Find the surface area of each prism below

Answer:

17

Step-by-step explanation:

The original price was $20, so the discount price would be 20 * 15% = $3.

Therefore, the sale price would be 20 - 3 = $17.

The mass of the vessel if it is made of metal of density 10 g/cm³ is 1993 g.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

Volume of sphere = 4/3 πr³

Hence, For internal;

⇒ Volume of sphere = 4/3 πr³

⇒ Volume of sphere = 4/3 × 3.14 × (6)³

⇒ Volume of sphere = 904.32 cm³

For external;

⇒ Volume of sphere = 4/3 πr³

⇒ Volume of sphere = 4/3 × 3.14 × (6.4)³

⇒ Volume of sphere = 1097.5 cm³

Thus, Volume of sphere between sphere is,

⇒ 1097.5 - 904.32

⇒ 193.2 cm³

Here,  it is made of metal of density 10 g/cm³.

Hence, the mass of the vessel is,

⇒ 193.2 × 10

⇒ 1932 g

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The correct answer is option C. The system has a nontrivial solution.

One way to determine if a system has a nontrivial solution is to use Gaussian elimination to reduce the augmented matrix to row echelon form. If the row echelon form has a row of zeros except for the last entry in the augmented part, then the system has only a trivial solution.

If there is a row of zeros in the row echelon form that corresponds to a free variable, then the system has a nontrivial solution. In this case, it is possible to use Gaussian elimination to see that the row echelon form of the augmented matrix has a row of zeros except for the last entry in the augmented part, which is not zero, indicating that the system has a nontrivial solution.

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If we consider all possible mixed strategies for player 2, then the number of strategies that player 2 has is infinite.

In the extensive-form game provided, player 2 has two decision points where they can choose between two actions, C and F in the first decision point and G and not-G in the second decision point. Therefore, player 2 has 2 x 2 = 4 pure strategies.

However, player 2 can also mix their strategies in each decision point, choosing a probability distribution over the available actions. For example, in the first decision point, player 2 can play a mixed strategy where they choose C with some probability and F with the complementary probability. Similarly, in the second decision point, player 2 can mix their strategies by choosing to play G with some probability and not-G with the complementary probability.

So, if we consider all possible mixed strategies for player 2, then the number of strategies that player 2 has is infinite.

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In the extensive-form game that follows, how many strategies does player 2 have?

Since the mean number of book read per child is 1, the value of x is 4.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of books, we have;

Total number of book = 0(4) + 12(1) + 2(x)

Total number of book = 12 + 2x

Mean = (12 + 2x)/(16 + x)

1 = (12 + 2x)/(16 + x)

16 + x = 12 + 2x

2x - x = 16 - 12

x = 4.

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I runner is running at the speed of 6.8 miles/hr and he wants to run 10.1 km then he runner must run for 9.3 minutes.

To calculate this, we first need to convert the given speed from miles per hour to kilometers per hour. 6.8 mi/hr is equal to 10.9 km/hr.

Then, we need to divide the total distance (10.1 km) by the speed (10.9 km/hr) to get the total time it will take for the runner to complete the 10.1 km run.

10.1 km/10.9 km/hr = 0.922 hr = 9.3 minutes.

Therefore, the runner must run for 9.3 minutes in order to complete the 10.1 km run.
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The probability that the ball will fall into a red slot during the following spin is 0.14.

To calculate the probability of an occurrence, divide the total number of outcomes by the total number of possible outcomes. The concepts of probability and odds are distinct. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. When we toss the coin in the air, the probability that it will land with the heads side up is calculated. Here is a practical use of probability that you are probably already familiar with. We always check the weather forecast before a significant outing.

[tex]\frac{1}{7}=0.142857[/tex]

The probability is 0.14

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The probability of the ball landing on a red slot in a single spin of a fair roulette wheel is 1/2, as there are an equal number of red and black slots.

The outcome of each spin is independent, meaning that the outcome of one spin does not affect the outcome of another. Therefore, the probability that the ball will land on a red slot in the next spin is still 1/2, regardless of the results of the previous seven spins.

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Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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The graph in option - B represents the correct alternative.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given is the function as -

f(x) = 12(1/3)ˣ

At {x = 0}, we get -

y = 12 x 1 = 12

The {y - intercept} would be at (0, 12).

It is a exponential function of the form -

y = A(B)ˣ.

Refer to the graph attached. We can conclude that option B is the correct graph.

Therefore, the graph in option - B represents the correct alternative.

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Answer:

10

Step-by-step explanation:

2x - 7 = 13

+7. +7

2x = 20

20/2x = 10

The total zeros the function has is 4

See below for other solutions

This is the degree of the function

The degree of f(x) = -x^4 + x^3 - 7x2 + 9x + 18 is 4

So, the number of zeros is 4

Start by writing out the factors of the leading coefficient and the constant term

p = ±(1, 2, 3, 6)

q = ±1

So, we have

p/q = ±(1, 2, 3, 6)/±1

p/q = ±(1, 2, 3, 6)

Here, we find the number of changes in sign in the coefficients of the polynomial function.

f(x) = -x^4 + x^3 - 7x2 + 9x + 18

Number of sign changes = 3

Calculate f(-x) for the negative zeros

f(-x) = -(-x)^4 + (-x)^3 - 7(-x)^2 + 9(-x) + 18

f(-x) = -x^4 - x^3 - 7x^2 - 9x + 18

Number of sign changes = 1

This means that there is the possibility of 3 positive zeros, 1 negative zero, and 1 complex zero.

Here, we make use of the leading term, -x4, which is negative.

This implies that the graph will approace -∝ as x approaches +∝ and will approach +∝ as x approaches -∝.

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Answer:

multiply 2, 7 times

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 x 2 x 2

= 128

The required area of the circle with diameter 15.8 cm is 196.06 cm^2.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To find the area of a circle, we use the formula: pi * (radius)^2. The diameter of the circle is given as 15.8 cm,

so the radius can be calculated by dividing the diameter by 2,

giving us a radius of 15.8 cm / 2

= 7.9 cm.

Plugging the radius into the formula, we get:

pi * (7.9 cm)^2

= 3.14 * 62.41.

Finally, rounding the answer to the nearest hundredth, we get: 62.41 * 3.14

= 196.06 cm^2.

Thus, requi9red answer is 196.06 cm^2.

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The number of possible seating arrangements depends on the conditions specified in the problem is 435,456,000

Permutation is the arrangement of objects in a specific order.

a. The mathematics majors occupy the first 6 seats:

The number of permutations of the mathematics majors is simply 6! (6 factorial), since they all have to sit together in a block. After the mathematics majors are seated, we have 12 chairs left for the chemistry and physics majors, who can be arranged in (5 + 7)! / (5! x 7!) ways.

Finally, the total number of permutations for the mathematics majors to occupy the first 6 seats is

=>  6! x (5 + 7)! / (5! x 7!).

=> 570240

b. The mathematics majors cannot occupy the first 6 seats:

In this case, the number of permutations of the mathematics majors is (18 - 6)! / (6! x (12 - 6)!). This is because they cannot occupy the first 6 seats and have to be arranged in the remaining 12 chairs.

Next, the number of permutations for the chemistry majors is (12 - 6)! / (5! x (12 - 6 - 5)!).

Finally, the number of permutations for the physics majors is (12 - 6 - 5)! / 7!.

The total number of permutations for this scenario is

=> (18 - 6)! / (6! x (12 - 6)!) x (12 - 6)! / (5! x (12 - 6 - 5)!) x (12 - 6 - 5)! / 7!.

=> 668250

c. Students with the same major sit in a block:

In this case, the number of permutations of the chemistry majors is simply 5! since they have to sit together in a block.

Similarly, the number of permutations of the mathematics majors is 6! and the number of permutations of the physics majors is 7!.

Finally, the total number of permutations for students with the same major to sit in a block is

=> 5! x 6! x 7!.

=> 435456000

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TLDR: 88%

The probability of neither event happening is the complement of the probability of either event happening, which is 100 - 12 = 88.

Cheers,

qxxi

When the expression y² + 10 y + 33 is written as a combination of a square of a binomial expression and an integer, the value of the integer is 8

We are given an expression y² + 10 y + 33 and this expression can be written as a combination of a square of a binomial and an integer. we need to find the value of the integer.

                        = y² + 10 y + 33

Write 10 y = 2 (5) (y)

                        = y² + 2 (5) (y) + 33

Write 33 = 25 + 8

                        = y² + 2 (5) (y) + 25 + 8

Write 25 = 5²

                        = y² + 2 (5) (y) + 5² + 8

Write y² + 2 (5) (y) + 5² = (y + 5)²

                        = (y + 5)² + 8

So, here (y + 5)² is the square of the Binomial expression and 8 is the integer.

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the ratio representing the above-described number are given as follows;

In mathematics, parity refers to whether an integer is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd. For instance, 4, 0, 82 are even because 3, 5, 7, and 21 are all odd numbers.

With regard to the above ratios:

1) Odd numbers to all numbers involved:

There are 10 odd numbers from 1 to 20 (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). So, the ratio of odd numbers to all numbers involved is 10/20 = 1/2.

2) Numbers divisible by 5 to even numbers:

There are 4 numbers from 1 to 20 that are divisible by 5 (5, 10, 15, 20). Out of these 4 numbers, 2 are even (10, 20). So, the ratio of numbers divisible by 5 to even numbers is 4/2 = 2/5.

3) Numbers greater than 7 to numbers less than 12:

There are 4 numbers less than 12 (1 to 7) and 5 numbers greater than 7 (8 to 20). So, the ratio of numbers greater than 7 to numbers less than 12 is 5/4.

4) Even numbers greater than 5 but less than 17 to all numbers involved:

There are 6 even numbers greater than 5 but less than 17 (6, 8, 10, 12, 14, 16). So, the ratio of these even numbers to all numbers involved is 6/20 = 3/10 = 1/2 * 3/5 = 3/10.

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The value of the element t11 is 34 and the value of the element at d12 is 15.

Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.

M + W = Indoor= [26 55] Outdoor = [32 49]

The value indicates the sum of the indoor volunteers ages 18-39,\

34.

To create a matrix by subtracting the women's matrix from the mens matrix.

Now the difference;

M – W = Indoor = 8 15 Outdoor = -16 3

This value indicates the difference of the volunteers indoors 40 so

Therefore the value would be 15.

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The graph represents this situation:

B) graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y= 30+ 10x

Now, take x= 0

y= 30

and, x= 1

y= 30+ 10

y= 40

and, x= 2

y= 30+ 20

y= 50

and, graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars.

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Answer: The answer to this equation is 50.

Step-by-step explanation:

Evaluate the equation like this using PEMDAS.

2 x (1 + 4) ^2

2 x ( 5 ) ^ 2

2 x 25

 50

Hope this helps!

Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.

The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.

In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.

So,  Based on the information provided, it is consistent.

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Answer:

5

Step-by-step explanation

32 -12 =20 divided by

4= 5

The x intercept shown in the table are -2 and 2

The y intercept shown in the table is -4

The x-intercept of a graph is the point at which the graph crosses the x-axis, i.e., the y-coordinate of the point is 0. In other words, it's the solution to the equation y = 0.

The y-intercept of a graph is the point at which the graph crosses the y-axis, i.e., the x-coordinate of the point is 0. In other words, it's the solution to the equation x = 0.

In the table x- and y-intercepts are the values where the y values and x value are zero

x intercepts = -2 and 2

y intercepts = -4

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In the polygon KLMN KL = 10, LM = 17, MN = 10, NK = 17 and

KL || MN, and LM || NK hence the polygon KLMN is a parallelogram.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

Given, A polygon in which KL || MN, and LM || NK and also from the given information opposite sides are of equal length.

We know in a parallelogram opposite sides are parallel and equal in length.

Now, If in this parallelogram all individual interior angles measures

90° then this parallelogram would be a rectangle.

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A)

Gracie has 130 stamps after 3 months.

B)

The point (2, 100) represents that the number of stamps after 2 months is 100.

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Coordinate grid labeled points (0, 40), (1, 70), (2, 100).

Each month Gracie adds 30 stamps to her collection.

So,

(3, 130)

Now,

A)

130 stamps after 3 months.

B)

(2, 100) represents that the number of stamps after 2 months is 100.

Thus,

130 stamps after 3 months.

(2, 100) represents that the number of stamps after 2 months is 100.

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There will be 130 stamps  Gracie have after 3 months,

and (2, 100) represents the number of stamps in the collection after 2 months is 100.

A coordinate grid has two perpendicular lines, or axes labeled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.

Given Gracie's grandmother gave her 40 stamps.

Then, each month Gracie adds 30 stamps to her collection,

Coordinate grid labeled points (0, 40), (1, 70), (2, 100), and (3, ?)

A: since she adds 30 stamps each month,

stamps in 3rd month are 100 + 30 = 130.

130 stamps in 3rd month.

B: What does the point  (2, 100),

the graph is plotted between the number of stamps and months,

which gives the  change of stamp each month,

the coordinates (2, 100) say that Gracie has 100 stamps in 2 months.

so option B is correct.

Hence There will be 130 stamps  Gracie have after 3 months,

and The number of stamps Gracie added to her collection in 2 months is 100.

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The solutions for the infinite solutions have the same set of coefficients on both sides of the equations

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A be

ax + by = 0

Let the second equation be represented as B

Now , the value of B be

cx + dy = 0

For the system of equations to have infinite solutions , the coefficients of both the equations should be same

So , when a = c and b = d

ax + by = cx + dy

Hence , when the coefficients of the equations are same , the system has infinite solutions

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