The largest Volume of the box possible is 4000 cm³ .
In the question ,
it is given that
the box has a square base ,
let the length and width of the box = "x" , because it is a square
let the height of the box [tex]=[/tex] h
the total surface area of the box = 1200
also the total surface area with open top is = x² + 4xh
So , x² + 4xh = 1200
h = (1200 - x²)/4x
According to the question ,
the volume of the box = x²h
Substituting the value of h = (1200 - x²)/4x ,
we get ,
Volume = x² × (1200 - x²)/4x
V = (1/4)(1200x - x³)
to Maximize the volume dV/dx = 0
(1/4)(1200 - 3x²) = 0
1200 - 3x² = 0
3x² = 1200
x² = 400
x = -20 , +20
length cannot be in negative , hence x = 20 ,
So , Volume = (1/4)[1200(20) - 20³]
= 4000 cm³
Therefore , The largest Volume of the box possible is 4000 cm³ .
Learn more about Volume here
https://brainly.com/question/29373895
#SPJ4
QUESTION 2 1 POINT
A stock broker allocated $100,000 to an account earning 4% per year compounded continuously. If no withdrawals are
made, how much was in the account at the end of four years? Round the answer to nearest dollar.
Answer: 16,000
100,000 x 0.04 x 4
p x I x T.
Can somebody help me on this
Answer:
Ummm I dont even kno but s1
Step-by-step explanation:
-5(13d+ 11) how can i simplify this?
Answer:
-65d - 55
Step-by-step explanation:
Given expression,
→ -5(13d + 11)
Simplifying the expression,
→ -5(13d + 11)
→ (-5 × 13d) + (-5 × 11)
→ -65d + (-55)
→ -65d - 55
Thus, answer is -65d - 55.
Question 3 (2 points)
2
-2 -1
3-
1
-1+
-2+
-3
1 2 3
The function f(x)is graphed on the coordinate plane.
What is f(4)?
Enter your answer in the box.
f(4) =
The value of f(4) = 0 by the given graph.
What is graph?
Graph is diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Given graph is straight line, and the equation of line is given as
y =mx+b
where m is the slope and as we know y is dependent variable,
we can write it as
f(x)= mx +b
The coordinates are (4,0) and (0,2)
m = 2-0/0-4
m = -1/2
y = -1/2 x +b
we can see the line intersect the y-axis at 0,2
b =2
y = -1/2 x +2
at x =4
f(4) = -2+2=0
To know more about graph, visit:
https://brainly.com/question/6320133
#SPJ1
Look at the linear expression:
. 4a-4+6a-11
What are the like terms in the expression?
:
The like terms to the Linear expression: 4a-4+6a-11 is 10a - 15
What is linear expression?A Linear equations are the equations of degree 1. It is the equation for the straight line.
Collect the like terms of the expression
4a +6a -4 -11
Add the like terms
10a -15
Therefore the like terms in the linear expression is 10a -15
Learn more about linear expression here; https://brainly.com/question/12788590
#SPJ1
Claudia buys 12 postcards, 12 stamps, and 1 pen. The postcards cost twice as much as the stamps. The pen costs $14.10. How much does each postcard cost? Show your work.
According to the unitary method, the cost of each postcard is $0.7.
Unitary method:
Unitary method is used to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
Given,
Claudia buys 12 postcards, 12 stamps, and 1 pen. The postcards cost twice as much as the stamps. The pen costs $14.10.
Here we need to find the cost of the postcard.
In the given question, we have two variables, the price of the postcard and the price of the stamp, since the price for the pen is known.
And we also have the total cost of the purchase that is $14.1.
Therefore, now we have to create an equation as shown:
=> (12 x postcards) + (12 x stamps) + pen = 14.1
This equation refers the total amount spent by Claudia, but here we know that each pen costs $1.5, therefore:
When we apply the value on the equation then we get,
=> (12 x postcards) + (12 x stamps) + 1.5 = 14.1
=> (12 x postcards) + (12 x stamps) = 14.1 - 1.5
Therefore, (12 x postcards) + (12 x stamps) = 12.6
Here we also know that the postcards cost twice as much as the stamps, Then it can be written as,
postcards = 2 x stamps
By apply this value on the equation then we get the value of the stamp as,
=> (12 x (2 x stamps)) + (12 x stamps) = 12.6
=> (24 x stamps) + (12 x stamps) = 12.6
=> 36 x stamps = 12.6
Then the value of on stamp is stamps = 12.6/36
Therefore, the value of the stamps is 0.35
When we apply these values, then we get,
postcards = 2 x stamps = 2 x 0.35 = 0.7
Therefore, each postcard cost $0.7.
To know more about Unitary method here.
https://brainly.com/question/21648365
#SPJ1
if electricity power failures occur according to a poisson distribution with an average of 3 failures over 4 weeks, what is the probability that there will be 4 failure during a particular week. what is e[x] are v(x)?
The probability that there will be 4 failure in particular week is 0.00622.
e(x) = 0.75 = v(x)
Given,
If electricity power failures occur according to a Poisson distribution with an average of 3 failures over 4 weeks, what is the probability that there will be 4 failures during a particular week?
To know e(x) are v(x);
From the given info,
So 3/4 failure per 4/4 weeks.
That means on average 0.75 failures per week.
The probability that there will be 4 failure in particular week,
[tex]\frac{e^{-0.75}0.75^{4}}{4!}=\frac{0.4723*0.3164}{24}=0.00622[/tex]
e(x) = Average = 0.75
Poisson distribution have mean and variance same.
So v(x) = 0.75
Hence, the probability that there will be 4 failure in particular week is 0.00622.
e(x) = 0.75 = v(x)
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
please help me this is geometry
Answer:
largest angle is angle L
Step-by-step explanation:
the angle across the largest side of the triangle is the largest angle
A manufacturing machine has a 7% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect?.
A manufacturing machine has a 7% defect rate. If 4 items are chosen at random,
The probability of randomly choosing atleast one defective item would be 0.3043
Given the Parameters :
Defect rate = P(defect) = 0.07
Probability = required outcome / Total possible outcomes
P(atleast 1 is defective) = 1 - P(none is defective)
P(not defective) = 1 - P(defective) = 1 - 0.07 = 0.93
P(none is defective) = P(non defective)^4
P(none defective) = 0.93 × 0.93 × 0.93 × 0.93 = 0.7480
P(atleast one is defective) = 1 - 0.7480 = 0.252
Therefore, probability of atleast one defective item is 0.252.
Hence the answer is, the probability of randomly choosing atleast one defective item would be 0.3043
To Learn more about probability click here https://brainly.com/question/24756209
#SPJ4
2 1/4 x 3 1/5 answer for the following as a fraction
Answer:
I don't know which one you needed so here you go.....
144/20 (improper fraction version)
7 4/20 (Mixed number answer.) 7 1/5 (Mixed number version simplified)
36/5 (Simplified improper fraction version)
Step-by-step explanation:
2 1/4. I'm going to multiply 4 and 2 which is 8. Then I'll do 1+8=9 so now I can put the 9 on top so it's going to look like this 9/4.
3 1/5. I'm going to multiply 5 and 3 which is 15. Then I'll do 15+1=16 so now I can put the 16 on top and it's going to look like this 16/5.
Now that we have our two numbers (numbers that are bolded), let's multiply them. So first we want to multiply the numerators so 16*9=144. So 144 is going to be the numerator to our answer.
Since we have multiplied the numerator we now multiply the denominators by each other so, 5*4=20
So our answer is going to be 144/20 (improper fraction version)
Or 7 4/20 (Mixed number answer.)
Hope this helps!!! (Please mark me brainliest)
PLEASE HELP! I NEED THIS BADLY! Is (x-3) a factor of 2x^3-4x^2-6?
YES OR NO?
find the remainder of 2x^3-4x^2-6
(just type the answer!)
Answer: 1. no 2. 104
Step-by-step explanation:
\sum _{n=1}^{9}(7n-17)
n=1
∑ (7n−17)
9
Answer:
162
Step-by-step explanation:
You want the sum of the first 9 terms described by ...
a[n] = 7n -17
Add the termsThere are several ways the sum can be found. Most straightforward is simply adding up the terms:
For n=1, 7n-17 = -10
For n=2, 7n -17 = -3
The remaining 7 terms are 4, 11, 18, 25, 32, 39, 46.
The sum is ...
-10 -3 +4 +11 +18 +25 +32 +39 +46 = 162
Arithmetic sequenceThe terms form an arithmetic sequence with first term -10 and last term 46. The sum will be the average term multiplied by the number of terms:
((-10 +46)/2)(9) = 18(9) = 162
Sum formulasThe sum can be decomposed into the sums whose formulas we know:
[tex]\displaystyle \sum_{n=1}^9(7n-17)=7\sum_{n=1}^9{n}-17\sum_{n=1}^9{1} =7\cdot\left.\dfrac{n(n+1)}{2}-17n\right|_{n=9}\\\\= 7\cdot\dfrac{9\cdot10}{2}-17(9)=315-153=\boxed{162}[/tex]
Please help hurry it is worth 12 points if you help me solve
Answer:
Since [tex]s=\frac{3}{4}ft[/tex],
27 ÷ s² = 27 ÷ [tex](\frac{3}{4})^{2}[/tex]
= 27 ÷ [tex]\frac{9}{16}[/tex]
= [tex]\frac{27}{1}[/tex] × [tex]\frac{16}{9}[/tex]
= 48
∴ Mr Grant would need to buy 48 of such square tiles.
Step-by-step explanation:
what that simply means is that the area he needs the files for is 27 ft².
as the tiles are squares, each one has an individual area of s² = 3/4 × 3/4 = 9/16 ft²
how many tiles do we need ?
as b many as how often the area of one tile fits into the total area :
27 ÷ s² = 27 / 9/16 = 27/1 / 9/16 = 27/1 × 16/9 =
= 3/1 × 16/1 = 3×16 = 48
he has to buy 48 tiles.
Suppose the length and width of the rectangle are doubled. What effect would this have on the area? Justify your answer.
The area is increased by 204 ft².
What is rectangle?
A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Initial length l= 4 ft
Initial width l= 17 ft
Area = l*w = 4*17 = 68 ft²
When length and width of the rectangle are doubled:
l=2*4=8 ft
w= 2*17= 34 ft
Area= 8*34= 272 ft²
Difference = 272 - 68 = 204 ft²
Thus, the area is increased by 204 ft².
To learn more about the rectangle from the given link
https://brainly.com/question/25292087
#SPJ1
I need assistance working these problem out.
Inverse [tex]f^{-1}(x) = \frac{log(x)}{log7}[/tex] and [tex]f(x) = 10^{x}[/tex].
[tex]f(x) = 7^{x}[/tex]
First, replace f(x) with f(y).
Now, [tex]y = 7^{x}[/tex] will become [tex]x = 7^{y}[/tex]
Taking log on both sides,
log(x) = y(log 7)
y = log(x)/log 7.
Similarly, [tex]f^{-1}(x) = log_{10}x[/tex]
replace f(x) with f(y).
[tex]x = f^{-1}(y) = log_{10}y[/tex]
[tex]y = 10^{x}[/tex]
Hence, [tex]f(x) = 10^{x}[/tex].
To learn more about Inverse here:
https://brainly.com/question/13715269
#SPJ1
Using your work from the first problem on Tuesday find the area of the triangle if x=3/2 and the height of the triangle was 6x+10. Help me please!!
If the height of the triangle is (6x + 10) and the base of the triangle is (3/2) the area of the triangle is 14.25 square units.
What is the area of the triangle?
The area of a triangle is the region bounded by its perimeter or its three sides.
If the height of the triangle is 'h' and the base is 'b', the area of the triangle would be
Area = 1/2 × height × base
The base of the triangle is x = 3/2.
Height of the triangle = 6x + 10 = 19.
Area of triangle = 1/2×3/2×19
= 14.25 square units.
Hence, If the height of the triangle is (6x + 10) and the base of the triangle is (3/2) the area of the triangle is 14.25 square units.
To learn more about the area of the triangle visit:
https://brainly.com/question/17335144
#SPJ9
A cable on a fishing boat lowers a fish trap into a lake at a rate of 3 1/2 feet per second. What is the change in depth of the fish trap after 12 seconds?
Answer:
After 12 Seconds the cable would be 42 Ft down in depth
Step-by-step explanation:
3 1/2 Ft = 1 Second
3 1/2 Ft x 12 Seconds = 42Ft in Depth
The change in the depth of the fish trap after 12 second is 30 feet.
What is multiplication?The mathematical operation of multiplication is arithmetic. Additionally, it involves repeating the same forms of statements.
Example: 2 + 3 signifies that 2 is multiplied by 3 or that 3 is multiplied by 2 times.
Given, a cable on a fishing boat lowers a fish trap into a lake at a rate of 3 1/2 feet per second.
[tex]3\frac{1}{2}[/tex] = 5/2 feet per second.
To find the change in depth of the fish trap after 12 seconds:
Multiplied by 12 to the rate of feet per second.
5/2 x 12
= 30 feet
The change of rate is 30 feet per 12 second.
Therefore, the change in depth is 30 feet per 12 second.
To learn more about the multiplication;
https://brainly.com/question/19634536
#SPJ2
Select the best answer for the question.
15. A basketball team's free-throw percentage (FT%) is calculated using two other statistics: their free throws attempted (FTA) and free throws made
(FTM). Which of these shows the correct formula?
O A. FT% = FT/FTM* 100%
O B. FT% = FT/FTA * 100%
O C. FT% = (FTM-FTA) * 100%
O D. FT% = (FTA-FTM)* 100%
The correct formula to represent the free throw percentage for the basketball team is given by FT% = FTM/FTA × 100%
The percentage of any quantity is measured by multiplying the ratio of the successful amount and the total amount by 100.
Here
Total number of free throws attempted = FTA (this is the total amount)
Total number of free throws made = FTM (this is the successful amount)
Required percentage = (FTM / FTA ) × 100%
Hence the required correct option is the second one:
FT% = FTM/FTA × 100%
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100. It is a relationship, in other words, where the value of the whole is always taken to be 100.
Calculating a percentage in terms of 100 is known as calculating a percentage. You can determine a percentage in one of two ways:
We employ a unitary method by changing the denominator of the fraction to 100.
To learn more about percentage visit:
https://brainly.com/question/12334060
#SPJ1
The picture shows 2 questions (separated with the long straight line)
X = - 4
Pleade help me
Answer:
4[tex]x^{4}[/tex]
6[tex]x^{5}[/tex]
Step-by-step explanation:
For the first problem. I am not sure what is going on with the -4. Is it being added or multiplied by 2[tex]x^{2}[/tex]? I left it out.
[tex](2x^{2}) ^{^{2} }[/tex] means 2[tex]x^{2}[/tex] (2[tex]x^{2}[/tex]) Which is 4[tex]x^{4}[/tex]
(2[tex]x^{2})\\[/tex]([tex]3x^{3)}[/tex] multiple the 2 and the 3 and add the exonents
6[tex]x^{5}[/tex]
Solve for x. 3x^3/5 +6=30
x = [tex]\sqrt[3]{40}[/tex] = 3.42 ( approx.) is the value of x by given equation .
What are exponents ?We often read numbers in words like hundred, thousand, hundred thousand, and ten million. Which number has more digits than we can read? For example, the mass of the Earth is 5972190000000000000000000 kg. This cannot be read in simple words. Therefore, exponents are used to pronounce these kinds of numbers.
Exponents can be observed in four different types: positive, negative, zero, and rational/fractional. Numerical values can be interpreted using exponents as the total number of times a base must be multiplied by the same base.
Calculation3x^3/5 = 24
3x^3 = 120
x^3 = 40
x = [tex]\sqrt[3]{40}[/tex] = 3.42 ( approx.)
learn more about exponents here :
brainly.com/question/5497425
#SPJ13
Andy says that all rectangles with an area of 24cm² have the same perimeter
Show that Andy is wrong.
Answer:
no because area is multiplication, but perimeter is adding.
SHOW WORK FOR BRAINLIST
Answer:
Below
Step-by-step explanation:
Graph the two lines....where they intersect is the solution:
(-4,3)
OR sub in x = -4 into the first equation to find y = 3
100 POINTS!
PLEASE ANSWER FAST
y=8x+1 in standard form step by step
Answer: y = 8
Step-by-step explanation:
Answer: -8x+y=1
Step-by-step explanation:
Standard form is Ax+By=C
y=8x+1
Move the 8x to the other side of the equation.
y-8x=1
-8x+y=1
A camera store develop 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls. What is the ratio of rolls with double prints to rolls develop?
A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls, then the ratio of rolls with double prints to rolls develop would be 5:7.
What is the ratio in mathematics?
A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.
A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls.
Then the ratio of rolls with double prints to develop = 1500/2100
Simplifying the above ratio we get
= 5/7
Hence, the ratio of rolls with double prints to rolls develop would be 5:7.
To learn more about ratios, visit:
https://brainly.com/question/12024093
#SPJ9
A taxi company charges a flat fee of $5.50 plus an additional $1.50 per mile. Write an equation in slope-intercept form that represents the total cost, c, of a ride that is m miles long.
Two buildings are 18.5 meters apart. The angles of elevation from the top of one building to the top of the other is 18 degrees. If the taller building is 15 meters tall, how tall is the shorter building?
Answer: 9m
Step-by-step explanation:
If we draw a right triangle, we can get a triangle with an angle of 18 degrees and a base of 18.5m. To get the height, we would do TOA or tan = opp / adj:
tan18 = x / 18.5
Multiply both sides by 18.5 to isolate x:
x = 18.5 * tan18
x = 6m (approximately)
This means that the taller building is 6 meters taller, so:
15m - 6m = 9m
Ariany run a farm tand that ell grape and apple. Each pound of grape ell for $3. 75 and each pound of apple ell for $4. Ariany made $251. 75 from elling a total of 64 pound of grape and apple. Determine the number of pound of grape old and the number of pound of apple old
Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
pound apple cost = 0.60 dollar1 pound of grapes cost = 1 dollarTotal fruits bought = 12 poundsTotal money paid = 10 dollarsTotal grapes that can be bought with 10$ = 10/1Pounds = 10Total apple that can be bought with 10$ = 10/0.6Pounds = 16.66To buy 12 pounds of fruit in 10 dollars each pound cost = 12/10= 1.2$ per poundRatio of grapes and apple in 12 pound fruits = 1/0.6= 1 : 1.6Apples in 12 pounds = 0.6×5Cost = 3$Grapes in 12 pounds = 1×7Cost = 7$Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
in a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (round your answers to four decimal places.) if a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
The probability that the player will receive a blackjack from a player is dealt 2 cards from a standard deck of 52 well-shuffled cards is 0.0483.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
Combinations of drawing 1 ace * combinations of drawing 1 face cards / all possible 2 card combinations
4C1 * 16C1 / 52C2
4 * 16 / (52 * 51/2)
=64/1326
=.0483
When a player is dealt two cards from a standard deck of 52 properly shuffled cards, the likelihood that they will get a blackjack is 0.0483.
To know more about probability,
https://brainly.com/question/11034287?referrer=searchResults
#SPJ4
solve each system by substitution 5x+4y=-16 y= 2x+9 what is the anwser
x=-20/13 and y=77/13 are solutions of 5x+4y=-16 and y= 2x+9
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
5x+4y=-16 ...(1)
Five x plus 4 y equal to minus sixteen.
y= 2x+9 ...(2)
y equal to two times of x plus nine.
Substitute 2 in 1.
5x+4y=-16
5x+4(2x+9)=-16
5x+8x+36=16
13x+36-16=0
13x+20=0
13x=-20
x=-20/13=-1.53
substitute the value of x in y.
y=2(-20/13)+9
y=(-40+117)/13
y=77/13
Hence the value of x is -20/13 and y value is 77/13.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
The midpoint of a segment with endpoints (10, a) and (b, 6) is (-1, -1). What are the values of a and b?
A. a=12, b=6
B. a=-8, b=-12
C. a= 12, b=-8
D. a= -12, b=-8
Applying the midpoint formula, the values of a and b are:
B. a = -8, b = -12
How to Apply the Midpoint Formula?The midpoint formula is used to find the coordinates of the midpoint of a segment, which is given as:
M(x, y) = [tex](\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].
Given the points below:
(10, a) = [tex](x_1, y_1)[/tex]
(b, 6) = [tex](x_2, y_2)[/tex]
M(-1, -1) = (x, y)
Plug in the values:
(-1, -1) = [(b + 10)/2, (6 + a)/2]
Solve the variables separately
-1 = (b + 10)/2
-2 = b + 10
-2 - 10 = b
b = -12
-1 = (6 + a)/2
-2 = 6 +a
-2 - 6 = a
a = -8
The answer is: B. a = -8, b = -12
Learn more about midpoint formula on:
https://brainly.com/question/13115533
#SPJ1
