The angle θ is maximized when c = 2 (halfway between two points).
What is maximized angle?The maximum angle at which a conveyor may be inclined and still deliver a predetermined quantity of bulk material within a given time. As the maximum angle is approached, the rate of handling of bulk material is usually decreased.
Given that, in the figure, find the value of c in the interval [0, 4] on the x-axis that maximizes angle θ.
Express θ as a function of c, Let α be the angle to the left of θ and let β be the angle to the right, then,
tanα = 2/c
and tanβ = 2/(4-c)
At this point, we suppose that it might be easier to use cotangent in order to keep c inn numerator,
cotα = c/2
cotβ = (4-c)/2
We have, α+β+θ = π, so,
θ = π-α-β
= π-cot⁻¹c/2-cot⁻¹(4-c)/2
Differentiate, set equal to 0 and solve
dθ/dc = 1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2)
Put dθ/dc = 0
1/1+(c/2)².1/2+1/1+(4-c/2)²(1/2) = 0
1/1+(c/2)²-1/1+(4-c/2)² = 0
1/1+(c/2)² = 1/1+(4-c/2)²
(4-c/2)² = (c/2)²
(c/2) = (4-c/2)
4-c = c
2c = 4
c = 2
Hence, The angle θ is maximized when c = 2 (halfway between two points).
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kevin's shoe size is 12.5, what is the z score of kevin's shoe size compared to the normal population
Z-score of Kevin's shoe size compared to the normal population is, 2.5.
How to find comparation of Kevin shoe size to normal population?
A z-score is the standardized score which gives an idea about how far the data point is from the mean. This is the formula for z-score is defined as follows, Z = X - μ /б.Here X is the raw score, μ is the mean, and б is the standard deviation.The distribution of shoe sizes for males is approximately normally distributed with a mean of 10 and a standard deviation of 1. And Kevin's shoe size is given to be 12.5.Then, Z= 12.5 - 10 / 1 (formula for z-score), and z result was 2.5.Thus, we can say 2.5 is Z-score of Kevin's shoe size compared to the normal population.Learn more about Z-score calculation here: brainly.com/question/29187588
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Stella is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $0.75 per mile driven. How much would a taxi ride cost if Stella is riding for 7 miles? How much would a taxi ride cost that is m miles long?
Cost of ride, 7 miles:
Cost of ride , m miles:
The amount that would a taxi ride cost for 7 miles is $7.75 and The amount that would a taxi ride cost that is m miles long is $(2.5 + 0.75m).
What is the equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.
Given:
The taxi charges $2.50 just for the pickup and then an additional $0.75 per mile driven,
Write the equation for the following statement,
y = 2.5 + 0.75x
Here, y is the total amount and x is the number of miles,
Calculate the cost of the ride, put x = 7
y = 2.5 + 0.75 × 7
y = 7.75
Calculate the cost of the ride, put x = m
y = 2.5 + 0.75m
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in the triangle below, with right angle
7.6u-(30 divided by 6) + 12
Answer:
7.6u+7
Step-by-step explanation:
7.6u-(30/6)+12
30/6=5
7.6u-5+12
7.6u+7
ELYSE OWNS 2,000 SHARES OF A
CORPORATION THAT PAYS A QUARTERLY
DIVIDEND OF $0.51 PER SHARE. HOW MUCH
SHOULD SHE EXPECT TO RECEIVE IN A YEAR?
Using the mathematical operations of multiplication, if Elyse owns 2,000 shares of a corporation that pays a quarterly dividend of $0.51 per share, she should expect yearly dividends of $4,080.
What are mathematical operations?Mathematical operations involve the use of operands and mathematical operators to solve mathematical problems.
Mathematical operations follow the PEMDAS rule, which states that Parentheses, Exponents, Multiplication, and Divisions in that order should be solved first before Additions and Subtractions.
The number of shares owned = 2,000
Quarterly dividend per share = $0.51
Quarters in a year = 4
Yearly dividends = $4,080 (2,000 x $0.51 x 4)
Thus, applying the multiplication operation, the annual dividend Elyse should receive is $4,080.
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please help me solve this linear expression
Answer:
substitute a=-5 and c=5 into a=-3c
Step-by-step explanation:
a= -3c
(-5)= -3(5)
-5= -15
Find g(x), where g(x) is the reflection across the x-axis of f(x)=4x+10
Answer:
To find the reflection of a function across the x-axis, we simply need to change the sign of the y-coordinates of the function's points. Therefore, the reflection of f(x) = 4x + 10 across the x-axis is g(x) = -(4x + 10) = -4x - 10.
Step-by-step explanation:
To find the reflection of a function across the x-axis, we can follow these steps:
Start with the equation of the original function, which in this case is f(x) = 4x + 10.Change the sign of the y-coordinates of the function's points. This means that we need to multiply the entire equation by -1.Substitute the result from step 2 into the original equation to find the reflected function. In this case, we get g(x) = (-1)(4x + 10) = -4x - 10.Here is an example of how this works in practice. Let's say that the original function f(x) has the points (1,14) and (2,18).
The reflection of these points across the x-axis would be (1,-14) and (2,-18), respectively.
To find the equation of the reflected function g(x), we would simply substitute these points into the equation from step 3 to get g(x) = -4x - 10.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
-3/4
Step-by-step explanation:
equation of a line : y=mx+c
m= slope= 4/3
perpendicular slope is the inverse of m
this is because m1 * m2 = -1
thus perpendicular slope = -3/4
Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?
On a coordinate plane, the point (0, 3) is graphed.
On a coordinate plane, the point (0, 4) is graphed.
On a coordinate plane, the point (3, 0) is graphed.
On a coordinate plane, the point (4, 0) is graphed.
The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.
What is an ordered pair?The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.
Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.
Given, Ramon is graphing the function f(x) = 3 + (4)x.
We know the initial value of a function is determined when the independent variable is set to zero.
Here the independent variable is 'x'.
Now, at x = 0,
f(0) = 3 + (4)(0).
f(0) = 3.
So, The ordered pair is (0, 3).
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Answer:
a
Step-by-step explanation:
A cylindrical container has radius 1 m.
The cylinder contains 628 litres of water.
Calculate depth of water in the cylinder giving your answer in cm
take pi to be 3.14
The depth of water in the cylinder is 20 cm
How to calculate depth of water in the cylinderFrom the question, we have the following parameters that can be used in our computation:
Volume = 628 litres
Radius = 1 m
Convert litres and meters to cm cube and cm
So, we have the following representation
Volume = 628000 cm cubed
Radius = 100 cm
The volume is the calculated as
V = πr²h
So, we have
628000 = 3.14 * 100² * h
Evaluate
628000 = 31400 * h
Divide by 31400
h = 20
Hence, the height is 20 cm
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a cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. how much work is done in pumping a full tank of water up to ground level? (the water weighs 9800 newtons per cubic meter.)
The work is done in pumping a full tank of water up to ground level is 470400πNm.
Tank sizes variety from 6 ft. to one hundred twenty ft. in diameter with a roof, and as much as two hundred toes in diameter as an open pinnacle tank. Tanks with a roof have capacities starting from seven-hundred gallons to 500,000 gallons at the same time as the open pinnacle tanks may be constructed with even large capacities
The radius of the layer = 2m
V= pi (2)^2 (Delta y) m^3 = four pi Delta y m^3V=π(2) 2 (Δy)m 3 =4πΔym 3
Weight of the layer =9800 (four pi Delta y)=9800(4πΔy)
Weight of the water = 9800 frac=9800 m 3 N
So, weight of the layer = 39200 pi Delta y=39200πΔy
distance layer is moved =5-y=5−y
W=int_^{four} (5-y)(39200 pi dyW=∫ 04 (5−y)(39200πdy
=39200 pi int_^{four} (5-y) dy=39200π∫ 04 (5−y)dy
=39200 pi left[ 5y - frac y^2 right]_^{four}=39200π[5y− 21 y 2 ] 04
=-39200 pi (12) = 470400 pi Nm=−39200π(12)= 470400πNm.
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The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. What i the leat number of DVD the library can have?
The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. then the least number of DVD the library can have is 45
What is the function of DVD?
Short for digital versatile disc or digital video disc, a DVD or DVD-ROM is a disc capable of storing a significant amount more data than a standard compact disc. DVDs are widely used for storing and viewing movies and other data.
45 is the least common multiple of 3, 5, and 9.
45 can be equally divided by 3, 5, and 9:
45 ÷ 3 = 15
45 ÷ 5 = 9
45 ÷ 9 = 5
the least number of DVD the library can have is 45
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Describe how to shift the ordered pairs to create a sketch of the function.
shift left by 7 and down by 1
shift right by 7 and down by 1
shift right by 7 and up by 1
shift left by 7 and up by 1
Answer:
the 4th answer option : shift left by 7 and up by 1
Step-by-step explanation:
the "+1" at the end is simply adding 1 to every y (function result) of f(x). so, that moves everything up by 1.
the "+7" in the function argument is a little bit more complex : it means that the function value of x is the function value that would have been originally created for x+7. so, it happens 7 units "earlier". therefore, this means a shift to the left.
The ratio of the same side interior angles of two parallel lines is 1:14. find the measures of all eight angles formed by the parallel lines and transversals.
Answer:
x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.
Step-by-step explanation:
The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.
Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.
Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.
Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.
In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.
the perimeter of regular hexagon equals the perimeter of an equilateral triangle. if the area of the triangle is 10, what is the area of the hexagon?
If the perimeter of the regular hexagon equals to the perimeter of an equilateral triangle then the area of the hexagon is 18.
A hexagon can be be known as a polygon that has six sides and angles. Regular hexagons have six equal sides and angles and are composed of six equilateral triangles. first we have to write down the formula for finding the area of a hexagon if you know the side length. Since a regular hexagon is comprised of six equilateral triangles, the formula for finding the area of a hexagon is derived from the formula of finding the area of an equilateral triangle.
Let a be the side of equilateral triangle ∴ [tex]\sqrt{3}[/tex] /4 [tex]a^{2}[/tex] = 12
Perimeter of triangle = 3a = Perimeter of Hexagon
3a=6h ,where h is the side of hexagon.
⇒ h = 1/2 a
The area of the hexagon =6× [tex]\sqrt{3}[/tex]/4 [tex]h^{2}[/tex]
=6× [tex]\sqrt{3}[/tex]/4 . ( a/2 ) 2 = 6/4 ×12
= 18
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What is the perimeter, in units, of ΔABC
Δ
A
B
C
with A(−1,−6)
A
(
−
1
,
−
6
)
, B(7,−6)
B
(
7
,
−
6
)
, and C(3,−3)
C
(
3
,
−
3
)
?
Answer:
To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).
Applying this formula, we can find the lengths of the sides of the triangle as follows:
AB = sqrt((7 - (-1))^2 + (-6 - (-6))^2) = sqrt(8^2 + 0^2) = sqrt(64) = 8
BC = sqrt((3 - 7)^2 + (-3 - (-6))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
AC = sqrt((-1 - 3)^2 + (-6 - (-3))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
Thus, the perimeter of triangle ABC is 8 + 5 + 5 = 18 units.
Each heet of metal on a roof i perpendicular to the top line of the roof. What can you conclude about the relationhip between the heet of roofing? Jutify your anwer
The sheets of metal on the roof must be parallel to each other in order to be perpendicular to the top line of the roof. This means that the sheets of metal are parallel to each other and that their relationship is one of parallelism. This parallelism is necessary so that the roof can maintain its structure and be waterproof.
The relationship between sheets of metal on a roof is one of parallelism. This is because each sheet must be perpendicular to the top line of the roof in order to maintain the structure and be waterproof. In order for the roof to remain secure and waterproof, the sheets must be parallel to each other. This parallelism is necessary in order for the roof to form one complete structure and for the sheets to remain secure. Without the parallelism of the sheets, the roof would be unable to maintain its structure and could easily be damaged by wind and rain. This is why the relationship between the sheets of metal on a roof is one of parallelism.
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Select the correct answer from each drop-down menu.
Consider absolute value function f.
ƒ(x) = -²|x + 4|
The vertex of the function is a
Answer:
the vertex is a maximum at (-4,0)
Step-by-step explanation:
bonjour
voici un programe de calcul
.choisir un nombre relatif
.multiplier par-3
.ajouter -5
1quel nombre obtient-on avec ce programme lorsqu'on choisit au départ:
a.7 ? b.-4 ?
2. Léa a obtenu 1avec ce programme de calcul.
quel nombre avait-elle choisi au départ
Answer:
1a. -26
1b. -17
2. -2
Step-by-step explanation:
1.
a.
7
7 × (-3) = -21
-21 + (-5) = -26
b.
-4
-4 × 3 = -12
-12 + (-5) = -17
Formule:
r = -3n - 5
2.
r = -3n - 5
1 = -3n - 5
-3n = 6
n = -2
Question 8 of 10
f(x) = x +4
g(x) = 3x² - 7
Find (f.g)(x).
O A. (f.g)(x) = 3x³ + 12x² - 7x - 28
O B. (f.g)(x) = 3x³ + 12x² + 7x + 28
O c. (f.g)(x) = 3x³ - 28
OD. (f g)(x) = 3x³ +28
The composite function (f.g)(x) has a value of (d) (f.g)(x) = 3x³ + 12x² - 7x - 28
How to determine the composite functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x +4
g(x) = 3x² - 7
The composite function is given as
(f.g)(x)
This is calculated as
(f.g)(x) = f(x) * g(x)
Substitute the known values in the above equation, so, we have the following representation
(f.g)(x) = (x + 4) * (3x² - 7)
So, we have
(f.g)(x) = 3x³ + 12x² - 7x - 28
Hence, the function is (d) (f.g)(x) = 3x³ + 12x² - 7x - 28
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Multiply. 4x(y + x + 2)
Step-by-step explanation:
4xy + 4x² + 8x
Can also be rearranged as
4x²+8x+4xy
Super Express Couriers charges a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30.
If Kevin's postage fee was 150 less than 5 times the weight of his parcel, how much did his parcel weigh?
Answer:
Step-by-step explanation:
я хз
The weight of Kevin's parcel is 60 g.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30. and Kevin's postage fee was 150 less than 5 times the weight of his parcel,
Let the weight of the parcel be x
Establishing the equations,
5x - 150 = 30 + 2x
5x - 2x = 30 + 150
3x = 180
x = 180/3
x = 60
Hence, the weight of Kevin's parcel was 60g
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if a and b are independent events with p(a) = 0.35 and p(b) = 0.20, then, p(a è b) =
The probability of a intersection b, represented by P(a ∩ b) is equal to 0.07.
What is independent probabilityOne of the axioms of probability states that is two events say A and B are independent that is the probability of occurrence of one of them is not affected by the occurrence of the other, then P(A ∩ B) = P(A) × P(B)
We have from the question two events a and b which are said to be independent events,
P(a) = 0.35
P(b) = 0.20
then;
P(a ∩ b) = 0.35 × 0.20
P(a ∩ b) = 0.07
Therefore, the value 0.07 is the probability of the intersection of the two independent events a and b.
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The universal set, &, and sets F and G
are defined below.
{integers from 1 to 14 inclusive}
F = {x: 1≤ x <5}
G = {x:3 < x≤ 9}
A value is chosen at random from §.
Work out P(FG).
Give your answer as a fraction in its
simplest form.
-
Answer:7/8
Step-by-step explanation:your mom
under what circumstances is a discretized b state matrix equivalent to a continuous time b state matrix
A continuous time system can behave roughly throughout a variety of periods using a discretized state matrix. A continuous time condition matrix should be used in its place if these requirements are not satisfied since a discretized state matrix might not adequately depict the performance of a continuous time system.
A continuous time condition matrix is a matrix that is used to indicate the state of a system at any moment, as opposed to a discretized state matrix, which is used to describe the status of a system at discrete time intervals. Under the following conditions, a discrete-time state matrix is identical to a time series state matrix:
The system may be regarded as being in stable equilibrium at each time point since the time gaps between every discretization are short enough. This indicates that the behavior of the system does not drastically vary from one-time point to the next.
Over the time frames between each discretization, a linear model accurately predicts the behavior of the system. This means that the behavior of the system can be precisely predicted by a linear equation of the type "Ax = Bu," where A as well as B are matrices and x as well as u are vectors that, respectively, represent the system's state and input.
Over the intervals between each discretization, the system's input remains constant. This indicates that the system's input does not drastically vary from one-time point to the next.
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Which of the following statements is true for all real symmetric matrices Mcq?All the eigenvalues are realAll the eigenvalues are positiveAll the eigenvalues are distinctSum of all the eigenvalues is zero
Option A is the correct answer. All the eigenvalues of a real symmetric matrix are always real.
Symmetrix matrix: A matrix is said to be a Symmetrix matrix if A=A^T the matrix should be equal to the transpose of A.
All the eigenvalues of the Symmetric matrix are real. Eigenvectors corresponding to distinct eigenvalues are orthogonal.
Skew-Symmetrix matrix: A matrix 'A' is said to be a Skew-Symmetrix matrix if A=-A^T
Eigenvalues of the skew-symmetric matrix are zero or purely imaginary.
Skew-Hermitian matrix: A square matrix is said to be a Skew-Hermitian matrix if it is equal to the negotiation of its complex conjugate transpose.
A=-(A)^T
Eigenvalues of the Skew-Hermitian matrices are zero or imaginary.
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The vector field F = [tex](3x^2y + z^3, x^3 + 2yz, y^2 + 3xz^2)[/tex] has a nonzero divergence and a nonzero curl, indicating that it is not a conservative vector field. F cannot be expressed as the curl of another vector field.
To compute the divergence of F, we take the partial derivatives of each component with respect to their corresponding variables and sum them up. The divergence of F is given by div(F) = ∇·F = (∂/∂x)[tex](3x^2y + z^3)[/tex] + (∂/∂y)[tex](x^3 + 2yz)[/tex] + (∂/∂z)[tex](y^2 + 3xz^2)[/tex]. Evaluating these partial derivatives, we find div(F) = 6xy + 3z^2 + 2yz + 6xz.
To compute the curl of F, we take the curl operator (cross product of the del operator with F) and expand the determinant. The curl of F is given by curl(F) = ∇×F = (∂/∂y)[tex](y^2 + 3xz^2)[/tex] - (∂/∂z)[tex](x^3 + 2yz)[/tex], (∂/∂z)[tex](3x^2y + z^3)[/tex] - (∂/∂x)[tex](y^2 + 3xz^2)[/tex], (∂/∂x)[tex](x^3 + 2yz)[/tex] - (∂/∂y)[tex](3x^2y + z^3)[/tex]. Simplifying these expressions, we obtain curl(F) = [tex](-2xz, -3z^2, -6xy)[/tex].
The divergence of F is nonzero, indicating that F does not satisfy the divergence theorem, which states that a vector field with zero divergence is conservative. Additionally, the curl of F is nonzero, indicating that F does not satisfy the curl theorem, which states that a vector field with zero curl is conservative. Therefore, F is not conservative and cannot be expressed as the curl of another vector field.
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Complete the table to find 430 percent of 90.
A=
B=
100%
90
100%
90
Percent
100%
90
Using a
100%
90
a Diagram
30%
A
Total
430%
B
Answer:
387
Step-by-step explanation:
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
I need help ive been trying to figure them out for an hour and i also want to know if some are correct
The correct answer for question 1 is C) CA=XY
what is congruence in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.
Given here ΔABC≅XYZ
Therefore AB=XY , BC=YZ , AC=XZ & ∠A=∠X , ∠B=∠Y , ∠C=∠Z but clearly CA≠XY
The full diagram is attached please refer to the diagram for clarity
Hence, option c is the correct answer.
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The table below shows that the number of miles driven by Hakeem is directly proportional to the number of gallons he used.
\text{Gallons Used}Gallons Used \text{Miles Driven}Miles Driven
3636 1274.41274.4
4141 1451.41451.4
4545 15931593
\text{What is the rate of gas usage, in miles per gallon?}
What is the rate of gas usage, in miles per gallon?
The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, A table below shows that the number of miles driven by Hakeem is directly proportional to the number of gallons he used.
According to the table,
There are 36, 41, 45 gallons of gas are used for 1274.4 mile, 1451.4 and 1593 miles respectively,
So, for finding unit rates, we will divide the total mile to total gallons used, in one journey,
unit rate = 1593/45 = 1274.4/36 = 1451.4/41 = 35.4
Hence, The rate of gas usage, in miles per gallon, is 35.4 miles/gallon.
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Can someone help me this is hard
Answer:
m ≥ 28.5
Step-by-step explanation:
He wants to bike at least 28.5 miles, like he did last year
also whats up with the anime tab TT no judgement tho