write equations for total edge length E, total surface area A, and volume V of a cube with side lengths of s.
side length--volume
3. 9
5. 25
9.5. 90.25
s. s*3^2
Answers
If the length of a side of cube is "s", then total edge length (E = 12s), total surface area (A = 6s²) and Volume (V = s³).
As per the question statement, the length of a side of cube is "s".
We are required to write down the equations for total edge length "E", total surface area "A" and Volume "V" of the cube with respect to "s".
To solve this question, we need to know a couple of basic structural properties of a cube, that is,
There are 12 edges in a cube, all of equal length,
And, there are 6 faces in a cube, all of equal surface area.
[A reference image is attached hereby for better understanding;
The 12 edges of the cube are: AB, BC, CD, AD, CG, DH, BF, AE, EF, FG, GH and EH,
And, the 6 Faces of the cube are: ABCD, ABEF, CDGH, BCFG, ADEH and EFGH]
Therefore, total edge length (E) = (12 * s) = 12s,
Or, (E = 12s)
Total surface area (A) = [6 * (s)²] = 6s²,
Or, (A = 6s²)
[Since, area of a square of edge length "s" = s², and every face of a cube is a square]
Finally, Volume (V) of the cube = [s * s * s] = s³,
Or, (V = s³).
Cube: In Mathematics, particularly in Geometry, a Cube is a three-dimensional figure, which has 6 square faces, each having equal edge length and surface area, 8 vertices and 12 equal edges.To learn more about Cubes, click on the link below.
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Related Questions
There are 21 cats and 17 dogs in an animal shelter. What fraction of the animals are cats?
A)21/38
B)21/17
C)17/21
D)17/38
Answers
Answer: B) 21/17
Step-by-step explanation:
Answer:
21/38
Step-by-step explanation:
Demonoator= 21+17=38
Numerator= number of cats
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the function h is defined by the following rule. =hx+−x1
Answers
The complete table of values for the x values in function h(x) is
x | -2 -1 0 1 2
h(x) | 3 2 1 0 -1
How to complete the table of the function h(x)?From the question, the definition of the function is given as
h(x) = 1 - x
Also, from the table of the values;
We have the following x values
x = -2, -1, 0, 1 and 2
The next step is that
We substitute each value of x in the equation h(x) = 1 - x
So, we have
When x = -2
h(-2) = 1 + 2
Evaluate
h(-2) = 3
When x = -1
h(-1) = 1 + 1
Evaluate
h(-1) = 2
When x = 0
h(0) = 1 + 0
Evaluate
h(0) = 1
When x = 1
h(1) = 1 - 1
Evaluate
h(1) = 0
When x = 2
h(2) = 1 - 2
Evaluate
h(2) = -1
When represented on a table of values, we have
x | -2 -1 0 1 2
h(x) | 3 2 1 0 -1
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Possible question
The function h is defined by the following rule h(x) = 1 - x
Find H(x) For Each x-Value In The Table
x = -2, -1, 0, 1 and 2
State one rational number between -0.45 and -0.46 (answer must be in decimal form.)
Answers
A rational number between the two given ones is -0.455, such that:
-0.45 > -0.455 > -0.46
How to find a rational number between the two given ones?A rational number is any number that can be written as a quotient between two integer numbers.
Particularly, any number with a finite number of digits after the decimal point is also a rational number.
So to find a rational number between -0.45 and -0.46 we could se:
-0.455, such that:
-0.45 > -0.455 > -0.46
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A bag contains 1 gold marbles, 7 silver marbles, and 25 black marbles. Someone offers to play this game: You randomlyselect one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.What is your expected value if you play this game?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the expected value for the game, so we obtain the following:
We will substitute in the following formula:
Expected Value=(Black Gain)*Black Chance (Gold Gain)*Gold Chance+(Silver Gain)*Silver Chance
Expected Value=(-1)*(25/33)+(3)*(1/33)+(2)*(7/33)
Expected Value≈-0.24
Finally we obtain that the expected value is approximately $-0.24.
f(n)=(x + 1)(x - 5)| has three solutions. What is the value of f(n)? How would you describe the location of this solution?
Answers
The equation given is a quadratic equation that has roots -1 and 5.
Roots of Quadratic EquationTo solve this problem, we have to find the roots of the quadratic equation and we can simply multiply through and then calculate the roots.
[tex](x+1)(x-5) = x^2 -5x + x - 5\\f(n) = x^2 -4x - 5[/tex]
Let's solve this quadratic equation above.
Using factorization method, we can find the factors of the quadratic equation and simplify.
[tex]x^2 - 4x -5 = 0\\(x+1)(x-5) = 0\\x + 1 = 0\\or \\x - 5 = 0\\x = -1 or x = 5[/tex]
The roots to the equation (x + 1)(x - 5) = 0 are - 1 and 5.
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which of the following is the equation of the line that passes through the point (-3,7) and is parallel to the y-axis.
Answers
ANSWER
[tex]x=-3[/tex]EXPLANATION
We want to write the equation of the line that passes through the point (-3, 7) and is parallel to the y-axis.
The general equation of a line is given as:
[tex]y=mx+c_{}[/tex]where m =slope
c = y intercept
A line parallel to the y-axis is a vertical line. The slope of a vertical line is undefined and so the equation of a vertical line is given as:
[tex]x=a[/tex]where a is the x coordinate of any point that it passes through.
Therefore, since the line passes through (-3, 7), the equation of the line is:
[tex]x=-3[/tex]Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)? O y=1/3x-1 Oy=1/3x+5/3 O y=1/3 x-5/3 O y=3x+1
Answers
Explanation:
The equation of a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We have that the line has a slope of 1/3:
[tex]y=\frac{1}{3}x+b[/tex]To find the y-intercept b we have to use the point. Replace x = -2 and y=1 and solve for b:
[tex]\begin{gathered} 1=\frac{1}{3}(-2)+b \\ 1=-\frac{2}{3}+b \\ b=1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]Answer:
The equation is:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]Cameron is playing 9 holes of golf. He needs to score a total of at most 11 over par on the last four holes tobeat his best golf score. On the last four holes, he scores 5 over par, 3 under par, 6 over par, and 3 underpar.Part 1 out of 3Enter and find the value of an expression that gives Cameron's score for 4 holes of golf.The expression is? Cameron's score is?Can someone please help?
Answers
Let the numbers over par is (+) and the numbers under par is (-)
he scores 5 over par, 3 under par, 6 over par, and 3 under
par.
so, the expression is : (5) + (-3) + (6) + (-3)
So, the result will be:
over par = 5 + 6 = 11
under par = 3 + 3 = 6
subtract under par from over par
so, 11 - 6 = 5
So, the Cameron's score = 5
Brand A granola is 25% nuts and dried fruit and brand B granola is 20% nuts and dried fruit. How much of sweet item A and sweet item B should be mixed to form a 10-lb batch of sweetsthat is 22% nuts and dried fruit?The batch of sweets should contain of Brand A granola and of Brand B granola.
Answers
The batch of sweet should contain 4 lb of Brand A granola
The batch of sweet should contain 6 lb of Brand B granola
Explanations:Total amount of sweet items = 10 lb
Let the amount of brand A granola be x
Amount of brand B granola = 10 - x
Amount of nuts and dried fruits in the total sweet items = 22% of 10
Amount of nuts and dried fruits in the total sweet items = 0.22 x 10
Amount of nuts and dried fruits in the total sweet items = 2.2lb
Amount of nuts and dried fruits in brand A granola = 25% of x
Amount of nuts and dried fruits in brand A granola = 0.25x
Amount of nuts and dried fruits in brand B granola = 20% of (10-x)
Amount of nuts and dried fruits in brand B granola = 0.2(10 - x)
Amount of nuts and dried fruits in brand A granola + Amount of nuts and dried fruits in brand B granola = Amount of nuts and dried fruits in the total sweet items
0.25x + 0.2(10 - x) = 2.2
0.25x + 2 - 0.2x = 2.2
Collect like terms
0.25x - 0.2x = 2.2 - 2
0.05x = 0.2
x = 0.2 / 0.05
x = 4 lb
The batch of sweet should contain 4 lb of Brand A granola
Amount of brand B granola = 10 - x
Amount of brand B granola = 10 - 4
Amount of brand B granola = 6 lb
The batch of sweet should contain 6 lb of Brand B granola
In 1991 the average family income was about 39000, and in 2011 it was about 66820.
Let
x
=
0
represent 1991,
x
=
1
represent 1992, and so on. Find values for
a
and
b
(rounded to one decimal place if necessary) so that
f
(
x
)
=
a
x
+
b
models the data
a
=
b
=
What was the average family income in 2006?
$
Answers
The average family income in 2006 is $59865.
What is the income?Based on the information illustrated, the required model is given as:
y = ax + b
y = average family income
x = years since 1991
The slope based on the information given is b = 39000.
Therefore, the family income in 2006 will be:
= (1391 × 15) + 39000
= 59865
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A monk crossbred plants, which can have purple or white flowers, and obtained 518 plants with white flowers and 229 plants with purple flowers. Find the
empirical probability that a plant had each type of flower.
The probability a plant had white flowers is. (Round to the nearest hundredth as needed.)
Answers
Probability that a plant had each type of flower. 0.36 and 0.64
What is Probability?
Probability is a branch of mathematics that quantifies the Probability of an event occurring or the Probability of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.
Number of white flower plants = 660
Number of purple flower plants = 368
To discover the empirical Probability that a plant had each sort of flower.
Formula
empirical Probability is found by rehashing an test and watching the outcomes.
P(event) = (the number of time the occasion happens) ÷ (add up to number of trial)
Here, Total number of plants = (660+368) = 1028
Now, Probability of white flower plant = = 0.64
And,
Probability of purple flower plant = = 0.36
Hence, The empirical Probability of white flower is 0.64 and the empirical Probability of purple flower is 0.36
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Write a formula for the function of tamed when the graph is shifted as described below
Answers
Given the function
[tex]f(x)=|x|[/tex]Then, the function is shifted down 3 units means you subtract 3 to f(x).
[tex]f(x)=|x|-3[/tex]And the function is shifted to the right 1 unit means you subtract 1 from the argument of f(x), this is "x". Therefore, the new function is:
[tex]f(x)=|x-1|-3[/tex]Answer:
[tex]f(x)=|x-1|-3[/tex]I need help with my pre-calculus homework, please show me how to solve them step by step if possible. I need help with how to apply the problem on the calculator. The image of the problem is attached.Instructions: Make sure your calculator is in degree mode.
Answers
To convert 81 degrees to radian, we will apply the conversion:
1 π rad = 180°
let the 81° in rad = y
1 π rad = 180°
y = 81°
cross multiply:
1π rad (81) = 180 y
To get y, we divide both sides by 180:
[tex]\begin{gathered} \text{y = }\frac{1\pi rad\text{ }\times\text{ 81}}{180} \\ y\text{ = }\frac{81\text{ }\pi}{180}\text{ = }\frac{9\times9\text{ }\pi}{9\times0}\text{ } \\ 9\text{ is co}mmon\text{ to numerator and denominator. }It\text{ cancels out} \\ y\text{ = }\frac{9\pi}{20} \\ \\ 81\degree\text{ = }\frac{9\pi}{20}\text{ radians (option A)} \end{gathered}[/tex]Which subtraction expression does the number line model show? A number line with arrowed movements. Start at 0 on the right and move 4 units to the left. From that number, move 9 more units to the left. End at negative 13. –13 + 4 –4 – 13 –4 – 9 –4 + 9ne with arrowed movements. Start at 0 on the right and move 4 units to the left. From that number, move 9 more units to the left. End at negative 13.
Answers
The subtraction expression which the given number line model (see attachment) show is: C. -4 - 9
What is a number line?In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Note: Each interval on this number line represents -1 unit.
Next, we would add the given numbers together as follows:
Number = -4 + (-9)
Number = -4 - 9
Number = -13.
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Complete Question:
Which subtraction expression does the number line model show?
-13 + 4
-4 - 13
-4 -9
-4 + 9
Pythagorean Theorem• Create a real-world problem involving three lengths that form a right triangle• Give the measurement of the “legs”, then solve for the missing hypotenuse
Answers
Solution
Problem
A ladder is leaning on a wall that is 6 feet tall. The distance from the bottom of the ladder to the wall is 8 feet wide.
Solution
Therefore, using the Pythagorean Theorem, 6^2 + 8^2 = 36 + 64 = 100. The square root of 100 is 10. The triangle's hypotenuse or the ladder's length is 5 feet.
Add.
−2.35+(−1.602)
Enter your answer in the box.
Answers
Answer:
i think its
-3.952
5) 3 people exercising on an oval. It takes Tony 2 minutes to complete a cycle by bicycle, Malcolm 4 minutes by running and Julie 6 minutes by walking. If they start together at a same point how long does it take them to meet each other again?
Answers
Answer: 12 minutes
Step-by-step explanation:
Julie needs 6 minutes, when she completes one, she will be at the bgining, Malcolm at half, and Tony with her, therefore you will need to double it.
1. Suppose a designer has a palette of 6 colors to work with, and wants to design a flag
with 5 vertical stripes, all of different colors.
How many possible flags can be created?
2. Evaluate the expression P(9,3), equivalently 9P3
Answers
Part a: The total possible flags can be created using 6 colours is 720.
Part b: ⁹P₃ = 60480.
What is defined as the permutation?When the order of the arrangements matters, a permutation is a mathematical method that calculates the number of possible arrangements in a set. A common mathematical problem involves selecting only a few items from the a set of items in a specific order.For the given question;
Part a: A designer has total 6 palette of colors.
A flag has to made with 5 vertical stripes, all of different colors.
The, this could be done by using permutation.
= 6!
= 6×5×4×3×2×1
= 720
Thus, the total possible flags can be created is 720.
Part b: The value of the expression P(9,3), equivalently ⁹P₃.
⁹P₃ = 9!/3!
⁹P₃ = (9×8×7×6×5×4×3!)3!
⁹P₃ = 9×8×7×6×5×4
⁹P₃ = 60480.
Thus, the equivalent value of the expression is ⁹P₃ = 60480.
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twice a number is increased by one-third the same number. the result is 28.Find the number?
Answers
To begin solving this question, let us represent the unknown number by x.
First
We are told that twice a number is increased by one-third the same number
so, we can represent this as
[tex]2\times x+\frac{1}{3}x[/tex][tex]2x+\frac{1}{3}x[/tex]Next, we are told that the result is 28, thus
[tex]2x+\frac{1}{3}x=28[/tex]The final step will be to simplify the expression
[tex]\frac{7x}{3}=28[/tex]Cross multiply to get x
[tex]\begin{gathered} 7x=3\times28 \\ x=\frac{3\times28}{7} \\ x=3\times4 \\ x=12 \end{gathered}[/tex]Hence, the number is 12
At the movie theatre, child admission is 5.40 and adult admission is 8.90On Monday, three times as many adult tickets as child tickets were sold, for a total sales of \$706.20 How many child tickets were sold that day?
Answers
Solution
Step 1
Let the number of adult tickets = 3m
The number of child tickets = m
Step 2
[tex]\begin{gathered} Total\text{ cost of adult tickets = 26.7m} \\ Total\text{ cost of child tickets = 5.4m} \end{gathered}[/tex]Step 3:
Total sales = $706.20
[tex]\begin{gathered} 26.7m\text{ + 5.4m = 706.2} \\ 32.1m\text{ = 706.2} \\ m\text{ = }\frac{706.2}{32.1} \\ \text{m = 22} \end{gathered}[/tex]Number of child tickets that were sold that day = 22
Define a variable, used let statements, set up an equation, then solve. Morgan is making two cookie recipes. Recipe A calls for one-third third less than twice the number of cups of sugar that Recipe B calls for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?
Answers
EXPLANATION
Let's see the facts:
-Morgan is making ----------------> 2 cookie recipes.
Recipe A ---> A = 2RecipeB -(1/3) 2RecipeB
-She needs-----------> Recipe A + Recipe B = 4 1/6 cups of sugar
Now, we have a system of equations:
(1) A = 2B -(1/3)2B
(2) A + B = 4 1/6
Multiplying both sides of (1) by 3:
3A = 6B - B
Simplifying:
3A = 5B
Isolating B:
B = 3/5 A
Substituting B-value in (2)
[tex]A\text{ + }\frac{3}{5}A\text{ = 4}\frac{1}{6}[/tex]Reordering:
[tex]A+\frac{3}{5}A=\text{ }\frac{25}{6}[/tex]Multiplying both sides by 30:
[tex]30A\text{ + 18A = 25}\cdot5[/tex][tex]48A\text{ = 125}[/tex]Dividing both sides by 48:
[tex]A\text{ = }\frac{125}{48}[/tex]Representing as mix fraction and rounding:
[tex]A=\text{ 2}\frac{2}{3}[/tex]ANSWER: She will need two and two-thirds cups of Recipe A.
Finding Slope
HELP ME PLS
Answers
Answer:
-3 because (-1,-7) and (1,-13) takes -6 to get from -7 to -13 and 2 to get from -1 to 1. -6/2 is -3, so the slope/answer is -3.
Step-by-step explanation:
Answer:
Formula for finding slope is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Slope = -13-(-7) ÷ 1-(-1)
= (-13+7) ÷ (1+1)
= -6 ÷ 2
= -3
Please help me I’ll mark u brainly
Answers
Answer:
yes
Step-by-step explanation:
for each point, both the x and y coordinates are inverted
i need help with this problem. im not sure if b is the correct answer. please help
Answers
From the graph, we can't see any clear asymptote. Also, the arrow at the right tip of the graph tells us that it continues indefinitely, i.e., both the number of years and the population increases indefinitely.
Now, notice that the population increases as the number of years increases.
Therefore, the only true statement is:
As the number of years increases without bound, the population increases without bound.
Hello, may I please have some help on this practice question? Thank you.
Answers
Data:
• p1 = ,the proportion of Republican voters in the first state
,• p2 =, the proportion of Republican voters in the second state
,• P1 = ,the proportion of Republican voters in the sample from the first state
,• P1 = ,the proportion of Republican voters in the sample from the second state
,• n = ,sample
Procedure
0. Finding the mean proportions
[tex]p_1-p_2=0.52-0.47=0.05[/tex]2. Finding the standard deviation of the difference
[tex]\sigma=\sqrt[]{\frac{0.52\cdot(1-0.52)}{100}+\frac{0.47\cdot(1-0.47)}{100}}=0.0706[/tex]To have a greater percentage of republicans in the second state than in the first, the difference should be less than zero. Thus, the value of the difference of the proportion corresponds to zero.
[tex]Z=\frac{0-0.05}{0.0706}=-0.7080[/tex]Using the Standard Normal Table, the value of Z previously calculated corresponds to 0.2394.
Therefore, the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state is 0.24.
Answer: C) 0.24
A physics class has 40 students. Of these, 18 students are physics majors and 17 students are female. Of the physics majors, seven are female. Find the probability that a randomly selected student is female or a physics major.
Answers
Answer:
Probability (Physics Major or Female) = 28/40 = 0.7
Step-by-step explanation:
The probability of being a female is 17/40
The probability of being a physics major is 18/40
The number of students counted twice is 7/40
Probability (Physics Major or Female) = 17/40 + 18/40 - 7/40
Probability (Physics Major or Female) = 28/40 = 0.7
Polynomial equation
Answers
Using the Factor Theorem, the polynomial function with the desired characteristics is given by:
f(x) = -x(x² + 9)(x - 1)(x - 2).
Factor TheoremThe Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative), determining the end behavior of the function.
For this function, we have:
Two complex roots, hence a factor of (x² + 9).A root at x = 0, hence f(x) = ax(x² + 9).The two other roots are free, hence I am going to attribute x = 1 and x = 2, hence the equation is:
f(x) = ax(x² + 9)(x - 1)(x - 2).
The end behavior is that the function increases to the left and decays to the right, meaning that the leading coefficient is negative, hence a possible function is given by:
f(x) = -x(x² + 9)(x - 1)(x - 2).
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Why do y’all not explain like please I went on brainly for a reason
Answers
What are three fractions equivalent to 5/4
Answers
The Three Fractions are :-
10/8, 15/12, 20/16
Determine the cost of a taxi trip of 9 miles if the fare is $1.10 forthe first 1/6 mile and $.20 for each additional 1/6 mile (or fraction).a. $1.80b. $10.50c. $9.30d. $11.70
Answers
We are given :
-Cab fare for the first 1/6 mile = $1.10
-subsequent miles = $20
- total miles = 9
Calculations :
• 9 -1/6 = 54/6
= 54/6 - 1/6
= 53/6
• y = 1.10 + 53* 0.20 =$11.70
So correct option is number D