Answer:
175 cal
Step-by-step explanation:
if 12oz = 300 cal
then, 7 oz = ?
cross multiplication
12×?= 7×300
? = 2100/12
? = 175 cal
NB: you can replace the question mark with any variable.
Suppose you invested $1000 every 3 months over a 15 year period. If money earns an annual rate of 6.5% compounded quarterly, how much would be available at the end of the time period. How much is the interest earned? Show all your calculations
Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.
What is the future value formula?The future value formula is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
In which:
P is the periodic payment.i is the equivalent yearly interest rate.n is the number of periods.For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:
P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.
Hence the amount available is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]
F = $100,336.67
The amount deposited was:
15 x 4 x $1000 = $60,000.
Hence the amount earned in interest was:
$100,336.67 - $60,000 = $40,336.67
More can be learned about the future value formula at https://brainly.com/question/5025949
#SPJ1
Find the general solution of the given second-order differential equation. 12y'' − 5y' − 3y = 0
The general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
According to the given question.
We have a differential equation
[tex]12y^{"} -5y^{'} -3y = 0[/tex]
The above equation can be written as
[tex](12D^{2} -5D -3)y = 0[/tex]
The auxillary equation for the above differential equation is
[tex]12m^{2} -5m-3 = 0[/tex]
[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]
⇒ 3m(4m - 3) +1(4m - 3) = 0
⇒ (3m + 1)(4m -3) = 0
⇒ m = -1/3 or 3/4
Therefore,
[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]
Here, P.I = 0
As we know that the general solution of the differential equation is given by
y = PI + CF
Thereofre, the general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
Find out more information about general solution of the differential equation here:
https://brainly.com/question/4537000
#SPJ4
Please help
Thank you!
The given transformation is a reflection across the y-axis that changes the coordinates EFGH into E'F'G'H' as follows:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
What is the transformation rule for reflection?The transformation rules for reflection are:
Reflection at y-axis: y = f(-x);
Reflection at x-axis: y = -f(x);
Calculation:The given polygon has four vertices EFGH.
Their coordinates are:
E(-4, -1), F(-2, -1), G(-1, -2), and H(-1, -4)
When the transformation rule: reflection across the y-axis is applied, the coordinates become:
y = f(-x); rule
For E(-4, -1), x-coordinate is -4. So, -(-4) = 4
⇒ E'(4, -1)
For F(-2, -1), x-coordinate is -2. So, -(-2) = 2
⇒ F'(2, -1)
For G(-1, -2), x-coordinate is -1. So, -(-1) = 1
⇒ G'(1, -2)
For H(-1, -4), x-coordinate is -1. So, -(-1) = 1
⇒ H'(1, -4)
Thus, the transformed coordinates are:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
Learn more about the reflection across the y-axis here:
https://brainly.com/question/1854517
#SPJ1
Multiply (x + 2)(3x² - 4x + 5).
a. 3x³ + 2x²-3x+10
b. 3x³-4x² + 5x+10
c. 3x³ - 2x²-3x+10
d.
3x² +10x² + 13x+10
Answer:
a. 3x^3 + 2x^2 - 3x +10
Step-by-step explanation:
(x+2)(3x^2-4x+5)
x(3x^2-4x+5) +2(3x^2-4x+5)
3x^3-4x^2+5x+6x^2-8x+10
3x^3-4^2+6x^2+5x-8x+10
3x^3+2x^2-3x+10
What is the value of 2√4+3√9
[tex]2 \sqrt{4} + 3 \sqrt{9} \\ 2(2) + 3(3) \\ 4 + 9 = 13[/tex]
Answer:
13
Step-by-step explanation:
2×√4+3×√(9
2x2+3x3
A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fifth graders has a mean depression score of 4.4. Use the .01 level of significance.
1. The counselor calculates the unbiased estimate of the population's variance to be 15. What is the variance of the distribution of means?
A) 15/20 = 0.75
B) 15/19 = 0.79
C) 152/20 = 11.25
D) 152/19 = 11.84
2. Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis?
A) Reject it
B) Fail to reject it
C) Postpone any decisions until a more conclusive study could be conducted
D) There is not enough information given to make a decision
3. Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance) is .85. What is the effect size?
A) 5/.85 = 5.88
B) .85/5 = .17
C) (5 - 4.4)/.85 = .71
D) .85/(5 - 4.4) = 1.42
1. The variance of the distribution of means option A) 15/20 = 0.75
2. The decision that counselor should make regarding the null hypothesis is that: option "Fail to reject it"
3. The effect of the size is: option c: (5 − 4.4)/.85 = .71
What is the variance about?Note that:
Sample size = 20.
Note that for us to be able to get the answer in question one, we have to divide the unbiased estimate for the population variance by the use of 20 so that we can be able to get our unbiased estimate for the variance: And as such;
15/20 = 0.75.
The term fail to reject implies that the null hypothesis is one that has not been disproven or wrong and therefore the use of the term "failure to reject." It is one that should not be taken with acceptance.
Therefore, 1. The variance of the distribution of means option A) 15/20 = 0.75
2. The decision that counselor should make regarding the null hypothesis is that: option "Fail to reject it"
3. The effect of the size is: option c: (5 − 4.4)/.85 = .71
Learn more about variance from
https://brainly.com/question/15858152
3SPJ1
Helpppppp show your work
Answer:
-5/3
Step-by-step explanation:
Do PEMDAS
8 - 11 = -3
-3 ^ 3 = -27
-(-27) = 27
I-14I = 14
3 x 14 = 42
27 - 42 = -15
2^4 = 16
16 - 7 = 9
-15/9 = -5/3
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:
A [tex] \dfrac{2x^3}{3yw} [/tex]
Step-by-step explanation:
[tex] \dfrac{xy(24x^2y^3w)}{36y^5w^2} = [/tex]
[tex] = \dfrac{2 \times 12 x^3y^4w}{3 \times 12y^5w^2} [/tex]
[tex] = \dfrac{2x^3}{3yw} [/tex]
G
Which point is located at (-3.5.-4.5)?
Y
A
(1
-5-4-3-2-1
point A
point K
point R
4
-3-
2
10
-I ? ? + 4
2
3
2 3 4
en.
5
X
A computer chip factory produces 520 chips in 13 minutes. at this rate, how many chips does it produce in 1 hour?
An observer (o) spots a plane (p) taking off from a local airport and flying at a 29° angle horizontal to her line of sight and located directly above a tower (t). the observer also notices a bird (b) circling directly above her. if the distance from the plane (p) to the tower (t) is 6,000 feet, how far is the bird (b) from the plane (p)? round to the nearest whole number. two parallel lines bp and ot with a transversal running through p and o. dotted red line from p to t and from b to o. angle pot is 29 degrees. the length of pt is 6000. the length of bp is x. 6,857 feet 10,824 feet 12,371 feet 22,063 feet
The distance between the bird and the aircraft is 10824 feet.
What is right angled triangle?Any triangle with one angle at a right angle or two perpendicular sides is referred to as a right triangle, right-angled triangle, orthogonal triangle, or more formally, a rectangle triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
What is Tangent?The straight line that "just touches" the curve at a certain point is known as the tangent line to a plane curve. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another.
According to the given information:Angle of elevation = 29°
Length of plane to the tower = 6000 feet
So, it forms a right angled triangle.
So, we will use "Tangent":
tan29° = AB/CB
.55 = 6000/CB
CB = 6000/0.55
CB = 10824ft
Consider, ΔABC,
Hence, The distance between the bird and the aircraft is 10824 feet.
To know more about right angled triangle visit:
https://brainly.com/question/12158049
#SPJ4
________ If an arc has measure 7π/4 radians, what is its measure in degrees?
________ What is 60° in radians?
If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
Given that arc has measure of 7π/4.
We are required to convert the measure from radian to degree measure.
Converting means chaning of units from one to another.
To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.
7π/4=7*180/4
=7*45
=315 degrees
Now we have to convert 60 degrees into radians.
60 degrees=60*π/180
=π/3
Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
Learn more about arc at https://brainly.com/question/2005046
#SPJ1
THIS IS REALLY IMPORTANT I NEED IT DONE BY TODAY PLEASE
Answer:
15. 155°
16. 115°
Step-by-step explanation:
15.
Use the big triangle.
At the top, the supplement of 60° is 120°.
The angle measuring 120° and the angle measuring 35° are the remote interior angles to exterior angle x.
120° + 35° = x
x = 155°
16.
See picture below.
x = 115°
Answer:
15) x = 155°
16) x = 115°
Step-by-step explanation:
The theorem that relates an exterior angle of a triangle to the opposite (remote) interior angles is helpful for these problems. It says the exterior angle is equal to the sum of the remote interior angles.
15)
Remove the altitude line and consider the interior angle of the triangle next to the exterior angle marked 60°. That interior angle will be ...
180° -60° = 120°
Then the angle we just found and the one marked 35° are "remote" to the exterior angle marked x. The theorem cited at the beginning tells us ...
x = 35° +120°
x = 155°
16)Extend the left side of the "parallelogram" (the side with the arrow) upward until it meets the top horizontal line. This cuts off a triangle with an exterior angle marked x, an interior angle marked 50°, and another remote interior angle at the top edge of that triangle.
The opposite angles of a parallelogram are congruent, so the external angle to the triangle at the top edge will be x, and the adjacent interior angle in the triangle will be (180° -x).
The exterior angle (x) is equal to the sum of the remote interior angles (50° and (180° -x)), so we have ...
x = 50 +(180 -x)
2x = 230 . . . . . . add x, simplify
x = 115 . . . . . . . divide by 2
The measure of the angles marked x is 115°.
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 40 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of the halfpipe is Option A , (0, 20); Y equals one over eighty times x squared plus 20.
The equation of the halfpipe is Y = X²/80 +20.
What is parabola ?
A parabola is the set of points in a plane that are the same distance from a given point and a given line in that plane. The given point is called the focus, and the line is called the directrix. The midpoint of the perpendicular segment from the focus to the directrix is called the vertex of the parabola.The equation of parabola is given by
(X-h)² = 4p(Y-k)²
In this case h = 0
So we get
Y = X²/4P +k
Focus point is (h, p+k) , (p+k) = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X²/80 +20
Therefore, the equation of the halfpipe is Y = X²/80 +20
Learn more about parabola
brainly.com/question/21685473
#SPJ4
The complete question is -
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
n January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?
Answer: The gas would not have remained liquid
Step-by-step explanation:
Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid
Find the indicated maximum or minimum value of f subject to the given constraint. maximum: f(x,y,z)=x2y2z2; x2 y2 z2=4
The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.
An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.
A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development. Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.
Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.
From &22 = x²y 2
2
Given 2²+7+2=5
= <**,4),2=>
By Logange's multijet
(2643805 = 12'aresta
Mithaling by by and
and y
x²²* = P ←
: +(1,2,2) = $
= 125
279
The maximum value is 12r
Learn more about constraints here https://brainly.com/question/14825041
#SPJ4
1/4a-3=1/4a(a-?) I need to finish this quick can someone repy fast!
Answer:
12
Step-by-step explanation:
Factoring out a 1/4 from 1/4a - 3, you get 1/4 (a - 12) as 12 * 1/4 = 3. Thus, ? = 12.
Using the online tool, find two different combinations of radius and height that produce two cylinders with nearly the same volume. Record the
dimensions and volumes of the two cylinders below.
The radii and the heights of the two cylinders are
Cylinder 1: Height = 6 and Radius = 5Cylinder 2: Height = 10 and Radius = 3.87How to determine the combinations of radius and height?The volume of a cylinder is
V = πr²h
When the volumes of two cylinders are almost equal, then it means that:
V1 ≈ V2
This gives
πr²h ≈ πR²H
Divide both sides by π
r²h ≈ R²H
Assume that r = 5 and h = 6
So, we have:
5² * 6 ≈ R²H
Evaluate the product
150 ≈ R²H
Assume H = 10
So, we have:
150 ≈ R² * 10
Divide by 10
R² ≈ 15
Take the square root of both sides
R ≈ 3.87
Hence, the radii and the heights of the two cylinders are
Cylinder 1
Height = 6 and Radius = 5
Cylinder 2
Height = 10 and Radius = 3.87
Read more about cylinder volume at:
https://brainly.com/question/9554871
#SPJ1
Answer:
These radius and height values will produce the same volume:
radius = 6 units and height = 18 units
radius = 9 units and height = 8 units
In the figure, what is the ratio of the area of square KLMN to the area of LOK?
the ratio of the area of square KLMN to the area of LOK is 2a^2/b h
How to determine the ratioFrom the image given, we can deduce the following;
KLMN is a squareLOK is a triangleThe formula for area of a square is
Area = a^2
Where, 'a' is the side
The formula for area of a triangle
Area = 1/ 2 base × height
Now, let's find the ratio
Ratio = area of KLMN/ area of LOK
Ratio = [tex]\frac{a^2}{\frac{1}{2} bh}[/tex]
Ratio = [tex]\frac{a^2}{\frac{bh}{2} }[/tex]
make the expression linear
Ratio = 2a^2/bh
The ratio of the area of square KLMN to the area of LOK is 2a^2/bh
Thus, the ratio of the area of square KLMN to the area of LOK is 2a^2/b h
Learn more about area here:
https://brainly.com/question/25260313
#SPJ1
A plate of vegetables and white rice. jace is a vegetarian, eating at a local restaurant. he chooses a grilled tofu salad that includes vegetables. what change can he request to make his meal healthier? he can ask for the tomatoes to be left out. he can ask for brown rice instead of white rice. he can ask for his tofu to be fried instead of grilled. he can ask for fewer sprouts, peas, and cucumbers.
I’m stuck on this problem
The value of the f(-8) from the given f(x) is 1/53.
According to the statement
we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).
So, For this purpose,
The given value of f(x) :
The function f(x) is
f(x) = 1 / x^2 -11
Now we find the value of the f(-8) then
For this put Put x is -8 in the f(x) then the equation become
f(x) = 1 / x^2 -11
f(-8) = 1 / (-8)^2 -11
f(-8) = 1 / 64 -11
f(-8) = 1 / 53.
here the value becomes 1/53.
So, The value of the f(-8) from the given f(x) is 1/53.
Learn more about function f(x) here
https://brainly.com/question/4025726
#SPJ1
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!
[tex]y = - 5x + n \\ [/tex]
( -1 , -2 ) satisfies the equation of y[tex] - 2 = - 5( - 1) + n \\ - 2 = 5 + n \\ n = - 7[/tex]
[tex]y = - 5x - 7 \\ 5x + y = - 7[/tex]
Option 2Answer:
○ [tex]5x + y = -7[/tex]
Step-by-step explanation:
The formula for forming the equation of a line given a point and a slope is:
[tex]\boxed{y- y_1 = m(x - x_1)}[/tex],
where:
m = slope (-5)
[tex]y_1[/tex] = y-coordinate of point (-2)
[tex]x_1[/tex] = x-coordinate of point (-1).
Substituting these values into the formula:
[tex]y - (-2) = -5(x - (-1))[/tex]
⇒ [tex]y + 2 = -5(x + 1)[/tex]
⇒ [tex]y + 2 = -5x -5[/tex] [expanding the brackets]
⇒ [tex]y = -5x -5 - 2[/tex] [subtracting 2 from both sides]
⇒ [tex]y = -5x - 7[/tex]
⇒ [tex]5x + y = -7[/tex] [adding [tex]5x[/tex] to both sides]
This means that the second option is correct.
Read more on point-slope form at:
https://brainly.com/question/15143525
Which congruence postulate or theorem is stated below?
The congruence postulate or theorem that is stated is the: C. AAS congruence theorem.
What are Congruent Triangles?Triangles that are referred to as congruent triangles are triangles that have corresponding congruent sides and corresponding congruent angles.
What is the Angle-angle-side Congruence Theorem (AAS)?According to the angle-angle-side congruence theorem (AAS) two triangles are congruent if two angles and a non-included side of one triangle are congruent to two corresponding angles and a non-included side of the other are congruent to each other.
For example, in triangles GUM and RED given in the image attached below, we have the following:
∠G ≅ ∠R [a pair of congruent angles]
∠M ≅ ∠D [a pair of congruent angles]
GU ≅ RD [a pair of non-included congruent side]
Thus, both triangles are congruent by the AAS, which is the congruence theorem that is stated above.
The answer is: C. AAS.
Learn more about the AAS congruence theorem on:
https://brainly.com/question/3168048
#SPJ1
Answer:
aas
Step-by-step explanation:
Which of the following relationships will have a positive slope? Select all that apply.
42. There are eight squares on each side of a chessboard. How many squares are on a chessboard? Write an expression in exponent form then evaluate.
Answer:
Number of the squares on chessboard = 64
Exponent form = [tex]8^{2}[/tex]
Step-by-step explanation:
8 x 8 = 64
exponent form of of the chessboard
= [tex]8^{2}[/tex]
PLEASE HELP IM SERIOUSLY STUCK
Formula for the Slope: (y2 - y1) / (x2 - x1)
You can use any two points to find the slope, as long as those two points are on the line.
Point 1 = (-2, 8)
Point 2 = (0, 0)
Slope = (0 - 8) / (0 - - 2)
Slope = -8 / 2
Slope = -4
Hope this helps!
Answer:
-4
Step-by-step explanation:
The formula to find the slope is (change in y)/(change in x). In other words, rise over run.
If we look at the data, we can see that the x and y value changes.
x value: -3 --> -2 --> -1 --> 0 --> 1
y value: 12 --> 8 --> 4 --> 0 --> -4
When y changed from 12 to 8, the x changed from -3 to -2.
y: 12 --> 8
x: -3 --> -2
There was a difference of -4 in the y and a difference of 1 in the x.
At the top, I wrote that the slope was (change in y)/(change in x)
With -4 and 1 we found, we can say that the slope is -4/1.
If we simplify this answer, we end up with -4.
So -4 is the slope of the data.
Write the algebraic expression that represents the following: The difference of thirteen and a number
[tex]\Large\texttt{Answer}[/tex]
[tex]\bold{n-13}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Again letting n be the number
[tex]\bold{n}[/tex]
⇨ Subtract 13 from n
[tex]\bold{n-13}[/tex]
*unlike addition, the order DOES matter, because
[tex]\bold{n-13\ne 13-n}[/tex]
Hope that helped
A binary operation * is defined on the set of Real numbers,R by m*n=(√m +√n) (√m-√n).Find the values of P,if P*3=1
The value of P such that P*3=1 is 4
How to solve for P in the set?The set of Real numbers, R is given as
m*n=(√m +√n) (√m-√n).
The values of P, if P*3=1 is represented as:
P * 3=(√P +√3) (√P-√3).
The result of this operation is 1.
So, we have:
(√P +√3) (√P-√3) = 1
Apply the difference of two squares
P - 3 = 1
Add 3 to both sides
P = 4
Hence, the value of P such that P*3=1 is 4
Read more about binary operations at:
https://brainly.com/question/8649831
#SPJ1
A painter needs to measure the height from the ground to the base of a 2nd story window. He props his ladder against the base of the window. He finds the height from one rung of the ladder to the point on the ground below it, and the distance from that point to the base of the ladder. This is shown in the figure.
If XY = 8 inches, WY = 24 inches, and XZ = 48 inches, the height from the ground to the base of the window is inches.
The height from the ground to the base of the window is 16 inches.
What is the height from the ground to the base of the window is inches?The ladder and the wall of the window form a right angled triangle. A right angled triangle is a three-sided polygon. The square of the longest side of a right angled triangle is equal to the sum of the squares of the other two sides.
In order to determine the length from the ground to the window, the law of similar triangles would be used. The similar triangles are triangle WXY and triangle VXZ. It is expected that the length of the sides are proportional to each other.
XY / XZ = WY / VZ
(8 / 24) = WY / 48
WY = (8 X 48) / 24 = 16 inches
To learn more about similar triangles, please check: https://brainly.com/question/10658464
#SPJ1
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