Having the probability distribution in the range from 0 to 20, the sum of all probabilities should give 1. This will be useful to estimate the missing value (P(x = 15)).
Let's establish the sum of probabilities:
[tex]P(x=0)+P(x=5)+P(x=10)+P(x=15)+P(x=20)=1[/tex]Now, we can replace values and solve for P(x = 15):
[tex]0.11+0.3+0.21+P(x=15)+0.1=1[/tex][tex]0.72+P(x=15)=1[/tex][tex]\begin{gathered} P(x=15)=1-0.72 \\ P(x=15)=0.28 \end{gathered}[/tex]The probability of selling 15 cheesecakes on a given day is 0.28 (28%)
Now, to estimate the probability of selling at least 10 cheesecakes can be calculated by summing the probabilities of selling 10, 15, or 20. In this case, we include the 10 because it says at least. Then:
[tex]P(x\ge10)=P(x=10)+P(x=15)+P(x=20)[/tex]Replacing values:
[tex]P(x\ge10)=0.21+0.28+0.1[/tex][tex]P(x\ge10)=0.59[/tex]The probability of selling at least 10 is 0.59 (59%))
Complete the proof of the transitive property of parallel lines Theorem
The most appropriate choice for parallel line has been given by
Transitive property of parallel lines Theorem has been proved.
What are parallel lines?
Parallel lines
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal
Transversal is a line that intersects two or more parallel lines
Here,
The diagram has been attached
line l ║ line m and line m ║ line n.
To prove line l║ line n
line l ║ line m
∠ABC = ∠ADE [Corrosponding angles are equal]
line m ║ line n.
∠ADE = ∠AFG [Corrosponding angles are equal]
So, ∠ABC = ∠AFG
So corrosponding angles of line l and line n are equal. So,
line l ║line n
Transitive property of parallel lines Theorem has been proved.
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Two sides of an isosceles triangle have lengths of 3 and 6. What is the length of the third side?A. 6B. 9C. 3D. 5
It is given that the triangle is isosceles and the sides are 3 and 6.
Since the triangle is isosceles so third side will be either 3 or 6 .
If third side is 3 then we have
[tex]3+3=6[/tex]which is a contradiction to the fact that sum of two sides of a triangle is greater than the third side.
So the third side will be 6.
Hence the correct option is (A).
Help me finish show ur steps pls 1/8+3/14 simplify
Answer:
Step-by-step explanation:
1/8+3/14
=14/112+24/112
=38/112
=19/56
Without graphing, group the systems based on the number of solutions. y=2x-3 y=-2x+3. So my question is how can I find if it has one solution no solution or infinity solutions
Step 1:
two system of linear equations has one solution
Step 2:
Let deduce the number of solution in the two linear equations
y = 3x - 3 ...............................equation 1
y = -2x + 3 ..............................equation 2
Step 3:
use substitution method to solve the system o
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the thiside of each triangle.A6.5X3.6B5.2YZCProvide your answer below:MORE INSTRUCTIONayFEEDBACK4.5SUBMIT
Since the triangles are similar this means that the ratios between similar sides have to be equal; this means that:
[tex]\begin{gathered} \frac{6.5}{3.6}=\frac{5.2}{y} \\ \frac{6.5}{3.6}=\frac{a}{4.5} \end{gathered}[/tex]Solving the first equation we have:
[tex]\begin{gathered} \frac{6.5}{3.6}=\frac{5.2}{y} \\ y=\frac{5.2}{\frac{6.5}{3.6}} \\ y=2.88 \end{gathered}[/tex]Solving the second equation:
[tex]\begin{gathered} \frac{a}{4.5}=\frac{6.5}{3.6} \\ a=4.5(\frac{6.5}{3.6}) \\ a=8.125 \end{gathered}[/tex]Therefore, a=8.125 and y=2.88
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
______ knots
The distance is changing at 153 nots at 5 P.M.
According to the Pythagoras Theorem, the square of the hypotenuse of a right angle triangle is equal to the sum of squares of the other two sides of the triangle. A derivative is suppose x and y are two variables, then the rate of change of x with respect to y is called a derivative. Differentiation is a process of finding the derivative of a function.
According to the question,
At noon, ship A is 50 nautical miles due west of ship B. (given)
Ship A is sailing west at 17 knots (given)
ship B is sailing north at 17 knots (given)
using the Pythagorean Theorem,
c^2 = a^2+b^2
Here, c is the distance between them at any point
a is the distance of ship A from initial point
b is the distance of ship B from initial point
Now,
initially ship A is due by 50 nautical miles (given)
and in 5 hours it travels 35*17 miles (given)
So, a = 50+5*17 = 50+85 = 135 nautical miles
Similarly b = 5*17 = 85 nautical miles
c^2 = 135^2+85^2 = 18225+7225
= 25450
c = √25450
c = 159.53 nautical miles
But we need to find how fast (in knots) is the distance between the ships changing
that is we need dC/dt (differentiation)
c^2 = a^2+b^2
Differentiating we get,
2cdc/dt = 2a*da/dt + 2b* db/dt
(the power comes on front during differentiating)
We now have da/dt = 17
db/dt = 17
So, dc/dt = (135*17+85*17)/(159.53) = 153 approx. knots
Therefore, we can conclude that the distance is changing at 153 nots at 5 P.M.
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a store pays $10 for a bracelet and the markup is 115%. A customer will also pay 5 and a half sale tax . what will be the total cost to the nearest cent ?
ANSWER:
$22.68
STEP-BY-STEP EXPLANATION:
Given:
Bracelet = $10
Markup percentage = 115% = 115/100 = 1.15
The markup amount can be calculated as follows:
[tex]\begin{gathered} \text{ markup amount = cost price }\cdot\text{ markup percentage} \\ \text{ replacing} \\ \text{markup amount }=10\cdot1.15=11.5 \end{gathered}[/tex]Therefore, the total price would be:
[tex]t=10+11.5=21.5[/tex]Now we apply sales tax for the price and calculate the price after tax, like this:
[tex]\begin{gathered} t=21.5+21.5\cdot\frac{5.5}{100} \\ t=21.5+1.1825 \\ t=22.6825\cong22.68 \end{gathered}[/tex]$22.68 is the total cost of the bracelet
Find the inverse of the following function
h(x) = 2x+16/5
A)h¯¹ (x) = 52 - 16
B)h ¹(x) = 16x+2/5
C)h 1 (z) = 5x-16/2
D)h¹(x) = 2x+ 16
Answer:
C
Step-by-step explanation:
Which pair of variables would most likely have a positive association?
Answer:
• The age of a kitten and its weight
,• Temperature and the sales of ice cream
,• The number of notebooks bought and the total cost.
Explanation:
Two variables have a positive association when an increase in the values of one of the variables also leads to an increase in the value of the second variable.
From the given options, those with a positive association are explained below:
(a)The age of a kitten and its weight
The older a kitten gets, the more the weight of the kitten until it gets to adulthood.
(b)Temperature and the sales of ice cream
When the temperature increases, people tend to purchase more ice cream.
(c)The number of notebooks bought and the total cost.
• If 1 notebook costs $5, then:
,• 2 notebooks will cost $10.
As the number of notebooks bought increases, the total cost also increases.
Which statements about the graph of the function ) =22-X-6 are true? Select two options3The domain of the function is falx2)The range of the function is all real numbersThe verter of the function is7227The function has two x-intercepts.The function is increasing over the interval (-5)
True statements about the graph of the function f(x) = 2 x 2 - x -6 include:
The range of the function is all real numbers
The function has two x-intercepts.
What is function?In mathematics, functions are the foundation of calculus. Functions are specific types of relationships. In math, a function is represented as a rule that produces a unique output for each input x. In mathematics, mapping or transformation is used to represent a function.
These functions are typically denoted by letters such as k, g, and h. The domain is defined as the set of all the values that the function can accept while it is defined. The range contains all of the values returned by the function in question. The co-domain is the set of values that have the potential to be outputs of a function.
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Given: C is midpoint of BD, BD perpendicular to DE, AB perpendicular to BD.
Prove: triangle ABC is congruent to triangle EDC.
(1.)statement = the given above. (1.)reason=given.
△ABC is congruent to △EDC (△ABC ≅ △EDC) under the SAS congruency condition.
What do we mean by the congruency of triangles?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.These triangles can be moved, turned, flipped, and rotated to produce the same appearance.When moved, they are parallel to one another.Three important theorems establish the connection between equality and congruence.Two angles are only referred to as being congruent if and only if their measures are equal.Two segments are congruent if and only if there are equal amounts of each in them.Two triangles are said to be congruent if and only if all of the corresponding angles and sides are in agreement.So, △ABC ≅ △EDC:
BC = CD (C is the midpoint of BD: Given)CBA = CDE = 90° (BD ⊥ BA and DE: GIven)AC = CE (Angles in front of them are the same, then lines in front of angles will also be similar)Then, △ABC ≅ △EDC under SAS congruency condition.
Therefore, △ABC is congruent to △EDC (△ABC ≅ △EDC) under the SAS congruency condition.
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Write an equation in point slope form and slope intercept form for each line passes through (8,-4). Slope =1/2
Part 1
The equation in point-slope form is
y-y1=m(x-x1)
we have
point (8,-4)
m=1/2
substitute
[tex]y+4=\frac{1}{2}(x-8)[/tex]Part 2
The equation in slope-intercept form
y=mx+b
we have
y+4=(1/2)(x-8)
isolate the variable y
so
y+4=(1/2)x-(1/2)(8)
y+4=(1/2)x-4
y=(1/2)x-87. Brittany and Hanna can paddle 12 mi upstream in the same
time it takes to paddle 28 mi downstream. Determine their
paddling rate in still water if the stream flows at 2 mi/hr.
Answer and Step-by-step explanation: Paddling 12 miles upstream will take you 12 mi / (vp - 2 mi/hr) = 12 / (vp-2) hr. (If you're having trouble figuring out how to calculate time from speed and distance, just look at the units. Time (hr) is required as a result. We have two units: miles and miles per hour. Divided by mi/hr, mi is equal to mi * hr/mi, which equals hr. 28 / (vp + 2) is the time it takes to paddle 28 miles downstream. Also, these ought to be equal: 12 / (vp-2) = 28 / (vp+2) (cross multiplication) (cross-multiplication) 28 * (vp-2) = 12 * (vp+2) 28 vp - 56 = 12 vp + 24 (collect vp terms on one the left side and constants on the right side) (collect vp terms on one the left side and constants on the right side) (28-12) vp = 24 + 56\svp = 80/16
What is the perimeter, P, of a rectangle that has a length of x + 6 and a width of y-1?OP=x+y+5OP=x+y-7OP=2x + 2y + 10OP=2x+2y-10
GIVEN
A rectangle with length (x + 6) units and width (y - 1) units.
TO FIND
The perimeter of the rectangle.
SOLUTION
The perimeter of a rectangle is calculated using the formula:
[tex]P=2\left(l+w\right)[/tex]Substitute the values of the length and width into the formula:
[tex]P=2(x+6+y-1)[/tex]Simplify:
[tex]\begin{gathered} P=2(x+y+5) \\ P=2x+2y+10 \end{gathered}[/tex]ANSWER
[tex]P=2x+2y+10[/tex]Question 4Given AGEO 2 AFUMZE = (42.)in/N = 40mZU = 80ånd m_G = 60find the value of a(The problem is sort of messed up because of canvas)
It is stated in the problem that ΔGEO is congruent with ΔFUN. On the first triangle, the measurement of angle E and angle G is given but the measurement of angle O is not given. Using the congruence relation of the two triangles, it is true that
[tex]m\angle O\cong m\angle N[/tex]The measurement of angle N is provided in the problem, which is equal to 40 degrees. Hence, we can say that angle O has also an angle measurement of 40 degrees base on the statement above.
The sum of the interior angles of the triangle is equal to 180 degrees. This means that if we add up the interior angles of the triangle GEO, we have the following equation
[tex]m\angle G+m\angle E+m\angle O=180[/tex]Substitute the measurement of each angle on the equation above and compute, we get
[tex]\begin{gathered} 60+4x+40=180 \\ 4x+100=180 \\ 4x=180-100 \\ \frac{4x}{4}=\frac{80}{4} \\ x=20 \end{gathered}[/tex]Therefore, the value of x is equal to 20 degrees.
PLEASE ANY ONE IF YOU KNOW THIS ANSWER IT PLEASE DONT NOT I REPEAT DONT ANSWER IF YOU DO NOT KNOW IT OK THANK YOU.
Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Down Under Boomerang, Inc., is considering a new 3-year expansion project that requires an initial fixed asset investment of $2.37 million. The fixed asset falls into the 3-year MACRS class (MACRS schedule). The project is estimated to generate $1,765,000 in annual sales, with costs of $664,000. The project requires an initial investment in net working capital of $360,000, and the fixed asset will have a market value of $345,000 at the end of the project. a. If the tax rate is 21 percent, what is the project’s Year 0 net cash flow? Year 1? Year 2? Year 3? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to two decimal places, e.g., 1,234,567.89.) b. If the required return is 11 percent, what is the project's NPV? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to two decimal places, e.g., 1,234,567.89.)
Reduce this fraction to lowest terms.
35/49
Select the correct answer.
5/7
5/6
6/7
4/9
Answer:
the answer to your problem is 5/7.
Identify the missing terms in the polynomial.x3-9O x2-term, x-termSO x-termO x4-term, x2-term, x-termO x-term
We must identify the missing terms in the polynomial:
[tex]x^3-9.[/tex]The general form of a 3th grade polynomial is:
[tex]a_3\cdot x^3+a_2\cdot x^2+a_1\cdot x+a_0.[/tex]We see that the missing terms are x² and x.
Answer
The missing terms are: x2-term, x-term.
Find the remainder when f(x) = x³ - 4x² - 6x-3 is divided by x + 1.
A.-2
B. -14
C. 6
D. -12
The remainder of the given function [tex]x^{3} -4x^{2} -6x-3[/tex] is -2, founded by using division of polynomial
The correct option is option A).
What is division of polynomial?
Polynomial division is a generalized variant of the well-known arithmetic operation known as division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.
Our given polynomial is [tex]x^{3} -4x^{2} -6x-3[/tex]
We have to divide this polynomial by x+1 .
This can be done by
Therefore the remainder on division of the polynomial is -2
Hence the correct option is A)
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x-8=29Write which property of equality you used
The given expression is
[tex]x-8=29[/tex]We have to use the addition property of equality, which means we are going to sum 8 on each side.
[tex]\begin{gathered} x-8+8=29+8 \\ x=37 \end{gathered}[/tex]Hence, the property is "the addition property of equality".Determine which set of side measurements could be used to form a triangle.
12, 23, 7
10, 7, 2
8, 3, 11
5, 11, 8
Answer:
Among the given, the set of side measurements (5, 11, 8) could be used to form a triangle.
Step-by-step explanation:
As we know,
For forming a triangle, "The sum of the length of any two sides of a triangle is greater than the length of the third side."
The side opposite the largest angle of a triangle is the largest side. Any exterior angle of the triangle is equal to the sum of its interior opposite angles.
Now taking the value given in the option:
We have the first set of values: 12, 23, 7
As here, let us assume that, a = 12, b = 23, c = 7
So, for the formation of triangle a + b > c
So, 12 + 7 = 19 < 23
Hence, this set of values can't form a triangle.
We have the second set of values: 10, 7, 2
As here, let us assume that, a = 7, b = 2, c = 10
So, for the formation of triangle a + b > c
So, 7 + 2 = 9 < 10
Hence, this set of values can't form a triangle.
We have the third set of values: 8, 3, 11
As here, let us assume that, a = 8, b = 3, c = 11
So, for the formation of triangle a + b > c
So, 8 + 3 = 11 < 11
Hence, this set of values can't form a triangle.
We have the fourth set of values: 5, 11, 8
As here, let us assume that, a = 5, b = 8, c = 11
So, for the formation of triangle a + b > c
So, 5 + 8 = 13 > 11
Hence, this set of values can form a triangle.
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Suppose that on January 1 you have a balance of $3,100 on a credit card whose APR is 13%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. The monthly payment is?b. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part (b) is interest?
The monthly payment M of an initial balancen P, with a APR r during a period of t months is given by:
[tex]M=P\frac{\frac{r}{12}(1+\frac{r}{12})^t}{(1+\frac{r}{12})^{12}-1}[/tex]a) For P = $3,100, r = 13% and t = 12 months, we have:
[tex]M=3100\frac{\frac{0.13}{12}(1+\frac{0.13}{12})^{12}}{(1+\frac{0.13}{12})^{12}-1}\approx\text{ \$}276.88[/tex]b) The total payment after 12 months will be:
[tex]T=12\cdot M=12\cdot276.88=\text{ \$}3322.60[/tex]c) The total interest is given by:
[tex]I=\frac{T}{P}-1=\frac{3322.60}{3100}-1\approx0.072=7.2\%[/tex]If I got a 92% and there were 40 questions how many did I get wrong?
Answer: 3.2 were wrong
92% of 40 is 36.8 so you got 3.2 wrong
I hope this helps / Is correct
This test is timed so i need it quickly
Answer: D!!
Step-by-step explanation: No explanation so you can move on quickly!!!!:))
5,624 ÷ 72 using estimation
Answer: 5,624 rounded would be 5,600 and 72 rounded would be 70.
5,600/70= 80
Step-by-step explanation:
Yea I do agree that with this one ☝️ I will be coming
Solution
- The equation for the potential given is:
[tex]V(t)=320e^{-3.1t}[/tex]Question 1:
- To find when the potential is 150V, we simply substitute the value of V = 150 into the equation and then find the corresponding value of t.
- Thus, we have:
[tex]\begin{gathered} V=150 \\ \\ 150=320e^{-3.1t} \\ \\ \text{ Divide both sides by 320} \\ \\ e^{-3.1t}=\frac{150}{320}=\frac{15}{32} \\ \\ \text{ Take the natural log of both sides} \\ \\ \ln e^{-3.1t}=\ln(\frac{15}{32}) \\ \\ -3.1t=\ln(\frac{15}{32}) \\ \\ \text{ Divide both sides by -3.1} \\ \\ t=-\frac{1}{3.1}\ln(\frac{15}{32}) \\ \\ t=0.2444s\text{ \lparen To 4 decimal places\rparen} \end{gathered}[/tex]Question 2:
- The rate at which the changing occurs is gotten by differentiating the function with respects to time.
- That is,
[tex]\begin{gathered} V(t)=320e^{-3.1t} \\ \\ V^{\prime}(t)=\frac{d}{dt}(320e^{-3.1t}) \\ \\ V^{\prime}(t)=320(-3.1e^{-3.1t}) \\ \\ V^{\prime}(t)=-992e^{-3.1t} \end{gathered}[/tex]- Now that we have the expression for the rate of change of potential with time, we can proceed to find how fast the changing of potential V is happening at t = 0.2444s.
- Thus, we have:
[tex]\begin{gathered} V^{\prime}(t)=-992e^{-3.1t} \\ put\text{ }t=0.2444 \\ \\ V^{\prime}(t)=-992e^{-3.1\times0.2444} \\ \\ \therefore V^{\prime}(t)=-465.02125...\approx-465.0\text{ v/s} \end{gathered}[/tex]Question 3:
- The voltage is changing at -50v/s when we substitute V'(t) = -50 into the equation for V'(t).
- We have that:
[tex]\begin{gathered} V^{\prime}(t)=-992e^{-3.1t} \\ \\ V^{\prime}(t)=-50 \\ \\ -50=-992e^{-3.1t} \\ \\ \text{ Divide both sides by -992} \\ \\ e^{-3.1t}=\frac{-50}{-992}=\frac{25}{496} \\ \\ \text{ Take the natural log of both sides} \\ \ln e^{-3.1t}=\ln(\frac{25}{496}) \\ \\ -3.1t=\ln(\frac{25}{496}) \\ \\ \text{ Divide both sides by -3.1} \\ \\ \therefore t=-\frac{1}{3.1}\ln(\frac{25}{496}) \\ \\ t=0.96377...\approx0.9638seconds\text{ \lparen To 4 decimal places\rparen} \end{gathered}[/tex]Final Answers
Question 1: 0.2444 seconds
Question 2: -465.0v/s
Question 3: 0.9638 seconds
Gianna went shopping for a new camera because of a sale. The price on the tag was $26, but Gianna paid $13 before tax. Find the percent discount.
The percent discount of the camera is 50%.
What is percentage discount?Percentage discount is a discount that is given to a product or service that is given as an amount per hundred.
In other words, the percent discount is list price minus the sale price then divided by the list price and multiplied by 100 to get a percentage.
Hence,
she bought the camera for $13 but the price tag is $26.
Therefore,
percentage discount = tagged price - sale price / tagged price × 100
tagged price = 26 dollars
sale price = 13 dollars
percentage discount = 26 - 13 / 26 × 100
percentage discount = 13 / 26 × 100
percentage discount = 1 / 2 × 100
Therefore,
percentage discount = 50%
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The jones brother, Carl,Cameron, and Carlos, are painters. Together they can paint a standard sized room in 2 hours. If Carl is alone on the job he can paint the room in 5 hours. If Cameron is alone he can paint the room in 6 hours.a)what equation can be used to determine how long it would take Carlos to paint the room alone? b)How long would it take Carlos to paint the room alone?
The workdone by the three(3) is equal to the painting of 1 room in 2 hours.
Time taken by
Carl alone = 5 hours
Cameron alone = 6 hours
Let time taken by Carlos alone = x hours
In One(1) hour, the size of the that will be covered by each of them is:
[tex]\begin{gathered} \text{Carl alone = }\frac{1}{5}\text{ of the room} \\ \text{Cameron alone=}\frac{1}{6}\text{ of the room} \\ \text{Carlos alone= }\frac{1}{x}\text{ of the room} \end{gathered}[/tex]a) Hence, the equation that can be used to determine how long it would take Carlos to paint the room alone is:
[tex]\frac{1}{5}\text{ + }\frac{1}{6}\text{ + }\frac{1}{x}=\frac{1}{2}[/tex]b) We will solve for the value of x in the equation above
[tex]\begin{gathered} \frac{1}{5}\text{ + }\frac{1}{6}\text{ + }\frac{1}{x}=\text{ }\frac{1}{2} \\ \\ \frac{1}{x}=\frac{1}{2}\text{ - }\frac{1}{5}\text{ - }\frac{1}{6} \\ \\ \frac{1}{x}=\frac{15-6-5}{30} \\ \\ \frac{1}{x}=\frac{4}{30} \\ \\ x=\frac{30}{4} \\ x=\frac{15}{2} \\ x=7.5\text{ hours} \end{gathered}[/tex]Hence, it will take Carlos 7.5 hours to paint the room alone
Question ID: 97725The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for Te.3 in4 inA = 37.12 square inches, Pz 16.28 inchesA = 18.28 square inches, P 22.56 inchesA = 37.12 square inches, P = 22.56 inchesA ~ 18.28 square inches, P 16.28 inches
Solution
For this case we can find the area as the sum of the rectangle and the semicircle so we have this:
A1= 3in * 4in= 12 in^2
A2 = (pi/2) *(2in)^2 = 6.28 in^2
then the total area is:
A= A1+ A2= 12+ 6.28 in^2 = 18.28 in^2
And then the perimeter similarly we have:
P= 2*4 in + 2*3in + 2pi*(4in/2) = 8+ 6+ 12.56 in= 26.56in
Then the final answer is:
Area ~18.28 in^2 and Perimeter ~26.56 in
