Evaluate ∫SF⃗ ⋅dA⃗ , where F⃗ =(bx/a)i⃗ +(ay/b)j⃗ and S is the elliptic cylinder oriented away from the z-axis, and given by x2/a2+y2/b2=1, |z|≤c, where a, b, c are positive constants.

Answer:

128

Step-by-step explanation:

2x2x2x2x2x2x2 is 128

Answer:

B

Step-by-step explanation:

Answer: n=3

Step-by-step explanation: 5n+3=18

18-3=15

15/5=3

Answer:

Step-by-step explanation:

5n +3 =18

5n = 18- 3

5n = 15

Dividing through with 5

n =15/5

n = 3

Answer:

You don't need "models and equations"; if the denominator is the

same, just subtract the numerators.

Step-by-step explanation:

Answer:

1. Airspeed = 201.17 mph

2. Bearing  = 358.93⁰

Step-by-step explanation:

Given Data:

d = 700 mi

t = 3.5 hrs

speed of wind Vx = 10 mph

velocity of plane Vy = d/t

                                  = 700/3.5

                                  = 200 mph

1. Air speed (V) is calculated using the formula;

V² = V²x + V²y -2*Vx *Vy*cos∝

But ∝ = 338 - 180 = 158°

Substituting into the equation, we have

V² = 10² + 200² - 2*10*200*Cos 158

    = 40100 - 400 *(-0.92718)

    = 40100 + 370.872

 V²   = 40470.872

V = √40470.872

V = 201.17 mph

2. calculating the bearing using cosine rule, we have;

sin∅/Vx = sin∝/V

sin∅/10 = sin158/201.17

sin∅ = 10*sin 158/201.17

        = 3.746/201.17

       = 0.0186

∅ = sin⁻¹ 0.0186

   = 1.07

Therefore,

Bearing = 360 - 1.07

              = 358.93⁰

The airspeed is 201.17 mph and bearing is [tex]358.93^\circ[/tex] and this can be determined by using the vector form of velocity.

Given :

Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 ​mph.

To determine the airspeed the following formula can be used.

[tex]\rm V^2 = V^2_x +V^2_y-2V_xV_y cos \theta[/tex]    ---- (1)

where, [tex]\theta = 338-180 = 158^\circ[/tex], [tex]\rm V_y[/tex] is the velocity of the plane and [tex]\rm V_x[/tex] is the velocity of the wind.

Now, put the value of [tex]\rm V_y[/tex], [tex]\rm V_x[/tex] and [tex]\theta[/tex] in the equation (1).

[tex]\rm V^2 = 10^2+200^2+2\times 10\times 200\times cos158[/tex]

[tex]\rm V^2= 100 + 40000+4000(-0.9271)[/tex]

V = 201.17 mph

Now, using cosine rule:

[tex]\rm \dfrac{sin \alpha}{V_x}=\dfrac{sin \theta }{V}[/tex]

[tex]\rm \dfrac{sin\alpha }{10}=\dfrac{sin158}{201.17}[/tex]

[tex]\rm sin\alpha =10\times \dfrac{sin158}{201.17}[/tex]

[tex]\rm sin \alpha = \dfrac{3.746}{201.17}[/tex]

[tex]\rm sin\alpha =0.0186[/tex]

[tex]\alpha = 1.07^\circ[/tex]

Therefore, the bearing is given by 360 - 13.07 = [tex]358.93^\circ[/tex]

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Answer: 17.28

Step-by-step explanation:

18*12 =216*.02=4.32

18*12=216*.10=21.6

21.6-4.32=17.28

In a year, by opting for online e-checks at a rate of $.02 per check instead of paper checks at $.10 per check for an average of 18 checks per month, your savings amount to $17.28.

The subject of your question is a practical application of mathematics, specifically an area often referred to as personal finance. To find out how much you've saved over a year by sending e-checks online instead of writing paper checks, we first need to calculate the cost of each method and then compare the two.

First, let's calculate how much it would cost for the e-checks. The bank charges you $0.02 for each e-check you send. If you send an average of 18 checks per month over a year (12 months), that's 18 checks/month x 12 months/year = 216 checks/year. At $0.02 a check, that comes out to 216 checks/year x $0.02/check = $4.32/year.

Now let's calculate the cost if you were writing paper checks. The bank charges $0.10 for each paper check you write, so that would have been 216 checks/year x $0.10/check = $21.60/year.

So, by choosing to send e-checks online instead of writing paper checks, you've saved $21.60/year - $4.32/year = $17.28/year.

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Answer:

Find the degree of the equation to determine if linear.

"Not Linear"

Step-by-step explanation:

Answer:

  not linear, degree 2

Step-by-step explanation:

The degree of this equation is the highest sum of the exponents of the variables in any given term.

Here, there is one variable term. The variables are x and y. They each have an exponent of 1, so the degree of the variable term is 1+1 = 2.

Since the degree of the equation is not 1, it is not a linear equation.

Answer:

The standard deviation of the sampling distribution of x overbar, denoted sigma subscript x overbar, is called the Standard Error of the Mean.

Step-by-step explanation:

Standard deviation of the sampling distribution, or sigma Subscript x overbar, is also known as the standard error of the mean. It represents how much the sample means deviate from the population mean. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size.

The standard deviation of the sampling distribution, represented by the symbol sigma Subscript x overbar is also known as the standard error of the mean. This term refers to the standard deviation of the population of all possible sample means from samples of a specific size.

The basic formula to calculate the standard deviation is Σ(x – μ)2 / N for the population and Σ(x – x)² / (n-1) for the sample. Greek symbol µ represents the population mean while 'x' is the sample mean.

The standard error can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). Thus, lesser the standard error, closer are the sample means to the population mean and vice versa. This is a very important concept in statistics as it allows one to estimate an unknown population parameter using sample data.

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The function for the amount of chlorine in the tank as a function of time is [tex]y(t) = \left(\frac{20}{1000^{\frac{5}{3}}} \right) (1000 - 15t)^{\frac{5}{3}}[/tex].

Let y(t) be the amount of chlorine in grams in the tank at time t seconds. The initial amount of chlorine is given by the concentration of chlorine times the volume of the tank: y(0) = 0.02 g/L * 1000 L = 20 grams.

The tank has a mixture being pumped out at a rate of 25 L/s, and fresh water is being pumped in at a rate of 10 L/s. The change in the volume of the tank per second is -15 L/s (since more is being pumped out than in).

The rate of change of the amount of chlorine in the tank, dy/dt, can be described as the rate of chlorine leaving the tank minus the rate of chlorine entering the tank. Fresh water has 0 g/L concentration, so the rate of chlorine entering the tank is 0. Chlorine is leaving the tank with the water at a rate proportional to the concentration of chlorine in the tank.

The volume of water in the tank at any time t can be written as V(t) = 1000 - 15t. The concentration of chlorine in the tank at any time is y(t) / V(t). Therefore, the rate of chlorine leaving the tank is:

[tex]\frac{dy}{dt} = - \left(\frac{25y}{V(t)}\right)[/tex]

Substitute V(t) into the equation:

[tex]\frac{dy}{dt} = - \left(\frac{25y}{1000 - 15t}\right)[/tex]

This is a separable differential equation. We can solve it by separating variables and integrating both sides.

[tex]\frac{dy}{y} = - \frac{25}{1000 - 15t} dt[/tex]

Integrate both sides:

[tex]\int \frac{1}{y} dy = -25 \int \frac{1}{1000 - 15t} dt[/tex]

The integral of [tex]\frac{1}{y}[/tex] is[tex]\ln|y|,[/tex] and the integral of [tex]\frac{1}{1000 - 15t}[/tex] can be found using a substitution method. Let u = 1000 - 15t, then du = -15 dt, or [tex]dt = -\frac{1}{15}[/tex] du.

[tex]\int \frac{1}{1000 - 15t} dt = - \frac{1}{15} \int \frac{1}{u} du = - \frac{1}{15} \ln|u| = - \frac{1}{15} \ln|1000 - 15t|[/tex]

Putting it all together:

[tex]\ln|y| = \frac{25}{15} \ln|1000 - 15t| + C[/tex]

Simplify further:

[tex]\ln|y| = \frac{5}{3} \ln|1000 - 15t| + C[/tex]

Exponentiate both sides to solve for y:

[tex]y = e^{\frac{5}{3} \ln|1000 - 15t| + C} = e^C (1000 - 15t)^{\frac{5}{3}}[/tex]

Let K = [tex]e^C[/tex]. Then:

[tex]y(t) = K(1000 - 15t)^{\frac{5}{3}}[/tex]

Using the initial condition y(0) = 20:

[tex]20 = K 1000^{\frac{5}{3}}[/tex]

Solve for K:

[tex]K = 20 / 1000^{\frac{5}{3}}[/tex]

This equation describes the amount of chlorine in the tank over time, taking into account the rates at which water is pumped in and out.

Answer:

Step-by-step explanation:

Find attach the solution

The equation of the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)

How to determine the graphed rational function

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we have vertical asymptotes at

x = 2 and x = -2

This means that the denominator of the function is

(x + 2)(x - 2)

Looking through the list of options, we have the function with a denominator of (x + 2)(x - 2) to be f(x) = (x + 1)/(x + 2)(x - 2)

Hence, the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)

The rational functions is graphed below is [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] (after dividing both the numerator and denominator by (x)). The correct answer is C.

1. Analyze the graph's behavior:
The graph has vertical asymptotes at x = -3 and x = 2. This means the denominator of rational function must have factors (x + 3) and (x - 2).
The graph intersects y-axis at (0, -1). when x = 0, function value is -1.
As x approaches positive / negative infinity, graph approaches line y = 0. The numerator's degree must be smaller than denominator degree.
2. Consider the answer choices:
Only option C, [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] has correct vertical asymptotes and a numerator degree of 1.
3. Verify the answer choice:
Let's substitute x = 0 into option C:
[tex]F(0) = \frac{(0 - 1)}{(0)(0 - 3)} = \frac{-1}{0} = -\infty[/tex]
This doesn't match the graph's behavior at x = 0. However, this is a common issue with rational functions when the numerator and denominator have a common factor. In this case, both the numerator and denominator have a factor of (x). Dividing both the numerator and denominator by (x) gives:
[tex]F(x) = \frac{\cancel{(x - 1)}}{\cancel{x}(x - 3)} = \frac{1}{(x - 3)}[/tex]
Now, let's substitute x = 0:
[tex]F(0) = \frac{1}{(0 - 3)} = -\frac{1}{3}[/tex]
This matches the graph's behavior at x = 0.

Complete and correct question:

Which of the following rational functions is graphed below?

[tex]A. F(x)=\frac{(x+1)}{(x+3)(x-2)}\\\\B. F(x)=\frac{(x-1)}{(x+2)^{2}}\\\\C. F(x)=\frac{(x-1)}{x(x-3)}\\[/tex]

Answer:

A. 191.54 ft²

B. $2011.17

Step-by-step explanation:

Part A involves multiplying to find the area of the living room using the formula to find the area of a rectangle.

A = b*h (original formula)

A = 15.7*12.2 (substitute values)

A = 191.54 (multiply)

The area of his living room is 191.54 ft²

Next, you need to multiply the number of ft² by the cost per ft² to find the cost to tile the living room

Cost = $10.50*191.54 (equation)

Cost = $2011.17 (multiply)

The total cost of tiling the living room would be $2011.17

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3x4=12

Answer:

Probability that the sample proportion will be greater than 0.5 is 0.8133.

Step-by-step explanation:

We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.

Suppose that the polling organization takes a simple random sample of 500 voters.

Let [tex]\hat p[/tex] = sample proportion

The z-score probability distribution for sample proportion is given by;

               Z = [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion

           p = population proportion = 48%

           n = sample of voters = 500

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample proportion will be greater than 0.5 is given by = P( [tex]\hat p[/tex] > 0.50)

  P( [tex]\hat p[/tex] > 0.50) = P( [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\frac{0.50-0.48}{\sqrt{\frac{0.50(1-0.50)}{500} } }[/tex] ) = P(Z < 0.89) = 0.8133

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.

Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.

Answer:

288

Step-by-step explanation:

2/x = 576

you have to make the x by itself so you would have to multiply 1/2 to 2/x for the first part

then you would carry the 1/2 over to 576 and multiply that by 1/2

the answer would become x = 288

Answer:

1/288

Step-by-step explanation:

[tex]\frac{2}{x} = 576[/tex]

Multiply both sides by x to get rid of the fraction.

2 = 576x

Divide to get x by itself.

2 / 576 = .00347222222

Also = 1/288

Answer:

The given question is:

"Mention the role of the comma in the sequence: - Well, what do you say?"

The role of the comma is to indicate a separation between words to make a specific sense of the statement.

Actually, the official function of commas is to separate words, ideas, phrases to prevent a misreading, and to give a specific signification so readers won't capture the intended sense.

Answer:

list all the statistics

Step-by-step explanation:

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= [tex]\pi r^2h[/tex]

According to the problem,

[tex]\pi r^2 h=25[/tex]

[tex]\Rightarrow h=\frac{25}{\pi r^2}[/tex]

The surface area of the base of the can is = [tex]\pi r^2[/tex]

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× [tex]\pi r^2[/tex])

The lateral surface area of the can is = [tex]2\pi rh[/tex]

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× [tex]2\pi rh[/tex])

                                                 [tex]=\$2.5 \pi r h[/tex]

Total cost of metal is C= 2.00 [tex]\pi r^2[/tex]+[tex]2.5 \pi r h[/tex]

Putting [tex]h=\frac{25}{\pi r^2}[/tex]

[tex]\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}[/tex]

[tex]\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}[/tex]

Differentiating with respect to r

[tex]C'=4\pi r- \frac{62.5}{ r^2}[/tex]

Again differentiating with respect to r

[tex]C''=4\pi + \frac{125}{ r^3}[/tex]

To find the minimize cost, we set C'=0

[tex]4\pi r- \frac{62.5}{ r^2}=0[/tex]

[tex]\Rightarrow 4\pi r=\frac{62.5}{ r^2}[/tex]

[tex]\Rightarrow r^3=\frac{62.5}{ 4\pi}[/tex]

⇒r=1.71

Now,

[tex]\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0[/tex]

When r=1.71 cm, the metal cost will be minimum.

Therefore,

[tex]h=\frac{25}{\pi\times 1.71^2}[/tex]

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

The radius should be approximately 1.7 cm, and the height should be approximately 2.77 cm.

We are to find the dimensions of a cylindrical can without a top that will minimize the cost while containing 25 cubic centimeters (cm³) of liquid.

The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height.

Given V = 25 cm³, we can express the height h in terms of the radius r:

h = V / (πr²) = 25 / (πr²)

The cost involves the lateral surface area (sides) and the bottom area:

Lateral surface area: As = 2πrh

Bottom area: Ab = πr²

Cost of the sides: $1.25 per square cm (let's denote the lateral cost by Cs)

Cs = 1.25 * 2πrh = 2.5πrh

Cost of the bottom: $2.00 per square cm (let's denote the bottom cost by Cb)

Cb = 2.00 * πr² = 2πr²

Total cost C is given by:

C = Cs + Cb = 2.5πrh + 2πr²

Substituting h = 25 / (πr²) into the total cost formula,

C = 2.5πr(25 / πr²) + 2πr² = 62.5 / r + 2πr²

To minimize the cost, we take the derivative of C with respect to r and set it to zero:

dC/dr = -62.5 / r² + 4πr = 0

Simplifying, we get:

4πr³ = 62.5

r³ = 62.5 / 4π = 4.978

r = ∛(4.978) ≈ 1.7 cm

Now, calculate the height h:

h = 25 / (π * 1.7²) ≈ 2.77 cm

Thus, the dimensions of the can that minimize the cost are approximately: radius = 1.7 cm and height = 2.77 cm.

Answer:

0.0217391304

Step-by-step explanation:

Answer:

1/46 gallons per mile

Step-by-step explanation:

Take the gallons used and divide by the number of miles driven  

5 gallons /230 miles

1/46 gallons per mile

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

(9+11)/2 = 10

Answer:

[tex] 22\sqrt 2 [/tex] cm

Step-by-step explanation:

[tex] in \: a \: 45 \degree - 45 \degree - 45 \degree \: \triangle \\ leg = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \therefore \: 22 = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \purple{ \bold{ \therefore \: hypotenuse = 22 \sqrt{2} cm}}[/tex]

Answer:

45 degrees

Step-by-step explanation:

Answer:

[tex]\frac{1}{5^{4}}[/tex] = [tex]\frac{1}{625}[/tex] = 0.0016

Step-by-step explanation:

I'm assuming you mean [tex]5^{-4}[/tex] (which could also be written as 5^-4, for future reference).

Negative exponents actually mean you'd use the term in the denominator, taking away the negative portion. It's difficult to explain in words, and is easier to see.

[tex]5^{-4}[/tex] = [tex]\frac{1}{5^{4}}[/tex]

Notice how the -4 changes to 4, and it becomes the denominator.

[tex]5^{4}[/tex] is also 625, so [tex]5^{-4}[/tex] is also 1/625, or the decimal version (0.0016).

I hope this helps!

Answer:

The approximate probability that there are fewer than 100 accidents in a year = .9251

Step-by-step explanation:

Given -

Mean [tex](\nu )[/tex] =2.2

Standard deviation [tex]\sigma[/tex] = 1.4

Let [tex]\overline{X}[/tex]  be the mean number of accidents per week at the intersection during a year (52 weeks)

Then [tex]\overline{X}[/tex] = [tex]\frac{100}{52}[/tex] = 1.92

the approximate probability that there are fewer than 1.92 accidents per week  in a year

[Z   = [tex]\frac{\overline{X} - \nu }{\frac{\sigma}{\sqrt{n}}}[/tex] ]

=  [tex]P(\overline{X} < 1.92 )[/tex]  = ([tex]P(\frac{\overline{X} - \nu }{\frac{\sigma}{\sqrt{n}}}< \frac{1.92 - 2.2 }{\frac{1.4}{\sqrt{52}}})[/tex]

 = P( [tex]Z < -1.442[/tex] )   ( Using Z table)

=  .9251

Answer:

A decimal number can be divided in a decimal part, a whole part and the decimal point which separates the first two.

So, all numbers that are placed leftside of the decimal point can be classified in units, tens, hundreds, thousands, and so on. Basically, each value depends on a base of 10. This means that thousands are ten times more than hundreds, hundreds are ten times more than tens, tens are ten times more than units.

If we want to a specific value of the whole part in a decimal number, we just need to look units, tens, hundreds, thousands or millions.

For example, if we have the number 1235.8456, the whole part would be 1235, and the value of the numbers that are leftside of the decimal point is 1235 units.

Answer:

The name of the numbers that go to the left of the decimal point is INTEGERS. This is the whole number part of the decimal number.

Step-by-step explanation:

The english translation is

What is the name of the numbers that go to the left of the decimal point?

A number with decimal numbers has 3 parts.

- The whole number part that are to the left of the decimal point. This whole number part is called the INTEGER part.

- The decimal point. The decimal point separates the whole numbers part of the number on the left and the mantissa part that has numbers to the right of the decimal point.

- The numbers to the right of the decimal point constitute a value less than 1. This part of a decimal is called the MANTISSA.

Hope this Helps!!!

Answer:

The number at tenth place is 6. Therefore, I guess there's 6 tens.

Step-by-step explanation:

There are 6 tens in the number 49,869.

To find the number of tens, we look at the digit in the tens place, which is the second digit from the right.

4 is in ten thousand place.

9 is in thousand place.

8 is in hundred place.

6 is in ten place.

As the digit in the tens place is 6.

The digit 6 represents six groups of ten in the number.

So, in the number 49,869, there are 6 tens.

Therefore, the correct answer is that there are 6 tens in the number 49,869.

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Answer:

B. t<2 hours

Step-by-step explanation:

If Tim has to mow his lawn in under two hours.

It means:

Tim must finish mowing the lawn before two hours, therefore t<2 is the correct option.

To express that Tim must mow his lawn in under two hours, the correct inequality is t < 2. This indicates that the time, t, must be less than two hours to complete the task. Option B.

To express the condition that Tim has to mow his lawn in under two hours as an inequality, we represent the time it takes to mow the lawn with the variable t. The inequality that represents the situation is t < 2, meaning the time must be less than two hours. This is conveyed using the less than symbol (<).

In the context of other example inequalities, such as t=0, which represents a starting time, and t=t+1, which indicates an increment of time, these are used to express discrete points or changes in time. However, to represent a range of time under a specific amount, we use an inequality like t < 2 to denote that the time taken should not exceed two hours, option B.

Answer:

The letters of the word readers can be arranged in 1260 distinct ways.

Step-by-step explanation:

A word has n letters.

The are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times

So the number of distincts ways the letters can be arranged is:

[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]

In this question:

Readers.

Has 7 letters.

E repeats twice.

R repeats twice.

So

[tex]N = \frac{7!}{2! \times 2!} = 1260[/tex]

The letters of the word readers can be arranged in 1260 distinct ways.

The word 'READERS' can be arranged in 1260 distinct ways, considering the repetition of letters.

The problem involves finding the number of distinct ways the letters in the word 'READERS' can be arranged. This is a topic in combinatorics, or counting, in mathematics.

The formula for the number of ways of arranging n objects where some objects are identical is n!/r1!r2!... where r1, r2, ... are the numbers of each type of similar object.

In the word 'READERS', there are 7 letters in total (n=7). Three of these letters are 'E', 'R' and 'R' (r1=2) and two of these letters are 'E' (r2=2).

The remaining letters 'A', 'D' and 'S' are all distinct (r3=1, r4=1 and r5=1). So, applying the formula, we get the number of distinct arrangements as 7!/(2!2!1!1!1!) = 1260.

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Answer:

1a

Step-by-step explanation: