A card is drawn one at a time from a
well-shuffled deck of 52 cards. In 11
repetitions of this experiment, 2 kings
are drawn. If E is the event in which a
king is drawn in the 11 trials, find the
experimental probability P(E).

Answer:

3,120 in 4 months

Step-by-step explanation:

9,360 divided by 12 = 780

780 x 4 = 3,120

The sum of angles in a triangle is always 180 degrees. Therefore, the angle C measures 60 degrees.

In triangle ABC, we know that angle A measures 75 degrees, and angle B measures 45 degrees.

To find the measure of angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:

Angle A + Angle B + Angle C = 180

Substituting the values we know:

75 + 45 + Angle C = 180

Simplifying:

120 + Angle C = 180

Subtracting 120 from both sides:

Angle C = 60

Therefore, angle C measures 60 degrees.

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The experiment is not a binomial experiment.

A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.

The conditions for a binomial experiment include:

1. Each trial should be classified either as a success or a failure.

2. There are a fixed number of observations

3. The trials are independent.

4. The number of trials are fixed.

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Answer:

Step-by-step explanation:

The pattern is easy to see.

After 4 hours on the turnpike, the car is approximately 278 miles from the town.

To solve this problem using a linear function, we can use the formula for distance: distance = speed × time. In this case, the speed is given as 64 miles per hour, and the time is given as 4 hours.

Let's define the distance from the town as a variable, say "d." Since the car travels north, the distance from the town will increase as time passes. At the start, the car is 22 miles north of the town.

Now, we can set up a linear function to represent the distance from the town as a function of time:

d = 22 + (64 × t)

In this function, "t" represents time in hours. The initial distance of 22 miles is added to the product of the speed (64 mph) and time (t).

To find the distance from the town after 4 hours, we substitute t = 4 into the function:

d = 22 + (64 × 4)

d = 22 + 256

d = 278 miles

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Answer:

y=3x-8

Step-by-step explanation:

Answer:

x=-4 is the answer to you equation

Step-by-step explanation:

Answer:

-5/6

Step-by-step explanation:

By the application of Analytical geometry the rate of change of y with respect to x is -5/6.

what is Analytical geometry?

Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.

The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.

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Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

326

Step-by-step explanation:

l x w

7x8

25x6

4x30

326

The simplified expression is -7.1y - 7.8x + 14.8.

The given expression is 2.6y + 14.8 - 7.8x - 9.7y. To combine like terms, we first identify the terms that have the same variable with the same exponent. In this case, we have two terms with y, and they both have the exponent 1. So, we can combine these terms together by adding their coefficients, which are 2.6 and -9.7.

2.6y - 9.7y can be simplified as (2.6 - 9.7)y, which is equal to -7.1y. Therefore, the expression can be written as:

-7.1y - 7.8x + 14.8

We cannot combine any other terms in this expression since they do not have the same variable or exponent.

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Answer:

210 cm²

Step-by-step explanation:

Area of the surface having dimensions 6 cm × 11 cm

\(A_1\) = 11 × 6 = 66 cm²

Area of the surface having dimensions 3 cm × 6 cm

\(A_2\) = 3 × 6 = 18 cm²

Area of the surface having dimensions 7 cm × 6 cm

\(A_3\) = 7 × 6 = 42 cm²

Area of the surface having dimensions 5 cm × 6 cm

\(A_4\) = 5 × 6 = 30 cm²

Area of the trapezoidal surface on the top = \(\frac{1}{2}(b_1+b_2)h\)

\(A_5\) = \(\frac{1}{2}(11+7)3\)

    = 27 cm²

Area of the trapezoidal base \(A_6\) = Area of the surface on the top = 27 cm²

Total surface area = \(A_1+A_2+A_3+A_4+A_5+A_6=66+18+42+30+27 + 27\)

                                               = 210 cm²

Therefore, total surface area of the trapezoidal prism = 210 cm²

an

expression which represents the sum of(-52 +10) and (–72 +9) in

simplest terms

Answer: 59, 218

Step-by-step explanation:

5 ten thousands = 50,000

9 thousands = 9,000

2 hundreds = 200

1 ten = 10

8 ones = 8

50,000 + 9,000 + 200 + 10 + 8 = 59,218

Answer: 59,218

Step-by-step explanation:

The number that has 5 ten thousands, 9 thousands, 2 hundreds, 1 ten, and 8 ones is 59,218.

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Answer:

1st triangle and 4th triangle

Answer:

Part A: 146°

Part B: 70°

Part C: 104°

Step-by-step explanation:

Part A:

m<SHI = 34° (given)

m<SHI + m<MIH = 180° (same side interior angles of a transversal are supplementary)

34° + m<MIH = 180° (Substitution)

Subtract 34° from each side

m<MIH = 180° - 34°

m<MIH = 146°

Part B:

m<HAL = 110° (given)

m<HAV + m<HAL = 180° (linear pair)

m<HAV + 110° = 180° (substitution)

Subtract 110° from each side

m<HAV = 180° - 110°

m<HAV = 70°

m<AVM = m<HAV (alternate interior angles are congruent)

m<AVM = 70°

Part C:

The obtuse angle formed = m<HAV + SHI (exterior angle of a triangle = the sum of two opposite interior angles of a ∆)

The obtuse angle formed = 70° + 34° = 104°

Based on the information in the image, it can be inferred that the sides of the box measure 5 cm each.

To find the measure of the sides of the box we must carry out the following mathematical procedure:

As we know the volume of a cube is the equivalent to the length of its sides raised to the cube (raised to the 3). In this case, to identify the value of the sides we must find the cube root of the volume and the result is the length of the sides.

So this cube has a volume of 125cm³, so its sides would be the cube root of 125.

\(\sqrt[3]{125} = 5\)

According to the above, the length of the sides is 5 taking into account that all the sides are equal.

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Answer:

10

Step-by-step explanation:

because if you divide it by it self that is what it is

Answer:

10

Step-by-step explanation:

50 million divided by 5 million would be 10. what you do is if the 5 is the same then it is one, after that since 50 million has 1 more zero then 5 million then you add a zero to the right of one. Therefore the answer is 10.

hope I helped.

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

  72

Step-by-step explanation:

First differences are ...

  18 -17 = 1

  22 -18 = 4

  31 -22 = 9

  47 -31 = 16

We observe that these are square numbers. The next square number is 25, so we expect the next number in sequence to be ...

  47 +25 = 72

Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.

Hence:

Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.

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The different sums are possible are 18.

As, the number of different sums possible is given by the equation:

Number of different sums = n x m

In other words, we multiply the number of outcomes for the first spinner by the number of outcomes for the second spinner to get the total number of unique sums.

So, the different sums are possible

= 2 x 3 x 3

= 18

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Answer:

Ddkdkdckkpooooooopppppp

Step-by-step explanation: