Answer:
lol
Step-by-step explanation:
Circle A and circle B are congruent. CD is a cord of both circles. if AB = 24 inches in the radius is 13 inches how long is CD A.10in B.26in C.12in D.9in
Option A
Length of CD is 10 inches
Solution:
The diagram is attached below
Given that, Circle A and circle B are congruent
CD is a cord of both circles
AB = 24 inches
Radius = 13 inches
To find: length of CD
Draw a straight line connecting A and C
AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches
Given in question that AB = 24 inches
Therefore from figure, AO = AB/2 = 24/2 = 12
AO = 12
Let "b" be the length of CO
Therefore, CD = CO + OD = b + b
AOC forms a triangle, so we can use pythogoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition for triangle AOC
[tex]AC^2 = AO^2 + OC^2[/tex]
Substituting AC = 13 and AO = 12 and OC = b
[tex]13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5[/tex]
Thus length of CD is:
CD = b + b = 5 + 5 = 10
Thus length of CD is 10 inches
the sum of 3x and 14 equals the difference of 20 and 2x
Answer. 17<18
The sum of 3x + 14 equals 17x.
The difference between 20 - 2x equals 18x.
Therefore the equation is not equal to each other.
There are 30 chairs in the band room mr avery wants to have the same number of chairs in each row there must be more than 1 row and the number of chairs in each row must also be greater than the number of rows explain how mr avery could arrange the chairs
Final answer:
Mr. Avery can arrange the 30 chairs in 5 rows of 6 chairs each or 3 rows of 10 chairs each to satisfy the conditions of having more than one row and the chairs per row being greater than the number of rows.
Explanation:
Mr. Avery can arrange the 30 chairs in the band room in multiple configurations but must satisfy two conditions: there must be more than one row and the number of chairs in each row must be greater than the number of rows. To find such arrangements, we can look for factors of 30 that adhere to these conditions. One possible arrangement is 5 rows with 6 chairs in each row. This satisfies the conditions because there are more than one row, and the number of chairs per row (6) is greater than the number of rows (5).
Another possible arrangement could be 3 rows with 10 chairs each. Here, the condition is also met since there are more than one row and the number of chairs per row (10) is greater than the number of rows (3). Mr. Avery must ensure there's enough space to move around, so he may need to rearrange the chairs to provide adequate pathways between rows.
I kinda need help with this i’ve already done all the other questions but this one and i really want these 600 points :( <3
I think that the answer is A, because in the range, none of the numbers should be the same, and the numbers are all different in choice A
A garden is rectangular with an area of 6/7 square miles. If the length of the garden is 3/5 miles, what is its width?
Answer:
Step-by-step explanation:
Area= length x width
area=6/7, length=3/5, width=?
6/7=3/5 x width
6/7 divided by 3/5= 6/7 x 5/3 (you have to multiply by the recipricol, or flip the fraction.)
6/7 x 5/3=30/21= 1 3/7=width
The area of a 2D form is the amount of space within its perimeter. The width of the rectangle is 10/7 miles.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of a rectangle is the product of its length and its width, therefore, the width of the rectangle can be written as,
Area = Length × Width
Width = Area / Length
Given the area of the rectangle is 6/7 square miles, while the length of the rectangle is 3/5 miles, therefore, the width of the rectangle is,
Width = (6/7)/(3/5)
Width = (6×5)/(7×3) = 10/7
Hence, the width of the rectangle is 10/7 miles.
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If the range of f (x) = StartRoot m x EndRoot and the range of g (x) = m StartRoot x EndRoot are the same, which statement is true about the value of m? m can only equal 1. m can be any positive real number. m can be any negative real number. m can be any real number.
Answer:
b. m can be any positive real number.
Step-by-step explanation:
The value of m can be any positive real number. The correct answer is option b) m can be any positive real number.
Step 1
To determine the value of m that makes the ranges of [tex]\( f(x) = m^x \)[/tex] and [tex]\( g(x) = x^m \)[/tex] the same, we need to analyze the ranges of both functions.
Analyzing [tex]\( f(x) = m^x \)[/tex] :
- If [tex]\( m > 0 \)[/tex], [tex]\( m^x \)[/tex] is an exponential function.
- For [tex]\( m > 1 \)[/tex], [tex]\( f(x) = m^x \)[/tex] increases and its range is [tex]\( (0, \infty) \)[/tex].
- For [tex]\( 0 < m < 1 \)[/tex], [tex]\( f(x) = m^x \)[/tex] decreases and its range is also [tex]\( (0, \infty) \)[/tex].
Step 2
Analyzing [tex]\( g(x) = x^m \)[/tex] :
- The range of [tex]\( x^m \)[/tex] depends on whether m is positive or negative:
- For positive m :
- When [tex]\( m = 1 \)[/tex], [tex]\( g(x) = x \)[/tex], the range is all real numbers, [tex]\( \mathbb{R} \)[/tex].
- When [tex]\( m > 1 \)[/tex] or [tex]\( 0 < m < 1 \)[/tex], the function is defined for [tex]\( x > 0 \)[/tex] and its range is [tex]\( (0, \infty) \)[/tex] .
- For negative m :
- The function [tex]\( x^m \)[/tex] is undefined for [tex]\( x = 0 \)[/tex] and for negative x, and thus its range is [tex]\( (0, \infty) \)[/tex].
Both [tex]\( f(x) = m^x \)[/tex] and [tex]\( g(x) = x^m \)[/tex] have the range [tex]\( (0, \infty) \)[/tex] for any positive [tex]\( m \)[/tex], but for any negative m, [tex]\( g(x) \)[/tex] is undefined at zero and for negative x.
The value of m can be any positive real number (option b).
Complete question : If the range of f(x) = ^mx and the range of g(x) = m ^ x are the same, which statement is true about the value of m?
a) m can only equal 1.
b) m can be any positive real number.
c) m can be any negative real number.
d) m can be any real number.
The quadrilateral shown is a rhombus. What is m∠4?
Answer:
m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)
Step-by-step explanation:
In the diagram. check attach image
m∠A + m∠B + m∠C + m∠D = 360º.
Every quadrilateral can be decomposed (cut apart) into two triangles, each of whose angles' measures sum to 180º.
m∠A + m∠1 + m∠ 3 = 180º
m∠C + m∠2 + m∠4 = 180º
m∠A+m∠1+m∠3+m∠C+m∠2+m∠4 = 360º
therefore :
m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)
................... i got roasted by someone I don’t know wow
Turn both into improper fractions.
6 1/3 = 19/3
4 1/9 = 37/9
Find common denominators
19/3 = 57/9
37/9
Subtract.
57/9 - 37/9 = 20/9
Turn back into a mixed number.
20/9 = 2 2/9
Best of Luck!
Answer:
2 2/9
Step-by-step explanation:
Cuz yeah
Benson played 12 games of trivia. He had
a perfect score on every game and received
35 bonus points per game. He earned a
total of 1,260 points. How many points did
he earn per game not including the
bonus points?
Benson earned 70 points per game not including the bonus points.
Step-by-step explanation:
Given,
Games of trivia played = 12
Bonus points received per game = 35 points
Bonus points for 12 games = 35*12 = 420 points
Total points earned = 1260 points
Points earned in games = Total points - bonus points
Points earned in games = 1260 - 420 = 840 points
As he scored 840 points in 12 games, therefore,
12 games = 840 points
1 game = [tex]\frac{840}{12} = 70\ points[/tex]
Benson earned 70 points per game not including the bonus points.
Keywords: subtraction, division
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Omar has 2 3/4 cups of dough to make dumplings. If he uses 3/16 cups of dough for each dumpling, how many whole dumplings can Omar make?
Plsss help me
Answer: Omar can make 14 whole dumplings.
Step-by-step explanation: Make 2 3/4 an improper fraction. To do this, multiply 2 by the denominator, 4. From this, you get 8. Then add 8 to the numerator, which is 3, and you get 11. Keep the denominator and you'll have 11/4.
To divide fractions, you make 3/16 its reciprocal by basically flipping the fraction so that the numerator becomes the denominator and vise versa, making it 16/3. Then multiply 11/4 and 16/3. 11 x 16 is 176; 4 x 3 is 12. The result is 176/12. Simplify by dividing the numerator and denominator by 4. Your resulting answer should be 44/3. Simplify even further by simple division. Your final answer should be 14 2/3. Discard the 2/3 because Omar needs to make whole dumplings. So the answer is 14.
Final answer:
Omar can make 14 whole dumplings with 2 3/4 cups of dough when each dumpling requires 3/16 cups of dough.
Explanation:
The student's question asks how many whole dumplings Omar can make with 2 3/4 cups of dough if each dumpling uses 3/16 cups of dough.
Convert 2 3/4 cups to an improper fraction: 11/4 cups.
Divide the total cups of dough (11/4) by the amount needed for one dumpling (3/16) to find the number of dumplings Omar can make.
Perform the division: (11/4) \/ (3/16) = 11/4 \\* 16/3 = 44/3.
Omar can make 44/3 dumplings, which is 14 whole dumplings with some dough left over.
Omar can make 14 whole dumplings with 2 3/4 cups of dough when each dumpling uses 3/16 cups of dough.
ASAP!!!!!!10 POINTS I NEED HELP!!!!!!!! A beekeeper pours honey into jars. Each large jar holds 18 ounces of honey. Each small jar holds 12 ounces of honey. The beekeeper fills 32 large jars and 46 small jars.
Which answer is the most reasonable estimate of the total amount of honey in the jars?
Answer:
1,100
Step-by-step explanation:
The total number of ounces that were put in jars was 1,128 Oz so your answer would be 1,110 rounded to the nearest hundred.
The answer is;
20 x 30 + 10 x 50 = 1,100
Which angle is an acute angle?
(Full question above)
Answer:
∠CPB is an acute angle.
Step-by-step explanation:
Firstly, lets go over what an acute angle is. An acute angle is any angle that is less than 90°.
In the problem, we are told that ∠APE is a right angle. This means that it is 90°.
As ∠APE and ∠BPD are vertical angles, they must have the same measure. This means that ∠BPD is also 90°
As ∠BPD has the line PC in the middle of it, this angle could be split into ∠CPB and ∠CPD. These two angles must add up to be the same as ∠BPD, which is 90°. As these two angles must add to be 90° they must be less than 90°. This means that both ∠CPB and ∠CPD are acute angles.
As ∠CPD is not one of the options for the question, ∠CPB is the only correct answer.
Acute angles measure less than 90°. Among the options, only C) Angle CPB fulfills this condition. It's the only angle clearly smaller than a right angle in the image.
An acute angle is an angle that measures less than 90 degrees. In the image you sent, only one of the angles measures less than 90 degrees.
-angle APE is a right angle, which measures exactly 90 degrees.
-angle CPE and angle APC are both obtuse angles, which measure more than 90 degrees but less than 180 degrees.
-angle CPB is the only angle that measures less than 90 degrees, so it is the only acute angle.
Therefore, the answer is C) Angle CPB.
9.014 which digit is in the hundredths place
Final answer:
The digit in the hundredths place of the number 9.014 is 1. Significant figures and rounding concepts determine that if the digit in the thousandths place is 5 or greater, the hundredths place digit is rounded up.
Explanation:
The digit in the hundredths place of the number 9.014 is 1. When dealing with decimal numbers, the first place to the right of the decimal point is the tenths place, the second place is the hundredths place, and so on. In the context of significant figures and rounding, if we need to round a number to the hundredths position, and the digit in the thousandths place (the third position to the right of the decimal) is 5 or greater, we round the hundredths digit up.
For example, if the calculator answer is 921.996 and we need to round to the hundredths place, we look at the thousandths place digit. Since it is greater than 5, we round up, changing the answer to 922.00.
To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz. However, when Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz. What is the percent error?
(Explain in a detailed way on how you got your answer)
The percent error is 4.17 %
Solution:
To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz
When Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz
To find: percent error
Percent error is the difference between a measured and known value, divided by the known value, multiplied by 100%
[tex]\% \text { error }=\frac{\text {approximate value}-\text {exact value}}{\text {exact value}} \times 100[/tex]
Here approximate value = 2.5 oz and exact value = 2.4 oz
[tex]\% \text { error }=\frac{2.5-2.4}{2.4} \times 100\\\\\% \text { error }= \frac{0.1}{2.4} \times 100 = 4.17[/tex]
Therefore percent error is 4.17 %
8 over 15 minus 1 over 5
Answer:
1/3
Step-by-step explanation:
(8/15) - (1/5)
change 1/5 to 3/15 (which is equivalent to 1/5)
(8/15) - (3/15) = (5/15)
Simplify
(5/15) = (1/3)
Answer:
1/3
Step-by-step explanation:
8/15-1/5=8/15-3/15=5/15=1/3
mr.james runs a petting zoo. he records the number of visitors each week,v, t weeks, after opening the petting zoo. according to the table what is the average rate of change over the interval [2,5]
a.57 visitors per month
b. 28 visitors per month
c. 36 visitors per month
d 19 visitors per month
Answer:
[tex]\large \boxed{\text{19 visitors/mo}}[/tex]
Step-by-step explanation:
The average rate of change is the change in the number of visitors divided by the change in the number of months.
1. Change in number of visitors
Change in visitors = 182 -125 = 57 visitors
2. Change in number of weeks
Change in time = 5 - 2 = 3 months
3. Average rate of change
[tex]\begin{array}{rcl}\text{Average rate of change} &= &\dfrac{\text{change in visitors}}{\text{change in months}}\\\\&= &\dfrac{\text{57 visitors}}{\text{3 mo}}\\\\& = & \textbf{19 visitors/mo}\\\end{array}\\\text{The average rate of change is $\large \boxed{\textbf{19 visitors/mo}}$}[/tex]
Which is the MOST REASONABLE approach for the company to take to lessen the number of latecomers to work?
A) Relocate the company to an area with less traffic.
B) Deduct the lost time for any reason from vacation time.
C) Delay the start time of work days when there is bad weather.
D) Implement better procedures at the security gate.
Answer:
D. implement better procedures at the security gate.
Step-by-step explanation:
did the usa test prep
what is the slope of the line x=2
Answer:
infinite
Step-by-step explanation:
The slope is the amount the line moves in y direction when you go move unit in the x direction. For a vertical line that is infinite...
Which of the following values would complete the ordered pair if the point is on the graph of ƒ(x) = -2x - 1? (-2, ___)
A. 3
B. 4
C. 5
Option A: 3 is the right answer
Step-by-step explanation:
Given
[tex]f(x) = -2x-1[/tex]
In an ordered pair, the x-coordinate is the input to the function and y-coordinate is the output of the function on specified input.
In the given ordered pair,
x-coordinate is -2 so we will put it into the function to get the y-coordinate
So,
[tex]f(-2) = -2(-2)-1\\= 4-1\\=3[/tex]
3 will complete the ordered pair of the point on the graph
Hence,
Option A: 3 is the right answer
Keywords: functions, variables
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Answer:
A
Step-by-step explanation:
(x coodinate, y coodinate) = (x, f(x))
(-2, ___) is saying us x=-2, and question is asking y =?
f(x) = -2x -1
f(-2) = -2.-2 -1
f(-2)= 4 -1
f(-2) = 3
so, y= f(-2) = 2
(x, f(x)) = (-2, f(-2)) = (-2,3)
Hope this helps ^-^
Solve for y in terms of x: 3y-2x=7
Answer will be: y=7/3+2x/3
Answer:
y = 2/3x + 7 / 3
Step-by-step explanation:
Step 1: Add 2x to both sides.
−2x+3y+2x=7+2x
3y=2x+7
Step 2: Divide both sides by 3.
3y / 3 = 2x+7 / 3
y= 2 / 3x + 7 / 3
an airport shuttle company owns cars that have a maximum capacity of 3 passengers and vans that have a maximum capacity of 8 passengers . their 12 vehicles have a combination maximum capacity of 61 passengers. write and solve a system of equations to determine how many vans the company owns
Answer:
The Total number of car is 7 and The Total number of van is 5 .
Step-by-step explanation:
Given as :
The maximum capacity of car = 3 passengers
The maximum capacity of van = 8 passengers
Total number of vehicles = c + v = 12 vehicles
The maximum capacity of vehicles combination = 61 passengers
Let The Total number of car = c
Let The Total number of van = v
Now, According to question
c + v = 12 .........A
3 c + 8 v = 61 ............B
Now, Solving eq A and B
I.e (3 c + 8 v) - 3 × (c + v) = 61 - (3 × 12)
Or, (3 c - 3 c) + (8 v - 3 v) = 61 - 36
Or, 0 + 5 v = 25
∴ v = [tex]\dfrac{25}{5}[/tex]
i.e v = 5
So,The Total number of van = v = 5
Now Put the value of v into eq A
∵ c + v = 12
So, c + 5 = 12
∴ c = 12 - 5
i.e c = 7
So,The Total number of car = c = 7
Hence,The Total number of car is 7 and The Total number of van is 5 . Answer
The student's question is about determining the number of vans owned by a company using a system of linear equations. By setting up two equations and using the elimination method, we find that the company owns 5 vans and 7 cars.
Explanation:The question involves solving a system of linear equations to determine how many vans a company owns. We know that the company has a total of 12 vehicles, which are either cars with a capacity of 3 passengers or vans with a capacity of 8 passengers. The total capacity of all 12 vehicles combined is 61 passengers. To solve this problem, we will create two equations based on this information:
Let c represent the number of cars and v represent the number of vans.The first equation is based on the number of vehicles: c + v = 12.The second equation represents the total capacity: 3c + 8v = 61.We can solve this system using substitution or elimination methods.Using elimination to solve the equations:
Multiply the first equation by -3 to align the passenger capacity of the cars: -3c - 3v = -36.Add this result to the second equation: (-3c - 3v) + (3c + 8v) = -36 + 61.Simplify the equation: 5v = 25.Divide both sides by 5 to find v: v = 5.Substitute v back into the first equation: c + 5 = 12.Solve for c: c = 7.Therefore, the company owns 7 cars and 5 vans.
Jerry needs to buy nails and screws for the construction site. Nails cost $2.75 per pound and screws cost $3.25 per pound. If he
only has $500 to spend on nails and screws, which inequality represents the situation where he buys x pounds of nails and y
pounds of screws?
A)
3.25x +2.75y s 500
B)
3.25x + 2.75y 2 500
2.75x + 3.25y s 500
D)
2.75x + 3.25y 2 500
Answer:
C) 2.75x+3.25y ≤ 500
Step-by-step explanation:
Here are the correct options given:
A) 3.25x +2.75y ≤ 500
B) 3.25x + 2.75y ≥ 500
C) 2.75x + 3.25y ≤ 500
D) 2.75x + 3.25y ≥ 500
Given: Nails cost is $2.75 per pound
Screw cost is $3.25 per pound
Jerry has only $500 to spend on nails and screws.
x represent quantity of nail bought and y represent quantity of screw bought.
As given we know that Jerry has only $500 to spend, so the total cost has to be less than or equal to $500. It cannot go more than $500.
Remember, Total cost= [tex]\textrm{cost of goods per pound}\times quantity[/tex]
Now, Inequality to represent the cost of buying nails and screw.
[tex]\$2.75\times x\ pounds+ \$3.25\times y\ pounds\leq \$ 500[/tex]
∴ [tex]2.75x+3.25y\leq 500[/tex]
Mike is making a scale model of his favorite car. The actual car is 8 feet long and four feet wide. Mike wants his model to be 12 inches in length. Which of the following proportions could be used to find the width, w, of his model?
A:8/4=12/w B:8/4=w/12 C: 8/12=w/4 D:12/8=4/w
Answer:
A. 8/4=12/w
Step-by-step explanation:
8/4=12/x
8feet long 12 inches
---------------- = ----------------
4feet wide X because we dont know exact width
Answer:
A. 8/4=12/w
Step-by-step explanation:
A collector has 120 movie posters and 100 band posters. She wants to sell 24 movie posters but still have her poster collection maintain the same ratio of 120:100. If she sells 24 movie posters, how many band posters should she sell? Explain.
Answer:
20
Step-by-step explanation:
120x=100*24
x= 100*24/120
I dont kno if how much is Multiple add or subtract please help.
Answer:
You have to subtract 1.01 from 4.12 because it says how much it rained on Tuesday.
Step-by-step explanation:
The equation says that it rained 4.12 inches on Monday and 1.01 less on Tuesday.
So to write in number form = 4.12 - 1.01 = 3.11
So your answer is 3.11 inches.
It rained 3.11 inches on Tuesday.
Hope this helps!
Help me find 7x+6=41
Answer:
x=5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
what i did was..
41-6 = 30
30/7 = 5
x=5
A factory runs nonstop for three 14 - hour shifts. The first shift starts at 9.00 AM. At what times does their third shift end?
Answer:
Step-by-step explanation:
3 fourteen hr shifts.....that (14 * 3) = 42 hrs....thats 1 day and 18 hrs
first shift starts at 9 AM......
one day later will make it 9 AM the next day....now we have the 18 hrs.....so from 9 AM to 9 PM is 12 hrs.....so we are at 9 PM and have 6 hrs left.....making the last shift end at 3 AM <==
3:00 pm is the time where does their third shift end.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that A factory runs nonstop for three 14 - hour shifts.
The first shift starts at 9.00 AM.
We need to find the times does their third shift end.
First shift:
9:00Am to 11:00Pm (14 hours)
second shift:
11:00pm to 1:00 am (14 hours)
Third shift
1:00 am to 3:00 pm (14 hours)
Hence, 3:00 pm is the times where does their third shift end.
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anyone good in LAW OF SINES??
Answer:
Step-by-step explanation:
Answer:
b = 6.7cm
Step-by-step explanation:
The law of sines is:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex] OR [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
Each section represents an angle (capital) and its opposite side (lowercase). When you use it, only use two sections at a time. You may have one missing piece of information when using it. Use the formula that puts the missing information in the numerator (top).
This problem:
We are given one set of information, 8cm and 55°. This can be "a" and "A" (not labelled).
We need angle B to find side b.
Since we are given two of the three angles in the triangle, and the sum of all interior angles of any triangle is 180°, we can find the missing angle.
∠B = 180° - (∠A + ∠C)
∠B = 180° - (55° + 82°)
∠B = 43°
Use the law of sines with sections "A" and "B", with the lowercase letters in the top.
[tex]\frac{a}{sinA} =\frac{b}{sinB}[/tex] Substitute known measurements
[tex]\frac{8cm}{sin(55)} =\frac{b}{sin(43)}[/tex] Rearrange to isolate "b"
[tex]b = \frac{8cm}{sin(55)}X{sin(43)}[/tex] Solve, degree mode on calculator
[tex]b = 6.660...cm[/tex] Exact answer
[tex]b = 6.7cm[/tex] Rounded to nearest tenth
Therefore side b is 6.7cm.
There are 12 grams of sugar in 1/3 of a piece of candy. How much sugar is in 3/4
of a piece of candy?
grams
12. The results of an election
for mayor are shown
at the right. Which candidate
received the
most votes and which received
the least votes?
DATA
Candidate
Leonard Hansen
Margaret O'Connor
Jillian Garcia
Number of Votes
12,409
12,926
12,904
Answer:
Margaret O'Connor has the highest votes.. 12,926.
Leonard Hansen has the least votes.. 12,409
Final answer:
Margaret O'Connor received the most votes with 12,926, while Leonard Hansen received the least with 12,409. Margaret would win in a plurality election, but a runoff would be needed in a majority election as no candidate won over 50% of the votes.
Explanation:
In the results of an election for mayor, which candidate received the most votes and which received the least?
Margaret O'Connor received the most votes with a total of 12,926. Leonard Hansen received the least number of votes, totaling 12,409. If this were a plurality election, Margaret O'Connor would be declared the winner since she has more votes than any other candidate. In a majority election, a runoff would likely be necessary because no single candidate received more than 50% of the votes.