 61.281°
Then angle C is ...
C = 180° -70.812° -61.281° = 47.907°
Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]
[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]
next,
g(f(-5)) represents value of y at x = f(-5) = 1
hence,
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\sf \:g(f( - 5)) = 5[/tex]HELP!!! MATH!!! 100 PTS !!!
Suppose f is a one-to-one, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that
(f^−1)′(x)=1/(f′(f^−1(x)))
Find (f^−1)′(6) if f(−1)=6 and f′(−1)=3/7.
Answer:
(f^−1)′(6)=1/(f'(f^-1(6)))
(f^−1)′(6)=1/(f'(f^-6)))
I hope this helps.
What is the range of the function f(x) = |x + 4| + 2?
R: {f(x) ∈ ℝ | f(x) ≤ 2}
R: {f(x) ∈ ℝ | f(x) ≥ 2}
R: {f(x) ∈ ℝ | f(x) > 6}
R: {f(x) ∈ ℝ | f(x) < 6}
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]
You need to remember that the form of an Absolute Value Function is:
• For the vertex:
[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]
[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]
• For the definition:
If "a" is positive (+) , then the range of the function is:
[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]
If "a" is negative (-), the range of the function is:
[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]
In this case we can identify that:
[tex]\small\longrightarrow \sf{a = 1}[/tex]
[tex] \small\longrightarrow\sf{a = 2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]
Please help!!!
The diagram to the right shows a square pyramid. The point C is the centre of the base, and TC is perpendicular to the base. (More information in the screenshot)
(i) The measures of the angles are m ∠ TCM = m ∠ TCQ = m ∠ CMQ = 90°.
(ii) The lengths of sides CM and CQ are 2 cm and 2√2 cm, respectively.
(iii) The angle between the side face and the base is equal to θ = cos⁻¹ (2 / MT) and the angle between the slant edge and the base is θ = cos⁻¹ [2√2 / √(4 + MT²)].
How to analyze a right pyramid
In this problem we have a right pyramid as line segment TC is perpendicular to the base PQRS, which means that any line coplanar with PQRS is perpendicular to line segment TC. i) the measures of the angles are m ∠ TCM = m ∠ TCQ = 90°.
Besides, the base PQRS is a square, which is equivalent to four right triangles with angles 45° - 45° - 90° and each triangle can be divided into two right triangles. Hence, the measure of the angle CMQ is 90°.
ii) The length of the sides can be found by the 45-45-90 theorem, which states that the length of the hypotenuse is √2 times the length of any of the legs:
CQ = (√2 / 2) · PQ
CQ = (√2 / 2) · (4 cm)
CQ = 2√2 cm
CM = (√2 / 2) · (2 √2 cm)
CM = 2 cm
iii) The angle between the side face, one of them contains the line segment MT and the base can be found by the following inverse trigonometric relation: (value of the pyramid height is missing)
θ = cos⁻¹ (CM / MT)
θ = cos⁻¹ (2 / MT) (1)
Similarly, the angle between the slant edge and the base is found by Pythagorean theorem and inverse trigonometric relation: (value of the pyramid height is missing)
θ = cos⁻¹ (CQ / TQ)
θ = cos⁻¹ [2√2 / √(QM² + MT²)]
θ = cos⁻¹ [2√2 / √(4 + MT²)] (2)
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Write as a single term from Pascal's Triangle in the form t_nr(1 mark)
t_13,8 + t_13,9
¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
What is Pascal's triangle?
Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.
What is combination?Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!
How to write a single term from Pascal's Triangle in the form t_nr = t_13,8 + t_13,9.Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that
¹³C₈ = 13!/8!(13 - 8)! = 13!/8!5! and ¹³C₉ = 13!/9!(13 - 9)! = 13!/9!4!So, ¹³C₈ + ¹³C₉ = 13!/8!5! + 13!/9!4!
= 13!/(8! × 5 × 4!) + 13!/(9 × 8! × 4!)
= 13!/8!4![1/5 + 1/9]
= 13!/8!4! × [(9 + 5)/45]
= 13!/8!4! × 14/45]
= 13!/8!4! × 14/(9 × 5)]
= 14 × 13!/8! × 9 × 4! × 5)]
= 14!/9!5!
= 14!/9!(14 - 9)!
= ¹⁴C₉
So, ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
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What does the point (1, 2) represent? parking costs $1 per hour for the entire day. parking costs $2 per hour for the entire day. the total cost of 2 hours of parking is $1. the total cost of 1 hour of parking is $2.
The point which is indicated in the task content; (1, 2) represents; parking costs $2 per hour for the entire day.
What is the interpretation of the point given in the task content; (1,2)?
It follows from convention that the coordinate systems are structured such that the independent variable, x be placed 1st and the dependent variable, y be placed second.
Consequently, since the cost of parking is dependent on the time for which the car is parked, then, it represents parking costs 2 per hour for the entire day.
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Solve for P : p/10 = 7.2/3
P/10 = 7.2/3
P = 7.2x10/3
P=72/3
P= 24
Find the slope of the line shown below
Answer:
[tex] \frac{3}{2} [/tex]
Step-by-step explanation:
From the attached photo, we can deduce:
(2,2) as (x1,y1)
(-2,-4) as (x2,y2)
Slope Formula =
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Now we can substitute these values into the formula to find the slope.
Slope of line =
[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]
Pick the correct answer
Thanks so much :)
The linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
Line I is decreasing, hence it has a negative slope.Line K is constant, hence it has a slope of zero.Line J is increasing, hence it has a positive slope.Hence the linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
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identify this problem plssss
Answer:
The answer is cot(x)
Step-by-step explanation:
Greetings ![tex] \tan(x) \csc {}^{2} (x) - \tan(x) [/tex]
Rewrite using trig identity
[tex] - \tan(x) + \csc {}^{2} (x) \tan(x) [/tex]
use the Pythagorean idea
[tex] \csc {}^{2} (x) = 1 + \cot {}^{2} (x) [/tex]
[tex] - \tan(x) + (1 + \cot {}^{2} (x)) \tan(x) [/tex]
simplify
[tex] \cot {}^{2} (x) \tan(x) [/tex]
use basic trigonometric identity
[tex] \tan(x ) = \frac{1}{ \cot(x) } [/tex]
simplify
[tex] \cot {}^{2} (x) \frac{1}{ \cot(x) } [/tex]
gives you
[tex] \cot(x) [/tex]
Hope it helps!
What is the area of the shape?
The area of the shape is 35 square units
How to determine the area of the shape?The given shape is a trapezoid, and it has the following side lengths
Parallel bases = 6 and 8
Height = 5
The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height
Substitute the known values in the above equation
A = 0.5 * (6 + 8) * 5
Evaluate the product
A = 35
Hence, the area of the shape is 35 square units
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The area of the given trapezoid is given as 35 square units
How to determine the area of a trapezoid?The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;
A = 1/2(a+b)*h
where
a and b are parallel sides
h is the height of the trapezoid.
Given the following parameters
a =6units
b = 8 units
h - 5 units
Substitute to have:
A = 1/2(6 + 8) * 5
A = 1/2(14) *5
A = 7 * 5
A = 35 square units
Hence the area of the given trapezoid is given as 35 square units
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The odds of rolling a die and getting an even number is 50%. Write out the success set and the sample set to use the definition of probability to show that this is true.
Answer:
It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).
A box is to constructed with a rectangular base and a height of 5cm. if the rectangular base must have a perimeter of 28cm, which quadratic equation best models the volume of the box ? a. y=5(28-8)(x) b.y=5(28-2x)(x) c. y=5(14-x)(x) d. y=5(14-2x)(x)
y=5(14-x)(x) quadratic equation best models the volume of the box .
What is volume of cuboid?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape. The volume of a cuboid is found by multiplying the length by the breadth by the height.Perimeter = 2(width + length) =28
Let x=width of base, then length of base = (28/2)-x = 14-x
Volume of box = length*width*height
=x(14-x)*5 ⇒ 5x(14-x)(x)
Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .
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The lines shown below are perpendicular. If the green line has a slop of 2/5, what is the slope of the red line?
The slope of the red line that is perpendicular to the green line is: -5/2.
What are the Slope Values of Perpendicular Lines?When one line lies perpendicular to another line, the slope of one must be the negative reciprocal of the other line.
What is the Negative Reciprocal of a Number?If given a number, i.e. a/b, the negative reciprocal of a/b would the opposite value of the reciprocal of a/b.
Reciprocal of a/b is b/a. Negative reciprocal of a/b would therefore be: -b/a.
Given that the slope of the green line is: 2/5. And it is perpendicular to the red line. The slope of the red line would be the negative reciprocal of 2/5.
Negative reciprocal of 2/5 is -5/2.
Therefore, the slope of the red line is: -5/2.
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d) The perimeter of room is 28 m. and the height is 3.5 m. Find the area of 4 walls.
it's hurry give me answer fast please
Answer: 98
Step-by-step explanation:
Area of four walls = Curved surface area
= perimeter × height
= 28 × 3.5
= 98 m square
Use a left-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
25 / 4
Step-by-step explanation:
To find the left sum, you need to....
1.) Find Δx
2.) Find [tex]x_{k-1}[/tex]
3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx
4.) Solve for the left sum
What is the probability that the battery life for an ipad mini will be at least 11 hours?
Answer:
0.2857
Step-by-step explanation:
We want to determine,
The probability that the battery life is at least 11 hours is 0.2857.
Need this soon please -
Select the correct answer.
What is the inverse of function
f(x)=√x + 7
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Option A is correct[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Find inverse of given function :
[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]
[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]
[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]
Next, replace x with f-¹(x) and y with x ~
[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]
we got our inverse function.
Condition : x should be greater or equal to 7
because we will get same value of y for different x if we also include values less than 7.
[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option is A[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]
To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.
[tex]\bold{Becomes,}[/tex]
Next step we switch sides for x and y variables and then solve for the y variable as shown below,
[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]
[tex]\bold{Then,}[/tex]
[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]
[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]
[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]
[tex]\small\bold{Square \: both \: sides }[/tex]
[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]
[tex]\sf{(x-7)^2=y}[/tex]
We now re-write in function notation. Take note however that this is the inverse:
[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]
[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]
[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]
Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?
The Measure of the reference angle is 45
cos(0)= √ 2/2
tan(0)=1
sin(0)=√ 2/2
the measure of the referance angle is 30
the measure of the referance angle is 60
Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, the given angle is as follows:
[tex]\theta = \frac{5\pi}{4}[/tex]
It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:
[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]
The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].More can be learned about equivalent angles at https://brainly.com/question/24787111
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Answer:
The measure of the reference angle is 45 degrees
tan(theta) = 1
Step-by-step explanation:
Could I get some help with this?
Answer:
Step-by-step explanation:
base=b=7.2yd
height =h=7yd
area of parallelogram = b x h
. =7.2yd x 7yd
=50.49[tex]yd^{2}[/tex]
A bin in the school gymnasium holds different colored balls. a ball is picked at random and then replaced. the probability of picking a green ball is 0.5, the probability of picking a blue ball is 0.4, and the probability of picking a red ball is 0.1. if a ball is picked and replaced 140 times, how many times should you expect a blue ball to be picked? a. 14 b. 48 c. 56 d. 70
Correct answer is C. the number of times blue ball appears is 56
Given,
probability of picking a green ball is 0.5,
the probability of picking a blue ball is 0.4,
the probability of picking a red ball is 0.1.
a ball is picked and replaced = 140
Probability = (the number of ways of achieving success) / (the total number of possible outcomes)
Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.
For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times and the probability of picking a blue ball (which is equal to 0.4)
= (140)(0.4) = 56
Therefore, we should expect that the blue ball will be picked 56 times.
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Csn u please help me o have no idea
Answer:
D.= √29
Step-by-step explanation:
Greetings!The distance between the two complex numbers,
Z₁=a+bi and Z₂=c+di in the complex plane is
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is
[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]
To find the distance between the two complex numbers using the formula
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
where,
a=4b=3c=6d=-2[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]
Roger owns a one-acre piece of land. the length of the land is 484 feet. what is the width of his property? (hint: one acre = 43,560 square feet)
Answer:
90ft
Step-by-step explanation:
43,560ft² = L × l
43,560ft² = 484ft × l
43,560ft² ÷ 484ft = l
l = 90ft
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]f(x)=-2(x-3)^2+2[/tex]
Step-by-step explanation:
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.
x-intercept(s): (2,0),(4,0)
y-intercept(s): (0,−16)
Answer:
D f(x) = -2(x - 3)² + 2
Step-by-step explanation:
The y-intercept occurs at x = 0.
A
f(x) = 2x(x + 14) - 64
f(0) = -64 Not -16
B
f(x) = (x + 4)² + 2x
f(0) = 16 Not -16
C
f(x) = (x - 16)² + 4
f(0) = 260 Not -16
D
f(x) = -2(x - 3)² + 2
f(0) = -18 + 2 = -16 <-------------------- this is it
18 times the quantity g plus 5
Comparing it to a system of equations, the expression is represented as follows:
18g + 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, we consider g as the variable. Then:
18 times the quantity g is 18g.Adding 5 to the expression, we have that 18g + 5.More can be learned about a system of equations at https://brainly.com/question/24342899
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Which expression is equivalent to x^2 + 5x - 6? Explain how.
(1) (x + 3) (x - 2)
(2) (x + 2) (x - 3)
(3) (x - 6) (x + 1)
(4) (x + 6) (x - 1)
Answer:
(4) (x + 6)(x - 1)
Step-by-step explanation:
Hello!Given expression
[tex]x { }^{2} + 5x - 6[/tex]
Find numbers when they are multiplied gives 6 and when they are added which gives 5.
Thus, these numbers are -1 & 6.
[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]
Can also check the multiplied values of these two values.
Hope it helps!
Answer:
(4)
Step-by-step explanation:
Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).
Multiples are: +6 and -1
input the two multiples in place of the middle term (+5x)
=x^2+6x-1x-6
Collect like terms
=x(x+6)-1((x+6)
Answer= (x+6)(x-1)
Confirm answer above:
Open bracket
x(x-1)+6(x-1)
x^2-x+6x-6
x^2+5x-6 (initial equation).
16. a) In the given figure, OB bisects ABC and OC bisects ACB, prove that BOC - BAC = ABO+ACO.
Answer:
Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.
Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.
m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB
m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO
m<ABO + m<ACO = m<BOC - m<BAC
