what is pythagorus theorum?

Answer:

1. The appropriate null hypothesis for this problem is H0: μ = 72.55 2. We can find the critical value associated with a 95% confidence level and 24 degrees of freedom. 3. We can compare the test statistic to the critical value to make a conclusion regarding the null hypothesis. 4.The critical value is not provided, the exact conclusion cannot be determined without that information.

The appropriate null hypothesis for this problem is:

H0: μ = 72.55

This means that there is no significant difference between the mean reading comprehension score of seniors in the local high school (μ) and the mean reading comprehension score of students in the GED program.

To determine the critical value, we need to consider the significance level (α) and the degrees of freedom. In this case, the significance level is 0.05, which corresponds to a 95% confidence level. Since we have a sample size of 25, the degrees of freedom for a one-sample t-test would be 25 - 1 = 24. Using a t-distribution table or a statistical software, we can find the critical value associated with a 95% confidence level and 24 degrees of freedom.

The calculated test statistic for a one-sample t-test is given by:

t = (x-bar - μ) / (s / sqrt(n))

where x-bar is the sample mean (79.53), μ is the population mean (72.55), s is the sample standard deviation (12.62), and n is the sample size (25).

To draw a conclusion, we compare the calculated test statistic (t) with the critical value. If the calculated test statistic falls in the rejection region (i.e., it exceeds the critical value), we reject the null hypothesis. If the calculated test statistic does not exceed the critical value, we fail to reject the null hypothesis.

Based on the provided information, the calculated test statistic can be computed using the formula in step 3. Once the critical value is determined in step 2, we can compare the test statistic to the critical value to make a conclusion regarding the null hypothesis. However, since the critical value is not provided, the exact conclusion cannot be determined without that information.

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The appropriate null hypothesis for this problem is H0: μ = 72.55 2. We can find the critical value associated with a 95% confidence level and 24 degrees of freedom. 3. We can compare the test statistic to the critical value to make a conclusion regarding the null hypothesis. 4.The critical value is not provided, the exact conclusion cannot be determined without that information.

The appropriate null hypothesis for this problem is:

H0: μ = 72.55

This means that there is no significant difference between the mean reading comprehension score of seniors in the local high school (μ) and the mean reading comprehension score of students in the GED program.

To determine the critical value, we need to consider the significance level (α) and the degrees of freedom. In this case, the significance level is 0.05, which corresponds to a 95% confidence level. Since we have a sample size of 25, the degrees of freedom for a one-sample t-test would be 25 - 1 = 24. Using a t-distribution table or a statistical software, we can find the critical value associated with a 95% confidence level and 24 degrees of freedom.

The calculated test statistic for a one-sample t-test is given by:

t = (x-bar - μ) / (s / sqrt(n))

where x-bar is the sample mean (79.53), μ is the population mean (72.55), s is the sample standard deviation (12.62), and n is the sample size (25).

To draw a conclusion, we compare the calculated test statistic (t) with the critical value. If the calculated test statistic falls in the rejection region (i.e., it exceeds the critical value), we reject the null hypothesis. If the calculated test statistic does not exceed the critical value, we fail to reject the null hypothesis.

Based on the provided information, the calculated test statistic can be computed using the formula in step 3. Once the critical value is determined in step 2, we can compare the test statistic to the critical value to make a conclusion regarding the null hypothesis. However, since the critical value is not provided, the exact conclusion cannot be determined without that information.

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Answer:

(9π - 18) m²

Step-by-step explanation:

Area of sector = (angle / 360) X area of circle

Length of arc = (angle / 360) X circumference of circle

Area of circle = π r ²

= π (6) ²

= 36π

angle TSR = 90° (the little square means 90). there are 360° in a full circle.

area of sector (the triangle including the shaded part) = (90/360) X 36π

= 9π.

now we need to find the area of the triangle.

ST and SR will be same length (both are radius).

this means that angles STR and SRT will be equal.

there are always 180° in a triangle.

if TSR is 90°, then  STR and SRT combined will be 180 - 90 = 90°.

since they are both equal, STR = 45° and SRT = 45°.

Area of triangle = ½ ab sin C  (where a and b are the side lengths, ie both are 6, C is the angle between them. ie 90°)

= 1/2 (6) (6) Sin 90

= 18.

we now have the area of our sector (9π) and area of our triangle (18).

the shaded section is the difference between the two.

so we just subtract the area of the triangge from the area of the sector:

9π - 18 = (9π - 18) m²    ........ this roughly = 10.27 m²

For a point with a slope 3/4 and which passes through the points  (-2, 6) and (-8, k), the value of k is 1.5

The line passes through the points (-2, 6) and (-8, k)

That is, \(x_1=-2, y_1=6, x_2=-8, y_2=k\)

The slope of the line, m = 3/4

The formula for calculating the slope of a line is given as:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Substitute   \(x_1=-2, y_1=6, x_2=-8, y_2=k, m = \frac{3}{4}\) into the formula above

\(\frac{3}{4} = \frac{k-6}{-8-(-2)} \\\\\frac{3}{4} = \frac{k-6}{-8+2}\\\\\frac{3}{4} = \frac{k-6}{-6}\\\\-6(3)=4(k-6)\\\\-18=4k-24\\\\4k=-18+24\\\\4k=6\\\\k=\frac{6}{4} \\\\k=1.5\)

Therefore, the value of k is 1.5

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Answer: Slope: 3/2

Step-by-step explanation:

Coordinates: (1, -3), (3, 0)

Slope formula: m=(y2-y1)/(x2-x1)

m=(0-(-3))/(3-1)

m=(0+3)/2

m=3/2 ==> Slope: 3/2

The statement given is false. The reason for this is that the convergence of a function does not necessarily imply anything about the value of its derivative. To disprove the statement, we can consider the function f(x) = x^2, which converges for all x, but its third derivative f'''(x) = 0, which means that f'''(0) is also equal to 0. Hence, f′′′(0) is not equal to 2.

In general, it is important to note that the convergence of a function does not provide any information about the behavior of its derivatives. Moreover, a function may converge at some points and diverge at others, and this can be determined by analyzing the behavior of its terms or by using convergence tests. In this case, it is necessary to compute f′′′(0) directly using the definition of the derivative or by applying differentiation rules.

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The slope of the line is going to be m = 163.

Here, we have been told that the sum of the numbers is going to be -

= ∑\(w _{k}\)= 3 + 504i (i)

The other set of complex numbers is (z₁, z₂, ....\(z_{k}\)) and their sum is going to be = ∑\(z_{k}\)= 3 + 504i (ii)

If we write the number 3+504i in the standard form for complex numbers i.e., a+bi with respect to the summations, we get -

=  ∑\(a_{k}\)= 3 (III)

= ∑\(b_{k}\)= 504 (Iv)

The standard equation is of the form, y = mx+3. Substituting the polar coordinates, we get -

= \(b_{k}\) = m\(a_{k}\) + 3

Now, if we use all of the given values in equations (iii) and (iv) for k, we get -

= 504 = 3m + 15

Now, on simply solving for m, we get -

= 3m = 504 - 15 = 489

= m = 489/3

= m = 163

Henceforth, we find out that the slope of the line, m is 163.

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Answer:

Volume=LXWXH

=(6cmx5cm)x2cm

=30cm²x2cm

60cm²

Step-by-step explanation:

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."

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Answer:

2 x^2 sqrt(13)

Step-by-step explanation:

sqrt( 52x^4)

sqrt( 4*13 * x^2 * x^2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt( 4)*sqrt(13) *sqrt( x^2) *sqrt( x^2)

2 sqrt(13) x*x

2 x^2 sqrt(13)

52|2

26|2

13|13

1

\(\sqrt{52x^4}=\sqrt{2^2\cdot13\cdot(x^2)^2}=2x^2\sqrt{13}\)

Answer:

180°

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

The total is 10*7=70

The largest number possible that would occur when all the integers are 1

That would be 5 integers with 1 value, or 5

plus 12 for the median, leaving 53 for the largest

Answer: 1:2  or 1/2 or 1 to 2

Step-by-step explanation:

Boys=10

Girls= 20

Boys:Girls::10:20::1:2

Answer:

x=23

Step-by-step explanation:

You simplify both sides of the equation, then isolate the variable.

Answer:

x=23

Step-by-step explanation:

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

-23x+1

Step-by-step explanation:

91-14x - (9x+90)

91-14x-9x-90

-23x+1

Answer:

1-23x

Step-by-step explanation:

7(13-2x)-9(x+10)

7(13)+7(-2x)-9(x)-9(10)

91-14x-9x-90

Combine like terms

91-90 = 1

-14x-9x = -23x

1-23x

Answer:

Cube of a number is three times of the same number. Cube of any mathematical expression is represented by the superscript 3. For example a 3 of the number is a x a x a. It can also be told as the number multiplied by its square. a 3 = a x a 2 can you please help me

Step-by-step explanation:

Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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The domain is the set of all real values and the range is y = -4

From the question, we have the following parameters that can be used in our computation:

The equation y = -4

The equation y = -4 implies that, the output is always -4 irrespective of the input value

This means that the domain is

Domain = All real values

The range is

Range = -4

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Answer:

The answer to your problem is, D. If the data is categorical

Step-by-step explanation:

What a pictograph is:

Remember that a pictographs are less useful for comparing change over time or for presenting large sets of numerical data, as they can become cluttered and difficult to read.

Here is a little example, if you want to show how the population of a city has changed over the years, a line graph or a bar graph would be a better choice than a pictograph

Thus the answer to your problem is, D. If the data is categorical

Step-by-step explanation:

It is NOT equal to 75.81. The correct answer is 705.81

This is because you first multiply each parenthesis then add them together.

So, it would be: 700 + 5 + 0.8 + 0.01= 705.81 not 75.81.

You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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a) A function that expresses f(x) is f(x) = 1.5x.

b) A graph of the function is shown in the image below.

c) The domain and range of the function are all real numbers or [-∞, ∞].

Assuming the variable x represent the amount of a transaction and the variable f(x) represent the amount Isabel is charged for the transaction, a linear function charges on each sale by the credit card company can be written as follows;

f(x) = 1.5x

Part b.

In this exercise, we would use an online graphing tool to plot the function f(x) = 1.5x as shown in the graph attached below.

Part c.

By critically observing the graph shown below, we can logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-∞, ∞] or all real numbers.

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Complete Question:

A transaction is positive if there is a sale and negative when there is a return. Each time a customer uses a credit card for a transaction, the credit company charges Isabel. The credit company charges 1.5% of each sale and a fee of 0.5% for returns.

a) Let x represent the amount of a transaction and let f(x) represent the amount Isabel is charged for the transaction. Write a function that expresses f(x).

b) Graph the function.

c) What are the domain and range of the function?

This model provides a mathematical representation of the rate of change of annual U.S. factory sales of consumer electronic goods from 1990 to 2001.

The rate of change of annual U.S. factory sales of consumer electronic goods to dealers from 1990 through 2001 can be modeled by the equation s(t) = 0.12t2 - t + 5.7 billion dollars per year.

This equation represents the rate at which the sales are changing over time.

The coefficient of t2, which is 0.12, determines the acceleration or deceleration of the sales growth.

The coefficient of t, which is -1, represents the linear component of the growth.

The constant term, 5.7 billion dollars per year, is the initial rate of change at t=0.

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The complete question is

The given model for the rate of change of annual u.s. factory sales (in billions of dollars per year) of consumer electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.12t2 − t + 5.7 billion dollars per year?

This parametrization allows you to express any point on the line by choosing a value for the parameter t.

From the equation y + z = 3, we can express y in terms of z as y = 3 - z.

Substituting this expression for y into the equation x + y + z = 9, we have x + (3 - z) + z = 9.

Simplifying, we get x + 3 = 9.

Rearranging the equation, we have x = 6.

Now we have the following parametrization:

x = 6

y = 3 - z

z = t

where t is a parameter representing the value of z.

Thus, the parametrization of the line formed by the intersection of the planes x + y + z = 9 and y + z = 3 is:

x = 6,

y = 3 - t,

z = t.

This parametrization allows you to express any point on the line by choosing a value for the parameter t.

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Answer:

The ball will be rolling at a rate of about 9 inches per minute after 19 minutes.

Step-by-step explanation:

Answer: f(-4) = 17

Step-by-step explanation: Substitute (-4) for x.

The volume of the triangular prism is 105 cubic units.

To find the volume of the triangular prism, we need to multiply the area of the base by the height. The base of the prism is a triangle with a base of 7 units and a height of 6 units, so its area is (1/2)76 = 21 square units.

The height of the prism is 5 units. Therefore, the volume of the prism is 21*5 = 105 cubic units. It is important to note that the unit of measurement is cubic because we are measuring a three-dimensional object.

The volume of the prism is a measure of the space it occupies and is useful in many real-world applications, such as calculating the capacity of containers or determining the amount of material needed for construction projects.

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Answer:

Distance = 5

Step-by-step explanation:

x2 = 3

y2 = 1

x1 = 7

y1 = -2

=> d = Square root of (3 - 7)^2 + (1 + 2)^2

=> d = Square root of (-4)^2 + (3)^2

=> d = Square root of 16 + 9

= d = Square root of 25

d = 5

The distance between (7,-2) and (3,1) is 5.

The distance between two points of a line is given as:

Distance = √(c - a)² + (d - b)²

Now,

Let,

(a, b) = (7, -2) and (c, d) = (3, 1)

Distance between (7, -2) and (3, 1).

= √(c - a)² + (d - b)²

= √(3 - 7)² + (1 + 2)²

= √(16 + 9)

= √25

= 5

Thus,

The distance between (7,-2) and (3,1) is 5.

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Answer:

Kindly check explanation

Step-by-step explanation:

Using visual comparison :

SHAPE :

Both plots are fairly left skewed as their peaks are more shifted to the right and tails to the left of the distribution.

The centre :

Both softball and basketball plots are centered around the median of the distribution. With softball having a centre (median value) of 5'4'' and basketball has a value of 5'8''.

Spread :

The softball plot spread from 4'9'' through 5'6''

While basketball spreads from 5'2'' through 6'0''