Width of the box is the dimension which gives the gives maximum value.
Width of the box = 9 cm
Length of the box = 9 cm
Given,
The perimeter of the rectangular bottom of the box = 36 cm
The height of the box = 4 cm
We have to find the dimension which gives maximum value.
Volume = lwh
Perimeter = 2(l + w)
36 = 2l + 2w
l = (36 - 2w)/2
l = 18 - w
Now,
Volume = length × width × height
V = (18 - w) × w × 4
V = 72w - 4w²
Lets find w by using w = -b/2a
That is,
w = -72/2(-4) = -72/-8 = 9
That is,
Width of the box is 9 cm and it is the dimension which gives the maximum value.
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Yall please help i need to turn this in i have too many demerits
The answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.What is constant proportionality?The ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two specified quantities determines the value of the proportionality constant.So, (A) To make the same shade of green:
Cups of blue paint: 2Cups of yellow paint: 10Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5
Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.
(B) New pair of numbers to make the same green shade:
Old pair:
Cups of blue paint: 2Cups of yellow paint: 10Another pair:
Cups of blue paint: 1Cups of yellow paint: 5The new pair would be:
Cups of blue paint: 2 × 2 = 4Cups of yellow paint: 10 × 2 = 20Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.
(C) Proportional relationship:
Let cups of blue paint be: xCups of yellow paint be: yOld pair:
Cups of blue paint: 2Cups of yellow paint: 10Proportional relationship will be:
2x/10y = x/5y ⇒ x : 5yTherefore, the proportional relationship of the table will be x : 5y.
(D) Constant of proportionality:
According to part (C), the Constant of proportionality will be x : 5y.
Therefore, the answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.Know more about constant proportionality here:
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3x = 0Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation
we have the equation
3x=0
is the same that
x=0
This is a vertical line (is the equation of the y-axis)
two ordered pairs that lies in this line are
(0,4) and (0,10)
graph the line
plot the points and join them
see the attached figure
11) Translate the following phrases into algebraic expressions
a. The difference of a number k and four
b. Eight less than a number x
e. The sum of six and a number d
d. The product of a number and five
e The quotient of eight and a number
f. The product of two and a number increased by seven
g. Half of a number decreased by twelve
A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. The translation is as follows:
a) 4 - k
b) 8 - x
c) 6 + d
d) x + 5
e) 8 / x
f) 2 + x = 8
g) 1/2n-12
What is meant by algebraic expressions?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.
The translation is as follows:
a) 4 - k
b) 8 - x
c) 6 + d
d) x + 5
e) 8 / x
f) 2 + x = 8
g) 1/2n-12
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4) The ratio of the side length of a square to the square perimeter is always 1 to 4. Peter
drew a square with a perimeter of 28 inches.
What is the side length of the square Peter drew
The side length of a square is 7 inches drawn by the Peter.
Whats is termed as the perimeter of the square?A square's perimeter is described as the amount length of its boundary. The distance around any looped geometrical shape is used to calculate its perimeter. The perimeter of a square can be determined by adding all of its sides. It is four times this same length of every side of a square because all 4 sides are equal.According to the question, the ratio of a square's side length to its perimeter is always one to four.
According to the story, Peter drew a square with such a perimeter of 28 inches.
Divide 28 inches by 4 to get the side length of a square Peter drew.
= 28/4
= 7 inches
As a result, the side length of a square is 7 inches.
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Solve 3x > 174, and use the interactive number line tool to graph the solution. What is true about the graph? Check all that apply.
There is an open circle at 58.
There is a closed circle at 58.
There is an open circle at 174.
There is a closed circle at 174.
The arrow points right.
The arrow points left.
Answer:
there is an open circle at 58
the arrow points right
Step-by-step explanation:
3x>174/:3
x>58 we have a strict x more than 58 that's why it's an open circle and right because x is more, but not less
x represents a positive interger
X < 7
How should I solve this? It would help with a step by step guide
If x represents a positive integer and x<7, then the values of x = {1,2,3,4,5,6}
The x represents a positive integers
Positive integers are the integers greater than 0. In number line the positive number will be at the right side of the 0. The negative integers are the integers less than 0. In number line the negative number will be at the left side of the 0.
The given inequality is
x<7
The inequality is the mathematical expression represents the relation between the two values that is not equal
Here x is less than 7 and a positive integer
Therefore,
x = {1, 2, 3, 4, 5, 6}
Hence, if x represents a positive integer and x<7, then the values of x = {1,2,3,4,5,6}
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By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is.
Step-by-step explanation:
If the data shows a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line, which minimizes the vertical distance from the data points to the regression line.
Find the length of side x in simplest radical form with a rational denominator. I will give brainliest please help asap
Answer:
[tex]x=\frac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
x^2+x^2=1
x^2=1/2
x=1/sqrt2
x=sqrt2/2
:]
write four cubed in expanded form and then evaluate
Answer:
64
Step-by-step explanation:
4^3 = 4 x 4 x 4 which can be written as 2^6 which is equivalent to 64 too
(If this is what you're asking)
help pls
1
3
144
432
The value of the given equation is 12.
What is the value of the equation?In order to solve this question, the BODMAS rule would be used. The BODMAS rule gives the order in which mathematical operations can be solved. The order is:
Bracket OfDivision Multiplication Addition SubtractionIn the numerator:
the addition would be done first: 3² + 1 = 9 + 1 = 10
Then the subtraction would be done next = 14 - 10 = 4
Now determine the square of the term in the bracket : 4²= 16
In the denominator:
The multiplication would be solved first: 3 x 1/4 = 3/4
The next step is to solve the division : 1 ÷ 3/4 = 1 x 4/3 = 4/3
The fraction becomes : 16 ÷ 4/3
16 x 3/4 = 12
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Answer:
The answer is 432
Step-by-step explanation:
I did the k 12 quiz and I got it right! good luck
12/1-(2x+3)
How to simplify this fraction
Step-by-step explanation:
so, it is
12 / (1 - (2x + 3))
yes, that is
12 / (1 - 2x - 3) = 12 /(-2x -2) | divide both sides by -2
-6/(x + 1)
What calculation will give us the estimated volume of the Great Pyramid of Giza in cubic meters?
The option that would give the estimated volume of the Pyramid of Giza is = [tex]\frac{53,000 . 150 }{3}[/tex]
What is the volume?A pyramid is a 3-dimensional shape that is made up of a polygonal base and 4 triangular faces. The 4 triangular faces are joined at a vertex. Types of pyramids include a square pyramid, rectangle pyramid, triangle pyramid.
The volume of a pyramid is the amount of space that is a three-dimensional shape.
Volume of a pyramid = 1/3 x (base area x height)
1/3 x (53,000. 150)
= [tex]\frac{53,000 . 150 }{3}[/tex]
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Please help or answer questions 2, 3, and 4. You may answer question 1 if you’d like but I do not need it. I have already done question 2 but confirming my answers would be nice. I will give out brainliest.
The ratios that can be used to compare the soda and punch recipes are as follows;
1. Emily:
Mason's recipe for soda is y = (1/2)•x
Tyler's recipe; y = (3/5)•x
Julio's
Mason's recipe; y = (1/3)•x
Tyler's recipe; y = (3/8)•x
2. Please see the completed values in the table in the elucidation that follows
3. The equivalent ratio relationship in each graph is given by the constant ratio of each coordinate pair.
4. The recipe that has the strongest lemon lime taste is given by the graph that has the steepest slope
What is the slope of a graph?The slope of a graph is given by the ratio of the rise to the run of a graph
1. The unit rate for Mason's recipe is (1/2) cup of lemon–lime per cup of club
While the unit rate for Tyler's recipe for club soda is (3/5) cup of lemon and lime per cup of club
Mathematically, we have
Emily;
Mason's recipe; y = (1/2)•x
Tyler's recipe; y = (3/5)•x
Julio;
Mason's recipe; y = (1/3)•x
Tyler's recipe; y = (3/8)•x
Carlos's recipe; y = (2/5)•x
Zeb's recipe; y = (1/5)•x
2. The values in the table becomes;
MasonLemon–lime; 1/3, 2/3, 1, 4/3, 5/3, 6/3
Total punch; 1, 2, 3, 4, 5, 6
Tyler'sLemon–lime; 3/8, 3/4, 9/8, 3/2, 15/8, 9/4
Total punch; 1, 2, 3, 4, 5, 6
Carlos'sLemon–lime; 2/5, 4/5, 6/5, 8/5, 2, 12/5
Total punch; 1, 2, 3, 4, 5, 6
Zeb'sLemon–lime; 1/5, 2/5, 3/5, 4/5, 1, 6/5
Total punch; 1, 2, 3, 4, 5, 6
3. Each graph represents equivalent ratios given that the value of the ratio of data point is a constant, that is, we have;
For Mason, 1:(1/3) = 2:(2/3) = 3:1...
For Tyler, 1:(3/8) = 2:(3/4) = 3:(9/8)...
For Carlos, 1:(2/5), 2:(4/5), 3:(6/5)...
For Zeb, 1:(1/5), 2:(2/5), 3:(3/5)...
4. The slope of each graph is given by the number of cups of lemon–lime per one cup of total punch,
The recipe that has the strongest lemon–lime taste is given by the recipe that has the most lemon–lime per each cup of total punch
Which gives;
The recipe that has the strongest lemon–lime can be found from the graph that has the largest slope, which is given by Carlos's recipe.
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peruvian cafe bought ad time on radio station wkoi. during the first four weeks, 4,000 different people heard the spot six times, while 2,000 heard it only three times during the same period. what is the average frequency?
The average frequency of people hearing the spot on the radio station is equal to 5.
Average frequency can be defined as the average number of times an individual is exposed to an Advertising schedule.
Average frequency can be calculated by using the formula;
average frequency = total / n
As 4000 people heard the spot 6 times and 2000 people heard it three times; therefore
n = 4000 + 2000 = 6000
total = number × frequency = (6 × 4000) + (3 × 2000) = 24000 + 6000 = 30,000
Substituting these values in the equation;
average frequency = 30,000 / 6000
average frequency = 5
Hence the average frequency of people hearing the spot on the radio station wkoi is calculated to be 5.
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Please answer quick i really need help
Answer:
( - 36, 24 )
Step-by-step explanation:
(- 9, 6)
( - 9×4, 6×4)
( - 36, 24 )
a license plate consists of 3 letters followed by 4 digits. how many license plates are possible if the first digit cannot be 0, and letters and digits may repeat?
There are 158,184,000 possible license plates consisting of 3 letters followed by 4 digits.
Based on the given information, since the letters and digits may be repeated, there are:
26 ways to fill in the first letter
26 ways to fill in the second letter
26 ways to fill in the third letter
9 ways to fill in the first digit *(first digit cannot be 0)
10 ways to fill in the second digit
10 ways to fill in the third digit and
10 ways to fill in the first digit
Thus, by Fundamental Principle of Counting, there are 158,184,000 possible license plates.
26 x 26 x 26 x 9 x 10 x 10 x 10 = 158,184,000
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82.8 cm measured to the nearest tenth of a cm.
one customer has two chances to receive a prize. if the customer keeps the higher of the two prizes awarded, what is the probability the customer will receive at least $100?
If the customer keeps the higher of the two prizes awarded, the probability the customer will receive at least $100 is 0.10
The probability that the customer will receive at least $100, P(X>100) is obtained below:
The probability that the customer will receive at least $100 is obtained by adding the corresponding probabilities of X=100 and, X=1000
Given from the table of probabilities, P(X=100)=0.08, and P(X=1,000)
P[X>100]=P(X=100)+P(X=1,000)
=0.08+0.02
=0.10
The question is incomplete, the complete question is given below:
A real estate developer is awarding one of four prizes to customers who view new properties. The prizes are awarded randomly through drawings. Prize values and their associated probabilities follow:
PRIZE VALUE PROBABLITY
$10 0.80
$20 0.10
$100 0.08
$1000 0.02
one customer has two chances to receive a prize. if the customer keeps the higher of the two prizes awarded, what is the probability the customer will receive at least $100?
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Friday
Use the equation to fill in the table.
y = 2x -7
Answer:
x=7
Step-by-step explanation:
7=2x-7
-2x-7-7
-2x=-14
x=-14÷2
x=-7
Marybeth rides her skateboard 5 miles in 30 minutes. If she maintains this rate, how far will she ride her skateboard in 4 hours?
MEAN The mean A of two numbers, x and y, is given by A =*+. Solve for y.
The mean can be written as mean A= x+ y/2
What is Mean?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set.
Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.
The mean formula is
= {Sum of Observation} ÷ {Total numbers of Observations}
Given:
mean A of two numbers, x and y
So, the mean can be written as
mean A= x+ y/2
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Using the SSS congruence is criterion what additional information is needed to show that triangle RST is congruent to triangle UTS?
The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
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Answer:
Step-by-step explanation:The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?
To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
The animals at a safari park include crocodiles, deer and penguins.
There are 16 more deer than there are crocodiles. 4 There are 3 times as many penguins as there are crocodiles. There are the same number of deer as there are penguins.
How many crocodiles are there at the safari park?
Answer:
8
Step-by-step explanation:
8x3 = 24
8+ 16 = 24
Determine which statement completes each open sentence:
32+8+1
15 (1+2)
4²
4.2
3(x - 4 + x)
when x = 4
111
3(x-4 + x)
when x = 2
32-1
15 +1 +2
3x4+x
3x4+x
1. is equal to
2. is NOT equal to
The statement which completes each of the open sentences are given below:
32 ÷ 8 + 1 is not equal to 3² - 1
15 ÷ ( 1 + 2) is not equal to 15 ÷ 1 +2
4² is not equal to 4 . 2
3 ( x - 4 + x) is not equal to 3x - 4 + x when x = 4
3 ( x - 4 + x) is not equal to 3x - 4 + x when x = 2
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Basic Geomtry Help, Easy
Answer:
A
Step-by-step explanation:
Because it's has no straight to it
use the aleks calculator to find 46% of 20 do not round
The value of the part of 20 that is 46% is 9.2.
How to determine the percentage of a number?Percentage is simply a number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Percentage = 46%Whole = 20Part = ?Plug the given values into the above formula and solve for the part.
Percentage = ( Part / Whole ) × 100%
46% = ( Part / 20) × 100%
46/100 = ( Part / 20 ) × 100/100
46/100 = ( Part / 20 ) × 1
46/100 = Part / 20
Cross multiply
46 × 20 = Part × 100
920 = Part × 100
Part = 920/100
Part = 9.2
Therefore, 9.2 is 46 percent of 20.
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equivalent to 6+12x?
Answer:
Step-by-step explanation:
6 + 12x
6 ( 1 + 2x )
The blueprint for the moreno’s living room has a scale of 2 inches= 5 feet. The family wants to use a scale of 1 inch= 3 feet. What is the width of the living room on the new blueprint
The width of the living room on the new blueprint is 15 feet.
How to calculate the width?Based on the information, the scale of the original blueprint will be:
= 2 in / 5 ft
The width of the original blueprint is 6 inches, the actual width of the living room will be:
2/5 = 6/x
where x = width of living room
Cross multiply
x = 5 × 6 / 2
x = 15 feet.
The width is 15 feet.
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Two parallel lines are cut by a transversal as shown belc
Suppose m 8 =107 Find m2 1and m2 3
1
2
4
3
5
6
8
7
The values of the angles m∠1 and m∠3 is equal to 73°.
A transversal may be defined as a line which cuts a pair of parallel lines and forms several angles. When transversal cuts parallel lines the alternate interior angles are equal as well as the corresponding angles are equal. Also, the pair of vertically opposite angles are equal. From the figure attached. ∠4 = ∠8 as they are corresponding angles. So, m∠8 = m∠4 = 107°. Now, we know that ∠1 and ∠4 formed a pair of linear angles and the sum of the measures of the linear angles is 180°. So,
m∠1 + m∠4 = 180°
We know, m∠4 = 107°
m∠1 = 180° - 107°
m∠1 = 73°
Now, ∠1 and ∠3 are vertically opposite angles, so they are equal as the parallel lines are cut by transversal. Therefore, m∠1 = m∠3
=> m∠1 = 73°
=> m∠3 = 73°
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The water level will be 10 feet or lower by tomorrow.
The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.
The given statement is "The water level will be 10 feet or lower by tomorrow."
What is a inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
The inequality for the given statement is x≤10
The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Choose the inequality that represents the statement.
The water level will be 10 feet or lower by tomorrow.
A. x≤10
B. x<10
C. x>10
D. x=10