There is a 20% chance that a particular volcano will erupt during any given decade. A random number generator generated 10 sets of random numbers from 1 to 5 as shown. The number 1 represents the volcano erupting. Find the experimental probability that the volcano will erupt in 1 or 2 of the next 5 decades

A. To construct a grouped frequency distribution for the given data, we first need to determine the range of the data:

Range = Maximum value - Minimum value

Range = 39 - 5

Range = 34

Next, we need to decide on the width of each class interval. A common rule is to choose the number of classes to be between 5 and 20, and then choose a class width that is a convenient number. In this case, we will choose 8 classes and a class width of 5.

Class width = Range / Number of classes

Class width = 34 / 8

Class width ≈ 4.25

We can round up the class width to 5 to get a convenient number. The class intervals are:

5 - 9.99

10 - 14.99

15 - 19.99

20 - 24.99

25 - 29.99

30 - 34.99

35 - 39.99

40 - 44.99

Next, we count the number of observations that fall into each class interval. This gives us the frequency of each interval. The grouped frequency distribution is:

Class Interval Frequency

5 - 9.99 5

10 - 14.99 8

15 - 19.99 9

20 - 24.99 16

25 - 29.99 7

30 - 34.99 6

35 - 39.99 1

40 - 44.99 0

B. To draw the histogram, frequency polygon, and cumulative frequency curves, we first need to calculate the cumulative frequencies. The less than cumulative frequency is the running total of the frequencies up to each class interval, while the more than cumulative frequency is the running total of the frequencies from each class interval to the end.

Class Interval Frequency Less than Cumulative Frequency More than Cumulative Frequency

5 - 9.99 5 5 62

10 - 14.99 8 13 57

15 - 19.99 9 22 49

20 - 24.99 16 38 40

25 - 29.99 7 45 24

30 - 34.99 6 51 17

35 - 39.99 1 52 11

40 - 44.99 0 52 10

Now we can draw the graphs:

Histogram:

   20 |

       |           __

       |          |  |

       |    __    |  |

       |   |  |   |  |

       |   |  |   |  |

       |   |  |   |  |

       |___|__|___|__|__

           5  10  15  20

Frequency polygon:

   25 |

       |  __

       | |  |     __

       | |  |    |  |

       | |  |    |  |

       | |  |

Answer:

The distance covered by a wheel is given by the formula:

distance = circumference of the wheel x number of revolutions

The circumference of the wheel can be found using the formula:

circumference = 2πr

where r is the radius of the wheel.

Substituting the given values, we get:

circumference = 2π(1.4) = 2π(1.4) = 2(22/7)(1.4) = 8.8 meters

Therefore, the distance covered by the wheel in 250 revolutions is:

distance = 8.8 x 250 = 2200 meters

So, the wheel covers a distance of 2200 meters if it makes 250 revolutions.

Answer:

[tex]\text{Radius} = 1.4 m[/tex]

[tex]\text{Distance covered in One revolution} = 2\pi r[/tex]

[tex]2\pi r =[/tex]

[tex]2\times22=\dfrac{1.4}{7}[/tex]

[tex]= 8.8 \ \text{m}[/tex]

[tex]\text{Distance covered in 250 revolutions}[/tex]

[tex]= 8.8 \ \text{m}\times 250[/tex]

[tex]\bold{= 2200 \ m}[/tex]

[tex]\it{Hope \ this \ is \ the \ answer \ you \ were \ looking \ for.}[/tex]

The value of x is 7.3

The six trigonometric functions of an angle in a right-angled triangle are related by a set of fundamental identities in trigonometry known as the Circle identities.

Given below figure; diameter AC = 33.4 and length AM = 13.8

So, radius OA = 33.4/2 = 16.7

Here the right angle triangle ΔAMO;

So, OA² = AM² + OM²

or, , OM² = OA² - AM²

By putting all values and find OM,

OM² = (16.7)² - (13.8)²

OM² = 278.89 - 190.44

OM = √88.45

OM = 9.40

here, ON = OA = 16.7   (both are radius of circle)

ON = OM + x    

x = ON - OM     (Put the values here and find x value)

x = 16.7 - 9.40 = 7.3

Therefore, the value of x is 7.3

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Answer:

a) (720 - 12xp) p

b) (960 - 17xp) p

Step-by-step explanation:

240 pence = 1 pound

Eliot's change

= 240x3 - (x  ×  12p)

= 720 - (x  ×  12p)

= 720 - 12xp

Maya's change

= 240 x 4 - ( x × 17p)

= 960 - ( x × 17p )

= 960 - 17xp

The measure of ∠U to the nearest degree using Cosine rule is 154⁰.

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The law of cosines states that:

c² = a² + b² - 2ab cos(C)

where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite to the side c.

According to our figure,

UW²=UV²+VW²-2(UV).(VW).Cos V

UW²=1²+2.8²-2(1)(2.8).Cos 17⁰

UW²=3.49

Taking square root on both sides, we get

UW=√3.49

UW=1.87

Now,

Cos U=(UW²+UV²-VW²)/2(UV)(UW)

Cos U=(1.87²+1²-2.8²)/2·(1)·(1.87)

Cos U=-3.34/3.74

Cos U=-0.89

Taking inverse, we get

U=Cos⁻¹(-0.89)

U≈152.37

Rounding to the nearest value in option, we get U=154⁰.

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the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

To determine if the function f: P(A) → P(A), where f(X) = A-X, is onto, one-to-one, neither, or both, we need to consider the following:

Onto: A function is onto if every element in the codomain has a corresponding preimage in the domain. In other words, for every Y in P(A), there exists an X in P(A) such that f(X) = Y.

Let Y be any subset of A. Then, we need to find an X such that f(X) = Y. Since f(X) = A-X, we need to find an X such that A-X = Y. Solving for X, we get X = A-Y. Therefore, we can choose X = A-Y, and we have f(X) = A-(A-Y) = Y. Hence, f is onto.

Next, we need to prove that f is not one-to-one. To do this, we need to find two different sets X1 and X2 such that f(X1) = f(X2).

Hence, the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.

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The quotient using a synthetic method of division is 3x² - x + 10 - 64/(x + 7)

The quotient expression is given as

(3x³ + 20x² + 3x + 6) divided by x + 7

Using a synthetic method of quotient, we have the following set up

-7 |   3    20   3   6

    |__________

Bring down the first coefficient, which is 3:

-7 |   3    20   3   6

    |__________

       3

Multiply 3 by -7 to get -21, and write it below the next coefficient and repeat the process

-7 |   3    20   3   6

    |____-21__7_-70____

       3      -1   10    -64

So, the quotient is 3x² - x + 10 and the remainder is -64

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a. Yes, she will make a profit of around $300.

b. It will take 4 years to earn back her initial investment.

According to the given data, there is a 20% chance that the new business will lose $10,000, a 40% chance it will break even, a 30% chance it will make $5,000 in profits, and a 10% chance it will make $8,000 in profits.

By calculating the expected value, we get an estimate of $300.

To find the expected value :

0.2 × (-10,000) + 0.4 × (0) + 0.3 × 5,000 + 0.1 × 8,000 = $300

a. Yes, Claire should invest in the company. she will make a profit of around  $300 in a year.

b. If Claire's expected value will be $300 and her initial investment $1200.

1200 ÷ 300 = 4 years

It will take around 4 years to earn back her initial investment.

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Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be Option '' value of money" is correct.

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

The phrase "In 2018, Apple's net worth was $945 billion" refers to the company's valuation in that particular year.

So, the appropriate choice is:

the company's market worth.

Option : '' value of money" is correct.

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The balance of the loan after 2 monthly payments is $246,778 (rounded to the nearest dollar).

Compounding refers to the process of earning interest on both the principal amount and the interest earned on that principal over time. In other words, it is the process of reinvesting earnings so that those earnings can also earn money, creating a compounding effect.

Compound interest is calculated on the initial principal amount and also on the accumulated interest of previous periods. This means that the interest earned in each period is added to the principal, and the interest for the next period is calculated on the new total.

To find the balance of the loan after 2 monthly payments, we first need to calculate the total number of payments over the life of the loan. Since the loan is paid over 25 years with monthly payments, the total number of payments is:

25 years x 12 months/year = 300 months

Next, we can use the formula for the present value of an ordinary annuity to calculate the remaining balance after 2 monthly payments. The formula is:

PV = PMT x ((1 - (1 + r)⁻ⁿ) / r)

where PV is the present value or remaining balance, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.

The monthly interest rate is the annual interest rate divided by 12, so in this case, it is:

6% / 12 = 0.005

Plugging in the values, we get:

PV = $1,610.75 x ((1 - (1 + 0.005)⁻³⁰⁰) / 0.005)

PV = $240,902.43

This is the remaining balance after 2 monthly payments. To find the balance after the second monthly payment, we need to subtract two monthly payments from the original loan amount:

$250,000 - ($1,610.75 x 2) = $246,778.50

Therefore, the balance of the loan after 2 monthly payments is $246,778 (rounded to the nearest dollar).

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You can expect the coin to land on heads 2 times when it is tossed 4 times, on average.

The total of the numbers 2, 5, 8, 11, and 14 is thus 40 as the series contains 5 terms.

An arithmetic progression (AP) is a series of numbers where each term is created by multiplying the previous term by a fixed constant (also known as the common difference). In other words, an AP is a set of numbers whose any two consecutive terms' differences are always the same.  For instance, the mathematical progression 2, 5, 8, 11, and 14 has a common difference of 3. An algebraic progression generally takes the following form: "a," "a+d," "a+2," "a+3,"... where a denotes the sequence's first word, d is its common difference, and the ellipsis (...) denotes that the series is infinite. Mathematical progressions are crucial and are utilised in many disciplines, such as algebra, calculus, and number theory.

given

We can use the arithmetic sum formula to determine the sum of the mathematical series with initial term a=2 and common difference d=3:

Sn = (n-1)d/2(2a + n-1)a

where Sn is the sequence's initial n phrases added together.

The value of the nth term can be determined by substituting n into the arithmetic calculation, a = 3n - 1:

We can use the following words to get the value of n for the final term in the sequence:

a n = 14 = 3n - 1

3n = 15

n = 5

Hence, the series contains 5 terms. Now we can calculate the sum using the arithmetic sum formula:

S5 = 5/2(2(2) + (5-1)3)

S5 = 5/2(4 + 12)

S5 = 5/2(16) (16)

S5 = 40

The total of the numbers 2, 5, 8, 11, and 14 is thus 40 as the series contains 5 terms.

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Answer:

Step-by-step explanation: ¼ +6 ⅓;

= [tex]\frac{1}{4}[/tex] +[tex]\frac{19}{3}[/tex];

= [tex]\frac{3+76}{12}[/tex];

= [tex]\frac{79}{12}[/tex];

= 6[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

Well to add fractions, you should make the denominator (denominator means the lower part for example 4 in ¼) the same for all numbers.

Forget the 6 for now, take only ¼ and ⅓ into consideration, make it have the same denominator

For 1/4 you multiply both up and down by 3 so it will become 3/12

For 1/3, multiply both by 4, so it becomes 4/12

You now have 3/12 and 4/12, let's not forget about the 6 now.

How do you obtain 6 if you have to make 12 denominator? (If you do 12×6 you get 72 right?) so 6 = 72/12

Your answer will be obtained like this

1/4 + 6 + 1/3 = 3/12 + 72/12 + 4/12 = 79/12 and you can make it a whole number if you can.

Ans : 79/12 which is also equal to 6 and 7 over 12 (6 7/12)

The y intercept of this quadratic equation is (0, -22)

Any subset of a Cartesian product is a relation.

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B. Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set). As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A graph, which is a collection of all ordered pairs (x, f (x)), is the only way to represent a function.

As you can see from these definitions, every function is a relation to X.

To find the y intercept, set x =0 and solve for y

f(0)=-0²+10×0-22

  = -22

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A model that is shaded to represent a fraction that is equivalent to 9/12 is: A. model A.

In Mathematics, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction is typically composed of two (2) main parts and these include the following:

In order to determine a model that is correctly and appropriately shaded in order to represent a fraction that is equivalent to 9/12, we would have to simplify the fraction as follows;

Fraction = 9/12

By dividing by 3, we have:

Fraction = 3/4

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The terminal point of the unit circle of angle 270° is (0, -1). The correct answer is (C).

Unit Circle is a circle with a radius of one unit. In trigonometry, it is commonly used as a reference circle to understand the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for different angles.

From the unit circle question given above,

angle 0 = 360° represents the point (1,0) on the x-axis,

angle 90° represents the point (0,1) on the y-axis.

angle 180° represents the point (-1,0) on the negative x-axis,

angle 270° represents the point (0,-1) on the negative y-axis.

Therefore, if 0 = 270° in a unit circle, the terminal point would be (0,-1), which is option C.

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The cumulative area corresponds to the​ z-score is 1.67

What is the cumulative area?

The likelihood that a real-valued random variable, X, will assume a value less than or equal to x is represented by the cumulative distribution function of X, or simply by the distribution function of X, assessed at x.

Here, we have

Given: the following cumulative area is 0.952.

We have to find the Z-score that corresponds to the following cumulative area.

p(z<z)=0.952

p(z<1.67)=0.952

z=1.67 (from the standard normal table)

Hence, The cumulative area corresponds to the​ z-score is 1.67

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answer

.0056

explanation

1000 has 3 zeroes so

decimal has to

3 spaces to the left if

dividing

5.6 ÷ 1000 = .0056

Answer:

  31.25 weeks

Step-by-step explanation:

You want to know how many weeks it took to construct 93.75 km of road at the rate of 3 km/week.

The relation between time, rate, and quantity is ...

  time = quantity/rate

  time = (93.75 km)/(3 km/wk) = (93.75/3) wk = 31.25 wk

It took the crew 31.25 weeks to build 93.75 km of road.

Answer:

t > 28.

Step-by-step explanation:

First, write it and collect like terms:

t / 4 > 7

t > 7 x 4

t > 28.

We can conclude after answering the provided question that Therefore, function g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.

In mathematics, a function appears to be a connection between two sets of numbers in which each member of one set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from a set and produces output from another. The variable x has now been frequently sometimes used represent the inputs, and the flexible y is used to represent the outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 represents a linear model in which each x-value yields a unique value of y.

So, g(x) = f(x + 3) = (x + 3)² = x² + 6x + 9.

g(x) = x² + 6x + 9

= 1(x² + 6x + 9)

= 1(x² + 6x + 9 + 9 - 9)

= 1((x + 3)² + 9 - 9)

= 1(x + 3)² + 0

Therefore, g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.

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Answer:

Step-by-step explanation:

The correct definition of volume is: "the amount of space a 3-dimensional object takes up."

so the answer is d

The equation that relates C to R, given the number of cars that Latoya has to rent and the number of cars left after renting, is C = 23 - R.

The number of cars left after 8 cars have been rented is 15 cars.

To write an equation relating the number of cars left (C) to the number of cars rented (R), we can use the total number of cars available (23) and subtract the number of cars rented:

C = 23 - R

Now, to find the number of cars left after renting 8 of them, we can substitute R = 8 into the equation:

C = 23 - 8

C = 15

So, Latoya would have 15 cars left after renting 8 of them.

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There are approximately 720 blue balls, 1080 red balls, 360 green balls, 540 orange balls, and 900 yellow balls in the bin.

To predict how many of each color are in the bin, we can assume that the ratio of each color in the bin is the same as the ratio in the sample of 20 balls.

First, we calculate the total number of each color in the sample:

Blue: 4 balls

Red: 6 balls

Green: 2 balls

Orange: 3 balls

Yellow: 5 balls

Next, we calculate the total number of balls in the sample:

4 + 6 + 2 + 3 + 5 = 20

Now, we can set up proportions to estimate the number of each color in the bin:

Blue: (4/20) * 3600 = 720

Red: (6/20) * 3600 = 1080

Green: (2/20) * 3600 = 360

Orange: (3/20) * 3600 = 540

Yellow: (5/20) * 3600 = 900

Therefore, we predict that there are approximately 720 blue balls in the bin.

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Answer:

Let's use "x" to represent the number of animals in the shelter.

The fixed weekly expenses of the animal shelter are $750, and each animal costs an additional $6 per week. Therefore, the total weekly expenses of the animal shelter would be:

Total Weekly Expenses = Fixed Weekly Expenses + (Cost Per Animal * Number of Animals)

Total Weekly Expenses = 750 + 6x

We know that during the winter month, the weekly expenses are at most $900. So we can write the following inequality to represent this situation:

Total Weekly Expenses ≤ 900

Substituting the expression for the total weekly expenses, we get:

750 + 6x ≤ 900

Simplifying this inequality, we get:

6x ≤ 150

Dividing both sides by 6, we get:

x ≤ 25

Therefore, the inequality that represents the number of animals in the shelter for expenses to be at most $900 a week is:

x ≤ 25

This means that the shelter can have at most 25 animals during the winter month for the expenses to be within the limit of $900 a week.

Step-by-step explanation:

I hope it's help full for you

Therefore, the probability that a randomly selected light bulb will last between 750 and 900 hours is 0.4772, or 47.72%.

What is deviation?

The degree to which anything deviates from a norm or expected value is referred to as its deviation. The deviation of a collection of data from the average or mean value in statistics is a measurement of how dispersed the data are. Absolute deviation and standard deviation are the two different types of variance.

We may determine that, according to the 68-95-99.7 rule, 68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations.

Here, we're trying to determine the likelihood that a randomly chosen light bulb would live between 750 and 900 hours. One standard deviation to two standard deviations above the mean define this range.

First, we need to standardize the values using the formula:

z = (x - μ) / σ

where x is the value, we want to standardize, μ is the mean, and σ is the standard deviation.

For x = 750

z = (750 - 750)/75 = 0

For x = 900

z = (900 - 750)/75 = 2

Now we need to find the area under the standard normal distribution curve between z = 0 and z = 2. We can use a table or calculator to find this area, which is approximately 0.4772.

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Complete question:

Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 750 and 900 hours.

525, 600, 675, 750, 825, 900, 975.

What will be the value of P = [? ]%

Hint: use the 68 - 95 - 99.7 rule.

The odds in favor of it raining tomorrow are 1 to 6.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

To find the odds in favor of it raining tomorrow, we need to calculate the ratio of the probability that it will rain to the probability that it won't rain. The probability that it won't rain is 1 - 1/7 = 6/7.

So, the odds in favor of it raining are:

Probability of raining / Probability of not raining

= (1/7) / (6/7)

= 1/6

Therefore, the odds in favor of it raining tomorrow are 1 to 6.

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