[tex]\maltese \: \: \underline{\underline{\frak{Understanding~the~question :-}}} \\ \\[/tex]
For solving this question, we will take the help of the branch of mathematics that studies the sizes of different shapes may they be 2D or 3D, called mensuration.
⠀
There are two parts in the question, in the first part we have been asked to calculate the ratio of the total surface area of the two cubes, for that we will calculate their total surface areas and divide them in order to calculate the ratio. In the second part, we have been asked to calculate the ratio of the volume of the two cubes, and in order to calculate the ratio, at first we will calculate the volumes of the respective cubes and then divide them. And, thus, in this way, we will get our required answer.
⠀
[tex] \maltese \: \underline{ \underline{ \frak{Given :-}}} \\ \\ [/tex]
Two cubes in which the sides measure,
Cube 1 say A = 1 inchCube 2 say B = 10 inch⠀
[tex] \maltese \: \: \underline{ \underline{ \frak{Formula~Applied :-}}} \\ \\ [/tex]
[tex] \bigstar \begin{cases} \sf 1.~Volume_{cube} = {a} ^3\\ \\\sf 2.~T.S.A._{cube} = 6{a}^2\end{cases} \\ \\ [/tex]
[tex] \maltese \: \underline{ \underline{ \frak{Solution :-}}} \\ \\ [/tex]
Calculating the total surface areas,
⠀
[tex] \sf \longrightarrow TSA \: of \: A = 6( {1)}^{2} \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: A =6 \times 1 \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: A = {6 \: inch}^{2} \\ \\ [/tex]
[tex]\sf \longrightarrow TSA \: of \: B =6 {(10)}^{2} \: \: \: \: \: \: \\ \\ \\\sf \longrightarrow TSA \: of \: B =6 \times 100 \: \: \: \\ \\ \\ \sf \longrightarrow TSA \: of \: B = {600 \: inch}^{2} \\ \\ [/tex]
Thus, now we can calculate the ratio,
⠀
[tex]\sf \longrightarrow Ratio = \dfrac{TSA~of~A} {TSA~of~B} \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{6}{600} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \cancel \dfrac{6}{600} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{1}{100} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio =1 : 100 \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio of the total surface area of the cubes is 1 : 100. Now, moving to the second part of the question, and calculating the volume of the cubes, we have,
⠀
[tex]\sf \longrightarrow Volume \: of \: A= {(a)}^{3 } \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: A= {(1)}^{3} \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: A= {1 \: inch}^{3} \\ \\ [/tex]
[tex]\sf \longrightarrow Volume \: of \: B = {(a)}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: B = {(10)}^{3} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Volume \: of \: B = {1000 \: inch}^{3} \\ \\ [/tex]
Now, calculating the ratio,
⠀
[tex]\sf \longrightarrow Ratio =\dfrac{Volume ~of~A} {Volume~of~B} \: \: \\ \\ \\ \sf \longrightarrow Ratio = \dfrac{ {1 \: inch}^{3} }{1000 \: {inch}^{3} } \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio = \cancel\dfrac{ {1 \: inch}^{3} }{ {1000 \: inch}^{3} } \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Ratio =1 : 1000 \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio of the volume of the cubes is 1 : 1000.
⠀
[tex] \underline{ \rule{227pt}{2pt}} \\ \\ [/tex]
solve each logarithmic equation. Round your answer to two decimal places.
log4 16 = x
my attempt:
log4 16 (x+x) = x
--
x
log 4 (x+16) = 1
(x + 16) = 1
x + 16/1 =17
x+ 16 = 17
x= 8/9
Answer:
x = 2Step-by-step explanation:
Given equation
[tex]log_416=x[/tex]Use the property of logarithm
[tex]log_ab=c[/tex] ⇒ [tex]b = a^c[/tex]Apply to the given equation
[tex]16 = 4^x[/tex][tex]4^2=4^x[/tex][tex]2 = x[/tex][tex]x=2[/tex]Let's see
[tex]\\ \rm\Rrightarrow log_416=x[/tex]
[tex]\\ \rm\Rrightarrow 16=4^x[/tex]
[tex]\\ \rm\Rrightarrow 4²=4^x[/tex]
[tex]\\ \rm\Rrightarrow x=2[/tex]
Done!
What is the diameter of a sphere with a volume of 397\text{ m}^3,397 m
3
, to the nearest tenth of a meter?
REsponse: 9.1
Step 1: –10 8x < 6x – 4 step 2: –10 < –2x – 4 step 3: –6 < –2x step 4: ________ what is the final step in solving the inequality –2(5 – 4x) < 6x – 4? x < –3 x > –3 x < 3 x > 3
The final step of the inequality equation –10 + 8x < 6x – 4 is x > 3. Then the correct option is D.
What is inequality?Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.
The inequality equation is given below.
–10 + 8x < 6x – 4
This can be simplified as
–10 + 8x < 6x – 4
–10 < –2x – 4
–6 < –2x
–3 < –x
x > 3
More about the inequality link is given below.
https://brainly.com/question/19491153
Mr. Sims bought 9 tickets to a puppet show and spent $57. He bought a combination of child tickets for $3 each and adult tickets for $9 each.
Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?
Answer:
x =number of child tickets
y=number of adult tickets
x + y = 9
3x +9y = 57
x = 9-y
3(9-y) + 9y =57
27 - 3y + 9y = 57
6y = 30
y=5 adult tickets
x = 4 child tickets
Answer:
adult's tickets a=5
child's tickets c=4
Step-by-step explanation:
a+c=9
9a+3c=57
c=9-a
3a+c=19
3a+9-c=19
2a=10
a=5
c=9-a=9-5=4
Brian invests £990 into his bank account. He receives 2.6% per year simple interest. How much will Brian have after 3 years? Give your answer to the nearest penny where appropriate
Answer:
£1067.22.
Step-by-step explanation:
Interest I= PRT/100 where P = Initial investment, R = % rate, T = time.
So I = 990*2.6* 3 / 100
= £77.22
So total he will have in the bank
= 990+77.22
= £1067.22.
Find the missing value.
(√24-√k)(√24+√k)=5
Answer:
k = 19Step-by-step explanation:
Identity
(a + b)(a - b) = a² - b²Simplifying the LHS (Left Hand Side)
(√24-√k)(√24+√k)(√24)² - (√k)²24 - kEquating to the RHS
24 - k = 5k = 24 - 5k = 19Answer:
19
Step-by-step explanation:
[tex](\sqrt{24} -\sqrt{k} )(\sqrt{24} +\sqrt{k} )\\\\As,\\\\\hookrightarrow a^{2} -b^{2} =(a+b)(a-b)\\\\Subtitute:\\\\a=\sqrt{24} \\\\b=\sqrt{k} \\\\Now,\\\\\hookrightarrow (\sqrt{24} -\sqrt{k} )(\sqrt{24} +\sqrt{k} )=5\\\\\hookrightarrow (\sqrt{24} )^{2} -(\sqrt{k} )^{2} =5\\\\\hookrightarrow 24-k=5\\\\\hookrightarrow 24-5=k\\\\\hookrightarrow 19[/tex]
What is the solution to the system of equations below?
(Hint: Solve using substitution!)
−5x−y=5
x=7y−1
(
Answer:
x = -1, y = 0 or (-1, 0)Step-by-step explanation:
We have two equations :
-5x - y = 5x = 7y - 1Take the value of x in Equation 2 and substitute in Equation 1.
-5(7y - 1) - y = 5-35y + 5 - y = 5-36y = 0y = 0Now, take the value of y and substitute in Equation 2.
x = 7(0) - 1x = -1Solution
x = -1, y = 0 or (-1, 0)Answer:
The lines intersect at the point (-1, 0)
Step-by-step explanation:
−5( )−y=5
-5(7y-1) - y = 5 substitute the x=7y-1 into first equation
-35y + 5 - y =5 multiply -5
-36y + 5 = 5 combine like terms
-36y = 0 subtract 5
y=0 divide by -36
x=7(0)-1 substitute 0 for y in x=7( )-1
=-1 simplify
The lines intersect at the point (-1, 0)
A bicycle manufacturer wants to find out which features most cyclists prefer to have in the newest model of bicycles to be manufactured next year. What is the population from which the manufacturer should choose a sample?
A. Subscribers to a national bicycling magazine. B. Cyclists who purchased bicycles from this manufacturer before. C. Visitors to the manufacturer’s Web site. D. Members of a bicycling club.
Answer:
It's B
Step-by-step explanation:
I did the test
which is greater - 3/4 or - 5/6
Answer:
-3/4
Step-by-step explanation:
see picture below
Answer:
[tex]-3/4~ > -5/6[/tex]
Step-by-step explanation:
Using the given inputs
[tex]3/4~and~5/6[/tex]
The least common denominator (LCD) is 12.
Rewriting as equivalent fractions with the LCD:
[tex]-\frac{3}{4} ~becomes-\frac{9}{12}[/tex]
And
[tex]-\frac{5}{6}~becomes-\frac{10}{12}[/tex]
Comparing the numerators of the equivalent fractions we have
[tex]-9/12 > -10/12[/tex]
Therefore, the comparison shows:
[tex]-3/4~ > -5/6[/tex]
Hope this Helps! :3
have a great day! :3
((454 x 344)/4) + 4854
Solve order of operations
Answer:
43,898
Step-by-step explanation:
1. 454 x 344 = 156,176
2. 156,176 / 4 = 39,044
3. 39,044 + 4,854 = 43,898
graph the line y= 4/3x
Answer:
RISE/RUN
Step-by-step explanation:
You start at (0,0)move up 4move right 3the base of the rectangular prism is shaded what is the lateral surface area ( show work pls )
LSA
2×H(L+B)2(4.5)(11+3)9(14)126ft²a department store has guft boxes that are 20 inches long, 12 1/2 inches wide, and 5 1/2 inches high what is the volume
You decide that you are going to flip a coin, and a six sided die.
What is the probability of the following events?
Tails and an even number? (Round to two decimal places)
Tails and the number 9?
Heads or a number bigger than 4? (Round to two decimal places)
Heads or the number 2? (Round to two decimal places)
Probability helps us to know the chances of an event occurring. The probability of getting a tail and an even number is 0.25.
What is Probability?
Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Since a coin has two faces, therefore, the probability of getting either of the sides of the coin is (1/2). While a die has six faces, so the probability of getting any side of the die is (1/6).
A.) The probability of getting a tail and an even number can be written as,
[tex]\text{Probability of getting a tail} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of Even Number(2,4,6) } = \dfrac{3}{6} = \dfrac{1}{2}[/tex]
[tex]\text{Probability (Tails and an even number)} = \dfrac12 \times \dfrac12 = 0.25[/tex]
B.) The Probability of getting tails and the number 9 can be written as,
[tex]\text{Probability of getting a tail} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of Number 9} = \dfrac{0}{6} = 0[/tex]
[tex]\text{Probability of the tails and the number 9} = 0[/tex]
C.) The Probability of getting Heads or a number bigger than 4 can be written as,
[tex]\text{Probability of getting a Head} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of a number bigger than 4 (5,6) } = \dfrac{2}{6} = \dfrac{1}{3}[/tex]
[tex]\text{Probability (Heads or a number bigger than 4 )} = \dfrac12 + \dfrac13 = \dfrac{5}{6} = 0.83333[/tex]
D.) The Probability of getting Heads or the number 2 can be written as,
[tex]\text{Probability of getting a Head} = \dfrac{1}{2}[/tex]
[tex]\text{Probability of the number 2} = \dfrac{1}{6}[/tex]
[tex]\text{Probability (Heads or the number 2 )} = \dfrac12 + \dfrac16 = \dfrac{8}{12} = 0.6666[/tex]
Learn more about Probability:
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Select the reason that best supports statement both 2 and 8 in the given proof.
hElp me I need help with this question
Answer:
Jackie divided the number of quarts by 2. There are 2 pints in each quart. She should have multiplied by 2; so Jackie made 20 pints of lemonade.
Which of the following is an example of a linear system of equations?
5
x
2
+
6
y
=
13
6
x
−
12
y
=
14
5
x
+
6
y
=
13
6
x
−
12
y
2
=
14
5
x
+
6
y
=
13
6
x
2
−
12
y
=
14
5
x
+
6
y
=
13
6
x
−
12
y
=
14
Yw :D pls mark me brainiest
how to graph y = x + 10
Answer:
if you use desmos graphing calculator it will make graphing equations like this easier.
Step-by-step explanation:
by easier i mean it just graphs it for you. hope this helps:)
Tulong bwhahahhahahaha
Mr. Hollins determines that he gives away $800 each month. If he gives away 16% of his budget, then how much is his overall budget
Answer:
5000 dollars
Step-by-step explanation:
Let his budget be x
16% of x is 800 dollars
.16 * x = 800
Divide each side by .16
.16x/.16 = 800/.16
x=5000
His budget is 5000 dollars
em sa
1.
She bikes at a constant speed of 13 miles per hour for
the entire 20 minutes.
Hint 20 minutes is what fraction of an hour? Look back
at the answer to problem 4.
Answer:
4.33 miles
Step-by-step explanation:
20 minutes=1/3 of an hour
because 1 hour=60minutes
so 20/60 = 1/3
for your answer
13× 1/3=4.33
therefore she was able to bike 4.33 miles in 20 minutes at a constant speed
100 POINTS
Solve the following inequality, if it is known that function f is increasing on its domain. f(4x-3)[tex]\geq[/tex]f(2-[tex]x^{2}[/tex]), D_f = (-8, 4)
This solution is arrived at using the principles of Quadratic Functions and Inequalities. It is to be noted that the function increases at (-8, 4).
What are Quadratic Functions?A quadratic function can be defined as that is written in the following way: f(x) = ax2 + bx + c: Where a, b, and c are numbers not equal to zero.
How do we solve the problem above?To solve the problem f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4), we:
A) 4x - 3 ≥ 2 - x²
Rewrite as: x² + 4x - 2 - 3 ≥ 0
B) Collect the like terms
x² + 4x - 5 ≥ 0
C) Expand to have x² + 5x - x - 5 ≥ 0
D) Factorizing the expression we have
x(x + 5) - 1(x + 5) ≥ 0, from this we Factor away x + 5
(x - 1)(x + 5) ≥ 0
E) Solving for x we obtain: x ≥ 1 or x ≥ -5
This can also be rewritten to read:
-5 ≤ x ≤ 1
Learn more about quadratics and inequalities at:
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help thanksSSSSSSSSSS
Answer:
[tex]\boxed{\sf{x=24}}[/tex]Step-by-step explanation:
GIVEN:
To find the missing number in the proportion, you have to isolate it the term of x from one side of the equation.
[tex]\sf{\dfrac{8}{7}=\dfrac{x}{21} }[/tex]
First, thing you do is switch sides.
[tex]\sf{\dfrac{x}{21}=\dfrac{8}{7} }[/tex]
Multiply by 21 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{21x}{21}=\dfrac{8*21}{7} }[/tex]
Solve.
Multiply the numbers from left to right.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract[tex]\Longrightarrow: \sf{\dfrac{8*21}{7}=\dfrac{168}{7}=24 }[/tex]
[tex]\Longrightarrow: \boxed{\sf{x=24}}[/tex]
Therefore, the final answer is x=24.I hope this helps. Let me know if you have any questions.
Where does most regular lightning occur?
A. The stratosphere
B. The troposphere
C. The Mesosophere
is it true or false?
Answer:
True
Step-by-step explanation:
plug in numbers
4(-3)+15=3
-12+15=3
-3+15=12
PLEASE CHOOSE CORRECT OPTION AND WITH EXPLANATION 25 POINTS
Answer:
d
Step-by-step explanation:
Each point has been moved 2 spaces to the right and 5 units down.
Moving 2 spots to the right means x updates to x+2
Moving 5 units down tells us to change y to y-5
Therefore, [tex](x,y) \to (x+2, y-5)[/tex]
The net below shows a square pyramid. What is the lateral surface area?
A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2
Answer: B
Step-by-step explanation:
1/2 8 *7 = 28
because there is 4 triangles you do this 28+28+28+28
28+28+28+28 = 112
The lateral surface area of the pyramid is 112 sq. in.
The correct answer is an option (B)
From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.
Hence, The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.
Using the formula of the area of triangle, the lateral surface area would be,
A = 4 × (1/2 × base × height)
A = 4 × (1/2 × 8 × 7)
A = 4 × (4 × 7)
A = 4 × 28
A = 112 sq. in.
Thus, This is the required lateral surface area.
So, The correct answer is an option (B) 112 in²
Learn more about the surface area here:
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what is the volume of the cone below
Answer:
Its C because the formula to find the volume of the cone is π x radius² x height / 3 and in this case the radius is 4 and the height is 27 so π x 27 x 4² which is 452.16 and 144 x π is 452.16
Step-by-step explanation:
Please mark as brainliest
Rewrite the following linear equation in slope-intercept form. Write your answer with no spaces.
V-5= 3(x+1)
Answer:
V=3x+6
Step-by-step explanation:
slope intercept form: y=mx+b
V-5=3(x+1)
[open parentheses]
V-5=3x+1
[combine like terms; add 5 to both sides]
V=3x+6
why is it v tho
Can someone answer these 2 questions, thanks!
Answer:
1, answer ..
b, 50% because add this
40+10=50
Step-by-step explanation:
and 2nd one i dont know but i studied it i did not remember