#1: Solve the linear system below using the elimination method. Type your
answer as an ordered pair in the form (#,#).*
2x + 5y = -16
-3x + 7y = -5

Answer:

149.59062 cm^2

Step-by-step explanation:

area of circle=πr^2

=3.142*(6.9)^2

=3.142*47.61

=149.59062 cm^2

The numbers on the mailboxes could be considered either categorical or quantitative data. The correct Option is C: Either categorical or quantitative data.

The numbers on the mailboxes can be considered either categorical or quantitative data, depending on the context in which they are being used.

If the numbers are simply labels for the mailboxes, with no inherent numerical value or order, then they can be considered categorical data. In this case, the numbers would be treated as labels for the different categories or groups, rather than as measurements with numerical significance.

On the other hand, if the numbers are being used to represent a quantity or a position in a sequence, then they can be considered quantitative data. For example, if the numbers represent the physical location of the mailbox within a building, or the order in which mail is sorted and delivered, then they can be treated as numerical measurements.

Therefore, without further context, the numbers on the mailboxes could be considered either categorical or quantitative data.

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To calculate the width of the loss cone at a radius of 25,000 km, we can use trigonometry by taking the arctangent of the ratio of the width to the radius.



The loss cone is a concept used in plasma physics to describe the region of particles' pitch angles that are vulnerable to being lost or escaping from a confined plasma system. The width of the loss cone can be calculated using trigonometry.At a given radius of \( 25,000 \) km, we can consider a line connecting the center of the system to the point on the loss cone. This line represents the magnetic field line. The width of the loss cone can be determined by the angle formed between this line and the tangent to the loss cone.

To calculate this angle, we need the radius of the system, which is \( 25,000 \) km. Assuming a spherical system, we can consider the tangent to the loss cone as a line perpendicular to the radius. In this case, we have a right triangle where the radius is the hypotenuse.Using basic trigonometry, we can determine the angle by taking the inverse tangent of the ratio of the width of the loss cone (opposite side) to the radius (hypotenuse). The width of the loss cone will be the arctangent of the ratio.



Therefore, To calculate the width of the loss cone at a radius of 25,000 km, we can use trigonometry by taking the arctangent of the ratio of the width to the radius.

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Answer:

\(33 units^{2}\)

I counted the squares.

The steps and reason to prove the angle theorems is; Table 3

The internal angles of the given triangle are given as;

a, b, c and d.

Now, we know that the sum of interior angles in a triangle is equal to 180°;

∠a + ∠b + ∠c = 180°

Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.

∠c + ∠d = 180°

Thus, by transitive properties, we can say that;

∠a + ∠b + ∠c = ∠c + ∠d

Therefore by subtraction property of equality we have;

∠a + ∠b = ∠d

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Answer:

235

Step-by-step explanation:

The correct answer is 4) observed score.

The observed score refers to the actual score that is recorded or measured in a particular situation. This score can be influenced by various factors such as measurement error, observer bias, or the conditions under which the score was obtained.

The observed score represents the result that is directly obtained from a test, questionnaire, or any other measurement tool.

The true score refers to the actual ability, knowledge, or any other characteristic that the individual possesses. The true score is typically unobservable and is often estimated by considering the average of multiple observed scores.

The error score represents the difference between the observed score and the true score. This score reflects the extent to which measurement error or other factors influenced the recorded score.

False score refers to a score that is intentionally or unintentionally altered or manipulated to present a different picture of an individual's performance or ability. It is different from the error score in the sense that it is not a result of measurement error, but rather an intentional manipulation of the score.

Therefore, the score that you would actually record is an example of the observed score.

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A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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Answer:

time = 70 minutes

The root of this equation is determined to be approximately 0.567143.The root is found to be approximately -0.673253.

The Newton-Raphson method is an iterative numerical technique used to find the roots of equations. In the first equation, y = f(x) = e^x - x, the initial approximation x0 is set to 0. By applying the Newton-Raphson method, successive approximations of the root are calculated until convergence is achieved. The root of this equation is determined to be approximately 0.567143.

In the second equation, x^3 + 2x^2 + 6x + 3 = 0, the root is sought within the range (-1, 0). The Newton-Raphson method is employed again, starting with an initial approximation x0 of -1. Through iterative calculations, the root is found to be approximately -0.673253.

Both equations demonstrate the effectiveness of the Newton-Raphson method in finding roots within specific ranges by iteratively refining approximations until a satisfactory solution is obtained.

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x²/21 + y²/25 = 1 is the equation of the ellipse

Given: the length of the major axis = 10 and foci = (0, ± 2)

Since the foci are on the y-axis, the major axis will be along the y-axis. Thus, the equation of the ellipse is:

x²/b² + y²/a² = 1

Since the length of the major axis = 2a. Thus:

2a = 10

a = 10/2 = 5

a² = 5² = 25

c = 2

c² = a² - b²

2² = 5² - b²

4 = 25 - b²

b² = 25 - 4 = 21

Substitute a² = 25 and b² = 21 into the equation:

x²/b² + y²/a² = 1

x²/21 + y²/25 = 1

Therefore,  the equation of the ellipse is x²/21 + y²/25 = 1

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Answer:

2,676

Step-by-step explanation:

2,676=223x12

Answer:

The factors of 32 are 32, 16, 8, 4, 2, 1. The factors of 72 are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1. The common factors of 32 and 72 are 8, 4, 2, 1, intersecting the two sets above.

plz mark brainliest :DD

Answer:

The gcf of 32 and 72 can be obtained like this: The factors of 32 are 32, 16, 8, 4, 2, 1. The factors of 72 are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1. The common factors of 32 and 72 are 8, 4, 2, 1,

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}\)

so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}\)

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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A ratio shows us the number of times a number contains another number. The two areas that have buckeyes and monarchs are in the same proportion as A and D.

A ratio shows us the number of times a number contains another number.

The ratio of buckeyes and monarch butterflies in different areas can be written as,

Area A,

Buckeyes/Monarchs = 15/16

Area B,

Buckeyes/Monarchs = 27/36 = 3/4

Area C,

Buckeyes/Monarchs = 12/25

Area D,

Buckeyes/Monarchs = 24/32 = 3/4

Area E,

Buckeyes/Monarchs = 44/33 = 4/3

Hence, the two areas that have buckeyes and monarchs are in the same proportion as A and D.

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Answer:B and D

Step-by-step explanation:

i just took the test

a) The mean of the data is given as follows: 226.75

b) The standard deviation of the data is given as follows: 39.76.

The mean of the data is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

Hence it is given as follows:

Mean = 4535/20

Mean = 226.75.

The standard deviation of the data is obtained as the square root of the sum of the differences squared between each observation and the mean divided by the number of observations.

Using a calculator, the standard deviation is given as follows:

s = 39.76.

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Answer:

6

Step-by-step explanation:

9 x 6 = 54

3 x 6 = 18

54 - 18 = 36

Answer:

9x-3x=36

6x=36

x=36/6

x= 6

3y+4y=49

7y=49

y= 49/7

y= 7

10r-2r+5=69

8r=69-5

8r=64

r=64/8

r=8

Step-by-step explanation:

if it helps don't forget to like and mark me

Answer:

12

Step-by-step explanation:

Perimeter is using addition and if its a square, all of the sides are the same.

If one side = 3 cm, then 3cm + 3cm + 3cm + 3cm=12 cm

Answer:

12

Step-by-step explanation:

A square with 3cm long side

Area = 2 sides multiplied

Perimeter = All sides added

3 + 3 + 3 + 3 = 12cm

or

3 × 4 = 12cm

The specific gravity of the combined product is 1.22

Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.

Given,

The total quantity of portion= 50 ml

Specific gravities of the three syrups = 1.10,1.25 and 1.32

Then,

The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)

= 1.22

Hence, the specific gravity of the combined product is 1.22.

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Answer:

254.5

Step-by-step explanation:

area of circle = pi (3.142) x 9squared

answer 254.5 or 81 pi

Answer:

v=− 1± i  √35 /6

Step-by-step explanation:

Solve the equation for  v  by finding  a ,  b , and  c  of the quadratic then applying the quadratic formula.

To determine the minimum thickness of the iron, we need to calculate the diffusion flux of hydrogen through the iron and equate it to the maximum allowed hydrogen loss.

The diffusion flux (J) of hydrogen through a material can be calculated using Fick's first law of diffusion:

J = -D * (∆C/∆x)

Where:

J is the diffusion flux

D is the diffusion coefficient of hydrogen in iron

∆C is the difference in hydrogen concentration across the thickness (∆C = C1 - C2)

∆x is the thickness of the iron

We are given:

Maximum allowed hydrogen loss = 50 g/cm²/year

Temperature (T) = 400 °C (673 K)

Hydrogen concentration at surface 1 (C1) = 0.05 H atom per unit cell

Hydrogen concentration at surface 2 (C2) = 0.001 H atom per unit cell

First, we need to convert the hydrogen concentrations into a common unit. The atomic mass of hydrogen (H) is approximately 1 g/mol. The number of atoms in a unit cell for BCC iron is 2.

Concentration in g/cm³:

C1 = (0.05 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.025 g/cm³

C2 = (0.001 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.0005 g/cm³

Now, we can calculate the difference in hydrogen concentration across the thickness:

∆C = C1 - C2 = 0.025 g/cm³ - 0.0005 g/cm³ = 0.0245 g/cm³

Next, we need to determine the diffusion coefficient of hydrogen in iron at 400 °C. The diffusion coefficient can be estimated using the following equation:

D = D0 * exp(-Q/RT)

Where:

D0 is the pre-exponential factor

Q is the activation energy for diffusion

R is the gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

For hydrogen diffusion in iron, typical values are:

D0 = 5 x 10^-7 cm²/s

Q = 40,000 J/mol

Plugging in the values:

D = (5 x 10^-7 cm²/s) * exp(-40000 J/mol / (8.314 J/(mol·K) * 673 K))

D ≈ 2.70 x 10^-12 cm²/s

Now, we can substitute the values into Fick's first law of diffusion and solve for the thickness (∆x):

J = -D * (∆C/∆x)

Rearranging the equation:

∆x = -D * (∆C/J)

Substituting the given values:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year))

Converting the year unit to seconds:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year)) * (1 year / 3.1536 x 10^7 s)

Calculating:

∆x ≈ -0.000347 cm ≈ 3.47 μm

The negative sign indicates that the thickness (∆x) is measured in the opposite direction of the hydrogen diffusion. Thus, the minimum thickness of the iron required to limit the hydrogen loss to no more than 50 g per year through each square cent.

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Answer:

1) y = 2x - 2

2) y = - x - 1

3) y = 2/3 x + 1

4) y = 4x - 4

5) y = 3x + 6

6) y = -3x -3

7) y = 3 - x

8) y = 4 - 4x

(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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The size of the reflex angle POR is 302 degrees.

Since the angle PQR is given as 29 degrees and it lies on the circumference of the circle, we know that it is an inscribed angle that intercepts the arc PR. The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, we can find the measure of the arc PR as:

Arc PR = 2 × Angle PQR = 2 × 29 = 58 degrees

Since angle POR is a reflex angle that contains the inscribed angle PQR and the arc PR, we can find its measure by subtracting the measure of angle PQR from 360 degrees:

Angle POR = 360 - Arc PR = 360 - 58 = 302 degrees

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Answer:

22666.02986

Step-by-step explanation:

Answer:

a.)2 b.)6

Step-by-step explanation:

a.) solve 7x+4=18 because EC bisects making FEC = CEG

b.) solve 12y+18=90 because AED is 90 degrees

The proof of  AB ≅ CD is given below.

What is triangle?

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

Given:  BD and AC bisect each other.

So, AE = AC  and BE = ED

Consider the triangles  ΔAEB and , ΔECD

Given,

AE = EC                         ...S

BE = ED                         ....S

Here, lines BC and AD intersects at point E, so

 m ∠AEB = m ∠DEC               ....A

Therefore, from SAS congruency,

ΔAEB ≅ ΔECD

Hence,  AB ≅ CD

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