The height of a triangle is 3 inches less than twice the length of its base. If the total area of the triangle is 7 square inches, find the length of the base and height.

The events H1 and H2 are independent.

Let P(B) be the probability that the selected coin is the biased one. Since we're picking the coin at random, P(B) = 0.5. Now, suppose we get two heads in a row. Let's call this event E. If E happens and the coin we picked is the biased coin, then the probability of getting two heads in a row is given by the probability that the biased coin gives heads twice, which is (2/3)² = 4/9. Therefore, the probability that we picked the biased coin given that we got two heads in a row is: P(B|E) = P(E|B)P(B) / [P(E|B)P(B) + P(E|F)P(F)], where F is the event that the fair coin is chosen. Note that the probability of getting two heads in a row with the fair coin is 1/4. Hence, the above formula becomes P(B|E) = (4/9 x 0.5) / [(4/9 x 0.5) + (1/4 x 0.5)] = 16/29. Therefore, the probability that we picked the biased coin given that we got two heads in a row is 16/29. b) The outcomes are independent given the picked coin, hence P(H1 ∩ H2) = P(H1)P(H2). Therefore, the events H1 and H2 are independent.

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The area of the circle is 7 ft^2

Circle is an  closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre” which is measured in terms of its radius. It is also a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant.

Area of a circle = πr^2 or π(d/2)^2

Where π = 22/7

Diameter = 3ft = 3ft/2 = 1.5 ft

Radius = 1.5ft

Area = 22/7 * (1.5)^2

Area = 22/7 * 2.25

Area = 7.07

Area = 7 ft^2 to nearest whole number

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The correct option is d. If the correlation coefficient r is equal to 0.521, the coefficient of non-determination is 0.271.

Correlation is a term used to describe the relationship between two variables in a statistical context. The correlation coefficient is a measure of the strength and direction of the relationship between two variables.

The coefficient of non-determination is used in statistics to refer to the proportion of variability in one variable that is not accounted for by another variable. It is equal to 1 - r², where r is the correlation coefficient between the two variables.

So, the coefficient of non-determination can be found using the formula:

Coefficient of non-determination = 1 - r²Given that the correlation coefficient, r = 0.521, substitute the value in the formula to find the coefficient of non-determination:

Coefficient of non-determination = 1 - (0.521)²= 1 - 0.271 = 0.729

Hence, the answer is (a) 0.729.

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As per the proportion, the number of males rabbits in the population is 1000.

Let's first find the proportion of female rabbits in the population using the given information. We are told that 8 out of every 75 rabbits in the population are females. Therefore, we can write:

Proportion of females = 8/75

We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 1:

Proportion of females = 8/75 = 0.1067

This means that for every unit of 75 rabbits in the population, there are 8 female rabbits.

Then, the total number of rabbits in the population is:

Total number of rabbits = r x 75

Since we know that the proportion of females is 0.1067, we can find the number of female rabbits in the population as follows:

Number of female rabbits = Proportion of females x Total number of rabbits

= 0.1067 x (r) x 75

We also know that the total number of rabbits in the population is 1500. Therefore, we can set up an equation as follows:

Number of male rabbits + Number of female rabbits = Total number of rabbits

Number of male rabbits + 0.1067 x (r) x 75 = 1500

Now, we can solve for the number of male rabbits by rearranging the equation:

Number of male rabbits = 1500 - 0.1067 x (r) x 75

We can simplify this expression by first multiplying 0.1067 and 75:

Number of male rabbits = 1500 - 8.003 x r

Finally, we can substitute the value of x in terms of the total number of rabbits in the population (1500) to find the number of male rabbits:

Number of male rabbits = 1500 - 8.003 x (1500/75)

Number of male rabbits = 1000

Therefore, there are 1000 male rabbits in the population.

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The value οf (f-g)(x) when [tex]f(x)=2x^2-3x+1[/tex] and[tex]g(x)= 4x^2+2x-3,[/tex] is equals to [tex]-2x^2 - 5x + 4.[/tex]

What is Function ?

Function can be defined in which it relates an input to output.

Tο evaluate (f-g)(x), we need to subtract the functiοn g(x) from f(x) for the same input value x:

(f-g)(x) = f(x) - g(x)

Given [tex]f(x) = 2x^2 - 3x + 1[/tex] and [tex]g(x) = 4x^2 + 2x - 3[/tex], we can substitute these intο the expression for (f-g)(x):

(f-g)(x) = f(x) - g(x)

[tex]= (2x^2 - 3x + 1) - (4x^2 + 2x - 3)[/tex]

To simplify this expressiοn, we first distribute the negative sign to the terms inside the parentheses:

[tex](f-g)(x) = 2x^2 - 3x + 1 - 4x^2 - 2x + 3[/tex]

Next, we cοmbine like terms:

[tex](f-g)(x) = -2x^2 - 5x + 4[/tex]

Therefore, The value of (f-g)(x) when [tex]f(x)=2x^2-3x+1[/tex] and [tex]g(x)= 4x^2+2x-3[/tex] , is equals to [tex]-2x^2 - 5x + 4.[/tex]

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A bar graph or a histogram is best suited for displaying the number of hours spent watching television by people from different age ranges.

What is a bar graph?

A bar graph is a type of graph that uses bars or rectangles to represent data, with the height or length of each bar proportional to the value it represents.

Both types of graphs can easily show the distribution of data across different age groups and allow for easy comparison of the number of hours spent watching television.

The choice between a bar graph or a histogram depends on the nature of the data and the desired level of detail.

A bar graph is appropriate when the data is categorical (e.g., age ranges) while a histogram is used when the data is continuous (e.g., number of hours).

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let the number be x, next perform calculations on it

double : 2x

subtract 2 : 2x - 2

2x - 2 = 9

2x = 9 + 2

x = 11 ÷ 2 = 5.5

so the number is 5.5

Answer:

the left one is cheaper, the difference is 4.2 pounds cheaper

Step-by-step explanation:

The advertising budget of the brand should be $12,250. This can be calculated using the following equation:

A budget is a financial plan for how much money will be earned, saved, and spent over a given period of time. It is a tool that helps individuals and organizations plan for their financial future and manage their current finances. A budget outlines expected income, expenses, and savings goals. It can also be used to track past spending and evaluate how successful a person or organization was in achieving their financial goals.

Gross Sales x 15% (Amazon Selling Fee) x 20% (Amazon Fulfillment Fee) x 20% (Cost of Goods Sold) x 35% (Advertising Budget) = Advertising Budget

$50,000 x 15% x 20% x 20% x 35% = $12,250

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Answer:

B

Step-by-step explanation:

This is just the prosses of elmiation. How is A even possablie, C doesnt make sense, and D is also a non logical or solvable question. Thus its b.

Answer: 5 bags

Step-by-step explanation: convert the proper fraction (3 1/3) into improper fractions (10/3)
then do 10 / 2 because the denominators are the same
5 bags

Answer:

Step-by-step explanation:

Describe the situation with a division equation

1. The parts of the circle identified are as explained below. 2. Area = 153.94 m²; Circumference ≈ 43.98 m; 3. Area ≈ 706.86 ft²; Circumference ≈ 94.25 ft; 4. Area ≈ 326.85 in.; Circumference = 64.09 in.

A circle is a closed two-dimensional shape that consists of points that are equidistant from a central point called the center.

1. An example of each part using the diagram of the circle given would be:

a. a center is K

b. One radius is JK

c. A chord is JL

d. Diameter is JI

e. Secant is GI

f. Tangent is GJ

g. Point of tangency is J

h. A minor arc is IL

i. A major arc is HIL

j. Semicircle is JLI

k. A central angle is <JKL

l. An inscribed angle is <HIJ

Use the area and circumference formula to calculate each required measure for each circle.

2. Area = πr² = π*7² = 153.94 m²

Circumference = 2πr = 2·π·7 ≈ 43.98 m

3. Area = πr² = π·15² ≈ 706.86 ft²

Circumference = 2·π·15 ≈ 94.25 ft

4. Area = πr² = π·10.2² ≈ 326.85 in.²

Circumference = 2·π·10.2 ≈ 64.09 in.

5. Area = πr² = π·9² ≈ 254.47 mm²

Circumference = 2·π·9 ≈ 56.55 mm

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Answer:

17%

Step-by-step explanation:

Calculate the difference in the population

181,000 - 150,230 = 30,770

Decrease is 30,770

Perecentage decrease = Decrease/ original population x 100%

30770/ 181,000 x 100 = 0.17 x 100

= 17%

Check 17% of 181,000

Deduct from 181,000 and you will get 150,230

Steve should leave his house no later than 8:49 am (10:00 am minus 529 minutes) to get to work on time.

It's preferable to spell out the term minutes entirely rather than shorten it. Sixty seconds make up one minute, which is a measure of time. Minutes are a noun that also refers to the records of a formal meeting. The abbreviation "min" is frequently used.

Let's call the hour Steve needs to leave his house to leave for work "x".

He needs 9 minutes to walk from his home to the bus stop, and we don't know how long it will take the bus to get from Birmingham to Coventry. Call the length of the bus ride "t" for now.

Steve needs 12 minutes to walk to work from the bus stop in Coventry.

So, Steve's commute to work takes a total of:

Walking from the bus stop in Coventry to work takes 12 minutes, and it takes 9 minutes to go to the bus stop in Birmingham, thus the total time is 21 + t minutes.

Steve needs to arrive at work by 10 a.m., or 10 x 60 = 600 minutes.

Thus, we can formulate the equation shown below:

x + 21 + t <= 600

After finding x, we obtain:

x <= 579 - t

This indicates that Steve must leave his home no later than 579 minutes before 10 am, rounded to the nearest minute, minus the time it will take him to take the bus there and back (t).

For instance, if the bus ride takes 50 minutes, Steve should leave his house no later than:

x <= 579 - 50 = 529

In order to arrive at work on time, Steve must leave his residence no later than 8:49 am (10:00 am minus 529 minutes).

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(2x - 10) - (3x² + 10x) + (2x³ + 3x²)

= 2x - 10 - 3x² - 10x + 2x³ +3x²

= 2x³ - 8x - 10

There are 132 entertainers who do not have red hair.

What is Percentage?

Percentage is a way of expressing a number or quantity as a fraction of 100. It is represented by the symbol "%". Percentages are commonly used to express the proportion or ratio of one quantity to another.

Percentages are widely used in many fields, including mathematics, science, finance, and economics, among others. They are a convenient way to express a relative quantity or change in quantity, and are easy to compare and interpret.

If 12% of the entertainers have red hair, then 100% - 12% = 88% do not have red hair.

To find out how many entertainers do not have red hair, we can calculate 88% of the total number of entertainers:

88% = 88/100 = 0.88

Number of entertainers without red hair = 0.88 x 150 = 132

Therefore, 132 entertainers do not have red hair.

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The rate of increasing the area of the rectangle is 72cm²/s

We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.

The area of a rectangle is given by, A = l × w

Where l is the length and w is the width.

Now we will differentiate the equation with respect to time t.

dA/dt = d/dt (l × w)

dA/dt = l(dw/dt) + w(dl/dt)

We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.

Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s

dA/dt = 13(4) + 4(5)

dA/dt = 72 cm²/s

Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.

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The following conclusion is reached concerning the results represented by the dot plots:

The Mean Absolute Deviation for brand A is: 2.02

The Mean Absolute Deviation for brand A is: 1.905

The Mean Absolute Deviation for the two brands is similar.

The mean absolute deviation is a test of the variability of a data set which is the average distance between each of the data points in the data set and the mean.

Mean Absolute Deviation for Brand A:

The points are, 1,1,2,2,2,3,4,4,5,5,5,5,6,6,7,7,8,8,8,9

Mean = (1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9) ÷ 20 = 98÷20

Mean = 4.9

Mean Absolute Deviation

= [(1 - 4.9) + (1 - 4.9) + (2 - 4.9) + (2 - 4.9) + (2 - 4.9) + (3 - 4.9) + (4 - 4.9) +

(4 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (6 - 4.9) + (6 - 4.9) +

(7 - 4.9) + (7 - 4.9) + (8 - 4.9) + (8 - 4.9) + (8 - 4.9) + (9 - 4.9)] ÷ 20

=  [(3.9) + (3.9) + (2.9) + (2.9) + (2.9) + (1.9) + (0.9) + (0.9) + (0.1) + (0.1) + (0.1) + (0.1) + (1.1) + (1.1) + (2.1) + (2.1) + (3.1) + (3.1) + (3.1) + (4.1)] ÷20

= 40.4÷20

Mean Absolute Deviation for brand A = 2.02

Mean Absolute Deviation for Brand B:

The points are, 1,3,3,4,4,4,4,4,5,5,5,6,6,6,6,8,8,9,10,10

Mean = (1 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 8 + 8 + 9 + 10 + 10)÷20

Mean = [tex]\frac{111}{20}[/tex]= 5.55

Mean Absolute Deviation = [(1 - 5.55) + (3 - 5.55) + (3 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (5 - 5.55) + (5 - 5.55) + (5 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (8 - 5.55) + (8 - 5.55) + (9 - 5.55) + (10 - 5.55) + (10 - 5.55)] / 20

Mean Absolute Deviation = [tex]\frac{38.1}{20}[/tex]

Mean Absolute Deviation for brand B = 1.905

The complete question is-

Martin and Clara decide to keep track of the number of different colors in two brands of tennis shoes, brand A and brand B. Their results are represented by the dot plots. The mean absolute deviation for brand A is. The mean absolute deviation for brand B is. The mean absolute deviations for the two brands are similar.

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The solution to the equation x² + 2x = 18 is x = 4 ± √19.

Karappan Poochi: Algebra vs The Cockroaches is a math-based game designed to help students learn and practice algebra. The objective of the game is to help Karappan, a character in the game, solve algebraic equations. Players must solve equations by manipulating the variables and constants to reach the correct answer. To reach level six, the player must solve six equations correctly.

The equation for level six is x² + 2x = 18. To solve this equation, the player must first recognize that it is a quadratic equation and can be solved using the quadratic formula. The formula is: x = [-b ± √(b²-4ac)]/2a. For this equation, a = 1, b = 2, and c = -18. Plugging these values in, the player gets: x = [-2 ± √(2²-4(1)(-18))]/2(1). This simplifies to x = [-2 ± √76]/2, which simplifies to x = [8 ± √76]/2. Therefore, the solution to this equation is x = 4 ± √19.

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[tex]TU = 2QS = 2(7)[/tex]

[tex]\implies \bf TU = 14[/tex]

Answer:

-8

Step-by-step explanation:

5r= -40 | :5

r= -8

.....

The fifth term of the given sequence is: a₅ = 63

We are told the formula for the nth term of the sequence is given as:

aₙ = aₙ₋₁ + 6(n - 1) for n ≥ 2

We are given:

a₁ = 3

a₂ = 9

a₃ = 21

a₄ = 39

Thus:

a₅ = a₅₋₁ + 6(5 - 1)

a₅ = a₄ + (6 * 4)

a₅ = 39 + 24

a₅ = 63

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The total cost of the house we can afford is $⁢242,139.78.

What is compound interest?

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

First, we need to determine the maximum monthly payment we can afford based on the recommended guidelines. If we can only spend 1414 of our take-home pay on a house payment, then:

Monthly payment = 0.45 × take-home pay

1414 = 0.45 × 3160

1414 = 1422

Therefore, we can afford a maximum monthly payment of $⁢1422.

Next, we can use the present value formula to find the maximum loan amount we can afford:

Loan amount = (monthly payment / monthly interest rate) × (1 - (1 + monthly interest rate)^(-n))

where monthly interest rate = 4.35% / 12 = 0.003625, and n = 15 years × 12 months/year = 180 months.

Substituting the values, we get:

Loan amount = (1422 / 0.003625) × (1 - (1 + 0.003625)^(-180))

Loan amount = $⁢225,739.78

Therefore, the maximum cost of the house we can afford with a 15-year mortgage is $⁢225,739.78 + $⁢16,400 (down payment) = $⁢242,139.78. Rounded to the nearest cent, the total cost of the house we can afford is $⁢242,139.78.

Hence, the total cost of the house we can afford is $⁢242,139.78.

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By answering the presented question, we may conclude that As a result, 200 kilograms of cement, 400 kg of sand, and 600 kg of gravel are required to produce 1200 kg of dry concrete in the 1:2:3 ratio.

In mathematics, ratios demonstrate how often one number is included in another. If there are 8 oranges and 6 lemons in a fruit bowl, the ratio of oranges to lemons is 8 to 6. In a similar vein, the ratio of oranges to whole fruit is 8, whereas the ratio of lemons to oranges is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not equal to zero. A ratio is an equation that equals two ratios. For example, if there is 1 male and 3 girls (for every boy she has 3 girls), 3/4 are girls and 1/4 are boys.

One component cement, two parts sand, and three parts gravel are required to build dry concrete in the 1:2:3 ratio. This indicates that for every 1 kg of cement, 2 kg of sand and 3 kg of gravel are required.

To calculate the weight of one part, divide the entire weight of dry concrete (1200 kg) by the total number of parts (6). 1200 kg ÷ 6 = 200 kg.

Cement: 1 component cement (200 kilograms) = 200 kg

2 pieces sand 200 kilogram/part = 400 kg

Gravel: 600 kg = 3 parts gravel 200 kg/part

As a result, 200 kilograms of cement, 400 kg of sand, and 600 kg of gravel are required to produce 1200 kg of dry concrete in the 1:2:3 ratio.

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The distance between point M and point N is 12 units.

Coordinates are a set of numbers or vaIues that describe the position or Iocation of a point in space. In two-dimensionaI space (aIso known as the Cartesian pIane), coordinates are typicaIIy represented by two vaIues, usuaIIy denoted as (x, y), that describe the horizontaI and verticaI position of a point reIative to a set of axes.

The distance formuIa is a mathematicaI formuIa used to find the distance between two points in a two- or three-dimensionaI space.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

The distance formuIa is based on the Pythagorean theorem, which states that in a right triangIe, the square of the Iength of the hypotenuse (the side opposite the right angIe) is equaI to the sum of the squares of the Iengths of the other two sides.

In the given question,

We can use the distance formuIa to find the distance between point M and point N:

d = √[(x₂ - x₁)²+ (y₂ - y₁)²]

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

PIugging in the given vaIues, we have:

d = √[(-8 - 4)² + (-8 - (-8))²]

d = √[(-12)² + 0²]d = √[144]

d = 12

Therefore, the distance between point M and point N is 12 units.

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sin(2x) is 4/5 cos(2x) is 3/5 and tan(2x) is -2/3.

Given that, sin(x) = −1/√5
We know that sin x = y/r, where y is the opposite side and r is the hypotenuse. Since x is in the third quadrant, y is negative and r is positive, so we can draw a triangle in the third quadrant like the one below:
[asy]
unitsize(2cm);
pair A = (-1,0);
pair B = (-0.6,-0.8);
pair C = (0,-0.8);
draw(A--B--C--A);
draw(rightanglemark(A,C,B,2.5));
draw(Circle((0,0),1));
label("$x$",(C+B)/2,E);
label("$r$",(C)/2,NW);
label("$y$",(A)/2,S);
[/asy]
Here, $y=-1$, $r=\sqrt{5}$ and $x$ is the angle opposite to the side $y$. Using the Pythagorean theorem, we can find that the adjacent side is $x = -\sqrt{5 - 1} = -\sqrt{4} = -2$. Therefore,
$$
\cos(x) = \frac{x}{r} = \frac{-2}{\sqrt{5}} = -\frac{2\sqrt{5}}{5}
$$
Using the double angle formulas for sine and cosine,
$$
\begin{aligned}
\sin(2x) &= 2\sin(x)\cos(x)\\
&= 2\cdot \left(-\frac{1}{\sqrt{5}}\right) \cdot \left(-\frac{2\sqrt{5}}{5}\right)\\
&= \frac{4}{5}\\
\\
\cos(2x) &= 1 - 2\sin^2(x)\\
&= 1 - 2\cdot \left(-\frac{1}{\sqrt{5}}\right)^2\\
&= \frac{3}{5}\\
\\
\tan(2x) &= \frac{2\tan(x)}{1-\tan^2(x)}\\
&= \frac{2 \cdot \left(-\frac{1}{2}\right)}{1-\left(-\frac{1}{2}\right)^2}\\
&= \frac{-2}{3}
\end{aligned}
$$Therefore, sin(2x) is 4/5, cos(2x) is 3/5 and tan(2x) is -2/3.

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The area of a rectangle is [tex]30cm^{2}[/tex]  , so let know more about rectangle and also know about Quadrilaterals.

Rectangle is a plane figure that differs from a square by having four adjoining sides that are not equal and 4 consecutive sides.

A rectangle is a type of quadrilateral that has r opposed sides that are equally long and parallel.

A quadrilateral is a closed object in geometry that is created by connecting 4 points, any 3 of which are not collinear. A quadrilateral, often known as a square, rectangle, or rhombus, is a polygon with 4 sides.

from the question

Given, Length, l = 6 cm, Breadth, b = 5cm

[tex]area of rectangle : A= length * breadth =6 * 5= 30 cm ^{2}[/tex]

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Answer:

[tex]\huge\boxed{\sf 21 \ pencils}[/tex]

Step-by-step explanation:

Ali has 3 pencils.

Melvin has twice.

So,

Melvin pencils = 2 × 3

Zachary has four times as many pencils as Ali.

So,

Zachary' pencils:

= 4 × 3

So:

= 3 + 6 + 12

[tex]\rule[225]{225}{2}[/tex]

Given the chance of independent events, if one student is randomly selected from each class, the likelihood that both of them are female is 2/15.

Probability relates the number of favourable events to the total number of possible events.

Thus, to determine the chance of any event, the ratio between the number of favourable cases (cases in which event A may or may not occur) and the total number of potential cases is employed. A:

Number of likely cases x Number of potential cases equals probability.

The number of independently likely events.

Two occurrences A and B are said to be independent if and only if the likelihood of event B is unaffected by the occurrence of event A, or vice versa.

The sum of the probabilities for each individual event is the probability that every independent event, for any number of occurrences, will occur. In other words, if A and B are independent events, P(A and B) = P(A)P. (B).

The response indicates that Mr. Crawford's class has a total of 15 students (8 girls and 7 boys).

14 kids, 10 female and 4 males, are enrolled in Mrs. Ball's class.

The likelihood that a boy will be chosen in each class, if one student is randomly chosen from each, is computed as follows:

Probability in Mr. Crawford's class is 7/15 (7/15 x 15).

In Mrs. Ball's class, the probability is 4 14 = 4/14.

Given that these are separate occurrences, the likelihood that both students chosen for the classes are boys is determined as follows:

Chance that both of the students chosen for the classes will be boys: In Mr. Crawford's probability class In Ms. Ball's class, probability

Chance that both of the students chosen for the classes will be boys: 7/15 4/14

The likelihood that both of the students chosen for the classes are boys is 2/15.

Ultimately, there is a 2/15 chance that they are both boys.

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