A square church hall had an area of 289m². What is half the perimeter?​

The values of x and y are 5,10

x=5;y=10

parallel lines are straight lines which do not intersect at any point, parallel lines have the special property of maintaining the same slope.

Any parallel lines are intersected by another line is called transversal

Parallel lines, when cut by a transversal, have equal alternate interior angles.

Parallel lines, when cut by a transversal, have equal alternate of exterior angles.

Parallel lines, when cut by a transversal, have an equal corresponding angles.

Parallel lines, when cut by a transversal, have consecutive interior angles on the same side as a supplementary.

13y +(8x+y) = 180°

13y = 20x+3y

14y+8x=180

10y= 20x => y = 2x

y=2x

14y+8x=180

14(2x) +8x = 180

28x+8x=180

36x=180

x=180/36

x=5

14y+8x=180

14y +8x5=180

14y+40=180

14y= 180-40

14y = 140

y=140/14

y=10

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Answer:

(x+3)^2+(y+1)^2=25

Step-by-step explanation:

the distance of the center and the point is the radius of the circle

distance=(4^2+3^2)^(1/2)=5

(x+3)^2+(y+1)^2=25

a. To determine if the test scores of contact sport athletes are significantly lower than noncontact athletes, we need to conduct a one-tailed t-test with a significance level of 0.01. The mean score for noncontact athletes is 7.7 and the mean score for contact sport athletes is 7.1. The pooled standard deviation is 3.34 and the t-value is -1.02. The critical t-value for a one-tailed test with 15 degrees of freedom and a significance level of 0.01 is -2.947. Since our t-value (-1.02) is not less than the critical t-value (-2.947), we cannot reject the null hypothesis. Therefore, we cannot conclude that the test scores of contact sport athletes are significantly lower than noncontact athletes.

To calculate the t-value, we first need to find the difference between the means of the two groups (7.7 - 7.1 = 0.6). Then we need to calculate the standard error of the difference between the means, which is the pooled standard deviation divided by the square root of the sample size (3.34 / sqrt(16) = 0.835). The t-value is then the difference between the means divided by the standard error of the difference (0.6 / 0.835 = 0.718). Since our t-value is negative, we look up the critical t-value for a one-tailed test with 15 degrees of freedom and a significance level of 0.01 in the t-table. The critical t-value is -2.947.

c. The one-tailed t-test revealed that there was no significant difference in test scores between contact sport athletes and noncontact athletes (t(15) = -1.02, p > 0.01). Additionally, the effect size, measured by Cohen's d, was small (d = 0.18). This suggests that exposure to head impacts during one season does not have a significant effect on cognitive performance in varsity athletes.
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Answer: 3 shirts

Step-by-step explanation:

so they are 20 a piece

5+45=50

they need to raise $50

1= 20

2=40

3=60

Answer:

Step-by-step explanation:

Answer: points

Jjj

Step-by-step explanation:

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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11) The pre-image, R at the point (-2, 3) on the grid shown produces an image following the reflection across the line y = 2·x - 3 as follows;

I. The line \(\overline{RR'}\) which is obtained from the image R' following a reflection across the line y = 2·x - 3, is perpendicular to the line y = 2·x - 3, because the points R and R' are vertically opposite each other, therefore, the slope is the negative inverse of the slope of y = 2·x - 3, which is -0.5

II. Please find attached the graph made using MS Excel showing the points R and R'

A reflection transformation is one in which a point is reflected across a line such that the distances of the image and the pre-image from the line are the same and the line acts like a mirror producing an image of the object.

The coordinates of point R = (-2, 3)

The equation of the line of reflection is; y = 2·x - 3

The coordinates of the image of a point, (x₁, y₁) reflected across a line, a·x + b·y + c = 0, is found as follows;

The image of is found using the formula;

\(\dfrac{x - x_1}{a} =\dfrac{y-y_1}{b} = -\dfrac{2\cdot (a\cdot x_1+b\cdot y_1+c)}{a^2+b^2}\)

The equation, y = 2·x - 3, can be expressed in the form a·x + b·y + c = 0, as follows;

y = 2·x - 3

0 = 2·x - 3 - y

Therefore;

a = 2, b = -1, and c = -3

(x₁, y₁) = (-2, 3)

\(\dfrac{x - (-2)}{2} = -\dfrac{2\times (2\times (-2)- 3-3)}{2^2+(-1)^2}=4\)

\(\dfrac{x +2}{2} = 4\)
x = 2× 4 - 2 = 6

x = 6

\(\dfrac{y-3}{-1} = 4\)

y = 4 ×(-1) + 3 = -1

The coordinates of the image, (x, y) = (6, -1)

The slope of the line is -(1/2)

The equation of the perpendicular line is therefore;

(y - 3) = -0.5·(x - (-2)) = -0.5·x - 1

y = -0.5·x - 1 + 3 =  -0.5·x + 2

Equation of the perpendicular line through R; y = -0.5·x + 2

The intersection point is therefore;

-0.5·x + 2 = 2·x - 3

2.5·x = 5

x = 5 ÷ 2.5 = 2

y = 2×2 - 3 = 1

y = 1

The point is therefore, (2, 1)

The difference in the x-values = 2 - 2 = 4

The difference in the y-value = 1 - 3 = -2

Therefore, 4 is added to the x-value of the point (2, 1) and 2 is subtracted to get the image as follows;

(x, y) = (2 + 4, 1 - 2) = (6, -1)

The slope of \(\overline{RR'}\) = (3 - (-1))/(-2 - 6) = -0.5

b. Graphically, the equation of the line \(\overline{RR'}\) can be used to find the point R', by adding the horizontal distance and subtracting the vertical distance of the point R from the the point of intersection of the two lines.

Please find attached the graph showing R and the image R' created with MS Excel.

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Out of 25 students in the class, 40% are male is: Descriptive statistics.

Descriptive statistics is the process of summarizing and organizing data from a sample or population in order to provide an overview of the main characteristics. In this case, the data provided tells us that out of 25 students in the class, 40% are male.

This information is a summary of the gender distribution within this specific class, rather than making any predictions or generalizations about a larger population.

In contrast, inferential statistics is the process of using data from a sample to make predictions or draw conclusions about a larger population. If we were given data about a sample of classes and asked to estimate the proportion of male students in all classes, that would be an example of inferential statistics.

To summarize, the situation you provided, which states that out of 25 students in the class, 40% are male, is an example of descriptive statistics as it only provides a summary of the data for that specific class.

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Answer:

36

Step-by-step explanation:

I don’t know if this half the problem or something because you only need to know what a equals but...

1. Substitute x for 4 since x=4... so the equation would then be (4)^2+10(4)-20

2. You simplify so 4 squared is 16 because when you square something you times it by it self so 4^2 is simply 16 because 4*4=16 then 10*4 is 40 so then you get 16+40-20

3. So you can simplify that again to 56-20 and then to 36

Sorry I’m really bad at explaining but I hope this helps

(a) The relative rate of growth of x can be defined as the derivative of x concerning time, dx/dt. and (b) The relative rate of growth of y, 1/y * dy/dt, is related to the relative rate of growth of x, 1/x * dx/dt, by the equation 1/y * dy/dt = a/x * dx/dt.

The answers to the above asked questions can be computed as,

(a) The derivative dx/dt denotes the instantaneous rate of change of x concerning time. x grows exponentially over time in the setting of a power law relationship. As a result, the derivative dx/dt may be thought of as x's relative rate of growth since it shows how rapidly x increases at a given point in time about its current value.

(b) To demonstrate the link between the relative rates of increase of y and x, we may use the time derivative of the power law equation:

d/dt(y) = d/dt(kx^a)

Using the chain rule and the fact that dx/dt = a * x^(a-1) (which can be derived by taking the derivative of the power law equation concerning x), we can simplify this expression:

d/dt(y) = a * k * x^(a-1) * dx/dt

Now, we can rearrange this equation to express the relative rates of growth of y and x:

d/dt(y) / y = a * dx/dt / x

This equation states that the relative rate of growth of y (i.e., how quickly y grows relative to its current value) is proportional to the relative rate of growth of x (i.e., how quickly x grows relative to its current value), with a proportionality constant equal to the power law equation's exponent an. This is an example of an allometric equation, which illustrates how two variables' relative rates of growth are connected.

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98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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Given:

a = 2 and b = -2.

To find:

The value of \(a^3+3b^2\).

Solution:

We need to find the value of expression \(a^3+3b^2\) at a = 2 and b = -2.

Substituting a = 2 and b=-2 in \(a^3+3b^2\), we get

\((2)^3+3(-2)^2\)

\(=8+3(4)\)

\(=8+12\)

\(=20\)

Therefore, the value of expression \(a^3+3b^2\) at a = 2 and b = -2 is 20.

Answer:

B and C

Step-by-step explanation:

AND SHE SAID SHE SAID SHES FROM HAWAI ‍♀️DO U KNOW HOW TO ‍♀️SAY CUTE IN JAPANESE "KAWAII"

if the family gives up two nights in the hotel, they could afford d) 5 meals

The family has a budget of $800 for meals and hotel accommodations. If they could afford eight nights in a hotel without buying any meals, we can determine the cost of one night at the hotel. To do this, we can divide the total budget by the number of nights:

$800 / 8 nights = $100 per night

Now, let's consider the scenario where the family gives up two nights in the hotel. This would free up $200 from their budget ($100 per night x 2 nights). We can then use this amount to determine how many meals the family can afford by dividing the available funds by the cost of one meal:

$200 / $40 per meal = 5 meals

Therefore, if the family gives up two nights in the hotel, they could afford 5 meals. The correct answer is d. 5.

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Answer:

5/9

Step-by-step explanation:

You can verify me by using the y2-y1/x2-x1 formula

Answer:

Reflection and then translation

Step-by-step explanation:

It is a reflection because it flips across and then a translation because it moves down. I hope this helps you.

Answer:

Reflection then translation.

Hope this helps!

The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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Depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

To plot an ordered pair starting from the origin and moving 0.25, we need both an x-coordinate and a y-coordinate.

We are starting from the origin (0, 0), we can apply the movement of 0.25 to either the x-axis or the y-axis.

If we move 0.25 units on the x-axis, the x-coordinate of the ordered pair would be 0.25, and the y-coordinate would remain 0 since there is no movement on the y-axis. Therefore, the ordered pair would be (0.25, 0).

Similarly, if we move 0.25 units on the y-axis, the x-coordinate would remain 0 since there is no movement on the x-axis, and the y-coordinate of the ordered pair would be 0.25. In this case, the ordered pair would be (0, 0.25).

So, depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

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Answer:

y=16

Step-by-step explanation:

If x=-2, then we can substitute for x in the y+3(-2)=10. y-6=10, we add 6 to both sides to isolate y giving y=16

The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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The minimum value of the function \($f(x,y,z)=x^2+y^2+z^2$\) subject to the constraint \($g(x,y,z)=x+y+z-1=0$\) is \(\[f(1/3,1/3,1/3)=\frac13+\frac13+\frac13=\frac13.\]\)

The name of a surface of this type is an ellipsoid.

At the intersection of the surface with any plane parallel to the xy-plane, the curves of intersection are ellipses. At the intersection of the surface with any plane parallel to the xz-plane, the curves of intersection are hyperbolas. To find z_x and x_y, we differentiate the given equation with respect to x and y respectively:

\(\[\begin{aligned}\frac{\partial}{\partial x}(x^2+2y^2-3z^2)&=2x, \\ \frac{\partial}{\partial y}(x^2+2y^2-3z^2)&=4y. \end{aligned}\]\)

Therefore, z_x=0 and x_y=0.

The function to minimize is \($f(x,y,z)=x^2+y^2+z^2$\) subject to the constraint \($g(x,y,z)=x+y+z-1=0$\).

We will use the method of Lagrange multipliers. The objective function is $f(x,y,z)=x^2+y^2+z^2$, the constraint function is \($g(x,y,z)=x+y+z-1$\), and the Lagrange multiplier is \($\lambda$\).

We need to solve the system of equations:

\(\[\begin{aligned} \nabla f(x,y,z)&=\lambda\nabla g(x,y,z), \\ g(x,y,z)&=0. \end{aligned}\]\)

Using the given functions, we have

\(\[\begin{aligned} \nabla f(x,y,z)&=2x\mathbf{i}+2y\mathbf{j}+2z\mathbf{k}, \\ \nabla g(x,y,z)&=\mathbf{i}+\mathbf{j}+\mathbf{k}. \end{aligned}\]\)

Hence, we obtain the following system of equations:

\(\[\begin{aligned} 2x&=\lambda, \\ 2y&=\lambda, \\ 2z&=\lambda, \\ x+y+z&=1. \end{aligned}\]\)

Since 2x=2y=2z, we have x=y=z.

Substituting this into the last equation, we

\(\[\begin{aligned} 2x&=\lambda, \\ 2y&=\lambda, \\ 2z&=\lambda, \\ x+y+z&=1. \end{aligned}\]\)

get 3x=1, so x=y=z=1/3.

Therefore, the minimum value of the function \($f(x,y,z)=x^2+y^2+z^2$\) subject to the constraint \($g(x,y,z)=x+y+z-1=0$\) is\(\[f(1/3,1/3,1/3)=\frac13+\frac13+\frac13=\frac13.\]\)

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Answer:

∡b = 53°

∡d = 127°

∡c = 127°

Step-by-step explanation:

in trapezoids, the two top angles are equal and the two bottom are equal

also, there are 360 degrees in any 4-sided polygon

53 + 53 + x + x = 360

2x + 106 = 360

2x = 254

x = 127

Answer:

127

Step-by-step explanation:

Answer:

R and Z

Step-by-step explanation:

A point that "touches" the circle once.

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Through the given information in the question, the value of x could be 12.

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is calculated by adding together the length of all four sides of the rectangle. If the length of the rectangle is denoted by 'l' and the width is denoted by 'w', then the formula for the perimeter (P) of the rectangle is:

P = 2l + 2w

Alternatively, the formula can also be written as:

P = 2(l + w)

The perimeter of a rectangle is given by the sum of the lengths of all four sides. Therefore, we can write:

AB + BC + CD + DA = 22

We know that AB = CD = 9 since they are opposite sides of the rectangle. We also know that DA = BC = x - 5, since they are the other two sides of the rectangle.

Substituting these values into the perimeter equation, we get:

9 + x - 5 + 9 + x - 5 = 22

Simplifying the equation, we get:

2x - 2 = 22

2x = 24

x = 12

Therefore, the value of x could be 12.

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