I have the answers I just need someone to work it out I’ll mark as brainlesttt

The alternative hypothesis is a statement that contradicts the claim made in the null hypothesis.

The alternative hypothesis is a fundamental concept in hypothesis testing. In this statistical framework, the null hypothesis represents the default assumption or claim about a population parameter.

The alternative hypothesis, on the other hand, contradicts the null hypothesis and proposes an alternative explanation or claim.

When conducting a hypothesis test, we collect data and analyze it to determine whether the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.

The alternative hypothesis is typically what the researcher is trying to establish or prove.

It is important to note that the alternative hypothesis does not necessarily specify a specific alternative value or hypothesis.

It simply states that there is a difference or relationship between variables, contrary to the null hypothesis.

The specific form of the alternative hypothesis depends on the research question and the nature of the investigation.

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To find the power series representation of f(t) = ln(1-t)^2t, we can use the formula for the power series representation of ln(1+x), which is: ln(1+x) = sum((-1)^(n+1) * x^n / n, n=1 to infinity)

Substituting -t for x, we get: ln(1-t) = sum((-1)^(n+1) * t^n / n, n=1 to infinity)
Multiplying both sides by 2t, we get: f(t) = ln(1-t)^2t = 2t * sum((-1)^(n+1) * t^n / n, n=1 to infinity)
Expanding the product using the distributive property, we get: f(t) = 2t * sum((-1)^(n+1) * t^n / n * t^n, n=1 to infinity)
Simplifying the exponent, we get: f(t) = 2 * sum((-1)^(n+1) * t^(2n-1) / n, n=1 to infinity)
This is the power series representation of f(t). The radius of convergence can be found using the ratio test:
lim(n->infinity) |a(n+1) / a(n)| = lim(n->infinity) |(-1)^(n+2) * t^(2n+1) / (n+1) * (-1)^(n+1) * t^(2n-1) / n|
= lim(n->infinity) |t^2 / (n+1)|
= 0, since t is a constant and n+1 grows faster than t^2
Therefore, the radius of convergence is infinity, which means that the power series representation of f(t) converges for all values of t.

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The radius of the cylindrical shaped soup can is r = 3.3 cm

Given data ,

A company is designing a soup can that is in the shape of a right circular cylinder. The height of the can will be 3 times the radius of the can. The volume of the can will be 350 cubic centimeters

Now , Volume of Cylinder = πr²h

where h = 3r

On simplifying , we get

350 = πr²3r

350 = 3πr³

Divide by 3π on both sides , we get

r³ = 37.13615

Taking cube root on both sides , we get

r = 3.3 cm

Hence , the radius of soup can is r = 3.3 cm

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The difference quotient for the function f(x) = 64x^2 is (f(x + h) - f(x))/h.

The difference quotient measures the rate of change of a function at a particular point. For the given function f(x) = 64x^2, we can find the difference quotient as (f(x + h) - f(x))/h.

To calculate the difference quotient, we substitute f(x + h) and f(x) into the formula and simplify:

(f(x + h) - f(x))/h = (64(x + h)^2 - 64x^2)/h

Expanding and simplifying, we get:

= (64(x^2 + 2hx + h^2) - 64x^2)/h

= (64x^2 + 128hx + 64h^2 - 64x^2)/h

= 128hx/h + 64h^2/h

= 128x + 64h

The difference quotient for the function f(x) = 64x^2 is 128x + 64h.

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The domain and range of the function whose vertex is (-1, -2) would be; (-∞, +∞) and (-∞, 2] respectively.

Since we know that graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

In the given graph, the vertex is (-1, -2).

Since the domain of the function indicate the values of x,

The values of x can be all real numbers;

Domain = (-∞, +∞)

And the range of the function shows the value of y,  is less than or equal to 2,

So range = (-∞, 2].

The domain of the function is (-∞, +∞) and the range of the function will be (-∞, 2].

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Answer:

1/2 =0.5

Step-by-step explanation:

The estimated probability of the spinner landing pink is 0.41.

The given table,

Section    Outcomes

Blue            45

Black           73

Pink            82

Here, number of favorable outcomes = 82

Total number of outcomes = 45+73+82

= 200

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Now, probability of an event = 82/200

= 0.41

Therefore, the estimated probability of the spinner landing pink is 0.41.

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Part A: It can be written as y = sin(x - c), where c represents the amount of phase shift. Part B: We can use the equation y = sin(x - a), where a represents the amount of rightward shift. Part C: The period is the distance between corresponding points on the graph, such as two peaks or two troughs. Part D: There are infinitely many equations that can be written to map the parent sine function onto itself.

1. Part A: To introduce a phase shift to the parent sine function y = sin(x), we subtract a constant value c from the input variable x. The equation y = sin(x - c) has an identical graph to the parent sine function, but it is shifted horizontally by an amount of c units to the right or left. The value of c determines the amount of phase shift, where a positive value shifts the graph to the right, and a negative value shifts it to the left.

2. Part B: To map the parent sine function onto itself by shifting it to the right, we can use the equation y = sin(x - a), where a represents the amount of rightward shift. By subtracting a constant value a from the input variable x, the graph is shifted a units to the right while maintaining the same shape.

3. Part C: The equations in parts A and B indicate that the period of the sine function remains the same. The period of the sine function is the distance between corresponding points on the graph, such as two peaks or two troughs. Introducing a phase shift or rightward shift does not alter the period; it only changes the starting point or position of the graph.

4. Part D: There are infinitely many equations that can be written to map the parent sine function onto itself. By combining different values of phase shifts and rightward shifts, we can obtain various equations. The sine function is periodic, meaning it repeats itself indefinitely. Any combination of phase shift and rightward shift will result in the same graph repeating after a specific interval, which is the period of the sine function. Therefore, there is no limit to the number of equations that can be written to achieve this mapping.

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Answer:  [tex]-\frac{\sqrt{29}}{5}\\\\[/tex]

This is the same as writing   -sqrt(29)/5

====================================================

Explanation:

tan(theta) < 0 and cos(theta) > 0 indicates angle theta is in quadrant IV.

In this quadrant, csc(theta) is negative.

The diagram is shown in the image below. We have these three sides

Cosecant is the ratio of hypotenuse over opposite. It is the reciprocal of sine.

[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{\sqrt{29}}{-5}\\\\\csc(\theta) = -\frac{\sqrt{29}}{5}\\\\[/tex]

The values of a and b are (2,3),  (-2,3),  (2,-1), and (-2,-1).

What is the curve?

A  curve is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point.

Here, we have

Given:  two curves given by

y₁ = ax(b-x) and y₂ = x/(x+2)

We have to find the value of a and b.

Here it says the two curves have one intersection point and at that point, they have a common tangent and at the same point, their curvatures are equal as well.

So this implies,

At the point of intersection, the two curves will have the same coordinate

y₁  = y₂

ax(b-x) = x/(x+2)....(1)

their slopes will be equal as well as at this point they have the same tangent line

y₁'  = y₂'

ab-2ax = 2/(x+2)²...(2)

For a two-dimensional curve written in the form y = f(x), the equation of curvature becomes

k = (d²y/dx²)/(1+(dy/dx)²)[tex]^{3/2}[/tex]

and at the point of intersection k₁ = k₂

y₁'' = -2a      and y₂'' = -4/(x+2)³

K₁ = |-2a|/[1+(ab-2ax)²]^(3/2)

K₂ = |-4/(x+2)³|/[1+(2/(x+2)²)²]^(3/2)

K₁ = K₂

= |-2a|/[1+(ab-2ax)^2]^(3/2)= |-4/(x+2)^3|/[1+(2/(x+2)^2)^2]^(3/2) ... (3)

So, now we have 3 equations and three variables a, b and x

We could solve the three and get the various a and b pairs for a particular x.

After solving we would get (2,3),  (-2,3),  (2,-1), and (-2,-1).

Hence, the values of a and b are (2,3),  (-2,3),  (2,-1), and (-2,-1).

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In the trapezium OABC, the value of y will be 1.

To find the value of y in the trapezium OABC, we can use the fact that O(0,0), A(2,-1), B(4,3), and C(0,y). Since OABC is a trapezium, we know that the line segments OA and BC are parallel.

Therefore, their slopes are equal. The slope of OA is (0 - (-1))/(0 - 2) = 1/2. The slope of BC is (y - 3)/(0 - 4) = (3 - y)/4. Setting these slopes equal to each other, we get:

1/2 = (3 - y)/4

Multiplying both sides by 4, we get:

2 = 3 - y

Subtracting 3 from both sides, we get:

y = 1

Therefore, the value of y in the trapezium OABC is 1.

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The areas of the figures are listed below:

In this problem we need to determine the areas of eleven figures, each of which can be found by means of following area formulas:

Triangle (Heron's formula)

A = √[s · (s - a) · (s - b) · (s - c)]

s = 0.5 · (a + b + c)

Where:

Triangle (standard formula)

A = 0.5 · w · h

Rectangle / Parallelogram

A = w · h

Trapezoid

A = 0.5 · (w + w') · h

Where:

Semicircle

A = 0.5π · r²

Circle

A = π · r²

Where r is the radius.

Now we proceed to determine the areas:

Case 1

A = (21 m) · (33 m)

A = 693 m²

Case 2

A = (11 in) · (7 in) + 0.5 · (4 in) · (7 in)

A = 77 in² + 14 in²

A = 91 in²

Case 3

A = π · (2.9 ft)²

A = 26.420 ft²

Case 4

A = 0.5 · (27 cm) · (16 cm)

A = 216 cm²

Case 5

A = 0.5 · (38 m + 13 m) · (32.7 mi)

A = 0.5 · (51 m) · (32.7 mi)

A = 833.85 mi²

Case 6

A = (17.6 mm)²

A = 309.76 mm²

Case 7

A = (19 yd) · (7.8 yd)

A = 148.2 yd²

Case 8

A = 0.5π · (22 in)²

A = 760.265 in²

Case 9

A = (16.4 ft) · (11.8 ft)

A = 193.52 ft²

Case 10

x = √[(29.1 in)² - (14.6 in)²]

x = 25.172 in

x' = 25.172 in - 20.4 in

x' = 4.772 in

A = 0.5 · (25.172 in) · (14.6 in) - 0.5 · (4.772 in) · (14.6 in)

A = 148.92 in²

Case 11

s = 0.5 · (30 cm + 30 cm + 26 cm)

s = 43 cm

A = √[(43 cm) · (43 cm - 30 cm)² · (43 cm - 26 cm)]

A = 351.481 cm²

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Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q but not a finite extension of Q since every element in this extension is algebraic over Q.

To prove that the extension Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q, we need to show that every element in this extension is algebraic over Q.

Let's consider an arbitrary element in the extension, say √2. We know that √2 is algebraic over Q because it is a root of the polynomial x² - 2 = 0. Similarly, for ∛2, it is a root of the polynomial x³ - 2 = 0. The same logic applies to ⁴√2 and other elements in the extension. Each of these elements is algebraic over Q because they satisfy polynomial equations with coefficients in Q.

Therefore, Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q.

To prove that it is not a finite extension of Q, we need to show that there is an infinite number of elements in the extension. We can observe that for every positive integer n, there exists an element in the extension that is the nth root of 2. For example, √2 is the square root (n = 2), ∛2 is the cube root (n = 3), ⁴√2 is the fourth root (n = 4), and so on. Since there are infinitely many positive integers, there are infinitely many elements in the extension. Hence, Q(√2, ∛2, ⁴√2, ...) is not a finite extension of Q.

Therefore, we have proven that Q(√2, ∛2, ⁴√2, ...) is an algebraic extension of Q but not a finite extension of Q.

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A graph of the image of △PQR after a dilation with center (0, 0), a scale factor of 2, and a reflection across the y-axis is shown below.

In Geometry, a dilation is a type of transformation which typically changes the dimension (size) or side lengths of a geometric object, but not its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.

In this scenario an exercise, we would dilate the coordinates of the vertex at (3, 3) by applying a scale factor of 2 that is centered at the origin as follows:

P (-1, 1) → (-1 × 2, 1 × 2) = P' (-2, 2).

Q (-2, 3) → (-2 × 2, 3 × 2) = Q' (-4, 6).

R (-2.5, 1) → (-2.5 × 2, 1 × 2) = R' (-5, 2).

By applying a reflection over the y-axis to the vertices of triangle P'Q'R', we have the following transformed coordinate:

(x, y)                                              →                 (-x, y).

P' (-2, 2)                                        →                 P'' (2, 2)

Q' (-4, 6)                                        →                 Q'' (4, 6)

R' (-5, 2)                                        →                 R'' (5, 2)

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Complete Question:

Graph △P'Q'R', the image of △PQR by a dilation with center (0, 0), a scale factor 2, and a reflection across the y-axis.

The answer is that the double integral with limits of integration as ∫-1^0 ∫-x^x+1 (8x+4y)2 dy dx evaluates to 80/9 when solving for the triangle with vertices (−1,0),(0,1),(−1,0).

To solve this problem, we first need to find the bounds for the double integral. We can see that the triangle RR is bounded by the lines y = x + 1, y = -x, and x = -1. We can rewrite these bounds in terms of x and y as -x ≤ y ≤ x + 1 and -1 ≤ x ≤ 0.
Now, we can set up the double integral as follows:
∬R(8x+4y)2dA = ∫-1^0 ∫-x^x+1 (8x+4y)2 dy dx
We can evaluate the inner integral first by using the power rule for integration:
∫-x^x+1 (8x+4y)2 dy = [ (8x+4y)3 / 12 ] from y = -x to y = x + 1
= (2/3)(8x+4(x+1))3 - (2/3)(8x+4(-x))3
= (2/3)(8x+4)3 - (2/3)(8x)3
= (2/3)(64x3 + 96x2 + 48x + 8)
Now, we can evaluate the outer integral by using the linearity of integration:
∫-1^0 ∫-x^x+1 (8x+4y)2 dy dx = ∫-1^0 (2/3)(64x3 + 96x2 + 48x + 8) dx
= (2/3)(16 - 8/3) = 80/9
Therefore, ∬R(8x+4y)2dA = 80/9.
In conclusion, the answer is that the double integral with limits of integration as ∫-1^0 ∫-x^x+1 (8x+4y)2 dy dx evaluates to 80/9 when solving for the triangle with vertices (−1,0),(0,1),(−1,0).

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Answer: The answer is 166

Step-by-step explanation:

i used a calculator on my phone!!!!! Hope this helps!!!!

Answer: 166

Step-by-step explanation:

Complete the paranthesis first

2(35)+2(28)+2(20)=

Multiply

70+56+40=

Add

=166

The phase shift of the given trigonometric equation is 4.

The given trigonometric equation is y=5sin(x-4)+3.

Use the form asin(bx−c)+d to find the amplitude, period, phase shift, and vertical shift.

Amplitude: 5

Period: 2π

Phase Shift: 4 (4 to the right)

Vertical Shift: 3

Therefore, the phase shift of the given trigonometric equation is 4.

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The cofunction for secant (sec) is the cosine (cos) function. To express sec(π/6) in terms of its cofunction, we can use the cofunction identity: sec(x) = 1/cos(x). So, sec(π/6) = 1/cos(π/6).

In mathematics, the term "cofunction" typically refers to the trigonometric functions that are reciprocals or inverses of each other. For example, the cofunction of sine (sin) is cosine (cos), and the cofunction of cosine is sine.

If you have a specific trigonometric function you would like to express in terms of its cofunction, please provide the function, and I'll be happy to help you with the appropriate cofunction.

The common cofunction pairs are:

Sine (sin) and Cosine (cos): sin(x) = cos(90° - x) and cos(x) = sin(90° - x)

Tangent (tan) and Cotangent (cot): tan(x) = cot(90° - x) and cot(x) = tan(90° - x)

Secant (sec) and Cosecant (csc): sec(x) = csc(90° - x) and csc(x) = sec(90° - x)

The cofunction identities are useful in simplifying trigonometric expressions and solving trigonometric equations.

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The cofunction of secant is cosine, so we can write sec(π/6) in terms of cosine. Since secant is the reciprocal of cosine, we have sec(π/6) = 1/cos(π/6).

Using the unit circle, we can see that cos(π/6) = √3/2. Therefore, sec(π/6) = 1/(√3/2) = 2/√3.
In summary, sec(π/6) = 2/√3. To express sec(π/6) in terms of its cofunction, we need to understand that the cofunction of secant (sec) is the cosine (cos) function. The relationship between secant and cosine is: sec(x) = 1/cos(x). To find the cofunction of sec(π/6), we need to first find the complement angle, which is π/2 - π/6 = π/3. Now, we can write sec(π/6) in terms of its cofunction using the relationship:
sec(π/6) = 1/cos(π/6)
Since cos(π/3) is the cofunction of sec(π/6), we have:
sec(π/6) = 1/cos(π/3)
Thus, sec(π/6) is expressed in terms of its cofunction as 1/cos(π/3).

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The value of x  is 8

To determine the value of the variable, we need to know the triangle sum theorem.

The triangle sum theorem is a mathematical theorem stating that the sum of the interior angles in a triangle is equal to 180 degrees.

This is represented as;

a + b + c = 180

Now, from the information given, we have that;

(15x+2)

39 degrees

19degrees

Equate the angles

15x + 2 + 39 + 19 = 180

collect the like terms, we have;

15x = 180 - 60

15x = 120

Divide both sides by the coefficient

x = 8

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To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

Answer:

False.

Step-by-step explanation:

The statement "1:24,000" is not an example of a verbal statement. It is a numerical ratio or scale commonly used in cartography and map scales. Verbal statements typically involve spoken or written language rather than numerical representations. :)

Answer: three students.

Step-by-step explanation: That said, 25 is correct since the worst case scenario is that the class has two students born in each month, so adding an additional student ensures that you will have at least one month with at least three students born in that month.

Hope it helped :3

Answer:

Solution is in attached photo.

Step-by-step explanation:

Do take note for this question, it tests on angle properties such as sum of angles on a straight line and sum of angles in a triangle.

Answer:

-1

Step-by-step explanation:

If we just plug the -3 into the equation...

3*9+(-18)-10

27-28

-1

Feel free to tell me if I did anything wrong! :)

The fourth step in constructing a circle that circumscribes a triangle is B. Draw the perpendicular bisector to each side of the triangle to find the circumcenter

After drawing a triangle, construct the perpendicular bisectors for each side. The intersection of these bisectors is the circumcenter. Next, set your compass to the distance between the circumcenter and any vertex of the triangle.

This is the radius of the circle. The fourth step is to position the point of the compass at the circumcenter and draw a circle.

This circle will pass through all three vertices of the triangle, meaning it perfectly circumscribes the triangle.

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The features of cross-tabulation include its versatility in creating a wide range of tables and its effectiveness as a tool for summarizing survey data.

Cross-tabulation, also known as contingency table analysis or crosstab, is a statistical technique used to analyze the relationship between two or more categorical variables.

It involves organizing data into a table format to display the frequency distribution of variables across different categories.

One feature of cross-tabulation is that it allows for the creation of a variety of tables based on the specific research question or objective.

Researchers can choose different variables to cross-tabulate and arrange the categories in various ways, providing flexibility in examining relationships and patterns within the data.

This versatility allows for the exploration of different hypotheses and the identification of significant associations between variables.

Another feature of cross-tabulation is its effectiveness as a tool for summarizing survey data.

By organizing data into a table format, cross-tabulation provides a clear and concise summary of the relationships between variables.

It allows research analysts to compare the frequencies and proportions of different categories across variables, making it easier to identify patterns, trends, and associations within the data.

This summary information is valuable for gaining insights, drawing conclusions, and making informed decisions based on the survey results.

In conclusion, cross-tabulation offers the advantages of versatility in creating a wide range of tables and providing research analysts with a powerful tool to summarize survey data effectively.

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The quadratic function graphed in this problem is defined as follows:

y = (x + 4)² - 1.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

The coordinates of the vertex in this problem are given as follows:

(-4, -1).

Hence:

y = a(x + 4)² - 1.

When x = 0, y = 15, hence the leading coefficient a is obtained as follows:

15 = a(0 + 4)² - 1

16a = 16

a = 1.

Hence the equation is:

y = (x + 4)² - 1.

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Based on the evaluations above, the correct answers are:

True

True

True

False:

Let's evaluate each statement based on the given deck of 18 cards labeled 1 through 18:

It is impossible that a card with a number greater than 19 is selected.

True. Since the deck only contains cards labeled 1 through 18, it is impossible to select a card with a number greater than 19 because such cards are not present in the deck.

It is likely that a card with a number greater than 2 is selected.

True. Since the deck contains cards labeled 1 through 18, the majority of cards have numbers greater than 2. Therefore, it is likely that a card with a number greater than 2 will be selected.

It is certain that a card with an odd or even number is selected.

True. Every card in the deck has either an odd or even number. Therefore, it is certain that a card with an odd or even number will be selected.

It is equally likely that a card with a number less than 5 is selected.

False. The deck contains cards labeled 1 through 18, so there are more cards with numbers greater than 5 than there are cards with numbers less than 5. Therefore, it is not equally likely to select a card with a number less than 5.

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Answer:

980

Step-by-step explanation:

A simple way to do this is to do a quick estimate, which I truthfully did.

Since 5% of 1000 is 50, I simply counted back.

5% of 990 is 49.5. Notice the slight change? Use this to your advantage. What would happen if we subtracted 10 from 990, just like we did with 1000? This would be equivalent to removing 0.5 from 49.5.

5% of 980 is 49.