How are the zeros of the polynomial function p(x)=(2x−1)(5x+7)(8x+9)
related to the coefficients of p(x)
written in standard form?

Answer:

Since we are given the standard deviation of the sample, we can use the formula:

variance = standard deviation^2

Substituting the given value:

variance = 10.3695^2 kg^2

Calculating:

variance ≈ 107.495 kg^2

Therefore, the variance of the weights of the 10 subjects is approximately 107.495 kg^2.

The probability density function for the average length of life of the two components is fU(u) = (1/7)[tex]e^{(-u/7)}[/tex], u ≥ 0

The length of life of each component is governed by an exponential distribution with a mean of 7, which means that the probability density function for the length of life of each component is given by:

fX(x) = (1/7)[tex]e^{(-x/7)}[/tex], x ≥ 0

The average length of life of the two components is given by:

U = (X1 + X2)/2

where X1 and X2 are the lengths of life of the two components.

To find the probability density function for U, we can use the convolution formula:

fU(u) = ∫fX(x)fX(2u-x)dx

where the limits of integration are from 0 to u if u ≤ 7, and from u-7 to 7 if u > 7.

Plugging in the expressions for fX(x) and fX(2u-x), we get:

fU(u) = ∫(1/7)[tex]e^{(-x/7)}[/tex](1/7)[tex]e^{-(2u-x/7)}[/tex]dx

= (1/49)∫[tex]e^{-(2u-2x/7)}[/tex]dx

= (1/49)∫[tex]e^{(-t/7)}[/tex]dt (where t = 2u - 2x)

= (1/49)(-7[tex]e^{(-x/7)}[/tex])|0 to 2u

= (1/7)[tex]e^{(-u/7)}[/tex], u ≥ 0

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Reason: It fails the vertical line test. It is possible to pass a single vertical line through multiple points on this blue graph.

For instance, we can have a vertical line through x = 1. This vertical line intersects infinitely many points.

In other words, the input x = 1 leads to more than one output, which is a counter-example to show we do not have a function.

A function is only possible if each input in the domain leads to exactly one output in the range.

Since we don't have a function, you don't need to worry about filling in the domain and range boxes.

The graph is a function with a domain of (-infinity, infinity) and a range of (-infinity, infinity).

The graph represents a function because for each value of x, there is exactly one corresponding value of y. As a result, the vertical line test is passed.

The domain of the function is the set of all x-values for which the function is defined. In this case, it appears that the graph extends from x = -infinity to x = infinity, so the domain is (-infinity, infinity).

The function's range is the set of all y-values that the function can yield. According to the graph, the y-values vary from y = -infinity to y = infinite, resulting in the range (-infinity, infinity).

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Answer:

Step-by-step explanation:

To find the average speed for the round trip, we can use the formula:

average speed = total distance / total time

We know that Steve drives 5 miles to school and 5 miles back home, so the total distance is:

total distance = 5 miles + 5 miles = 10 miles

To find the total time, we need to calculate the time it takes for Steve to drive to school and the time it takes for him to return home. We can use the formula:

time = distance / speed

For the first part of the trip, Steve drives 5 miles at 10 mph, so the time it takes is:

time to school = 5 miles / 10 mph = 0.5 hours

For the second part of the trip, Steve drives 5 miles at 40 mph, so the time it takes is:

time to home = 5 miles / 40 mph = 0.125 hours

The total time for the round trip is the sum of the time to school and the time to home:

total time = time to school + time to home

total time = 0.5 hours + 0.125 hours

total time = 0.625 hours

Now we can calculate the average speed using the formula:

average speed = total distance / total time

average speed = 10 miles / 0.625 hours

average speed = 16 miles per hour (rounded to the nearest integer)

Therefore, Steve's average speed for the round trip is 16 mph.

Answer:

16 mph

Step-by-step explanation:

The given sum of money in cents as 375 cents.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

Given that, person has a toonie, a loonie, and three quarters.

1 Toonie = 2 dollars

1 Loonie = 1 dollar

3 quarters = 0.75 dollars

So, sum of money = 2+1+0.75

= 3.75 dollars

1 Toonie = 200 cents

1 Loonie = 100 cents

3 quarters = 75 cents

Sum of money = 200+100+75

= 375 cents

1 Toonie = 8 quarters

1 Loonie = 4 quarters

So, in quarters = 8+4+3

= 15 quarters

Therefore, the given sum of money in cents as 375 cents.

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Answer:

Since triangle ABC is similar to triangle FGH, their angle measures are proportional. We can use the ratios of their angle measures to find the missing angle measures.

Let's call the missing angle measures x, y, z, and w, where x is m∠F, y is m∠G, z is m∠H, and w is m∠C.

From the given information, we have:

m∠A / m∠F = 22 / x

m∠B / m∠G = 75 / y

Since m∠A + m∠B + m∠C = 180 degrees, we can write:

w = 180 - (m∠A + m∠B)

m∠H / m∠C = z / w

Now we can use the ratios to find the missing angle measures:

x = 22 / (22 / x) = 22

y = 75 / (75 / y) = 75

z = m∠H / (m∠H / z) = m∠H

w = 180 - (22 + 75) = 83

So, the missing angle measures are:

m∠F = 22 degrees

m∠G = 75 degrees

m∠H = m∠H (unknown)

m∠C = 83 degrees

Answer:

Step-by-step explanation:

[tex]25-(2x-9)^{2}[/tex]=[tex](25-2x+9)(25+2x-9)=(34-2x)(16+2x)=4(17-x)(8+x)[/tex]

On expanding the expression, we get -

{x³ - 2x²y + xy² - x²y + 2xy² - y³}

Given is the expression as -

(x - y) (x² - 2xy + y²)

The given expression is -

(x - y) (x² - 2xy + y²)

x {x² - 2xy + y²} - y {x² - 2xy + y²}

x³ - 2x²y + xy² - x²y + 2xy² - y³

Therefore, on expanding the expression, we get -

{x³ - 2x²y + xy² - x²y + 2xy² - y³}

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Step-by-step explanation:

x + 2 > 5

x > 5-2

x> 3.

TO FND THE VALUE OF X

2 IS PART OF THE SOLUTION AND 5 TOO also >

with the absence of > you can not find x since the question will be algebraic.

The differential equation for the amount of salt A(t) in the tank at time t is  12 - A(t)/(200 + 3t)  and the amount of salt in the tank when it is full is 290.72 pounds.

To set up a differential equation for the amount of salt A(t) in the tank at time t, we need to determine how the amount of salt changes over time. The rate of change of the amount of salt in the tank is determined by the difference between the rate at which salt flows into the tank and the rate at which salt flows out of the tank.

Since the incoming brine contains 3 pounds of salt per gallon, the rate at which salt flows into the tank is 3 pounds per gallon times 4 gallons per minute, or 12 pounds per minute. Since the mixture flows out of the tank at a rate of 1 gallon per minute, the rate at which salt flows out of the tank is A(t)/V(t), where V(t) is the volume of the mixture in the tank at time t.

Since the volume of the mixture in the tank at time t is the sum of the initial volume and the volume of incoming brine minus the volume of outgoing mixture, we have:

V(t) = 200 + 4t - t = 200 + 3t

Therefore, the rate at which salt flows out of the tank is A(t)/(200 + 3t) pounds per minute. Thus, the differential equation for the amount of salt A(t) in the tank at time t is:

dA/dt = 12 - A(t)/(200 + 3t)

To find the amount of salt in the tank when it is full, we need to find the time t when the tank is full. The tank is full when its volume is 500 gallons, so we have:

200 + 4t - t = 500

Simplifying this equation, we get:

3t = 300

t = 100

Therefore, the tank is full after 100 minutes. To find the amount of salt in the tank when it is full, we can solve the differential equation for A(t) using an appropriate initial condition (i.e., the amount of salt in the tank at t=0):

dA/dt = 12 - A(t)/(200 + 3t)

A(0) = 90

Solving this differential equation, we get:

A(t) = 360 - 270e^(-t/300)

Therefore, the amount of salt in the tank when it is full (i.e., after 100 minutes) is:

A(100) = 360 - 270e^(-1/3)

which is approximately 290.72 pounds.

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The selling price of the bicycle is equal to R1,102.

In Mathematics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling a bicycle can be calculated by using the following function:

Profit made = Cost price - Selling price

Making selling price the subject of formula, we have:

Selling price = Cost price - Profit made

Selling price = R1489 - R387.

Selling price = R1,102.

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Answer:

Step-by-step explanation:

a) the probability of having exactly 10 days of precipitation in the month of April

Answer:

3/4

Step-by-step explanation:

Event A: Choosing a student who is a girl

Event B: Choosing a student who is a senior

Therefore, the events are not mutually exclusive because one student can be a girl and a senior at the same time.

Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to happen.

The correct equation is:

P (G or S) =  P(G) + P(S) - P(G and S)

= 800/1400 + 300/1400 - 200/1400

= 900/1400

= 9/14

This means that 9 out of 19 students is either a girl or a senior.

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The values of data measured on this scale are labels or names. -> Nominal Scale

The values of data measured on this scale can be rank ordered. -> Ordinal Scale. The values of data measured on this scale can be rank ordered and have meaningful an absolute zero point. -> Ratio Scale

The values of data measured on this scale can be rank ordered. In addition, the differences between two adjacent ranks are equal. -> Interval Scale

Nominal Scale: In the nominal scale, the values of data are labels or names used to categorize or classify items into mutually exclusive groups. Nominal data cannot be ordered, measured, or compared. Examples of nominal data include gender (male, female), eye color (blue, brown, green), or car brands (Toyota, Honda, Ford).

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The missing side length of the figure is given as follows:

6 cm.

The segment addition postulate is a geometry axiom that states that a segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, we have that:

Hence the missing side length of the figure is obtained as follows:

16 - 10 = 6 cm.

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To determine which expression has a value of 18, we can evaluate each expression and see which one equals 18.

5 × (40 – 25) – 50 = 5 × 15 – 50 = 75 – 50 = 25, which is not equal to 18.

6x (3212) (100 +50) - (6 + 18+6) + 15 + 10 = 6 × 3212 × 150 - 30 + 25 = 29,021,770, which is not equal to 18.

07+ (16-7)+3+8 = 7 + 9 + 3 + 8 = 27, which is not equal to 18.

Therefore, none of the given expressions has a value of 18.

The probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)

Probability in mathematics is the process of finding chances of an event to happen.

Given that, a deck of card have,

Red cards = 1,2,3

Blue cards =1,2,3,4,5,6

Pr(R) =  Drawing a red card = 3/9 = 1/3

Pr(B) = Drawing a blue card = 6/9 = 2/3

Pr(E) = Drawing an even card = 4/9

Pr(O) = Drawing an odd number card = 5/9

Probability of drawing the red 5 = P(red 5) = 1/9

From the options, we have :-

(A) R or O = Pr(R) + Pr(O)  = 1/3 + 1/9 = 8/9 ≠ 1/9

(B) B and O = Pr(B) × Pr(O) =  2/3 × 5/9 = 10/21 ≠ 1/9

(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27 ≠ 1/9

(E) R'. E' = 1-Pr(R)-1-Pr(E) = 1-1/3 =2/3- 1-4/9 =5/9

= 2/3-5/9

= 1/9

Hence, the probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)

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Answer:

To construct a 90% confidence interval for the mean amount of juice in all such bottles, we first need to find the sample mean and sample standard deviation:

Sample mean, x = (15.2 + 15.5 + 15.9 + 15.5 + 15.0 + 15.7 + 15.0 + 15.7)/8 = 15.4375

Sample standard deviation, s = s = sqrt[((15.2-15.4375)^2 + (15.5-15.4375)^2 + (15.9-15.4375)^2 + (15.5-15.4375)^2 + (15.0-15.4375)^2 + (15.7-15.4375)^2 + (15.0-15.4375)^2 + (15.7-15.4375)^2)/7] = 0.339

Using a t-distribution with degrees of freedom (n-1) = 7 and a 90% confidence level, we can find the t-value as 1.895.

The 90% confidence interval can then be calculated as:

x plus or minus (t-value)*(s/sqrt(n))

= 15.4375 plus or minus (1.895)*(0.339/sqrt(8))

= (15.16, 15.72)

Therefore, the answer is A.

To find a 99% confidence interval for the mean monthly income for all workers at the plant, we use the formula:

x plus or minus (z-value)*(σ/sqrt(n))

where x is the sample mean, σ is the population standard deviation, n is the sample size, and z-value is the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.

Plugging in the given values, we get:

x  plus or minus (z-value)*(σ/sqrt(n))

= 2150  plus or minus (2.576)*(250/sqrt(18))

= (2096, 2204)

Therefore, the answer is A.

The dependent and independent variables are b and t respectively.

A variable is a mathematical symbol, which do not have any fixed value, it can be a function, which changed according to the property given.

Given that, a committee is organizing a music festival in Jefferson County,

The time which reserved by venue, gives the number of band that will play at there,

We need to determine the dependent and independent variables,

Dependent variable :-

Dependent variable is a kind of variable which depends on the factors given, and do not change by its own.

Independent variables :-

The independent variable in the given study is the cause by which the dependent variable works, it does not manipulate by any other variable given.

Here,

The number of bands depends upon the amount of the time that the venue has been reserved for.

Therefore, the number of band is a dependent variable.

Hence, the dependent and independent variables are b and t respectively.

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(a) 0.52, (b) -0.54, (c) 0.68, (d) -0.71, (e) -1.44 - Percentiles for standard normal distribution using z-table.

(a) To find the 71st percentile, we search for the z-score that relates to a combined area of 0.71 to one side of the mean. From the standard typical circulation table, we find that the nearest z-scores are 0.67 and 0.72, with relating areas of 0.7486 and 0.7642, individually. To interject, we utilize the equation:

z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))

where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.71). Connecting the qualities, we get:

z = 0.67 + (0.72 - 0.67) * ((0.71 - 0.7486)/(0.7642 - 0.7486)) = 0.52

Consequently, the 71st percentile is z = 0.52.

(b) To find the 29th percentile, we search for the z-score that compares to a combined area of 0.29 to one side of the mean. From the standard ordinary conveyance table, we find that the nearest z-scores are - 0.53 and - 0.52, with relating areas of 0.2981 and 0.3050, individually. To add, we utilize the recipe:

z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))

where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.29). Connecting the qualities, we get:

z = - 0.53 + (- 0.52 - (- 0.53)) * ((0.29 - 0.2981)/(0.3050 - 0.2981)) = - 0.54

Consequently, the 29th percentile is z = - 0.54.

(c) To find the 76th percentile, we search for the z-score that relates to an aggregate area of 0.76 to one side of the mean. From the standard ordinary appropriation table, we find that the nearest z-scores are 0.73 and 0.77, with relating areas of 0.7673 and 0.7794, separately. To interject, we utilize the equation:

z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))

where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.76). Connecting the qualities, we get:

z = 0.73 + (0.77 - 0.73) * ((0.76 - 0.7673)/(0.7794 - 0.7673)) = 0.68

Consequently, the 76th percentile is z = 0.68.

(d) The 24th percentile compares to a z-score of - 0.71, meaning 24% of the standard ordinary conveyance misleads its left.

(e) The seventh percentile relates to a z-score of - 1.44, meaning 7% of the standard typical conveyance misleads its left.

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The Probability (less than 4) when the spinner is spun once is 0.5, the correct option is D.

When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

E = favorable event

S = total sample space

Then:

P(E) = [tex]\dfrac{A(E)}{A(S)}[/tex]

where A(E) is the area/volume/length for event E, and similar for A(S).

Given that;

Spinner is divide in eight sections that has 3blue, 1 red, 2 purple, 2 yellow

Now,

The coloured spinner is divided into = 8 colour sections

The P event;

=4/8

=1/2

=0.5

Therefore the probability of event will be 0.5.

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The 22 half-pieces Kristin had from cutting the sheets she started with and the 7 pieces she found, indicates, that the solution to the word problem is that the number of sheets of paper Kristin started with are;

A word problem is a mathematical question in which the scenario of the question is described using verbal terms, or complete sentences, rather than mathematical symbols or expressions, but which are solved using mathematical calculations.

Let x represent the initial number of paper Kristin had.

The extra number of papers Kristin found = Seven more pieces

The size in which Kristin cut each piece of paper = In half

The number of pieces she had after cutting the papers = 22 half-pieces

Therefore, the following equation can be used to find the number of sheets of paper, x, she started with;

2 × (x + 7) = 22

2 × (x + 7)/2 = 22 ÷ 2 = 11

x + 7 = 11

x = 11 - 7 = 4

The number of sheets of paper Kristin started with, x = 4 sheets of paper

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There are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.

In mathematics, the Cartesian product is a binary operation that takes two sets and forms a set consisting of all possible ordered pairs of elements from the two sets. The resulting set is often denoted by A × B, where A and B are the two original sets.

Formally, if A and B are two sets, the Cartesian product A × B is defined as:

A × B = {(a, b) : a ∈ A and b ∈ B}

This means that the Cartesian product contains all possible ordered pairs (a, b) where a is an element of A and b is an element of B. For example, if A = {1, 2} and B = {x, y}, then A × B would be {(1, x), (1, y), (2, x), (2, y)}.

The Cartesian product B × C is the set of all ordered pairs (b, c) where b is an element of B and c is an element of C. Since B has 5 elements and C has 3 elements, there are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.

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The rate of change on a slope graph is 25.

How do you find the rate of change on a slope graph?

The rate of change for a line is the slope, the rise over run, or the change in over the change in. The slope can be calculated from two points in a table or from the slope triangle in a graph.

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.

Given :

Y - variations = 0 , 25 , 50 ,75 , 100 , 125..........

X - variations = 0 , 1 , 2 , 3 , 4 , 5 , 6 .........

Thus , we can formulate the points as,

(0,0) , (1,25) , (2,50) , (3,75) and so on ...

for rate of change of graph with (x1 , y1) and (x2 , y2) as co-ordinate point we know that,

rate of change = (y2-y1)/(x2-x1)

Similarly ,by taking any two points(let (0,0) and (1,25)) from formulated points , we can say that

rate of change = (25-0)/(1-0)

rate of change = 25

Hence , the rate of change on a slope graph is 25.

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Every point of an open set in R2 is a limit point, but only the boundary points of a closed set are limit points.

Every point of every open set E in R2 is a limit point of E. This is because an open set is characterized by the fact that all of its boundary points are included in the set. Therefore, all of the points in the set are limit points because they are all on the boundary of the set.

For closed sets in R2, the answer is not the same. A closed set is characterized by the fact that it is determined by its boundary points and all of its interior points. Therefore, only the boundary points of a closed set are limit points, while the interior points are not.

Every point of an open set in R2 is a limit point, but only the boundary points of a closed set are limit points.

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The statement that is NOT true about brake drum inside diameter measurements with a brake drum micrometer is B.

If the drum diameter is less than specified, replace the drum. In fact, if the drum diameter is less than the minimum specified limit, the drum can be machined to a larger diameter to restore its proper dimension. This will depend on the manufacturer's recommendations, and the minimum thickness limits of the drum should also be checked to ensure it is within safe tolerances.

                          The other statements are true: A. The drum should be cleaned before measuring the diameter, to avoid errors due to dirt or rust. C. The diameter should be measured at two locations around the drum, usually at the top and bottom of the friction surface, to check for taper or out-of-roundness. D. The drum diameter variation should not exceed 0.035 in (0.009 mm), to ensure proper brake function and minimize vibration or noise.

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The probability of a positive test result given that the subject actually lied is 0.962

In simple terms, probability is the measure of the likelihood of an event occurring. In this question, we are asked to find the probability of a positive test result given that the subject lied.

Let's break down the question and use the formula for conditional probability. Conditional probability is the probability of an event occurring, given that another event has already occurred.

P(A|B) = P(A and B) / P(B)

In this case, A represents the event of a positive test result, and B represents the event of the subject lying.

From the question, we know that 2% of the subjects lie, and 90% of those who lie test positive. This means that out of the 98 subjects, 2% or 1.96 subjects lied. And out of those 1.97 subjects, 90% or 1.78 subjects tested positive.

So, the probability of a positive test result given that the subject lied is

=> P(A|B) = 1.78/1.97 = 0.962.

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Complete Question:

If one of the 98 test subjects is randomly selected, find the probability that the subject had a positive test result GIVEN

POSITIVE TEST RESULT      13            40

NEGATIVE TEST RESULT    34            11

that the subject actually lied.

A 0.962

B 0.654

C 0.784

D 0.456

The angles are vertically opposite angles and the measure of x = 81

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.

Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.

When lines intersect, two angle relationships are formed:

Opposite angles are congruent

Adjacent angles are supplementary

Given data ,

Let the first line be represented as m

Let the second line be represented as n

Now , the lines m and n intersect at point O and the resulting lines are formed

where ∠A = ∠B ( vertically opposite angles )

So , the measure of ( x + 3 )° = 84°

On simplifying , we get

x + 3 = 84

Subtracting 3 on both sides , we get

x = 81

Hence , the measure of angles are opposite angles

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Answer:

3000 liters

Step-by-step explanation:

To calculate the volume of the tin can, we can multiply its dimensions:

Volume = 2m × 1.5m × 1m = 3 cubic meters

Since a liter is equivalent to 0.001 cubic meters, we can convert the volume of the tin can to liters:

Volume (in liters) = 3 cubic meters × 1000 liters/cubic meter = 3000 liters

Therefore, the tin can can hold 3000 liters of kerosene oil.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

a) The probability of scoring a one is 1/7, since a one is not the loaded number six and all other scores are equally likely.

b) The probability of scoring a six is 3/7, since a six is the loaded number and occurs three times as often as any other score.

Let p be the probability of scoring any number except six. Then the probability of scoring a six is 3p, since a six is scored three times more often than any other score. Since there are six equally likely possible scores on a die, we have:

p + 3p + p + p + p + p = 1

Simplifying, we get:

7p = 1

Dividing both sides by 7, we get:

p = 1/7

Therefore, the probability of scoring any number except six is 1/7, and the probability of scoring a six is 3/7. We can now answer the questions:

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