solve the initial value problem. ′=−2,(0)=−10 (express numbers in exact form. use symbolic notation and fractions where needed.) =

On solving the provided question, we can say that so the equation formed is  1540-6x = 236 +6 x and in 108  2/3 minutes the tanks become equal with 888 gallons each

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

when does tank 1 = tank 2  when there is 6 gpm

tank 1 = 1540

tank2 = 236

so the equation formed is

1540-6x = 236 +6 x

1304 = 12x

108 * 2/3  = x

6*108*2/3  = 652 gallons

236+652=888

1504-652=888

in 108  2/3 minutes the tanks become equal with 888 gallons each

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The solution to the inequality 5/w > 4/45, using interval notation, is given as follows:

(-∞, 56.25).

The inequality for this problem is defined as follows:

5/w > 4/45.

Applying cross multiplication, we have that the solution can be obtained as follows:

4w < 45 x 5

w < 45 x 5/4

w < 56.25.

The solution is found similarly to an equality, isolating the desired variable, and finding the desired range of values.

The solution w < 56.25 is composed by values to the left of x = 56.25 on the number line, that is, values between negative infinity and 56.25, hence the interval is given as follows:

(-∞, 56.25).

The problem is incomplete, hence it was adapted to show the solution to an inequality, and then written in interval notation.

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The total price is 40.8, which can be represented by the coordinates (15, 40.8).

The equation y = 2.72x can be used to calculate the price of gasoline in terms of the number of gallons purchased.

The equation y = 2.72x can be used to calculate the total price of any number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons. If we input 15 gallons into the equation, we can calculate the total price of gasoline. To do this, we must substitute 15 for x in the equation, giving us y = 2.72(15). We can then calculate the total price by multiplying 2.72 and 15, which yields 40.8. Thus, for 15 gallons of gasoline, the total price is 40.8, which can be represented by the coordinates (15, 40.8).

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The perimeter of the larger figure is: 20 units.

Similar figures have perimeters and side lengths that are related in such a way that, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.

Therefore, if x represents the perimeter of the larger figure, then:

x/15 = 4/3

Cross multiply to find x:

3x = 60

x = 60/3

x = 20

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The statement that is true in this situation is "the lower money factor with Hillspring's Auto will give Jennifer the lowest monthly payment" (option B).

This is a term used when you lease a car or a similar product. This term is a synonym for the "lease fee", which means it is a percentage of money that you need to pay for the lease.

Based on the previous ideas a lower money factor is better because this means the payment will be lowered and this is offered by Hillspring's Auto (option B).

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The three types of Data analysis can be : Descriptive Analysis, Diagnostic Analysis nad Predictive Analysis.

In order to find relevant information, support inferences, and help decision-making, data analysis is the process of analyzing, cleaning, manipulating, and modeling data.

Using both recent and old data, descriptive analytics seeks out patterns and connections. Because it only describes patterns and associations without going any further, it is frequently referred to as the most basic kind of data analysis.

A type of advanced analytics called diagnostic analytics looks at data or information to determine "why it happened." Techniques like drill-down, data discovery, data mining, and correlations are used to describe it.

Using data, statistical algorithms, and machine learning approaches, predictive analytics determines the likelihood of future events based on previous data. The objective is to provide the most accurate prediction of what will happen in the future in addition to understanding what has already occurred.

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Answer: y=2x+3

Step-by-step explanation:

2x−y=−3

Step 1:

Add -2x to both sides.

2x−y+−2x=−3+−2x−y=−2x−3

Step 2: Divide both sides by -1.−y−1=−2x−3−1y=2x+3

The solutions of the system tend towards zero, as the exponential term dominates the other terms.

The general solution of the given system of equations can be expressed as:

x(t) = c1e^(-t) + c2te^(-t)

y(t) = c3e^(-t) + c4te^(-t)

where c1, c2, c3 and c4 are constants of integration.

The direction field of the system can be drawn by plotting the slopes of the two equations at each point. The trajectories of the solutions can be sketched by plotting the solutions of the system at different points in time. As t approaches infinity, the solutions of the system tend towards zero, as the exponential term dominates the other terms.

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The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.

Let the relation R R R be asymmetric. A loop in the directed graph corresponds to an ordered pair of the form ( a , a ) (a , a) (a , a). By the definition of asymmetric, the relation R R R cannot contains any ordered pairs of the form ( a , a ) (a , a) (a , a) and thus the directed graph cannot contain any loops.

They are typically represented by labeled points or small circles. We connect vertex a to vertex b with an arrow, called an edge, going from vertex a to vertex b if and only if arb. This type of graph of a relation r is called a directed graph or digraph .

It is a set where either there are many components or only the beginning or ending are provided. By n(A), we refer to the total number of components, and if n(A) is a characteristic number, then the set is constrained.

Let A be finite non-empty set.

Then the exist relation R on A which is both equivalence and order relation.

Suppose A = {[tex]a_{1} , a_{2} , a_{3} , ...... a_{n} ,[/tex]}

And, R = { [tex](a_{1} ,a_{1}) , (a_{2} ,a_{2} ) ,(a_{3} ,a_{3} )........(a_{n} ,a_{n} )[/tex] }    

R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric.

Then R is equivalence relation and an order relation.

Therefore,

The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.

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Answer:

Step-by-step explanation:

We can use similar triangles to solve this. The bigger triangle is made up of the water tower as the height and the long horizontal line as its base, and the smaller triangle fitted inside the larger is made up of the tripod of the camera as the height and the distance Brian lies on the ground beyond it as the base for that triangle. We have to add this distance to the distance of the larger triangle's base. Setting it up as a proportion:

[tex]\frac{watertower}{base} =\frac{camera}{base}[/tex]

but since everything is in different measurements, we have to sort that out first. Let's change everything to feet.

The water tower's distance is 100 yards + 2 feet 9 inches:

[tex]100yds*\frac{3ft}{1yd}=300'[/tex] and now we add in 2 feet 9 inches which is 2.75 feet to get a total of 302.75 feet from the base of the water tower to the point of the triangle. Since we have already converted Brian's distance to feet we're ready to set up the proportion:

[tex]\frac{x}{302.75} =\frac{5}{2.75}[/tex] and we cross multiply.

2.75x = 1513.75 and divide to get

x = 550.45 feet tall.

Answer:

The volume of each cylinder is given by the formula: V = πr^2h, where r is the base radius and h is the height of the cylinder.

When 25 cylinders are put into the half-filled container, the water level rises to the top of the container, which means that the total volume of the 25 cylinders is equal to the volume of the container. Let's assume the volume of the container is V_container.

So, 25 * πr^2 * h = V_container

Dividing both sides by 25πh gives: r^2 = V_container / (25πh)

Taking the square root of both sides gives: r = √(V_container / (25πh))

Since h = 10 cm, we can substitute this value in the formula above: r = √(V_container / (25π * 10))

Since r is the base radius of the cylinder, it must be positive. So, the final equation becomes:

r = √(V_container / (25π * 10)) cm = 5√(5/π) cm. shown

By using 3.14 for the value of π, we can calculate the value of r:

r = 5√(5/π) = 5√(5/3.14) = 5 * √(5/3.14)

= 5 * √(1.5873) = 5 * 1.259 = 6.295 cm (rounded to the first decimal place)

So, the base radius of the cylinder is approximately 6.3 cm.

The percentage of actual yield to theoretical yield of SO3 + H2O → H2SO4

is B. 86.9%

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500g but the theoretical yield is 575g.

Therefore, The percentage of actual yield to theoretical yield is,

= (500/575)×100%.

= 0.8695×100%.

= 86.95%.

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Answer:

[tex]\boxed{\sin D = 0.39 }[/tex]

Step-by-step explanation:

DEF is a right triangle with hypotenuse = 18 and one leg = 7

The law of sines states that the ratios of the sides of a triangle to the sine of the angle opposite that side must be the same for all sides

[tex]\dfrac{18}{\sin 90} = \dfrac{7}{sin D}[/tex]

sin(90) is 1

So the above equation becomes

[tex]18 = \dfrac{7}{\sin D}[/tex]

Cross multiplying we get
[tex]\sin D = \dfrac{7}{18}\\\\\sin D = 0.3889\\[/tex]

Rounded to the nearest hundredth ( i.e. 2 decimal places):

[tex]\sin D = 0.39 \quad \quad \textrm{ANSWER}\\\\[/tex]

The value of s on the right triangle is s = 4.

Here we can assume that the two triangles are similar triangles, then, the measures of the hypotenuses of the right triangles must be the same one.

Remember that the hypotenuse is the side that is opposite to the 90° angle, then we can write the equation:

s + 43 = 47

s = 47 - 43 = 4

That is the value of s.

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The true statement is Option B, The midpoint Riemann sum approximation overestimates the definite integral.

Given data,

In this case, since the function f changes from increasing to decreasing and the graph of f changes from concave up to concave down, we can infer that the function has a local maximum point within the interval [1, 3].

The midpoint Riemann sum approximation for the definite integral breaks the interval [1, 3] into four subintervals of equal width, and it uses the midpoint of each subinterval to approximate the value of the function within that subinterval.

Now, when the function is increasing, the midpoint Riemann sum approximation will tend to underestimate the value of the definite integral since it approximates the function using values that are smaller than the actual function values.

However, when the function changes from increasing to decreasing, the midpoint Riemann sum approximation will tend to overestimate the value of the definite integral since it approximates the function using values that are larger than the actual function values.

Hence , the midpoint Riemann sum approximation overestimates the definite integral.

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Answer:

Step-by-step explanation:

note that all adjacent triangles will share an angle.

for 13 and 14 this is the case.

for 13 and 14 the adjacent sides are also multiples of each other proportionately. find this by dividing one side by the other for both triangles. if equal they are proportionately larger.

13 and 14 are both similar

for 15 and 16 the same logic can be applied to the side lengths. however, we are not given any information on the angles and cannot determine the angles mathematically.

for 17 and 18 the same logic can be applied again for the sides and given that the angles are confined within each other, the angles are the same.

for 17 and 18 you must add the side lengths for each side together and divide to determine the ratio and compare that to the ratio of the initial triangle

4^4 and 678^678  are the only two interesting numbers that divide 2023^2023.

To find all interesting numbers that divide 2023^2023, we need to find all positive integers n such that n^n divides 2023^2023.

Since 2023^2023 = 2023 * 2023 * ... * 2023 (2023 times), we can see that the factors of 2023^2023 are simply the powers of 2023.

So, a number n^n divides 2023^2023 if and only if 2023^(n-1) divides 2023^2023. This means that n-1 must be a factor of 2023.

The factors of 2023 are 3 and 677. Therefore, the values of n that satisfy the condition are 4 (3+1) and 678 (677+1), which correspond to the interesting numbers 4^4 and 678^678. These are the only two interesting numbers that divide 2023^2023.

Therefore, 4^4 and 678^678  are the only two interesting numbers that divide 2023^2023.

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The expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2) and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|

Given the complex function f(x) = 1/(1-ix), where I = √-1, we can find the real part, imaginary part, and magnitude as follows:

Real part: The real part of a complex number is equal to the real part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the real part of the numerator is 1. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The real part of the complex function is then given by:

Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2)

Imaginary part: The imaginary part of a complex number is equal to the imaginary part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the imaginary part of the numerator is 0. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The imaginary part of the complex function is then given by:

Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)

Magnitude: The magnitude of a complex number is equal to the square root of the sum of the squares of the real and imaginary parts. The magnitude of the complex function is then given by:

|f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|

Therefore, the expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)

and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|.

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The value of

x₁/x₂ = y₁/y₂ = c₁/c₂

the given lies are parallel to each other having no solution .

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are no solutions when the lines are parallel, and there are a finite number of solutions when the two equations graph as the same line.

The equation are

x + y = 25

2x + 2y = 50

The value of

x₁/x₂ = y₁/y₂ = c₁/c₂

So the given lies are parallel to each other having no solution .

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Answer:

x = 9

Step-by-step explanation:

(8x+16) + (9x+11) = 180

17x + 27 = 180

180 - 27 = 153

17x = 153

153/17 = 9

x = 9

Answer:

To solve the equation 8x+16+9x+11=180, add 8x and 9x to both sides to get 17x+27=180. Subtract 27 from both sides to get 17x=153. Divide both sides by 17 to get x=9.

The probability of getting colors in order green-yellow-green is 24/245 and the probability of getting 2 green and 1 yellow ball is 72/245.

(a) The probability that the first ball drawn is green is 3/7. Given that the first ball is green, the probability that the second ball drawn is yellow is 4/6. Given that the first two balls are green and yellow respectively, the probability that the third ball drawn is green is 2/5. The final answer is (3/7) * (4/6) * (2/5) = 24/245.

(b) There are several ways to order 2 green and 1 yellow ball, such as green-green-yellow or green-yellow-green. The total number of such combinations is C(3,2) * C(4,1) = 3 * 4 = 12. The probability of getting any of these combinations is (3/7) * (2/6) * (4/5), so the total probability is 12 * (3/7) * (2/6) * (4/5) = 72/245.

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The probability of getting colors in order green-yellow-green is 24/245 and the probability of getting 2 green and 1 yellow ball is 72/245.

(a) The probability that the first ball drawn is green is 3/7. Given that the first ball is green, the probability that the second ball drawn is yellow is 4/6. Given that the first two balls are green and yellow respectively, the probability that the third ball drawn is green is 2/5. The final answer is (3/7) * (4/6) * (2/5) = 24/245.

(b) There are several ways to order 2 green and 1 yellow ball, such as green-green-yellow or green-yellow-green. The total number of such combinations is C(3,2) * C(4,1) = 3 * 4 = 12. The probability of getting any of these combinations is (3/7) * (2/6) * (4/5), so the total probability is 12 * (3/7) * (2/6) * (4/5) = 72/245.

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The density and uncertainty in the density of the sphere is (1828.28 ± 0.0984)  kg/m³

The radius of a sphere is (6.20 ± 0.30)  cm

Mass of the sphere is (1.81 ± 0.09)  kg

We know that the formula for the density,

Density = mass/volume

d = m/V

As we know tha volume of the sphere is, [tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} \pi r^3\\\\V=\frac{4}{3} \pi (6.2\times 10^{-2})^3\\\\V=0.00099~m^3[/tex]

So, the density would be,

d = (1.81) / (0.00099)

d = 1828.28 kg/m³

We can find the uncertainty in volume as follows :

[tex]\frac{\delta V}{V}=3\frac{\delta r}{r}\\\\\frac{\delta V}{V}=3\times \frac{0.003}{0.0620} \\\\\frac{\delta V}{V}=0.0484[/tex]

and the uncertainty in the mass would be,

[tex]\frac{\delta m}{m}=\frac{0.09}{1.81} \\\\\frac{\delta m}{m}=0.05[/tex]

The uncertainty in the density of the sphere would be,

[tex]\frac{\delta d}{d}=\frac{\delta V}{V}+\frac{\delta m}{m}\\\\\frac{\delta d}{d}=0.0484+0.05\\\\\frac{\delta d}{d}=0.0984[/tex]

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The probability that the system gets damaged is P(AUBUC)=0.76

If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events.

The two events are said to be independent events if the outcome of one event does not affect the outcome of another.

The formula can be defined as:

P(A and B) = P(A)×P(B)P(A and B) = P(A)×P(B)

For independent events U and V we have P(U∩V)=P(U)P(V)

if the viruses are truly independent then the probability that the system gets damaged=

P(AUBUC)=P(A)+P(B)+P(C)-P(AnB)-P(anc)-P(bnc)+P(AnBnC).

0.4+0.5+0.2-0.4*0.5-0.4*0.2-0.5*0.2+0.4*0.5*0.2=1.1-0.2-0.08-0.1+0.04

P(AUBUC)=0.76

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The ith observation in the data set is represented by the number xi. The sample's average value is. V stands for variation. All of the values in a data set are added up to form x.

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The rule for the transformation above include the following: B. (x' , y') = (x - 6 , -y + 1).

In Geometry, a reflection over the x-axis is given by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive:

(x, y)                               →              (x, -y)

This ultimately implies that, the parallelogram was reflected over the x-axis and then translated by 6 units to the left, and followed by a vertical translation downward by 1 unit.

(x' , y') = (x - 6 , -y + 1)

(x' , y') = (1 - 6 , -2 + 1)

(x' , y') = (-5, -1)

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Assuming that the rates are constant, we can see that Tom can paint the fence in 7.5 hours.

Here we will use equations of the form:

(rate at which person x paints)*(time) = 1 fence painted.

We know that Chuck can paint a fence in 5 hours, then if C is the rate (assuming this is constant), we can write:

C*5 hours = 1 fence

C = (1/5) fences per hour.

And let's say that Tom's rate is T.

When they work together, the rate is:

(C + T)

And they can paint the fence in 3 hours, then:

(C + T)*3 hours = 1 fence

Replacing the value of T we will get:

( 1/5 fences per hour + T)*3 hours = 1 fence

1/5 fences per hour + T = 1/3 fences per hour.

T = (1/3 - 1/5) fences per hour

T = (5/15 - 3/15) fences per hour

T = 2/15 fences per hour.

Then Tom paints the fence in:

(15/2) hours = 7.5 hours.

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The perimeter of Rebekah's new mural is 9 meters.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

A rectangular mural measures 1 meter by 3 meters.

Rebekah creates a new mural that is 0.5 meters longer.

The perimeter of Rebekah's new mural,

= 2 (1.5 + 3)

= 9 meters.

Therefore, the perimeter is 9 meters.

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Answer:

9

Step-by-step explanation:

To make the price at the two gyms equal, Sarah would have to purchase three training sessions.

The unit is a method of conundrum that entails measuring the value of an individual unit, multiplied that value, and then calculating the required value. To put it plainly, using unit method is employed to derive a minimum unit value from just a specified multiple. One writer costs Four rupees, thus 40 pens would pay 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, discrete mathematics, mathematical analysis, and its adjoint and reciprocal are all equivalent.

given

Let S stand in for the monthly membership fee for Silver Gym.

Let F stand in for the monthly expense of using Fit Factor.

The number of training sessions used during the month will be denoted by T.

S = 45 +25T

F = 75 +15T

In order for the expenses to be equal, we need to find T. S = F, where 45 + 25T

= 75 + 15T,

10T = 30, and deduct 45+15T.

T = 3 is divided by 10 using the following formula:

To make the price at the two gyms equal, Sarah would have to purchase three training sessions.

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The Correct answer for the weighted average of given numbers  is 4.

What is Weighted average?

Weighted average is one of the most commonly employed measures in statistical data to find the average of quantities when each quantity has a certain weight.

Formula for weighted average:

x= Σ(Weights × Quantity)/Σ(Weights)

In the given question,

first number is 1, Weight of the one of the number given is [tex]\dfrac{1}{4}[/tex](one fourth of first number (1)), The weight of three fourth of the second number  is [tex]\dfrac{3}{4}*5[/tex],  second number is 5.

Weighted average,

[tex]\dfrac{(\dfrac{1}{4}*1 + \dfrac{3}{4}*5)}{\dfrac{1}{4}+\dfrac{3}{4}}[/tex]

[tex]= \dfrac{16}{4}\\\\=4[/tex]

The weighted average of the numbers 1 and 5 with given condition is 4.

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The average acceleration over the given time interval is option C -10 m/s²

By dividing the change in velocity by the change in time, the average acceleration will be determined. Therefore, let's first determine the velocity function:

x = 4t² - 3t³

v = dx / dt

v = d( 4t² - 3t³) / dt

v = 8t - 9t²

Then,

at t = 0 sec , v = 0 m/s.

at t = 2 sec , v = 8(2) - 9(2²) = 16 - 36 = -20 m/s.

Average acceleration;

The rate of change in velocity is referred to as the average acceleration. To calculate the average acceleration of anything, we divide the change in velocity by the time since the initial measurement. A crazy ball's average acceleration, for instance, would be 20 cm/s/s if its velocity rose from 0 to 60 cm/s in 3 seconds.

avg.acc = (- 20 - 0) / (2 - 0) = -20 / 2 = -10 m/s²

That is,

-10 m/s² (option c) will be the average acceleration over the given interval.

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The given question is incomplete. Completed question is here;

The coordinates of an object is given as a function of time by x=4t^2-3t^3,where x is in meter and t is in second .what is its average acceleration over the time interval from 0 to 2 seconds