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If n conducting a test on the hypotheses H0: µ = 50 and Ha: µ > 50, then the type of error is option (B) Type I error

The error that results from rejecting a true null hypothesis is known as a Type I error, while the error that results from failing to reject a false null hypothesis is known as a Type II error.

In this case, the null hypothesis is that the population mean is 50, and the alternative hypothesis is that the population mean is greater than 50. Since the sample mean is found to be 55, which is greater than 50, it would be tempting to reject the null hypothesis in favor of the alternative hypothesis. However, we cannot be certain that the population mean is truly greater than 50 based on the sample mean alone.

Therefore, the correct option is (B) Type I error

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Answer:

Type I error

Step-by-step explanation:

Got this right on the test. Good luck, my FLVS fellows!

The function F(x) satisfies the property that for any value of x, F(-x) = -F(x). Geometrically, an odd function has symmetry with respect to the origin, meaning that if we reflect the graph of the function across the y-axis, we get the same graph back but "flipped" over the x-axis.

To determine if F(x) is odd, even or neither, we need to check whether F(-x) is equal to -F(x) for all x.

First, we use the identity sec(-x) = sec(x) to rewrite sec(-x) as sec(x). Next, we use the identity sin(-x) = -sin(x) to rewrite sin(-x) as -sin(x).

Substituting these expressions into F(-x), we get:

F(-x) = 3(sec(-x))(sin(-x))

= 3(sec(x))(-sin(x))

= -3(sec(x))(sin(x))

Comparing this with F(x) = 3(sec(x))(sin(x)), we see that F(-x) = -F(x). This means that the function F(x) is an odd function.

In other words, the function F(x) satisfies the property that for any value of x, F(-x) = -F(x). Geometrically, an odd function has symmetry with respect to the origin, meaning that if we reflect the graph of the function across the y-axis, we get the same graph back but "flipped" over the x-axis.

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By providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship, we have

(i) \(3^{n/2}\) = O(2^n)

(ii) \(8^{\log n}\) = θ(\(n^2(\log n)^4\) ≤ 3n^3)

(iii) √n + (log n)^5 = O(\((2)^{1/2\times\log n}\))

We have to compare the following function pairs by providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship

i) The first function is \(3^{n/2}\) vs. 2^n

We can write  \(3^{n/2}\) as

\(3^{n/2}\) = \((\sqrt{3})^n\)

\(3^{n/2}\) = (1.732)^n

Clearly, we get for c = 1 and n ≥ 0, then

0 ≤ 1.732n ≤ 2n

Hence, \(3^{n/2}\) = O(2^n)

ii) The second function is \(8^{\log n}\) vs. n^2(log n)^4 + 2n^3

We can write it as

\(8^{\log n}\) = \(n^{\log 8}\)

\(8^{\log n}\) = \(n^{\log 2^3}\)

\(8^{\log n}\) = n^3

For n ≥ 0, c(1) = 1 and c(2) = 3, we have

0 ≤ n^3 ≤ \(n^2(\log n)^4\) ≤ 3n^3

Hence, \(8^{\log n}\) = θ(\(n^2(\log n)^4\) ≤ 3n^3)

iii) The third function is  \((\sqrt{2})^{\log n}\) vs. √n + (log n)^5

We can write \((\sqrt{2})^{\log n}\) as

\((\sqrt{2})^{\log n}\) =  \((2)^{1/2\times\log n}\)

For c = 2 and n ≥ 2, we have

0 ≤ √n + (log n)^5 ≤ \((2)^{1/2\times\log n}\)

Hence, √n + (log n)^5 = O(\((2)^{1/2\times\log n}\))

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The complete question is:

Show your complete work when comparing the following function pairs. provide the c and k values in the formal definition when asserting a big O, Ω or θ relationship(e.g. f(n) is O(g(n)) if there exists C>0 and k≥0 such that f(n)≤Cg(n) for all n≥k).

(i) \(3^{n/2}\) vs. 2^n

(ii) \(8^{\log n}\) vs. n^2(log n)^4 + 2n^3

(iii) \((\sqrt{2})^{\log n}\) vs. √n + (log n)^5

Answer:

4y - 8x = 24

Step-by-step explanation:

4y -8x = 24  Add 8x to both sides

4y = 8x + 24  Divide both sides by 4

y = 2x + 6  

This slope is 2 which would great a line parallel to y = 2x + 9

Desmos is a free program that can help you graph.  See the picture below.  You just type in the equation and it graphs it for you.  Cool

The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

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What is remainder R when the polynomial p(x) is divided by (2x - 1)? is (2x - 1) factor of p(x)?

p(x) = 2x² + 3x + 1

Answer :

R = 3

and (2x - 1) not factor of p(x) because, if (2x - 1) factor of p(x) remainder R when the polynomial p(x) divided by (2x - 1) is R = 0

∴ so the answer is option A

« Attached »

Answer:

$34.89

Step-by-step explanation:

Here, we want to calculate the price of the pair of shoes.

Let the price of the belt be $x, we know that the price of pair of shoes would be x-1.79

so adding;

x + x-1.79 = 71.57

2x = 71.57 + 1.79

2x = 73.36

x = 73.36/2

x = $36.68

The price of pair of shoes = x-1.79 = 36.68-1.79 = $34.89

Given the following question:

y = total amount of money

x = total number are weeks

For the first part we are being asked the chance per week.

The chance per week is 40, since the number varies depending on the x value. So if x is = to 2 you would then multiply 40 by 2. So your chance per week is 40.

Your starting amount is 450, because 450 is consistent and it does not change no matter what the x value is. You will always have to add 450 because 450 is the money you already have which then equals y which is the total amount of money in your account.

To sum up your answers are...

40 for change per week

450 for starting amount.

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Since they form corresponding Angle pair ~

Answer:

\( = 2x - 2 + 3x < 2 \\ 5x < 2 + 2 \\ 5x < 4 \\ x < \frac{4}{5} < 0.8 \\ 0 \: is \: answer\)

Answer:

1 ounce is 0.05

Step-by-step explanation:

Answer:

A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function. Functions can be written as ordered pairs, tables, or graphs. The set of input values is called the domain, and the set of output values is called the range.

Hope this helps :P

Answer:

x^5√x

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

x

5

√

x

Answer:

A

Step-by-step explanation:

The formula is 5*x=4*10. Then simplify to 5*x=40. Divide both sides by 5. x=8

The intersect method involves spliting an equation to a system of equations

The solutions to the equation are (-1, 3) and (3,-5)

The equation is given as:

-2x + 1 = -x^2 + 4

Using the intersect method, we have the following equations

y = -2x + 1

y = -x^2 + 4

Next, we plot the graph of both equations

From the graph (see attachment), we have the following points of intersection

(x,y) = (-1, 3) and (3,-5)

Hence, the solutions to the equation are (-1, 3) and (3,-5)

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Answer:

v= 37.8 miles/ 2.7 hours = 14 miles/hrs

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The distance between the points (-5, -5) and (1, 3) is 10 units.

To find the distance between the points (-5, -5) and (1, 3), we can use the distance formula.

The distance formula is:
\(d = \sqrt{((x_2 - x_1)^2+ (y_2 - y_1)^2)}\)
Let's substitute the values into the formula:

\(d = \sqrt{((1 - (-5))^2 + (3 - (-5))^2)}\\d = \sqrt{((1 + 5)^2 + (3 + 5)^2}\\d = \sqrt{(6^2 + 8^2)}\\d = \sqrt{(36 + 64)}\\d = \sqrt{100}\\d = 10\)

Therefore, the distance between the points (-5, -5) and (1, 3) is 10 units.

Explanation:
The distance formula is derived from the Pythagorean theorem.

It calculates the length of the hypotenuse of a right triangle formed by the coordinates of two points.

In this case, we have a right triangle with legs of length 6 and 8.

Using the Pythagorean theorem, we find that the hypotenuse (the distance between the two points) is 10 units.

Remember to round your answer to the nearest tenth, so the final answer is 10 units.

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The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c.  m² -3m + 2 = 0.

The equation is equal to,

(x² - 5)² - 3x² + 15 = -2

let the value of m be equals to x² - 5.

Simplify the equation we have,

⇒ ( x² - 5 )² - 3x² + 15 = -2

Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,

⇒ ( x² - 5 )² - 3 (x² - 5 )  = -2

Now replace x² - 5 by m to get the equivalent equation,

⇒ ( m )² - 3 (m ) = -2

⇒ m² -3m + 2 = 0

Therefore, the equivalent equation to the given equation is written as option c.  m² -3m + 2 = 0.

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Answer:

Ok so I don't have a graphing thing on my computer but on the y axis you are going to put a dot on the one then go up 47 and to the right 1 and put a dot sorry that is as much as i can help you

Answer:

Step-by-step explanation:

Your bill is $62.50

$62.50 * .06 = $3.75 (this is your sales tax added)

So your total is up to: $66.25

Adding the tip the same way using $66.25 *.18 = $11.93

Tip would be $11.93

Total coming to: $78.17

hope this helps

Answer:

$77.50

Step-by-step explanation:

Tax:

62.50x0.06= 3.75

3.75+62.50= 66.25

Tip:

62.50x0.18= 11.25

Answer:

66.25+11.25= 77.50

Answer:

65

Step-by-step explanation:

115 - 50 = 65

Answer:

\(\huge\boxed{\sf < VUT = 65\°}\)

Step-by-step explanation:

The sum of interior angles is equal to the non-adjacent exterior angle.

So,

∠UVT + ∠VUT = ∠UTP

50 + ∠VUT = 115

Subtract 50 to both sides

∠VUT = 115 - 50

\(\rule[225]{225}{2}\)

Answer:

38.66

Step-by-step explanation:

Answer: D

Step-by-step explanation:

plugged it into desmos

Answer:

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.

Step-by-step explanation:

The opportunity cost of washing a car for Ted is 4 cars, and the opportunity cost of washing a car for Ishana is 3 cars.

To determine each person's opportunity cost of washing a car, we need to compare the alternative activity they would have to give up in order to wash a car.

For Ted:

Ted can wax 4 cars or wash 12 cars. So, the opportunity cost of washing a car for Ted is the number of cars he could have waxed instead. In this case, Ted would have to give up waxing 4 cars to wash a car.

For Ishana:

Ishana can wax 3 cars or wash 6 cars. So, the opportunity cost of washing a car for Ishana is the number of cars she could have waxed instead. In this case, Ishana would have to give up waxing 3 cars to wash a car.

Therefore, the opportunity cost of washing a car for Ted is 4 cars, and the opportunity cost of washing a car for Ishana is 3 cars.

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Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You can travel approximately 312.44 miles until your battery runs out.

To determine how far you can travel until your battery runs out, we need to find the point at which the charge (C) reaches 0%. We can use the given information to determine the equation of the line representing the relationship between the charge and the distance traveled.

Let's use the two data points provided:

Point 1: (89 miles, 64% charge)

Point 2: (250 miles, 18% charge)

Using the point-slope form of a linear equation, we can calculate the equation of the line:

m = (C2 - C1) / (d2 - d1)

m = (18 - 64) / (250 - 89)

m = -46 / 161

Using the slope-intercept form of a linear equation, we can substitute one of the points and the slope to find the equation:

C - C1 = m(d - d1)

C - 64 = (-46 / 161)(d - 89)

Simplifying further:

C - 64 = (-46 / 161)d + (89 * 46 / 161)

C = (-46 / 161)d + (89 * 46 / 161) + 64

C = (-46 / 161)d + 89.42

Therefore, the equation representing the relationship between the charge (C) and the distance traveled (d) is C = (-46 / 161)d + 89.42.

To determine how far you can travel until your battery runs out (when the charge reaches 0%), we can set C to 0 and solve for d:

0 = (-46 / 161)d + 89.42

(46 / 161)d = 89.42

d = (89.42 * 161) / 46

d ≈ 312.44 miles

Therefore, you can travel approximately 312.44 miles until your battery runs out.

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It is important in the definition of logarithm that the base of the logarithm does not equal 1 because log base 1 is undefined and leads to mathematical inconsistencies.

The logarithm of a number is defined as the exponent to which a specific base must be raised to obtain that number. However, when the base of the logarithm is equal to 1, the definition becomes problematic.

If the base of the logarithm is 1, we have log₁(x) = y, where 1^y = x. Since any number raised to the power of 0 equals 1, we would have 1^0 = x, which implies that x equals 1 for all values of x. This creates a contradiction, as it would suggest that all numbers are equal to 1, which is not true.

To avoid this inconsistency, the definition of logarithms excludes the base 1. By excluding 1 as a possible base, logarithmic functions maintain their essential properties, such as the logarithmic identities and the relationship between exponentiation and logarithms.

Therefore, the restriction that the base of the logarithm cannot equal 1 is necessary to ensure mathematical consistency and clarity in the definition of logarithmic functions. It helps prevent mathematical contradictions and allows logarithms to be defined in a meaningful and consistent manner.

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To graph the function f(x) = (x)sin(x) in MATLAB using the fplot command, you can follow the steps below:

matlab

Define the function

f = (x) (x.)sin(x);

Set the range of x values

x = linspace(0, 2.5, 100);

Plot the function

fplot(f, [0, 2.5])

Add labels and title

xlabel(x)

ylabel(f(x))

title(Graph of f(x) = (x)sin(x))

Display the grid

grid on

In this code, we first define the function f(x) = (x)sin(x) using an anonymous function (x). Next, we create a range of x values using linspace from 0 to 2.5 with 100 points. Then, we use the fplot command to plot the function f over the specified range. Finally, we add labels, title, and grid to the graph.

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