simplify (2x^2+3)(x+4

Graph-2 shows an exponential growth function.

Exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an equation that describes a real-world situation gives us a method for making predictions. Seeing their graphs gives us another layer of insight for predicting future events.

Exponential growth is modeled by functions of form f(x)=b^x  where the base is greater than one. Exponential decay occurs when the base is between zero and one. We’ll use the functions f(x)=2^x  and g(x)=(1/2)^x to get some insight into the behavior of graphs that model exponential growth and decay. In each table of values below, observe how the output values change as the input increases by  1.

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:   3pi/2

This is equivalent to 1.5pi

The units for the area are in square centimeters.

===============================================

Work Shown:

The larger semicircle has radius 2 cm.

So r = 2 is plugged into the area of a semicircle formula below

A = (pi*r^2)/2

A = (pi*2^2)/2

A = (4pi)/2

A = 2pi

The area of the larger semicircle is 2pi square cm.

Repeat those steps but now use r = 1. This will compute the area of the unshaded smaller semicircle

A = (pi*r^2)/2

A = (pi*1^2)/2

A = pi/2

The area of the smaller unshaded semicircle is pi/2 square cm.

------------------------

From here, we subtract the two results to get the shaded area:

(larger semicircle area) - (smaller semicircle area) = (2pi) - (pi/2) = 3pi/2

This is equivalent to 1.5pi since 3/2 = 1.5

Answer:

{-10, 10)

Step-by-step explanation:

| | - means to only take the number inside, not the sign

x=-10 or 10

Answer:

i dont understand what you want me to answer

Step-by-step explanation:

㏒₅x in Natural logarithm is \(\frac{lnx}{ln5}\).

The base-e logarithm of an integer x, where e is a mathematical constant roughly equal to 2.718, is the natural logarithm of that number. Instead of the expected abbreviated notation ㏒ex, it is typically written using ㏑x. A natural logarithm can be expressed in exponential form as follows:

㏑x=a⇒\(x=e^a\)

Natural logarithm, is like a normal logarithm it follows all the basic algebraic laws, like addition, subtraction, multiplication of logarithms.

The natural logarithm follows the same as common logarithms of base 10. That is, \(ln (ab) = ln a + ln b\); \(ln (\frac{a}{b} ) = lna-lnb\);  The natural logarithm and the common logarithm are related through

㏒₅x=\(\frac{logx}{log5}\);

\(\frac{logx}{log5} *\frac{lne}{lne} ;\\\frac{logx}{lne} *\frac{lne}{log5} ;\\\)

㏑x×(\(\frac{1}{ln5}\));

⇒\(\frac{lnx}{ln5}\).

㏒₅x in Natural logarithm is \(\frac{lnx}{ln5}\).

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Answer:

Step-by-step explanation:

Rate of change for function A is:

Rate of change of function B is:

Comparing the values:

Function A has a greater rate of change

Answer:

Answer:

5; -4.5; Function A

Step-by-step explanation:

Rate of change for function A is:

(15 - 10)/(5.5 - 4.5) = 5/1 = 5

Rate of change of function B is:

-4.5 as the slope is the rate of change

Comparing the values:

5 > - 4.5

Function A has a greater rate of change

The slope of the line that goes through the origin and the point (6, -4) is -2/3.

To find the slope of a line that goes through two given points (x₁, y₁) and (x₂, y₂), you can use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, one of the points is the origin, which has coordinates (0, 0), so x₁ = 0 and y₂ = 0. The other point is (6, -4), so x₂ = 6 and y₂ = -4. Substituting these values into the slope formula gives:

slope = (-4 - 0) / (6 - 0) = -4/6 = -2/3

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Answer:

15

Step-by-step explanation:

so the amount for apples are 3 for 8.so if you multiply 8 x 5 it is 40.3 is for 8 and there is the answer

The replacement set, only \(x = 18\) makes the inequality \(x - 3 > 12\) true. The values \(x = 6\), \(x = 10\), and \(x = 14\) do not satisfy the inequality.

To determine which values in the replacement set make the inequality \(x - 3 > 12\) true, we can substitute each value from the replacement set into the inequality and evaluate whether the inequality holds.

Let's check each value:

1. For \(x = 6\):

  Substituting \(x = 6\) into the inequality, we have:

  \(6 - 3 > 12\)

  \(3 > 12\)

  The inequality is not true when \(x = 6\).

2. For \(x = 10\):

  Substituting \(x = 10\) into the inequality, we have:

  \(10 - 3 > 12\)

  \(7 > 12\)

  The inequality is not true when \(x = 10\).

3. For \(x = 14\):

  Substituting \(x = 14\) into the inequality, we have:

  \(14 - 3 > 12\)

  \(11 > 12\)

  The inequality is not true when \(x = 14\).

4. For \(x = 18\):

  Substituting \(x = 18\) into the inequality, we have:

  \(18 - 3 > 12\)

  \(15 > 12\)

  The inequality is true when \(x = 18\).

In summary, out of the values in the replacement set, only \(x = 18\) makes the inequality \(x - 3 > 12\) true. The values \(x = 6\), \(x = 10\), and \(x = 14\) do not satisfy the inequality.

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Answer:

90 - 5 = 85/2 =  42.5 degrees

Answer:

90 - 5 = 85/2 =  42.5 degrees

Step-by-step explanation:

Hope i helped i tried :3 <3

The slope of the regression line predicting y from x is 0.30.

Given that,

x              y

29          215

62          225

75          173

99         129

108        111

So, the coordinate points are (29, 215) and (62, 225)

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (225-215)/62-29)

= 10/33

= 0.30

Therefore, the slope of the regression line predicting y from x is 0.30.

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Answer:

A

Step-by-step explanation:

It went down 5 so y-5 and it also went left 6 so x-6

(x-6,y-5)

I'm pretty sure the top right is before it was moved

Brainliest Appreciated! :)

Answer:

D

Step-by-step explanation:

lets take one point of each triangle

A(-5,-4) A´(1,1)

-5 to 1 is 6

-4 to 1 is 5

( x + 6, y - 5 )

The investment of $18,500 at 17.6% compounded quarterly for 7.5 years will be worth (a future value of) $67,326.60.

The future value is the present value compounded periodically at an interest rate.

Compounding involves computing interest on interest.

The future value of the investment after the stated period can be determined using an online finance calculator as follows:

N (# of periods) = 30 years

I/Y (Interest per year) = 17.6%

PV (Present Value) = $18,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $67,326.60

Total Interest = $48,826.60

Thus, in 7.5 years' time, the investment will be worth $67,326.60.

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Answer:

D

Step-by-step explanation:

PLEASE GIVE ME BRAINLIEST!

I hope this helps.  thank you and have a good day ;)

Answer:

{6,341}

Step-by-step explanation:

{-3,453+5,748} is the same as 5,748 - 3,453, which is equal to 2,295.{8,9703-12,749} is the same as 8,703 - 12,749, which is equal to -4,046.

{2,295} - {-4,046} = {6,341}

The prediction for the weekend is it will take him 11 hours to mow 12 lawns

Given data ,

A student mows lawns on the weekends

It takes him 110 minutes to mow 2 lawns

Now , the time taken for mowing 12 lawns is given by the proportion ,

where 110 / 2 = A / 12

Multiply by 12 on both sides , we get

A = 6 x 110

On further simplification, we get:

A = 660 minutes

On converting 660 minutes to hours

1 hour = 60 minutes

So , 660 minutes = 11 hours

A = 11 hours

Hence , the time taken is 11 hours

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The energy of each photon in the beam is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. Substituting the values, we get E = (6.626 x 10^-34 J s)(2.998 x 10^8 m/s)/(500 x 10^-9 m) = 3.98 x 10^-19 J.

The intensity of the beam is the rate at which energy is passing through a unit area perpendicular to the direction of propagation of the beam, given by I = P/A, where P is the power and A is the area. The power of the beam is the product of the energy of each photon and the number of photons passing through a unit area per unit time, given by P = nEAv, where n is the concentration of photons, A is the area, v is the speed of the beam, and E is the energy of each photon.

Substituting the values, we get P = (1.7 x 10^13 m^-3)(3.98 x 10^-19 J/photon)(1 m^2/s)(2.998 x 10^8 m/s) = 1.02 W. The area of the beam is not given, so we cannot calculate the intensity directly. However, if we assume a circular beam with a radius of 1 cm (area = πr^2 = π(0.01 m)^2 = 3.14 x 10^-4 m^2), we can calculate the intensity as I = P/A = 1.02 W/3.14 x 10^-4 m^2 = 3.24 x 10^3 W/m^2, which is closest to option E) 3.2 x 10^2 W/m^2 (after rounding to the nearest tenth).

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Answer:

(- 1, 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ \(\frac{1}{2}\) (x₁ + x₂ ), \(\frac{1}{2}\) (y₁ + y₂ ) ]

Here (x₁, y₁ ) = A(- 3, 5) and (x₂, y₂ ) = B(1, 7) , thus

midpoint = [ \(\frac{1}{2}\) (- 3 + 1 ), \(\frac{1}{2}\) (5 + 7) ] = (- 1, 6 )

If you take a random sampling of 100,000 human beings and find that only 1 of them has substituted an a at a location where the other 99,999 have a t, this would be considered a rare event.

In statistics, when a random sampling of a large population reveals an extremely rare occurrence or outlier, it is considered an unusual event or anomaly.

In the scenario described, where out of 100,000 human beings, only 1 individual has substituted an 'a' at a location where the other 99,999 individuals have a 't', this finding would be considered an extremely rare event.

Such occurrences can raise suspicion and warrant further investigation. It may indicate a potential error or anomaly in the data collection process, genetic mutation, transcription error, or other factors that caused the observed difference.

Statistical analysis can help assess the significance of this occurrence by calculating probabilities, conducting hypothesis tests, or considering the context of the situation.

Additionally, careful examination of the methodology, data collection procedures, and potential sources of bias is necessary to ensure the validity and reliability of the results.

In summary, finding a single individual with a different substitution in a random sampling of 100,000 human beings would be considered an unusual and potentially significant event, prompting further investigation and analysis to understand its underlying causes and implications.

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Answer: The two functions are

f(x) = sqrt(64x^2+64)

g(x) = -sqrt(64x^2+64)

Graphing these together forms a hyperbola

To get these two functions, we need to solve for y

y^2 - 64x^2 = 64

y^2 = 64x^2 + 64

y = sqrt(64x^2 + 64) or y = -sqrt(64x^2 + 64)

The last line is similar to how x^2 = 9 has two solutions (x = plus or minus 3)

Answer:

300000 km per second

18000000 km per minute

126000000 km in 7 minutes

Step-by-step explanation:

In 10 minutes there are (10*60) seconds, which is 600 seconds.

180000000/600 = 300000

To find km per minute,

180000000/10 = 18000000

To find km in 7 minutes,

18000000*7=126000000

Light travels 18000000 kilometers per minute and 300000 kilometers per second.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, light travels about 180000000 kilometers in 10 minutes.

A) We know that, 1 minute =60 seconds

10 minutes =600 seconds

Now, number of kilometers per second

= 180000000/600

= 300000 kilometers/second

B) Number of kilometers per minute

= 180000000/10

= 18000000 kilometers per minute

C) Number of kilometer light travel in 7 minutes

= 18000000×7

= 126000000

Therefore, light travels 18000000 kilometers per minute and 300000 kilometers per second.

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Approximately 16.35% of the light bulbs will last at least 940 hours.

To find the percent of light bulbs that will last at least 940 hours, we need to calculate the area under the standard normal distribution curve to the right of the given z-score (-0.98).

Using a standard normal distribution table or a calculator, we can find the corresponding area, which represents the percentage.

The z-score of -0.98 corresponds to a cumulative probability of approximately 0.1635 or 16.35%.

Therefore, approximately 16.35% of the light bulbs will last at least 940 hours.

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Answer:

180 - a = b and a + b = 180

Step-by-step explanation:

The feature that will be the same as the original is:

The perimeter is the same.

The coordinate of C' is (3, 4).

The slope of A'C' is 1/4.

We have,

To rotate a point 180 degrees clockwise around another point, you can follow these steps:

- Calculate the displacement vector from the center of rotation to the point you want to rotate.

- Reverse the direction of the displacement vector.

- Apply the reversed displacement vector to the center of rotation.

- Let's apply these steps to each vertex of triangle ABC to find the coordinates of A', B', and C'.

So,

- Coordinate of A' (rotated point of A around (3, 4)):

Displacement vector: (A' - Center of rotation) = (A - Center of rotation) = (-5, 2) - (3, 4) = (-8, -2).

Reverse the direction of the displacement vector:

Reversed displacement vector: (-8, -2) * (-1) = (8, 2).

Apply the reversed displacement vector to the center of rotation:

Coordinate of A': (3, 4) + (8, 2) = (11, 6).

- Coordinate of B' (rotated point of B around (3, 4)):

Displacement vector: (B' - Center of rotation) = (B - Center of rotation) = (-2, 5) - (3, 4) = (-5, 1).

Reverse the direction of the displacement vector:

Reversed displacement vector: (-5, 1) * (-1) = (5, -1).

Apply the reversed displacement vector to the center of rotation:

Coordinate of B': (3, 4) + (5, -1) = (8, 3).

- Coordinate of C' (rotated point of C around (3, 4)):

Displacement vector: (C' - Center of rotation) = (C - Center of rotation) = (3, 4) - (3, 4) = (0, 0).

Reverse the direction of the displacement vector:

Reversed displacement vector: (0, 0) * (-1) = (0, 0).

Apply the reversed displacement vector to the center of rotation:

Coordinate of C': (3, 4) + (0, 0) = (3, 4).

So,

The coordinate of A' is (11, 6).

The coordinate of B' is (8, 3).

The coordinate of C' is (3, 4).

To find the perimeter and area of a triangle, we can use the coordinates of its vertices.

Let's start by finding the perimeter and area of triangle ABC.

Triangle ABC:

A = (-5, 2)

B = (-2, 5)

C = (3, 4)

The perimeter of triangle ABC:

The perimeter of a triangle is the sum of the lengths of its sides. We can use the distance formula to calculate the lengths of each side and then sum them up.

Length of side AB:

\(d_{AB} = \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\)

= √((-2 - (-5))² + (5 - 2)²)

= √(3² + 3²)

= √(18)

= 3√2

Length of side BC:

\(d_{BC} = \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\)

= √((3 - (-2))² + (4 - 5)²)

= √(5² + 1²)

= √(26)

Length of side CA:

\(d_{CA}= \sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)\)

= √((-5 - 3)² + (2 - 4)²)

= √((-8)² + (-2)²)

= √(64 + 4)

= √(68)

= 2√17

The perimeter of triangle ABC:

\(P_{ABC} = d_{AB} + d_{BC} + d_{CA}\)

= 3√2 + √26 + 2√17

Area of triangle ABC:

The area of a triangle can be calculated using the coordinates of its vertices with the Shoelace formula.

Area of triangle ABC:

A_ABC = 1/2 x |(x1 x y2 + x2 x y3 + x3 x y1) - (y1 x x2 + y2 x x3 + y3 x x1)|

= 1/2 x |((-5 x 5) + (-2 x 4) + (3 x 2)) - ((2 x -2) + (5 x 3) + (4 x -5))|

= 1/2 x |(-25 - 8 + 6) - (-4 + 15 - 20)|

= 1/2 x |-27 - (-9)|

= 1/2 x |-27 + 9|

= 1/2 x |-18|

= 9

Now let's find the perimeter and area of triangle A'B'C', which is the rotated triangle of ABC.

Triangle A'B'C':

A' = (11, 6)

B' = (8, 3)

C' = (3, 4)

The perimeter of triangle A'B'C':

Using the same approach as before, we calculate the lengths of the sides:

Length of side A'B':

d_A'B' = √((x2 - x1)^2 + (y2 - y1)^2)

= √((8 - 11)^2 + (3 - 6)^2)

= √((-3)^2 + (-3)^2)

= √(18)

= 3√2

Length of side B'C':

d_B'C' = √((x2 - x1)^2 + (y2 - y1)^2)

= √((3 - 8)^2 + (4 - 3)^2)

= √((-5)^2 + 1^2)

= √(26)

Length of side C'A':

d_C'A' = √((x2 - x1)^2 + (y2 - y1)^2)

= √((3 - 11)^2 + (4 - 6)^2)

= √((-8)^2 + (-2)^2)

= √(68)

= 2√17

The perimeter of triangle A'B'C':

P_A'B'C' = d_A'B' + d_B'C' + d_C'A'

= 3√2 + √26 + 2√17

Area of triangle A'B'C':

Using the same Shoelace formula as before:

Area of triangle A'B'C':

A_A'B'C' = 1/2 x |(x1 x y2 + x2 x y3 + x3 x y1) - (y1 x x2 + y2 x x3 + y3 x x1)|

= 1/2 x |((11 x 3) + (8 x 4) + (3 x 6)) - ((6 x 8) + (3 x 3) + (4 x 11))|

= 1/2 x |(33 + 32 + 18) - (48 + 9 + 44)|

= 1/2 x |(83) - (101)|

= 1/2 x |-18|

= 9

Now,

The perimeter of triangle ABC is 3√2 + √26 + 2√17, and the area of triangle ABC is 9.

The perimeter of triangle A'B'C' is 3√2 + √26 + 2√17, and the area of triangle A'B'C' is 9.

The slope of A'C' can be calculated using the coordinates of A' and C'.

The slope of a line can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

For A'(11, 6) and C'(3, 4), the slope of A'C' is:

slope = (4 - 6) / (3 - 11)

= -2 / -8

= 1/4

Thus,

The feature that will be the same as the original is:

The perimeter is the same.

The coordinate of C' is (3, 4).

The slope of A'C' is 1/4.

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Answer:

Represents decay ( because .72 < 1  )

The amount decreases 72% each 'x' time period

Step-by-step explanation:

Answer:

First we write y and its derivatives as power series:

y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2

Next, plug into differential equation:

(x+2)y′′+xy′−y=0

(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

Move constants inside of summations:

∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0

∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0

Change limits so that the exponents for  x  are the same in each summation:

∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0

Pull out any terms from sums, so that each sum starts at same lower limit  (n=1)

∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0

Combine all sums into a single sum:

4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0

Now we must set each coefficient, including constant term  =0 :

4a2−a0=0⟹4a2=a0

2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0

We would usually let  a0  and  a1  be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since  a0=4a2 , I’ll choose  a1  and  a2  as the two arbitrary constants. We can still express all other constants in terms of  a1  and/or  a2 .

an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)

a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2

a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2

a5=−(4⋅3)a4+2a32(5⋅4)=15!a2

a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2

We see a pattern emerging here:

an=(−1)(n+1)n−4n!a2

This can be proven by mathematical induction. In fact, this is true for all  n≥0 , except for  n=1 , since  a1  is an arbitrary constant independent of  a0  (and therefore independent of  a2 ).

Plugging back into original power series for  y , we get:

y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯

y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯

y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)

Notice that the expression following constant  a2  is  =4+  a power series (starting at  n=2 ). However, if we had the appropriate  x -term, we would have a power series starting at  n=0 . Since the other independent solution is simply  y1=x,  then we can let  a1=c1−3c2,   a2=c2 , and we get:

y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)

y=c1x+c2∑n=0∞(−1)n+1n−4n!xn

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Given the coordinates above, the area of the trapezoid is approximately 41.

We have,

A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.

For the calculation showing the above solution:

Step 1 - Given:

A = (-3,2)

B = (1, 5)  = ⊥

C = (-7, -3)

D = (0.-2)

Step 2 - To get the distance between the points we need to use the formula for Distance between two points which is given as:

d=√((x2 – x1)² + (y2 – y1)²).

Distance of Line AB =

√((1 – (-3))² + (5 – 2)²).

= √[(4)² + (3)²]

= √( 16 + 9)

= √25

AB= 5

Repeat this for  BC, CD, DA and we'd get the following

BC =  11.313708498985

CD = 7.0710678118655

DA = 5

Step 3  - From the above structure, [see attached] we then apply the formula for the area of a Trapezoid (Trapezium) which is given as:

A = [(a+b)/2] h

Where a = 5

b = 11.313708498985

h = 5

=  [(5+11.313708498985)/2] 5

= 40.7842712475

= 41

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complete question:

What is the area of trapezoid ABCD?

Enter your answer as a decimal or whole number in the box. Do not round at any steps.

units²

Trapezoid A B C D on a coordinate plane with vertex A at negative 3 comma 2, vertex B at 1 comma 5, vertex C at negative 7 comma negative 3, and vertex D at 0 comma negative 2. Angle B is shown to be a right angle.

The probability that a randomly chosen person has diabetes is approximately 10.45%.

The probability that a randomly chosen person has diabetes can be calculated by dividing the number of people with diabetes by the total population. Using the given data, we have:

Total population = 100%Probability of having diabetes = 10.5%Number of people with diabetes = 34.2 million

To find the probability of a randomly chosen person having diabetes, we divide the number of people with diabetes by the total population as follows:

Probability of having diabetes = (Number of people with diabetes / Total population) x 100%

= (34.2 million / 327 million) x 100%

= 0.1045 or 10.45%

Therefore, the probability that a randomly chosen person has diabetes is approximately 10.45%.

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The chi-square statistic of 3.86 is not statistically significant if the critical value obtained from the distribution of chi-square is 6.63 with an alpha level of .01.

To determine if the obtained chi-square statistic of 3.86 is statistically significant or not, we need to compare it to the critical value obtained from the distribution of chi-square, which is 6.63, at a significance level of 0.01.

In this case, the obtained chi-square value is less than the critical value, indicating that we fail to reject the null hypothesis. This means that the observed frequencies in the sample are not significantly different from the expected frequencies based on the null hypothesis. The alpha level of 0.01 indicates that we are willing to accept a 1% chance of making a Type I error, which is rejecting the null hypothesis when it is actually true. Since the obtained chi-square value is not greater than the critical value, we do not have sufficient evidence to reject the null hypothesis.

In summary, the results are not statistically significant at the 0.01 significance level, based on the obtained chi-square statistic of 3.86 and the critical value of 6.63. This means that there is no significant difference between the observed and expected frequencies, based on the null hypothesis.

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Answer:

(B). \(\frac{2\pi }{3} x\)

Step-by-step explanation: