A) A polynomial function in factored form modeling the volume V of the box is; V(x) = x²(20 - x)
B) The maximum possible volume of the box is; 1185.19 in³
C) The way the maximum possible volume is found is by finding the derivative and equation to zero. Thereafter, we substitute the value into the first equation.
How to Maximize Volume?The formula for volume of a rectangular box is;
V =L * W * Height
Where;
L is length
W is width
H is height
We are given;
Height; h
Square base and so;
L = W = x
Thus, the volume is;
V = (x)(x)(h)
The combined length of a side of the square base and the height is 20 in. Thus; x + h = 20
h = 20 - x
Thus, volume is;
V(x) = x²(20 - x)
2) The expanded form of the volume is; V(x) = 20x² - x³
dV/dx = 40x - 3x²
The function has maxima and minima when dV/dx = 0. Thus;
40x - 3x² = 0
Solving for x gives;
x = 0 or 40/3
Maximum possible volume is;
V(40/3) = 20(40/3)² - (40/3)³
V(40/3) = 1185.19 in³
c) The way the maximum possible volume is found is by finding the derivative and equation to zero. Thereafter, we substitute the value into the first equation.
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Greg collected cash donations for a local food bank as part of a service project. He collected
$400 altogether. He had expected to collect 37.5% less than that. How much money had
Greg expected to collect?
Answer:
$250
Step-by-step explanation:
He expected to collect 37.5% less than $400.
First, we find 37.5% of $400.
Then we subtract that amount from $400.
37.5% of $400 is:
37.5% of $400 = 0.375 × $400 = $150
Now, subtract $150 from $400:
$400 - $150 = $250
Answer: $250
help me please , i dont kow what to type for this
Given RWS~TUV find the values of x and y
The values of x and y will be 10 and 4 respectively, using congruent of the triangle.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Here, ΔRWS ≅ ΔTUV
Here 2y + 10 = 30
2y = 30-10
y=20/2
y=10.
Agian ∠R = ∠T
Here ∠T = 90 -32 =58°
So 8x+26 = 58°
8x = 58-26
x = 32/8
x = 4.
Hence the values of x and y will be 10 and 4 respectively.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 5. If there were 6412 yes votes, what was the total
number of votes?
The total number of votes which is reduced by the ratios of yes and no votes will be: 4580; + 6412 = 10992;
What are Ratios?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the part to the whole is 5: 10, meaning that 5 out of every 10 people enjoy reading.
In the given question, we have:
The ratio of yes votes to no votes was 7 to 5.
Total Number of Yes votes = 6412;
So, Let us assume the total number of no votes be x;
So, according to the question,
[tex]\frac{7}{5} = \frac{6412}{x}[/tex]
Cross Multiplying the terms:
⇒7 × x = 6412 ×5
⇒x = 4580;
So, The total number of no votes is 4580;
So, The total number of votes will be: 4580; + 6412 = 10992;
Hence,
The total number of votes will be: 4580; + 6412 = 10992;
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Help please please please please
Answer:
Step-by-step explanation
TS=13 as opp sides in an isosceles triangle are equal
AngleT=60
as 60+60+T=180
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x = 10 + y
-3x + y = -28
We know that:
x = 10 + y
In the next equation {-3x + y = -28} x is the same as the first, so:
-3(10 + y) + y = -28
-30 - 3y + y = -28
-30 - 2y = -28
We add 30 to both sides:
-2y = 2
and divide both sides by (-2):
y = -1
Now we can put y = -1 to the first equation:
x = 10 + y
x = 10 - 1
x = 9
So,
the solution of this system of equations is: (9, -1)Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.
The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .
In the question ,
it is given that ,
the equation is given as |y [tex]+[/tex] 6| [tex]=[/tex] 2 ,
after removing the modulus , we get the two equations , that are
y + 6 = 2 and y + 6 = -2
Solving y + 6 = 2 , we get
y + 6 = 2
Subtracting 6 from both LHS and RHS ,
we get
y = 2 - 6
y = -4
On Solving y + 6 = -2 ,
we get
y + 6 = -2,
Subtracting 6 from both LHS and RHS ,
we get
y = - 2 - 6
y = -8 .
the two solutions are y = -8 and y = -4 .
Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .
The given question is incomplete , the complete question is
Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.
(a) There will be one solution
(b) There will be two solutions.
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Find the measure of angle L?
Answer:
C. 137======================
Sum of interior angles of 6-sides polygon is:
S = 180(6 - 2) = 180*4 = 720Set equation for the sum of interior angles and solve for x:
120 + 90 + 5x + 7x - 3 + 6x - 7 + 8x = 720200 + 26x = 72026x = 520x = 20Find the measure of angle L:
7x - 3 = 7*20 - 3 = 140 - 3 = 137Correct choice is C.
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ (120)+(8x)+(6x-7)+\stackrel{\measuredangle L}{(7x-3)}+(5x)+\stackrel{\measuredangle O}{(90)}=720\implies 26x+200=720 \\\\\\ 26x=520\implies x=\cfrac{520}{26}\implies x=20~\hfill \underset{\measuredangle L}{\stackrel{7(20)~~ - ~~3}{\text{\LARGE 137}}}[/tex]
Two triangles are shown in the figure. are the triangles similar, and why?
Answer:Yes, the obtuse angles for both triangles are equailateral
Step-by-step explanation:
The dimensions of a right rectangular prism are (8)/(5)cm,(10)/(3)cm, and (7)/(4)cm.
What is the volume of the prism?
A. (25)/(12)cm^(3)
B. (7)/(3)cm^(3)
C. (16)/(3)cm^(3)
D. (28)/(3)cm^(3)
Please help
If the dimensions of a right rectangular prism are (8)/(5)cm,(10)/(3)cm, and (7)/(4)cm. Then volume of the prism is 401/60 cm³
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases
The dimensions of a right rectangular prism are width is 8/5 cm, Length is 10/3cm and Height is 7/4cm
Volume=Width×Height×Length
=8/5×10/3×7/4
=96+200+105/60
=401/60 cm³
Hence volume of the right rectangular prism is 401/60 cm³
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Use the order of operations to evaluate 1 fourth + 1 third (10 − 1).
Answer:
[tex]\frac{13}{4}[/tex]
(Decimal: 3.25)
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Answer:
5.25
Step-by-step explanation:
1/4+1/3(10-1)
*do what's in parenthesis first!*
10 - 1 = 9
1/4 + 1/3 = 7/12
then you multiply 7/12 x 9 = 5.25
DONT FORGET!
Please Excuse My Dear Aunt Sally
P E M D A S
(100 points and brainly)
Which expression is equivalent to (6^−2 • 3^5)^−2?
three raised to the third power divided by six raised to the fourth power
negative three raised to the third power divided by six raised to the fourth power
six raised to the fourth power divided by three raised to the tenth power
negative six raised to the fourth power divided by three raised to the tenth power
Answer: 16\/729
Step-by-step explanation:
Answer:
six raised to the fourth power divided by three raised to the tenth power
Step-by-step explanation:
(6^−2 • 3^5)^−2 = 6^(-2*-2) * 3^(5*-2) = 6^4 * 3^(-10) = 6^4 / 3^10
hanna properties specializes in custom-home resales in an exclusive subdivision of phoenix, arizona. a random sample of nine custom homes currently listed for sale is provided in the following table, in size (hundreds of square feet) and price of the home (thousands of dollars):the data is shown in the following table: square feet 26 27 33 29 29 34 30 40 22 price 259 274 294 296 325 380 457 523 215 if you wanted to predict the sales price based upon square footage for homes in this subdivision, what would be the slope of the least squares regression line? a. approx 15.89 b. approx -140.00 c. approx 0.68 d. none of the above
To determine what satisfying assumptions 1-3 would mean by considering the variable under consideration.
The regression-inference Assumptions 1-3 must be satisfied if β°, β¹ and σ are constants, which ensures the x dimensions and price of every custom home to be normal, with β° + β¹ and a σ standard deviation.
The residuals should not be linear if the normal probability plot is followed.
In the diagram above, the assumptions for regression inferences appear to be unsatisfactory.
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There are nine red marbles and five blue marbles in a bag what is the ratio of red marbles to blue marbles??? what is the ratio of blue marbles to all marbles in the bag ???
Answer:
9:5
5:14
Step-by-step explanation:
Write the polynomial in standard form g(x) = 3(x + 2)(4x - 1)(x - 5)
12x³ - 39x² - 111x + 30 is polynomial in standard form .
What in mathematics is a polynomial?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents.
standard form g(x) = 3(x + 2)(4x - 1)(x - 5)
g(X) = 3[ 4x² - x + 8x - 2 )( x - 5 ) ]
= 3[ ( 4x² + 7x - 2 ) ( x - 5 )]
= 3 [ 4x³ + 7x² - 2x - 20x² - 35x + 10 )]
= 3[ 4x³ - 13x² - 37x + 10 ]
= 12x³ - 39x² - 111x + 30
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[tex]\sqrt{\frac{36}{\:81}}[/tex]
Answer:
2/3
Step-by-step explanation:
Since 6 *6 = 36 , the square root of 36 is 6
In other words:
[tex]\sqrt{36} \\= 6\\[/tex]
Since 9*9 = 81, the square root of 81 is 9
[tex]\\\/\sqrt{81}\\ = 9[/tex]
Now we have the fraction [tex]\frac{6}{9}[/tex]
Now we reduce [tex]\frac{6}{9}[/tex] to lowest terms:
[tex]\frac{6}{9 } = \frac{2}{3}[/tex]
Therefore, the answer is [tex]\frac{2}{3}[/tex]
Hope this helps :)
Which of the following is NOT a valid arrangement of 24 flowers?
Four rows of six flowers.
Two rows of twelve flowers.
Four rows of nine flowers.
Eight rows of three flowers.
Complete the equation of the line through 6, -6 and 8,8
slope = m = (8 - (-6)) / (8 - 6) = 7
y = mx + b
y = 2x + b
plug in (8, 8) to find b
8 = 2(8) + b
b = -8
y = 2x - 8
17. A group of 36 people attended a ball game. There were twice as many children as adults in the group. Set up a
system of equations that represents the numbers of adults and children who attended the game and solve the
system to find the number of adults and the number of children who were in the group.
Answer:
36 = 2x + y
x = y
x = 12
y = 12
Step-by-step explanation:
Answer:A=12 C=24
Step-by-step explanation:
there are 3 shares[2x and theunknown]
36=3shares so 1 share=36divided by3=12
ad=12
ch=12x2=24
12+24=36
5/If AB is 12, what is the
length of A' B'?
B
3
40°
B'
A
2
6
A'
4
C
Answer:
8
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so:
[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]
What are the answers to this ?! Help plsssss.
ONLY ANSWER IF YOU KNOW ! ANY OTHER ANSWERS WILL BE REPORTED.
We must combine 3 servings of Ta-sty Pocket, 2 serving of P-ita Roll, and 1 serving of In-sta Pancake to get 754 calories, 19.2 g of f-at, and 78.9 g of carbohydrates.
According to the question,
Three brands of breakfast food represents the calories , f-at, and carbohydrates.
To get 754 calories, we should combine
= 450 + 238 + 66
= 3 (150) + 2 ( 119) + 1 (66)
= 3 serving of Ta-sty Pocket + 2 serving of P-ita Roll + 1 serving of In-sta Pancake
To get 19.2g of f-at, we should combine
= 14.4 + 4.6 + 0.2
= 3(4.8) + 2( 2.3) + 1(0.2)
= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake
To get 78.9 g of carbohydrates, we should combine
= 29.4 + 28 + 21.5
= 3(9.8) + 2( 14) + 1 (21.5)
= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake
Hence, we should combine 3 serving of Tasty Pocket, 2 serving of P-ita Roll, 1 serving of In-sta Pancake
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Please answer this. I’ve been stuck on it for 30 mins
Using the GCF to factor and the distributive property 28 + 24 = 4(7 + 6)
How to write numbers as a factor using the greatest common factor?28 + 24 as a product of the two factors using greatest common factor and the distributive property can be represented as follows:
The greatest common factor is defined as the largest number that is a factor of two or more numbers.
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
Therefore, lets solve 28 + 24 using GCF and the distributive property.
The GCF of 28 and 24 is 4. Hence,
28 + 24 = 4(7 + 6)
Therefore,
28 + 24 = 4(7 + 6)
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i need help bru dis is mh last try
What is the inverse of ƒ (x) = (2x + 1)² for x ≥ −½1⁄?
The inverse of the given function is (f^-1)(x) = (1/2)×(√x - 1) for x ≥ 0.
We are given a function f(x). The function f(x) is defined as (2x + 1)². The domain of the given function f(x) is x ≥ -1/2. We need to find the inverse of the function f(x).
Let us suppose that the function f(x) is represented by the variable "y".
y = f(x)
y = (2x + 1)²
Now we will take the square root on both sides of the equation.
√y = √[(2x + 1)²]
When we cancel out the even powers, we need to take the absolute value using modulus.
√y = |2x + 1|
We already know that x ≥ -1/2, so, modulus will open with a positive sign.
√y = +(2x + 1)
√y = 2x + 1
√y - 1 = 2x
x = (1/2)×(√y - 1)
At last, we replace the variables y and x by x and (f^-1)(x).
(f^-1)(x) = (1/2)×(√x - 1) for x ≥ 0
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In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and four shirts cost $55, while four sweaters and five shirts costs $110, find the price of one sweater and the price of one shirt.
Price of one shirt: $10Price of one sweater: $15Step-by-step explanation:
The price of one sweater - x
The price of one shirt - y
From what the problem states, we can assume:
x + 4y = 55
4x + 5y = 110
Multiply both sides of x +4y = 55 by four. This results in 4x + 16y = 220. We then subtract 16y on both sides, resulting in 4x = 220 - 16y. We then insert this into the other equation, which, as a reminder, is 4x + 5y = 110. We replace 4x with 220 - 16y, which results in 220 - 16y + 5y = 110. Now, we can solve it.
220 - 16y + 5y = 110220 - 11y = 110110 - 11y = 0110 = 11yy = $10Now that we have found out the value of y, we can replace all instances of y in the first equation.
x + 4y = 55x + 40 = 55x = $15
What is the slope of the ramp shown in the diagram below?
O A.
OB.
3
10
OD.
C. -1/3
ო|e Pm p|ო
3
10
According to the Pythagoras theorem, the value of the slope of the ramp is 10.44
Pythagoras theorem
Pythagoras theorem states that the sum of squares of the sides equal to the square of the hypotenuse.
The general form of the Pythagoras theorem is,
c² = a² + b²
where
c refers the hypotenuse
a and b refers the sides of the triangle.
Given,
Here we have the ramp with the side values 3 and 10.
Now, we have to find the value of the slope.
Let us consider x be the hypotenuse or slope of the ramp.
We know that the Pythagoras theorem states that the square of the hypotenuse is equal to the sum of square of the sides.
So, it can be written based on these,
x² = 3² + 10²
x² = 9 + 100
x² = 109
x = √109
When we simplify this one then we get the value of slope as 10.44.
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Use the model below to estimate the average annual growth rate of a certain country’s population for 1950, 1988, and 2010, where x is the number of years after 1900.
y= -0.0000081x^3+0.00267x^2+8.231
The growth rates in 1950, 1988 and 2010 are 13.9%, 23.4 and 29.8% respectively
How to estimate the country's population?The function of the growth rate equation is given as:
y = -0.0000081x^3+0.00267x^2+8.231
Rewrite properly
So, we have
y = -0.0000081x³ + 0.00267x² + 8.231
From the question, we have
x represents the number of years after 1900
In 1950, x = 50
So, we have
Growth rate in 1950, y = -0.0000081 x 50³ + 0.00267 x 50² + 8.231
Growth rate in 1950, y = 13.9
In 1988, x = 88
So, we have
Growth rate in 1988, y = -0.0000081 x 88³ + 0.00267 x 88² + 8.231
Growth rate in 1988, y = 23.4
In 2010, x = 110
So, we have
Growth rate in 2010, y = -0.0000081 x 110³ + 0.00267 x 110² + 8.231
Growth rate in 2010, y = 29.8
Hence, the growth rate in 2010 is 29.8%
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what is the prime factorization of 540
WHO EVER GETS IT RIGHT WILL GET TO BE THE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
540= 2x2x3x3x3x5
or
540= [tex]2^{2}[/tex]x[tex]3^{3}[/tex]x5
Step-by-step explanation:
Given the function f(x) = 3x2+2x+4, find f(−2). You must show at least 3 lines of work.
Solving for f(-2) in the function f(x) = 3x^2 + 2x + 4 gave the solution
f(-2) = 12How to calculate for f(-2)From the given function f(x) = 3x^2 + 2x + 4 we substitute for x = -2 which is same as function of -2
f(x) = 3x^2 + 2x + 4
pugging in x = -2
f(-2) = 3(-2)^2 + 2(-2) + 4
solving the squared and opening the parentheses
f(-2) = 3 * 4 + -4 + 4
f(-2) = 12 - 4 + 4
f(-2) = 12
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Jane and Jill collect yo-yos. The ratio of the number of Janes yo-yos to the number of JIlls yo-yos is 5:4. If jane will give 15 of her yo-yos to her little brother, Jane and Jill will have the same number of yo-yos in their collections. How many yo-yos do both girls have together?
Answer:
5u - 4u = 1u
1u = 15
9u = 135
∴ Both girls have 135 yo-yos together.
A customer withdrew $45 from a bank account. The customer then deposited $150 into the bank account the next day. Write an equation to show the net effect of these transactions. What is the equation?
The equation to show the net effect of these transactions is x - 45 + 150.
The equation is x + 105.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the customer withdrew $45 from a bank account and the customer then deposited $150 into the bank account the next day.
Let the initial amount in the account be x. The amount after the transaction will be:
= x - 45 + 150
= x + 105
The equation is x + 105.
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