Consider a set of data in which the sample mean is 33. 7 and the sample standard deviation is 7. 2. Calculate the z-score given that x=30. 2. Round your answer to two decimal places

The value of sin θ is -[tex]\frac{7\sqrt{130} }{130 }[/tex] and cos θ is [tex]\frac{9\sqrt{130} }{130 }[/tex] . The solution has been obtained by using trigonometry.

What is trigonometry?

The study of right-angled triangles, including their sides, angles, and connections, is referred to as trigonometry.

We are given that tan θ is -7/9. The minus sign is there because it lies in the fourth quadrant.

This means that the perpendicular is 7 and the base is 9.

Let the hypotenuse be x.

Now, by using Pythagoras theorem, we get

⇒ [tex]7^{2}[/tex] + [tex]9^{2}[/tex] = [tex]x^{2}[/tex]

⇒ 49 + 81 = [tex]x^{2}[/tex]

⇒ [tex]x^{2}[/tex] = 130

⇒ x = √130

By trigonometry,

⇒ Sin θ = -[tex]\frac{7}{\sqrt{130} }[/tex]

⇒ Sin θ = -[tex]\frac{7\sqrt{130} }{130 }[/tex]

Similarly,

⇒ Cos θ = [tex]\frac{9}{\sqrt{130} }[/tex]

⇒ Cos θ = [tex]\frac{9\sqrt{130} }{130 }[/tex]

Hence, the values for sin θ and cos θ have been obtained.

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The length on drawing​ with the given scale is 14.15 cm.

Using the given scale of 1cm to 2m, we can set up the following proportion to find the length on the drawing:

1 cm : 2 m = x cm : 28.3 m

where x is the length on the drawing that we want to find.

To solve for x, we can cross-multiply and simplify:

1 cm * 28.3 m = 2 m * x cm

Evaluate the products and remove the units

28.3 = 2x

Divide both sides by 2 to solve for x

x = 28.3 / 2

Evaluate

x = 14.15

Therefore, the length on the drawing is 14.15 cm.

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1. The surface area of the pool is given as follows: 2,202,000 square feet.

2. The amount of water that the pool holds is of: 10,000,000 cubic feet.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions for this problem are given as follows:

l = 10000, w = 100, h = 10.

Hence the surface area is given as follows:

S = 2 x (10000 x 100 + 10000 x 10 + 100 x 10)

S = 2,202,000 square feet.

The volume of a rectangular prism is given by the multiplication of it's dimensions, hence:

V = 10000 x 100 x 10

V = 10,000,000 cubic feet.

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To find the dimensions of a parallelogram, you need to know the length of its base and the perpendicular distance from the base to the opposite side, which is also called the height or altitude of the parallelogram.

A quadrilateral (a four-sided polygon) with two pairs of parallel sides is referred to as a parallelogram. This means that the opposite sides of the parallelogram are parallel and have the same length, while the adjacent sides are unequal in length.

The properties of a parallelogram include:

The opposing sides seem to be congruent and parallel (equal in length)

Congruent opposite angles (equal in measure)

The angle adjacent to each other are supplementary (their sum is 180 degrees)

Diagonals bisect each other (the diagonals divide each other into two equal parts)

If you have the measurements of the sides and angles of the parallelogram, you can use trigonometry and geometry to find the length of the base and the height. For example, if you have the lengths of two adjacent sides and the angle between them, you can use the sine function to find the height. The base can be found by using the formula for the area of a parallelogram, which is base times height.

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Using probability, we can find that the probability of getting a triangle shape block when selected at random is 1/5.

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Therefore, the percentage of successful results cannot be zero.

In the question,

Malaya has 5 different shapes of blocks.

Malaya has 10 blocks of each shape.

So, the total no. of blocks = 5 × 10 = 50.

Now, Malaya has 10 blocks of triangular shape.

probability of getting a triangular shape is:

P = 10/50

= 1/5

Therefore, the probability of getting a triangle shape block when selected at random is 1/5.

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The complete question is:

Malaya has 5different shapes of blocks: rectangle, rhombus, square, trapezoid, and triangle. She has 10 of each shape. She selects a block at random. What is the probability of getting a triangle shape block when selected at random?

The values of p are -3 or 3 such that the rank of A is 3.[1,1,-1,0][4,4,-3,1][p,2,2,2][9,9,p,3] are the values of A.

Given, A = [[1,1,-1,0],[4,4,-3,1],[p,2,2,2],[9,9,p,3]] To find the value of p, such that the rank of A is 3.

Rank of a matrix is defined as the maximum number of linearly independent row vectors or column vectors. It is denoted by R(A).When a matrix is in echelon form, its rank is equal to the number of pivots.The rank of a matrix is equal to the maximum number of linearly independent rows or columns in the matrix.Here, A is a matrix,The rank of A is 3.Thus, we can say that there will be 3 linearly independent rows or columns in the matrix.

The augmented matrix [A|0] should have 1 pivot for each linearly independent rows.Therefore, [A|0] will have 3 pivots.Then, the last row of [A|0] should be a linear combination of the first three rows.To find the value of p,Let the matrix A is in echelon form [1,1,-1,0][0,0,1,1][0,0,0,0][0,0,0,0]Let's analyze the matrix A for rank 3If we swap R2 and R3,R2 <-> R3 [1,1,-1,0][p,2,2,2][4,4,-3,1][9,9,p,3]Then, the matrix in echelon form is [1,1,-1,0][0,0,1,1][0,0,0,0][0,0,0,0]We can see that the third row is not a linear combination of the first two rows. Therefore, the first three rows of A are linearly independent.Then, A has rank 3 if we can get rid of the fourth row using linear combinations of the first three rows.

9R1 + (-9)R2 + (-p)R3 = 0Thus, 9 - 9p - p² = 0p² + 9p - 9 = 0(p + 3)(p - 3) = 0p = -3 or 3So, the values of p are -3 or 3 such that the rank of A is 3.[1,1,-1,0][4,4,-3,1][p,2,2,2][9,9,p,3] are the values of A.

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Answer:

To find the area of a parallelogram, we need to multiply the base by the height. In this case, we need to find the height of the parallelogram.

We can see that segment AL and segment RI are both perpendicular to segment AR. Therefore, we can use either of them to find the height.

Let's use segment AL as our height. To find the length of segment L​S, we can use the Pythagorean theorem:

L​S² = A​R² - R​I²

L​S² = 6.2² - 5.3²

L​S² = 16.21

L​S = √16.21

L​S ≈ 4.02 feet

Now we can find the area of the parallelogram:

Area = base x height

Area = AL x LS

Area = 26.5 x 4.02

Area ≈ 106.23 square feet

Therefore, the area of parallelogram RALS is approximately 106.23 square feet.

Step-by-step explanation:

Answer:

13.2

Step-by-step explanation:

using Pythagorean theorem, create the equation for the unknown side, x.

x^2+9^2=16^2

subtract 9^2

x^2=16^2-9^2

Use difference of squares.

x^2=(16-9)*(16+9)

Solve

x^2=7*25

x^2=175

Take the square root of both sides

x=sqrt175

x=13.2

Answer:

8

Step-by-step explanation:

Not sure this is correct

substitute y in the second equation

X+2(-1/4x)=4

X-2/4x=4

4/4x-2/4x=2/4x

2/4x=4

4 /2/4

4•4/2

16/2

8

For the given inequality x < -7 we draw a straight line at the point -7. The inequality is not strict, hence the line is dotted.

A mathematical statement called an inequality compares two numbers or expressions, typically by employing a symbol. Inequalities show that two quantities are not equal and that one is more than or less than the other.

Number lines can be used to visualise inequality conditions. Depending on whether the endpoint is part of the solution set or not, numbers that meet the inequality are shaded in or denoted by an open or closed circle. A number line would, for instance, show the inequality x > 2 with an open circle at 2 and shading to the right to show all values higher than 2.

In many areas of mathematics as well as in other disciplines like economics and social sciences, inequality is used.

For the given inequality x < -7 we draw a straight line at the point -7.

The inequality is not strict, hence the line is dotted.

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(A) A 95% confidence interval estimate for the percentage of all voters who believe competence is more important than character is (0.538, 0.602).

(B) This is due to the interval's lower bound's value of 0.538, which is higher than 0.5.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample

(A) Using the method below, we can calculate an estimate with a 95% confidence interval for the proportion of voters who think competence is more significant than character:

CI equals p z*(sqrt(p*(1-p)/n)/p)).

where: p = the percentage of voters who say character is more essential than competence = 0.57; n = the sample size; 1000; and z = the z-score for a 95% confidence level; 1.96.

By entering the numbers, we obtain:

CI = 0.57 1.96*(sqrt(0.57*(1-0.57)/1000)), which equals 0.57 0.032. (0.538, 0.602)

the 95% confidence interval estimate for the proportion of respondents overall who think competence is more significant than character is (0.538, 0.602).

(B) Based on the range discovered in part, it is reasonable to infer that the majority of voters value competence over character (a). This is due to the interval's lower bound's value of 0.538, which is higher than 0.5. Therefore, we can state with 95% certainty that the actual proportion of voters who think competence is more crucial than character is at least 53.8%, which is a majority.

(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample, then roughly 95% of those intervals would contain the actual proportion of voters who believe competence is more significant than character. That is to say, we have a 95% confidence interval (0.538, 0.602) that contains the actual proportion of voters who think competence is more significant than character.

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Erica can make a maximum of 5 hamburger patties with the amount of meat she has.

In scientific and mathematical computations, unit conversions are crucial because they guarantee that data are stated in the proper units, enabling consistency and correctness. To combine or compare numbers and to understand the findings meaningfully, values must be converted to a standard unit of measurement. Calculation mistakes and erroneous conclusions can result from improper unit conversion.

Given that, a hamburger patty weighs about 6 ounces before it is cooked.

Thus,

2.2 pounds = 35.2 ounces (1 pound = 16 ounces)

35.2 ounces / 6 ounces per patty = 5.87

Erica can make a maximum of 5 hamburger patties with the amount of meat she has.

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10,-2

Step-by-step explanation: 10-2, -9,6, 5-8, 2,-4

Domain: 10,-9, 5, 2,

Range -8, 6,-4, -2

The area of the rectangle is increasing at a rate of 27,900,000 meters³ per year when the width of the region is 450 meters.

The inner-city revitalization region is a rectangle that is twice as long as it is wide. At a time when the area is 450 meters wide, the width of the region is increasing at a rate of 31 meters per year. The aim is to find out how quickly the area is changing at this point in time. The area of the rectangle is given by the formula,

Area = length × width

Given that the width of the rectangle is increasing at a rate of 31 meters per year. Let's say the width of the rectangle is w meters, and the rate of change in width is dw/dt meters per year. Then, we can say, dw/dt = 31 meters per year

Width of the rectangle is w meters

Length of the rectangle is twice the width, or 2w meters

Area of the rectangle is given by the formula, A = lw= 2w × w= 2w²

Now, we need to find dA/dt, the rate at which the area of the rectangle is changing with respect to time (t).We can find it using the formula,

dA/dt = dA/dw × dw/dt

dA/dw = 4w (differentiate 2w² with respect to w)

dw/dt = 31 meters per yeard

A/dt = dA/dw × dw/dt= 4w × 31= 124w meters² per year

From the given information, the width of the rectangle is 450 meters wide. So, the width is w = 450 meters.

dA/dt = 124w meters² per year

= 124 × 450 meters² per year

= 27,900,000 meters³ per year

Which is the increasing rate of the rectangle.

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Answer:

If a = -1/2 is a root of the quadratic equation 8x² - bx - 3, then we know that when x = -1/2, the equation is equal to 0. We can use this information to solve for b.

Substituting x = -1/2 into the equation, we get:

8(-1/2)² - b(-1/2) - 3 = 0

Simplifying and solving for b, we get:

2 - (b/2) - 3 = 0

b/2 = -1

b = -2

Therefore, b = -2 is the value we are looking for.

To find the other root, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the leading coefficient. In this case, the constant term is -3 and the leading coefficient is 8. Therefore, the product of the roots is:

(-1/2) times the other root = -3/8

Solving for the other root, we get:

(-1/2) times the other root = -3/8

other root = (-3/8) / (-1/2)

other root = (3/8) * 2

other root = 3/4

Therefore, the other root is 3/4.

Finally, to find (1/a - 1/b)², we can substitute a = -1/2 and b = -2 into the expression:

(1/a - 1/b)² = (1/(-1/2) - 1/(-2))²

= (-2 - 1/2)²

= (-5/2)²

= 25/4

Therefore, (1/a - 1/b)² is equal to 25/4.

Answer:

[tex]b=2[/tex]

[tex]\textsf{Other root} = \dfrac{3}{4}[/tex]

[tex]\left(\dfrac{1}{a}-\dfrac{1}{b}\right)^2=\dfrac{25}{4}[/tex]

Step-by-step explanation:

Roots are also called x-intercepts or zeros.  They are the x-values of the points at which the function crosses the x-axis, so the values of x when f(x) = 0.

If x = α is a root of a polynomial f(x), then f(α) = 0.

Therefore, given that a = -1/2 is a root of the quadratic equation 8x² - bx - 3, substitute x = -1/2 into the equation and set it to zero:

[tex]\implies 8\left(-\dfrac{1}{2}\right)^2-b\left(-\dfrac{1}{2}\right)-3=0[/tex]

Solve for b:

[tex]\implies 8\left(\dfrac{1}{4}\right)+\dfrac{1}{2}b-3=0[/tex]

[tex]\implies \dfrac{8}{4}+\dfrac{1}{2}b-3=0[/tex]

[tex]\implies 2+\dfrac{1}{2}b-3=0[/tex]

[tex]\implies \dfrac{1}{2}b-1=0[/tex]

[tex]\implies \dfrac{1}{2}b=1[/tex]

[tex]\implies b=2[/tex]

Therefore, the quadratic equation is:

[tex]\boxed{8x^2-2x-3}[/tex]

The product of the roots of a quadratic equation is equal to the constant term divided by the leading coefficient.  

The constant term of the quadratic equation is -3 and the leading coefficient is 8.  Let the other root be "r". Therefore:

[tex]\implies a \cdot r=\dfrac{-3}{8}[/tex]

Substitute the known value of a = -1/2 and solve for r:

[tex]\implies -\dfrac{1}{2} \cdot r=\dfrac{-3}{8}[/tex]

[tex]\implies r=\dfrac{3}{4}[/tex]

Therefore, the other root of the quadratic equation is 3/4.

To find the value of (1/a - 1/b)²​, substitute the given value of a and the found value of b into the equation and solve:

[tex]\implies \left(\dfrac{1}{a}-\dfrac{1}{b}\right)^2[/tex]

[tex]\implies \left(\dfrac{1}{-\frac{1}{2}}-\dfrac{1}{2}\right)^2[/tex]

[tex]\implies \left(-2-\dfrac{1}{2}\right)^2[/tex]

[tex]\implies \left(-\dfrac{5}{2}\right)^2[/tex]

[tex]\implies \dfrac{25}{4}[/tex]

Answer:

-6.99 , -4 , -6.9 , -2 , -6.999 , -6 , 1

Step-by-step explanation:

Any number to the right of -7 is greater than -7.

The probability that client C, the 25-year-old you’re considering for a 30-year policy, lives to be 55 years old is 1.

The potential is implied by the word "probability". This area of mathematics studies how random events occur. The range is the set of values between 0 and 1. Probability has been incorporated into the mathematics to forecast the likelihood of various events. In essence, probability refers to the degree to which something is likely to occur. You can appreciate the possible results of a random experiment using this fundamental probability theory, which is also applied to a probability distribution. Before assessing how likely an event is to occur, we need to know how many possible outcomes there are.

Gerald age = 25 years

Policy considered = 30 years

Age at the end of the policy = 55 years

The probability that Geraldo lives to be 55 years will be:

= P(A + B)

= (25÷55) + (30÷55)

= 55÷55

= 1

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Answer: The y-intercept of the line of fit can be found by looking at the point where the line crosses the y-axis. From the given information, we know that the line passes through the points (0, 40) and (2, 70). To find the equation of the line, we can use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We can find the slope of the line by using the two points:

m = (y2 - y1) / (x2 - x1)

m = (70 - 40) / (2 - 0)

m = 30

So the equation of the line is:

y = 30x + b

To find the y-intercept, we can plug in one of the points and solve for b. Let's use the point (0, 40):

40 = 30(0) + b

b = 40

Therefore, the y-intercept of the line of fit is 40. In the context of the data, this means that a student who did not study at all (0 hours) is predicted to earn a grade of 40 on the test. However, it's important to note that this prediction is based on the data collected from the sample of 8 students and the line of fit may not accurately predict the grades of all students who did not study.

Your welcome.

According to the given information, Mack should make 4 necklaces and 8 wristbands to maximize his profit.

What are linear programming problems?

LPP stands for Linear Programming Problems. Linear programming is a mathematical optimization technique used to maximize or minimize a linear objective function subject to a set of linear constraints. An LPP involves identifying a set of decision variables, an objective function that depends linearly on these variables, and a set of constraints that specify linear relationships between the variables. The objective is to find the values of the decision variables that optimize the objective function while satisfying all the constraints.

To solve this problem, we need to use a system of linear inequalities to represent all the constraints. Let's start by defining the variables:

x = number of necklaces

y = number of wristbands

Now we can write the constraints:

Time constraint: Mack has 360 minutes to make the necklaces and wristbands.

40x + 25y ≤ 360

Production constraint: Mack wants to make no more than 12 items.

x + y ≤ 12

Non-negative constraint: Mack cannot make a negative number of necklaces or wristbands.

x ≥ 0, y ≥ 0

To maximize Mack's profit, we need to define the objective function as the total profit:

P = 3x + 2y

Now we can graph these constraints and find the feasible region:

40x + 25y ≤ 360

x + y ≤ 12

x ≥ 0, y ≥ 0

As shown in attachment 1.

The feasible region is the shaded polygon bounded by the lines: x=0, y=0, x + y ≤ 12, and 40x+25y=360.

To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region:

Corner point A: (0,0)

P = 3(0) + 2(0) = $0

Corner point B: (0,12)

P = 3(0) + 2(12) = $24

Corner point C: (4,8)

P = 3(4) + 2(8) = $28

Corner point D: (9,0)

P = 3(9) + 2(0) = $27

The maximum profit is $28, which occurs when Mack makes 4necklaces and 8 wristbands. Therefore, Mack should make 4 necklaces and 8 wristbands to maximize his profit.

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The graph of the piecewise function is shown in the image attached below.

In this problem we need to graph a piecewise function formed by two linear equations, a horizontal line and an oblique line. According to Euclidean geometry, a line can be formed from two distinct points set on Cartesian plane. The procedure is summarized below:

Lastly, the piecewise function is shown in the image attached below.

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The length of arc of the sector is 52.2 cm and the area of the sector is 260.8 cm²

Arc length is defined as the distance between the two points placed on the circumference of the circle and measured along the circumference. Arc length is the curved distance along the circumference of the circle.

area of an arc = tetha/360 × πr²

l = 299/360 × 3.14 × 10²

l = 93886/360

l = 260.8 cm² ( 1 dp)

The length of arc of the sector

=( tetha)/360 × 2πr

= 299/360 × 2 × 3.14 × 10

= 18777.2/360

= 52.2 cm

therefore the area of the sector is 260.8cm² and the length of the arc is 52.2 cm

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High Voltage, Inc. should use the following notation to construct its null and alternative hypotheses:                           Null Hypothesis: H0: μ1 - μ2 = 0; Alternative Hypothesis: H1: μ1 - μ2 ≠ 0; where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.

The notation High Voltage should use to construct its null and alternative hypotheses is:

(i) Null Hypothesis: H0: μ1−μ2=0

where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.

(ii) Alternative Hypothesis: Ha: μ1−μ2≠0

Where,μ1 and μ2 are the mean lifespan of the light bulbs of High Voltage and its competitor, respectively.

In this problem, paired samples t-test should be used to test the hypotheses.

Paired sample t-test: It is a statistical procedure used to compare two population means with two samples of dependent observations, where the dependent variable is the same or the same subject measured under different conditions. It is used when the observations are paired, i.e., each pair of observations consists of two measurements made on a single subject or item.

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the distance between the points (10, 4) and (1, -8) is 15 units. We round this to the nearest tenth by looking at the first decimal place after the decimal point, which is 5. Since 5 is greater than or equal to 5, we round up the tenths place, giving us a final answer of 15.0 units.

To find the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = √[(x2 - x1)² + (y2 - y1)²]    

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

In this case, the coordinates of the two points are (10, 4) and (1, -8). Substituting these values into the distance formula, we get:

d = √[(1 - 10)² + (-8 - 4)²]

= √[(-9)² + (-12)²]

= √(81 + 144)

= √225

= 15

Therefore, the distance between the points (10, 4) and (1, -8) is 15 units. We round this to the nearest tenth by looking at the first decimal place after the decimal point, which is 5. Since 5 is greater than or equal to 5, we round up the tenths place, giving us a final answer of 15.0 units.

In summary, to find the distance between two points in a coordinate plane, we can use the distance formula. In this case, we found that the distance between the points (10, 4) and (1, -8) is 15 units, rounded to the nearest tenth as 15.0 units.

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Answer:

[tex]The \: problem \: probably \\ \: assumes \: direct \: variation \: \\ \\

y \: = \: k \: x \\ \\

IF \: so, \: then \: plug \: in \: the \: \\ values \: and solve \: for \: k \\ \\

27 \: = \: k(8) \\ \\

k \: = \: \frac{27}{8}

\\ \\

y \: = \: ( \frac{27}{8} )x. \\ \\ Now \: let \: x \: = \: 11 \\ \\

y \: = \: ( \frac{27}{8} )11 = \\ \\ \frac{27(11)}{8} \\ \\ = 37.125 = \\ \\ \frac{371}{8y} \\ \\

y \: = \frac{371}{8}

[/tex]

The measure of angle A is equal to 41.11 rounded to two decimal place, using trigonometric ratio for the cosine of the angle A. The correct option is B.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

cos A = 55/73 {adjacent/hypotenuse}

A= cos⁻¹(55/73) {cross multiplication}

A = 41.1121

Therefore, the measure of angle A is equal to 41.11 rounded to two decimal place, using trigonometric ratio for the cosine of the angle A

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a)  The probability that there will be exactly four droughts in the region over the next decade is approximately 0.193.

b) The probability that it will be a severe drought given that exactly one drought actually occurred in 2 years is approximately 0.164.

c)  The probability that all three droughts that actually occurred in 5 years will be moderate is 0.016.

To determine the probability of there being exactly four droughts in the region over the next decade, the expected value of droughts over a decade must first be calculated. λ, the expected number of droughts over a period, can be calculated using the formula:λ = (number of droughts in the last 60 years)/(60 years)λ = (6+16)/(60)λ = 0.367

Therefore, the expected number of droughts in the region over the next decade is 0.367 x 10 = 3.67.Using the Poisson distribution formula, the probability of there being exactly four droughts in the region over the next decade can be calculated as:P(4) = (e^-3.67)(3.67^4)/(4!)P(4) ≈ 0.193

Therefore, the probability that there will be exactly four droughts in the region over the next decade is approximately 0.193.

Assuming that exactly one drought actually occurred in 2 years, the probability that it will be a severe drought can be calculated using Bayes' theorem:P(severe | 1) = P(1 | severe)P(severe) / P(1)First, P(1) must be calculated:P(1) = P(1 | severe)P(severe) + P(1 | moderate)P(moderate)P(1 | severe) = e^-λ(λ^1) / 1! = e^-0.367(0.367^1) / 1! ≈ 0.312P(1 | moderate) = e^-λ(λ^1) / 1! = e^-0.367(0.367^1) / 1! ≈ 0.592P(moderate) = 16 / 60 = 0.267P(severe) = 6 / 60 = 0.1P(1) ≈ 0.312(0.1) + 0.592(0.267) ≈ 0.279Next, P(severe | 1) can be calculated:P(severe | 1) = P(1 | severe)P(severe) / P(1)P(severe | 1) ≈ (0.312)(0.1) / 0.279 ≈ 0.164

Therefore, the probability that it will be a severe drought given that exactly one drought actually occurred in 2 years is approximately 0.164.

Assuming that exactly three droughts actually occurred in 5 years, the probability that all will be moderate droughts can be calculated using the binomial distribution formula:P(3 moderate) = (n choose k)(p^k)(1-p)^(n-k)where n = 3, k = 3, and p = 16 / 60 = 0.267(n choose k) = (n! / k!(n-k)!) = (3! / 3!(3-3)!) = 1P(3 moderate) = (1)(0.267^3)(1-0.267)^(3-3) = 0.016

Therefore, the probability that all three droughts that actually occurred in 5 years will be moderate is 0.016.

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