draw an appropriate tree diagram, and use the multiplication principle to calculate the probabilities of all the outcomes. hint [see example 3.]there is a 60% chance of rain today and a 60% chance of rain tomorrow. assume that the event that it rains today is independent of the event that it rains tomorrow. what is the probability that there will be no rain today and no rain tomorrow?

The  explicit formula for nth term geometric sequence is aₙ = a x rⁿ⁻¹.

let a geometric series is of the form

a, a², a³, a⁴ a⁵, ....

where a₁ = a = first term and other terms are obtained by multiplying by

r.

Now, each term is r times of previous term.

So, to get the nth term we have to multiply (n-1) by r.

Thus, the explicit formula for nth term geometric sequence is

aₙ = a x rⁿ⁻¹

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Using the laws of outside angle, we can find the value of the angle x° to be = 77°.

The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.

Here in the question,

The measure of the 2 arcs is given as 85° and 172°.

The measure of the 3rd arc that is subtended by the tangents is:

360° - 85° - 172°

= 103°

As per the outside angle theorem,

x° = 180° - 103°

= 77°

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When we factor the expression, we are going to obtain the result;

9a(9a + 4) + 4

Factoring an expression involves breaking it down into simpler parts that can be multiplied together to obtain the original expression. The specific method used to factor an expression depends on the type of expression.

It's important to note that factoring can sometimes be a challenging process, and not all expressions can be factored using real numbers.

We can carry out this factorization by the use of the nesting method, Hence;

81a^2 + 36a + 4

(81a^2 + 36a ) + 4

9a(9a + 4) + 4

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Answer:

19,322 cubic feet.

Step-by-step explanation:

Volume = Length × Width × Height

Given the measurements provided:

Length = 24 1/2 feet

Width = 14 feet

Height = 11 feet

We need to convert the mixed number for the length, 24 1/2 feet, into a single fraction.

24 1/2 feet = 24 + 1/2 feet = 48/2 + 1/2 feet = 49/2 feet

Now we can substitute the given values into the formula for volume:

Volume = (Length) × (Width) × (Height)

= (49/2 feet) × (14 feet) × (11 feet)

Next, we can multiply the lengths, widths, and heights together:

Volume = (49/2 feet) × (14 feet) × (11 feet)

= 49 × 14 × 11 cubic feet / 2

Finally, we can calculate the volume by dividing the product by 2:

Volume = 49 × 14 × 11 cubic feet / 2

= 19,322 cubic feet

Answer:

d Because I just took the test and got it right

Answer:

The top right graph shows the solution to this system of linear equations.

Sev needs to run 9 miles as per the below calculations to complete his target.

The target that Sev needs to achieve is 18 miles in a week. A week has 7 days. Sev is already done running for 5 days.
Day 1: 1.4 miles

Day 2: 1.4 miles

Day 3: 1.4 miles

Day 4: 2.4 miles

Day 5: 2.4 miles

Thus, Sev has run for 1.4*3 = 4.2 miles in the first 3 days.

Sev has run for 2.4*2 = 4.8 miles in the last 2 days.

So far, she has run 4.2 + 4.8 = 9 miles. Since her goal is to run 18 miles, she needs to run an additional: 18 - 9 = 9 miles to meet her goal.

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The simplified rational expression for this problem is given as follows:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

The rational expression in the context of this problem is defined as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]

The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]

Applying the subtraction of perfect squares, the denominator is given as follows:

2² x 3 - 7 = 12.

The numerator is:

[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]

Thus the simplified expression is:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

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The percent of change in the price of the book is 50%.

To calculate the percent of change, we first need to find the difference between the original price and the new price. In this case, the original price of the book was $10, and the new price is $5. To find the difference, we can subtract the new price from the original price, which is:

$10 - $5 = $5

Now, we need to express this difference as a percentage of the original price. To do this, we divide the difference by the original price and then multiply by 100. In other words, we need to find the percentage that the original price has changed by. This can be represented mathematically as:

Percent of change = (Difference / Original price) x 100

Plugging in the values we found earlier, we get:

Percent of change = ($5 / $10) x 100

Percent of change = 0.5 x 100

Percent of change = 50%

This means that the price of the book has decreased by 50% from the original price of $10 to the sale price of $5.

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The probability of winning something from the Pepsi sales promotion with winning symbols under the caps of 10% of all Pepsi bottles in a six-pack is 46.9%.

The probability of winning something from the Pepsi sales promotion depends on the total number of bottles in the six-pack and the percentage of bottles with winning symbols under the caps.

Assuming that the six-pack contains six bottles, and 10% of all Pepsi bottles have winning symbols under the cap, the probability of winning something from the promotion can be calculated using the following formula:

Probability of winning = Number of bottles with winning symbols / Total number of bottles

Since 10% of all Pepsi bottles have winning symbols, the probability of finding a winning symbol under one bottle cap is 10%. Therefore, the probability of winning from a six-pack is the same as finding at least one winning bottle cap in six bottles.

To calculate the probability of winning, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.

So, the probability of not winning from a single bottle is 1 - 0.1 = 0.9. The probability of not winning from all six bottles is 0.9^6 = 0.531. Therefore, the probability of winning something from a six-pack is 1 - 0.531 = 0.469 or 46.9%.

In conclusion, the probability of winning something from the Pepsi sales promotion with winning symbols under the caps of 10% of all Pepsi bottles in a six-pack is 46.9%. This means that nearly half of the customers who buy a six-pack are likely to win something from the promotion.

However, it is important to note that this probability may vary depending on the total number of bottles and the percentage of winning symbols used in the promotion.

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There are 5 markers in each cup

Nicholas splits 27 green markers equally into 9 cups

Hence the number of green markers in one cup is

= 27/9

= 3

He then spilt 18 yellow markers equally into the same 9 cups

The number of yellow markers in one cup is

= 18/9

= 2

The total number of markers in each cup is

= 3 + 2

= 5

Hence there are 5 markers in each cup

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The value of x, obtained using the property of bisected angles is 10

Bisected angles are angles that are split by a line segment in two to create two angles of the same measure.

The specified information indicates;

[tex]\overrightarrow{GI}[/tex] bisects ∠DGH

m∠DGI = x - 3

m∠IGH = 2·x - 13

The angle addition postulate indicates that we get;

m∠DGH = m∠DGI + m∠IGH

The definition of the bisected angle ∠DGH indicates that we get;

∠DGI = ∠IGH

Therefore;

x - 3 = 2·x - 13

2·x - 13 = x - 3

2·x - x = 13 - 3 = 10

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4 is the correct value from the set {1, 2, 3, 4} which is the solution to the equation 3x + 3 = 15.

A solution of an equation refers to a value or values that satisfy the given equation. It is the value or values that make the equation true when substituted for the variable(s) in the equation. Equations are mathematical expressions that contain an equals sign and can have one or more variables. A solution is typically represented as a number, but it can also be a set of numbers, a range of values, or an expression. Finding the solutions of an equation is an important part of solving mathematical problems and has many practical applications in fields such as engineering, physics, and finance.

Solution of the given equation 3x + 3 = 15 means when we put a value in x we should get the result as 15, that is left hand side of the equation should be equal to the right hand side of the equation.

Solving the equation we get,

3x + 3 - 3 = 15 - 3

3x = 12

x = 4

Therefore, the value 4 is a solution to the equation.

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The area covered by grass in the nursery school playground is 5760 square meters.

To find the area covered by grass in the nursery school playground, we first need to calculate the total area of the playground, and then subtract the areas of the swings and the paths.

Given:

Length of playground = 160 m

Width of playground = 80 m

Width of swings = 80 m

Width of paths = 1.5 m

Total area of the playground = Length × Width = 160 m × 80 m = 12800 m²

Area of the swings = Width of swings × Width of swings = 80 m × 80 m = 6400 m²

Since there are two sides of the swings that are parallel to the length of the playground, we need to subtract the area of the paths along those two sides. The total width of the paths is 1.5 m + 1.5 m = 3 m.

Area of the paths along the length = Length of playground × Width of paths = 160 m × 3 m = 480 m²

Similarly, since there are two sides of the swings that are parallel to the width of the playground, we need to subtract the area of the paths along those two sides.

Area of the paths along the width = Width of playground × Width of paths = 80 m × 3 m = 240 m²

Now, we can calculate the remaining area covered by grass by subtracting the area of the swings and the areas of the paths from the total area of the playground:

Area covered by grass = Total area of playground - Area of swings - Area of paths along length - Area of paths along width

Area covered by grass = 12800 m² - 6400 m² - 480 m² - 240 m²

Area covered by grass = 5760 m²

So, the area covered by grass in the nursery school playground is 5760 square meters.

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In circle L in which secant lines TQ and SQ intersect at point Q outside the circle value of x = 54°, m ST = 143°, m PR = 79°

∠PQR = 1/2( ST - PR)

∠PQR = 32°

m ST = (3x - 19)°

m PR = (x + 25)°

Putting the value in the equation we get

32 = 1/2( 3x - 19 - (x + 25) )

32 × 2 = 3x -19 -x -25

64 = 2x - 44

64 + 44 = 2x

108 = 2x

x = 54°

m ST = (3x - 19)°

m ST = 3(54) -19

m ST = 162 - 19

m ST = 143°

m PR = (x + 25)°

m PR = 54 + 25

m PR = 79°

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An association class is frequently required for a many-to-many relationship.

In object-oriented programming, an association class is a class that is used to represent an association between two or more other classes. An association class is typically used when the relationship between the other classes is many-to-many, which means that each instance of one class can be associated with multiple instances of another class, and vice versa.

For example, consider a database that stores information about students and the courses they are enrolled in. Each student can be enrolled in multiple courses, and each course can have multiple students.

To represent this many-to-many relationship between students and courses, we can create an association class called "Enrollment" that has attributes such as the date of enrollment and the grade received. The Enrollment class would have a many-to-one relationship with both the Student class and the Course class.

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An association class is frequently required for a "c. many to many" relationship. therefore, option c. many to many is correct.

In this type of relationship, multiple instances of one class can be associated with multiple instances of another class.

The association class helps to capture additional information about the relationship between these instances.

An association class is most commonly required for a many-to-many relationship between two classes.

a relationship that explains the causes of the relationship and the rules that control it between two classifiers, such as

classes or use cases.

An association class is frequently required for a "c. many to many" relationship. therefore, option c. many to many is correct.

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The total amount of water Keisha drinks in 12 days is 12 + 18 = 30 quarts.

Algebra is a branch of mathematics that involves using letters and symbols to represent numbers and quantities in mathematical equations and formulas. It includes a variety of topics, such as solving equations, manipulating expressions, working with functions and graphs, and studying abstract structures such as groups and rings.

At its core, algebra is about understanding the relationships between numbers and how they can be manipulated using various operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to model real-world situations and solve problems in fields such as physics, engineering, and finance.

To find the total amount of water Keisha drinks in 12 days, we need to add up the amounts of water she drinks each day:

1 1/2 + 2 1/4 + 2 + 1 1/2 + 1 3/4 + 1 1/2 + 1 1/4 + 2 + 2 1/4 + 1 1/2 + 2 + 1 1/2

We can simplify the mixed numbers by converting them to improper fractions:

3/2 + 9/4 + 2 + 3/2 + 7/4 + 3/2 + 5/4 + 2 + 9/4 + 3/2 + 2 + 3/2

Then we can add the fractions together:

(3/2 + 3/2 + 3/2 + 2 + 2 + 2) + (9/4 + 7/4 + 5/4 + 9/4 + 3/2 + 3/2)

Simplifying the sum of the whole numbers, we get:

12

Simplifying the sum of the fractions, we get:

(18/4 + 14/4 + 10/4 + 18/4 + 6/4 + 6/4) = 72/4 = 18

So the total amount of water Keisha drinks in 12 days is:

12 + 18 = 30 quarts.

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The complete  question is:

For 12 days, Keisha keeps track of how much water she drinks per day. 1 1/2 quarts, 2 1/4 quarts, 2 quarts, 1 1/2 quarts, 1 3/4 quarts, 1 1/2 quarts, 1 1/4 quarts, 2 quarts, 2 1/4 quarts, 1 1/2 quarts, 2 quarts, 1 1/2 quarts. What is the total amount of water that Keisha drinks the 12 days?

The side of the house which the ladder will reach now is equal to 14.2 feet.

In Mathematics and Geometry, Pythagorean's theorem is represented or modeled by the following mathematical equation:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine how far up the side of the house will the ladder reach, we would have to apply Pythagorean's theorem as follows;

21² + y² = 35²

y² = 1,225 - 441

y² = 784

y = √784

y = 28 feet.

Since Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, we have:

New Length = 28 + 4 = 32 feet.

Therefore, the required length is given by;

Distance = √(35² - 32²)

Distance = 14.2 feet.

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The lateral surface area of the rectangular prism is 308 units² and the total surface area is 398 units²

The formula of lateral surface area of the rectangular prism is given as;

LSA = 2(l +b)h

substituting the values into the formula;

LSA = 2(5 + 9) * 11

LSA = 308 units²

The total surface area is given by

TSA = 2(lb + bh + lh)

TSA = 2[(5*9) + (9*11) + (11*5)

TSA = 398 units²

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Answer: The formula for the volume of a cone is V=1/3hπr²

Step-by-step explanation: The volume or capacity of a cone is one-third of its corresponding cylinder. This means that when a cone and a cylinder have the same base dimension and height, the volume of the cone is one-third of the volume of the cylinder.

Using Pythagoras Theorem, we have the solutions as:

3) Length of AB = 32 in

4) x = 24

5) Perimeter of PRQ = 35

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

3) Using Pythagoras theorem, we can say that:

Radius = √(16² - 5²)

Radius = √231

Radius = 15.2

Thus, AB will be twice the measurement of 16 as the perpendicular distance to bth chords are the same. Thus:

AB = 16 * 2 = 32 in

4) Using Pythagoras theorem,

x = √((18 + 7)² - 7²)

x = √(625 - 49)

x = 24

5) Using Pythagoras theorem, we can say that:

PC = 8.66

RC = √((14² - 8.66²)

RC = 11

Thus:

Perimeter of PRQ = 14 + 10 + 11 = 35

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The height of the center of the Ferris wheel 51 m.

The height of capsule M is 51 m and the height of capsule T is 102 m.

Using this information, we can calculate the height of the center of the Ferris wheel, the height of capsule M, and the height of capsule T.

Height of the center of the Ferris wheel:

The center of the Ferris wheel is the midpoint of its diameter. Therefore, the height of the center of the Ferris wheel is half of the height of the top of the wheel above the ground.

Height of center of Ferris wheel = 102 meters / 2 = 51 meters.

Height of capsule M:

Since capsule M is at the same height as the center of the Ferris wheel, the height of capsule M is also 51 meters.

Height of capsule T:

Since capsule T is at the very top of the Ferris wheel, its height above the ground is equal to the height of the top of the Ferris wheel above the ground.

Height of capsule T = 102 meters.

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The scale factor used to create the image include the following: C. 2.

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

By substituting the given side lengths or dimensions into the formula for scale factor, we have the following;

Scale factor = 2/1

Scale factor = 2.

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Answer:

Step-by-step explanation:

see it simple it's not asking quite much if I do my calculation right it would be 8[tex]\pi[/tex]

Answer: for future k-12 kids :)

Step-by-step explanation:

Answer:

  (a)  x² +y² -2x -6y -26 = 0

Step-by-step explanation:

You want the equation for the circle with center (1, 3) and radius 6 written in general form.

The standard form equation for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

The radius and center are found from the graph, attached. For the circle centered at (h, k) = (1, 3) and radius r = 6, this is ...

  (x -1)² +(y -3)² = 6²

Expanding this equation gives ...

  x² -2x +1 +y² -6y +9 = 36

Written in general form, the equation becomes ...

  x² +y² -2x -6y -26 = 0 . . . . matches choice A

__

Additional comment

There is an image of this question showing the correct answer choice is the third one. However, that answer choice shows up first on this instance of the question. You will need to read and compare answer content to make sure you have the correct choice. You cannot go by the order of the the answers.

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Answer: the answer is d) 0.3466.

Step-by-step explanation:

Starting with the equation:

6e^(4x) - 3 = 21

Add 3 to both sides:

6e^(4x) = 24

Divide both sides by 6:

e^(4x) = 4

Take the natural logarithm of both sides:

ln(e^(4x)) = ln(4)

Use the property of logarithms that ln(e^y) = y:

4x ln(e) = ln(4)

Simplify:

4x = ln(4)

Solve for x by dividing both sides by 4:

x = (1/4) ln(4)

Using a calculator, we get:

x ≈ 0.3466

Therefore, the answer is d) 0.3466.

The calculated value of each boy's share is shown below

Let's call the amount of oranges the third boy gets "x".

According to the problem, the second boy gets twice the amount of oranges as the third boy, so he gets 2x oranges.

And the first boy gets twice more oranges than the second boy, so he gets 2(2x) = 4x oranges.

So the total number of oranges is x + 2x + 4x = 7x, and we need to divide this equally among the three boys.

Therefore, the first boy gets 4/7 of the total oranges, which is 4x/3, the second boy gets 2/7 of the total oranges, which is 2x/3 and the third boy gets 1/7 of the total oranges, which is x/3.

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