Ethan drew a scale drawing of a house. He used the scale 1 millimeter : 5 meters. The actual

length of the garage is 10 meters. How long is the garage in the drawing?

millimeters

The estimate of the impact that a successful preventive program might have can be derived from

attributable risk.

In epidemiology, attributable risk or excess risk is a phrase equivalent with risk difference, which has also been used to express the attributable proportion among the exposed and the population.

Attributed risk assists in determining how much of an outcome is attributable to a certain risk factor (i.e., an estimate of the excess risk) in a population exposed to that factor.

The rate (percentage) of a health result (illness or death) in exposed persons that can be linked to the exposure is known as the attributable risk (AR). Attribitable risk measures how much more common a result is in absolute terms among the exposed than the non-exposed.

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The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given \($m =\frac{y_2 - y_1}{x_2 - x_1}\)  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is \(m*2=-1\)  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.\(m*-1=-1\) i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. \(3=-1/2*3+b\)  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

\(y=-x/2+9/2\)

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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There were 10 different combinations to the multiple choice questions.

Combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

It is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

\(C_{n,r} = \frac{n!}{(n-r)! r!}\)

where n = 5

r = 3

\(C_{5,3} = \frac{5!}{(5-3)!3!} \\= \frac{5!}{2!3!}\)

= \(\frac{5(4)(3!)}{2!3!}\)

= 20/2

= 10 ways

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The underlying function f(x - i) that generates the observed points f'(x - i) in the plot can be determined by integrating the observed points. By integrating f'(x - i), we can obtain f(x - i) up to a constant of integration.

The constant of integration can be determined by incorporating additional information or constraints related to the problem or by considering the behavior of the function at a specific point.

To find the underlying function f(x - i) that generates the observed points f'(x - i), we need to integrate the observed points.

Integration is the reverse process of differentiation, so by integrating f'(x - i), we can recover f(x - i) up to a constant of integration.

The constant of integration arises because integration does not provide a unique solution.

The constant represents an arbitrary additive term that can vary depending on the specific problem or additional constraints.

To determine the constant of integration, we may need additional information or consider specific conditions related to the problem.

It is also important to note that the accuracy of estimating the underlying function f(x - i) depends on the quality and quantity of the observed data points f'(x - i). More data points and precise measurements can lead to a better estimation of the underlying function.

Additionally, the behavior of the function at a specific point can provide valuable insights for determining the constant of integration and refining the estimation of the underlying function.

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Answer:

$73.20

Step-by-step explanation:

original bill: $60

Tip: 22%  $13.20

Total: $73.20

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The Laplace transform of y(t). F(s) = ∫₀^∞ e^(-t)t³ e^(-st) dt = 3! / (s + 1)^4 (e) y(t) = (t – 4)²u₄(t) Let F(s) be the Laplace transform of y(t). F(s) = ∫₀^∞ (t – 4)²e^(-st) dt = 2! / s^3 + 8 / s^2 + 8 / s

The Laplace transform is an integral transform used to transform functions of time, t, to functions of complex frequency, s. It is named after Pierre-Simon Laplace, a French mathematician, and astronomer. The Laplace transform is a powerful mathematical tool that can be used to simplify and solve differential equations. There are a few Laplace transforms of various functions. In this question, the Laplace transforms of some functions are being asked. The Laplace transforms of the given functions are: (a) y(t) = t⁴ Let F(s) be the Laplace transform of

y(t). \(F(s) = ∫₀^∞ t⁴e^(-st) dt = 4! / s^5 (b) y(t) = e³t\)

Let F(s) be the Laplace transform of y(t).

F(s) = ∫₀^∞ e³t e^(-st) dt = 1 / (s - 3) (c) y(t) = sin(2t)

Let F(s) be the Laplace transform of y(t).

\(F(s) = ∫₀^∞ sin(2t) e^(-st) dt = 2 / (s^2 + 4) (d) y(t) = e^(-t)t³\) Let F(s) be the Laplace transform of y(t). F(s) =\(∫₀^∞ e^(-t)t³ e^(-st) dt = 3! / (s + 1)^4 (e) y(t) = (t – 4)²u₄(t)\) Let F(s) be the Laplace transform of y(t). \(F(s) = ∫₀^∞ (t – 4)²e^(-st) dt = 2! / s^3 + 8 / s^2 + 8 / s.\)

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Jorge is a recent college graduate who is eagerly seeking new job opportunities after completing his degree.

Currently, he is working part-time to cover his expenses, but his true ambition lies in finding a job that aligns with his long-term career plans. In order to achieve this, Jorge has been actively applying to various positions that match his professional aspirations and utilize the knowledge and skills he acquired during his college education.

Jorge's qualifications can be measured by various factors such as his college degree, GPA, relevant coursework, internships, and any additional certifications he may have obtained. These factors contribute to his overall level of qualification, denoted as x.

Mathematically, we can express this as:

C(x) ≥ D(x)

This inequality indicates that Jorge's qualifications need to meet or surpass the demands of the job market for him to be considered a strong candidate for the career opportunities he desires.

In summary, Jorge's current situation involves a pursuit of a fulfilling career that matches his aspirations.

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Answer for this system: (-1, 4)

Answer:

not similar

Step-by-step explanation:

hope it help

Answer:

y = 1/2x + 7

Step-by-step explanation:

The single transformation that is equivalent to a reflection over the x-axis, followed by a rotation of 90 degrees, is a reflection over the y-axis.

Here, we have,

we know that,

When you reflect a figure over the x-axis, all the points are flipped vertically, so a point (x, y) would become (x, -y).

Then, when you rotate the reflected figure by 90 degrees counterclockwise, the x-coordinate and y-coordinate swap places, resulting in (-y, x).

If we perform a reflection over the y-axis on the original figure (x, -y), the y-coordinate is negated, resulting in (-x, -y).

Then, when we rotate this figure by 90 degrees counterclockwise, the x-coordinate and y-coordinate swap, giving us (-y, -x), which is equivalent to (-y, x).

Therefore, a reflection over the y-axis achieves the same result as a reflection over the x-axis followed by a rotation of 90 degrees.

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Answer:

Option D

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Checking the given graph, it can be seen that the range of values of x is

The range of values of x are the values of the domain of the graph function

A. -4; -4 does not satisfy the function of the graph

The option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

In a mathematical relation, for a given value of x, there can only be one unique value of y.

It is a requirement that a function must follow.

In option A, the x values are all different, so y is a function of x

In option B, there are two (0,0) and (0,9) which means for x=0 there are two possible values of y, thus y is not a function of x.

In option C, there is a repetition of the x-value, 15, so y is not a function of x

In option D, there is a repetition of the x-value, 13, so y is not a function of x.

So, the correct option is A (7,-7), (-7,-5), (-7,-3), (-7,-1)

Hence, the option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.

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Answer:

10

Step-by-step explanation:

Because 10 is the only number that can be used as a division problem, and still get a whole number between the two numbers.

Answer: yes because they both go to the 0 and has the same shape.

Step-by-step explanation: yes

Answer:

B., C., E.

Step-by-step explanation:

A)  78546 - 60015 = 18531

B)  25972 - 5988 = 19984

C)  43568 - 22185 = 21383

D)  24560 - 5000 = 19560

E)  99756 - 45875 = 53881

Answer:

sin^2(a) I believe. Delete my response if needed.

Step-by-step explanation:

tan²(α) (2 cos²(α) + sin²(α) - 1)

Recall that sin²(α) + cos²(α) = 1 for all α. Then sin²(α) - 1 = -cos²(α) :

tan²(α) (2 cos²(α) - cos²(α))

tan²(α) cos²(α)

Rewrite tan(α) = sin(α) / cos(α) :

(sin(α) / cos(α))² cos²(α)

(sin²(α) / cos²(α)) cos²(α)

Cancel the factors of cos²(α) :

sin²(α)

Answer:

B i think

Step-by-step explanation:

b

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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Answer:

it would have been required that 221 has only two divisors. i.e., itself and 1. However, 221 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 221 = 13 x 17, where 13 and 17 are both prime numbers.

Step-by-step explanation:

To find the height of the steeple, we can use trigonometric ratios and the given information.

Let's assume the height of the steeple is represented by 'h'. We can create a right triangle with the base being the distance from the point to the base of the church, which is 45 feet.

We know that the angle of elevation to the bottom of the steeple is 40°. This means that the angle between the base of the church and the line of sight to the bottom of the steeple is 40°.

Similarly, the angle of elevation to the top of the steeple is 47°. This means that the angle between the base of the church and the line of sight to the top of the steeple is 47°.

We can now set up the trigonometric ratios to solve for the height of the steeple.

Let's consider the angle of elevation to the bottom of the steeple:

\(\[\tan(40^\circ) = \frac{h}{45}\]\)

Simplifying the equation:

\(\[h = 45 \cdot \tan(40^\circ)\]\)

Now, let's consider the angle of elevation to the top of the steeple:

\(\[\tan(47^\circ) = \frac{h + x}{45}\]\)

where 'x' represents the additional height from the bottom of the steeple to the top of the steeple.

Simplifying the equation:

\(\[h + x = 45 \cdot \tan(47^\circ)\]\)

We can subtract the first equation from the second equation to eliminate 'x':

\(\[(45 \cdot \tan(47^\circ)) - (45 \cdot \tan(40^\circ)) = h\]\)

Evaluating this expression, we can find the height of the steeple:

\(\[h = (45 \cdot \tan(47^\circ)) - (45 \cdot \tan(40^\circ))\]\)

Calculating the expression:

\(\[h \approx 45.97 \, \text{feet}\]\)

Therefore, the height of the steeple is approximately 45.97 feet.

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Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

Answer:

l think the answer is C

32.70m

Step-by-step explanation:

we all know that perimeter is the distance round the shape.

so the first step is adding 6 +6 because the other side of the shape is also 6 then add 5 and this equals to 17.

After that we find the area of the circle

which is 3.14*5= 15,7

After getting this value we add it to 17

then we get 32.70m

Answer:C

Step-by-step explanation:

Answer:

y = 10x - 4

Step-by-step explanation:

10x - y = 4

Multiply both sides by -1

-1(10x - (-1)(y) = -1(4)

-10x + y = -4

Add 10x to both sides to get
y = 10x -4

Answer:

1/16

Step-by-step explanation:

litterly just did it, and I got it right

Answer:

its 1/16 i got it right

Step-by-step explanation:

Answer:

\(x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n\)

Step-by-step explanation:

Given equation:

\(\sin(2x)\sin(x)+\cos(x)=0\)

Rewrite sin(2x) using the trigonometric identity sin(2x) = 2sin(x)cos(x):

\(\implies 2\sin(x)\cos(x)\sin(x)+\cos(x)=0\)

\(\implies 2\sin^2(x)\cos(x)+\cos(x)=0\)

Factor out cos(x):

\(\implies \cos(x)\left[2\sin^2(x)+1\right]=0\)

Applying the zero-product property:

\(\textsf{Equation 1:}\quad\cos(x)=0\)

\(\textsf{Equation 2:}\quad2\sin^2(x)+1=0\)

Solve each part separately.

\(\underline{\sf Equation \; 1}\)

\(\begin{aligned}\cos(x)&=0\\x&=\arccos(0)\\x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n\end{aligned}\)

\(\underline{\sf Equation \; 2}\)

\(\begin{aligned}2\sin^2(x)+1&=0\\\sin^2(x)&=-\dfrac{1}{2}\;\;\;\;\;\;\leftarrow\;\textsf{No solution}\end{aligned}\)

Therefore, the solutions of the equation in radians are:

\(\boxed{x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n}\)

To construct a confidence interval for the proportion of defectives, we should use the plus four method.

Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes. 

The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.

To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.

This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.

The equation for the certainty interim utilizing the also four strategies is:

p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)

where:

p is the test extent (number of defectives/test estimate)

zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2

n is the test estimate (counting the included four nonexistent perceptions)

Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

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