The diagram shows a convex polygon. What is the sum of the interior angle measures of this polygon?​

Answer:

1296

Step-by-step explanation:

3 × 2 = 6

6 to the power -2 = 0.277777777777777777

0.277777777777777777 to the power -2 = 1296

Using the Cramer's Rule, the solution of the given system of equation is (-17/11, 48/11)

The given system of equations are

10x+4y=2

-6x+2y=18

Solving the equations by using Cramer's rule.

We know that, the solution of a system of linear equations in two unknowns

a(1)x+b(1)y = c(1)

a(2)x+b(2)y = c(2)

is given by ∆x=∆1, and ∆y=∆2.

where,

\(\Delta=\text{det}\left [ \begin{matrix} a(1)&b(1) \\ a(2) & b(2)\end{matrix} \right ], \Delta(1)=\text{det}\left [ \begin{matrix} c(1)&b(1) \\ c(2) & b(2)\end{matrix} \right ]\text{ and }\Delta(2)=\text{det}\left [ \begin{matrix} a(1)&c(1) \\ a(2) & c(2)\end{matrix} \right ]\)

Since the given equations are;

10x+4y=2

-6x+2y=18

Now,

\(\Delta=\text{det}\left [ \begin{matrix} 10&4 \\ -6 & 2\end{matrix} \right ]\)

∆ = [(10×2)-(-6×4)]

∆ = 20+24

∆ = 44

\(\Delta(1)=\text{det}\left [ \begin{matrix} 2&4 \\ 18 & 2\end{matrix} \right ]\)

∆(1) = [(2×2)-(18×4)]

∆(1) = 4-72

∆(1) = -68

\(\Delta(2)=\text{det}\left [ \begin{matrix} 10&2 \\ -6 & 18\end{matrix} \right ]\)

∆(2) = [(10×18)-(-6×2)]

∆(2) = 180+12

∆(2) = 192

By Cramer's Rule,

∆x = ∆(1)

44 × x = -68

x = -68/44

x = -17/11

Now,

∆y = ∆(2)

44 × y = 192

y = 192/44

y = 48/11

Hence, the solution of the given system of equation is (-17/11, 48/11).

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The right question is:

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.

10x+4y=2

-6x+2y=18

The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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The equation 2√w - 1 = √w + 2 is solved by squaring both sides and simplifying to find w = 9 as the only valid solution, without any extraneous solutions.

1. Given equation: 2√w - 1 = √w + 2
2. Add 1 to both sides of the equation to isolate the radical term: 2√w = √w + 3
3. Square both sides of the equation to eliminate the square root: (2√w)² = (√w + 3)²
  Simplifying the left side: 4w  
  Expanding the right side: (√w + 3)(√w + 3) = (√w)² + 2(√w)(3) + 3² = w + 6√w + 9
  Therefore, the equation becomes: 4w = w + 6√w + 9
4. Move all terms involving √w to one side and the remaining terms to the other side: 4w - w - 9 = 6√w
  Simplifying the left side: 3w - 9 = 6√w
5. Square both sides of the equation again: (3w - 9)² = (6√w)²
  Expanding the left side: 9w² - 54w + 81 = 36w
6. Rearrange the terms: 9w² - 90w + 81 = 0
7. Factor out a common factor of 9: 9(w² - 10w + 9) = 0
8. Factor the expression within the parentheses: (w - 1)(w - 9) = 0
9. Set each factor equal to zero and solve for w:
  w - 1 = 0 → w = 1
  w - 9 = 0 → w = 9
10. Check for extraneous solutions by substituting these values back into the original equation:
   - For w = 1: 2√1 - 1 = √1 + 2 → 2 - 1 = 1 + 2 → 1 = 3 (Not true)    
   - For w = 9: 2√9 - 1 = √9 + 2 → 6 - 1 = 3 + 2 → 5 = 5 (True)
Since w = 9 satisfies the original equation, it is the valid solution. The extraneous solution w = 1 is discarded.
Therefore, the solution to the equation 2√w - 1 = √w + 2 is w = 9.

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Step-by-step explanation:

\( \sin(20) = 3 \div x\)

Multiply both sides with x :

\( x \times \sin(20) = 3\)

And divide both sides with sin(20) :

\(x = 3 \div \sin(20) = 8.771\)

Which gives us x=8,771

Answer:

AB = 6

Step-by-step explanation:

sin 20° = 3/?

\(\frac{1}{2}\) = \(\frac{3}{x}\)

cross-multiply: x = 6

Answer:

-5m/2

Step-by-step explanation:

-m+ (-2m) +(-3m)+(-4m) +(-4m)+(-3m)+(-2m)+(-m)/8

-m-2m-3m-4m-4m-3m-2m-m/8

-20m/8

-5m/2

We have the following:

The unit rate would be the amount of calories per gram, so we must divide the number of calories by the number of grams

That is, there are 5 calories per gram in this candy bar.

The GCF of the expression given as -27x³y - 1/3xy² is -xy

From the question, we have the following expression

-27x3y - 1/3xy2

Rewrite the given expression as follows

This is represented using

-27x³y - 1/3xy²

Factor out x from the expression

So, we have the following representation

-27x³y - 1/3xy² = x(-27x²y - 1/3y²)

Factor out y from the expression

So, we have the following representation

-27x³y - 1/3xy² = xy(-27x² - 1/3y)

Factor out -1 from the expression

So, we have the following representation

-27x³y - 1/3xy² = -xy(27x² + 1/3y)

Hence, the GCF is -xy

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Step-by-step explanation:

5(1-2x) = -65

5-10x = -65

65+5 = 10x

70 = 10x

7 = x

x = 7

Answer:

X=7/2

Step-by-step explanation:

5(1 - 2x) = -65

5-20x=-65

-20x=-65-5

-20x=-70

Minus sign cancel from both side

So x=70/20

X=7/2

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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Solution

The measure of the angle

Alternate interior angles are "interior" (between the parallel lines), and they "alternate" sides of the transversal. Notice that they are not adjacent angles (next to one another sharing a vertex).

When the lines are parallel,

the alternate interior angles

are equal in measure.

Hence the angle in a parallel lines are said to be corresponding and equal

Therefore the measure of the angle 139°

The area between the curves y = 8/(1 + x⁴) and y = 4x² is approximately 6.193 square units.

To find the area between the curves, we need to determine the points of intersection and integrate the difference between the two functions over that interval.

To find the area between the curves y = 8/(1 + x^4) and y = 4x^2, we can plot the curves and calculate the definite integral of the positive difference between the two functions over the interval where they intersect. Here's how you can use a graphing calculator to visualize and calculate the area:

Turn on the graphing calculator and enter the equations of the curves:

For the first curve y = 8/(1 + x^4)

For the second curve, y = 4x^2

Adjust the appropriate window settings on the calculator to ensure that the region of interest is visible. You can set the x-axis range to span the intersection of two curves.

Graph the equations to see the area between the curves.

Determine the values ​​of x where the curves intersect. These are the x values ​​where the two equations have the same y values. You can use the intersection function of the calculator to find these points.

Once you have the intersections, calculate the definite integral of the positive difference between the two curves in the interval where they intersect. This integral will give you the area between the curves.

Alternatively, if you cannot use a graphing calculator or prefer to calculate the area by hand, you can proceed as follows:

Construct an equation to find the points of intersection:

8/(1 + x^4) = 4x^2

Solve the equation to find the values ​​of x where the curves intersect.

Once you have the intersections, set up an integral to find the area between the curves:

A = ∫[a, b] (8/(1 + x^4) - 4x^2) dx

Here [a, b] represents the interval where the curves intersect.

Calculate the definite integral using appropriate integration techniques or software.

The result of the integral will give you the area between the curves.

The area between the curves y = 8/(1 + x⁴) and y = 4x² is approximately 6.193 square units.

Please note that the above steps provide a general guideline for finding the area between two curves. The actual calculations and values ​​will depend on the specific intercepts and integration limits you get from solving graphs or equations.

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named width in java with a value of 1.55.

double length = 3.5; double width = 1.55;

Double is a data type in Java that supports storing decimal numbers. It is used to represent values that include a fractional component and is a 64-bit floating-point data type. When exact decimal numbers are required, as in financial or scientific computations, the double data type is frequently utilized. A double's range is roughly  ±\(5.0 \times 10^{-324}\) to ±\(1.7 \times 10^{308\) having a 15–17 decimal digit degree of accuracy.

For example:

double myDouble = 3.14; Alternatively, you may define a double variable without first giving it a value and then give it one later on in your code.

3.5 double length, 1.55 double width;

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Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Answer:

Step-by-step explanation:

First, let’s flip the first term.

2^-x = 8^2-x

we can take ^3 out of the 8 to simplify

2^-x = 2^3(2-x)

-x = 3(2-x)

Now we solve for x.

x = 6

Hope this helps!

Answer: it’s C

Step-by-step explanation: ^

Answer:

the domain of f(x) is x > 0

Step-by-step explanation:

mark brainliest

The absolute value of 7 - 5i is sqrt(74). To graph the number 7 - 5i, we plot the point (7, -5). This point represents the complex number 7 - 5i.

The complex plane is a coordinate system with the real numbers on the horizontal axis and the imaginary numbers on the vertical axis.

The absolute value of a complex number is its distance from the origin. The absolute value of 7 - 5i can be found using the Pythagorean theorem. The real part of 7 - 5i is 7 and the imaginary part is -5. The distance formula gives us:

|7 - 5i| = sqrt(7^2 + (-5)^2) = sqrt(49 + 25) = sqrt(74)

Therefore, the absolute value of 7 - 5i is sqrt(74).

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120=!3÷!6

!2-!5=!3

to 120 modes

Answer:

You would get 8in of rain Hope this Helped

Step-by-step explanation:

Step-by-step explanation:

Hey hi,

Please mark it as brainliest!

Answer:

  (a) AC = 4√2 cm

  (b) AM = 2√2 cm

  (c) EM = √41 cm

  (d) EF = 3√5 cm

Step-by-step explanation:

You want to solve for various lengths in the right square pyramid shown with base edge 4 cm and lateral edge 7 cm.

Each right triangle can be solved for unknown lengths using the Pythagorean theorem: the square of the hypotenuse is the sum of the squares of the other two sides.

Right triangles of interest here are ...

  ADC . . . . for finding AC and AM (isosceles right triangle)

  CME . . . . for finding EM

  FME . . . . for finding EF

AC is the hypotenuse of ∆ADC, so ...

  AC² = AD² +DC²

  AC = √(4² +4²)

  AC = 4√2 . . . . cm

M is the midpoint of AC, so ...

  AM = AC/2 = (4√2)/2

  AM = 2√2 . . . . cm

FM is half the length of one side of the base, so is 2 cm. CM = AM = 2√2.

  CE² = CM² +EM²

  EM = √(CE² -CM²) = √(7² -(2√2)²)

  EM = √41 . . . . cm

EF is the hypotenuse of ∆EMF.

  EF² = EM² +FM²

  EF = √(EM² +FM²) = √(41 +2²) = √45

  EF = 3√5 . . . . cm

The amount of copper in a body that weighs 150 pounds in standard form is 1.4357 x 10^-5

Given,

The human body contains tiny amounts of copper.

The exact amount of copper is 2.3 x 20^-4 for a person weighing 150 pounds.

We need to find how much copper is in the body of a 150-pound person and write in standard form.

It is a way of writing a number in a decimal number between 1 and 10 along with a power of 10.

Find the amount of copper in a body that weighs 150 pounds.

We have,

2.3 x 20^-4 for a person weighing 150 pounds.

Write 2.3 x 20^-4 in standard form.

2.3 x 20^-4 can be written as:

= 2.3/20^4

= 2.3 / 160000

= 0.000014375

= 1.4375 / 100000

We need a decimal point between 1 and 10 so,

1.4357 x 10^-5 is our answer.

Thus the amount of copper in a body that weighs 150 pounds in standard form is 1.4357 x 10^-5

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The area of the shaded region will be 8 square unit as per the given figure.

The rectangle has dimensions 2 x 4, so its area is:

Area of rectangle = length x width = 2 x 4 = 8 square units

The triangle has dimensions 4 x 8, so its area is:

Area of triangle = (1/2) x base x height = (1/2) x 4 x 8 = 16 square units

To find the area of the shaded region, we need to subtract the area of the triangle from the area of the rectangle.

Area of shaded region = Area of the triangle - Area of rectangle

Area of shaded region = 16-8

Area of shaded region = 8

The area of the shaded region will be 8 square units.

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Complete question:

Step-by-step explanation:

There are 5 different positions of 666:

666////

/666///

//666//

///666/

////666

The forward dashes represent any number from 0 to 9.

Case 1: "666////"

Number of ways = 10⁴ = 10,000.

Case 2: The other positions.

Since the 1st forward dash cannot be 0 (leading digit),

Number of ways for each position = 9 * 10³ = 9,000

Number of ways for all 4 positions = 9,000 * 4 = 36,000.

Total evil numbers = 10,000 + 36,000 = 46,000.

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

The function is 130/2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

According to question,

\(\int\limits^9_0 {f(x)} \, dx \\ \int\limits^7_0 {f(x)} \, dx+\int\limits^9_7 {f(x)} \, dx\\ \int\limits^7_0 {7} \, dx + \int\limits^9_7 {x} \, dx\\ (7x)^{7} _{0} + (\frac{x^{2} }{2})^{9} _{7}\)

7x7 - 7x0 + 81/4 - 49/4

49 + 32/2

130/2

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We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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Answer:

12b + 14p - 7

Step-by-step explanation:

It is already simplified.

can i get brainlist too

The solution to the equation 4x^2 + 16x + 19 = 0 is "no real solutions". The given quadratic equation is 4x^2 + 16x + 19 = 0.

Using the Quadratic Formula, we have:

\(x = (-b ± sqrt(b^2 - 4ac)) / 2a\)

where a = 4, b = 16, and c = 19.

Substituting the values, we get:

x = (-16 ± sqrt(16^2 - 4(4)(19))) / 2(4)

x = (-16 ± sqrt(16 - 304)) / 8

x = (-16 ± sqrt(-288)) / 8

Since the value under the square root is negative, the quadratic equation has no real solutions.

Therefore, the solution to the equation 4x^2 + 16x + 19 = 0 is "no real solutions".

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