What is the equation of the line that passes through the points (10, 7) and (3, 4)?

The mean of the distribution of sample means is 56.7, and the standard deviation of the distribution of sample means is approximately equal to 4.82.

To calculate the mean of the distribution of sample means, we use the fact that the mean of a sample is an unbiased estimate of the population mean, and therefore the mean of the distribution of sample means is equal to the population mean. Thus, the mean of the distribution of sample means is 56.7.

To calculate the standard deviation of the distribution of sample means, we use the formula for the standard error of the mean, which is the population standard deviation divided by the square root of the sample size. Thus, the standard deviation of the distribution of sample means is equal to 75.9 divided by the square root of 246, which is approximately equal to 4.83.

Therefore, the mean of the distribution of sample means is 56.7, and the standard deviation of the distribution of sample means is approximately 4.83

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In linear regression, we are trying to forecast the dependent variable based on the independent variable.

Option C is the correct answer.

We have,

In linear regression, the dependent variable is the outcome variable or the response variable that we want to predict or explain, while the independent variable is the predictor variable or explanatory variable that helps us in predicting the dependent variable.

The beta parameter and y-intercept are coefficients of the linear regression equation that help in determining the relationship between the dependent and independent variables.

Thus,

In linear regression, we are trying to forecast the dependent variable based on the independent variable.

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you are correct

Step-by-step explanation:

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Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

Answer:

 \(\frac{1}{3}\)n  + 4  = 6  

6

Step-by-step explanation:

Given problem:

      4 more than one third of a number n is 6

Unknown:

The equation = ?

Solution of the number  = ?

Solution:

 let the number  = n

So, 4 more than one third of a number;

  One third of n = \(\frac{1}{3}\)n

  4 more;

                \(\frac{1}{3}\)n  + 4

   is 6;

             \(\frac{1}{3}\)n  + 4  = 6   (equation of the expression)

Let us now solve the equation:

                         \(\frac{1}{3}\)n  + 4  = 6  

                    \(\frac{1}{3}\)n = 6 - 4

                   \(\frac{1}{3}\)n = 2

                     n = 6

The length of the hypotenuse of a 45-45-90 triangle is √2x units.

To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:

Leg 1 = Leg 2 = x

To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:

x² + x² = h²

Simplifying this equation, we get:

2x² = h²

To solve for h, we need to take the square root of both sides of the equation:

√(2x²) = √(h²)

√2 * x = h

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Answer:

D)44 degrees

Step-by-step explanation:

2y+y+48=180

3y=132

Y=44

Answer: No, because in order for two or more numbers to combine, both or all of them need to have the same variables, or else they are not like terms and you cannot combine them.

Step-by-step explanation:

hope it helped!!!

Answer:

6

Step-by-step explanation:

f(6) = -6   this is the value when the x value is 6

g(5) = -5 this is the value when the x value is 5

4 * f(6) -6*g(5)

4*-6 - 6* -5

-24 + 30

6

Answer:

6

_____________________

The inequality 4P[(X - 1) < 4] > (2 - m)(2 + m) holds for the given density function and any positive value of m.

To prove the inequality 4P[(X - 1) < 4] > (2 - m)(2 + m), where X is a random variable with the given density function, we can follow these steps:

1. Start by finding the cumulative distribution function (CDF) of X. We integrate the density function from negative infinity to x:

  F(x) = ∫[1/(2m^2)](t - 1) dt from -∞ to x

2. Evaluate the integral to obtain the CDF:

  F(x) = (1/2m^2)(x^2 - 2x + 1) for x ≥ 1

3. Next, calculate the probability P[(X - 1) < 4] using the CDF:

  P[(X - 1) < 4] = F(5) - F(1)

4. Substitute the values of F(5) and F(1) into the equation:

  P[(X - 1) < 4] = (1/2m^2)(25 - 10 + 1) - (1/2m^2)(1 - 2 + 1)

                 = (1/2m^2)(16) = 8/m^2

5. Now, we need to prove that 4P[(X - 1) < 4] > (2 - m)(2 + m).

  Substitute the expression for P[(X - 1) < 4] into the inequality:

  4(8/m^2) > (2 - m)(2 + m)

6. Simplify the inequality:

  32/m^2 > 4 - m^2

7. Multiply both sides by m^2:

  32 > 4m^2 - m^4

8. Rearrange the equation:

  m^4 - 4m^2 + 32 < 0

9. Note that the left-hand side of the inequality is always positive since it represents the square of a real number. Therefore, the inequality holds for any positive value of m.

10. Hence, we have proven that 4P[(X - 1) < 4] > (2 - m)(2 + m) for all positive values of m.

In conclusion, we have shown that the given inequality holds for the given density function and any positive value of m.

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The height of the tower in Alex's drawing is 20.7 centimeters.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We need to find the height of the tower in Alex's drawing.

Let us multiply the actual height of the tower by the scale factor.

Scale factor = 1 : 4000

Height of the actual tower = 828 meters

Height of the tower in Alex's drawing = 828 meters x (1/4000) = 0.207 meters or 20.7 centimeters.

Therefore, the height of the tower in Alex's drawing is 20.7 centimeters.

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Answer:

Step-by-step explanation:

-Start by distributing the 2, -2(3m+1/2).

-Getting -6m-1, your equation should look like -40-6m-1=7m-2

-Combine -40 and -1 to get -41, and then add the -6m to the other side.

-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.

-Now, we have -39=13m. divide both sides by 13 to get m=-3.

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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The volume of the solid of revolution formed by rotating the region between \(y = \frac{x}{3}\) and \(y = \sqrt{x}\) around the line \(x = -1\) is determined using intersection points.

To find the volume of the solid of revolution, we need to determine the intersection points between the two curves \(y = \frac{x}{3}\) and \(y = \sqrt{x}\). Setting the equations equal to each other, we have \(\frac{x}{3} = \sqrt{x}\). Squaring both sides gives us \(\frac{x^2}{9} = x\), which simplifies to \(x^2 - 9x = 0\). Factoring out an \(x\), we get \(x(x - 9) = 0\), so the intersection points are \(x = 0\) and \(x = 9\).

Next, we need to determine the bounds of integration for rotating the region around the line \(x = -1\). Shifting the intersection points one unit to the left, we have \(x = -1\) and \(x = 8\) as the new bounds.

Using the method of cylindrical shells, the volume can be calculated as follows:

\[V = 2\pi \int_{-1}^{8} (x+1) \left(\frac{x}{3}-\sqrt{x}\right) \, dx\]

Evaluating this integral will give us the volume of the solid of revolution.

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a). To maximize production within the budget, 600 units of labor and 100 units of capital should be purchased. b). The maximum production under the budgetary constraint is approximately 8,366 units.

a). To maximize production, we need to allocate the budget efficiently between labor and capital. We can calculate the number of units of labor and capital by dividing the budgeted amount by the cost per unit. The budget of $576,000 divided by the cost of labor per unit ($400) gives us 1,440 units of labor. Similarly, dividing the budget by the cost of capital per unit ($2,400) gives us 240 units of capital. However, this allocation does not maximize production within the budgetary constraint.

b). To find the optimal allocation, we can use the partial derivatives of the production function with respect to L and K. Taking the partial derivative of the production function with respect to L, we get 37.5L^(-0.25)K^0.25. Equating this to the budgeted amount of labor (600 units), we can solve for K, which comes out to be 100 units. Similarly, by taking the partial derivative of the production function with respect to K, we get 12.5L^0.75K^(-0.75). Equating this to the budgeted amount of capital (100 units), we can solve for L, which comes out to be 600 units.

By substituting these values into the production function, we can calculate the maximum number of units of production, which is approximately 8,366 units.

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

The correct answer is: C. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 82% of the time, so the test is not statistically significant.

A p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. In this case, a p-value of 0.18 indicates that if the null hypothesis is true, there is an 18% chance of obtaining a test statistic as extreme or more extreme than the observed value. Since the generally accepted threshold for statistical significance is commonly set at 0.05 (or 5%), a p-value of 0.18 is higher than this threshold. Therefore, we fail to reject the null hypothesis and conclude that the test is not statistically significant.

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Answer:

$112.50

Step-by-step explanation:

To find how much he earns in interest after one year is to multiply the money in the account by 4.5%:

2500 x 4.5% = 112.5

Answer:

425.2

Step-by-step explanation:

v = 1/3\(\pi r^{2} h\)  If the diameter is 12,  then the radius is 6

v = \(\frac{3.14(6^{2})12 }{3}\)

v = \(\frac{3.14(36)(12)}{3}\)

v = 452.16

Helping in the name of Jesus.

The derivative formula for the function g(x) = 15 - 8ln(x) is g'(x) = -8/x.

To find the derivative of g(x), we can use the power rule and the chain rule. The power rule states that the derivative of x^n is n*x^(n-1), and the chain rule allows us to differentiate composite functions.

In this case, g(x) is a combination of a constant function (15) and the natural logarithm function (ln(x)). The derivative of the constant term (15) is 0 since it does not depend on x.

The derivative of the natural logarithm function, ln(x), is 1/x. Therefore, using the chain rule, the derivative of -8ln(x) is -8 * (1/x), which simplifies to -8/x.

Hence, the derivative of g(x) = 15 - 8ln(x) is g'(x) = -8/x.

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Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

The given function is `f(x) = x⁶ sin(10x⁵)`. We need to find the Taylor series of `f` centered at `0` (Maclaurin series of `f`).

Formula used: The Maclaurin series for `f(x)` is given by `f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...... + (f^n(0)/n!)x^n`.

Here, `f(0) = 0` because `sin(0) = 0`.

Differentiating `f(x)` and its derivatives at `x = 0`:`f(x) = x⁶ sin(10x⁵)`

First derivative: `f'(x) = 6x⁵ sin(10x⁵) + 50x¹⁰ cos(10x⁵)`

Differentiate `f'(x)`

Second derivative: `f''(x) = 30x⁴ sin(10x⁵) + 200x⁹ cos(10x⁵) - 250x¹⁰ sin(10x⁵)`

Differentiate `f''(x)`

Third derivative: `f'''(x) = 120x³ sin(10x⁵) + 1800x⁸ cos(10x⁵) - 2500x⁹ sin(10x⁵) - 5000x²⁰ cos(10x⁵)`

Differentiate `f'''(x)`

Fourth derivative: `f⁴(x) = 360x² sin(10x⁵) + 7200x⁷ cos(10x⁵) - 22500x⁸ sin(10x⁵) - 100000x¹⁹ cos(10x⁵) + 100000x²⁰ sin(10x⁵)`

Differentiate `f⁴(x)`

Fifth derivative: `f⁵(x) = 720x sin(10x⁵) + 36000x⁶ cos(10x⁵) - 112500x⁷ sin(10x⁵) - 1900000x¹⁸ cos(10x⁵) + 2000000x¹⁹ sin(10x⁵)`

Differentiate `f⁵(x)`

Sixth derivative: `f⁶(x) = 7200 cos(10x⁵) - 562500x⁶ cos(10x⁵) + 13300000x¹⁷ sin(10x⁵)`

Evaluate at `x = 0`:

The derivatives of `f(x)` evaluated at `x = 0` are:f(0) = 0f'(0) = 0f''(0) = 0f'''(0) = 0f⁴(0) = 0f⁵(0) = 0f⁶(0) = 7200

Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

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Answer:

Exp Date: 1/17/2017

Exp Time: 4:00am

Prep Date: 12/3/2016

Prep Time: 4:00am

Initials: 12/7/2016

Step-by-step explanation:

A well-detailed version of the question has been uploaded in form of an image for easier understand.

Looking at the question, it was said that she received her store order on 12/3/2016 at 4am, this implies that the prep date and time are 12/3/2016 and 4am respectively. Also, it was said that the expiration date was printed on the product and it is 1/17/2017. Obviously, the expiration time would also be 4am because it was prepared at 4am and if we calculate in. 24hours we would get 4am at the expiration date as well. Lastly, we were told she opened the product she received on 12/7/2016 which is the initial date the product was used. From all these we can deduce the following:

Exp Date: 1/17/2017

Exp Time: 4:00am

Prep Date: 12/3/2016

Prep Time: 4:00am

Initials: 12/7/2016

The value of the SW is 12 units.

What is a chord in a circle?

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle.

Since we want to find SW to get SV, we can change SW to x.

We already know the other lengths:

ST = 3

SU = 18

SW=x

SV=x-3

So, 3(18)=x(x-3).

From here, we see that when expanded, this becomes 54 = x² - 3x.

Solving the quadratic, we see that SW is 12, therefore SV is 9.

Hence, the value of the SW is 12 units.

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complete question: Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.

The Discrete Fourier Transform (DFT) of the given sequence, X(n) = 8(n) + 28(n-2) + 38(n-3), can be computed using the Decimation-in-Time Fast Fourier Transform (DIT-FFT) algorithm.

The DIT-FFT algorithm is a widely used method for efficiently computing the DFT of a sequence. It involves breaking down the DFT computation into smaller sub-problems, known as butterfly operations, and recursively applying them. The DIT-FFT algorithm has a complexity of O(N log N), where N is the length of the sequence.

To apply the DIT-FFT to the given sequence, we first need to ensure that the sequence is of length N = 3 or a power of 2. In this case, we have X(n) = 8(n) + 28(n-2) + 38(n-3). The sequence has a length of 3, so we can directly calculate its DFT without any further decomposition.

The DFT of X(n) can be expressed as X(k) = Σ[x(n) * exp(-j2πnk/N)], where k represents the frequency index ranging from 0 to N-1, n represents the time index, and N is the length of the sequence. By substituting the values of X(n) = 8(n) + 28(n-2) + 38(n-3) into the equation and performing the calculations, we can obtain the DFT values X(k) for the given sequence.

The DIT-FFT algorithm can be applied to find the DFT of the given sequence X(n) = 8(n) + 28(n-2) + 38(n-3). The DFT provides the frequency domain representation of the sequence, revealing the magnitude and phase information at different frequencies.

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Answer:

24 m²

Step-by-step explanation:

Given that:

Dimension of bedroom = 6 meter by 4 meter

To obtain how much carpet Lisa would need to cover the floor of her bedroom, we calculate the area of the room.

From the dimension given, the area of the room can be obtained using the Area if a rectangle formular :

Area of room = Length * width

Area of room = 6m * 4m

Area of room = 24 m²

Carpet required is 24m² of carpet

Answer:

24m

Step-by-step explanation:

if you times 6 and 4 that equals 24 really easy problem.

The random variable X represents the length of each engineering conference, and is measured in days.

The normal distribution should be used for this problem, as the underlying population is normal. The normal distribution is a continuous probability distribution that is characterized by a symmetric bell-shaped curve. It is a useful model for events that follow a normal or Gaussian pattern, such as the lengths of engineering conferences.

c. i. The 95% confidence interval for the population mean length of engineering conferences is (3.38, 4.50) days.

ii. The graph of the 95% confidence interval for the population mean length of engineering conferences is shown below.

iii. The error bound for the 95% confidence interval is 0.77 days. This can be calculated using the formula: Error Bound = 1.96*(standard deviation/√sample size). In this case, the error bound is calculated as: 1.96 * (1.28/√84) = 0.77.

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Answer:C

Step-by-step explanation:

Answer:0.01098 minutes

Step-by-step explanation:

To Print 7 pages book report, Jess took = 1/13 minutes

to  print a single page = she will take ??

Solving

7 pages book require = 1/ 13minutes

1 Page = (1 x 1/13)/ 7=0.01098 minutes

By the Distributive Property, the expression is 7h - 70

From the question, the expression is given as

7(h − 10)

As a general rule, the Distributive Property of algebra states that

a(b - c) =a * b - a * c

Using the above as a guide, we have

a = 7, b = h and c = 10

Substitute a = 7, b = h and c = 10 in the equation a(b - c) =a * b - a * c

So, we have

7(h − 10) =7 * h - 7 * 10

Evaluate

7(h − 10) =7h - 70

Hence, the simplified expression is 7h - 70

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To answer the questions related to the probability of droplet sizes, we'll use the normal distribution with the given mean and variance. Let's solve each part of the question:

a. Probability that the size of a single droplet is less than 1500 μm:

To find this probability, we need to calculate the cumulative distribution function (CDF) of the normal distribution up to 1500 μm. We'll use the z-score formula:

z = (x - μ) / σ

Where:

x = droplet size (1500 μm)

μ = mean (1050 μm)

σ = standard deviation (square root of the variance, which is sqrt(22500 μm))

Calculating the z-score:

z = (1500 - 1050) / sqrt(22500)

= 450 / 150

= 3

Using the z-score table or a calculator, we can find that the cumulative probability corresponding to z = 3 is approximately 0.9987.

Therefore, the probability that the size of a single droplet is less than 1500 μm is approximately 0.9987.

b. Probability that the size of a single droplet is between 1000 and 1500 μm:

Similar to part (a), we need to calculate the cumulative probability for two values: 1000 μm and 1500 μm. Let's calculate the z-scores for both values:

For 1000 μm:

z_1000 = (1000 - 1050) / sqrt(22500)

For 1500 μm:

z_1500 = (1500 - 1050) / sqrt(22500)

Once we have the z-scores, we can find the corresponding cumulative probabilities using the z-score table or a calculator. Then, we subtract the probability for 1000 μm from the probability for 1500 μm to find the probability between the two values.

c. Characterizing the smallest 2% of all droplets:

To characterize the smallest 2% of droplets, we need to find the droplet size that corresponds to the 2nd percentile of the normal distribution. In other words, we need to find the value x such that the cumulative probability up to x is 0.02. We can use the z-score formula to solve for x:

z = (x - μ) / σ

We'll find the z-score corresponding to the cumulative probability 0.02 using the z-score table or a calculator. Then, we can rearrange the formula to solve for x:

x = z * σ + μ

d. Probability that at least one of five independently selected droplets exceeds 1500 μm:

To find this probability, we'll use the complement rule. The probability that none of the five droplets exceed 1500 μm is the complement of the probability that at least one of them exceeds 1500 μm. We can calculate this probability by subtracting the probability of none from 1. We'll use the probability obtained in part (a) for a single droplet.

Learn more about probability  here:

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