Studies of Florida weather show that, historically, the Miami region is hit by a hurricane every 25 years. Calculate the following probabilities based on the historical record.
a. What is the probability that Miami will be hit by a hurricane in any given year? Show as a fraction.
b. What is the probability that Miami will be hit by hurricanes in both of the next two consecutive years? Show as a fraction.
c. What is the probability that Miami will be hit by hurricanes in either the next year or the year after? Show as a fraction. 1/25
d. What is the probability that Miami will be hit by at least one hurricane in the next seven years? Show as a percentage with three decimal places

Answer:

1)D

2)B

3(

4)A

5)B

Step-by-step explanation:

please mark me as brainlest

Answer:

1089

Step-by-step explanation:

by multiplying the 2 numbers in any order until 4 digits are obtained.

3 × 11 = 33

33 × 3 = 99

99 × 11 = 1089 ← divisible by 3 and 11

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

equivalent expression.

−2(5+7g) is -10-14g or -14g -10

The number of employees that must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean is 107 employees.

To estimate the mean number of hours worked by all grocery store employees in the county with 95% confidence and a margin of error of 1.5 hours, we can use the sample size formula:

n = (Z * σ / E)²

where:
- n is the required sample size
- Z is the critical value (1.96 for a 95% level of confidence)
- σ is the population standard deviation (7.9 from the previous study)
- E is the margin of error (1.5 hours)

Plugging in the given values:

n = (1.96 * 7.9 / 1.5)²

n ≈ 106.56

Since you cannot have a fraction of an employee, you need to round up to the nearest whole number. Therefore, the researcher must include 107 employees in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean.

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The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Data:

d = 336 mi (total distance)

v1 = 60 m/h (speed 1)

v2 = 48 m/h (speed 2)

In order to compute the time in hours, we can divide the distance by each speed.

Therefore, driving at 60mph Darius will spend 5.6 hours and driving at 48 mph he will spend 7 hours.

The volume of the solid region enclosed by the surface rho = 12 cos φ.

A. 288π

To find the volume of the solid region enclosed by the surface ρ = 12 cos φ in spherical coordinates, we integrate ρ^2 sin φ dρ dφ dθ over the appropriate ranges.

The range of φ is from 0 to π/2, and the range of θ is from 0 to 2π.

Setting up the integral, we have:

V = ∭ ρ^2 sin φ dρ dφ dθ

V = ∫[0, 2π] ∫[0, π/2] ∫[0, 12cosφ] (ρ^2 sin φ) dρ dφ dθ

Let's evaluate the integral step by step:

∫ ρ^2 sin φ dρ = (ρ^3 / 3) ∣[0, 12cosφ] = (12^3 cos^3 φ / 3) - (0^3 / 3) = (12^3 cos^3 φ / 3)

∫ (12^3 cos^3 φ / 3) dφ = (12^3 / 3) ∫ cos^3 φ dφ = (12^3 / 3) * (3/4) = 12^3 / 4

Now, we integrate with respect to θ:

∫ (12^3 / 4) dθ = (12^3 / 4) θ ∣[0, 2π] = (12^3 / 4) * 2π = 12^3 π / 2

Therefore, the volume of the solid region enclosed by the surface ρ = 12 cos φ is 12^3 π / 2.

Simplifying this expression, we get:

Volume = 12^3 π / 2 = 1728π / 2 = 864π

Therefore, the correct option is A. 288π.

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The population of Nigeria in 2011 is 366.466 million people. The population of Nigeria in 2021 is 469.557 million people. In the year 2080, the population of Nigeria reaches 2 billion people.

As per the question,

                          P( t )   =   279\(( 1 + 0.0251 )^{t}\)        → 1

where,          P( t )   =   population in millions

                        t     =    number of years since 2000

⇒ Population of Nigeria in 2011,

Substitute t = 11 in 1,

P( t )   =   279\(( 1 + 0.0251 )^{t}\)

          =   279\(( 1 + 0.0251 )^{11}\)

          =   279\(( 1.0251 )^{11}\)

          =   279( 1.3135)

P( t )   =   366.466

⇒ Population of Nigeria in 2021,

Substitute t = 21 in 1,

P( t )   =   279\(( 1 + 0.0251 )^{t}\)

          =   279\(( 1 + 0.0251 )^{21}\)

          =   279\(( 1.0251 )^{21}\)

          =   279( 1.683)

P( t )   =   469.557

⇒ Year in which the population of Nigeria becomes 2 billion i.e. 2000 million

Substitute P( t ) = 2000 in 1,

P( t )   =   279\(( 1 + 0.0251 )^{t}\)  

2000  =   279\(( 1 + 0.0251 )^{t}\)

\(( 1 + 0.0251 )^{t}\)  =   2000 / 279

\(( 1 + 0.0251 )^{t}\)  =   7.16845878

By applying log on both sides,

t log( 1.0251 )   =   log( 7.16845878 )

t   =    log( 7.16845878 ) / log( 1.0251 )

t   =   79.4547 ≅  80

Therefore, The population of Nigeria is 366.466 million in 2011, 469.557 million in 2021 and 2000 million i.e. 2 billion in 2080.

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The complete question is

The population of Nigeria can be modelled by the function

                             P( t )   =   279\(( 1 + 0.0251 )^{t}\)  

where measures the population in millions and represents the number of years since 2000. using this model, what was the population of Nigeria in 2011? predict the population of Nigeria in 2021. if this growth rate continues, in what year will the population of Nigeria reach 2 billion people?

Answer:

The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: . ... If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

Step-by-step explanation:

Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

Answer:

16

Step-by-step explanation:

Dealing with a fraction exponent on hand can be converted by using the fractional exponents rule where the fraction exponent is converted to something like this:

\(64^\frac{2}{3} = \sqrt[3]{64^{2}}\\\)

As you can see, the denominator of the fractional exponent is now the index of the radical. Here is a guide to know what goes where.

\(64^\frac{x}{y} = \sqrt[y]{64^{x}}\)

Both the original problem (64^2/3) and the converted formula can be put into a calculator.

Simplify (if you want to)

\(\sqrt[3]{64^{2}}\\\sqrt[3]{4096}\\16\)

64 to the power of 2/3 is 16.

Answer:

336 Peanuts

112 Walnuts

Step-by-step explanation:

So first, you can not change the order of the items in a ratio. So the 224 raisins will be in the middle.

It will look like _ : 224 : _

Next, divide 224 by 2 to get the number of walnuts, the number on the right.

So the number on the right will be 112.

Next, multiply 112 by 3 to get 336.

The measure of each exterior angle of a regular 12-sided figure is 30 degrees.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

We are given that;

The number of side of figure=12

Now,

The sum of the exterior angles of any polygon is 360 degrees. For a regular n-sided polygon, each exterior angle measures 360/n degrees.

So for a regular 12-sided figure (dodecagon), each exterior angle measures:

360/12 = 30 degrees

Therefore, the value of the angle will be 30 degrees.

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Answer:

80

Step-by-step explanation:

82-12+10

82+10-12

92-12

80

The number of people in the restaurant will be 80

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that there are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter.

The expression will be solved as below:-

E = 82-12+10

E = 82+10-12

E = 92-12

E = 80

Therefore, the number of people in the restaurant will be 80

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Answer:

It’s crossed my mined a couple times

Step-by-step explanation:

Answer:

The perfect factored square trinomial that is equivalent to the expression x^2 + 8x + 16 is:

(x + 4)^2

To see why this is the case, you can expand the expression (x + 4)^2 using the FOIL method:

(x + 4)^2 = (x + 4) * (x + 4)

= x^2 + 4x + 4x + 16

= x^2 + 8x + 16

So, x^2 + 8x + 16 can be factored as (x + 4)^2, which is a perfect square trinomial.

Answer:

1) c. 10 1/2 + 1/2 m > 14

2)

\(x\leq 3\)

hope this helped

Answer:

how to do this

Step-by-step explanation:

i need it

Step-by-step explanation:

10 % = .10  rate,  r,  in decimal form

interest = p r t        p = principal deposit = $ 20    t = time in years

 Interst =  $ 20 (.10)( 3 ) =  $ 6.00

In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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Answer:

You go to Target. You buy a box of mints for $2.25. You also want to buy some packs of Goldfish for snacks. They each cost $1.50. You have $12.75 to spend. How many packs of Goldfish can you buy along with the box of mints?

We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.

We know that , 1 kg=2.20462 pounds

Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb

Additionally we have, 1 lb = 0.35 mEq

Therefore, 45.195 lb=  0.35 mEq × 45.195 = 15.818 mEq.

Also, 8mEq=1 mL

By using unitary method,

1 mEq=1/8 mL

Converting 15.818 mEq to mL, we get

15.818mEq = 15.818 ÷ 8 = 1.9 mL

Thus, 15.818mEq  = 1.9 mL

Rounding off the answer we get,

The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL

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The Kanizsa triangle illusion helps us understand that our perceptual experiences are not simply the sum of the individual sensory inputs, but rather the result of a complex and variable process of perceptual organization.

Gestalt is a German word meaning "shape" or "form," and in psychology, it refers to a set of principles that describe how people perceive and organize sensory information into meaningful wholes. These principles propose that the whole is greater than the sum of its parts, and that we tend to organize our perceptual experiences into coherent, holistic forms rather than isolated, unrelated sensations.

Experimental examples such as the Necker cube, visual cliff, and others help demonstrate principles of perceptual organization by highlighting how our minds naturally try to impose structure and order on sensory input. For example, the Necker cube is a two-dimensional drawing that can be perceived as a cube that can be viewed from different angles. However, as one stares at the image, it appears to flip back and forth between different possible interpretations. This phenomenon illustrates the Gestalt principle of figure-ground, which describes how we tend to perceive objects as being distinct from their surrounding context.

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The amount or maturity value is Php 95645.18.

Given that Principal (P) = -80,000; Rate of Interest (R) = 6%; Time (t) = 3 years; Rate of Interest (r) compounded Semi-annually.

We need to find out the maturity value or Amount (A).

Step-by-step solution: Now,  since rate of interest is compounded semi-annually, then the rate of interest for every period will be R/2.

Therefore, we have rate of interest (r) compounded semi-annually as:r = R/2= 6/2= 3%Also, Time (t) is given as 3 years, but since the interest is compounded semi-annually, the total number of periods will be:

Total number of periods (n) = 2 × t

                                              = 2 × 3

                                              = 6 periods.

Using the formula for the Amount of an investment(A) that pays semi-annual interest :A = P(1 + r)nA

                                                                                                                                                  = (-80,000)[1 + 3%/2]^6A

                                                                                                                                                   = (-80,000)(1.03)^6A

                                                                                                                                                   = (-80,000)(1.19562)A

                                                                                                                                                   = -95,649.18

Note: Since the answer is asking for the amount at maturity value, this implies that the amount can't be negative.

Therefore, we will ignore the negative sign; which gives us :Amount (A) = Php 95,649.18

Therefore, the correct option is: a. Php 95645.18.

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Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

\(\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\\)

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We have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

To apply the Intermediate Value Theorem to the polynomial function f(x) = x^3 - x - 4 and show that it has a real zero between the integers 1 and 7, we need to verify that f(1) and f(7) have opposite signs.

Let's evaluate f(1) and f(7) to determine their signs:

f(1) = (1)^3 - (1) - 4 = 1 - 1 - 4 = -4

f(7) = (7)^3 - (7) - 4 = 343 - 7 - 4 = 332

From the calculations, we can see that f(1) = -4 and f(7) = 332.

Since f(1) is negative (-4) and f(7) is positive (332), they have opposite signs.

According to the Intermediate Value Theorem, if a continuous function changes sign between two points, then it must have at least one real zero between those points.

Since f(1) = -4 (negative) and f(7) = 332 (positive), the polynomial function f(x) = x^3 - x - 4 must have a real zero between the integers 1 and 7.

Therefore, we have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

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The cost of fencing the semicircular statutory garden is $616.80

The problem is requires fencing of a semicircular garden

The perimeter of a semicircle is given by the formula

= 1/2 ( πd ) + d

d = diameter = 30 feet

π = 3.14

calculating the perimeter

perimeter of the semicircle = 1/2 ( πd ) + d

perimeter of the semicircle = 1/2 ( π * 30 )+ 30

perimeter of the semicircle = 15π + 30

perimeter of the semicircle = 15 * 3.14 + 30

perimeter of the semicircle = 77.1

cost of the material

= perimeter of the garden * cost per linear foot

= 77.1 * 8

= $616.8

the cost of fencing the garden is calculated to be $616.80

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Step-by-step explanation:

the key is to understand that

12 in = 1 ft

1 ft³ (= a cube of 1 ft × 1ft × 1ft or 12in × 12 in × 12 in = 1728 in³) weighs 40 lbs.

her truck can only carry 1,700 lbs without breaking down.

but it would have space for 66×60×24 = 95040 in³ =

95040/1728 = 55 ft³ of soil, which would weigh

55 × 40 = 2200 lbs (too much for the truck).

the same ratio as for the weight her truck can carry applies for the filled volume of the truck bed with that weight :

1700/2200 = 17/22

so, she can only fill 17/22 of her truck bed volume with soil.

i)

percents are calculated by multiplying the ratio by 100 :

17/22 × 100 = 77.27272727... % ≈ 77%

she can fill about 77% of her truck bed with soil without going over the weight limit.

ii)

since she can transport only 1700 lbs in one trip, and 1 ft³ of soil weighs 40 lbs, she can transport

1700/40 = 42.5 ft³ of soil per trip.

she would then earn

42.5 × 1.5 = $63.75 per trip.