Answer:
The size square removed from each corner = 32.15 cm²
Step-by-step explanation:
The volume of the box = Length * Breadth * Height
Let r be the size removed from each corner
Note that at maximum volume, [tex]\frac{dV}{dr} = 0[/tex]
The original length of the cardboard is 119 cm, if you remove a size of r (This typically will be the height of the box) from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:
Length, L = 119 - 2r
Similarly for the breadth, B = 24 - 2r
And the height as stated earlier, H = r
Volume, V = L*B*H
V = (119-2r)(24-2r)r
V = r(2856 - 238r - 48r + 4r²)
V = 4r³ - 286r² + 2856r
At maximum volume dV/dr = 0
dV/dr = 12r² - 572r + 2856
12r² - 572r + 2856 = 0
By solving the quadratic equation above for the value of r:
r = 5.67 or 42
r cannot be 42 because the size removed from the corner of the cardboard cannot be more than the width of the cardboard.
Note that the area of a square is r²
Therefore, the size square removed from each corner = 5.67² = 32.15 cm²
In the equation, the value of a is:
Answer:
Please check if the answer is a = 4 or not
The graph of an absolute value function has a vertex of (2,3) and crosses the x-axis at (−1,0) and (5,0). What is the equation for this absolute value function when y=0? A 0=|x+2|+3 B 0=|x−2|+3 C 0=−|x+2|+3 D 0=−|x−2|+3
Answer:
Option D.
Step-by-step explanation:
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex]
where, a is a constant, (h,k) is vertex.
It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.
[tex]y=a|x-2|+3[/tex] ...(1)
It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.
[tex]0=a|5-2|+3[/tex]
[tex]-3=3a[/tex]
[tex]-1=a[/tex]
Put a=-1 in (1).
[tex]y=(-1)|x-2|+3[/tex]
[tex]y=-|x-2|+3[/tex]
Now, put y=0, to find the equation for this absolute value function when y=0.
[tex]0=-|x-2|+3[/tex]
Therefore, the correct option is D.
Answer:
I got this question on my test and I answered D cause if you look up the graph it matches the question
Step-by-step explanation:
D 0=−|x−2|+3
Question 15
1 pts
The cost of three avatars and three bats is $29.85. The cost of
three avatars and two bats is $23.90. How much will you pay
altogether if you purchase one of each.
O $5.95
O $8.92
$9.95
O $10.99
O $11.00
1 pts
Question 16
9
Answer:
$9.95.
Step-by-step explanation:
Let's say that you are buying a avatars and b bats.
3a + 3b = 29.85
Divide all terms by 3.
a + b = 9.95
You will pay $9.95 if you buy one of each.
Hope this helps!
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect. Choose the correct answer below. A. The statement is false. Double blinding has no effect on the placebo effect. B. The statement is false. Double blinding is used to increase the randomization. C. The statement is true. D. The statement is false. Double blinding is used to decrease the placebo effect.
Answer:
D. The statement is false. Double blinding is used to decrease the placebo effect.
Step-by-step explanation:
In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.
Therefore, a double-blind experiment is used to decrease the placebo effect.
Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 14, max = 121, 8 classes
Answer:
The class width is [tex]C_w \approx 13[/tex]
Step-by-step explanation:
From the question we are told that
The upper class limits is [tex]max = 121[/tex]
The lower class limits is [tex]min = 14[/tex]
The number of classes is [tex]n = 8 \ classes[/tex]
The class width is mathematically represented as
[tex]C_w = \frac{max - min}{n }[/tex]
substituting values
[tex]C_w = \frac{121 - 14}{8 }[/tex]
[tex]C_w = 13.38[/tex]
[tex]C_w \approx 13[/tex]
Since
Hommie Delicacies produces two products (Orapine and Banango) from a joint process. The joint cost of production is GH¢80,000. Five thousand units of Orapine can be sold at split-off for GH¢20 per unit or processed further at an additional cost of GH¢20,000 and sold for GH¢25 per unit. Ten thousand units of Banango can be sold at split-off for GH¢15 per unit or processed further at an additional cost of GH¢20,000 and sold for GH¢16 per unit. Advise Hommie on further processing each of the products?
Answer:
Orapine: do additional processingBanango: no additional processingStep-by-step explanation:
The processing cost of split-off Orapine units is ...
GH¢20,000/(5000 units) = GH¢4/unit
The increase in revenue from the further processing is ...
GH¢25 -GH¢20 = GH¢5
The increased processing cost is less than the increased revenue, so there is additional profit from further processing 5000 units.
__
The processing cost of split-off Banango units is ...
GH¢20,000/(10000 units) = GH¢2/unit
The increase in revenue from the further processing is ...
GH¢16 -GH¢15 = GH¢1
The increased processing cost is more than the increased revenue, so the company takes a loss from further processing 10000 units. No additional processing of Banango units should be undertaken.
Factor.
-7x2 + 49x
-7(x - 7)
01 - 7x2 + 49x)
-x(x – 7)
-7x(x – 7)
Answer:
Option 1: -7x (x - 7)
Step-by-step explanation:
Factor -7x out of -7x^2.
= -7x (x) + 49x
Factor -7x out of 49x.
= -7x (x) -7x (-7)
Factor -7x out of -7x (x) - 7x (-7).
= -7x (x - 7)
(Also I took the test and got this answer right)
What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes
Answer:
Step-by-step explanation:
I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be
(All of that is my point of view)
Average temperature 30 °
So :
30 ÷ 15 = 2 °
30 ÷ 10 = 3 °
30 ÷ 5 = 6 °
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
Find the area of the shaded region if the dimensions of the unshaded region are 14ft x 18ft . Use 3.14 for π as necessary. Answer Asap Please! That would be greatly appreciated! PLEASE HELP ME ON THIS ASAP FIRST ANSWER GETS BRAINLIEST
Answer:
867.44 ft²
Step-by-step explanation:
The area of the shaded region is A = 196π + 252.
We have the dimensions of the unshaded region are 14ft x 18ft.
We have to find the area of shaded region.
What is the area of a Rectangle and a Circle?The area of a rectangle is -
A(R) = Length x Breadth = L x B
and the area of Circle is -
A(C) = [tex]\pi r^{2}[/tex]
According to the question -
Dimensions of the unshaded region -
L = 18ft
B = 14ft
Area of the shaded region (A) = Total Area - Area of Rectangle
Total Area = Area of 2 semicircles of radius (7 + 7) 14ft + Area of rectangle of length 18ft and breadth 28ft.
Total Area = ( [tex]2\times \frac{1}{2}\times \pi \times14 \times 14[/tex] ) + ( 18 x 28)
Total Area = 196π + 504
Area of the shaded region (A) = 196π + 504 - 252 = 196π + 252
Hence, the area of the shaded region is A = 196π + 252.
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Datguy323 is going to complain again. What's the variables for: [tex]x^2+y^2=29\\x+y=7[/tex]
y<4
Answer: :o I FINALLY MADE IT
(5, 2)
x = 5
y = 2
Step-by-step explanation:
First, I graphed both equations. They meet at the points (5,2) and (2,5). Because y < 5, the solution is (5, 2)
Hope it helps <3
Answer:
[tex]x=5\\y=2[/tex]
Step-by-step explanation:
[tex]x^2 +y^2 =29[/tex]
[tex]x+y=7[/tex]
Solve for x in the second equation.
[tex]x+y=7[/tex]
[tex]x+y-y=7-y[/tex]
[tex]x=7-y[/tex]
Plug in the value for x in the first equation and solve for y.
[tex](7-y)^2 +y^2 =29[/tex]
[tex]y^2-14y+49+y^2 =29[/tex]
[tex]2y^2-14y+20=0[/tex]
[tex]2(y-2)(y-5)=0[/tex]
[tex]2(y-2)=0\\y-2=0\\y=2[/tex]
[tex]y-5=0\\y=5[/tex]
[tex]y<4[/tex]
[tex]y=2[/tex]
[tex]y\neq 5[/tex]
Plug y as 2 in the second equation and solve for x.
[tex]x+y=7[/tex]
[tex]x=7-y[/tex]
[tex]x=7-2[/tex]
[tex]x=5[/tex]
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answer:
See below
Step-by-step explanation:
Proof:
Statements | Reasons
AD ≅ BC | Given
AD ║ BC | Given
AC ≅ AC | Reflexive Property
∠DAC ≅ ∠ACB | If 2 || lines are cut by a trans., the | alternate interior ∠s are congruent.
ΔADC ≅ ΔBCA | S.A.S Postulate
BA ≅ DC | Corresponding sides of congruent Δs
So, quad. ABCD is a ║gm | If a quad. has its opposite sides
| congruent, the quad. is a parallelogram.
It is prove that given quadrilateral is a parallelogram.
Given that,AD ≅ BC and AD ║ BC
By reflexive property,AC ≅ AC
If two parallel lines are cut by a transversal. Then, alternate interior angles are congruent.So that, ∠DAC ≅ ∠ACB
By Side - angle - Side congruency rule,ΔADC ≅ ΔBCA
Since, the Corresponding sides of congruent triangles are congruent.So that, BA ≅ DC
Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.
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Which of the following points is a solution of the inequality y <-Ixl
You did not give any options but i will try to answer.
y < -lxl basically means that the value of y is less than the absolute value of x time - 1.
So if x = 2, then y is any number less than -2.
And if x is -3. then y is any number less than -3.
Happy to help!
Con proceso por favor
Answer:se
Step-by-step explanation:
Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs
of which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3
contains 3 defective and 4 functional bulbs. A box is selected at random and a bulb
drawn from it at random is found to be defective. Find the probability that the box
selected was Box 2.
Answer:
1/6
Step-by-step explanation:
As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.
The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2 divided by total number of defective bulbs.
P(defective in box 2)= N(defective in box 2)/N(defective total)
As we know there is only 1 defective lamp in box 2.
So N(defective in box 2)=1
Total number of defective bulbs is Box1- 2 defective bulbs, box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.
So N(defective total)=6
So P(defective in box 2)=1/6
Simplify the expression using the order of operations. 2[16-5⋅2]÷4
Answer:
3.
Step-by-step explanation:
Solve in the order of pemdas.
Answer:
[tex]\boxed{\sf 3}[/tex]
Step-by-step explanation:
Solve brackets first.
[tex]2[16-5 \cdot 2]\div4[/tex]
Multiply the terms in the brackets.
[tex]2[16-10]\div4[/tex]
Subtract the terms in the brackets.
[tex]2[6]\div4[/tex]
Divide the numbers.
[tex]2(\frac{6}{4} )[/tex]
Multiply.
[tex]\frac{12}{4} =3[/tex]
3+x=8 What would like match this answer
Answer:
x = 5
Step-by-step explanation:
x = 8 - 3
Thus, x = 5
A formal hypothesis test is to be conducted using the claim that the mean AC thermostat setting in restaurants is equal to 74degrees°F. What is the null hypothesis and how is it denoted?
Answer:
[tex]A. H_o: \mu = 74 ^{\circ} F[/tex]
Step-by-step explanation:
A null hypothesis refers to the hypothesis in which there is no important difference taken place and it is used in statistics and it also does not have any relation between the two measured events or variables or group association
It can be denoted by
[tex]A. H_o: \mu = 74 ^{\circ} F[/tex]
Therefore the above null hypothesis is the correct answer
The smaller of two numbers is one-half the larger, and their sum is 27. Find the numbers. Answer: The numbers are ___ ___ ___
Answer:
the smaller is 9 while the digger is 18
Please help with 4d.
Answer:
(Hemingway, The Old Man and the Sea)(Orwell, 1984)Step-by-step explanation:
A short web search will turn up the authors of the given titles:
The Old Man and the Sea - Hemingway
Huckleberry Finn - Twain
Moby D.ick - Melville
1984 - Orwell
Crime and Punishment - Dostoevsky
Question 6 of 10
Which equation matches the graph of the greatest integer function given
below?
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.
A rectangular vegetable garden will have a width that is 4 feet less than the length and an area of 140 square feet if x represents the length then the length can be found by solving the equation:
If x represents the length, then the length can be found by solving the equation: x(x-4)=140
Answer: x(x-4) = 140 This equation can be solve to find the length.
Step-by-step explanation:
If the width of the rectangle will be 4 less than the length and the length is represented by x then we could have the equation w=x - 4 for the width and the length is just x. And to find the area of a rectangle we multiply the length by the with so multiply x-4 by x for it to equal 140 because 140 is the area.
x(x-4) = 140 solve for x
[tex]x^{2}[/tex] - 4x = 140 subtract 140 from both sides
x^2 - 4x - 140 = 0 find a number that the product is 140 and the sum is -4
-14 and 10 works out.
[tex]x^{2}[/tex] - 14x + 10x - 140 = 0 factor by grouping
x(x -14) 10(x-14) = 0 factor out x-14
(x-14) ( x+10) = 0 set them both equal zero.
x-14= 0 or x+10 = 0
x = 14 or x= -10
Since -10 can't represent a distance, the answer is 14.
Check.
In this case the length is 14 and if the width is 4 less than the length then we will subtract 4 from 14.
14- 4 = 10 so the width is 10.
14 * 10 = 140
HELLPPPPPPPPPPPPP Solve x2 - 16x + 60 = -12 by completing the steps. First, subtract 60 from each side of the equation. Next, add 64 to each side of the equation to complete the square. Now, write x² - 16x + 64 = -8 as ✔ (x - 8)² = -8
Answer:
x = 8 ± 2i[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² - 16x + 60 = - 12 ( subtract 60 from both sides )
x² - 16x = - 72
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 8)x + 64 = - 72 + 64, thus
(x - 8)² = - 8 ( take the square root of both sides )
x - 8 = ± [tex]\sqrt{-8}[/tex] = ± 2i[tex]\sqrt{2}[/tex] ( add 8 to both sides )
x = 8 ± 2i[tex]\sqrt{2}[/tex]
The solution of the given expression is ±2√2i+8
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that
x² - 16x + 60 = - 12
Then subtract 60 from both sides;
x² - 16x = - 72
To complete the square then add ( half the coefficient of the x- term )² to both sides
x² + 2(- 8)x + 64 = - 72 + 64,
(x - 8)² = - 8 ( take the square root of both sides )
x = ±2√2i+8
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Please answer this correctly without making mistakes
Answer:
Step-by-step explanation:
2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.
Emma words in a coffee shop where she is paid at the same hourly rate each day. She was paid $71.25 for working 7.5 hours on Monday. If she worked 6 hours on Tuesday, how much was she paid on Tuesday
Answer:
$57
Since $71.25 was paid for working 7.5 hours.
That means he was being paid $9.5 per hour.
Which is 71.25÷7.5.
And on tuesday that's 9.5×6 which is $57
mark wants to invest $10,000 for his daughter’s wedding. Some will go into a short term CD that pays 12% and the rest in a money market savings account that pays 5% interest. How much should he invest at Each rate if he wants to earn $1095.00 in interest in one year.
The perimeter of an equilateral triangle with a side length of 12 units is:
Answer:
Hey there!
An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.
Thus, the perimeter for this equilateral triangle would be 3(12)=36
Hope this helps :)
Answer:
[tex]\boxed{Perimeter = 36 \ units}[/tex]
Step-by-step explanation:
Perimeter = sum of all sides
Perimeter = 12 +12 + 12
Perimeter = 36 units
A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is cubic units. A cylinder with the same height and radius as the cone will have a volume of cubic units. If a sphere has the same radius as the cylinder, its volume is the volume of the cylinder.
The above question is not complete because it was not written and arranged properly
Complete Question
1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.
2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.
3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.
Answer:
1) Volume of the cone = 134.04cubic units
2)Volume of the cylinder = 402.12cubic units
3) Volume of the sphere= 268.08 cubic units. Hence, if a sphere has the same radius as the cylinder, its volume is 2/3 times the volume of the cylinder.
Step-by-step explanation:
1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.
Volume of a cone = 1/3πr²h
h = 8 units
r = 4 units
Volume = 1/3 × π × 4² × 8
134.04cubic units
2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.
Volume of a cylinder = πr²h
Height and radius is the same as that of the cones hence,
h = 8 units
r = 4 units
= π × 4² × 8
= 402.12cubic units.
3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.
Volume of a Sphere = 4/3πr³
r = radius of the cylinder = 4 units
Volume of a Sphere = 4/3 × π × 4³
= 268.08 cubic units.
From the above question, we are asked to compare the volume of the sphere with the volume of the cylinder
Volume of the sphere : Volume of the cylinder
268.08 cubic units : 402.12 cubic units
268.08/402.12 = 2/3
Therefore, the volume of the sphere is 2/3 times the volume of the cylinder
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 3, 1) and point K is at (negative 8, 11). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –6 –5 5 7
Answer: (-5, 5)
Step-by-step explanation:
J = (-3, 1) K = (-8, 11) ratio 2 : 3 --> 2 + 3 = 5 segments
x-distance from J to K: -8 - (-3) = -5 units
y-distance from J to K: 11 - 1 = 10 units
Divide those distance into 5 segments:
x = -5/5 = -1 unit per segment
y = 10/5 = 2 units per segment
The partition is 2 segments from J:
x = -3 +2(-1) = -5
y = 1 + 2(2) = 5
The partition is located at (-5, 5)
Answer:
5
Step-by-step explanation: