Answer: The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Step-by-step explanation: This is a optimization with restrictions problem.
The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).
This restriction can be expressed as:
being x: the side of the square of the cross section and L: length of the package.
The volume, that we want to maximize, is:
If we express L in function of x using the restriction equation, we get:
We replace L in the volume formula and we get
To maximize the volume we derive and equal to 0
We can replace x to calculate L:
The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.
Athlete J runs 2/3 of a mile in 8 minutes. Athlete H runs 2 3/4 miles in 1/2 hour.
1. If Athlete J continues at that speed, how long will it take to run one mile?
2.How long will it take Athlete J to run 5 miles at that same speed?
3.Who runs faster, Athlete J or Athlete H? Explain your answer.
If Athlete J continues at that speed, it will take 12 minutes to run 1 mile
It will take Athlete J 60 minutes to run 5miles
Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.
The formula for calculating the speed of the athlete is expressed as:
Speed = Distance/Time
1) If Athlete J runs 2/3 of a mile in 8 minutes, this can be expressed as:
2/3 miles = 8 minutes
If the athlete runs for 1 mile, then;
1 mile = x
Divide both expressions
2/3 = 8/x
2x = 24
x = 12 minutes
Hence If Athlete J continues at that speed, it will take 12 minutes to run 1 mile
2) if athlete J run 5 miles, the time taken will be expressed as;
2/3(5) = 8/x
2/15 = 8/x
2x = 120
x = 60minutes
Hence it will take Athlete J 60 minutes to run 5miles
3) If Athlete H runs 2 3/4 miles in 1/2 hour, then the speed of athlete H will be expressed as:
Speed = (2 3/4)/0.5
Speed = 2.75/0.5
Speed = 5.5miles/hr
For Athlete J;
Speed = 5/1
Speed = 5 miles/hr
Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.
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Linear or non linear?
Answer:
Linear
Step-by-step explanation:
This is linear because using the data you have provided we can work out that the equation is y= -5x+27
y= mx+ c (c is the gradient)
This equation shows that the line is straight (also shown in the picture) and therefore must make it a linear graph.
For the graph to be non linear, the graph would be curved but this would mean the equation would have to be a quadratic - which it isn't.
Hope this helps!
rewrite the equation in Ax+By=C form, use intergers for A, B, and C.
Answer:
2x - y = - 8
Step-by-step explanation:
y - 4 = 2(x + 2) ← distribute
y - 4 = 2x + 4 ( subtract y from both sides )
- 4 = 2x - y + 4 ( subtract 4 from both sides )
- 8 = 2x - y , that is
2x - y = - 8 ← in standard form
with A = 2, B = - 1 and C = - 8
I need help because all the answer choices my teacher put were wrong so I dont know what to do
Answer:
Equivalent Expression: [tex]\displaytext\mathsf{\frac{a^7}{b^8}}[/tex]
Step-by-step explanation:
Given the exponential expression, [tex]\displaystyle\mathsf{\frac{a^{12}\:b^{-3}}{a^{5}\:b^{5}}}[/tex]:
We could use the Quotient Rule of Exponents where it states that:
[tex]\displaystyle\mathsf{\frac{a^m}{a^n}\:=\:a^{(m\:-\:n)}}[/tex]
Since we have the variables, a and b as the base, we could simply apply the Quotient Rule and subtract their exponents.
[tex]\displaystyle\mathsf{\frac{a^{12}\:b^{-3}}{a^{5}\:b^{5}}\:=\:a^{(12\:-\:5)}\:b^{(-3\:-\:5)}}[/tex]
[tex]\displaytext\mathsf{=\:a^{7}\:b^{-8}}[/tex]
Next, we must transform the negative exponent of base, b, into positive by applying the Negative Exponent Rule, where it states that:
[tex]\large\text{$ a^{-n}\:=\:\frac{1}{a^{n}} $}[/tex]
Applying the Negative Exponent Rule will result in the following exponential expression:
[tex]\LARGE\text{$ a^{7}\:b^{-8}\:=\:[a^{7}\:\times\:\frac{1}{b^8}]\:=\:\frac{a^7}{b^8} $}[/tex]
Therefore, the equivalent expression is: [tex]\LARGE\text{$ \frac{a^7}{b^8} $}[/tex].
Tessa wants to install a zipline between two trees. The zipline will be strung between the trees at points 42 feet and 3 feet high. Suppose the trees are 60 feet apart. What is the length of the zipline to the nearest tenth of a foot
The length of the zipline is found using Pythagoras's theorem, which gives
the length of the hypotenuse side of a right triangle.
Length of the zipline is approximately 71.56 feetReasons:
Height at which the zipline will be tied to one of the trees = 42 feet
Height at which the zipline will be tied to the other tree = 3 feet
The distance between the trees = 60 feet
Required:
The length of the zipline
Solution:
The length of the zipline is found as follows;
Taking one of the trees to be at the origin, the coordinates of one of the tying point = (0, 42)
The coordinates of the other tying point = (60, 3)
The in the imagined right triangle formed by the zipline and the distance
between the trees, the length of the zipline is given by Pythagoras theorem
as follows;
Length of zipline = [tex]\sqrt{(60 - 0)^2 + (3 - 42)^2} = 3 \cdot \sqrt{569}[/tex] ≈ 71.56
Length of the zipline ≈ 71.56 ft.
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factor completely. show full work
Answer:
here's the answer mark me brainliest!!
Answer:
Step-by-step explanation:
2p² + 8pq - pq - 4q² = 2p(p + 4q) - q( p + 4q)
= (p + 4q)(2p - q)
For question 1 please look at the image below
Answer:
Step-by-step explanation:
a) Number of families having income between $ 20000 - $ 40000 = 100
b) Number of families having income less than $40000 = 100 + 40 = 140
Can’t figure this out need help
Answer:
d
Step-by-step explanation:
range means y values so automatically a and b aren't right
there's no limits for y since it's linear, so it's D
that R sign basically means "all real numbers"
Solve for m. 3/5m>−30
m>−50
m<−50
m>−18
m<−18
Step-by-step explanation:
you need to be careful when writing/copying the text.
I assume this one here is actually
(3/5)m > -30
then
3m > -150
m > -50
Answer: m > -50
Step-by-step explanation: Got correct on test
Does anyone know this?
Answer:
all squares are quadrilaterala
Step-by-step explanation:
it has 4 sides and I just remember.
Answer:
All squares are quadrilaterals.
Step-by-step explanation:
Squares are defined as quadrilaterals with four right angles and four congruent sides.
Formen equipos de tres integrantes y realicen un proyecto en el que expresen mediante una ecuación lineal el tiempo que demoraran en reunir 10000 pesos para fundar la Sociedad Cultural Digital, si saben que los meses que tienen 31 dias sus padres donan un tercio de la cantidad total para el ahorro, mientras que en los de 30 dias logran ahorrar dos tercios de la cantidad final. En cuantos meses podrán reunir la cantidad deseada
Los estudiantes recaudarán un total de $ 10000 pesos en un mes de 31 días y un mes de 30 días.
En este caso, debemos construir una ecuación lineal en forma implícita, es decir, una ecuación de la forma:
[tex]a\cdot x + b\cdot y = c[/tex] (1)
Donde:
[tex]a, b[/tex] - Coeficientes de proporción de ahorro.[tex]c[/tex] - Coeficiente de proporción total del ahorro.[tex]x[/tex] - Cantidad de meses de 31 días.[tex]y[/tex] - Cantidad de meses de 30 días.Si sabemos que la solución consiste únicamente en números naturales y si [tex]a = \frac{1}{3}[/tex], [tex]b = \frac{2}{3}[/tex] y [tex]c = 1[/tex], entonces tenemos la única solución disponible:
[tex]\frac{1}{3}\cdot x + \frac{2}{3}\cdot y = 1[/tex]
[tex]x + 2\cdot y = 3[/tex]
[tex]2\cdot y = 3 - x[/tex]
[tex]y = \frac{3}{2}-\frac{1}{2}\cdot x[/tex]
[tex](x, y) = (1, 1)[/tex]
Los estudiantes recaudarán un total de $ 10000 pesos en un mes de 31 días y un mes de 30 días.
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PLEASE HELP! Economics
Answer: C. an increase in prices for domestically produced watermelons.
Rock Middle School is planning a field trip to a museum. The museum specifies that there needs to be one chaperone for every 4 students. If the maximum number of people allowed on the field trip is 700, what is the maximum number of students able to visit the museum?
Answer:
28000
Step-by-step explanation:
You multiply 4 and 700.
Answer:
525 students
Step-by-step explanation:
There will be 175 chaperones on the trip.
All you need to do is find 1/4 of 700 which is the number of chaperones.
Then subtract it by 700 to find the number of students.
I hope this helps!!
Which graph represents the equation y = 3/4x – 3 ?
Answer:
You haven't shown the graph image but here is what the graph looks like if the equation is y=3/4x -3
Step-by-step explanation:
Answer:
0.75x-3
Step-by-step explanation:
Mrs. Cho has 24 students in her class. Some of her students are also in the play.
Explain why it is not possible for exactly 24% of the students in Mrs. Cho’s class to be in the play.
914 1404 393
Answer:
24% of 24 is not a whole number
Step-by-step explanation:
24% of Mrs. Cho's students is ...
0.24 × 24 = 5.76 . . . students
This is not a whole number. The number of students must be a whole number. There cannot be part of a student in the play.
An online music store charges $1.15 for each song after you pay a $22 subscription fee. Write a function that represents the
arithmetic sequence. How many songs can you buy if you have $35 to spend?
Answer:
y = 1.15x + 22
help me asap. i’ve been stuck on this question for like two hours
Answer:
Step-by-step explanation:
how do I rewrite this using the distinctive property
6(-4)
To make fuel for the main engines of a space shuttle, 102,619.377 kilograms of liquid hydrogen and 616,496.4409 kilograms of liquid oxygen are mixed together in the external tank. How much fuel is
stored in the external tank?
There are kilograms of fuel stored in the external tank.
Answer:
There are 719,115.8179kg of fuel stored in the external tank
Step-by-step explanation:
102619.377 + 616496.4409 = 719,115.8179
John has $75 in his savings account. every week he deposits $7. which table represents the amount of money john has in his savings account after 5 weeks.
Answer: C
Step-by-step explanation: Depositing is the act of putting money inside the bank account usually to gain interest.
If John started with $75, you add his deposit ($7) which comes out to 82. Then add 82+7 which equals 89 and so on.
75+7= 82
82+7= 89
89+7= 96
96+7= 103
Answer: is the C
Step-by-step explanation:
bank account: 75$
1st week:75
2nd week:82
3rd week:89
4th week:96
5th week:103
Someone help meeee :))
Answer:
Step-by-step explanation:
1) 3x + y = 3
y = -3x + 3
When x = 0 ; y = 0 +3 = 3 (0 , 3)
When x = 1 ; y = -3*1 + 3 = -3 + 3 = 0 (1 , 0)
When x = 2 ; y = -3*2 + 3 = -6 +3 = -3 (2 , -3)
Plot the points (0 ,3 ) ; (1 ,0) and (2 , -3) in the graph and join them
2) y = x + 3
When x = 0 ; y = 0 +3 = 3 (0 , 3)
When x = 1 ; y = 1 + 3 = 4 (1 , 4)
When x = -3 ; y = - 3 + 3 = 0 (-3 , 0)
Plot the points (0,3) , (1, 4) and (-3 , 0) in the graph and join them
3) Plug in (4 , y) int he equation
y = x + 5
y = 4 + 5
y = 9
y = 9
5) 2x + y = 3
At x-intercept y = 0
2x + 0 = 3
2x = 3
x = 3/2
Which number has an absolute value that is greater than 50?
A
-62
B
-43
C
19
D
38
Step-by-step explanation:
Absolute value is the positive of a number.
Ex: -2 absolute value is 2
So -62 would have an absolute value greater than 50.
Answer:
-62
Step-by-step explanation:
1.8.3 practice - functions
15. State the domain and range of each of the following functions
[tex]f(x) = \frac{1}{x + 3} [/tex]
[tex]g(x) = \sqrt{x + 6} [/tex]
[tex]h(x) = x {}^{2} + 2x + 5[/tex]
Answer its 5982
Step-by-step explana
Look at the image and please help out! I need an answer.
Answer:
4b<30
Step-by-step explanation:
product means multiply so 4•b or 4b
less than so<
Step-by-step explanation:
addition means the sum of 2 numbers
so.....b+4 <30
b <30-4
B <26
in Littletown , the probability a team goes to the city playoffs is 0.20. the probability a team goes to the state playoffs given that the the team goes to the city playoffs is 0.50.
what is the probability that a randomly selected team from Littletown goes to goes to the city a state finals?
Answer: 10%
Step-by-step explanation:
A card is drawn from a deck of 52 playing cards. Given that it is a black card, what is the probability that it is the following? (Enter your probabilities as fractions.)
(a) a club
(b) a jack
Perform the operations indicated choose the correct answer 14+29
Answer:
14+29=43
Step-by-step explanation:just add it
What is the equation in point slope form of the line that passes through the point (3, 1) and has a slope of –2?
Drag and drop the appropriate number, symbol, or variable to each box.
Answer:
y - 1 = -2(x - 3)
Step-by-step explanation:
Given the point, (3, 1) and the slope of –2:
Let (x₁, y₁) = (3, 1)
slope: m = -2
Substitute these values into the following point-slope form:
y - y₁ = m(x - x₁)
y - 1 = -2(x - 3) ⇒ This is the point-slope form.
identify the antecedent and consequent of each conditional statement if they had a guard dog then no one would trust pass on their property
The antecedent is They had a guard dog and the consequent is No one would trust pass on their property.
The proposition given contains a conditional, whose form is [tex]p \implies q[/tex], representing a causal relationship, where:
(Antecedent) [tex]p:[/tex] They had a guard dog.
(Consequent) [tex]q:[/tex] No one would trust pass on their property.
Hence, the antecedent is They had a guard dog and the consequent is No one would trust pass on their property.
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PLEASE HELP MEEEEEEE
Answer:
PLEASE HELP MEEEEEEE TOOOOOOO
Evaluate the expression for x = 8
x + 5
5
8
3
13
Answer:
1st one
Step-by-step explanation:
:) pls mark brainliest
