Diagram 3 shows a piece of rectangularcardboard and an open box that is made from the cardboard.The box is made by cutting out four squares of equal size from the cornersof the cardboard then folding up the sides. Finda) the length in cm of sides of the squares to be cut out in order to get a box with largest volume.b) the minimum number of the boxes needed to fill with 5645 cm³ of pudding
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Diagram 3 shows a piece of rectangular cardboard and an open box that is made from the cardboard.
The box is made by cutting out four squares of equal size from the corners
of the cardboard then folding up the sides.
Find
a) the length in cm of sides of the squares to be cut out in order to get a box with the largest volume.
[tex]\begin{gathered} The\text{ volume of the rectangle would be expressed as:} \\ \text{V = ( 30-2x )(16-2x) ( x)} \\ Multiply\in g\text{ out, we have that:} \\ V=480x-92x^2+4x^3 \\ \text{Differentiating V with respect to x, we have that:} \\ \frac{dV}{dx}=480-184x+12x^2=0 \\ \text{Factorizing the quadratic equation, we have that:} \\ \text{x = 12 or x =}\frac{10}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{Differentiating again, we have that:} \\ \frac{d^2V}{dx^2\text{ }}\text{ = -184 + 24 x} \end{gathered}[/tex]To get the maximum, we need to substitute the values of :
[tex]\begin{gathered} x\text{ = 12, we have that:} \\ \frac{d^2V^{}}{dx^2\text{ }}\text{ = -184 + 24( 12) = }-184\text{ +288 = 104} \\ x=\frac{10}{3},\text{ we have that:} \\ \frac{d^2V}{dx^2}\text{ = -184 + 24 (}\frac{10}{3})\text{ = -184 +}\frac{240}{3}\text{ = - 184 + 80 = -104 }<0 \end{gathered}[/tex]At this stage, we can see that:
[tex]\begin{gathered} x\text{ =}\frac{10\text{ }}{3}cm\text{ is the length of the squares to be cut in order to get a box with } \\ \text{largest volume} \end{gathered}[/tex]b) Find the minimum number of the boxes needed to fill with 5645 cm³ of pudding
[tex]\begin{gathered} \text{From the equation,} \\ V=(30-2\text{x )(16-2x)(x)} \\ \text{put x =}\frac{10}{3}\text{ in the equation, we have that:} \\ V\text{ = \lbrack}30\text{ -2(}\frac{10}{3})\rbrack\text{ \lbrack 16-2(}\frac{10}{3}\rbrack\lbrack\frac{10}{3}\rbrack \\ V\text{ = ( 30 -}\frac{20}{3})\text{ ( 16 - }\frac{20}{3})(\frac{10}{3}) \\ V=725.93cm^3 \\ Now\text{, we asked to find the minimum number of boxes ne}eded^{} \\ to^{} \\ \text{fill with 5645cm}^{3\text{ }}\text{ of pudding.} \\ \text{Then, we ne}ed\text{ to do the following:} \end{gathered}[/tex]
Minimum number of boxes =
[tex]\begin{gathered} \frac{5645}{725.93} \\ =\text{ 7.78} \\ \approx\text{ 8} \end{gathered}[/tex]CONCLUSION:
A minimum of 8 boxes will be needed to fill with 5645 cm³ of pudding
Related Questions
graph the function f(x)=3-(x)
Answers
The given function is
[tex]f(x)=3-x[/tex]To graph this linear function we have to complete a table of values. We replace each x-value in the function to get each y-values to form coordinated pairs.
x f(x)
-2 5
-1 4
0 3
1 2
Let's do the calculations for each f(x) value.
[tex]\begin{gathered} f(-2)=3-(-2)=3+2=5 \\ f(-1)=3-(-1)=3+1=4 \\ f(0)=3-0=3 \\ f(1)=3-1=2 \end{gathered}[/tex]At last, we have to graph each point and draw a straight line. The graph below shows the graph for the function.
2. Find the radian measure of an angle of 320°. (Leave in terms of rr.) A. 9 16 0 B. 16 9t 0 90 ID 10
Answers
SOLUTION
Find the radian measure of an angle of 320°. (Leave in terms of rr.)
We have that 360° × π/180 = 6.283rad
Do you
320° x π / 180 =
Three girls play three rounds of a game. On each round there are two winners and one loser. The girl who loses on a round has to double the number of chips that each of the other girls has by giving up some of her own chips. Each girl loses one round. At the end of three rounds, each girl has 24 chips. How many chips did each girl have at the beginning of the game?
Answers
The Solution:
Let the 3 girls be represented with A, B, and C.
At round 1:
Let C be the loser while A and B are winners.
A has 12 chips
B has 21 chips
C has 39 chips
At round 2:
Let B be the loser while A and C are winners.
A has 24 chips
B has 42 chips
C has 6 chips
At round 3:
Let A be the loser while A and C are winners.
A has 24 chips.
B has 24 chips.
C has 24 chips.
Therefore, the girl A has 12 chips, girl B has 21 chips and girl C has 39 chips at the beginning of the game.
expand and simplify(p+4)(P+3)P-1)
Answers
In linear equation, p³ - 6p² + 5p - 12 is simplify od equation .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).(p+4)(P+3)(P-1)
= p² + 3p + 4p + 12
= ( p - 1 ) ( p² + 3p + 4p + 12 )
= p³ + 7p² + 12p - p² - 7p - 12
= p³ - 6p² + 5p - 12
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Solve the following equation for x. Please show all your solution steps. 2x - 5 + 3x = x - 41
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Trey made $2000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
Answers
SInce he made $2000 , and this is less than the limit for the first bracket, Trey will need to pay just 10% on his gain:
10% of $2000 = 0.1 * 2000 = $200.
His tax is $200.
Traci needs to change $300 US Dollars into Euros. the exchange rate is 1 euro for 1.25 dollars. how many euros does Traci get for her dollars?
Answers
Let's begin by identifying key information given to us:
Amount = $300
Amount (after changing) = ?
Exchange rate: €1 = $1.25
We will calculate how much Euros Traci gets for her dollar using simple proportion:
[tex]\begin{gathered} x=\text{\$}300 \\ \euro1=\text{\$}1.25 \\ \text{Cross multiply, we have:} \\ 1.25(x)=300\cdot1 \\ x=\frac{300}{1.25}=240 \\ x=\euro240 \end{gathered}[/tex]Therefore, Traci gets €240 for her dollars
The table below shows the number of months and the amount spent on internet service. Which equation represents the total cost (t) based on the number of months (m) of service?1. t=45m 2. t=2m 3. t=90m4. t=4me
Answers
Given:
Number of months and the amount spent on internet service is tabulated.
Let the total cost (t) and the number of months (m)
Therefore equation is
[tex]t=45m[/tex]An employee at a state park has 84 photos of animals found at the park. She wants to arrange the photos in rows so that every row except the bottom row has the same number of photos. She also wants there to be at least 8 rows. Complete the description of two different ways she can arrange the photos.
Answers
Reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.5 rows of 10 photos and last row with 3 photos,
6 rows of 8 photos and last row with 5 photos,
7 rows of 7 photos and last row with 4 photos,
Hence, reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
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a 180 ounce bag weighs more than an 11 lb bag true or false
Answers
Let's make a conversion:
[tex]180oz\times\frac{1lb}{16oz}=11.25lb[/tex]Since:
[tex]11.25lb>11lb[/tex]It's true
2 (3s' + 9s + 3) - (6s + 1) Submitadd and subtract polynomialswe're doing subtract for this one
Answers
SOLUTION
[tex]undefined[/tex]Unit 4 What is the rate of return when 20 shares of Stock A, purchased for $20/share, are sold for $490? The commission on the sale is $6. Rate of Return = [?] % Give your answer as a percent rounded to the nearest tenth.
Answers
Answer:
21%
Step-by-step explanation:
You want the rate of return on 20 shares of stock bought for $20 per share and sold for $490 with a commission on the sale of $6.
Rate of returnThe rate of return is the percentage change between the sale proceeds and the cost of the stock.
rate of return = (proceeds/cost -1) × 100%
= ((490 -6)/(20·20) -1) × 100% = 21%
The rate of return is 21%.
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In Exercises 1-3, the perpendicular blsectors of ABC Intersect at point G, or the anglebisectors of AXYZ intersect at point P. Find the Indicated measure. Tell which theoremyou used.
Answers
We have a line:
And we draw its perpendicular bisector:
Then, any point on the bisector is equidistant to the endpoints of the line:
This is called: the perpendicular bisector theorem.
1In this case we have that:
Since the line is the black one, the bisector is the purple one, then both red segments measure the same : 9.
Answer: BG = 9 (bisector theorem)
2In this case, as we can observe in the image, the red lines are equidistant then CG = 10
Answer: CG = 10 (bisector theorem)
Consider the following quadratic equation - x ^ 2 + 3x - 7 = 0 Step 1 of 2 Find the values of a , b, and that should be used in the quadratic formula to determine the solution of the quadratic equation
Answers
Recall that the quadratic formula states that the solution to the quadratic equation:
[tex]ax^2+bx+c=0[/tex]are:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]Notice that a is the coefficient of the quadratic part, b is the coefficient of the linear part and c is a constant.
We can rewrite the given equation as follows:
[tex](-1)x^2+3x+(-7)=0.[/tex]Therefore, the values a, b, and c that should be used in the quadratic formula to compute the solutions to the quadratic equation:
[tex]-x^2+3x-7=0[/tex]are:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5
Answers
As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]Now,
From the standard form of the line,
[tex]y=mx+b[/tex]Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
9. Leyla has 18 50-cent and 20-cent coins altogether. She has a total of $6.90. How many 20-cent coins does she have?
Answers
According to the information given in the exercise:
- Leyla has 18 coins of 50 cents and 20 cents.
. She has a total of $6.90.
Let be "f" the number 50-cent coins and "t" the number 20-cent coins.
Since 1 dollar is equal to 100 cents, you know that:
[tex]6.90dollars=690cents[/tex]Then, knowing the above, you can set up the following System of Equations:
[tex]\begin{cases}f+t=18 \\ \\ 50f+20t=690\end{cases}[/tex]To find the value of "t", you can apply the Substitution Method:
1. Take the first equation and solve for "f":
[tex]f=18-t[/tex]2. Substitute this equation into the second equation and solve for "t":
[tex]\begin{gathered} 50f+20t=690 \\ \\ 50(18-t)+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 50(18-t)+20t=690 \\ \\ 900-50t+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 900-30t=690 \\ \\ -30t=690-900 \\ \\ -30t=-210 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{-210}{-30} \\ \\ t=7 \end{gathered}[/tex]Therefore, the answer is: She has 7 coins of 20 cents.
An uber charges a flat fee of $1.50, plus an additional $0.75 per mile. If Max only
has up to $12 to spend?
Answers
Answer:
14 miles
Step-by-step explanation:
If you have $12 to spend and there's a flat fee $1.50
You subtract your $1.50 from $12
12-1.50=10.50
Then you divide 10.50 by .75
10.50÷.75=14
So you get 14 miles with $12
9. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel.
Answers
Answer:
If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel
Explanation:
When two lines are cut by a transversal so that alternate interiors, alternate exterior or corresponding, are congruent, then the line must be parallel
If;
[tex]\begin{gathered} \measuredangle a=\measuredangle b\text{ (alternate interior)} \\ \measuredangle x=\measuredangle y\text{ (alternate exterior)} \\ \measuredangle x=\measuredangle b\text{ (corresponding angles)} \end{gathered}[/tex]then the lines are parallel.
Diane opened a savings account 3 years ago the account earns 9% interest compounded monthly if the current balance is 100.00 how much did she despoit initially
Answers
Answer:
The amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]Explanation:
We want to find the amount of Principal she deposited initially.
Recall that the formula for calculating the Principal of a compound interest is;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Where;
P = Principal / initial amount
A = Future/ final amount
r = Interest rate (decimal)
n = number of times the interest is compounded per year.
t = Time in years
From the question, we were given the following;
A = $100.00
r = 9% = 0.09
n = monthly (12 months in a year) = 12 times
t = 3 years
Substituting the given values into the formula, we have;
[tex]\begin{gathered} P=\frac{100.00}{(1+\frac{0.09}{12})^{12(3)}} \\ P=\frac{100.00}{(1+0.0075)^{36}} \\ P=\frac{100.00}{(1.0075)^{36}} \\ P=76.41 \\ P=\text{ \$76.41} \end{gathered}[/tex]Therefore, the amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]what is the acceleration of a car that goes from 10 mph to the speed of 50 mph in four seconds
Answers
The acceleration is given by the variation of the speed divided by the time.
So:
[tex]\begin{gathered} a=\frac{v-v0}{t} \\ a=\frac{50-10}{4} \\ a=40/4 \\ a=10m/s^{2} \end{gathered}[/tex]Answer: 10m/s²
The following histogram represents the points earned by students on a vocabulary pre-test.
Answers
Explanation
By observation, the number of student scores represented on the histogram can be gotten by adding up the frequency. This can be seen below.
[tex]3+2+7+8+4=24[/tex]Answer: 24(option 1)
-0.15 decimal as a fraction or mixed number in simplified
Answers
Answer:
-3/20
Explanation:
Given the decimal number: -0.15
There are 2 digits after the decimal point, therefore in fraction form, we have:
[tex]-0.15=-\frac{15}{100}[/tex]Next, the fraction is reduced to its simplest form.
[tex]-\frac{15}{100}=-\frac{5\times3}{5\times20}=-\frac{3}{20}[/tex]The simplified form is -3/20.
[tex] \frac{1}{5} [/tex]convert into a prercentage
Answers
Answer:
20%
Explanation:
To convert a fraction into a percentage, multiply the fraction by 100.
Thus, the fraction 1/5 as a percentage is:
[tex]\begin{gathered} =\frac{1}{5}\times100 \\ =\frac{100}{5} \\ =20\% \end{gathered}[/tex]The percentage equivalent of 1/5 is 20%.
Sam paid $4.50 to have two shirts cleaned. If the dry cleaning service charges the same amount for any shirt, which equation can be used to represent the total cost, c, of having n shirts cleaned? A c = 4.5n B. c = 2.25n C. c = 4.5 +n D. c = 2.25 + n
Answers
Sam paid $4.50 to have two shirts cleaned.
If the dry cleaning service charges the same amount for any shirt then it means that for each shirt the rate is
[tex]\frac{\$4.50}{2}=\$2.25[/tex]If there are n shirts then the total cost (c) of the shirts can be represented by the following equation.
[tex]c=2.25n[/tex]If you substitute n = 2 shirts into the above equation then the total cost will be $4.50 which satisfies the given information.
Therefore, the correct answer is option B
to rent a booth at a County Fair cost $42 per day plus a one-time equipment fee of $85 find the number of days mr. Jones rented a booth if he paid a total of $337
Answers
5. The shadow of a tree extends 25 feet from the top of the tree to the ground. Sarah measures thatthe distance from the base of the tree to the tip of its shadow is 15 feet. How tall is the tree?A. 20 feetB. 25 feetC. 29.2 feetD. 40 feetO
Answers
Given :
The shadow of the tree = 25 feet from the top of the tree to the ground
the distance from the base of the tree to tip of its shadow is 15 feet
Let the height of the tree = x
So, 25 , 15 and x are forming a right angle triangle
25 is the hypotenuse of the triangle ,
x and 15 are the legs of the triangle
WE will find x using Pythagorean theorem
So,
[tex]\begin{gathered} x^2+15^2=25^2 \\ x^2=25^2-15^2=625-225=400 \\ x=\sqrt[]{400}=20 \end{gathered}[/tex]So, the height of the tree = 20 feet
The answer is option A. 20 feet
The product of two consecutive odd numbers is 323. Find the numbers.
Answers
Let the two consecutive numbers be x and (x+2).
According to the given condition,
The Panthers and the Vikings are competing for the state basketball championship. The data shows the height in inches of the starting lineup for
each team.
Panthers: 72, 74, 71, 73, 75
Vikings: 71, 77, 76, 74, 74
Which statement is true about the data?
Answers
The average height of the Viking's starting lineup is 1.4 inches greater than the average height of the Panther's starting lineup.
The Panthers and the Vikings are competing for the state basketball championship. The data shows the height in inches of the starting lineup for each team.
The heights of the players on the Panther's team are 72, 74, 71, 73, and 75. The heights of the players on the Viking's team are 71, 77, 76, 74, and 74.
Let the average height of the Panther's starting lineup be denoted by the variable "A1".
A1 = (72 + 74 + 71 + 73 + 75)/5
A1 = 365/5
A1 = 73
So, the average height of the Panther's starting lineup is 73 inches.
Let the average height of the Viking's starting lineup be denoted by the variable "A2".
A2 = (71 + 77 + 76 + 74 + 74)/5
A2 = 372/5
A2 = 74.4
So, the average height of the Viking's starting lineup is 74.4 inches.
The difference in the average height is calculated below.
d = A2 - A1
d = 74.4 - 73
d = 1.4
Hence, the average height of the Viking's starting lineup is 1.4 inches greater than the average height of the Panther's starting lineup.
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Find the Value of X, round your answer to the nearest 10th
Answers
The value of x is 13.31 units.
What is trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given a right angle with perpendicular = 8 units and base = x units and one acute angle = 59°
tangent of an angle = perpendicular/base
Therefore,
tan59° = x/8
x = tan59°*8
x = 13.31
Hence, the value of x is 13.31 units.
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Which of these frequency counts would be represented by the largest number of dots in a dot plot?
A. 25
B.23
C.24
D.22
Answers
The frequency count that a dot plot's greatest number of dots would depict is 25 (option A).
Given that,
The Option a is 25, b is 23, c is 24 and d is 22.
What is a dot plot?A dot plot is a graph that shows the frequency of a set of data and is comparable to a histogram. The frequency of the data is represented by the dots in the dot plot. The number of dots increases as the frequency of a data increases.
According to the information in this question, 25 would have the most dots, whilst 22 would have the fewest. A dot plot is a useful tool for displaying frequencies. Additionally, it works well with small data sets.
Therefore, The frequency count that a Gain on equipment sale equals selling price minus book value of equipment dot plot's greatest number of dots would depict is 25 (option A).
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