A factory makes candles. Each candle is in the shape of a triangular prism, as shown below. If the factory used 14,700 cm^3 of wax,how many candles did the factory make?
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Answer:
Explanation:
Step 1
First, we find the volume of one the triangular prism shaped candles.
The volume of a prism is calculated using the formula:
[tex]V=\text{ Cross-Sectional Area}\times\text{ Length}[/tex]The cross section of the prism is a triangle with:
• Base = 10cm
,• Height = 7cm
Length of the Prism = 6cm
Therefore:
[tex]\begin{gathered} V=\frac{1}{2}bh\times L \\ =\frac{1}{2}\times10\times7\times6 \\ =210\;cm^3 \end{gathered}[/tex]The volume of one of the candles is 210 cubic cm.
Step 2
Next, divide the volume of wax used by the factory by the volume of one candle.
[tex]\text{Number of candles made}=\frac{14700}{210}=70[/tex]Related Questions
timothy and freda were asked to solve 675÷5 who is correct and why I can send you a picture would you like that ??
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Since both came to the same answer using a different method, I would say that both are correct.
If a ^20 = (a^n)^m, which of the following could be values for m and n?obA) m = -5, n = -4B) m = 10, n = 10C) m = 22, n = -2D) m = 15, n = 5d
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a ^20 = (a^n)^m
When we have a number raised to a power two time, we can multiply the powers;
(a^n)^m = a ^ (n x m)
So, since both sides have the same base:
a^20 = a^ (nxm)
20 = n x m
So, the product of n and m must be 20
A) -5 x -4 = 20
B) 10 x 10 =100
c) 22 x -2 =-44
d)15 x 5 = 75
The correct answer is A.
Notation scientific ad and subtract2.4 *10^5 + 0.5*10^5 =
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We will operate as follows:
[tex]2.4\cdot10^5+0.5\cdot10^5=2.9\cdot10^5[/tex]Find the value of r in the equation below.11 = = 12
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in the triangle abc a =65 b =58 identity the longest side of the triangle
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We know two angles of a triangle, ∠A = 65° and ∠B = 58°, and we have to identify the longest side.
The longest side will be the one that is opposite to the widest angle. In our case, we don't know the measure of C, but we know that the sum of the three measures has to be 180°, so we can calculate it as:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 65+58+m\angle C=180 \\ m\angle C=180-65-58 \\ m\angle C=57\degree \end{gathered}[/tex]As the widest angle is at vertex A, the longest side will be its opposite, which correspond to the side formed by the other two vertices: B and C.
The longest side is BC.
Circumference and the area of a circle with radius 5 ft you
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The circunference formula is given by
[tex]C=2\pi r[/tex]where r is the radius. Since r measures 5 ft, we have
[tex]\begin{gathered} C=2\pi\cdot5 \\ C=10\pi \end{gathered}[/tex]By taking into account that Pi is 3.14, the circuference is equal to 31.4 ft.
On the other hand, the area formula is given by
[tex]A=\pi r^2[/tex]Then, by substituting r=5 into this formula, we get
[tex]\begin{gathered} A=(3.14)(5^2) \\ A=3.14\times25 \\ A=78.5ft^2 \end{gathered}[/tex]then, the area is equal to 78.5 square feet
In the above graph of y = f( x ), find the slope of the secant line through the points ( -4, f( -4 ) ) and ( 1, f( 1 ) ).
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Answer:
slope = 3 / 5
Explanation:
First, let us note from the graph that
[tex]f(-4)=1[/tex]and
[tex]f(1)=4[/tex]Therefore, the two points that lie on the secant line are
[tex]\begin{gathered} (-4,1) \\ (1,4) \end{gathered}[/tex]The slope of the line (the secant) passing through these two points is
[tex]slope=\frac{4-1}{1-(-4)}[/tex][tex]=\frac{3}{5}[/tex][tex]\boxed{slope=\frac{3}{5}\text{.}}[/tex]Hence, the slope of the secant is 3/5.
A private college advertise that last year their freshman students on average how do you score of 1140 on the college entrance exam. Assuming that the average refers to the mean, Which of the following claims must be true based on this information? Last year some of their freshman students had a score of exactly 1140 on the exam last year more than half of their freshman students had a score of at least 1140 on the exam last year all their freshman students have a score of at least 1140 on the exam next year at least one of their freshman students will have a score of at least 1140 on theexam last year at least one of their freshman students had a score of more than 900 on the exam or none of the above statements are true
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We know that the mean score obtained by the freshman students last year was 1140.
It means that the sum of all the freshman students' scores from last year, divided by the number of freshmen students resulted in the number 1140.
It doesn't mean necessarily that one or more students had a score of exactly 1140.
Step 1
Find an example showing that some of the statements must not be true.
A way of obtaining this score is if half the N students had a score of 0, and the other half had a score of 2280:
[tex]mean=\frac{\frac{N}{2}\cdot0+\frac{N}{2}\cdot2280}{N}=\frac{N\cdot1140}{N}=1140[/tex]From this example, none of the students had a score of exactly 1140, and half of them had a score less than 1140. So, we can conclude that the first three statements must not be true.
Step 2
Analyze the other statements.
The fourth statement must not be true because we can't conclude anything for sure for next year's scores based on the last year's scores.
Let's analyze the fifth statement. Suppose it must not be true, i.e., all the freshman students had scores equal to or less than 900. Then, since the mean score can't be greater than the maximum score, the mean score would be no more than 900. Wich is false because it was 1140 > 900.
Therefore, the fifth statement must be true.
Answer
The only claim that must be true is:
Last year, at least one of their freshman students had a score of more than 900 on the exam.
In rectangle ABCD, the diagonals intersect at E. If m angle∠AEB= 3x and m angle∠DEC= x+80, find m angle∠AEB and m angle∠EBA.
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Since the angles∠ AEB and ∠DEC are vertically opposite angles, they are congruent, so we have:
[tex]\begin{gathered} 3x=x+80 \\ 2x=80 \\ x=40 \end{gathered}[/tex]So the measure of angle ∠AEB is:
[tex]\begin{gathered} \angle\text{AEB}=3x \\ \angle\text{AEB}=3\cdot40=120\degree \end{gathered}[/tex]The diagonals of a rectangle are congruent and intersect in their middle point, so the segment AE is congruent to the segment EB, therefore the triangle AEB is isosceles, so the angle ∠BAE is congruent to ∠EBA.
The sum of the internal angles of a triangle is 180°, so in triangle AEB we have:
[tex]\begin{gathered} \angle\text{BAE}+\angle\text{EBA}+\angle\text{AEB}=180\degree \\ \angle\text{EBA}+\angle\text{EBA}+120=180 \\ 2\angle\text{EBA}=60 \\ \angle\text{EBA}=30\degree \end{gathered}[/tex]Dana rode her bike for 5 miles on Wednesday. On Thursday, she biked 4 1/3 times as far ason Wednesday. How many miles did Dana bike on Thursday?fraction or as a whole or mixed number.
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First, let's express the mixed number as a fraction:
[tex]4\text{ }\frac{1}{3}=\frac{4\cdot3+1}{3}=\frac{13}{3}[/tex]She rode her bike for 5 miles on wednesday and on thursday she biked 13/3 times as far as on wednesday, so:
5 miles * (13/3) =
[tex]5\times\frac{13}{3}=\frac{65}{3}\approx21.667miles[/tex]Suppose ABC is a right triangle of lengths a, b and c and right angle at c. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable.Find tan B when a=96 and c=100
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To begin with, we will have to sketch the image of the question
To find the value of tan B
we will make use of the trigonometric identity
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the diagram given
[tex]\tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{b}{96}[/tex]Since the value of b is unknown, we will have to get the value of b
To do so, we will use the Pythagorean theorem
[tex]\begin{gathered} \text{hypoteuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ b^2=100^2-96^2 \\ b=\sqrt[]{784} \\ b=28 \end{gathered}[/tex]Since we now know the value of b, we will then substitute this value into the tan B function
so that we will have
[tex]\tan \text{ B=}\frac{opposite}{adjecent}=\frac{b}{a}=\frac{28}{96}=\frac{7}{24}[/tex]Therefore
[tex]\tan \text{ B=}\frac{7}{24}[/tex]May I please get help with Solve for x: −3<−10(x+15)≤7
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Given the compound inequality;
[tex]-3<-10(x+15)\le7[/tex]We would begin by simplifying the parenthesis as follows;
[tex]\begin{gathered} -3<-10(x+15) \\ \text{AND} \\ -10(x+15)\le7 \end{gathered}[/tex]We shall now solve each part one after the other;
[tex]\begin{gathered} -3<-10(x+15) \\ -3<-10x-150 \\ \text{Collect all like terms and we'll have;} \\ -3+150<-10x \\ 147<-10x \\ \text{Divide both sides by -10} \\ \frac{-147}{10}>x \end{gathered}[/tex]We can switch sides, and in that case the inequality sign would also "flip" over, as shown below;
[tex]\begin{gathered} \frac{-147}{10}>x \\ \text{Now becomes;} \\ x<\frac{-147}{10} \end{gathered}[/tex]For the other part of the compound inequality;
[tex]\begin{gathered} -10(x+15)\le7 \\ -10x-150\le7 \\ \text{Collect all like terms and we'll have;} \\ -10x\le7+150 \\ -10x\le157 \\ \text{Divide both sides by -10} \\ \frac{-10x}{-10}\le\frac{157}{-10} \\ x\ge-\frac{157}{10} \end{gathered}[/tex]Therefore, the values are;
[tex]\begin{gathered} x<-\frac{147}{10} \\ \text{And } \\ x\ge-\frac{157}{10} \\ \text{Hence;} \\ -\frac{157}{10}\le x<-\frac{147}{10} \end{gathered}[/tex]Written in interval notation, this now becomes;
[tex]\lbrack-\frac{157}{10},-\frac{147}{10})[/tex]The diameter of a circle is 20 kilometers. What is the angle measure of an arc bounding a sector with area 10pi square kilometers?Give the exact answer in simplest form. ____°. (pi, fraction,)
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The area of a circular sector is given by:
[tex]A=\frac{1}{4}\cdot\pi\cdot d^2\cdot\frac{\theta}{360}[/tex]Where:
π ≈ 3.14159
d = diameter of the circle
θ = angle of the circular sector
In our problem we have that:
[tex]\begin{gathered} A=10\cdot\pi\cdot km^2 \\ d=20\operatorname{km} \end{gathered}[/tex]And we need to find the value of the angle θ. So in order to solve the problem, we replace the given data in the formula of above:
[tex]\begin{gathered} A=\frac{1}{4}\cdot\pi\cdot d^2\cdot\frac{\theta}{360^{\circ}} \\ 10\cdot\pi\cdot km^2=\frac{1}{4}\cdot\pi\cdot(20\operatorname{km})^2\cdot\frac{\theta}{360^{\circ}} \end{gathered}[/tex]And now we solve for θ:
[tex]\begin{gathered} 10\cdot\pi\cdot km^2=\frac{1}{4}\cdot\pi\cdot400\cdot km^2\cdot\frac{\theta}{360^{\circ}} \\ 10=100\cdot\frac{\theta}{360^{\circ}} \\ 360^{\circ}\cdot\frac{10}{100}=\theta \\ \theta=36^{\circ} \end{gathered}[/tex]So the answer is that the angle of the circular sector is: 36°
Kiera is decorating for a party. She wants balloons in 6 different locations. In each location, she will have 3 bunches of 4 balloons. How many balloons will Kiera need in all?
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6 x 12 = 70 balloons needed in total
Use point-slope form to write the equation of a line that passes through the point (-8,-16)(−8,−16) with slope 11.
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The general point-slope equation of a line is:
[tex]y=m\cdot(x-x_0)+y_0\text{.}[/tex]Where:
• m is the slope of the line,
,• and (x0,y0) are the coordinates of one of the points of the line.
In this problem we have:
• m = 11,
,• (x0,y0) = (-8,-16).
Replacing these values in the general equation, we have:
[tex]y=11\cdot(x+8)-16[/tex]Answer
The point-slope equation of the line is:
[tex]y=11\cdot(x+8)-16[/tex]U is defined as the set of all integers. Consider the following sets:A = {1, 2, 3, 4, 5}B = {x| 0 < x < 5}C = {p|P is an even prime number}D = {4. 5. 6. 7}E = {x| x is a square number less than 50}Find BDGroup of answer choices40, 1, 2, 3, 4, and 54 and 50, 1, 2, 3, 4, 5, 6, and 7
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We will have te following
BUD:
[tex]B\cup D\colon1,2,3,4,5,6,7[/tex]So BUD is 1,2,3,4,5,6 & 7.
Find x if g(x + 2) = 6
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Add the rational expressions and type your answer in simplest form. When typing your answers, type your terms with variables in alphabetical order without any spaces between your characters. \frac{\left(c+2\right)}{3}-\frac{\left(c-4\right)}{4} The numerator is AnswerThe denominator is Answer
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Solve the operation between rationals, proceed as if they were numerical fractions:
[tex]\begin{gathered} \frac{c+2}{3}-\frac{c-4}{4} \\ \frac{4(c+2)-3(c-4)}{12} \\ \frac{4c+8-3c+12}{12} \\ \frac{c+20}{12} \end{gathered}[/tex]According to this:
The numerator is c+20
The denominator is 12
1) 3 = x + 13I need help
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We have the following:
[tex]3=x+13[/tex]solving:
[tex]\begin{gathered} x=3-13 \\ x=-10 \end{gathered}[/tex]The answer is -10
Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hourWhat is the range of this relation
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Answer:
A. 3 ≤ y ≤ 5
Explanation:
The range is the set of values that the variable y can take. In this case, the variable y is the speed, so the range is the set of values of Rosalie's speed in her training.
Since the speed takes values from 3 miles per hour to 5 miles per hour, the range is
3 ≤ y ≤ 5
what is the slope of the line below?Show your work.
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To be able to determine the slope, let's identify at least two points that pass through the graph and use it in the following formula:
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let,
Point A: x1, y1 = -4, -4
Point B: x2, y2 = 4, -4
We get,
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{-4\text{ - (-4)}}{4\text{ - (-4)}}[/tex][tex]\text{ = }\frac{-4\text{ + 4}}{4\text{ + 4}}[/tex][tex]\text{ = }\frac{0}{8}\text{ = 0}[/tex][tex]\text{ Slope (m) = 0}[/tex]Therefore, the slope of the line is 0.
in looking for 450% of 80 I am not sure what I am looking for
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Given the expression 450% of 80, we are to evealuate it.
You must know that of means multiplication
Hence the expression becomes;
[tex]450\text{\%}\times\text{ 80}[/tex]Simplify:
[tex]\begin{gathered} =\frac{450}{100}\times80 \\ =\text{ }\frac{45}{10}\times80 \\ =45\times8\text{ } \\ =\text{ 360} \end{gathered}[/tex]Hence 450% of 80 will give 360
When solving the radical equation 2 + 20 + 11 = I, the values I =-1 and I = 7 are obtained. Determine if either of these values is a solution of the radical equation. Select the correct two answers. (1 point) Since substituting I = -1 into the original equation resulted in a true statement, I= -1 is a solution to this equation. Since substituting I = 7 into the original equation resulted in a false statement, I = 7 is a not solution to this equation. Since substituting I=-l into the original equation resulted in a false statement, r=-1 is not a solution to this equation. Since substituting I=7 into the original equation resulted in a true statement, I=7 is a solution to this equation.
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what are the solutions of the equation 2x ^ 2 equals 18 use a group of related function whose group answers the question
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The given expression is :
[tex]2x^2=18[/tex]Simplify the equation for x :
[tex]2x^2=18[/tex]Divide both side by 2 :
[tex]\begin{gathered} \frac{2x^2}{2}=\frac{18}{2} \\ x^2=9 \end{gathered}[/tex]taking square root on both side :
[tex]\begin{gathered} x^2=9 \\ \sqrt[]{x^2}=\sqrt[]{9} \\ x=\pm3 \end{gathered}[/tex]Answer :
if 5 plus 5 is 10 and 44 plus 87 plus 98 plus 1415 is what???
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Answer:
5+5=10
44+87= 131
98+131=229
1415+229=1644
Step-by-step explanation:
the answer is 1644 so all you need to kno w is to follow the procedure you use for the 5 plus 5 method
which expression are equivalent to[tex]( \frac{750}{512})^{ \frac{1}{3} } [/tex]
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Fractional exponents refer to the radicals
Option A (Correct)
[tex]\frac{\sqrt[3]{750}}{\sqrt[3]{512}}[/tex]Option B (Incorrect)
750 is not a perfect cube
Option C (Correct)
[tex]\sqrt[3]{\frac{750}{512}}[/tex]Option D (Incorrect)
The denominator does not have the root
Option E (Incorrect)
The numerator does not have the root
Option F (Correct)
[tex]\frac{5}{8}\sqrt[3]{6}[/tex]I’m trying to find out where the second point can be marked
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ANSWER
First point = (0, 3)
Second point = (1, -1)
Third point = (2, -5)
Graph:
EXPLANATION
To plot a graph using the slope and the y-intercept, simply apply the following rules:
1. Evaluate the function at x = 0, to determine the y-intercept which was (0,3) from the question
2. Determine the slope by finding the change in y divided by change in x. This was -4 according to the question. Which could also be written as -4/1; that is, rise divided by run
3. Now, from the value (0, 3) we got in step 1, we move down by 4 units and then to the right by 1 unit. This will lead us to the Second point of (1, -1). Also from this point, we move down by 4 units and then to the right by 1 unit to get to the Third point of (2, -5). You may decide to continue this pattern if you want more points.
4. Draw a straight line joining the 3 points together.
Mrs. Everett is shopping for school supplies with her children. Rose selected 3 one-inch binders and 1 two-inch binder, which cost a total of $23. Judy selected 5 one-inch binders and 3 two-inch binders, which cost a total of $49. How much does each size of binder cost?
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We define the following variables:
• x = cost of one-inch blinders,
,• y = cost of two-inch blinders.
From the statement of the problem, we know that:
• Rose selected 3 one-inch blinders and 1 two-inch blinder, which cost a total of $23, so we have that:
[tex]3x+y=23,[/tex]• Judy selected 5 one-inch blinders and 3 two-inch blinders, which cost a total of $49, so we have that:
[tex]5x+3y=49.[/tex]We have the following system of equations:
[tex]\begin{gathered} 3x+y=23, \\ 5x+3y=49. \end{gathered}[/tex]We must solve the system of equations using the elimination method, where you either add or subtract the equations to get an equation in one variable.
1) We multiply the first equation by 3, and we have:
[tex]\begin{gathered} 9x+3y=69, \\ 5x+3y=49. \end{gathered}[/tex]2) Now, we subtract the second equation to the first equation:
[tex]\begin{gathered} (9x+3y)-(5x+3y)=69-49. \\ 4x=20, \\ x=\frac{20}{4}=5. \end{gathered}[/tex]3) Replacing the value x = 5 in the second equation, and solving for y we get:
[tex]\begin{gathered} 5\cdot5+3y=49, \\ 25+3y=49, \\ 3y=49-25, \\ 3y=24, \\ y=\frac{24}{3}=8. \end{gathered}[/tex]We have found that:
[tex]\begin{gathered} x=5, \\ y=8. \end{gathered}[/tex]Answer
A one-inch binder costs $5, and a two-inch binder costs $8.
???. Can you help me .???I have to find the simple interest earned to the nearest cent for each principle, interest rate, and time
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Given:
Principal amount, P = $640
Time, T = 2 years
Interest rate, R = 3%
Let's find the simple interest.
To find the simple interest, apply the Simple Interest formula:
[tex]I=\frac{P\ast R\ast T}{100}[/tex]Substitute values into the formula:
[tex]\begin{gathered} I=\frac{640\ast3\ast2}{100} \\ \\ I=\frac{3840}{100} \\ \\ I=38.40 \end{gathered}[/tex]Therefore, the simple interest to the nearest cent is $38.40
ANSWER:
$38.40
(Please reference attached photo for problem.)Show your work please. Also, What is the perimeter?
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Solution:
Given the shape below:
The above shape is a combination of a semicircle and a rectangle labeled as A and B respectively.
To find the perimeter of the shape:
step 1: Evaluate the perimeter of the circle.
The perimeter of the semicircle is expressed as
[tex]\begin{gathered} perimeter\text{ of semicircle=2}\pi r \\ where\text{ r is the radius} \\ \pi\Rightarrow3.14 \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} perimeter=2\times3.14\times(\frac{10}{2}) \\ =31.4\text{ cm} \end{gathered}[/tex]step 2: Evaluate the perimeter of the rectangle.
The perimeter of the rectangle is expressed as
[tex]\begin{gathered} perimeter=2(l+w) \\ where \\ l\Rightarrow length \\ w\Rightarrow width \end{gathered}[/tex]In this case, we have
[tex]\begin{gathered} l=10\text{ cm} \\ w=4\text{ cm} \\ thus, \\ Perimeter\text{ = 2\lparen10+4\rparen} \\ =2(14) \\ =28\text{ cm} \end{gathered}[/tex]step 3: Sum up the perimeters.
Thus, we have
[tex]\begin{gathered} perimeter\text{ of shape = perimeter of circle + perimeter of rectangle} \\ =31.4+28 \\ \Rightarrow perimeter\text{ of shape = 59.4 cm} \end{gathered}[/tex]Hence, the perimeter of the shape is evaluated to be
[tex]59.4\text{ cm}[/tex]