The containers must be spheres of radius = 6.2cm
How to minimize the surface area for the containers?
We know that the shape that minimizes the area for a fixed volume is the sphere.
Here, we want to get spheres of a volume of 1 liter. Where:
1 L = 1000 cm³
And remember that the volume of a sphere of radius R is:
[tex]V = \frac{4}{3}*3.14*R^3[/tex]
Then we must solve:
[tex]V = \frac{4}{3}*3.14*R^3 = 1000cm^3\\\\R =\sqrt[3]{ (1000cm^3*\frac{3}{4*3.14} )} = 6.2cm[/tex]
The containers must be spheres of radius = 6.2cm
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How many interior angles does a 2D shape right arrow have and explain the answer?
The number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
How to determine the interior anglesIt is important that a 2D shape arrow is a shape with 8 sides
Sum of angles of a polygon = (n - 2) × 180
⇒ ( 8 - 2) × 180
⇒ 6 × 180
⇒ 1080
The number of interior angles are 8 and this is so because of the number of sides in the 2D shape right arrow
Thus, the number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
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56m² = ____________ GCF =
68m² = ____________ GCF =
The greatest common factor of the expression is 4m⁴.
What is GCF?GCF simply means the greatest common factor.
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Hence,
56m⁵
68m⁴
The greatest common factor of the expression is the largest positive expression that divides evenly into all numbers with zero .
Hence, the greatest common factor is 4m⁴
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What is the equation of the line that is perpendicular to the line defined by the equation 2y=3x+2 and goes through the point (3,2)
The equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
Equation of perpendicular linesThe equation is defined by 2y = 3x + 2
Rewrite the equation in the form y = mx + c
[tex]y=\frac{3}{2}x + 1[/tex]
The slope, m = 3/2
The y-intercept, c = 1
The equation perpendicular to the given line will be of the form:
[tex]y-y_1=\frac{-1}{m}(x-x_1 )[/tex]
Substitute [tex]x_1=3, y_1=2, and m=\frac{3}{2}[/tex] into the equation above
[tex]y-2=\frac{-2}{3} (x-3)\\\\y-2=-\frac{2}{3}x+2\\\\y=-\frac{2}{3}x+4[/tex]
Therefore, the equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
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50 POINTS!!! Answer the question well and I will also give Brainliest.
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which conclusion can be made from the given information?
A) The volume of the prism is half the volume of the cylinder.
B) The volume of the prism is twice the volume of the cylinder.
C) The volume of the prism is equal to the volume of the cylinder.
D) The volume of the prism is not equal to the volume of the cylinder.
Answer:
C) The volume of the prism is equal to the volume of the cylinder.
Step-by-step explanation:
volume of triangular prism = area of base × height
volume of cylinder = area of base × height
The cross sectional area are equal, so the bases have the same area.
The heights are also equal.
The volumes must be equal.
Answer: C) The volume of the prism is equal to the volume of the cylinder.
Answer:
C) The volume of the prism is equal to the volume of the cylinder.
Step-by-step explanation:
If the cross-sectional areas of the triangular prism and the right cylinder are congruent, it means that when you look at their shapes from the top or bottom, they have the same size and shape.
Since both the triangular prism and the right cylinder have a height of 5 units, and their cross-sectional areas are the same, it implies that they have the same volume as well. So, the volume of the triangular prism is equal to the volume of the cylinder.
Please mark me as Brainliest if you're satisfied with this answer
Which phrase best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)²?
O6 unit left
O6 unit right
O 1 unit left
O 1 unit right
Answer:
1 UNIT LEFT best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)².
Good recordkeeping helps protect assets and helps managers?
Answer:
yes i help yes of course he help
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations that can be used to find the lengths of the legs of the triangle are as follows:
100 = (x + 2)² + x²24 = 0.5 × (x + 2)(x)x² + 2x - 48 = 0How to find the equation of a right triangle?The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
10² = (x + 2)² + x²
100 = (x + 2)² + x²
Therefore, using the area of a triangle,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × (x + 2)(x)
24 = 0.5 × (x + 2)(x)
24 = x² + 2x / 2
cross multiply
48 = x² + 2x
x² + 2x - 48 = 0
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Find the surface area of the square pyramid below if the length of the sides of the base are 10 cm, and the slant height is 15 cm.
The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
Surface areaSurface area of the square pyramid
= a² + 2a√a²/4 + h²
where,
a = sides of base = 10 cmh = slant height = 15 cmSurface area of the square pyramid
= a² + 2a√a²/4 + h²
= 10² + 2(10)√10²/4 + 15²
= 100 + 20√100/4 + 225
= 100 + 20√25 + 225
= 100 + 20√250
= 100 + 20(15.81)
= 100 + 316.2
= 416.2 cm²
Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
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Find all primes p, q such that p^2-p=37q^2-q
The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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What is the range of possible sizes for side xxx?
Answer:
1.6 < x < 9.6
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
5.6 - 4 < x < 5.6 + 4
1.6 < x < 9.6
Write the equation of a parabola whose directrix is
y
=
−
1.5
y
=
-
1.5
and has a focus at
(
−
4
,
−
2.5
)
(
-
4
,
-
2.5
)
.
Answer:
y=0.5x²-4x-10.
Step-by-step explanation:
1) according to the definition of parabola:
d1=d2, then
[tex]2) \ |y+1.5|=\sqrt{(x+4)^2+(y+2.5)^2} ;[/tex]
3) after evolution:
-(2y+4)=(x+4)²; ⇔
[tex]y=-\frac{1}{2}x^2-4x-10.[/tex]
Please Evaluate C(6,3)
The value of the expression C(6,3) is 20
How to evaluate the expression?The expression is given as:
C(6, 3)
This means 6 combination 3.
And it can be written as:
[tex]^6C_3[/tex]
Apply the combination formula
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the expression
[tex]^6C_3 = 20[/tex]
Hence, the value of the expression C(6,3) is 20
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1. The correlation coefficient on a scatter plot representing the variables for the amount of weight a body builder can lift in a gym and the amount of protein the body builder takes each day is 0.76. Describe the meaning of this correlation coefficient.
A
very Strong positive linear relationship between the two variables
B
very Strong negative linear relationship between the two variables
C
moderate positive linear relationship between the two variables
D
no relationship between the two variables
A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.
What does the correlation coefficient mean?Correlation is a statistical measure used to measure the linear relationship that exists between two variables.
If the sign of the correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the correlation coefficient is, the stronger the linear relationship.
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Sets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}
Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.
Answer:
(C U B )=(q,x,y)
(C U B )n A=q
Solve the following system of equations.
{y=x−5
−x−3y=7
Write your answer as an ordered pair in the form (x,y).
Answer:
(2,-3)
Step-by-step explanation:
I am not sure if you meant the first equation to be y or -y. I solved it as y.
y = x-5 -x -3y =7
I am going to take the second equation and write it as x =
-x - 3y = 7 Give equation
-x = 3y +7 Add 3y to both sides
x = -3y-7 Multiplied each term in the equation by -1 so that x could be positive
I am going to substitute -3y-7 for x in the first equation up above
y = x - 5
y = -3y -7 - 5 Substitute -3y-7 for x
y = -3y -12 Combined -7-5
4y = -12 Added 3y to both sides
y = -3 Divided both sides by 4.
I now know that y is -3, I will plug that into x = -3y-7 to solve for x
x = -3(-3) -7
x = 9-7 A negative times a negative is a positive
x = 2
Find the zeros of the function. Enter the solutions from least to greatest. f(x) = (x - 2)(3x + 3)
The zeros of the given function are x = 2 and x = -1
Zeros of a functionFrom the question, we are to determine the zeros of the given function
The given function is
f(x) = (x - 2)(3x + 3)
To determine the zeros of a function, we will set the function equal to zero
That is,
(x - 2)(3x + 3) = 0
Then,
x - 2 = 0 OR 3x + 3 = 0
x = 2 OR 3x = -3
x = 2 OR x = -3/3
x = 2 OR x = -1
Hence, the zeros of the given function are x = 2 and x = -1
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If f(x) =2ײ+2 and g(x) =x² -1, find (f-g) (x)
Answer:
[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]
Step-by-step explanation:
Given :
f(x) = 2x² + 2g(x) = x² - 1Now, this problem can be used using a simple formula.
[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]
Let's solve.
(f - g)(x) = 2x² + 2 - (x² - 1)(f - g)(x) = 2x² - x² + 2 + 1(f - g)(x) = x² + 3∴ The answer will be x² + 3.
vRichard has a red card (R) and a black card (B). He picks a card randomly from the pair and then rolls a six-sided die. The sample space of the event is listed. B-1 R-1 B-2 R-2 B-3 R-3 B-4 B-5 R-5 B-6 R-6 The missing term in the list is . If there were three cards instead of two, the sample size would be .
The Sample space for three cards is
[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)[/tex][tex]\left(B,5\right),\left(R,5\right),\left(G,5\right),\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}[/tex]
There are two cards red(R) and black(B) and a six-sided die.
The event is one card is picked randomly and then rolls the die.
So, the Sample space is as follows.
[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(B,2\right),\left(R,2\right),\left(B,3\right),\left(R,3\right),\left(B,4\right),\left(R,4\right),\left(B,5\right),\left(R,5\right),\left(B,6\right),\left(R,6\right) \right \}[/tex]
Find Sample space if there are three cards.Consider there were three cards red(R), black(B) and green(G) a six-sided die.
The event is one card is picked randomly and then rolls the die.
So, the sample space will be as follows,
[tex]S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)[/tex][tex]\left(B,5\right),\left(R,5\right),\left(G,5\right)\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}[/tex].
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Find the missing side of the triangle.
pythagorean 4
A. 337‾‾‾‾√ km
B. 5‾√ km
C. 193‾‾‾‾√ km
D. 112‾√ km
Applying the Pythagorean theorem, the missing side of the triangle is: C. √193 km.
How to Apply the Pythagorean Theorem?To find the missing side (x) in the right triangle, based on the Pythagorean theorem, we would have the following equation:
x = √(12² + 7²)
x = √(144 + 49)
x = √193
The missing side of the triangle is: C. √193 km
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Answer:
C.) 193√ km
Step-by-step explanation:
I got it right on founders edtell
A cylindrical container has a radius of 17 inches and a height of 63 inches, how many gallons will it hold?
Answer:
=57198.98
Step-by-step explanation:
Volume of Cylinder = pi x radius^2 x height
= pi x 17^2 x 63
=57198.9774439
=57198.98
The table shows the multiplication of two linear expressions.
A 2-column table with 5 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3, Step 4. Second column is labeled Step with entries three-fourths x (negative 8 x + 6), (three-fourths x) (negative 8 x) + (three-fourths x) (6), three-fourths times (negative 8) times x times x + three-fourths times 6 times x, (three-fourths times (negative 8)) times (x times x) + (three-fourths times 6) times x, negative 6 x squared + 9 over 2 x.
What is the mathematical reasoning for Step 3?
associative property
commutative property
distributive property
simplify
The mathematical reasoning for Step 3 is a distributive property.
What is distributive property?It should be noted that the distributive property is the multiplication of the sum of two to more addends by a number that will give same result.
In this case, the mathematical reasoning for Step 3 is a distributive property.
Therefore, the correct option is C.
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Answer: C. Distributive Property
Bob drops a ball from a height of 400 feet. The height of the ball is given by
the function h(t) = -16t² + h, where t is the time in seconds. How long will it
take for the ball to hit the ground?
Answer: in 5 seconds it will take the ball to the ground.
Step-by-step explanation:
h=400 foot h(t)=-16t²+h
Height a ball will take for to hit the ground is 0 feet.
Hence,
-16t²+h=0
400=16t²
16*25=16*t² |:16
25=t².
t²=5²
t=5 с.
Good luck an' have a nice day!
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
The value of x is 2 and the length of JK is 4
How to solve the unknown variables?The given parameters from the circle are:
Center = Point SSegment JK = 8Segment LK = 2x + 4Congruent SN = SP = 7The lines SR and SQ are the radii of the circle P
This means that lines JK and JL are congruent
So, we have:
JK = KL
Substitute LK = 2x + 4 and JK = 4
4 = 2x + 4
Rewrite the above equation as:
2x + 4 = 8
Subtract 4 from both sides
2x + 4 - 4 = 8 - 4
Evaluate the difference
2x = 4
Divide both sides by 2
2x = 4/2
This gives
x = 2
Substitute x = 2 in LK = 2x + 4
LK = 2*2 + 4
Evaluate the product of 2 and 2
LK = 4 + 4
This gives
LK = 8
The point N divides JK into 2 equal segments
So, we have
JN = JK/2
JN= 8/2
JN = 4
Hence, the value of x is 2 and the length of JK is 4
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Has a base of 3, is reflected over the y-axis, has a horizontal shift right by 5 and an asymptote of y=-3
The equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
How to determine the equation?An exponential equation is represented as:
y = b^x
Where b represents the base.
The base is 3.
So, we have:
[tex]y = 3^x[/tex]
When reflected over the y-axis, we have:
[tex]y = 3^{-x[/tex]
When shifted right by 5 units, we have:
[tex]y = 3^{-x -5[/tex]
Lastly, the function has an asymptote of y=-3
So, we have:
[tex]y = 3^{-x -5} - 3[/tex]
Hence, the equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
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The number of bats in a colony is growing exponentially. After 3 years, there were 272 bats. After 5 years, there were 1088 bats.
If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.
The number of bats are expected to be in the colony after 11 years if the colony continues to grow at the same rate is 69,632
Exponential functionLet
Number of bat at a time = n(t)exponential function;
y = ax^t
When t = 3
272 = ax³
when t = 5
1088 = ax^5
divide both equation272/1088 = ax^3 / ax^5
1/4 = x^3-5
1/4 = x^-3
1/4 = 1/x²
1 × x² = 4 × 1
x² = 4
x = 2
Substitute x = 2 into
272 = ax³
272 = a × 2³
272 = a × 8
272 = 8a
a = 272/8
a = 34
Number of bat expected at the colony after 11 years
y = ax^t
= 34 × 2^11
= 34 × 2048
y = 69,632 bats
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which integer is closest to the third root of -23
Answer:
The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.
Step-by-step explanation:
Which of the following are equations for the line shown below? Check all that
apply.
(-2,-5)
(2,5)
A. y + 5 = 2.5(x+2)
B. y-5=2.5(x-2)
C. y-2=2.5(x - 5)
D. y+2=2.5(x+5)
Answer:
A
Step-by-step explanation:
A theater sells 2 types of fixed-price tickets - orchestra and balcony. Peter pays $50 for 1 orchestra and 4 balcony tickets. Justine pays $150 for 3 orchestra and 12 balcony tickets. А B The cost of 1 balcony ticket. The cost of 1 orchestra ticket. The quantity under A is greater than the quantity under B. The quantity under B is greater than the quantity under A. The quantities under A and B are equal. The information given is insufficient to make the comparison.
Using a system of equations, it is found that:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Cost of an orchestra ticket.Variable b: Cost of a balcony ticket.Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:
a + 4b = 50 -> a = 50 - 4b.
Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:
3a + 12b = 150.
a + 4b = 50 -> a = 50 - 4b.
The equations are equal, hence we suppose that the costs are equal, that is:
a + 4b = 50 -> 5a = 50 -> a = 10.
Hence:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.More can be learned about a system of equations at https://brainly.com/question/24342899
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Which number has a repeating decimal form?
A. √15
B. 11/25
C. 30
D. 2/6
Rewrite without parentheses.
−6w x5 (2w³ +7w¹x² – 5x²)
-
Simplify your answer as much as possible.
0
Step-by-step explanation:
Help me am lost somewhere