From a thin piece of cardboard 20 in. by 20 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.
The 20 in. by 20 in. cardboard used make the box by cutting out squares of length x from the corners gives;
The dimensions that will yield maximum volume are;
Length =
The dimensions of the cut square that gives the maximum volume is approximately 3.3 feet, while the dimensions of the box are;
Length; 13.3 feet
Width; 13.3 feet
Height; 3 feet
The maximum volume of the box is approximately 592.6 ft³
What is the maximum value of a function?The maximum value of a function is the peak or highest point on the graph of the function.
The volume, V, of a box of Length, L, Width, W and Height, H, is given by the formula;
V = L×W×H
The length, width, and height of the box obtained by cutting a square of side length, x from the corners are;
Height of the box formed = x
Length of the cardboard box = 20 - 2•x
Width of the cardboard box = 20 - 2•x
The volume of the box is therefore;
V(x) = (20 - 2•x)•(20 - 2•x)•x = 4•x³ - 80•x² + 400•x
At the maximum point, we have;
V'(x) = (3×4)•x² - (2×80)•x + 400 = 0
V'(x) = 12•x² - 160•x + 400 = 0
Which gives;
3•x² - 40•x + 100 = 0
(3•x - 10)•(x - 10) = 0
Therefore;
[tex] \displaystyle{x = \frac{10}{3} }[/tex] and x = 10
When x = 10, we have;
V(10) = 4×10³ - 80×10² + 400×10 = 0
When x = 10/3, we have;
V(10) = 4×(10/3)³ - 80×(10/3)² + 400×(10/3) ≈ 592.6
Therefore, the dimensions of the box that gives the maximum volume is [tex] \displaystyle{x = \frac{10}{3} \approx 3.3}
The dimensions that yield maximum volume are therefore;
Length = 20 - 2 × (10/3) feet = 13.3 feetWidth = 13.3 ft.Height = 3.3 feetThe maximum of the box is 592.6 ft³
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Maya is working two summer jobs making 7 dollars per hour washing cars and making 10 per hour landscaping in a given week she can work at most 12 total hours and must earn no less than 90 dollars if x represents the number of hours washing cars and y represents the E number of hours landscaping write and love a system of inequalities graphically and determine one possible solution
One of the possible solution is x = 0 and y = 12.
The amount of money earned by washing cars is 7 dollars per hour.
The amount of money earned by landscaping is 10 dollars per hour.
The maximum number of working hours is 12.
The minimum amount of money to be earned is 90 dollars.
The number of hours of washing cars is represented by "x".
The number of hours of landscaping is represented by "y".
The inequalities formed are given below :
x + y ≤ 12
7x + 10y ≥ 90
The solution is the area which is common to both the inequalities and in the first quadrant. The graph is attached below.
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Enter an algebraic expression to model the given context. Give your answer in the simplest form.The principal amount P originally deposited in a bank account plus 0.6% interest The algebraic expression is _____+______= ______
Given:
Principal amount = P (o
Interest = 0.6% = 0.006 (divide by 100 since it's in percentage)
The algebraic expression is:
P + 0.006P = 1.006P
ANSWER:
P + 0.006P = 1.006P
Find the X value. 7x-4-3x=-3x+10
Answer:
x = 2
Explanation:
The given expression is
7x - 4 - 3x = -3x + 10
First, we need to add the like terms on the left side
(7x - 3x) - 4 = -3x + 10
4x - 4 = -3x + 10
Add 4 to both sides
4x - 4 + 4 = -3x + 10 + 4
4x = -3x + 14
Add 3x to both sides
4x + 3x = -3x + 14 + 3x
7x = 14
Finally, divide by 7
7x/7 = 14/7
x = 2
Therefore, the answer is x = 2
HELP RIGNT NOW ASAP GIVING BRAINLY PLUS 15 points
Answer:
ITS THE ONE RIGTH AFTER THE QUESTION AKA THE SECOND PHOTO YOU SENT I SEARCHED IT UP FOR YOU
A taxi charges an initial fee of $5 and then $1.50 per mile. The cost of a taxi ride can be represented by the following expression:
5 +1.50z
where z is the number of miles traveled.
Select either True or False.
1.The expression has 3 terms.
2.The coefficient in the expression is 1.50.
3.The expression contains a quotient.
Answer:
1. False. The only term is the number of miles traveled or z
2. True 1.50 is being multiplied so it is a coefficient of z
3. False. there is no division being done.
please help me find the area of the regular polygon?Remember to round to the nearest tenth
The area of the polygon is 341.1
We need to find first the base of the triangle
using Pythagorean theorem, a^2+b^2 = c^2
we have the base of 4.18
since the polygon is symmetric and regular, we have 16 same triangles within the polygon
using the area of the triangle multiply by 16 we can get 341.1
find f (-4) in this equation
Answer:
f(-4) = -6
Step-by-step explanation:
- From the step wise function given, -4 is in range of the first function;
[tex]{ \tt{f(x) = - {(x + 1)}^{2} + 3 }} \\ \\ { \tt{f( - 4) = - \{( - 4) + 1) {}^{2} + 3}} \\ \\ { \tt{f( - 4) = - ( - 3) { }^{2} + 3}} \\ \\ { \tt{f( - 4) = - 9 + 3}} \\ \\ { \tt{f( - 4) = - 6}}[/tex]
Answer:
f(- 4) = - 6
Step-by-step explanation:
f(- 4) with x = - 4 is in the interval - 4 ≤ x < - 1 , then f(x) = - (x + 1)² + 3
thus
f(- 4) = - (- 4 + 1)² + 3
= - (- 3)² + 3
= - 9 + 3
= - 6
then f(- 4) = - 6
Find the surface area of the figure.
Answer:
20m
11m
20m2
5m
11m
8x8
11x2
What is the slope of the line on the graph?
Enter your answer in the box.
Answer:
m = -2
Step-by-step explanation:
because of rise/run you can simply see the slope
Which expression is equivalent to
(52)4⋅5 (5 2 ) 4 ⋅5 5
A 511
Applying properties of exponents, the equivalent expression is given as follows:
[tex](5^{-2})^{5} \times 5^4 = 5^{-6}[/tex]
Exponent propertiesThe expression is given as follows:
[tex](5^{-2})^{5} \times 5^4[/tex]
First the power of power rule is applied, which states that if we have a base elevated to multiple powers, the base is kept while the powers are multiplied, hence:
[tex](5^{-2})^{5} = 5^{-10}[/tex]
(as -2 x 5 = -10)
Then the expression is written as follows:
[tex](5^{-2})^{5} \times 5^4 = 5^{-10} \times 5^4[/tex]
Now we have the multiplication of two terms with the same base and different exponents, meaning that we keep the base and add the exponents.
Hence the equivalent expression is given as follows:
[tex]5^{-10} \times 5^4 = 5^{-6}[/tex]
(as -10 + 4 = -6).
Missing informationThe problem is given by the image at the end of the answer.
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for A=s^2 find A when s=25 ft
The value of A = 625 ft.
What is substitution?
Substitution is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Given,
A = [tex]s^{2}[/tex]
when s = 25, A = 25(25)
A= 625 ft.
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the amount of water used by a washing machine varies directly with the weight of the load being washed the washing machine uses 28 gallons to wash 7 pounds of clothing how many gallons of water with the machine use to was 24.5 pounds of laundry
1. Are all multiples of 3 also multiples of 6? Explain your answer.
2. If 9 is a factor of a number, is 3 a factor of the same number? Explain your answer.
3. If 8 is a factor of a number, is 4 a factor of the same number? Explain your answer.
4. If 4 is a factor of a number, is 8 a factor of the same number? Explain your answer.
5. Are all multiples of 4 also multiples of 2? Explain your answer.
6. Are all multiples of 2 multiples of 4? Explain your answer.
If both 2 and 5 are factors of a number, is 10 a factor of the same number? Explain your answer.
1) Yes, all multiples of 3 also multiples of 6.
2) Yes, If 9 is a factor of a number, 3 is a factor of the same number.
3) Yes, If 8 is a factor of a number, then 4 is a factor of the same number.
4) No, If 4 is a factor of a number, then 8 is not a factor of the same number.
5) Yes, all multiples of 4 are also multiples of 2.
6) No, not all multiples of 2 are multiples of 4.
7) Yes, If both 2 and 5 are factors of a number, is 10 a factor of the same number
What are the multiples of the Number?
1) Every multiple of 3 is a multiple of 6, and as such all multiples of 6 are also multiples of 3 because 3 is a factor of 6.
2) 3 is a factor of 9 because it is divisible by 9. Thus, every number that has 9 as a factor also has 3 as a factor.
3) 4 is a factor of 8 because it is divisible by 8. Thus, every number that has 8 as a factor also has 4as a factor.
4) Similar to answer 3 above, but this is not true because 8 is not a factor of 4.
5) 2 is a factor of 4 and this means that 2 is divisible by 4. Thus, all multiples of 4 must be divisible by 2 and as such all multiples of 4 are also multiples of 2.
6) Not all multiples of 2 are multiples of 4 because 4 is not a multiple of 2.
6) Yes if both 2 and 5 are factors of a number, then 10 is also a factor because 10 is divisible by 2 and 5.
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In ΔWXY, \overline{WY}
WY
is extended through point Y to point Z, \text{m}\angle YWX = (3x+17)^{\circ}m∠YWX=(3x+17)
∘
, \text{m}\angle XYZ = (10x-5)^{\circ}m∠XYZ=(10x−5)
∘
, and \text{m}\angle WXY = (3x+2)^{\circ}m∠WXY=(3x+2)
∘
. Find \text{m}\angle WXY.m∠WXY.
Answer:
20°
Step-by-step explanation:
Exterior angle property: The exterior angle of a triangle equals the sum of opposite interior angles.
∠XYZ = ∠YWX + ∠WXY
10x - 5 = 3x + 17 + 3x + 2
10x - 5 = 3x + 3x + 17 + 2
10x - 5 = 6x + 19
10x = 6x + 19 + 5
10x = 6x + 24
10x - 6x = 24
4x = 24
x = 24÷ 4
[tex]\sf \boxed{x = 6}[/tex]
∠WXY = 3x + 2
= 3*6 + 2
= 18 + 2
= 20°
Determine whether the two figures are similar.
Please help me, Thank you ;)
Answer:
Step-by-step explanation:
The first 2 are similar because the corresponding angles are equal.
The second 2 are also similar as correspond sides are in the same ratio
5/10 = 6/12 = 9/18.
An automobile uses 27 pints of fuel for every 63
miles traveled. How many pints of fuel does the
automobile use to travel 7 miles ?
DATE/0 12 2. ace of a clock has a circumference of 63 in. What is the area of ce of the clock? (Lesson 3:8) of these pairs of quantities are proportional to each othe
The area of the clock = 315.41 inch[tex]squre[/tex]
The clock's face has been provided to us, and it is = 63 inch
Explanation?
The clock's face has been provided to us, and it is = 63 inch
So the circumference of the clock is also that amount.
given that the clock has a circular shape.
[tex]2\pi (r)= 63inch[/tex]
So
We will use this information to compute the radius[tex](r)[/tex] (of the circular clock.
Then
[tex]2\pi (R) = 63 inch =63/2\pi =10.2 inch[/tex]
The area of the circle equation will now be changed to include this value of (r) in order to obtain the area of the clock.
Now
[tex]\pi ( r)^{2} = \pi (10.02)^{2} = 315.41 in^{2}[/tex]
The area of the clock's face is therefore = [tex]315.41in^{2}[/tex]
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Ana can bike 9 kilometers in 24 minutes. At this rate, how far can Ana bike in 1 minute?
Answer:
0.375 kilometers, or 3/8 of a kilometer.
Step-by-step explanation:
Answer: 0.375 or 3/8 of a kilometer
Step-by-step explanation:
divide the numbers
9 / 24
0.375 or 3/8 of a kilometer
Two angles are complementary to each other. If one angle measures 23.28°, what is the degree measure of the other angle?
A: 156.72°
B: 66.72°
C: 46.56°
D: 23.28°
Answer:B 66.72
Step-by-step explanation:
complementary means if two angles are added up they will equal 90. we and eliminate d cause 23.28+23.28=46.56 so d is wrong now let's try c 46.56+23.28=69.84 so c is wrong cause it doesn't equal 90 now let's try a 156.72+23.28=180 its wrong since we are using complementary angles instead of supplementary angles Supplementary are angle two angles that add up to 180. so that just leaves b cause 23.28+66.72=90. i hope this helps and i made sure to explain it as best as i can have a great day
The solution is Option B.
The measure of the complementary angles are 66.72° and 23.28°
What are Complementary Angles?When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.
Let the first angle and second angle be a and b respectively such that
a + b = 90°
Given data ,
Let the first angle be represented as A
Now , the value of A is = 23.28°
Let the second angle be represented as B
Now , the value of B is = B
The angles A and B are complementary ,
So , A + B = 90° be equation (1)
Substituting the values in the equation , we get
23.28° + B = 90°
On simplifying the equation , we get
Subtracting 23.28° on both sides of the equation , we get
B = 90° - 23.28°
B = 66.72°
Therefore , the value of B is 66.72°
Hence , the measure of the angle is 66.72°
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plssssssssssssssss my brother got to go to the mall so pls hurry
Answer:
Step-by-step explanation:
Try to solve with a different mindset and or perspective.
Answer: Part A: 460 x 0.10
Part B: 460/10
Part C: 460/10 = 46
Step-by-step explanation: If the price of 10 textbooks is $460, then 1 textbook is $46.
X[tex]\sqrt{x}[/tex] + 7x + 10
factor the equation
algebra 2
There is no real solution for the equation X√x + 7x + 10.
A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind. For instance, factorizing the number 15 as 3 5
Solve X√x + 7x + 10 for x.
Subtract 7x from both sides
X√x + 7x + 10 - 7x = -7x
X√x + 10 = -7x
Subtract 10 from both sides
X√x + 10 - 10 = -7x - 10
X√x = -7x - 10
Divide both sides by √x
X√x / √x = (-7x - 10) / √x
x = (-7x - 10) / √x
The defined range
(0 , ∝)
Hence, The equation Xx + 7x + 10 has no actual solution.
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could someone please answer this correctly?
Answer:
Equation of parallel line:
[tex]y = -5x + 6[/tex]
Equation of perpendicular line:
[tex]y = \dfrac{1}{5}x - \dfrac{22}{5}[/tex]
Step-by-step explanation:
Parallel lines have same slope
Slope of y = -5x + 9 is -5
Parallel line will also have slope -5
Equation is y = -5x + b where b is the y intercept to be determined
Since line passes through (2, -4) these values of x and y must satisfy the equation for the parallel line
Plugging in we get
-4 = -5(2) + b
-4 = -10 + b
b = 10 - 4 = 6
Equation of parallel line is y = -5x + 6
Perpendicular lines have slope = negative of reciprocal of each other
Original line has slope -5
Perpendicular line will have slope -(-1/5) = 1/5
Equation of perpendicular line is
y = -1/5 x + b
Plugging in (2, -4)
=> -4 = 1/5(2) + b
=> -4 = 2/5 + b
==> -4 - 2/5 = b
b = -22/5
Equation of perpendicular line is
y = (-1/5)x - 22/5
Evaluate (5.44×10−4)+(3.6×10−5) . Express the result in scientific notation.
Using BODMAS, the resultant answer of the given expression is 81.4.
What is BODMAS?BODMAS rule is a rule or order that is used to simplify the arithmetic expression involving more operators in mathematics.The full form of BODMAS is:Brackets (Parts of a calculation inside the bracket always come first).Precedence of brackets are : [{(bar)}]Orders (powers and square roots)DivisionMultiplicationAdditionSubtractionEach letter of the word stands for the first letter of an operator. If an expression involves two or more similar operators that appear in succession, then the precedence is from left to right. By using BODMAS, we can evaluate an expression in the correct order of precedence.Given, problem is (5.44×10−4)+(3.6×10−5):
First, solve inside the brackets, and will start with multiplication.
We get,
(54.4-4)+(36-5)now, solving the values inside the brackets, we get
=(50.4) +(31)Now, we will open the brackets and apply addition, we get
= 81.4Hence, the value is given by 81.4.
Therefore, using BODMAS, the resultant answer of the given expression is 81.4.
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A line passing through (p, 1/2) and (-8, q) has a slope of 3/4.
Find two possible values for each of p and q , and write the corresponding equations of the lines in slope-intercept form.
Can someone help me with this question...?
The corresponding equation is 4q + 3p = 22.
What is the slope of a line ?
The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.
Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.
Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).
The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.
Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.
m = (y2 - y1)/(x2 - x1)
34 = (q - 1/2)/-8 - p
-24 - 3p = 4q - 2
4q + 3p = 22
The corresponding equation is 4q + 3p = 22.
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There are 550 students in the school. Predict how many students at the school prefer track and field.
The size of the sample is 20 and 4 people's favorite sport is track and field. The probability is [tex]\frac{4}{20}[/tex].
Probability is the chance of an event to occur from a number of possible outcomes.
The number of students at the school who prefer track and field is 110.
What is probability?It is the chance of an event to occur from a number of possible outcomes.
It is given by:
Probability = Number of required event / Total number of outcomes
We have,
Number of students = 550
Sample:
Number of students = 20
Number of students whose favorite sport is track and field = 4
The probability of students whose favorite sport is track and field:
= 4/20
Now,
If 4 out of 20 students' favorite is track and field.
20 students = 4
Multiply 550/20 on both sides.
550/20 x 20 students = 550/20 x 4
550 students = 110
This means that,
There will be 110 students who prefer track and field.
Thus,
The number of students at the school who prefer track and field is 110.
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0.65×3.5 I need the answer today pls if you know how to do the problem pls help.
Answer:
2.2815
Step-by-step explanation:
4563/2000 X 2 and 563/2000
10 samples of different pastries are on display as customers leave a bakery, they are told that they can choose any 4 samples. how many different selections can a customer make?
The number of different selections that a customer can make is of 210.
How to find the number of different selections that the customer can make?To calculate the number of different selections that the customer can make, we need to verify if the order of the selections matters or not, then:
If the order matters, permutation is used.If the order does not matter, combination is used.In the context of this problem, the order does not matter, hence the combination formula is used.
The number of combinations, from a set of n elements, of x elements, is given according to the following rule:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, the number of selections is of 4 samples from a set of 10 samples, hence it is calculated as follows:
[tex]C_{10,4} = \frac{10!}{4!6!} = 210[/tex]
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The production manager is going to present this information to the company's board of directors. Which graph should the manager use to best emphasize that the number of defects has remained relatively consistent throughout the year?
Managers should utilize Graph 3 to stress that the defect rate has remained largely stable over the course of the year.
In graph 1, the timeline is typically placed on the horizontal axis for simplicity, and the amount to be measured is typically placed on the y-axis. The time is on the vertical axis (x-axis) in graph 1, making it a poor choice for the management. The vertical axis of time is used again in graph 2 in the same way. So using graph 2 is not a good idea.
The number of flaws in Graph 3 may be best highlighted by placing time on the horizontal axis and the quantity to be displayed on the vertical axis. Second, because the vertical axis range is less, it is simpler to see the data set on the graph rather clearly. The optimum choice is therefore graph 3.
Graph 4's vertical axis range is fairly large, which causes the dispersion or display of the data to be quite compressed and difficult to visualize. Graph 4's vertical and horizontal axes are situated correctly.
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1. There are 8 puppies, and 3 of them have red collars.
What fraction of the puppies have red collars?
Answer: 3 / 8 of the puppies have red collars
