HELPP!

Which value does 50% of the data lie above, and what is it called?

58, the median
56, the upper quartile
43, the lower quartile
49.5, the median

Answer:

$36.40

Step-by-step explanation:

.04x35

Answer:

I believe the answer is -60

Step-by-step explanation:

The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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Answer:

it's 70°

Step-by-step explanation:

well first by vertical angles we know that

\(\angle BAC = \angle DAE\\\\\angle DAE = 4x+6\) ( I don't know how to put the symbol xd)

and given we know that

\(\angle EAF = \angle EAD = 4x+6\)

solving for x

we know that

\(\angle CAD = 180\\\\\angle CAB + \angle ABD = 180\\\\4x+6+6x+14=180\\\\10x+20=180\\\\10x=160\\\\x=16\)

and now for \(\angle EAF\)

\(\angle EAF = 4x+6\\\\\angle EAF = 4(16)+6\\\\\angle EAF = 64+6\\\\\angle EAF = 70\)

The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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Answer: 3 years

Step-by-step explanation:

Interest = 1740 - 1200 = 540

SI = prt / 100

540 = 1200 x 0.15 x t

540 = 180t

t = 540 / 180 = 3

Find the interest amount.

\(I=1740-1200=540\)

Use the formula for simple interest.

\(I=prt/100\)

Solve for t.

\(540=1200 \times 15\% \times t\)

\(540=1200 \times \frac{15}{100} \times t\)

\(540=180t\)

\(t=\frac{540}{180}\)

\(t=3\)

The equation that relates xxx, yyy, zzz, and www is  xxxyyy = wwwzzz

Since Wilmer went up the hill for xxx minutes at a speed of yyy kilometeres per minute, the distance d he moves up the hill is d = speed × time = yyy × xxx = xxxyyy.

Also, Wilmer travels the same path at a speed of zzz kilometers per minute and it took him www minutes. So, the distance d' he moves down hill is d' = speed × time = zzz × www = wwwzzz.

Since the distance he moves up the hill equals the distance he moves down the hill, d = d'

So, xxxyyy = wwwzzz

So, the equation that relates xxx, yyy, zzz, and www is  xxxyyy = wwwzzz

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Answer:

xy = wz

Step-by-step explanation:

Answer:

Easy.......................B.

Step-by-step explanation:

I think that it is B

An augmented matrix is a matrix that is formed by appending one matrix to another. It is used to represent systems of linear equations.

A matrix is a rectangular array of numbers, also called elements, arranged in rows and columns. For example, a matrix with 2 rows and 3 columns would look like this:

[a11 a12 a13]

[a21 a22 a23]

An augmented matrix is a matrix that has an extra column appended to it, usually on the right side, and it is used to represent a system of linear equations. The extra column is used to represent the constants on the right side of the equation.

For example, the system of equations

2x + 3y = 5

4x + 5y = 7

can be represented in the form of an augmented matrix, like this:

[2 3 | 5]

[4 5 | 7]

The vertical bar "|" is used to separate the coefficients of the variables from the constants.

In linear algebra, the Gaussian elimination method and Gauss-Jordan elimination method are used to solve the system of linear equations by using the augmented matrix. The method involves a sequence of operations on the rows of the matrix, such as adding or subtracting a multiple of one row from another, in order to simplify the matrix and eventually find the solution of the system.

In summary, an augmented matrix is a matrix that is formed by appending one matrix to another, and it is used to represent a system of linear equations, which is a set of equations with multiple variables, and can be used to solve them using methods like Gaussian elimination or Gauss-Jordan elimination.

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Answer:

To solve the inequality |h + 3| < 5, we need to consider two cases, depending on whether the expression inside the absolute value bars is positive or negative:

Case 1: h + 3 >= 0

If h + 3 >= 0, then we can remove the absolute value bars without changing the inequality:

h + 3 < 5

Subtracting 3 from both sides, we get:

h < 2

So the solution for this case is h < 2.

Case 2: h + 3 < 0

If h + 3 < 0, then the inequality becomes:

-(h + 3) < 5

Multiplying both sides by -1 (and reversing the inequality), we get:

h + 3 > -5

Subtracting 3 from both sides, we get:

h > -8

So the solution for this case is h > -8.

Putting these two solutions together, we have:

-8 < h < 2

Therefore, the solution set in set-builder notation is:

{h | -8 < h < 2}

Answer:

2,09

Step-by-step explanation:

9.00 - 6.91 = 2.09

(a) To evaluate (x^2) for the ground state of the Harmonic Oscillator, we need to integrate x^2 multiplied by the square of the absolute value of the wavefunction ψ0(x).

(b) The expectation value of p^2 for the ground state of the Harmonic Oscillator is simply the eigenvalue corresponding to the momentum operator squared.

(c) By calculating the uncertainties in position (Δx) and momentum (Δp) for the ground state, we can verify that their product satisfies Heisenberg's uncertainty principle, Δx · Δp ≥ ħ/2.

(a) In the ground state of the Harmonic Oscillator, the wavefunction is given by \(\psi_0(x) = \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{2\sigma^2}}\), where \(\sigma\) is the standard deviation.

To evaluate \((x^2)\), we need to find the expectation value of \(x^2\) with respect to the wavefunction \(\psi_0(x)\). Using the formula for the expectation value, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \left|\psi_0(x)\right|^2 dx\)

Substituting the given wavefunction, we have:

\((x^2) = \int_{-\infty}^{\infty} x^2 \frac{1}{\sqrt{\sigma}}e^{-\frac{x^2}{\sigma^2}} dx\)

Evaluating this integral gives us the value of \((x^2)\) for the ground state of the Harmonic Oscillator.

To evaluate \(\sigma_2\), we can simply take the square root of \((x^2)\) and subtract the expectation value of \(x\) squared, \((x)^2\).

(b) To evaluate \((p^2)\), we need to find the expectation value of \(p^2\) with respect to the wavefunction \(\psi_0(x)\). However, in this case, it is clear that the ground state of the Harmonic Oscillator is an eigenstate of the momentum operator, \(p\). Therefore, the expectation value of \(p^2\) for this state will simply be the eigenvalue corresponding to the momentum operator squared.

(c) The Heisenberg's uncertainty principle states that the product of the uncertainties in position and momentum (\(\Delta x\) and \(\Delta p\)) is bounded by a minimum value: \(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\).

To show that the uncertainty product satisfies the uncertainty principle, we need to calculate \(\Delta x\) and \(\Delta p\) for the ground state of the Harmonic Oscillator and verify that their product is greater than or equal to \(\frac{\hbar}{2}\).

If the ground state wavefunction \(\psi_0(x)\) is a Gaussian function, then the uncertainties \(\Delta x\) and \(\Delta p\) can be related to the standard deviation \(\sigma\) as follows:

\(\Delta x = \sigma\)

\(\Delta p = \frac{\hbar}{2\sigma}\)

By substituting these values into the uncertainty product inequality, we can verify that it satisfies the Heisenberg's uncertainty principle.

Regarding the statement \((x) = 0\) and \((p) = 0\) for this problem, it seems incorrect. The ground state of the Harmonic Oscillator does not have zero uncertainties in position or momentum. Both \(\Delta x\) and \(\Delta p\) will have non-zero values.

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Answer:

5/13

Step-by-step explanation:

5+8=13
Red = 5/13

Blue = 8/13

The probability that 100 randomly selected college students will spend less than $10.00 on average for dinner is approximately 0.9525 or 95.25%.

We can utilize as far as possible hypothesis to inexact the conveyance of test implies for an enormous example size of 100. The example mean is regularly dispersed with a mean of the populace mean ($9.50) and a standard deviation of the populace standard deviation partitioned by the square base of the example size ($3/sqrt(100) = 0.3).

To find the likelihood that 100 arbitrarily chosen understudies will spend under $10.00 on normal for supper, we really want to find the z-score related with the worth $10.00 utilizing the recipe:

z = (x - mu)/(sigma/sqrt(n))

Subbing the given qualities, we get:

z = (10 - 9.5)/(0.3) = 1.67

Utilizing a standard typical dissemination table or number cruncher, we can find that the likelihood of a z-score under 1.67 is roughly 0.9525.

Accordingly, the likelihood that 100 haphazardly chosen understudies will spend under $10.00 on normal for supper is roughly 0.9525 or 95.25%.

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Answer:

What we have to find?

.....

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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a. the equation for the object's velocity is v(t) = -6 cos(t) - 1. b. the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

a) To find the equation for the object's velocity, we need to integrate the acceleration function with respect to time.

The integral of a(t) = 6 sin(t) with respect to t gives us the velocity function v(t):

v(t) = ∫(6 sin(t)) dt

Integrating sin(t) gives us -6 cos(t), so the equation for the object's velocity is:

v(t) = -6 cos(t) + C

To find the constant C, we use the initial velocity v(0) = -7 m/s:

-7 = -6 cos(0) + C

-7 = -6 + C

C = -1

Therefore, the equation for the object's velocity is:

v(t) = -6 cos(t) - 1

b) To find the object's displacement from time 0 to time 3, we need to integrate the velocity function over the interval [0, 3]:

Displacement = ∫[0,3] (-6 cos(t) - 1) dt

Integrating -6 cos(t) gives us -6 sin(t), and integrating -1 gives us -t. Applying the limits of integration, we have:

Displacement = [-6 sin(t) - t] from 0 to 3

Plugging in the upper and lower limits:

Displacement = [-6 sin(3) - 3] - [-6 sin(0) - 0]

Displacement ≈ -6 sin(3) + 3

Therefore, the object's displacement from time 0 to time 3 is approximately -6 sin(3) + 3 meters.

c) To find the total distance traveled by the object from time 0 to time t, we need to integrate the absolute value of the velocity function over the interval [0, t]:

Total Distance = ∫[0,t] |(-6 cos(t) - 1)| dt

Since the absolute value function makes the negative part positive, we can rewrite the equation as:

Total Distance = ∫[0,t] (6 cos(t) + 1) dt

Integrating 6 cos(t) gives us 6 sin(t), and integrating 1 gives us t. Applying the limits of integration, we have:

Total Distance = [6 sin(t) + t] from 0 to t

Plugging in the upper and lower limits:

Total Distance = [6 sin(t) + t] - [6 sin(0) + 0]

Total Distance = 6 sin(t) + t

Therefore, the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

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Answer:

-10

Step-by-step explanation:

-4 + (-6)

-4 - 6

-10

if you didnt know, there is always an invisable 1 before the parentheses unless there is a number there. so think about it as -4 + 1(-6). then, -6 times 1 is still -6.

hope this helps!!!

Answer:

The Answer is -10 because

Step-by-step explanation:

You just do pemdas (parentheses, equation, multiplication, division, adding, subtracting) so you obviously start with -6 and add that to -4 which gives you -10 :)

So, the coach could have participated in at least 14 handshakes.

The total number of handshakes is the sum of the handshakes between gymnasts from different teams and the handshakes between gymnasts from the same team and the coach.

The coach shakes hands with each gymnast from her own team, so the number of handshakes between the coach and gymnasts is equal to the number of gymnasts on the team.

Let's assume the number of gymnasts on a team is x. And the number of teams is y. So the number of handshakes between gymnasts from different teams is x*(x-1)*y/2.

Given the total number of handshakes is 281, we know that:

x*(x-1)*y/2 + x = 281

In order to get the minimum number of handshakes the coach could have participated in, we can assume the maximum number of gymnasts on a team, which is x = 14.

So the equation becomes:

1413y/2 + 14 = 281

So we can find the value of y by solving this equation:

y = (281-14)/(13/2) = 17

Therefore, with x = 14 and y = 17, the minimum number of handshakes the coach could have participated in is 14, which is the number of gymnasts on the team.

So the coach could have participated in at least 14 handshakes.

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The given sequence does not have a common difference (d) as it is a geometric sequence. The recurrence relation is aₙ = aₙ₋₁ * 2, and the closed-form solution is aₙ = 3 * 2^(n-1). This solution is proven using induction.

To find the common difference (d) in the given sequence, we need to observe the pattern between consecutive terms.

The given sequence is: 3, 6, 12, 24, 48

To go from one term to the next, we can see that each term is obtained by multiplying the previous term by 2. This suggests that the sequence is a geometric sequence with a common ratio of 2.

Let's calculate the common difference (d) using the formula for the common ratio in a geometric sequence:

Common Ratio (r) = (second term) / (first term)

r = 6 / 3 = 2

Since the common difference (d) is the difference between consecutive terms in an arithmetic sequence, and we have identified the given sequence as a geometric sequence, we can conclude that there is no common difference (d) in this sequence. Instead, we have a common ratio (r) of 2.

To write the recurrence relation for this sequence, we can use the formula:

aₙ = aₙ₋₁ * r

where aₙ represents the nth term of the sequence and r is the common ratio.

In this case, the first term (a₁) is 3 and the common ratio (r) is 2. Therefore, the recurrence relation is:

aₙ = aₙ₋₁ * 2

To find the closed-form solution for this geometric sequence, we can use the formula:

aₙ = a₁ * r^(n-1)

where aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the position of the term.

In this case, the first term (a₁) is 3, the common ratio (r) is 2, and n represents the position of the term.

The closed-form solution for this geometric sequence is:

aₙ = 3 * 2^(n-1)

To prove this closed-form solution using induction, we need to show that it holds true for the base case (n = 1) and then demonstrate that if it holds true for any arbitrary term, it also holds true for the next term.

Base case (n = 1):

Using the closed-form solution, when n = 1, we have:

a₁ = 3 * 2^(1-1) = 3 * 2^0 = 3 * 1 = 3

This matches the first term of the given sequence, which is 3. Therefore, the closed-form solution holds true for the base case.

Inductive step:

Assume that the closed-form solution holds true for an arbitrary term, let's say, aₖ, where k ≥ 1. In other words, assume that:

aₖ = 3 * 2^(k-1)

Now, let's consider the next term, aₖ₊₁. Using the recurrence relation, we have:

aₖ₊₁ = aₖ * 2

aₖ₊₁ = (3 * 2^(k-1)) * 2

aₖ₊₁ = 3 * 2^k

This matches the closed-form solution when n = k + 1. Therefore, if the closed-form solution holds true for aₖ, it also holds true for aₖ₊₁.

We can conclude that the closed-form solution, a = 3 * 2(n-1), is proven by induction for the given geometric sequence since the base case holds true and the inductive step has been shown.

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Answer: 3 hours

Step-by-step explanation: 65x4=260 455-260=195 195/65=3

The time taken by Jacob's family on the second day will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

The time is calculated as:-

For 4 hours of driving at an average speed of 65 miles per hour, the distance covered is,

d = 65 x 4 = 260 miles

Miles remaining for the second day is,

455 - 260 = 195 miles

Time taken to cover 195 miles second day is,

T = 195 / 65 = 3 hours

Therefore, the time taken by Jacob's family will be 3 hours.

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Answer:

The solution of \(x^3-2x^2+16x-32=0\) is \(\mathbf{x=2,x=4i,x=-4i}\)

So, the real solutions is: x = 2

Imaginary solutions are : x = 4i, x = -4i

Step-by-step explanation:

We need to find real and imaginary solutions to the equations \(x^3-2x^2+16x-32=0\)

First of all we will make groups

\((x^3-2x^2)(+16x-32)=0\)

Finding common terms from the groups

\(x^2(x-2)+16(x-2)=0\\(x-2)(x^2+16)=0\)

Now we know that if ab=0 then a=0 , b=0

\(x-2=0, x^2+16=0\\Simplifying:\\x=2, x^2=-16\\Taking\: square\: root\\x=2,\sqrt{x^2}=\sqrt{-16}\\x=2, x=\pm\sqrt{-16}\\x=2,x=\m\sqrt{-1}\sqrt{16} \\We\:know\:\sqrt{-1}=i \:and \sqrt{x} \:\sqrt{16}=4 \\x=2,x=\pm4i\\x=2,x=4i,x=-4i\)

The solution of \(x^3-2x^2+16x-32=0\) is \(\mathbf{x=2,x=4i,x=-4i}\)

So, the real solutions is: x = 2

Imaginary solutions are : x = 4i, x = -4i

32. Solving integral equation using the convolution theoremThe convolution theorem states that the convolution of two signals in the time domain is equivalent to multiplication in the frequency domain.

Therefore, to solve the given integral equation using the convolution theorem, we need to take the Fourier transform of both sides of the equation.

y(t) = ∫_{-∞}^{∞} sinh(−)g() + ∫_{-∞}^{∞} sinh(−−)g()Taking the Fourier transform of both sides, we haveY() = 2π[G()sinh() + G()sinh(−)]where Y() and G() are the Fourier transforms of y(t) and g(t), respectively.Rearranging for y(t), we gety(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]e^(j) d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)](cos()+j sin())d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d+ j(1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()dTherefore, the solution to the integral equation is given by:y(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d + (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()d

It is always important to understand the principles that govern an integral equation before attempting to solve them. In this case, we used the convolution theorem to solve the equation by taking the Fourier transform of both sides of the equation and rearranging for the unknown signal. The steps outlined above provide a comprehensive solution to the equation.  33. Fourier series representation of f(x)

The Fourier series representation of a periodic signal is an expansion of the signal into an infinite sum of sines and cosines. To find the Fourier series representation of the given signal, we need to first compute the Fourier coefficients, which are given by:an = (1/T) ∫_{-T/2}^{T/2} f(x)cos(nx/T) dxbn = (1/T) ∫_{-T/2}^{T/2} f(x)sin(nx/T) dxFurthermore, the Fourier series representation is given by:f(x) = a_0/2 + Σ_{n=1}^{∞} a_n cos(nx/T) + b_n sin(nx/T)where a_0, a_n, and b_n are the DC and Fourier coefficients, respectively. In this case, the signal is given as:f(x) = -1, -π

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Answer:

x = 1.5

Step-by-step explanation:

\(\frac{x}{3} =\frac{x+2}{7} \\\\7x=3(x+2)\\7x=3x+6\\4x=6\\x=1.5\)

The answers do not contradict Fubini's Theorem. We can say that the functions of the integral are not integrable, and the region is not rectangular.

Given, SS •dy dx CAS 51. Use a CAS to compute the iterated integrals x - y X - Y and -dx dy Jo Jo (x + y)² x y To (x + y) ²

The iterated integrals are, x - y X - Y = ∫[0,1]∫[0,1-x] (x - y) dy dx= ∫[0,1] [(xy - y²/2)]|_[0,1-x] dx= ∫[0,1] x(1-x) - (1-x)²/2 dx= ∫[0,1] (1/2)x² - (3/2)x + 1/2 dx= (1/6) - (3/4) + (1/2) = 1/12-dx dy Jo Jo (x + y)² x y

To (x + y) ² = ∫[0,1]∫[0,1-x] (x+y)² dy dx= ∫[0,1] [(x²y + 2xy² + y³/3)]|_[0,1-x] dx= ∫[0,1] x²(1-x) + 2x(1-x)² + (1-x)³/3 dx= ∫[0,1] (-2/3)x³ + (7/3)x² - (11/3)x + 1 dx= -(1/3) + (7/12) - (11/6) + 1= 1/4

Here, we have two expressions for the same integral, which are 1/12 and 1/4.

This result does contradict Fubini's Theorem. We have two solutions for the same integral. The integral's values from the two integrals differ, as shown by 1/12 and 1/4. As a result, we can say that the functions of the integral are not integrable, and the region is not rectangular. In a nutshell, the iterated integrals have two solutions, which demonstrate that Fubini's Theorem does not hold for the functions of the integral, and the region is non-rectangular.

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x=-8 All the values less than 7 are included in the number line. The graph on number line is shown in figure attached. In the options given

The value for Tan 2a = Cot ( a - 70) gives a= 53.33

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Tan 2a = Cot ( a - 70)

As, tan a= cot (90 - a)

So, cot (90- 2a) = Cot (a-70)

Now, comparing the angles we get

90 -2a = a - 70

90 + 70 = a + 2a

3a = 160

a = 160/3

a = 53.33

Hence, the value of a is 53.33.

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Answer:

I think it would be Maxine's, since they did more tests.

Answer:

-3.7

Step-by-step explanation:

1.  More = Addition

2. 0.65 + -4.35 = -3.7

\(\Large\maltese\underline{\textsf{A. What is Asked}}\)

0.65 more than -4.35

\(\Large\maltese\underline{\textsf{B. This problem has been solved!}}\)

The word more means addition, thus

-4.35+0.65=

\(\bf{-3.7}\)

\(\cline{1-2}\)

\(\bf{Result:}\)

            \(\bf{=-3.7}\)

\(\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}\)