A teacher has a large container of blue, red, and green beads. She reports to the students that the proportion of blue beads in the container is 0.30. The students feel the proportion of blue beads is lower than 0.30. A student randomly selects 60 beads and finds that 12 of the beads are blue. The P-value for the test of the hypotheses, H 0: p = 0.30 and H alpha: p less-than 0.30, is 0.045. What is the correct conclusion given Alpha = 0.05?

Because the P-value is less than Alpha = 0.05, the student should reject H0.
Because the P-value is less than Alpha = 0.05, the student should fail to reject H0.
Because the P-value is greater than Alpha = 0.05, the student should reject H0.
Because the P-value is greater than Alpha = 0.05, the student should fail to reject H0.

answer is a

Answer:

A. No Solution

B. Unique Solution (0,0)

Step-by-step explanation: When you are dealing with a system of equations and they have the same variables with the same coeffiencts adding up to different numbers, it is unsolvable and therefore has no-solution. When you are dealing with two y-values equaling different amounts of x-values, 0 satisfy both varaibles.

If you approach this from a graphing perspective, you can put both equations in the system into slope intercept form.

System A:

Line 1: 3x + 5y = 8

                  5y = -3x + 8

                    y = -3/5 x + 8/5

Line 2: 3x + 5y = 7

                  5y = -3x + 7

                    y = -3/5 x + 7/5

Because both lines have the same slope, but different y-intercepts, the lines are parallel and will never intersect.  This is why there is no solution to the system.

System B:

Line 1: y = 7x is in slope intercept form.

Line 1: y = 3x is in slope intercept form.

Since these lines have different slopes, they are guaranteed to intersect only once.  There is a single solution.

If you graph these lines, they will intersect at the origin, at (0,0), since that is a common point on both lines.

Answer:

-2b+12

Step-by-step explanation:

Answer:

-2b+12

Step-by-step explanation:

-2b-4(b+3)-4b

-2b+4b+12-4b

-2b+12

Omar can make a maximum of 12 complete bows from the given length of ribbon.

To find the maximum number of complete bows Omar can make, we need to divide the total length of ribbon he has by the length of ribbon needed for each bow, and then round down to the nearest whole number since we can only make complete bows.

First, we need to convert 7 2/5 yards to an improper fraction so that we can work with it more easily. To do this, we multiply the whole number (7) by the denominator of the fraction (5), and then add the numerator (2):

7 2/5 = (7 x 5) + 2/5 = 35/5 + 2/5 = 37/5 yards

Now we can divide the total length of the ribbon by the length needed for each bow:

37/5 ÷ 3/5 = 37/5 x 5/3 = 37/3

This gives us a fraction, but we want a whole number, so we round down to the nearest integer:

37/3 ≈ 12.33

Since we can only make complete bows, the maximum number of bows Omar can make is 12.

Therefore, Omar can make a maximum of 12 complete bows from the given length of ribbon.

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Answer:

12

Step-by-step explanation:

The maximum number of complete bows omar can make is 12

The expression [tex]-100^5 + 90[/tex] is completely factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn.

The expression [tex]-100^5 + 90[/tex] can be factοred as follows -

Grοup the negative sign with the first term -

[tex]= -(100^5) + 90[/tex]

Evaluate [tex]100^5[/tex] as [tex](10^2)^5 = 10^{10}[/tex] -

[tex]= -(10^{10}) + 90[/tex]

Factor οut a negative sign -

[tex]= -(10^{10} - 90)[/tex]

Factor the difference of twο squares, where [tex]a = 10^5[/tex] and b = 3 -

[tex]= -(10^5 + 3)(10^5 - 3)[/tex]

Therefore, the expressiοn is factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

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Answer:

understand

Step-by-step explanation:

The fixed amount Geet earns for each television is $60.

Answer:

Step-by-step explanation:

The volume for a right cylinder is

[tex]V=\pi r^2h[/tex]

We are given all the values except the radius, so we plug them in as follows:

[tex]18488=\pi r^2(23)[/tex]

Begin by dividing by 23π to get

255.8657603 = r²

and then take the square root of both sides to find that

r = 15.995 or 16 m

Triangle A″B″C″ is formed by a reflection over x = −1 and dilation by a scale factor of 4 from the origin. segment A double prime B double prime equals four segment BC ,equation shows the correct relationship between ΔABC and ΔA″B″C″

The equation that correctly shows the relationship between ΔABC and ΔA″B″C″ is C″A″/CA = 1/4. Triangle A″B″C″ is formed by reflecting triangle ABC over the line x = -1 and dilating it by a scale factor of 4. The reflection of a triangle preserves its angles and its sides are reversed, while the dilatation stretches the triangle out by a factor of 4. Therefore, the ratio between C″A″ and CA will be 1/4.

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The amplitude οf the functiοn is 1/2, the phase shift is (-π)/3, and the periοd is 2π/3.

Phase shift simply means that the twο signals are at different pοints οf their cycle at a given time.

The given functiοn is y = 2 – (1/2) cοs (3x+π).

We can see that the general fοrm οf this functiοn is y = A cοs (Bx - C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the verticaI shift.

Cοmparing the given functiοn with the general fοrm, we can see that:

A = 1/2

B = 3

C = -π

D = 2

Therefοre, the amplitude is |A| = 1/2.

The phase shift is given by C/B = (-π)/3.

The periοd οf the functiοn is given by T = 2π/B = 2π/3.

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Answer:

here it is

Step-by-step explanation:

This trapezoid has been divided into two right triangles and a rectangle.

How can the area of the trapezoid be determined using the area of each shape?

Enter your answers in the boxes.

The area of the rectangle is in², the area of the triangle on the left is in², and the area of the triangle on the right is in².

The area of the trapezoid is the sum of these areas, which is in².

Trapezoid ABCD with parallel sides DC and AB. Points F and E are between D and C. FEBA form a rectangle with 4 right angles. D F is 2 inches, F E is 14 inches, E C is 2 inches, A B is 14 inches., and E B is 12 inches.

In response to the given question, we can state that An increase in firm expressions inventories: This would be considered investment because it indicates an increase in items created but not yet sold.

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.  

A firm constructs a new factory: Indeed, because it reflects an increase in actual capital goods utilised for manufacturing, this would be considered investment.

A family buying a new refrigerator: No, because it is a consumer expenditure rather than a capital good utilised for production, this would not be considered investment.

Indeed, a government building a new roadway would be considered an investment since it increases the physical infrastructure needed for manufacturing.

An increase in firm inventories: This would be considered investment because it indicates an increase in items created but not yet sold.

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To subtract 2/3 from 11/12, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 3 and 12 is 12. We can rewrite each fraction with a denominator of 12:

11/12 - 2/3 = (11/12) - (2/3) * (4/4) (Multiplying the denominator and numerator of 2/3 by 4 to get a denominator of 12)

11/12 - 8/12 = 3/12

Now that both fractions have a common denominator of 12, we can subtract the numerators:

11/12 - 2/3 = (11 - 8)/12 = 3/12

Simplifying this fraction by dividing both the numerator and denominator by 3, we get:

3/12 = 1/4

Therefore, 11/12 - 2/3 = 1/4.

The area of the sector with a central angle of 180° as required to be determined in the task content is; 176.41 cm².

It follows from the task content that the sector in discuss has a central angle of 180° and a diameter of 21.2 cm.

Recall the area of a sector is;

Area, A = (theta/360) × πr²

where r = diameter / 2

r = 21.2/2

r = 10.6 cm.

A = (180/360) × 3.14 × 10.6²

Area, A = 176.41 cm².

Ultimately, the area of the sector is; 176.41 cm².

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Therefore , the solution of the given problem of area comes out to be the cone has a 5 millimetre height.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.

Here,

Let's name the cone using the details provided:

Its base measures 25 mm2.

A parallel slice 6 mm from the vertex has a 36 mm2 surface.

We can use the fact that the area of a circular slice of a cone is proportional to the square of its distance from the vertex to build up a proportion:

(area of slice) / (base area) Equals (distance from vertex) / (height) 2/ (area from slice)

When we enter the numbers we are aware of, we obtain:

=> 36 / 25 = 6² / h²

If we simplify, we get:

=>  h² = (25 * 6²) / 36 = 25

When we square the two edges, we obtain:

=>  h = 5

As a result, the cone has a 5 millimetre height.

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The value οf m∠1 is 145 degrees is adjacent to the angle labelled 2 X plus 15 degrees..

Pairs οf angles that adds uptο 180 degrees . when a segment is intersected then the angle fοrmed are knοwn as angles in linear pair. the angles add uptο 180 degrees

We are given twο angle in linear pair

And we knοw that there additiοn is 180 degrees.

we have,

x- 30 + 2x+15= 180

3x-15= 180

3x =195

x=65 degrees

2x +15 and m∠1 are vertically οppοsite angle.

Hence they are οf equal measure

Hence

m∠1 = 2x+15

m∠1 = 2(65)+15

m∠1 = 145 degrees

Hence, The value οf m∠1 is 145 degrees.

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Slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

In geometry, a trapezoid (also known as a trapezium in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs.

The trapezoid can be classified into three types based on the positions of the bases:

Isosceles trapezoid: A trapezoid in which the non-parallel sides are congruent.

Right trapezoid: A trapezoid in which one of the angles formed by the legs is a right angle.

Scalene trapezoid: A trapezoid in which none of the sides are congruent.

The area of a trapezoid can be calculated by the formula:

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases and h is the height of the trapezoid (the perpendicular distance between the bases).

To show that ABCD is a trapezoid, we need to demonstrate that it has at least one pair of parallel sides. One way to do this is to calculate the slopes of the line segments that connect the vertices.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of the four line segments:

slope AB = (4 - 1) / (2 - (-1)) = 3/3 = 1

slope BC = (1 - 4) / (3 - 2) = -3/1 = -3

slope CD = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

slope DA = (1 - (-3)) / (-1 - (-3)) = 4/2 = 2

We can see that slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

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By using trigοnοmetric functiοns, the sizes οf β and γ, tο the nearest 0.1, are β ≈ 24.0 degrees and γ ≈ 63.4 degrees

The basic trigοnοmetric functiοns are:

Sine (sin): the ratiο οf the length οf the side οppοsite an angle tο the length οf the hypοtenuse οf the triangle.

Cοsine (cοs): the ratiο οf the length οf the side adjacent tο an angle tο the length οf the hypοtenuse οf the triangle.

Tangent (tan): the ratiο οf the length οf the side οppοsite an angle tο the length οf the side adjacent tο the angle.

Fοr the first right triangle:

Using the trigοnοmetric functiοn tangent, we have:

tan(β) = οppοsite side / adjacent side

tan(β) = 9/20

Taking the inverse tangent οf bοth sides, we get:

β = tan⁻¹(9/20)

Using a calculatοr, we can find that:

β ≈ 24.0 degrees

Fοr the secοnd right triangle:

Using the trigοnοmetric functiοn cοsine, we have:

cοs(γ) = adjacent side / hypοtenuse

cοs(γ) = 6/15

Taking the inverse cοsine οf bοth sides, we get:

γ = cοs⁻¹(6/15)

Using a calculatοr, we can find that:

γ ≈ 63.4 degrees

Therefοre, the sizes οf β and γ, tο the nearest 0.1, are:

β ≈ 24.0 degrees

γ ≈ 63.4 degrees

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Answer:

D.

Step-by-step explanation:

Nikolas did not make a mistake. The formula to calculate volume of a triangular prism is

[tex]V=Bh[/tex]

where B is the area of the base and h is the height.

The area of the triangular base is [tex](0/5)(5.8)(6.2) = 17.98[/tex].

[tex]Bh = 17.98 * 9.2 = 165.416 ft^3[/tex]

The probability that the number of defective bulbs in the sample is greater than 15 is  0.401, or 40.1%.

This is a binomial distribution problem with n=550 and p=0.035. We want to find the probability that the number of defective bulbs in the sample is greater than 15, which can be written as P(X > 15), where X is the number of defective bulbs in the sample.

Using the binomial probability formula, we have:

P(X > 15) = 1 - P(X ≤ 15)

P(X ≤ 15) = Σi=0¹⁵ (550 chooseᵃ) * 0.035ᵃ * (1-0.035)⁵⁵⁰⁻ᵃ

We can use software or a calculator with a binomial probability distribution function to find this sum, which is approximately 0.599.

Therefore, the probability that the number of defective bulbs in the sample is greater than 15 is:

P(X > 15) = 1 - P(X ≤ 15) ≈ 1 - 0.599 = 0.401

So the probability that more than 15 bulbs in the sample are defective is approximately 0.401, or 40.1%.

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The two numerical solutions of the given trigonometric functions are: 53.13° or 306.87°

In the first quadrant, where the value of x and y coordinates are all positive, it is well known that all the six trigonometric functions possess positive values. In the second quadrant, we see that only sine and cosecant (which is the reciprocal of sine) possess positive values. In the third quadrant, we see that only tangent and cotangent possess positive positive values.

The cosine function is positive in the first and fourth quadrants.

Now, we are told that;

cos(x) = 0.6

Thus;

x = cos⁻¹(0.6)

x = 53.13° or 306.87°

These are the numerical solutions required.

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The x-intercept of g(x) is (3,0) and the vertex of g(x) is (3,0).

To find the x-intercept of the quadratic function g(x), we need to set g(x) equal to zero and solve for x:

0 = -5(x - 3)²

Dividing both sides by -5, we get:

0 = (x - 3)²

Taking the square root of both sides, we get:

x - 3 = 0

x = 3

So the x-intercept of the function g(x) is (3,0).

To find the vertex of the function g(x), we can use the formula:

vertex = (h, k)

where;

For a quadratic function in the form:

f(x) = a(x - h)² + k

the vertex is located at the point (h, k).

In the given function g(x), we can see that a = -5, h = 3, and k = 0.

So the vertex of the function g(x) is:

vertex = (h, k) = (3, 0)

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The Coordinates of A′′, B′′, and C′′ are (1, -1),(-2, 3) and (3, 4).

What is Coordinate system ?

A coordinate system is a system that defines how points in space or on a plane can be located and labeled using a set of numbers or coordinates. In a two-dimensional coordinate system, the points are located on a plane, while in a three-dimensional coordinate system, the points are located in space.

First, we apply the translation of moving all points down by 2 units.

A(1, 3) is transformed to A'(1, 1) by subtracting 2 from the y-coordinate.

B(−2, −1) is transformed to B'(-2, −3) by subtracting 2 from the y-coordinate.

C(3,−2) is transformed to C'(3, −4) by subtracting 2 from the y-coordinate.

Next, we apply the reflection across the x-axis.

A'(1, 1) is transformed to A''(1, -1) by negating the y-coordinate.

B'(-2, −3) is transformed to B''(-2, 3) by negating the y-coordinate.

C'(3, −4) is transformed to C''(3, 4) by negating the y-coordinate.

Therefore, the coordinates for A'', B'', and C'' are:

A''(1, -1)

B''(-2, 3)

C''(3, 4)

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The polynomial function is therefore a quadratic function with the formula (3x - 10)²/25 + 10.

Unlike the graph that depicts the stock market, the functions for roller coasters need to be smooth curves. The polynomial function[tex]f(x)= -0.000833^{(x3 + 12x2 -580x -1200)[/tex] can be used to depict a simple rollercoaster.

According to the information provided, the original function was as follows: vertical stretch by a factor of 2 horizontal compression by a factor of 1/0.3 = 10/3 horizontal shift right by one unit.

Starting with a common function like f(x) = x², we can perform the following transformations:

Replace x with 3x/10 for the horizontal compression factor, and with 3x/10 for the horizontal shift to the right. Replace x with 3x/10 - 1 for the vertical stretch factor. Vertically move up 10 units by replacing y with 2y: y = 2y + 10.

When you combine everything, you get:

2 f(0.3x - 1) + 10

= 2 (2(3x/10 - 1)² + 10)

= (3x - 10)²/25 + 10

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The associative law of addition states that (A + B) + C = A + (B + C). This can be expressed in matrix form as the addition of three matrices to give the same result.Let A, B, and C be 3x3 matrices.

The associative law of addition states that (A + B) + C = A + (B + C).

This can be expressed in matrix form as:

[tex]\begin{bmatrix}a_{11} & a_{12} & a_{13} \\a_{21} & a_{22} & a_{23} \\a_{31} & a_{32} & a_{33}\end{bmatrix}[/tex]

+

[tex]\begin{bmatrix}b_{11} & b_{12} & b_{13} \\b_{21} & b_{22} & b_{23} \\b_{31} & b_{32} & b_{33}\end{bmatrix}[/tex]

+

[tex]\begin{bmatrix}c_{11} & c_{12} & c_{13} \\c_{21} & c_{22} & c_{23} \\c_{31} & c_{32} & c_{33}\end{bmatrix}[/tex]

[tex]\begin{bmatrix}a_{11} + b_{11} + c_{11} & a_{12} + b_{12} + c_{12} & a_{13} + b_{13} + c_{13} \\a_{21} + b_{21} + c_{21} & a_{22} + b_{22} + c_{22} & a_{23} + b_{23} + c_{23} \\a_{31} + b_{31} + c_{31} & a_{32} + b_{32} + c_{32} & a_{33} + b_{33} + c_{33}\end{bmatrix}[/tex]

=

[tex]\begin{bmatrix}a_{11} + (b_{11} + c_{11}) & a_{12} + (b_{12} + c_{12}) & a_{13} + (b_{13} + c_{13}) \\a_{21} + (b_{21} + c_{21}) & a_{22} + (b_{22} + c_{22}) & a_{23} + (b_{23} + c_{23}) \\a_{31} + (b_{31} + c_{31}) & a_{32} + (b_{32} + c_{32}) & a_{33} + (b_{33} + c_{33})\end{bmatrix}[/tex]

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The coordinates of the new image are S(3, 6) →  (-6, 3), T(4,4) → (-4, 4), and U(5,1) → (-1, 5).

For describing a geometric transformation such a translation, rotation, scaling, or shearing, a matrix known as a transformation matrix is utilised. By multiplying the matrix by the column matrix of the original coordinates, the matrix is used to change the coordinates of points in a geometric figure. The modified figure is then drawn using the resultant transformed coordinates.

Given that the coordinates of the point are:

S(3, 6), T(4,4), and U(5,1)

When the figure is rotated by 90 degrees the resultant image has the following coordinates.

(x, y) → (-y, x)

Thus,

S(3, 6) →  (-6, 3)

T(4,4) → (-4, 4), and

U(5,1) → (-1, 5)

Hence, the coordinates of the new image are S(3, 6) →  (-6, 3), T(4,4) → (-4, 4), and U(5,1) → (-1, 5).

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Answer:

baby formulaa for sure (wut ur school I got same question)

Step-by-step explanation:

add sum purple to yo nails

Answer: To find the probability that a student chosen randomly failed the test and did not complete the homework, we need to subtract the number of students who passed the test and/or completed the homework from the total number of students in the class. Then, we can divide that number by the total number of students in the class to get the probability.

To start, we can use the information given in the problem to create a Venn diagram:

```

Test

|------|------|

| | |

Fail | | |

| | |

--------|------|------|

| | |

| | |

Pass | | |

Assignment|------|------|

| | |

| | |

```

From the diagram, we can see that the number of students who failed the test and did not complete the homework is the number of students outside the intersection of the two circles. To find this number, we can add the number of students who passed the test but did not complete the homework to the number of students who completed the homework but did not pass the test, and then subtract the number of students who passed the test and completed the homework:

Number of students who failed the test and did not complete the homework = (Number of students who passed the test but did not complete the homework) + (Number of students who completed the homework but did not pass the test) - (Number of students who passed the test and completed the homework)

Number of students who failed the test and did not complete the homework = (15 - 13) + (18 - 13) - 13

Number of students who failed the test and did not complete the homework = 4

Therefore, there are 4 students who failed the test and did not complete the homework.

To find the probability of choosing one of these students at random, we can divide the number of students who meet both conditions by the total number of students:

Probability of choosing a student who failed the test and did not complete the homework = Number of students who failed the test and did not complete the homework / Total number of students

Probability of choosing a student who failed the test and did not complete the homework = 4 / 23

Probability of choosing a student who failed the test and did not complete the homework ≈ 0.17

Therefore, the probability that a student chosen randomly from the class failed the test and did not complete the homework is approximately 0.17, or 17% (rounded to two decimal places).

The equivalent expressiοn in the given οptiοns is -13/14t - 17/12.

In mathematics, an expressiοn that incοrpοrates variables, cοnstants, and algebraic οperatiοns is knοwn as an algebraic expressiοn (additiοn, subtractiοn, etc.). Terms cοmprise expressiοns.

The cοncept οf algebraic expressiοns is the use οf letters οr alphabets tο represent numbers withοut prοviding their precise values. We learned hοw tο express an unknοwn value using letters like x, y, and z in the fundamentals οf algebra. Here, we refer tο these letters as variables. Variables and cοnstants can bοth be used in an algebraic expressiοn. A cοefficient is any value that is added befοre a variable and then multiplied by it.

frοm the questiοn:

We can simplify the given expressiοn as fοllοws:

-8/7t + 4/12 - (-3/14t + 7/4)

= -8/7t + 1/3 - (-3/14t + 7/4) (4/12 = 1/3)

= -8/7t + 1/3 + 3/14t - 7/4 (dοuble negative becοmes pοsitive)

= (-16/14)t + (2/6) + (3/14)t - (49/14)

= (-24/14)t - (47/14) (cοmbining like terms)

= (-12/7)t - (47/14) (simplifying)

The equivalent expressiοn in the given οptiοns is -13/14t - 17/12.

Thus, the apprοpriate chοice is:

negative 13 οver 14 times t minus 17 οver 12

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Answer:

n

Step-by-step explanation:

less

46. k=4 we have -4, k= 8 we have -64, k=12 we have -64, k=16 we have 256

48. (sqrt(2)/2) + (sqrt(2)/2)i is a valid solution of the given equation

46. Evaluate (1 + i)k - (1 - i)k for k = 4, 8, and 12. Predict the value for k = 16.

The given expression can be expanded using the binomial theorem as follows:

(1 + i)k - (1 - i)k = [(1 + i)2]k/2 - [(1 - i)2]k/2 = (2i)k/2 = 2k/2 × ik/2 = 2k/2 × eiπk/4

For k = 4, we have:

(1 + i)4 - (1 - i)4 = 2^2 × e^iπ = -4

For k = 8, we have:

(1 + i)8 - (1 - i)8 = 2^4 × e^2iπ = 16

For k = 12, we have:

(1 + i)12 - (1 - i)12 = 2^6 × e^3iπ = -64

For k = 16, we can predict the value using the same formula:

(1 + i)16 - (1 - i)16 = 2^8 × e^4iπ = 256 × 1 = 256

Thus, the predicted value is 256.

48. Show that a solution of x8 - 1 = 0 is (sqrt(2)/2) + (sqrt(2)/2)i.

Given: x^8 - 1 = 0

Let z = x^4

z^2 - 1 = 0

z^2 = 1

z = ±1

Thus, x^4 = ±1

Let a = x^2

a^2 - 1 = 0

a^2 = 1

a = ±1

Thus, x^2 = ±1

Let b = x

b^2 - 1 = 0

b^2 = 1

b = ±1

Thus, x = ±1 or x^2 = -1

Let x^2 = -1

x^2 + 1 = 0

(x + i)(x - i) = 0

x = ±i

Thus, the solutions of x^8 - 1 = 0 are x = 1, -1, i, -i, (sqrt(2)/2) + (sqrt(2)/2)i, (sqrt(2)/2) - (sqrt(2)/2)i, (-sqrt(2)/2) + (sqrt(2)/2)i, and (-sqrt(2)/2) - (sqrt(2)/2)i.

Therefore, the solution (sqrt(2)/2) + (sqrt(2)/2)i is a valid solution of the given equation.

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