The mentioned data of 50 kilometres in hours is speed of 50 kilometres per hour.
The 50 kilometres refere to the distance and hour is representative of time. Now, ratio of distance and time indicates the speed or rate of movement of the concerned thing.
The speed or rate of movement holds significance in real world calculations. Based on it, the speed of bucket carrying water from well can be increased or decreased, movement of vehicles which may cause accident, distance covered by trains, airplanes, ships and other transport objects by specific speed in particular time limit.
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a box with a square base and open top must have a volume of 4,000 cm3. find the dimensions of the box (in cm) that minimize the amount of material used. sides of base cm height
Therefore width = 10cm
height = 20cm
length = 20cm
given that
volume = 4,000[tex]cm^{3}[/tex]
let height = h
width = w
length = l
width and length are equal
height = length = h
volume of box = height × width × height
4000 = h × w × h
4000 = [tex]h^{2}[/tex]w
w = 4000/[tex]h^{2}[/tex]
surface area(SA) = area of base + sum of area of each side
= [tex]h^{2}[/tex] + hw + hw + hw + hw
= [tex]h^{2}[/tex] + 4hw
substitute y = 4000/[tex]h^{2}[/tex]
SA = [tex]h^{2}[/tex] + 4x(4000/ [tex]h^{2}[/tex] )
SA = [tex]h^{2}[/tex] + 16000/h
Taking the derivative:
SA' = 2h - 16000/ [tex]h^{2}[/tex]
making SA' = 0:
0 = 2h - 16000/ [tex]h^{2}[/tex]
2h = 16000/ [tex]h^{2}[/tex]
2[tex]h^{3}[/tex] = 16000
[tex]h^{3}[/tex] = 8000
h = 20 cm
w = 4000 / [tex]h^{2}[/tex] = 4000 / 20² = 10 cm
Therefore width = 10cm
height = 20cm
length = 20cm
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Taylor entered a 100 mile bike race. They know they can ride 32 miles in 160 minutes. At this rate, how long will it take them to finish the race? Use any strategy you find helpful.
~Describe the transformation(s) shown:
S varies directly as t. if s is 20 when t is 4 then t is ____ when s is 30
Answer:
Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.
Step-by-step explanation:
Direct variation means that the ratio between two variables is always constant. In this case, the constant ratio between s and t is equal to 20/4 = 5. This means that when t is equal to 4, s is equal to 20 and the ratio between the two is 5. If s is equal to 30, we can find the corresponding value of t by setting up the following equation:
s / t = 5
We can then solve for t by multiplying both sides of the equation by t to get:
s = 5 * t
If we substitute 30 for s, we get:
30 = 5 * t
We can solve for t by dividing both sides of the equation by 5:
t = 30 / 5
Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.
2. Find the distance between M(-3, 1) and N(2, 8) on a
coordinate plane.
F 6.1 units
G 6.9 units
H 7.3 units
J 8.6 units
Answer:
D=74
D solution 8.60233
Step-by-step explanation:
Write 45% as a fraction or mixed number in simplest form.
The simplest form is ?
Answer:
9/20
Step-by-step explanation:
hope it helps!
Could you please give me brainliest for this? Thank you!
What is the solution to this equation? –1.3x = 52
Answer:
Step-by-step explanation:
x=-40
Solve the equation: -6z - 3z =27
Answer:
Z= -3
Step-by-step explanation:
-6z-3z=27
-9z=27
/-9. /-9
z= -3
Hopes this helps please mark brainliest
a 5.0L v8 pickup truck takes 7.7 quarts of oil with a tolerance of 0.2 quarts. Write an equation representing the minimum and maximum fill capacity tolerated by this truck.
Answer:
Step-by-step explanation:
cdcdfcdfvdsfdf
the area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
The length of the perimeter of the rectangle = 112 cm or 44 inches
Given in the question,
Area = [tex]105in^{2}[/tex]
= 677.4 [tex]cm^{2}[/tex]
Length of one side of the rectangle = 7 inches
= 17.7 cm
∴ Since the length of one side of the rectangle is given in the question we need to find the width of the rectangle to calculate the total perimeter of the rectangle
⇒ Area = length x width
⇒ 677.4 = 17.7 x width
⇒ Width = [tex]\frac{Area}{Length}[/tex]
⇒ Width = [tex]\frac{677.4}{17.7}[/tex]
⇒ Width = 38.2 cm
As we got both the length and the width of the rectangle, now we can calculate the perimeter,
⇒ Perimeter = [tex]2( length + width)[/tex]
⇒ Perimeter = [tex]2(17.7 + 38.3)[/tex]
⇒ Perimeter = 2 x 56 cm
⇒ Perimeter = 112 cm
⇒ In inches = 44 inches
Therefore, the length of the perimeter is = 112cm or 44 inches
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Find x when y = 32, given that x varies inversely as y, and x = 132 when y = 4. 1,056 66 16. 5.
The Variable x varies inversely with y, and x = 132 when y = 4 then the value of x is 16.5 when y = 32.
So, the correct option is option(D).
Inverse variation can be expressed by the formula, xy=k or y=kx
That is, if there is a non-zero constant k such that xy = k or y = kx (x≠0,y≠0), then y varies inversely with x.
We have given that,
x varies inversely with y and we need to find x when y = 4 when x = 132
X varies inversely with y there exist a constant of proportionality say k such that :
=> (x)(y) = k ----(1)
Put the value of x and y in equation (1) to find the value of k
=> (132)(4) = k
Therefore, k = 528 , We get
=> (x)(y) = 528
Now, we find x when y = 32, so plug the value of y in equation (1)
=> (x)(32) = 528
=> x = 528/32
=> x = 16.5
Hence, the value of x is 16.5 when y = 32 .
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find the measure of the interior angles x, (x-24), and 68
Answer:
68, 68, 44
x = 68
x - 24 = 44
Step-by-step explanation:
If you have a shape with three interior angles, it is a triangle. The three angles in a triangle add up to 180. Use this idea to write and solve an equation.
x + (x - 24) + 68 = 180
Combine like terms.
2x + 44 = 180
Subtract 44.
2x = 136
Divide by 2.
x = 68
So we can find x - 24
68 - 24 is 44.
The three angles are 68 (given), 68 (because x = 68), and 44 (because x-24)
The angles are 68, 68, and 44
HELPPP PLSSS!!!
agile minds
Answer:
A = 2; B = 3; C = -3
Step-by-step explanation:
The curve goes to negative infinity as x decreases and positive infinity as x increases.
This looks like a 3rd degree polynomial.
f(0) = -3
f(x) = Ax^B + x + C
f(0) = A(0^B) + 0 + C = -3
C = -3
f(x) = Ax^B + x - 3
f(1) = A(1^B) + 1 - 3 = 0
A - 2 = 0
A = 2
f(x) = 2x^B + x - 3
f(1.125) = 2(1.125)^B + 1.125 - 3 = 1
2(1.125)^B + 1.125 - 3 = 1
2(1.125)^B = 2.875
(1.125)^B = 1.4375
log (1.125)^B = log 1.4375
B × log (1.125) = log 1.4375
B = (log 1.4375)/(log 1.125)
B = 3
f(x) = 2x^B + x - 3
Answer: A = 2; B = 3; C = -3
What are 3 rules that prove two triangles are similar?
Three rules that prove two triangles are similar AA, SAS, SSS.
When two shapes in geometry have the same shape but different sizes, they are said to be comparable. A square with sides of 21 cm and one with sides of 14 cm would be comparable. A square with sides of 14 cm and an equilateral triangle with sides of 21 cm are not comparable because they are different shapes.
Applying three triangle-specific theorems makes it simple to distinguish between similar triangles.
In geometry, correspondence refers to the exact relationship between a specific part on one polygon and a part that is similarly positioned on another polygon.
These theorems knows as
Angle-Angle (AA) = Two pairs of corresponding angles are equal.
Side-Angle-Side(SAS) = Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
Side-Side-Side(SSS) = Three pairs of corresponding sides are proportional.
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a phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phylum. a simple random sample of 50 alga is obtained and each alga is categorized as either being a cyanobacterium or not. the researcher found that 38 samples were, in fact, cyanobacteria. without relying on any previous knowledge, the researcher wanted to estimate the proportion of algae that were cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval. how large a sample size would be required?
The required sample size of the given problem with a margin of error of at most 0.01 in a 99% confidence interval is 16590.
What is margin of error?A margin of error is a factual estimation that records for the distinction among genuine and extended brings about an irregular overview test. In less complex terms, the margin of error you to measure the degree of unconventionality in information and exploration results.
According to question:Let p be the population proportion of cyanobacteria.
Given : E = 0.01
Critical value for 99% confidence interval : z = 2.576
If Ian does not want to rely on previous knowledge , then we assume p=0.5 because the largest standard error is at p=0.5.
Now, the required sample size = n
⇒0.5(1 - 0.5)([tex]\frac{2.576}{0.01}[/tex])^2
⇒ 0.25(257.6)^2
⇒ 0.25(66357.76)
⇒ 16589.44 ≈≈ 16590
Thus, the size of sample is 16590.
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find the sum or different 2b+8
This cannot be furtherly simplified because the sum or difference of 2b+8 depends upon the value of b.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 2b+8.
In the given expression b is the variable and 2 is the coefficient of the variable b. eight is the constant value and plus is the operator.
As there is a plus sign we need to add the two terms 2b and 8.
We do not know the value of b so we cannot simplify the expression further. The value of 2b plus eight depends upon the value of b, if it is positive then we add two terms and if it is negative we use difference,
Hence, the sum or difference of 2b+8 depends upon the value of b and cannot be furtherly simplified.
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Which of these transformations are isometrics?The diagrams are not drawn to scale.
PLEASE HURRY!!!30 Points and brainlest!!!!
Answer: Second Pic, Probably the third.
Step-by-step explanation: little bit of guesswork
Is it possible to write an equation for such a parabola in the form f(x)=(x-a)(x-b).
Yes. Parabola is possible to write an equation in the form f(x) = (x-a)(x-b)
Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
A parabola can be described in the form of a general equation
[tex]y=ax^{2} +bx+c[/tex], with a, b, c is integers.
The form f(x)=(x-a)(x-b) can be made in other forms :
[tex]y=(x-a)(x-b)[/tex]
[tex]y=x^{2} -bx-ax+ab[/tex]
[tex]y=x^{2} -(b+a)x+ab[/tex]
That form of the equation is the same as : [tex]y=ax^{2} +bx+c[/tex]
With :
a = 1
b = -(b+a)
c = ac
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Which transformations could have taken place to map △ ABC to △ ABC?
The question is a spam as the correct question should be:
Which transformations could have taken place to map △ABC to △A"B"C".
The following answer has been given keeping in mind the above question.
The transformations that should have been taken place are a rotation and a dilation.
What is a rotation?
Rotation is when we rotate a figure to a certain degree. In a rotation, points and figures are turned on a coordinate plane. Majorly, rotations are about to the origin. Rotating a point about the origin can be, imagine a line connecting the origin to a point, and then rotate the line clockwise by the correct angle of rotation.
What is a dilation?
Dilation is a process of transformation in which something can be made larger or smaller. In a dilation, a point, a set of points can be expanded or contracted in relation to the origin. In expansion, the points in a figure move far away from the origin, and the side lengths of the figure increase. In a contraction, the points of the figure move closer to the origin, and the side lengths in the figure tend to reduce.
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How do you use the sine rule to work out an obtuse angle?
The value of the obtuse angle by applying sine rule for the attached diagram is equal to x° = 38.2°.
As given in the question,
Diagram of the obtuse angle triangle is attached.
In the given triangle,
Name the vertex of angle x as 'C' and side opposite to angle x as AB.
Draw a perpendicular from point A to BC at point D such that AD = z .
Given m ∠ACB = x°
AB = 2y
AC = y
m ∠ABC = 18°
In ΔADB,
sinB = AD / AB
⇒ sin 18° = z / 2y __(1)
In ΔACD,
sin ACD = AD / AC
⇒ sin ( 180 - x )° = z / y __(2)
Divide (1) by (2) we get,
sin18° / sin ( 180 - x )° = ( z / 2y ) / ( z / y )
⇒ sin 18° / sinx° = 1 / 2
⇒ sinx° = 2sin18°
⇒ sinx° = 2 (0.309 )
⇒ x° = sin⁻¹( 0.618)
⇒x° = 38.2°
Therefore, the obtuse angle for the given attached diagram using sine rule is equal to 38.2°.
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a cruise director schedules 4 different movies, 2 bridge games, and 3 tennis games for a two-day period. if a couple selects 3 activities, find the probability that they attend 2 movies and 1 tennis game.
Do linear equations have 2 answers?
The Linear equations can have 2 or more answers if the lines overlap each other .
In the question ,
it is asked that can two linear equations have 2 answers or solutions .
We know that ,
(1) two linear equations can have No Solution / Zero Solution if two lines are parallel .
(2) two linear equations can have One Solution/Unique Solution if two line intersect at a point .
(3) two linear equations can have infinitely many solution if lines overlap on each other .
So from (3) , we can conclude that linear equations can have 2 or more solutions when the line are overlapping .
Therefore , Yes, the linear equations can have two answers .
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factor the following expression using imaginary numbers : 100x^2+1
Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].
What are the factorization?
Factorisation or factoring is defined as the breaking or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number.
Here given expression is
[tex]100x^2+1[/tex]
[tex](10x)^2+(1)^2[/tex]
[tex](10x+1)^2[/tex]
As we know that,
[tex](a+b)^2=a^2+b^2+2ab[/tex]
Here
[tex]a=10x\\b=1[/tex]
So,
[tex](10x+1)^2=(10x)^2+(1)^2+2(10x(1))\\\\(10x+1)^2=(10x)^2+(1)^2+20x\\\\(10x+1)^2=100x^2+1+20x[/tex]
Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].
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The factors of the expression 100x² + 1 are (10x+i) (10x-i).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
The given expression is 100x² + 1.
The given expression is a quadratic function.
The standard form of quadratic function:
ax²+bx +c, where a is not equals to zero.
Comparing with the standard form we get,
a = 100, b = 0 and c = 1
Simplifying,
100x² + 1
= 100x² - (-1)
= (10x)² - (-1)
= (10x)² - (i)² ,{i² = -1}
= (10x+i) (10x-i)
Therefore, (10x+i) (10x-i) are the factors.
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Find f(3)-(5) given f(x) = 8(.5) and gix) = 2x+1
Answer:
Hope it helps
Step-by-step explanation:
f(3)-g(5) = 8(.5) - (2(5)+1) = 4 - 11 = -7
a) how many license plates are possible if each plate must have three letters followed by three numbers?
The permutation combination of license plate is 35152000.
Numbers can be 10 digits (0, 1, 2, …, 9) and 26 letters (A, B, C, ..., Z).
Repetition is allowed, leaving 26 next choices for each letter used and 10 next choices for each digit used.
Therefore, according to the multiplication principle, the total number of different letter permutations.
26× 26 × 26 = 17576
and the total number of digit permutation: 10 × 10 × 10 = 1000
now, they can be in any order:
⁶C₃ = 6!/(6−3)!3!
We have to consider 20 different combinations of positions.
So the total number of different license plates possible by the multiplication principle is
17576 × 1000 × 20 = 351520000
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Someone, please help me!!!!
8. A square has an area of 40 square feet. What is the length of a side of the square, in feet? PLEASE HELP I NEED IT ASAP
A
[tex] \sqrt[4]{10} [/tex]
B
[tex]10[/tex]
C
[tex]20[/tex]
D
[tex] \sqrt[2]{10} [/tex]
Answer:
The length of the side of the square should be 10ft
Step-by-step explanation:
Calculation of the length of the side:
Since A square has an area of 40 square feet.
As we know that the square does have 4 sides
So, the length of the side of the square should be
40 divided by 4
= 10ft
Tabitha planted an evergreen tree in her front yard. It was 12 feet tall. The next year it was 20% taller. How much taller, in feet, was the evergreen tree in Tabitha’s yard?
The evergreen tree grew 2.4 feet taller the next year.
What are Percentages?Percentage can be derived by dividing the given value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
It is given by:
Percentage = (given value / total value) * 100%
From the question, the tree has a base height of 20m, if it grew 20% taller then;
tree height = 12 x (20/100)
tree height = 12 x 0.2
tree height = 2.4
Therefore, the tree grew 2.4 feet taller the next year.
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Find the value of x and y (8x-14) (5y+16) (5x34)
Answer:
x=16
y=10
Step-by-step explanation:
(8x-14) + (5y+16) =180, because together they make a straight line.
(5x+34) = (8x-14), because they are alternate exterior angles.
Solve for x:
48=3x
x=16
Let's plug that into the first equation, then solve for y.
(8(16)-14) + (5y+16) =180
128-14+5y+16=180
130+5y=180
5y=50
y=10
I need help:/
………………
Using system of linear equations, the number of students in year book is 25 and that of film making are 39
System of Linear EquationSystem of linear equations can be defined as the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
Using variables x and y to represent to unknown values;
x = number of students in film makingy = number of students in year bookx + y = 64 ...eq(i)
x = 14 + y ...eq(ii)
Put eq(iii) into eq(i)
14 + y + y = 64
14 + 2y = 64
2y = 64 - 14
2y = 50
y = 25
Put y = 25 into eq(ii)
x = 14 + 25
x = 39
The number of students in film making is 39 and year book is 25
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