Answer: z = 20
Explanation:
The given equation is
24z - 48 = 16z + 112
Subtracting 16z from both sides of the equation, we have
24z - 16z - 48 = 16z - 16z + 112
8z - 48 = 112
Adding 48 to both sides, we have
8z - 48 + 48 = 112 + 48
8z = 160
Dividing both sides by 8,
8z/8 = 160/8
z = 20
involving two rolls of a dieESEAn ordinary (falr) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a dle is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.Event A: The sum is greater than 8.Event B: The sum is an odd number.Write your answers as fractions.Ola(a) P(A) = 1х5?(b) P(B) = 0
Answer:
[tex]\begin{gathered} a)\text{ }\frac{5}{18} \\ \\ b)\text{ }\frac{1}{2} \end{gathered}[/tex]Explanation:
Here, we want to compute some probabilities
The first thing to do is to get the count of results in our sample space
In the sample space, the total possible results is 36
Now, let us get the probabilities
a) The event that the sum is greater than 8
We have to count possible results greater than 8 here
3, 6 (3 on the first die, 6 on the second)
6,3 (6 on the first die, 3 on the second)
6,4 (6 on the first die, 4 on the second)
4,6
4,5
5,4
5,5
5,6
6,5
6,6
The number of possible results greater than 8 is 10
Thus, we have the probability as the count of this divided by the total number of possible results
Mathematically, we have that as:
[tex]\frac{10}{36}\text{ = }\frac{5}{18}[/tex]b) The sum is an odd number
For the sum to be an odd number, we know that if we add a table of 6 rows for all the sums, the even sum on each line is 3
The total even sum is 6 * 3 = 18
The probability is thus:
[tex]\frac{18}{36}\text{ = }\frac{1}{2}[/tex]Evaluate h(x) at x = 6, x = 8, and x= 12. h(x)=1.31^×
Answer : h(6) = 5.054
h(8) = 8.673
h(12) = 25.542
Given that h(x) = 1.31^x
[tex]\begin{gathered} h(x)=1.31^x \\ \text{ find the value of h(6) when x = 6} \\ h(6)=1.31^6 \\ h(6)\text{ = 5.05}4 \\ \text{when x = 8} \\ h(8)=1.31^8 \\ h(8)\text{ = 8.67}3 \\ \text{when x = 12} \\ h(12)=1.31^{12} \\ h(12)\text{ = 25.54}2 \end{gathered}[/tex]Therefore,
h(6) = 5.054
h(8) = 8.673
h(12) = 25.542
In which quadrant does 0 lie if the following statements are true:sin 0 > 0 and sec 0 < 0Quadrant IQuadrant IIQuadrant IIIQuadrant IV
Given the conditions in the question:
1. sin θ > 0, therefore, it must be positive. From that, we can conclude that y must be on the positive side, therefore, located at the top of the coordinate plane.
2. sec θ < 0, therefore, it must be negative. From that, we can conclude that x must be on the negative side, therefore, located at the left side of the coordinate plane.
Therefore, the quadrant that the θ belongs to is in the top and left of the coordinate plane and that is Quadrant II.
Determine the input value for which the statementf(x) = g(x) is true.From the graph, the input value is approximatelyf(x) = 3 and g(x) = 3x-23 = {x-25= xThe x-value at which the two functions' values areequal is
You can see from the graph, f (x) is a constant value and g (x) = -5, when x = -2, g (x) = - 2, when x = 0 and g (x) = 1, when x = 2.
The Lyon Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 186 restaurants located in Boston, the average price of a dinner, including one drink and tip, was 48.60 Dollars. You are leaving on a business trip to Boston and will eat dinner 23 of these restaurants, randomly selected. Your company will reimburse you for a maximum of 50 dollars per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed 50 dollars.
a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that at most 12 of the meals will exceed the cost covered by your company? What is the probability that between 4 and 8 of the meals will exceed the cost covered by your company?
c. Calculate the expected number of restaurants that will exceed the cost covered by your company.
d. Calculate the probability of the first question by using the binomial distribution approximation. Therefore, in this case we will consider the possibility of repetition in the randomly selected restaurants. Define p=r/N as the success probability.N is the size of the population. r is the number of elements considered as successes in the population.
e. Calculate the probability of the second question by using the binomial disribution approximation.
f. Calculate the probability of the third question by using the binomial disribution approximation.
g. Calculate the expected number of the fourth question by using the binomial disribution aproximation
Using the binomial distribution, the probabilities are given as follows:
a. None: 0%.
b.
At most 12: 0.9814 = 98.14%.Between 4 and 8: 0.6249 = 62.49%.c. The expected number of restaurants that will exceed the cost covered by your company is of 7.67.
Using the normal approximation, the probabilities are:
a. None: 0.0008 = 0.08%.
b.
At most 12: 98.38 = 98.38%.Between 4 and 8: 0.6121 = 61.21%.The difference in these probabilities is due to the small sample size.
Binomial distributionThe formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In which the parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Considering that you will eat dinner at 23 restaurants, and at around one-third of them the meal cost will exceed 50 dollars, the values of these parameters are given as follows:
n = 23, p = 1/3 = 0.3333.
The probability that none will exceed is P(X = 0), hence:
P(X = 0) = (1 - 0.3333)^23 = 0% (rounded).
The probability of at most 12 is:
P(X <= 12) = P(X = 0) + P(X = 1) + ... + P(X = 12).
Using a binomial distribution calculator with the given parameters, the probability is:
P(X <= 12) = 0.9814 = 98.14%.
The probability that between 4 and 8 dinners are paid is:
P(4 <= X <= 8) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
Using a calculator, or the mass function P(X = x) and adding each probability, the desired probability is:
P(4 <= X <= 8) = 0.0493 + 0.0937 + 0.1405 + 0.1707 + 0.1707 = 0.6249 = 62.49%.
Normal approximationThe first step for the normal approximation is finding the mean and the standard deviation, as follows:
Mean = expected number: [tex]\mu = np = 23 \times 0.3333 = 7.67[/tex]Standard deviation: [tex]\sigma = \sqrt{np(1-p) = \sqrt{23 \times 0.3333 \times 0.6667} = 2.26[/tex]The probability of none, using continuity correction, is P(X < 0.5), which is the p-value of Z when X = 0.5, hence:
(the p-value of Z is found using the z-score table).
[tex]Z = \frac{X - \mu}{\sigma}[/tex] (z-score formula)
Z = (0.5 - 7.67)/2.26
Z = -3.17
Z = -3.17 has a p-value of 0.0008.
Hence the probability is 0.0008 = 0.08%.
The probability of at most 12 is P(X <= 12.5), using continuity correction, which is the p-value of Z when X = 12.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (12.5 - 7.67)/2.26
Z = 2.14
Z = 2.14 has a p-value of 0.9838.
Hence the probability is of 98.38 = 98.38%.
The probability of between 4 and 8 dinners being paid is P(3.5 <= X <= 8.5), which is the p-value of Z when X = 8.5 subtracted by the p-value of Z when X = 3.5, hence:
X = 8.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (8.5 - 7.67)/2.26
Z = 0.37
Z = 0.37 has a p-value of 0.6443.
X = 3.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (3.5 - 7.67)/2.26
Z = -1.85
Z = -1.85 has a p-value of 0.0322.
Hence the probability is:
0.6443 - 0.0322 = 0.6121 = 61.21%.
More can be learned about the binomial distribution at https://brainly.com/question/24756209
#SPJ1
a diver takes a dive in the red sea. He initially descends 100 feet. Then rises 28 before descending another 33. What is his final position
Descending: subtraction
Rises: Addition
The diver descends 100ft: Position -100 (the 0 is the sea level)
Then rises 28: Add 28 to the previous position: Position -72
[tex]-100+28=-72[/tex]...before descending another 33: Subtract 33 to the previous position:
[tex]-72-33=-105[/tex]Then, the final position is -105ft (105 ft under the sea level)
Puppets made by each puppeteer43ASCNumber of puppetsAsMYCol?0AlexKalinBruceMarcoMYPuppeteerProIf the mean of the data set is 3 puppets, find the number of puppets Marco made.ProTeapuppets
Remember that we can get the mean of a dataset by adding up each datum and dividing such sum by the number of data.
Now, let's call the number of puppets Marco made M
This way, we would have that:
[tex]\frac{1+4+3+M}{4}=3[/tex]Solving for M :
[tex]\begin{gathered} \frac{1+4+3+M}{4}=3 \\ \\ \rightarrow\frac{8+M}{4}=3 \\ \\ \rightarrow8+M=12\rightarrow M=12-8 \\ \Rightarrow M=4 \end{gathered}[/tex]Therefore, we can conclude that Marco made 4 puppets.
point).
Questions
1. (1) How many observations are collected? (2) How many variables are collected? (3) write
I
down quantitative variables (4) write down qualitative variables
2. Describe the data visually
2.1.(1) Make a frequency tables and histogram for the “Hour” variable (bin limit = 1), and (2)
describe the shapes of the histogram
2.2.(1) Make a frequency tables and histogram for the “Type” variable, and (2) prepare a 2-D
pie chart and write down the title of chart
2.3.(1) Make a frequency tables and histogram for the “Weekday” variable, and (2) prepare a 2-
D pie chart and write down the title of chart
2.4.(1) Make a frequency tables and histogram for the “Location” variable, and (2) prepare a 2-D
pie chart and write down the title of chart
2.5.(1) Make a scatter plot of the data for the “Time” and “Hour variables, placing “Hour" on the
X-axis and "Time" on the Y-axis. Add titles and modify the default colors, fonts, etc., to make
the scatter plot easy to understand. (2) Describe the relationship (if any) between X and Y.
Weak? Strong? Negative? Positive? Linear? Nonlinear?
2.6.(1) Make a dot plot of the “Hour" variable for the “Deposit Type" variable. (2) Make a dot
plot of the "Hour" variable for the "Withdraw Type” variable. (3) Compare the shapes of both
charts
1). 68 observations
1.2) 8 variables
1.3) Quantitative Variables: Type, Time, Date, DayCode, Hour, and Amount
1.4) Qualitative Variables: Location, Weekday
Question 1) Let's examine that table to find out the number of collected observations. Counting each row, we have 68 observations. Each one informing the type, time, date, day code, weekday, Location, Hour, and Amount
1.2) We have then 8 variables namely (type, time, date, day code, weekday, Location, Hour, and Amount)
1.3) The Quantitative Variables are the ones whose entries are numerical, so examining then we can state that:
Type, Time, Date, DayCode, Hour, and Amount each and every one of them receives a numerical entry.
1.4) Qualitative or Categoricals variables are the ones whose entry is not a numerical one. So we can enlist the following ones as Qualitative:
Location
Weekday
Hence the answers are:
1). 68 observations
1.2) 8 variables
1.3) Quantitative Variables: Type, Time, Date, DayCode, Hour, and Amount
1.4) Qualitative Variables: Location, Weekday
all you need is in the photo I DON'T WANT STEP BY STEP ANSWER FAST please fdsd
We have the following:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=5 \\ b=0 \\ c=-80 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} x=\frac{-0\pm\sqrt[]{0^2-4\cdot5\cdot-80}}{2\cdot5}=\frac{\pm\sqrt[]{1600}}{10}=\frac{\pm40}{10}=\pm4 \\ x_1=4 \\ x_2=-4 \end{gathered}[/tex]One package of markers has dimensions 6"×8"×1"what are the dimensions of the box that will hold 30 packages of markers and use the LEAST amount of cardboard? A. 6"×8"×30" B. 6"×16"×15" C. 10"×10"×10"D. 12"×8"×15" E. 18"×8"×10
The required Dimensions are 6'' x 8'' x 30'' , That is option A
Step by step solution thank you much appreciated
Answer:
11.796
Step-by-step explanation:
2nd term
[tex] {1.3}^{2} = 1.3 + \frac{1.3}{ \frac{10}{3} } [/tex]
[tex] {1.3}^{2} = 1.69[/tex]
add first term
[tex]27.8 + 1.69 = 29.49[/tex]
times by 0.4 or ×2/5
[tex]29.49 \times \frac{2}{5} = \frac{58.98}{5} [/tex]
[tex] = 11.796[/tex]
4 ft 12 ft The pitch of the roof is
As shown : in the figure
The pitch of the roof is the angle between the roof and the horizontal line
As shown we have a right angle triangle
The opposite side to the angle = 4 ft
And the adjacent side to the angle = 12 ft
According to the given sides, we will calculate the angle using tan function
So, let the angle = x
So,
[tex]\begin{gathered} \tan x=\frac{opposite}{adjacent} \\ \\ \tan x=\frac{4}{12}=\frac{1}{3} \\ \\ x=\tan ^{-1}\frac{1}{3}\approx18.435^o \end{gathered}[/tex]So, the pitch angle of the roof = 18.435
instead of writing the angle , just we will write the slope = rise/run
So, the pitch of the roof = 1/3
hello this the the problem Im stuck on. I need to know where to plot the point on the graph aswell. ty
Given:
The rent for trucks is $3750.
The additional charge per ton of sugar is $150.
To write: The equation relating the total cost C and amount of sugar S.
Explanation:
The equation represents the total cost C and the amount of sugar S is given by,
[tex]C=3750+150S[/tex]Let us find the three coordinates to plot the graph.
When
[tex]S=0[/tex]Then,
[tex]\begin{gathered} C=3750+150(0) \\ =3750 \end{gathered}[/tex]When
[tex]S=1[/tex]Then,
[tex]\begin{gathered} C=3750+150 \\ =3900 \end{gathered}[/tex]When
[tex]S=2[/tex]Then,
[tex]\begin{gathered} C=3750+150(2) \\ =3750+300 \\ =4050 \end{gathered}[/tex]So, the coordinates are,
[tex](0,3750),(1,3900),(2,4050)[/tex]The equation represents the total cost C and the amount of sugar S is given by,
[tex]C=3750+150S[/tex]The graph is,
geometry special parallelogramsSide GH =Side JG =Side FH =
we have that
In a rhombus the length sides are congruent
the diagonals bisect each other and are perpendicular
so
If mmIn the right triangle IFJ
mtan(30)=FJ/IJ
Remember that
[tex]\tan (30^o)=\frac{\sqrt[]{3}}{3}[/tex]FJ=4
substitute the given values
[tex]\begin{gathered} \frac{\sqrt[]{3}}{3}=\frac{4}{IJ} \\ \\ IJ=\frac{12}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=4\sqrt[]{3} \end{gathered}[/tex]Find the length side IF
Applying Pythagorean Theorem
IF^2=4^2+IJ^2
IJ^2=48
IF^2=16+48
IF^2=64
IF=8 units
that means
side GH=8 units
side JG=side IJ=4√3 units
side FH=2*side FJ=2*4=8 units
Which table shows a proportional relationship between miles traveled and gas used?
Miles Traveled Gas Used
27.3 mi 1.5 gal
49.16 mi 3.8 gal
Miles Traveled Gas Used
120 mi 6.2 gal
180 mi 12.2 gal
Miles Traveled Gas Used
135 mi 7.4 gal
135.5 mi 7.9 gal
Miles Traveled Gas Used
270 mi 15 gal
135 mi 7.5 gal
Answer:
D
Step-by-step explanation:
270mi 15gal
135mi 7.5gal
135/270=0.5
7.5/15=0.5
or
135/7.5=18
270/15=18
I need help with this practice from my ACT prep guide Having trouble
Given:
[tex]f(x)=-4\cos (\frac{2}{3}x+\frac{\pi}{3})-3[/tex]Hi, can you help me answer this question please, thank you!
Let x be a random variable representing the blood pressures of adults in the USA. Since it is normally distributed, we would apply the formula for determining z score which is expressed as
z = (mean - population mean)/standard deviation
From the information given,
population mean = 121
Standard deviation = 16
For stage 2 high blood pressure, the probability is
P(x greater than or equal to 160). It is also equal to 1 - P(x < 160)
Thus, for x = 160, we have
z = (160 - 121)/16 = 2.4375
From the standard normal distribution table, the probability value corresponding to a z score of 2.4375 is 0.9927
P(x < 160) = 0.9927
P(x greater than or equal to 160) = 1 - 0.9927 = 0.0073
Converting to percentage, it is 0.0073 * 100 = 0.73%
b) If 2000 peaople were sampled, the number of people with stage 2 high blood pressure would be
0.73/100 * 2000 14.6
To the nearest person, it is 15 people
c) For stage 1, the probability is
P(140 < x < 160)
For x = 140,
z = (140 - 121)/16 = 1.1875
From the standard normal distribution table, the probability value corresponding to a z score of 1.1875 is 0.883
Recall, for x = 160, the probaility is 0.9927
Thus,
P(140 < x < 160) = 0.9927 - 0.883 = 0.1097
Converting to percentage, it is
0.1097 * 100 = 10.97%
d) The 30th percentile refers to all values of blood pressure below k, where k is the 30th percentile. This means that we would find
P(x < k) = 0.3
The z score corresponding to a probability value of 0.3 is - 0.52
Thus,
(k - 121)/16 = - 0.52
k - 121 = - 0.52 * 16 = - 8.32
k = - 8.32 + 121
k = 112.68
The pressure for the 30th percentile is 112.68
Find the quotient32 divided by 517 what is quotient and what is remainder
Calculate the division as shown below
Therefore, the quotient is 16 and the remainder is 5
The answer is 16R5How far is the girl from the monument that is 30 ft high? Round your answer to a nearest foot. Show your work.
Given:
The diagram is shown alongside.
The height of the monument is 30 ft high.
The angle of elevation is 63 degrees
The objective is to find the distance between the monument and where the girl is standing.
Since it forms a right angled triangle so we can apply trigonometric ratios:
Now,
[tex]\tan 63^{\circ}=\frac{perpendicular}{\text{base}}[/tex]Perpendicular = 30 ft
Base = ?
Substituting the values,
[tex]\begin{gathered} \tan 63^{\circ}=\frac{30}{\text{base}} \\ \text{Base}=\frac{30}{\tan63^{\circ}} \\ \text{base}=\frac{30}{1.962610} \\ \text{base}=15.285767422\text{ ft} \end{gathered}[/tex]Therefore, the girl is at a distance of 15 ft from the monument.
Find the volume of the figure. 6 cm. 6 cm. 1 8 cm. 10 cm. Volume of the prism cm3
The volume of the pyramid is 144 cm³
Explanations:The volume of a prism is given by the formula:
V = BH
where B is the base area
and H is the height
The base of the the pyramid is the lateral triangle, and the area is given by the formula:
B = 0.5 x b x h
b = 8 cm
h = 6 cm
B = 0.5 x 8 x 6
B = 24 cm²
The volume is then:
V = BH, where H = 6 cm
V = 24 x 6
V = 144 cm³
Given that the shape below is a rectangle, we know that the diagonals, lines AD and CB, are ____.
The given information is the shape is a rectangle.
About the diagonals of rectangles, there are two known properties:
- The diagonals of a rectangle bisect each other
- Both diagonals have the same length
Then, the answer is option C. They have the same length
On December 13, 2007, one South African rand was worth 0.15 U.S. dollars.(a) On that date, how many rand was 44.11 dollars worth?Round your answer to the nearest hundredth of a rand.rand(b) On that date, how many dollars was 168.18 rand worth?Round your answer to the nearest hundredth of a dollars. I need help with this math problem.
Explanation
Part A
Given that one South African rand was worth 0.15 U.S. dollars. 44.11 dollars will be worth
[tex]\frac{44.11}{0.15}=294.07[/tex]Answer: 294.07 rands
Part B
On that date, how many dollars was 168.18 rand worth?
[tex]168.18\times0.15=25.23[/tex]Answer: 25.23 dollars
i need help with this question
The side AB = BD
7x + 10 = 9x - 2
SImplify for x :
Subtract 7x from both side :
7x + 10 - 7x = 9x - 7x - 2
10 = 2x - 2
Add 2 on both side :
10 + 2 = 2x - 2 + 2
12 = 2x
divide both side by 2 :
2x/2 = 12/2
x = 6
is it true that all whole numbers are rational numbers ? why or why not
all whole numbers are rational numbers
because we can write 21 as 21/1 in rational form.
.
We can write any whole number (a) into the form of
[tex]\frac{a}{b}[/tex]where b = 1,
so all whole numbers can be written in form of rational numbers.
Write these numbers from least to greatest: 0, -6.1, 4, 10/2
Answer:
10/2, 4, 0, -6.1
Step-by-step explanation:
It is the only answer that makes sense.
pls mark brainliest
Answer: -6.1, 0, 4 , 10/2
Step-by-step explanation:
-6.1 is the only negative number, so it is the least. Zero comes next. 10/2 is 5, so 4 comes before it. Therefore 4 is the 3rd installment in these ordered numbers.
How can I know how many students scored 5 in their test?
Based on the given table, consider that the value in the column frequency specifies the number of times that a certain score (first column) is repeated in a given data.
In this case, the value of the frequency for a specific score determines the number of students with such a score in their tests.
As you can notice, for the value of the frequency equal to 3, the corresponding value of the score is 5. It means that 3 student get 5 scores in their tests.
Quadrilateral ABCD is a rhombus.DA АC СBMatch the reasons that justifies the given statements.
A rhombus is a quadrilateral with 4 congruent sides.
For the Rhombus ABCD given
[tex]\begin{gathered} AB\mleft\Vert DC\text{ }\mright? \\ \\ \text{Opposite sides of a rho}mbus\text{ are parallel} \end{gathered}[/tex]Also,
[tex]\begin{gathered} DA\cong CB \\ \text{Opposite sides of a rhombus are congruent} \end{gathered}[/tex]Also,
[tex]\begin{gathered} <\text{ADC}\cong<\text{ABC} \\ \text{Opposite angles of a rhombus are congruent} \end{gathered}[/tex]A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. If x
represents the length, then the length can be found by solving the equation:
x(x-3) = 54
What is the length, x, of the garden?
The length is
feet.
The solution is?
To determine the length of the rectangular flower garden, we need to derive equations from the given measurements and relations. The given measurements are the area, and the relation of the width and the length. From these, we generate the equation needed. We do as follows:
Area = Length x Width
where length = x ft
width = x - 3 ft
area = 54 ft^2
54 ft^2 = x ft (x -3) ft
54 ft^2 = x^2 - 3x ft^2
Solving for the value of x, we will have two values which are
x = -6 ft ( NOTE: this value can't be the answer since we cannot have a negative value for the length)
x = 9 ft = length
I need help with finding the output y when x is -4 it's on a graph
As observed from the graph, the curve is a straight line from point (-2,-1) to (-5,2).
Consider that the equation of a straight line passing through two points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\times(x-x_1)[/tex]So the equation of the line passing through (-2,-1) and (-5,2) is given by,
[tex]\begin{gathered} y-(-1)=\frac{2-(-1)}{-5-(-2)}\times(x-(-2)) \\ y+1=\frac{3}{-3}\times(x+2) \\ y+1=-x-2 \\ y=-x-3 \end{gathered}[/tex]Note that this function is only for the interval [-2, -5].
Now, the value of 'y' corresponding to the input x=-4 is calculated as,
[tex]\begin{gathered} y=-(-4)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]Thus, the required output is y = 1 .
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
-3/8+(-9/10)
Answer:
-1 11/40
Step-by-step explanation:
-51/40 this is simplest form.
Step-by-step explanation: