Step-by-step explanation:
the surface area of a figure is always the result of a combination of multiplication(s) of 2 dimensions (side lengths).
and the volume of 3 dimensions (side lengths).
"similar figures" means that they share the same angles. and that there is one scaling factor that applies to all sides (and all other lines like heights).
so, no matter what sides are used to calculate the surface areas and the volumes, it is the same scaling factor used for each of them.
in a multiplication of 2 sides (for the area) the scaling factor is therefore applied twice and hence squared, in a multiplication of 3 sides it is applied 3 times and therefore cubed.
let's call the scaling factor f.
1472 × f³ = 2875
and then
928 × f² = large S.A.
let's use the first to get f :
1472 × f³ = 2875
f³ = 2875 / 1472 = (125 × 23) / (64 × 23) = 125/64
f = 5/4
f² = (5/4)² = 5²/4² = 25/16
large S.A. = 928 × 25/16 = 58 × 25 = 1450 m²
2. A small plastic vessel has the shape of a truncated cone as shown. A cubic centimeter is the same as a
milliliter. What is the volume of this cup to the nearest milliliter? Show the work you use to find the answer.
If the height of the frustum of the cone is 10 cm. Then the volume of this cup will be 47 milliliters.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A small plastic vessel has the shape of a truncated cone as shown. A cubic centimeter is the same as a milliliter.
Then the volume of this cup to the nearest milliliter will be
The volume is given as
[tex]\rm V = \dfrac{1}{3} \pi (r_2^2 - r_1^2) h[/tex]
We have
Height (h) = 10 cm = 0.1 m
Radius (r₁) = 3.2 cm = 0.032 m
Radius (r₂) = 2.4 cm = 0.024 m
Then the volume will be
[tex]\rm V = \dfrac{1}{3} \pi (0.032^2 - 0.024^2) \times 0.1\\\\\rm V = 4.7 \times 10^{-5} \ \ m^3[/tex]
Then the conversion of m³ to milliliters will be
4.7 × 10⁻⁵ m³ = 4.7 × 10⁻⁵ × 10⁶ millileters
4.7 × 10⁻⁵ m³ = 47 milliliters
More about the geometry link is given below.
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A video store specializes in three types of movies: children's, American West, and horror. It's known that:
60% of children's movies plus 50% of westerns account for 30% of all movies.
20% of children's movies plus 60% of westerns plus 60% of horror movies represent half of all movies.
X, y, z denote children's movies, western movies, and horror movies, respectively. The related system of equations is formed and solved.
[tex]\left\{\begin{matrix} \qquad\qquad\ \dfrac{60}{100}x + \dfrac{50}{100}y =\dfrac{30}{100}(x+y+z)\\ \dfrac{20}{100}x+ \dfrac{60}{100}y+ \dfrac{60}{100}z= \dfrac{1}{2}(x+y+z) \\ \ \ \ x+100=y \end{matrix} \right.\[/tex]
Simplifying the system of equations, we have
[tex]\left\{\begin{matrix} 3x + 2y -3z=0\\ -3x+ y+ z= 0 \\ \ \ \ x+100=y \end{matrix} \right.\ \ \Longrightarrow \ \left\{\begin{matrix} 5x-3z=-200\\ -2x+ z= -100 \end{matrix} \right.\[/tex]
[tex]\ \ \ 5x-3z=-200\\\underline{-6x+3z=-300} \ \Rightarrow \ x=500\\\ \ -x+0= \ 500[/tex]
[tex]y&=500+100=600\\ z&=3(500)-600=900[/tex]
The video store has 500 children's movies, 600 westerns and 900 horror movies.
The volume of a rectangular pyramid is 176 units³. If the length of the rectangular base measures 6 units and the width of the rectangular base measures 11 units, find the height of the pyramid.
Answer:
2.66unit
Step-by-step explanation:
volume=176
l×b
6×11=66
Therefore,176÷66=2.66unit
O
3
o A. -
B. 2
OC
3
mly
O D. -2
Answer:
A. -3/2
Step-by-step explanation:
» Concepts
The slope of a line describes the steepness, or the change in y over the change in x of a line. The formula to find the slope, given two points, is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where we put in the x- and y-coordinates of the two points.
» Application
In this case, we're given two points: (-2, 5) and (4, -4). We have to find the slope of the line containing them, so we must use our aforementioned formula.
» Solution
[tex]\frac{(-4)-(5)}{(4)-(-2)}[/tex] [tex]\frac{-9}{4+2}[/tex] [tex]-\frac{9}{6}[/tex] [tex]-3/2[/tex]Therefore, the answer is A. -3/2.
Given that the universe set U = {baseball, basketball, football, tennis ball, soccer ball, volleyball} and that the set A is the set of sports balls that are spherical, what is the complement of Set A?
The set A is the set of sports balls that are spherical, the complement of set A is {baseball}.
Given that the universe set U = {baseball, basketball, football, tennis ball, soccer ball, volleyball}.
What is set?Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set.
The set A is the set of sports balls that are spherical
Set A={basketball, football, tennis ball, soccer ball, volleyball}
So, the complement of Set A is {baseball}
Because, a baseball infield is in the shape of a square, with each base at a vertex.
Hence, the set A is the set of sports balls that are spherical, the complement of set A is {baseball}.
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I need help ASAP I can’t understand this question help please !
Answer:
424
Step-by-step explanation:
SF: 2{(8 x 4) + (4 x 15) + (8 x 15)}
therefore: 2 [32 + 60 + 120]
therefore: 64 + 120 + 240
therefore: 360 + 64
therefore: 424
Answer:
424
Step-by-step explanation:
To find the surface area, you need to find the area of all the faces of the shape. Because this is a rectangle, you only need to find the 3 different faces and then multiply them by 2. For the largest face, the dimensions are 8*15, which is 120. Multiply that by 2 and you get 240. For the long, slim face, the dimensions are 4*15, which is 60. Multiply that by 2 and you get 120. Finally, the smallest face's dimensions is 8*4, which is 32. Double that and you get 64. Now all you need to do is add all the products up. 240+120+64 is 424, which is your answer.
Hope this helped!
the distance of -17 from 0
i have no idea what to do :(((
complete the concept map by naming the sampling that you have learned in this module then briefly discuss each
In systematic sampling, individuals are selected at regular intervals from the sampling frame.
How to explain the sampling?Stratified sampling- In this method, the population is first divided into subgroups (or strata) who all share a similar characteristic
Clustered sampling.- a clustered sample, subgroups of the population are used as the sampling unit, rather than individuals. The population is divided into subgroups, known as clusters, which are randomly selected to be included in the study
Simple random sampling. -In this case each individual is chosen entirely by chance and each member of the population has an equal chance, or probability, of being selected.
Quota sampling--This method of sampling is often used by market researchers. Interviewers are given a quota of subjects of a specified type to attempt to recruit.
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24r + 48 write the expression in two other ways
Answer:
2(12r + 24)
12(r + 2)
The sum of two numbers is 12.One of the numbers is 8.78.Find the other number.
answer : 3.22
if the sum of 2 numbers is 12 and one of the numbers is 8.78, then the subtraction of the number from the sum will give you the other number.
Solve the system of equations below.
4x – 6y = 30
3x + 7y = 80
x =
, y =
Answer:
The answer is stated above:
x=15
y=5
Find the distance between the points (-8, 9) and (2, 9).
units
Answer:
Distance=√(x2−x1)2+(y2−y1)2
Step-by-step explanation:
How to Find Distance Between Two Points?
Note down the coordinates of the two given points in the coordinate plane as, A(x1,y1 x 1 , y 1 ) and B(x2,y2 x 2 , y 2 ).
We can apply the distance formula to find the distance between the two points, d = √[(x2 x 2 − x1 x 1 )2 + (y2 y 2 − y1 y 1 )2]
Write an algebraic expression for the phrase the quotient of 17 and k
Answer:
[tex] \frac{17}{k} [/tex]
does someone mind helping me with this problem? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's calculate the value of c using Pythagoras theorem ~
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 40 {}^{2} = {24}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: b² = \sqrt{40² - 24²} [/tex]
[tex]\qquad \sf \dashrightarrow \: b= \sqrt{1600-576} [/tex]
[tex] {\qquad \sf \dashrightarrow \: b= \sqrt{1024}} [/tex]
[tex]\qquad \sf \dashrightarrow \: b = 32 \: units[/tex]
The length of "b"
Solution:[tex] {c}^{2} = {a}^{2} - {b}^{2} [/tex]
[tex] {b}^{2} = {40}^{2} - {24}^{2} [/tex]
[tex]b = 1024[/tex]
[tex]b = \sqrt{1024} [/tex]
[tex]b = 32[/tex]
Hence, the length of "b" is 32.
(4h+5) and (h – 6). find the product
Answer:
4h²– 19h – 30
Step-by-step explanation:
(4h+5)(h-6)
=4h²–24h+5h–30
=4h²–19h–30
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\:how\:to\: solve\: }}}[/tex]
➣Given➣ (4h+5) and (h – 6) find the product➣ Let's start !
[tex] \qquad \sf{➛ \: (4h + 5) \times (h - 6)} \\ [/tex]
★ Opening brackets multiplying nd solving
[tex]\qquad \sf{➛( \: 4h \times h) +( 4h \times - 6) + (5 \times h) + (5 \times - 6)}\qquad \\ \sf{➛\: {4h}^{2} - 24h + 5h - 30 }[/tex]
★ arranging like terms and solving gives
[tex]\qquad \sf{➛ \: {4h}^{2} - 19h - 30\bold\green{✓}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
Hope it helps !
Rena used the steps below to evaluate the expression (StartFraction (x Superscript negative 3 Baseline) (y Superscript negative 2 Baseline) Over 2 (x Superscript 4 Baseline) (y superscript negative 4 Baseline) EndFraction) Superscript negative 3, when x = negative 1 and y = 2.
Step 1:
Substitute x = negative 1 and y = 2 into the expression.
(StartFraction (negative 1) Superscript negative 3 Baseline (2) Superscript negative 2 Baseline Over 2 (negative 1) Superscript 4 Baseline (2) superscript negative 4 Baseline) EndFraction) Superscript negative 3
Step 2:
Simplify the parentheses.
(StartFraction (2) Superscript 4 Baseline Over 2 (negative 1) Superscript 4 Baseline (negative 1) cubed (2) squared EndFraction) Superscript negative 3 Baseline = (StartFraction (2) squared Over 2 (negative 1) Superscript 7 Baseline EndFraction) Superscript negative 3
Step 3:
Evaluate the power to a power.
StartFraction (2) Superscript negative 6 Baseline Over 2 Superscript negative 3 Baseline (negative 1) Superscript negative 21 baseline EndFraction
Step 4:
Use reciprocals and find the value.
StartFraction 1 Over 2 cubed (2) Superscript 6 Baseline (negative 1) Superscript 21 Baseline EndFraction = StartFraction 1 Over 8 times 64 times (negative 1) EndFraction = Negative StartFraction 1 Over 512 EndFraction
In which step did Rena make the first error?
Step 1
Step 2
Step 3
Step 4
Answer:
step 4
Step-by-step explanation:
Can anyone help solve this
need help with this
The total numbers of A, B, C, D, and F grades are recorded in the table. What was the probability that a student earned a B? (Write as percent rounded to the nearest tenth)
Answer:
18.7%
Step-by-step explanation:
P(B) = 114/ (61+114+220+175+39) = 0.1872 = 18.7%
Solve for a. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Remark
a is one part of the cosine function. It is termed the adjacent side. The given number (12) is the hypotenuse of a right triangle. The reference angle is given as 25. You have all you need to solve for a
Givens
<B = 25o
AB = 12
a = a
Equation
Cos(B) = adjacent side / hypotenuse
Solution
Cos(25) = adjacent side / 12 Multiply both sides by 12
12*cos(25) = adjacent side
cos(25) = 0.90631
12*0.906331 = adjacent side
10.87 = adjacent side
Answer
a = 10.9
Do you still have to do summer school if you fail one class? (serious question please answer, and yes i know its in math i just need an answer!)
Answer:
In some schools yes but it depends is it a required class? if so then you'd have to retake it.
Answer:
well you might not have to do summer school but you might have to take a course during summer for that class you failed or you may have to redo that class in order to get the points needed to pass but also it depends because even though you might not pass that one class you can still pass the grade but you will be in the same class or a lower standard for that subject now i am not sure it honestly all depends on your teacher and school if they want you to go the next grade but they can also talk to teachers in the next grade to help you so that you can still pass but you have to do lower standard work for the class in that next grade
Step-by-step explanation:
hope it helps let me know if you have anymore questions or if you need anymore help understanding or if you need help with work so that you can pass i would be happy to help you
What is NOT a characteristic of a polyhedron?
A. faces
B. vertices
C. edges
D. lines
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
B
Step-by-step explanation:
There is two wholes and one half.
A paint mixture uses a specific blue to yellow ratio. for every 7 gallons of paint, 2 are blue. enter the ratio of yellow paint to total gallons of paint as a fraction?
Answer:
7:9
Step-by-step explanation:
For very 9 gallons of paint, it needs 7 gallons of yellow.
The radius of a circle is 1 meter. What is the circle's circumference?
Use 3.14 for .
Answer:
6.28
Step-by-step explanation:
D = R x 2
D = 2
2 x 3.14 =
6.28
In your Own words explain what in algebra the deffintion of
Mode
Median
Range
I will try to give brainliest to person who discribes in own words
Answer:
The mean means average. To find it, add together all of your values and divide by the number of addends. The median is the middle number of your data set when in order from least to greatest. The mode is the number that occurred the most often. The range is the difference between the highest and lowest values.
Step-by-step explanation:
hope this helps
have a good day <3
Answer:
hope this helps!!
Step-by-step explanation:
Mode: Are there two students who have the same number of children (could be zero)? If yes, that’s the mode. If not, there is no mode. Median: Put all five numbers in a row from lowest to greatest. The one in the middle is the median. Range: Take the difference of the greatest minus the lowest and that is the range.
Enter an equation and an answer to the following question:
What is the original list price if the discount is $25 and the discount rate is 12%?
Answer:
$208.30
Step-by-step explanation:
Discount:Let the original price be $ x
Discount % = 12%
Discount = $ 25
12% of x = 25
[tex]\sf \dfrac{12}{100}*x = 25[/tex]
[tex]\sf x = 25 * \dfrac{100}{12}=\dfrac{25*25}{3}\\[/tex]
= $ 208.30
Solve for the value of x
Answer: 12
Step-by-step explanation:
Please someone help me with my question
Answer:
∠A≅∠Z AB ≅ ZX
∠B≅∠X AC ≅ ZY
∠C≅∠Y BC ≅ XY
ΔCBA ≅ ΔYXZ
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
Fior 50 points solve this problem
Which graph represents the solution to the system of inequalities below?
5x-4y>4
x+y<2
B. is the correct graph.
See the attachment.
Answer:
Step-by-step explanation:
Use desmos to graph
B is The correct answer for this question
The area of the parallelogram below is square meters.
Answer: 48
Step-by-step explanation:
A = bh = (8)(6) = 48
