The new sides of the enlarged triangle are: New base = 4, New height = 4, New slant height = 6√2
How to determine the enlarged scale?A scale factor is a mathematical parameter used to change the size of a geometrical figure or shape with respect to its original size.
From the given right triangle, we can see that;
Base = 1 unit (1 square box)
Height = 4 units
Slant side = x
Get the slant side using Pythagoras theorem:
x² = 4² + 4²
x² =16 + 16
x² =32
x = √32
x = 4√2
Enlarging by a factor 1.5 means multiplying the sides by 1.5
New base = -2× 1.5 = 3
New height = 4 ×1.5 = 6
New slant height = 4√2 × 1.5 = 6√2
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Choose the correct slope of the line that passes through the points (−4, 8) and (−3, −6).
A. 0
B. 14
C. 7
d. -14
Answer:
The answer is option DStep-by-step explanation:
The slope of a line given two points can be found by using the formula
\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(−4, 8) and (−3, −6)
The slope is
\(m = \frac{ - 6 - 8}{ - 3 + 4} = \frac{ - 14}{1} \)
We have the final answer as
- 14Hope this helps you
Researchers at a medical center studied the amount of caffeine, in milligrams (mg), contained in a 16-ounce cup of coffee made at one machine at the center's cafeteria. They selected a random sample of 40 16-ounce cups of coffee made at different times of the day during a one-month period. The mean and standard deviation of the amount of caffeine in the sample were 159.88 mg and 36.72 mg, respectively. A graph of the sample data revealed a night skew with one outlier. The researchers will construct a confidence interval to estimate the amount of caffeine for all 16 ounce cups made at the machine
Which of the following conditions is not needed for the inference?
A)The samples were selected at random
B)The observations are independent of one another.
C)The sample size of 40 is less than 10% of the population size
D) The graph of the sample data is symmetric with no outliers
The sample size is large enough to assume that the sampling distribution of sample means is approximately normal
The condition that is not needed for the inference in this case is D) The graph of the sample data is symmetric with no outliers.
While it is generally desirable to have a symmetric distribution without outliers for making statistical inferences, it is not a necessary condition. The central limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution, as long as certain conditions are met (such as random sampling and independence of observations). Therefore, the shape of the sample data distribution and the presence of outliers do not affect the validity of constructing a confidence interval based on the sample mean.
However, the condition that is not needed for the inference is D) The graph of the sample data is symmetric with no outliers. While a symmetric distribution without outliers can make it easier to construct a confidence interval, it is not a necessary condition for inference. The other conditions listed (random sampling, independence, sample size less than 10% of population size, and a large enough sample size) are all necessary for inference.
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Round 45.4673
off each number
to two (2) Decimal Place
Answer:
45.47
Step-by-step explanation:
Which expression represents 3 more than x
The expression represents 3 more than x is function f(x) = x + 3. Option D is the correct answer.
The phrase "3 more than x" implies that we need to add 3 to x.
Therefore, the correct expression is option d, which is x + 3.
Option a, 3x, represents three times x, which is not the same as adding 3 to x.
Option b, 3/x, represents 3 divided by x, which is also not the same as adding 3 to x.
Option c, x - 3, represents subtracting 3 from x, which is the opposite of adding 3 to x.
Therefore, the correct expression is d, x + 3.
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The question is -
Which expression represents "3 more than x"?
a. 3x
b. 3/x
c. x - 3
d. x + 3
need answer by 11:45
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
The appropriate measure of center for the data, and what is its value is the median is the best measure of center, and it equals 19.
What are the mean and median?The appropriate measure of center for the data is the median since the box plot is skewed and there are outliers.
From the box plot, we can see that the line in the box is at 19, which means that 50% of the data falls below 19 and 50% falls above 19. Therefore, the median is the best measure of the center, and its value is 19.
Thus, the correct option is c. The median is the best measure of the center, and it equals 19.
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you are treating a 50-year-old man that was involved in a fire. he suffered 25% 2nd-3rd degree burns to the anterior chest, neck and face. he has singed nasal hairs, and you identify stridor on your primary survey. pulse oximetry is 88% on a 100% non-rebreather mask. a burn center is 45 miles away. the next most appropriate step prior to transfer is:
A 100% non-rebreather mask has a pulse oximetry reading of 88%. There is a burn centre 45 miles distant. the best course of action to do after transferring a serious burn side.
A 50-year-old man who was injured in a fire is being treated by you. He sustained 25% 2nd–3rd degree burns to his face, neck, and anterior chest. He has burned nasal hairs, and your initial survey reveals stridor.
Any damage that exceeds 10% in size should be treated in a similar manner, although significant burns are classified as those that encompass 25% or more of the total body surface area. Rapid evaluation is essential. Any blaze can be managed using the general strategy for a significant burn. The most crucial things are to take a thorough history.
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The area of a triangle is 0.2 of the area of a square. A rectangle has an area 0.7 times
the area of the square. The total area of the triangle, square and rectangle is 494 cm².
What is the difference in area between the triangle and the rectangle?
The difference between the area of the triangle and area of the rectangle is 130
What is area?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
Represent the area of triangle , square and rectangle by x, y, z respectively.
x = 0.2y
z = 0.7y
x+y+z = 494
therefore;
0.2y +y + 0.7y = 494
1.9y = 494
divide both sides by 1.9
y = 494/1.9
y = 260
x = 0.2 ×260
= 52
y = 0.7 × 260
= 182
y - x = 182 - 52
= 130
therefore the difference in area between the triangle and the rectangle is 130
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Tasha has a gift card to buy tickets to the movie theater. The initial value of the giftcard is $120. The function M(x)=120-12x represents the amount of money, M, in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of 12 each. The solution to M (x)=180 is x= DROP DOWN 1 which DROP DOWN 2 in terms of the given context.
The solution to the linear function M(x) = 180 is of x = -5, which is an extraneous solution in terms of the given context.
What is an extraneous solution?An extraneous solution is a solution that is outside the domain of the function in the given context.
In this problem, the function is defined as follows:
M(x) = 120 - 12x.
In which M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.
The domain of the situation is given as follows:
x ≥ 0. {discrete}
As the number of tickets cannot assume negative neither decimal values.
The equation is:
M(x) = 180.
Hence the solution is calculated as follows:
120 - 12x = 180
12x = -60
x = -60/12
x = -5.
Which is outside the function's domain, hence extraneous.
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PLEASE HELP ME WILL MARK BRAINLIEST!!! plot (-3,4) and (4,4) on a coordinate plane
also what is the distance between these two points?
Answer:
I left a graph, I think thats the answer.
The distance is 7
Step-by-step explanation:
A fleet of nine taxis is to be dispatched to three airports in such a way that two go to airport A, six go to airport B, and one goes to airport C. In how many distinct ways can this be accomplished
There are 252 distinct ways to dispatch the taxis to the three airports.
We need to find the number of distinct ways in which we can dispatch the taxis to the three airports, given that two taxis go to airport A, six go to airport B, and one goes to airport C.
First, we choose two taxis out of nine to send to airport A. This can be done in C(9, 2) = 36 ways.
Next, we choose six taxis out of the remaining seven to send to airport B. This can be done in C(7, 6) = 7 ways.
Finally, the last taxi is sent to airport C.
Therefore, the total number of distinct ways to dispatch the taxis is:
C(9, 2) x C(7, 6) = 36 x 7 = 252
There are 252 distinct ways to dispatch the taxis to the three airports.
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A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 110. Complete parts (a) through (c). (a) What percentage of standardized test scores is between 420 and 640? __% (Round to one decimal place as needed.)
(b) What percentage of standardized test scores is less than 420 or greater than 640? __% (Round to one decimal place as needed.) (c) What percentage of standardized test scores is greater than 750? __% (Round to one decimal place as needed.)
The percentage of standardized test scores between 420 and 640 is 68.3%, the percentage of standardized test scores less than 420 or greater than 640 is 112.4% and the percentage of standardized test scores greater than 750 is 2.28%.
(a) To calculate what percentage of standardized test scores is between 420 and 640, we need to convert the values into z-scores by using the following formula:z = (x - μ) / σWhere,x = 420, μ = 530 and σ = 110 for the lower boundary.x = 640, μ = 530 and σ = 110 for the upper boundary.Substituting these values into the formula, we get:z₁ = (420 - 530) / 110 = -1.00z₂ = (640 - 530) / 110 = 1.00Thus, the area between z₁ and z₂ is the same as the area between 0 and z₂ minus the area between 0 and z₁, which is given by the standard normal distribution table. Using the standard normal distribution table, we can find the area between 0 and 1.00, which is 0.3413. The area between 0 and -1.00 is also 0.3413. Therefore, the percentage of standardized test scores between 420 and 640 is given by: percentage = (0.3413 + 0.3413) × 100= 68.26 ≈ 68.3%Thus, the required answer is 68.3%. (b) To calculate what percentage of standardized test scores is less than 420 or greater than 640, we need to find the area to the left of 420 and the area to the right of 640. Using the standard normal distribution table, we can find the area to the left of -1.82, which is 0.0344. Therefore, the area to the right of 420 is: area = 1 - 0.0344 = 0.9656Similarly, the area to the right of 640 is: area = 1 - 0.8413 = 0.1587Therefore, the percentage of standardized test scores less than 420 or greater than 640 is given by: percentage = (0.9656 + 0.1587) × 100= 112.43 ≈ 112.4%. Thus, the required answer is 112.4%.
(c) To calculate what percentage of standardized test scores is greater than 750, we need to convert the value into z-score by using the formula:z = (x - μ) / σwhere x = 750, μ = 530, and σ = 110Substituting these values into the formula, we get:z = (750 - 530) / 110= 2.00Using the standard normal distribution table, we can find the area to the right of 2.00, which is 0.0228. Therefore, the percentage of standardized test scores greater than 750 is given by: percentage = 0.0228 × 100= 2.28Thus, the required answer is 2.28%. Therefore, the percentage of standardized test scores between 420 and 640 is 68.3%, the percentage of standardized test scores less than 420 or greater than 640 is 112.4% and the percentage of standardized test scores greater than 750 is 2.28%.
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A right triangle has an opposite side of 8th and an adjacent side of 6ft. What is the length of the missing side?
The length of the missing side (the hypotenuse) is 10 ft.
We have,
We can use the Pythagorean theorem to find the length of the missing side of the right triangle.
So,
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
In this case,
The opposite side (which is the leg) has a length of 8 ft, and the adjacent side (which is the other leg) has a length of 6 ft.
Let x be the length of the missing side. Then we have:
a = 8 ft
b = 6 ft
c = x
Plugging these values into the Pythagorean theorem, we get:
8² + 6² = x²
64 + 36 = x²
100 = x²
Taking the square root of both sides, we get:
x = √100 = 10 ft
Therefore,
The length of the missing side (the hypotenuse) is 10 ft.
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a tank is being filled with water at the rate of 2 3 450t gallons per hour with t > 0 measured in hours. if the tank is originally empty, how many gallons of water are in the tank after 5 hours?
The rate of filling water in the tank is 23450t gallons per hour.
Let's assume that the time taken to fill the tank is t hours.
The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.
The tank is originally empty, which means its volume = 0 gallons.
After 5 hours,
t= 5 hours
The volume of water filled in is given by \(V(5) = 23450 * 5= 1,17,250\) gallons of water.
Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.
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what is the equation of a line that is perpendicular to the line y=2x+1 and passes through the point (4,6).
i need help asap! work shown to help me thru the steps. y=mx+b
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
\(y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}\)
so we're really looking for the equation of a line with a slope of -1/2 and that it passes through (4 , 6)
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-6=- \cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}\)
Find the perimeter. Simplify your answer.
Answer:
20u-26
Step-by-step explanation:
To find the perimeter we have to add up all the sides
9u-6+u-7+9u-6+u-7
Combine light terms and we get
20u-26
Major went to the Appalachian Fair. The entrance fee was $10, and he purchased 25 tickets. Write an equation to find the price of each ticket if he spent a total of $47.50. You do NOT have to solve it.
Answer:
25x+10=47.50
Step-by-step explanation:
x represents the ticket amount and if he buys 25 tickets then that will be 25 times x. Plus the $10 entrance fee.
A resting heart rate for men on a chart say 62-65 beats per minute puts men in the good category of scott counted 238 heart beats in 3 1/2 minutes does his heart rate fall into the good category
1. Write an algebraic equation for the cost of 25 liters of gasoline, if x pesos
per liter is P3,902.00
2. Rhian is
Answer:
× + 3902.00 = 25litres
Step-by-step explanation:
x per litres
25÷ xlitres = 3902pesos
y = x4 - 3x2 + 4
Does the equation above represent a relation, a function, both a relation and a function, or neither a relation nor a function?
A.
neither a relation nor a function
B.
both a relation and a function
C.
function only
D.
relation only
The equation as given in the task content above can be said to represent; Choice C; function online.
What is the equation given in the task content representing?By definition, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
A relation, on the other hand defines the relationship between sets of values of ordered pairs.
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Write an equation for the transformed logarithm shown below, that passes through (3,0) and (0,2) f(x)= Question Help: −b Video
The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.
To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:
0 = -b * log(base a)(3 - h) + k
Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:
2 = -b * log(base a)(0 - h) + k
Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.
In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.
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19-4q+q-11 simply the experssion
━━━━━━━☆☆━━━━━━━
▹ Answer
8 - 3q
▹ Step-by-Step Explanation
19 - 4q + q - 11
Combine like terms in terms of q:
-4q + q = -3q
Combine like terms:
19 - 11 = 8
Final answer:
8 - 3q
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
a climber starts descending from 533 feet above sea level and keeps going until she reaches 10 feet below sea level. how many feet did she descend
If a climber starts descending from 533 feet above sea level and keeps going until she reaches 10 feet below sea level, then he descend 543 feet
A climber starts descending from 533 feet above sea level.
The height of the mountain = 533 feet
The sea level means its 0 feet
He is keep going until she reaches 10 feet below sea level
The distance between 533 feet above sea level to sea level = 533 feet
The distance between sea level and the 10 feet below sea level = 10 feet
Total distance that he descend = 533 + 10
= 543 feet
Hence, if a climber starts descending from 533 feet above sea level and keeps going until she reaches 10 feet below sea level, then he descend 543 feet
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What is 50. 7 / 7 bc im not sure I understand
The value of 50.7 / 7 is approximately equal to 7.24285714.
The given expression is 50.7 / 7.
Creating equal groupings or determining how many individuals are in each group after a fair distribution is the basic objective of division.
To simplify the expression, we need to perform the division operation.
In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
To solve this, we can perform the following steps:
First, we can write the given expression as:
50.7 ÷ 7
Then, we can perform the division operation as shown below:
50.7 ÷ 7
= 7.24285714 (rounded to 8 decimal places)
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Plot Z + 22-Im876532+++> Re2 3 4 5 6 7 8 9S G1A++ ++-9-8-7-6-5 -4 -3 -222-2 +-3 +-4--5--6-721B
Answer:
Explanation:
Here, we want to plot the graph of z1 plus z2
Firstly,let us identify the coordinates of z1 and z2
We can get this from the graph provided
z1 is (8,-4)
z2 is (-2,-3)
The sum of these two will be : (6,-7)
To plot this, we draw dotted vertical line at the point x = 6 and dotted horizontal line at the point y = -7
Wherever these two dotted lines meet is the point z
which of the following is an area of mathematics that studies how competing parties interact
An area of mathematics that studies how competing parties interact is known as "game theory."
Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.
Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.
The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.
Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.
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Joseph canned 15 liters of jam over 6 days.
How much jam did Joseph can if he spent 18 days making jam?
Slicing using unit rates
Answer:
45 liters of jam.
Step-by-step explanation:
15 liters of jam took 6 days.
6 * 3 = 18
15 * 3 = 45
Merry Christmas! :))
The SUBSET SUM problem asks to decide whether a finite set S of positive integers has a subset T such that the elements of T sum to a positive integer t. (a) Is (S,t) a yes-instance when the set S is given by S={2,3,5,7,8} and t=19 ? Prove your result. (b) Why is a brute force algorithm not feasible for larger sets S (c) Explain in your own words why the dynamic programming solution to SUBSET SUM given in https://www . cs. dartmouth . edu/ deepc/Courses/S19/lecs/lec6.pdf is not a polynomial time algorithm.
(a) To determine if (S,t) is a yes-instance for S={2,3,5,7,8} and t=19, we need to check if there exists a subset of S whose elements sum to 19. In this case, we can choose the subset T={2,7,10} where the elements sum to 19. Thus, (S,t) is a yes-instance.
(b) A brute force algorithm for the SUBSET SUM problem involves checking all possible subsets of S and calculating their sums to see if any sum equals t. However, the number of possible subsets grows exponentially with the size of S, making the algorithm impractical for larger sets. For example, if S has n elements, the number of subsets is 2^n, which becomes computationally infeasible for large values of n.
(c) The dynamic programming solution presented in the provided link is not a polynomial time algorithm because it still has to consider all possible subsets of S. Although it improves the efficiency by using memoization to avoid redundant calculations, the algorithm's time complexity is still exponential in the worst case. It explores all possible combinations of elements in S to determine if there exists a subset sum equal to t, resulting in a runtime that grows exponentially with the size of S. Thus, it cannot be classified as a polynomial time algorithm.
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You want to buy DVDs and are searching for the best price. You found two stores having sales on DVDS. Which is the one that offers the best percentage off? Then explain your reasoning.
Store 1 - Buy 2 for the price of one!
Store 2 - Buy 3 for the price of two!
Answer:
Store 1 Has a better deal as your paying 1.50 less which is 50 percent off
Step-by-step explanation:
Lets say a DVD costs 1.50
so if you bought 2 for the price of one it would be 1.50
3 for the price of 2 would be 3 dollars.
If you were to buy 2 CDS for the Price of 2 that would be 3 Dollars
3 CDS for the price of 3 would be 4.50
The Amount of money depends on the cost of 1 CD.
Store 1 has a 50 percent discount while Store 2 has roughly a 35 percent discount.
sorry if this was confusing^^
HELPP I HAVE A MATH EXAM TOMORROW AND IM WONDERING IF ANYONE KNOWS HOW TO WRITE THE RATIO 21 : 14 in its simplest form
Answer: The simplest form of 2114 is 32.
HELP!!
GIVING BRAINLIEST!!