For safety, the slope of a staircase must be > 0.58 and < 0.70. a staircase has a vertical rise of 2.4m over a horizontal run of 3.5m.

Answer:

\( \sqrt{ {9}^{2} + {14}^{2} } = \sqrt{81 + 196} = \sqrt{277} = 16.643\)

YZ =√277. To the nearest tenth, that is 16.6 units.

The completed statement on the exponential model that fits the data in the question is presented as follows;

The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.

The correlation coefficient is an indication of the level at which the variables are interdependent.

The table of values in the question can be entered into a spreadsheet application as follows;

The equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)

The growth rate from the above exponential function is 7·88% per year

The production 15 years after 1960 is therefore;

f(15) = 9.2179·e^(0.0788 × 15) ≈30.06

The number of plastic produced 15 years after 1960 is about 30 million metric tons

The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model

The prediction is correct based on the strong correlation between the year and the number of plastic produced.

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The answer choices that correctly describe the points labeled A, B, and C in the box plot include the following:

B. point C represents Q₃.

C. point A represents Q₁.

E. point B represents the median.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the box-and-whisker plot, the five-number summary for the given data set include the following:

Minimum (Min) = 1.

First quartile (Q₁) = 4.

Median (Med) = 7.

Third quartile (Q₃) = 10.

Maximum (Max) = 12.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

n^2

all the numbers on the right are squares of the numbers on the left

squares means the number times the same number

Answer:

Number 2, \(n^{2}\)

Step-by-step explanation:

The table shows at the top of the screen has a very specific pattern, when comparing side length and area.

When the side length is 4 the area is 16

When the side length is 5 the area is 25

What is happening?

They are being squared(Multipled by itself).

See here:

4*4 = 16

5*5 = 25

Understand how the table is working?

The table is a side to area comparision of a polygon.

The question asks to find the area of a similar polygon, if a side length is n.

Because we are squaring the side length, the answer is:

\(n^{2}\)

Answer:

2+2=4

Step-by-step explanation: btw what questions?

Answer:

Wait, wheres the questions?

Step-by-step explanation:

Hello There!

1.8C+32=37.3

1.8C=37.3-32

1.8C=5.3

Now divide both sides by 1.8 to isolate C:

C=2.9

Hope this helps!

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\(GraceRosalia :)\)

The surface area of the generated surface by revolving the curve about (a) the x-axis is 15π square units, and (b) the y-axis is 144π square units.

Let's consider the parametric curve given by x = 4t, y = 3t + 1, where 0 ≤ t ≤ 1. This curve lies on the xy-plane. We can rotate this curve about the x-axis to generate a surface, and the formula for the surface area of the generated surface by revolution is given by S = ∫(a,b) 2πy * √(dx/dt)^2 + (dy/dt)^2 dt.

Substituting x = 4t and y = 3t + 1, we can find dx/dt = 4 and dy/dt = 3. Thus, the formula for the surface area becomes S = ∫(0,1) 2π(3t + 1) * √(16 + 9) dt. Simplifying further, we have S = 2π∫(0,1) (3t + 1) * 5 dt = 2π [5(t^2/2 + t)]_0^1 = 2π [5(1.5)] = 15π.

Therefore, the surface area of the generated surface when the curve is rotated about the x-axis is 15π square units.

Now, let's consider rotating the curve about the y-axis to generate the surface. The formula for the surface area is S = ∫(c,d) 2πx * √(dx/dt)^2 + (dy/dt)^2 dt. To determine the limits of integration, we need to find the points where the curve intersects the y-axis.

The curve intersects the y-axis at (0, 1). When the curve is rotated about the y-axis, we obtain a solid with a hole in the middle. The surface area of the generated surface is the area of the outer surface minus the area of the inner surface.

The inner surface is generated by rotating the point (0, 1) about the y-axis, resulting in a cylinder with a radius of 1 and a height of 3. Hence, its surface area is 2πrh = 2π(1)(3) = 6π square units.

For the outer surface, we can take the limits of integration as c = 1 and d = 4. Substituting x = 4t and y = 3t + 1, we find dx/dt = 4 and dy/dt = 3. The formula for the surface area becomes S = ∫(1,4) 2π(4t) * √(16 + 9) dt. Simplifying further, we have S = 2π∫(1,4) (4t) * 5 dt = 2π [5(t^2)]_1^4 = 2π [5(15)] = 150π.

Therefore, the surface area of the generated surface when the curve is rotated about the y-axis is 150π - 6π = 144π square units.

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Answer:

x=(8,0)

y=(0,4)

Step-by-step explanation:

Answer:

x=(8,0)

y=(0,4)

Step-by-step explanation:

Hopes this helps

According to the National Survey on Drug Use and Health, approximately 18.53% of U.S. adults (ages 18 and older) experienced some form of mental illness in 2016.

Approximately 18.53% of U.S. adults suffered from mental illness in 2016. This percentage represents the prevalence of mental health disorders among the adult population, which is important to understand in order to address and provide support for those affected.

This includes a range of conditions such as anxiety disorders, depression, bipolar disorder, and schizophrenia. It's important to note that mental illness can vary in severity and can impact individuals differently, and seeking professional help can greatly improve one's quality of life.

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The dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

In the question,

The function is \(B(x) = 0. 06x^2 - 0. 2x^3\)

To find the maximum or minimum, take the derivative and set it equal to zero.

⇒ \(B'(x) = 2(0. 06)x - 3(0. 2)x^{2}\)

Setting it equal to zero, we get

⇒ \(0.12x - 0.6x^{2}=0\)

⇒ 0.6x (0.2-x) = 0

⇒ x = 0 or x = 0.2

Now substitute x = 0.2 in B(x), we get

⇒ \(B(0.2) = 0. 06(0.2)^{2} - 0. 2(0.2)^{3}\)

⇒ B(0.2) = 0.0024 - 0.0016

⇒ B(0.2) = 0.0008

To know B(0.2) is maximum, let us find the values for x = 1 and x = 0.01.

For x = 1,

⇒ \(B(1) = 0. 06(1)^{2} - 0. 2(1)^{3}\)

⇒ B(1) = 0.06-0.2

⇒ B(1) = -1.04

For x = 0.01,

⇒ \(B(0.01) = 0. 06(0.01)^{2} - 0. 2(0.01)^{3}\)

⇒ B(0.01) = 0.000006 - 0.0000002

⇒ B(0.01) = 0.0000058

Thus, x = 0.2 is the maximum.

Hence we can conclude that the dosage at which the resulting blood pressure is maximized is x at 0.2 and the maximum dosage is 0.0008.

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Answer:

x=23

Step-by-step explanation:

set them equal to each other since its not same sides

these are alternative exterior

8x-77=3x=38

5x=115

x=23

Answer:

23

Step-by-step explanation:

8x-77=3x+38 > 8x=3x+115 > 5x=115 > x=23

False. When conducting a cluster sample, it is typically preferable to have more heterogeneous clusters with fewer individuals.

This is due to the fact that when clusters are diverse, it is crucial to appropriately represent the population by capturing its diversity.

In such situations, the danger of sampling bias is increased by having fewer clusters with more individuals because a larger number of people from a single heterogeneous cluster would not fairly represent the overall community. Incorrect estimates and conclusions may result from this.

Having fewer clusters with more individuals, on the other hand, can assist raise the precision of the estimates when clusters are homogeneous by lowering the variance associated with sampling from a single cluster. In general, to achieve a precise representation of the population and to lessen the chance of sampling bias, the number of clusters and the size of each cluster should be balanced.

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If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.

To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):

Average speed = distance ÷ time

Average speed = 12 miles ÷ (1/5) hour

To divide by a fraction, we can multiply by its reciprocal, so:

Average speed = 12 miles × 5/1 hour

Average speed = 60 miles per hour

Therefore, Idil drove at an average speed of 60 miles per hour.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

36

Step-by-step explanation:

Answer:

36!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

6 x 6 = 36

A perfect square is a number that is gotten by multiplying it by itself.

An example of a perfect square is 25 and one that is not is 7.

A square number, sometimes known as a perfect square, is an integer that is the square of another integer; in other words, it is the product of another integer and itself. For instance, 9 is a square number since it equals 3² and may be expressed as 3 × 3.

A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 × 5 = 25. A perfect square is a positive integer formed by multiplying an integer by itself.

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Answer:

Area of diamond=8192

Area of trapezoid =72 square unit

Step-by-step explanation:

Area of diamond:

find the distance between the points:

(0,64), (64,0), (0,-64),(-64,0)

d=√(x2-x1)²+(y2-y1)²

d=√64²+64²

d=64√2=90.51( rounded to the nearest hundredth)

since it is shape of square then all sides are equal

A=length*width

A=64√2*64√2

4- Area of trapezoid= ((base a +base b)/2) h

base a=3, base b=6 height=8 ( from graph count the tiles)

Area of trapezoid = ((3*6)/2 )* 8

Area=18/2*8

Area=9*8=72 square unit

The area of a diamond is 8192 square units and the area of a trapezoid is 72 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The area of the diamond will be calculated as below:-

find the distance between the points:

(0,64), (64,0), (0,-64),(-64,0)

d=√(x2-x1)²+(y2-y1)²

d=√64²+64²

d=64√2=90.51( rounded to the nearest hundredth)

Since it is the shape of a square then all sides are equal

A=length x width

A=64√2 x 64√2

A=8192 square unit

The area of the trapezoid will be calculated as below:-

Area of trapezoid= ((base a +base b)/2) h

base a=3, base b=6 height=8 ( from graph count the tiles)

Area of trapezoid = ((3*6)/2 )* 8

Area=( 18/2 ) x 8

Area=9 x 8=72 square unit

Therefore, the area of a diamond is 8192 square units and the area of a trapezoid is 72 square units.

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To find f, we need to integrate the given derivative function and then determine the constant of integration. The function f(x) that satisfies f′(x) = 8x − 7 and f(8) = 0 is given by: f(x) = 4\(x^2\) − 7x - 200.

By integrating 8x − 7, we obtain f(x) + C, where C is the constant of integration. Then, by substituting the value x = 8 and f(8) = 0 into the equation, we can solve for the specific value of C and find the expression for f(x).

Given f′(x) = 8x − 7, we can integrate this expression to find f(x):

∫(8x − 7) dx = ∫8x dx − ∫7 dx

= 4\(x^2\) − 7x + C

So, f(x) = 4\(x^2\)− 7x + C, where C is the constant of integration.

To find the specific value of C, we use the condition f(8) = 0. Substituting x = 8 into the expression for f(x), we have:

f(8) = 4\((8)^2\)− 7(8) + C = 0

Simplifying the equation, we get:

256 - 56 + C = 0

200 + C = 0

C = -200

Therefore, the function f(x) that satisfies f′(x) = 8x − 7 and f(8) = 0 is given by:

f(x) = 4\(x^2\) − 7x - 200.

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Answer:

Step-by-step explanation:

There are 26 letters in the alphabet. Take 325 and divide it by 26 to get an answer of 12.5. We can round this number to 13. Therefore, the 13th letter in the alphabet is M and will be your answer.

Step-by-step explanation:

Dhuʻl-H. 7, 1441 AH · 2 answers

5)Find the value of x for which 2x ÷ 2- 4 = 45 6) Calculate the missing value of “x” in the following expression: (11/9)3 × (9/11)6 = (11/9)2x-1 7) 5 ...

Missing: ZKB = ‎150°. ‎(4х +

Answer:

y=-3x-1

Step-by-step explanation:

Use point-slope form:

(y-2)=-3(x+1)

y-2=-3x-3

y=-3x-1

Answer:

(y-0)=-3(x-2)

Step-by-step explanation:

im not sure if this os correct but i tried

The rate of each plane is,

First plane = 110 mph

Second plane = 15 mph

Let x = rate of the slower plane (First plane!)

x + 45 = rate of the faster plane (Second plane!)

The planes fly for 3 hours, where Distance = RT

Distance between the planes = SUM of the distances.

RT + RT= 795 miles

3x + 3(x + 45) = 795

3x + 3x + 135 = 795

6x + 135 = 795

6x = 795 - 135

6x = 660

x = 110 mph First plane

And, x + 45 = 110 + 45 = 15 mph Second plane.

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Answer:

284.012

Step-by-step explanation:

Hope this awnsers your question!

Answer:

284.012

Step-by-step explanation:

Answer:

D)0,4

Step-by-step explanation:

The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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Answer: I don't quite understand your question. Supplementary angles are angles that equal 180 degrees. You can find missing supplementary angles by adding the two that are given, and then subtracting them by 180.

The expected value of X given Y=y is given by 1/f(y) ∫x f(x,y) dx. This can be calculated by evaluating the integral ∫x f(x,y) dx over all possible values of X and dividing the result by f(y).

To find E[X|Y=y], we need to use the conditional expected value formula

E[X|Y=y] = ∫x f(x|y) dx

where the conditional density function of X for Y=y is denoted by f(x|y). f(x|y), the conditional density function, is defined as follows:

f(x|y) = f(x,y) / f(y)

where f(x,y) is the joint density function of X and Y, and f(x,y) is the marginal density function of Y.By integrating the joint density function across all possible values of X, given that we have the joint density function of X and Y, we may determine the marginal density function of Y:

f(y) = ∫f(x,y) dx from negative infinity to positive infinity.

Once we have the marginal density function of Y, we can then find the conditional density function of X given Y=y:

f(x|y) = f(x,y) / f(y)

Now, we can use the formula for the conditional expected value to find E[X|Y=y]:

E[X|Y=y] = ∫x f(x|y) dx

= [f(x,y)/f(y)] dx

= 1/f(y) ∫x f(x,y) dx

where the integral ∫x f(x,y) dx is over all possible values of X.

Therefore, to find E[X|Y=y], we need to evaluate the integral ∫x f(x,y) dx and divide the result by f(y). This will give us the conditional expected value of X given Y=y.

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