In the accompanying regular pentagonal prism, suppose that each base edge measures 7 in. and that the apothem of the base measures 4.8 in. The altitude of the prism measures 10 in.A regular pentagonal prism and a pentagon are shown side by side. The pentagon contains a labeled segment and angle.The prism contains a horizontal top and bottom and vertical sides. The front left face and front right face meet the bottom base at right angles.The pentagon is labeled "Base".A line segment starts in the center of the pentagon, travels down vertically, and ends at the edge. The segment is labeled a.The vertical segment forms a right angle with the edge.(a)Find the lateral area (in square inches) of the prism.in2(b)Find the total area (in square inches) of the prism.in2(c)Find the volume (in cubic inches) of the prism.in3
Answers
To determine the lateral area of the prism;
[tex]Lateral\text{ area=perimeter of the base}\times height[/tex][tex]Lateral\text{ area=5\lparen7\rparen }\times10=350in^2[/tex]To determine total area of the prism;
[tex]Total\text{ area=2\lparen area of base\rparen+Lateral area}[/tex][tex]\begin{gathered} Total\text{ area of the prism=2\lparen}\frac{1}{2}\times perimeter\text{ of the base}\times apotherm\text{\rparen+350} \\ \end{gathered}[/tex][tex]\begin{gathered} Total\text{ area of the prism=2\lparen}\frac{1}{2}\times5(7)\times4.8\text{\rparen+380=168+350=518in}^2 \\ \end{gathered}[/tex]To determine the volume of the prism;
[tex]Volume\text{ = base area }\times height[/tex][tex]Volume=\frac{1}{2}\times5(7)\times4.8\times10=840in^3[/tex]Hence
Related Questions
A circular path 4 feet wide has an inner diameter of 650 feet. How much farther is it around the outer edge of the path than around the inner edge? Round to the nearest hundredth. Use 3.14 for pie
Answers
step 1
Find out the circumference of the outer edge
Find out the radius
r=(650/2)+4
r=329 ft
so
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\cdot3.14\cdot329 \\ C=2,066.12\text{ ft} \end{gathered}[/tex]step 2
Find out the circumference of the inner edge
r=650/2=325 ft
substitute
[tex]\begin{gathered} C=2\cdot3.14\cdot325 \\ C=2,041\text{ ft} \end{gathered}[/tex]Find out the difference
2,066.12-2,041=25.12 ft
therefore
the answer is 25.12 ftA manager recorded the performance review scores for each employee and placed the results in the bar chart below. All employees received a rating on each of the Evaluation Categories. If Person 6 obtained the highest score possible, what score did Person 3 receive? Use the graph and tables below.EVALUATION CATEGORIESRATINGGeneral Quality of WorkDependabilityJob KnowledgeCommunication SkillsPersonalityManagement AbilityContribution to GroupProductivityAchievement of GoalsRating ScaleSCOREDESCRIPTION5Excellent4Very Good3Good2Fair1Poor253530
Answers
SOLUTION
Comparing the graphs and the options, it follows that each line on the graph represents 5 points. This means the person 6 obtained a score of 45, comparing this to the person 3, it means the person 3 obtained a score of 35.
So the answer is 35.
For the rating since person 6 has the highest possible score, which is 45, person 3 score becomes
[tex]\begin{gathered} \frac{35}{45}\times5 \\ =3.88888888 \\ which\text{ is approximately 4} \end{gathered}[/tex]so we can classify person 3 as very good
Which will hold more cake batter; the rectangular pan or two round pans? The volume of the rectangle pan is 234 in 3rd power. Find the volume of the two round pans and choose your decision. Round your answer to the nearest tenth if necessary.
Answers
Solution
Given a rectangular pan and two round pans
The volume, V, of the rectangular pan is 234 in³
A round pan is in the form of a cylinder
To find the volume, V, of the a round pan, the formula is
[tex]V=\pi r^2h[/tex]Where
[tex]\begin{gathered} d=8in \\ r=\frac{d}{2}=\frac{8}{2}=4in \\ r=4in \\ h=2in \end{gathered}[/tex]Substitute the variables into the formula above
[tex]\begin{gathered} V=\pi\left(4\right)^2\left(2\right)=100.53in^3\text{ \lparen two decimal places\rparen} \\ V=100.53in^3\text{ \lparen two decimal places\rparen} \end{gathered}[/tex]Since, there are two round pans, the volume of the two round pans will be
[tex]2\times100.53=201.06in^3[/tex]nce, the volume of the two round pans is 201.06 i³.
Since the volume of the two round pans (201.06in³) is less than the volume of the rectangular pan (234in³), the rectangular pan will hold more.
Hence, the answer is rectangular pan (option a)
A prism is completely filled with 80 cubes that have edge length of 1/2 cm what is the volume of prism
Answers
Thus,
[tex]\begin{gathered} \text{Volume of cube=(}\frac{1}{2})^3 \\ \text{Volume of cube=}\frac{1}{8}cm^3 \end{gathered}[/tex]80 cubes will have a volume of:
[tex]80\times\frac{1}{8}=10[/tex]Hence, the volume of the prism is 10 cubic metre
a. What is the value of f(1.2)?f(1.2) =b. What is the largest value of x for which f(x) = 1.5?x =
Answers
In order to find the value of f(1.2), we just need to find the value of f(x) in the graph that corresponds to x = 1.2.
Looking at the graph, when x = 1.2, the function f(x) is equal to 2.
Then, to find the largest value of x for which f(x) = 1.5, we look for the value 1.5 in the vertical axis, then find the corresponding value of x.
For this value, we have two possible values of x: 1.2 and 3.6.
So the largest value is x = 3.6
Why can the Vertical Angle Theorem NEVER be used to prove two triangles are congruent?
Answers
Solution
Why can the Vertical Angle Theorem NEVER be used to prove two triangles are congruent?
The Vertical angle theorem states that vertical angles are always congruent.
We can't use this to proof congruence between two triangles because this theorem not provide enough evidence to obtain the SSS, ASA, SAS, AAS, HHL. For this reason is not appropiate to use it for this case.
ocupo encontrar la x con procedimiento
les regalare coronas!!!!
Answers
La variable x asociada al sistema geométrico con dos ángulos alternos externos es igual a 23.
¿Cómo determinar la variable asociada a dos ángulos alternos externos?
En esta pregunta tenemos un sistema geométrico conformado por dos líneas paralelas atravesadas por una tercera línea. Este conjunto incluye dos ángulos alternos externos, que guardan la siguiente relación según la geometría euclídea:
6 · x - 28 = 4 · x + 18
A continuación, despejamos la variable x:
6 · x - 4 · x = 28 + 18
2 · x = 46
x = 23
El valor de la variable x es 23.
ObservaciónNo existen preguntas en español sobre ángulos alternos externos, por lo que se añade una pregunta en inglés.
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Given an example to show a quadratic that does not factor into binomial • binomial.
Answers
An example of the required quadratic equation is x(x+1)
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.
An example of the required quadratic equation is x(x+1)
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3 part golden raisin2 parts cashewhow many parts of golden raisins does jose need to make 30 total cups pf trail mix?a. 14 partsb. 18 partsc. 20 partsd. 25 parts
Answers
To get 1 cup of pf trail mix, we need to mix 2 parts of cashew and 3 part of golden raisin. This means that to make one cup of pf trail mis, we are using 5 parts in total (2 cashew+3 golden raisin). Then, this means that out of one cup the exactly amount of golden raisin is 3/5 of the cups we have. So, having this fraction in mind, we only need to multiply the total number of cups to calculate the parts we are using. In this case, we have 30 cups. So if we want to calculate the parts of golde raisin we multiply 30 by the previous fraction. That is
[tex]30\cdot\text{ }\frac{3}{5}\text{ = 6 }\cdot\text{ 3 = 18}[/tex]So to make 30 cups of pf trail mix, jose needs 18 parts.
why is 10'15 equal to 10'11? explain ur thinking. ___ 10'4
Answers
Exponent rule is the following:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex][tex]\text{Therefore, if for }\frac{10^{15}}{10^4}\text{ a is 15 and b is 4, therefore:}[/tex][tex]\frac{10^{15}}{10^4}=10^{15-4}[/tex][tex]So,\text{ }10^{\mleft\{15-4\mright\}}=10^{11}[/tex]Need help with 3,4,5,and 6 please. I don’t understand it
Answers
4. The triangle has 3 given sides but no angles but we can get the angles using cosine law
[tex]\begin{gathered} \cos R=\frac{t^2+s^2-r^2}{2ts} \\ \cos \text{ R=}\frac{23.7^2+48^2-35^2}{2\times23.7\times48} \\ \cos R=\frac{561.69+2304-1225}{2275.2} \\ \cos R=\frac{1640.69}{2275.2} \\ \cos R=0.7211190225 \\ R=\cos ^{-1}0.7211190225 \\ R=43.8530535482 \\ R=44^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \cos T=\frac{r^2+s^2-t^2}{2rs} \\ \cos T=\frac{35^2+48^2-23.7^2}{2\times35\times48} \\ \cos T=\frac{1225+2304-561.69}{3360} \\ \cos T=\frac{3529-561.69}{3360} \\ \cos T=\frac{2967.31}{3360} \\ \cos T=0.88312797619 \\ T=\cos ^{-1}0.88312797619 \\ T=27.977977493 \\ T=28^{\circ} \end{gathered}[/tex][tex]\begin{gathered} S=180-28-44 \\ S=108^{\circ} \end{gathered}[/tex]From largest to smallest it will be
[tex]\angle S,\angle R\text{ and}\angle T[/tex]The expression below is scientificnotation for what number?4.58x10^-2
Answers
Using the exponent rules, 10^-2 can be expressed as follows:
[tex]10^{-2}=\frac{1}{10^2}=\frac{1}{100}[/tex]Substituting into the expression in scientific notation, we get:
[tex]4.58\cdot10^{-2}=4.58\cdot\frac{1}{100}=\frac{4.58}{100}=0.0458[/tex]Use the figure below to find lateral surface area. Select one: O 92 square inches O 80 square inches O 60 square inches O 86 square inches
Answers
Area of the base = 10 x 3 = 30 in^2
Area of the lateral walls = 10 x 2.5 x 2 = 50 in^2
Area of the triangles = 3 x 2 /2 x 2 = 6 in^2
Total area = 30 + 50 + 6
= 86 in^2
The image point of A after a translation left 2 units and down 5 units is the pointB(-8, -11). Determine the coordinates of the pre-image point A.Submit Answer
Answers
Let the coordinates of the pre-image which is point A be (x,y)
The point after the translation left 2 units and down 5 units is B(-8, -11)
To get the x coordinate
we were tolt that the point was move 2 units left
So this implies x = -8+2 = -6
To get the y coordinates, we wre told that the point was moved down 5 units
This implies y = -11+ 5 = -6
Therefore, the coordinates of the pre-image point A is (-6, -6)
Variable Systems 2solve the following showings steps neatly and organized.
Answers
SOLUTION
perimeter of rectangle = 88cm
let the widht be x
now, according to question
lenght = 3x ( as it is triple of width)
formula of rectangle perimeter
88cm = 2* (length + width)
88cm = 2(3x+x)
88cm = 4x (2 will be transported to left )
88/2 cm = 4x
( 2 become in divide as in right it was in multiply)
44 cm = 4x
x= 44/4
x= 11cm
according to question,
width of rectangle = x = 11 cm
Triangle
A
B
C
was dilated with the origin as the center of dilation to create triangle ′′′
A
′
B
′
C
′
. The triangle was dilated using a scale factor of 14
1
4
.
The lengths of the sides of triangle
A
B
C
are given.
Enter the lengths of the sides of triangle ′′′
A
′
B
′
C
′
below.
(Decimal values may be used.)
Answers
The lengths of the sides of the Triangle A'B'C' is A'B'=2.25 units , B'C' = 2.75 units , C'A' = 1.25 units .
in the question ;
it is given that
the lengths of the sides of the Triangle ABC is
AB = 9 units
BC = 11 units
CA = 5 units
dilation scale = 1/4
the lengths of the dilated triangle can be found using the formula
(Side length)×(Dilation scale)=Dilated length
So,
A'B' = AB*(1/4)
= 9/4 = 2.25 units
B'C' = BC*(1/4)
= 11/4
= 2.75 units
C'A' = CA*(1/4)
= 5/4
= 1.25 units .
Therefore , the lengths of the sides of the Triangle A'B'C' is A'B'=2.25 units , B'C' = 2.75 units , C'A' = 1.25 units .
The given question is incomplete , the complete question is
Triangle ABC was dilated with the origin as the center of dilation to create triangle A′B′C′. The triangle was dilated using a scale factor of 1/4. The lengths of the sides of triangle ABC are given. Enter the lengths of the sides of triangle A′B'C′ . (Decimal values may be used.)
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What is the value of the number in the hundredths place?8.471A. 0.4B. 0.7 C 0.07D. 0.04
Answers
EXPLANATION
The value of the number in the hundreths place is 0.07
the coldest temperature ever recorded on earth is 135.8 Fahrenheit below zero recording in Antarctica on July 21st 1983 the hottest temperature ever recorded on earth is 134 Fahrenheit recorded in Death Valley California on July 10th 1913 what is the difference between those two temperature
Answers
Let's begin by listing out the information given to us:
The coldest temperature ever recorded on earth (T1) = -135.8 Fahrenheit
The hottest temperature ever recorded on earth (T2) = 134 Fahrenheit
The difference between the two temperature = Hottest - Coldest temperature
[tex]undefined[/tex]need help with math
Answers
The y intercept is when x = 0.Therefore,
[tex]\begin{gathered} \text{when} \\ x=0 \\ y=0 \end{gathered}[/tex]The vertex can be found below
Find the third side in simplest radical form: 25 24
Answers
Here, we want to get the length of the third side
Mathematically, we can get this by the use of Pythagoras' theorem
It states that the square of the length of the hypotenuse equals the sum of the squares of the two other sides
Let the missing side be s
From the diagram, we have the hypotenuse as 25 (the hypotenuse is the longest side and it is the side that faces the right angle
We have this as;
[tex]\begin{gathered} 25^2=s^2+24^2 \\ s^2=25^2-24^2 \\ s^2\text{ = 625-576} \\ s\text{ = }\sqrt[]{49} \\ s\text{ = 7} \end{gathered}[/tex]Hi, I am testing the service for Brainly. Can you help me find the median for this set of numbers: 3, 4, 15, 27, 53, 54, 68, 77?
Answers
To find the median of a set of numbers, the first step is:
1 - Put the numbers in crescent order
This set of numbers is already in crescent order, so we can skip this step
2 - Count how many numbers there are in the set.
In our set we have 8 numbers, so in this case, the median of the set will be the average value between the two central numbers (that is, the fourth and fifth numbers)
The fourth number is 27, and the fifth number is 53, so the median is the average of these two numbers:
[tex]\text{median = }\frac{(27\text{ + 53)}}{2}=\frac{80}{2}=40[/tex]So the median of this set of numbers is 40.
Below, the two-way table is given for a classof students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female 3463TotalIf a female student is selected at random, find theprobability that the student is a senior.
Answers
Conditional Probability
First, we must complete the totals in the table as follows:
The formula for the conditional probability is:
[tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex]Where A is an event we know has already occurred, B is an event we want to calculate its probability of occurrence, and P∩A is the probability of both occurring.
We know a female student has been selected, so that is our known event and:
[tex]P(A)=\frac{16}{30}=\frac{8}{15}[/tex]The probability that a female student is also a senior is:
[tex]P(A\cap B)=\frac{3}{30}=\frac{1}{10}[/tex]Substituting:
[tex]\begin{gathered} P(B|A)=\frac{\frac{1}{10}}{\frac{8}{15}} \\ \\ P(B\lvert\rvert A)=\frac{1}{10}\frac{15}{8}=\frac{3}{16} \end{gathered}[/tex]The required probability is 3/16
Complete the remander of the
table for the given function rule:
y = 3x-8
X= -4,-2,0,2,4
Y=-20,?,?,?
Answers
Step-by-step explanation:
what is the problem ?
all you need to do is put every different value of x into the spot of x and calculate the result.
x = -4
y = 3×-4 - 8 = -12 - 8 = -20
x = -2
y = 3×-2 - 8 = -6 - 8 = -14
x = 0
y = 3×0 - 8 = 0 - 8 = -8
x = 2
y = 3×2 - 8 = 6 - 8 = -2
x = 4
y = 3×4 - 8 = 12 - 8 = 4
last night Danielle had a birthday party. 1/3 of the cake was left over.She wanted to share the left over cake with 4 friends the next day .How much of birthday cake would each get
Answers
Solution
For this case we have a total cake representing 1
We also know that 1/3 of the cake was left over so then 1/3
And we want to share to 4 friends so we can do this:
1/3 * 1/4 = 1/12
So then each friend will recieve 1/12
what is the correct base and coefficient for the function:
Answers
The general form of a logarithmic function is:
[tex]y=a\cdot\log _b(x)[/tex]Where a is the coefficient and b is the base. In the given picture, we can see that the coefficient is equal to 1, while the base is equal to 2.
HELP PLEASEEEEE!!!!!!
Answers
The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -1/3 and -1/2
Tale LCM for 3 and 2 = 6
-1/3 x 2/2 and -1/2 x 3/3
-2/6 and -3/6
Now, multiply 10
-2/6 x 10/10 and -3/6 x 10/10
-20/60 and -30/60.
Hence, the rational number is -21/60.
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The net of a cone is shown below. What is the surface area of the cone rounded to the nearest tenth of a square inch? Use π = 3.14.A. 125.6 in²B. 1,256.6 in²C. 175.8 in²D. 251.3 in²
Answers
ANSWER
[tex](C)175.8in^2[/tex]EXPLANATION
The surface area of a cone can be found using the formula:
[tex]A=\pi r^2+\pi rl[/tex]where l = slant height
r = radius
The diameter of the cone is given, but we can find the radius since the radius is half the diameter:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{8}{2} \\ r=4\text{ units} \end{gathered}[/tex]From the figure, the slant height of the cone is 10 units.
Hence, its surface area is:
[tex]\begin{gathered} A=(\pi\cdot4^2)+(\pi\cdot4\cdot10) \\ A=50.24+125.6 \\ A\approx175.8in^2 \end{gathered}[/tex]The answer is option C.
Graph the solution set of the system. -2x-y ≥2 y ≥-2 x ≥-4
Answers
The graph of the given equations as;
-2x-y ≥2
The graph of the inequality y ≥-2
The graph of the inequality, x ≥-4
Now, the graph for the set of the system as;
...
You have a bag full of 4 green marbles and 1 blue marble. You pick a marble out at random. If it's blue, you stopbecause you win 20 points. If not, you get another chance. Without replacing the green marble, you pick again. It'sblue, you win 10 points, otherwise you lose 20 points. Let X be the number of points you eam in this game. If you playedthis game 100 times, how many points can you expect to win (or lose)?
Answers
As per given by the question,
There are given that, 4 green marbles and 1 blue marble contains in a box and pick a marble at randomly.
Now,
Here pick a marble out at random, so first pick a marble for blue;
Then,
Total number of green marbles is 4, and the total number of blue marble is 1, and;
The total numbers of marbles in a bag is, 4+1=5.
So,
For pick the blue marble from 5 marble,
Now,
[tex]\begin{gathered} 5_{C_1}=\frac{5!}{1!\times(5-1)!} \\ =\frac{5!}{1!\times4!} \\ =\frac{5\times4!}{1!\times4!} \\ =5 \end{gathered}[/tex]Now, for pick the green marble from 5 marbles.
Here, total green marble is 4.
So,
[tex]\begin{gathered} 5_{C_4}=\frac{5!}{4!\times(5-4)!} \\ =\frac{5\times4!}{4!\times1!} \\ =5 \end{gathered}[/tex]Now,
From the question, there are clearly mention that if pick a blue, then stop because you won 20 points.
So,
Probability of the blue marble that won the 20 points.
then,
[tex]\begin{gathered} P(x=20)=\frac{total\text{ number of blue marble}}{\text{total number of marble}} \\ P(x=20)=\frac{1}{5} \end{gathered}[/tex]Now,
There are also mention that, pick a green marbles without replacing and if its blue then win the 10 points,
So,
probability of the blue marbles that won 10 pointss is,
[tex]P(x=10)=\frac{1}{4}[/tex]Now,
Here, find the probability that no points for the first green ball is,
[tex]P(x=0)=\frac{4}{5}[/tex]Now,
If you played this game 100 time, then the probability is,
[tex]\begin{gathered} P(x=0)+_{}P(x=10)+P(x=20)=\frac{4}{5}+\frac{1}{4}+\frac{1}{5} \\ =1.25 \end{gathered}[/tex]now,
For 100 times,
[tex]1.25\times100=125\text{ points.}[/tex]Hence, 125 points can you expect to win.
A restaurant serving 150 side dishes of skinless mashed potatoes each day produces two orders of mashed potatoes from each 8 ounce potato. when the skins are discarded, the potatoes have a yield percentage of 90%. However, to reduce waste and promote sales, the potato skins are instead used as an appetizer. what is the edible portion of the potato skins in ounces?
Answers
The edible portion of the potato skins in ounces is = 0.8%
What are potatoes?Potatoes are vegetable tubers that can be eaten with the skin when properly cooked.
The number of side dishes of skinless mashed potatoes= 150
Two orders of mashed potatoes = 8 ounce potato.
The potatoes with discarded skin = 90% yield
The potatoe skin= 10% of the 8 ounces
That is;
= 10/100×8
= 80/100 = 0.8 ounce
Therefore, the portion of the potatoes that consists of the skin in ounce is = 0.8 ounce
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