1) Given that the sum of all probabilities must be equal to 1, and there are 6 plums, 14 clementines, and 12 nectarines we can tell there are 14+12+6 objects:
14+12+6= 32 this is our subspace.
2) So let's find first the probability of that teacher picking a nectarine:
[tex]{\textcolor{orange}{P(nectarine)}}=\frac{12}{32}[/tex]But notice, we don't want to know that we want the probability of not picking a nectarine so let's subtract that from 1 and write it this way:
3) We want to find the probability of the Complementary set to that:
[tex]\begin{gathered} {\textcolor{red}{P(NOT\: nectarine)}}=1-\frac{12}{32} \\ {\textcolor{red}{P(NOT\: nectarine)}}=\frac{32}{32}-\frac{12}{32} \\ {\textcolor{red}{P(NOTnectarine)}}=\frac{20}{32}=\frac{5}{8} \end{gathered}[/tex]Note that we simplified this.
Find the sum of the first 14 terms of the geometric series 1+4+16+64+….
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given geometric series
[tex]1+4+16+64+...[/tex]STEP 2: Write the formula to calculate the sum of nth terms of a geometric series
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]where r is the common ration
a is the first term
Sn is the sum of the nth term
n is the number of terms
STEP 3: Write the required data values
[tex]n=14,a=1,r=\frac{T_2}{T_1}=\frac{4}{1}=4[/tex]STEP 4: substitute the values to find the sum of the first 14 terms
[tex]\begin{gathered} S_{14}=\frac{1(4^{14}-1)}{4-1} \\ =\frac{268435456-1}{3}=\frac{268435455}{3}=89478485 \end{gathered}[/tex]Hence, the sum of the first 14 terms of the given geometric series is 89478485
Solve the following system of equations using any method you want. (1 pt)y = 2x + 33x + 2y = 34O No solution(3,9)(6,8)(4, 11)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
eq1. y = 2x + 3
eq2. 3x + 2y = 34
Step 02:
eq1. in eq2.
3x + 2 (2x + 3) = 34
3x + 4x + 6 = 34
7x = 34 - 6
x = 28 / 7
x = 4
eq1.
y = 2 (4) + 3
y = 8 + 3
y = 11
The answer is:
(4 , 11 )
I need to find x but am lost which equation I should use
In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side. In our triangle, 7 is the adjacent side to 30º, and x is the opposite side.
From this, we have the following relation
[tex]\begin{gathered} \frac{x}{7}=\tan (30^o) \\ x=7\cdot\tan (30^o) \end{gathered}[/tex]The tangent of 30º ise a known value
[tex]\tan (30^o)=\frac{1}{\sqrt[]{3}}[/tex]Solving for x, we have
[tex]\begin{gathered} x=\frac{7}{\sqrt[]{3}} \\ x=4.04145188433\ldots \end{gathered}[/tex]-×^2 - 7x + 7 = -2x^2 to the nearest tenth.
Solving Quadratic Equations
The general form of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]It can be solved by using the formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]we have the following equation:
[tex]-x^2-7x+7=-2x^2[/tex]we need to put this equation in standard form as explained above
Adding 2x^2:
[tex]\begin{gathered} 2x^2-x^2-7x+7=-2x^2+2x^2 \\ \text{Simplifying:} \\ x^2-7x+7=0 \end{gathered}[/tex]Now we have the equation in the correct form, we find the value of the variables as follows:
a=1, b=-7, c=7
Applying the formula:
[tex]x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(7)}}{2(1)}[/tex]Operating:
[tex]x=\frac{7\pm\sqrt[]{49-28}}{2}=\frac{7\pm\sqrt[]{21}}{2}[/tex]The square root of 21 is not exact, we use two decimals so far, and we'll round to one decimal at the very last time.
Taking the square root:
[tex]\begin{gathered} x=\frac{7\pm4.58}{2} \\ We\text{ have two solutions:} \\ x=\frac{7+4.58}{2}=7.79 \\ x=\frac{7-4.58}{2}=1.21 \end{gathered}[/tex]The solutions (to the nearest tenth) are:
x= 7.8
x=1.2
Answer complete
Did you understand the explanation?
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A rectangle has length=4x-3 and the width=-5x+7What is the perimeter?
You have a rectangle with length l = 4x - 3 and width w = -5x + 7
In order to know the perimeter of the rectangle you use the following formula:
P = 2w + 2l
where w and l are the width an length of the rectangle respectively.
By replacing the algebraic expressions for w and l into the previous equation for the perimeter you obtain:
P = 2(4x -3) + 2(-5x + 7) apply distribution property
P = 8x - 6 - 10x + 14
P = -2x + 8
P = 8 - 2x
Hence, the perimeter of the rectangle is 8 - 2x
Select all of the categories that apply for the figure below.quadrilateraltrapezoidparallelogramrhombusrectanglesquare
Answer:
Quadrilateral, Parallelogram & Rectangle
Explanation:
We were given the figure attached. From the figure, we can deduce that it has the following properties:
I. Opposite sides are congruent
II. All interior angles are congruent (right angles)
III. Adjacent angles are supplementary (sum up to 180 degrees)
IV. Adjacent sides are not congruent
V. Opposite sides are parallel
Rhombus & squares have all sides congruent but that is not the case in the figure given us:
From the above, the following figures tick the checklist:
Quadrilateral
Parallelogram
Rectangle
Hence, the correct options are: Quadrilateral, Parallelogram & Rectangle
A person plans to invest a total of $6500 in one bank account at 2.8% annual interest and another bank account at 18% annual interest. how much should he invest in each account so that the total interest in one year will be $410
We will do a system of equations
x amount invested at 2.8%
y amount invested at 18%
the first equation will be the total invest
x+y=6500
then the second equation is about the simple interest
0.028x+0.18y=410
then we isolate the x of the first equation
x=6500-y
we substitute this equation on the second equation
0.028(6500-y)+0.18y=410
then we simplify the expression
[tex]182-0.028y+0.18y=410[/tex]then we sum like terms
[tex]0.152y=410-182[/tex][tex]0.152y=228[/tex]then we isolate the y
[tex]y=\frac{228}{0.152}[/tex][tex]y=1500[/tex]then we substitute the value of y in the equations with x isolate
[tex]x=6500-1500[/tex][tex]x=5000[/tex]5000 amount invested at 2.8%
1500 amount invested at 18%
New company games 95 customers each year each year they also lose 16 customers write a linear function that represents the number of customers the company has acquired over time
A company gains 95 customers each year. They lose 16 each year. write a linear function that represents the number of customers the company has acquired over time
Let
x -----> the number of years
y ----> the number of customers the company has acquired over time
we have that
y=(95-16)x
therefore
the linear equation is
y=79xIdentify each congruence transformation that maps triangle ABC to triangle DEF
The first step is to write the coordinate of corresponding vertices in triangles ABC and DEF. Let us consider vertex C in triangle ABC and the corresponding vertex F in triangle DEF. The coordinates are
C = (3, 2)
F = (- 1, - 2)
We want to transform (3, 2) to (- 1, - 2)
Recall, if we reflect a vertex, (x, y) over the x axis, the x coordinate remains the same while the sign of the y coordinate is reversed. Thus, by reflecting (3, 2) over the x axis, the new coordinate is (3, - 2)
Also, if we reflect a vertex, (x, y) over the y axis, the y coordinate remains the same while the sign of the x coordinate is reversed. Thus, by reflecting (3, - 2) over the x axis, the new coordinate is (- 3, - 2)
Recall, if a vertex, (x, y) is translated d units to the right, the new vertex would be (x + d, y). If we translate (- 3, - 2) 2 units to the right, the new vertex would be (-3 + 2, - 2) = (- 1, - 2). This corresponds to vertex F
Thus, the correct option is
A reflection in the x axis, followed by a reflection in the y axis and then a translation, 2 units to the right
Also, if we rotate a point, (x,y) 180 degrees about the origin, the new point would be (- x, - y). By rotating (3, 2) by 180 degrees about the origin, the new vertex would be (- 3, - 2). If we translate (- 3, - 2) 2 units to the right, the new point is (-3 + 2, - 2) = (- 1, - 2). This corresponds to vertex F
Thus, another correct option is
A rotation 180 degrees about the origin followed by a translation 2 units to the right
purpose of bar graphs and data example
To compare the different variables and to know which variable has more percent compare to the others.
In this bar graph, we compare different frutis and which fruit prefer the people
Can someone pls help me thxs .Y - 3 = -3*Y - 43
We have the following:
[tex]Y-3=-3\cdot Y-43[/tex]Solving for Y:
[tex]\begin{gathered} Y+3\cdot Y=-43\text{ + 3} \\ 4\cdot Y\text{ = -40} \\ Y\text{ = }\frac{-40}{4} \\ Y\text{ = }-\text{10} \end{gathered}[/tex]Therefore the question is -10
Show the equations in slope intercept form and determine how many solutions does the system of equations have? Explain.2x - 9y = -5 4x - y = 2
first solve each equation for y
[tex]\begin{gathered} 2x-9y=-5 \\ -9y=-5-2x \\ y=\frac{5}{9}+\frac{2}{9}x \end{gathered}[/tex][tex]\begin{gathered} 4x-y=2 \\ -y=2-4x \\ y=-2+4x \end{gathered}[/tex]the equations are
[tex]\begin{gathered} y=\frac{5}{9}+\frac{2}{9}x \\ \\ y=-2+4x \end{gathered}[/tex]we can substract the equations to remove y
[tex]\begin{gathered} y=\frac{5}{9}+\frac{2}{9}x \\ \\ y=-2+4x \\ \\ ---------------- \\ 0=\frac{23}{9}-\frac{34}{9}x \end{gathered}[/tex]now solve x
[tex]\begin{gathered} \frac{23}{9}-\frac{34}{9}x=0 \\ \\ 23-34x=0 \\ 34x=23 \\ \\ x=\frac{23}{34} \end{gathered}[/tex]the value of x is 23/34, now replace on any equation to find Y, I will replace on the second
[tex]\begin{gathered} y=-2+4(\frac{23}{34}) \\ \\ y=-2+\frac{46}{17} \\ \\ y=\frac{12}{17} \end{gathered}[/tex]the value of y is 12/17
the solution point is ( 23/34 , 12/17)
If the side opposite to the 72° angle is 42 units, what is the length of the hypotenuse
Answer:
44.21 units
Explanation:
For a right angle with an angle of 72 degrees:
[tex]\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{19}{20}[/tex]Given that the side opposite to the 72° angle = 42 units
[tex]\begin{gathered} \implies\frac{19}{20}=\frac{42}{\text{Hypotenuse}} \\ \text{Hypotenuse}\times19=20\times42 \\ \text{Hypotenuse}=\frac{20\times42}{19} \\ \text{Hypotenuse}=44.21 \end{gathered}[/tex]The length of the hypotenuse is 44.21 units.
Original price $70; Markup 15%The retail price is $ ?
We can calculate the retail price R as the original price C plus the remark k*C:
[tex]R=C+k\cdot C=C(1+k)=70\cdot(1+0.15)=70\cdot1.15=80.5[/tex]Answer: The retail price is $80.50.
HELPP OMG ITS 1 IN THE MORNING AND THIS WAS DUE AT 12:00 AM
Answer: 4 units²
The formula for the Area of a Triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]Where:
b = base
h = height
If we rotate the triangle counterclockwise, we can see that the base is 4 units while the height is 2 units. Substitute these to the formula and we will get:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(4\text{ units})(2\text{ units}) \\ A=4\text{ units}^2 \end{gathered}[/tex]Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval x2 + 2x +2 x
In order to determine the area in the interval [-3, -3] of the function enclosed by:
[tex]f(x)=\begin{cases}x^2+2x+2 \\ 3x-4\end{cases}[/tex]When the first term is for x<2 and the second when x>=2.
We proceed as follows:
[tex]\int ^3_{-3}(x^2+2x+2)-(3x-4)\rbrack dx[/tex][tex]\Rightarrow\int ^3_{-3}(x^2-x+6)dx=\frac{x^3}{3}-\frac{x^2}{2}+6x|^3_{-3}=54[/tex]I need help with his geometry question can someone please help
Notice that
[tex]\angle BOM\cong\angle DON[/tex]Because they are vertical angles, and
[tex]\angle AOM\cong\angle DON[/tex]is a given congruence.
Therefore, we can conclude that
[tex]\angle AOM\cong\angle BOM[/tex]Because they are congruent to the same angle: Angle DON.
Therefore, the correct answer is Option D.
Solve the simultaneous equations
2x + 3y = 13
4x - y = -2
Answer:
x = 0.5, y = 4
Step-by-step explanation:
We have 4x - y = -2, so 4x = y - 2 and x = (y-2)/4.
Then, 2x = 2(y-2)/4=(y-2)/2. And, we have (y-2)/2 + 3y = 13, then y-2 + 6y = 26, 7y - 2 = 26 and y = 28/7 = 4.
Now it's very easy: if y = 4, we can modify second equation in 4х - 4 = -2. So, 4x = -2+4 = 2, and finally x = 2/4 = 0.5..
Hope that this was helpful.
I'm looking answer for my question please answer for me number one work out find value of k
if a polynomial P(x) is divided by a binomial (x-c) then the remainder is equal to P(c).
where c=-3
[tex]\begin{gathered} P(-3)=-19+9k=8 \\ \text{ }9k=8+19\text{ } \\ 9k=27 \\ k=\frac{27}{9} \\ k=3 \end{gathered}[/tex]the value of k=3
A glass blower can form 8 simple vases or 2 elaborate vases in an hour. In a work shift of no more than 8 hours, the worker must form at least 40 vases.
a. Let s represent the hours forming simple vases and e the hours forming elaborate vases. Write a system of inequalities involving the time spent on each type of vase.
b. If the glass blower makes a profit of $30 per hour worked on the simple vases and $35 per hour worked on the elaborate vases, write a function for the total profit on the vases.
c. Find the number of hours the worker should spend on each type of vase to maximize profit. What is that profit?
Answer:
[tex]\textsf{a)} \quad \begin{cases}s+e \leq 8\\8s+2e \geq 40\end{cases}[/tex]
[tex]\textsf{b)} \quad y = 30s + 35e[/tex]
c) 4 simple vases and 4 elaborate vases maximize profit.
The maximum profit is $260.
Step-by-step explanation:
Given information:
A glass blower can form 8 simple vases or 2 elaborate vases in an hour. In a work shift of no more than 8 hours, the worker must form at least 40 vases.Part (a)Define the variables:
Let s = the number of hours forming simple vases.Let e = the number of hours forming elaborate vases.Create a system of inequalities using the given information and defined variables:
[tex]\begin{cases}s+e \leq 8\\8s+2e \geq 40\end{cases}[/tex]
Part (b)Given information:
$30 = profit per hour for the simple vases.$35 = profit per hour for the elaborate vases.Let y be the total profit in dollars:
[tex]y = 30s + 35e[/tex]
Part (c)[tex]\begin{cases}s+e \leq 8\\8s+2e \geq 40\end{cases}[/tex]
To find the number of hours the worker should spend on each type of vase to maximize profit, find the point of intersection of the two equations.
Isolate e in the first equation:
[tex]\implies e\leq8-s[/tex]
Isolate e in the second equation:
[tex]\implies 2e \geq 40-8s[/tex]
[tex]\implies e \geq 20-4s[/tex]
Equate the two expressions for e and solve for s:
[tex]\implies 8-s=20-4s[/tex]
[tex]\implies 3s=12[/tex]
[tex]\implies s=4[/tex]
Therefore, the number of hours the worker should spend on each type of vase to maximize profit is:
Simple vases = 4 hours.Elaborate vases = 4 hours.Substitute the values of s and e into the function from part (b):
[tex]\implies y=30(4)+35(4)[/tex]
[tex]\implies y=120+140[/tex]
[tex]\implies y=260[/tex]
Therefore, the maximum profit is $260.
a. What trend line, in slope-intercept form, models the data? b. Explain why there could be no data points on a trend line, yet the line models the data.
a)We can take the points (3,68) and (7,60) to find an equation of the line in slope-intercept form:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{60-68}{7-3}=\frac{-8}{4}=-2 \\ m=-2 \\ \text{Equation in slope intercept form:} \\ y-y_1=m(x-x_1) \\ \Rightarrow y-68=-2(x-3)=-2x+6 \\ \Rightarrow y=-2x+6+68=-2x+74 \\ y=-2x+74 \end{gathered}[/tex]therefore, a possible model for the trend line is y=-2x+74
b)The model can have some points that represent the trend, but some others may be a little off, but when the model is represented using some of the points and trying to get the minimum distance from the line to the points that not necesarily are on the line, the model can represent with some significance level the trend line.
Please see the picture below I NEED BOTH A AND B. (A&B) not just A
To solve this question, use the law of cosines shown below:
[tex]c^2=a^2+b^2-2*a*b*cosC[/tex]In this question,
a = 6
b = 8
C = 10°
First, let's find c:
[tex]\begin{gathered} c^2=6^2+8^2-2*6*8*cos10 \\ c^2=36+64-94.54 \\ c^2=5.46 \\ \sqrt{c^2}=\sqrt{5.456} \\ c=2.34 \end{gathered}[/tex]Second, let's find A.
Now, a, b, and c are known, and Cos A is not known:
[tex]\begin{gathered} a^2=b^2+c^2-2bc*cosA \\ 6^2=8^2+2.34^2-2*8*2.34*cosA \\ 36=64+5.48-37.44*cosA \\ 36=69.48-37.44*cosA \\ \text{ Subtracting 69.46 from both sides:} \\ 36-69.48=69.46-37.44*cosA-69.46 \\ -33.48=-37.44*cosA \\ \text{ Dividing both sides by -37.44:} \\ \frac{-33.48}{-37.44}=\frac{-37.44}{-37.44}cosA \\ 0.8942=cosA \\ Then, \\ A=cos^{-1}(0.8942) \\ A=26.6 \end{gathered}[/tex]Answer:
c = 2.34 units
A = 26.6°
4. A plumber charges $50 to make a house call. He also charges $25.00 per hour for labor. A. Write an equation that you could use to the amount a plumber charges for a house call based on the number of hours of labor.How much would it cost for a house call that requires 2.5 hours of labor? C. If the bill from the plumber is $162.50, how many hours did the plumber work at your house?
We are given a problem that can be solved using a line equation. We are told that a plumber charges initialy $50 and from then he charges $25 per hour. Therefore, the amount charged must be equal to the initial amount
A group of students went on a field trip. There were 3 Boys for evrey 4 Girls in the group. if there were 20 girls, how many students in all went on the field trip?
Answer
35 students went on the field trip.
Explanation
We are told that for this field trip,
3 boys = 4 girls
We are then told that there were 20 girls on the trip.
Let the number of boys on the trip be x
3 boys = 4 girls
x boys = 20 girls
We can form a mathematical relationship by cross multiplying
x × 4 = 3 × 20
4x = 60
Divide both sides by 4
(4x/4) = (60/4)
x = 15 boys
Total number of students that went on the trip = 15 boys + 20 girls = 35 students.
Hope this Helps!!!
surface area of a sphere whos circle has a circumference of 14(pi symbol) cm
Given:
The circumference of a circle is
[tex]14\pi cm.[/tex]Required:
We need to find the surface area of a sphere whose circle has a circumference of
[tex]14\pi cm.[/tex]Explanation:
Consider the circumference of the circle formula.
[tex]C=2\pi r[/tex][tex]Substitute\text{ C=}14\pi cm\text{ in the formula.}[/tex][tex]14\pi=2\pi r[/tex][tex]Divide\text{ both sides by }2\pi.[/tex][tex]\frac{14\pi}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]7=r[/tex]We get r =7cm.
Consider the surface area of the sphere.
[tex]SA=4\pi r^2[/tex]Substitute r = in the formula,
[tex]SA=4\pi(7)^2[/tex][tex]SA=4\pi(49)[/tex][tex]SA=196\pi cm^2[/tex]Final answer:
[tex]The\text{ s}urface\text{ area of the sphere}=196\pi cm^2[/tex][tex]The\text{ s}urface\text{ area of the sphere}=196\times3.14cm^2[/tex][tex]The\text{ s}urface\text{ area of the sphere}=615.44cm^2[/tex]Find the equation of a line that is parallel to Y = 2x +5 and contains the points (2,-4)
GIVEN:
We are given the equation of a line as follows;
[tex]y=2x+5[/tex]Required;
To find the equation of a line that is parallel to this line and that contains the coordinates;
[tex](2,-4)[/tex]Step-by-step solution;
First thing to note is that, the equation of the line is given in the slope-intercept form. The slope-intercept form of a linear equation is generally written as;
[tex]\begin{gathered} y=mx+b \\ \\ m=slope,\text{ }b=y-intercept \end{gathered}[/tex]For a line that is parallel to another, the slopes are equal in value. This simply means the slope of the other line (the line parallel to the one given) is 2.
Note that the slope of the line given is;
[tex]\begin{gathered} y=mx+b \\ \\ y=2x+5 \\ \\ Therefore; \\ \\ m=2 \end{gathered}[/tex]For a line that contains the point (2, -4) and the slope is 2, we can now write the following;
[tex]\begin{gathered} y=mx+b \\ \\ Where,\text{ }x=2,y=-4,m=2 \\ \\ Then; \\ \\ -4=2(2)+b \\ \\ -4=4+b \end{gathered}[/tex]Now we subtract 4 from both sides of the equation;
[tex]\begin{gathered} -4-4=4-4+b \\ \\ -8=b \end{gathered}[/tex]Now we have the slope and the y-intercept as;
[tex]\begin{gathered} m=2 \\ \\ b=-8 \end{gathered}[/tex]We can now write the equation of the line as follows;
[tex]\begin{gathered} y=mx+b \\ \\ Hence; \\ \\ y=2x+(-8) \\ \\ y=2x-8 \end{gathered}[/tex]Therefore.
ANSWER:
[tex][/tex]a floral shop has ALL single roses marked 40 percent OFF. What is the amount of the discount if a single rose is $2.35?
The amount of the discount on a single rose is $0.94
OR
94 cents
Alex deposits $6,000 in a Certificate of Deposit (CD) with an APR of 1.2%, compounded monthly. How much will be in the CD in 6 years, to the nearest dollar? The formula for compound interest is given below.A=P(1+r/n) ^ntAmount in 6 years: $_____
Answer:
$
Explanation:
The formula for compound interest is given below:
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}\text{ where }\begin{cases}P=\text{Principal Invested} \\ r=\text{Interest Rate} \\ n=\text{Number of compounding periods}\end{cases}[/tex]For the given problem:
• The amount Alex deposited, P = $6,000
,• Annual Percentage Rate = 1.2% = 1.2/100 = 0.012
,• Time, t = 6 years
,• The number of compounding periods, n = 12 (Monthly)
Substitute these values into the formula above:
[tex]\begin{gathered} A=6000\left(1+\frac{0.012}{12}\right)^{12\times6} \\ =6000(1+0.001)^{72} \\ =6000(1.001)^{72} \\ =6447.70 \\ \approx\$6448 \end{gathered}[/tex]The amount in 6 years is $6,448 (correct to the nearest dollar).
y= 2x^2 +6x+11In vertex form
Given:
[tex]y=2x^2+6x+11[/tex][tex]y=2(x^2+3x+\frac{11}{2})[/tex][tex]y=2(x^2+3x+\frac{9}{4}-\frac{9}{4}+\frac{11}{2})[/tex][tex]y=2(x^2+3x+(\frac{3}{2})^2)-\frac{9}{2}+\frac{22}{2}[/tex][tex]y=2(x+\frac{3}{2}^{})^2+\frac{13}{2}[/tex]Above equation is the vertex form.
QUESTION IS IN IMAGE! DONT NEED TO SHOE WORK JUST NEED THE ANSWER!
Solution:
From the given circle
[tex]\begin{gathered} reflex\text{ m}\angle FEH=128\degree+126\degree=254\degree \\ reflex\text{ m}\angle FEH=254\degree \end{gathered}[/tex]Then,
[tex]\begin{gathered} m\angle FEH=360-254\degree=106\degree \\ m\angle FEH=106\degree \end{gathered}[/tex]To find ∠FGH,
[tex]m\angle FGH=\frac{1}{2}m\angle FEH[/tex]Substitute for ∠FEH
[tex]\begin{gathered} m\angle FGH=\frac{1}{2}\times106\degree=53\degree \\ m\angle FGH=53\degree \end{gathered}[/tex]Hence, ∠FGH is 53°