-2(n+3 = -12
Solve each equation.
Please explain the steps so i can also understand. thank you!

Answer:

13

Step-by-step explanation:

The expected time taken by the man to leave the maze is 15 minutes.

To find the expected time taken by the man to leave the maze, we'll first calculate the conditional expectation of time taken given that he chose each of the exits, and then use these conditional expectations to calculate the overall expectation.

Step 1: Calculate the conditional expectations :
- If he chooses Exit 1 (probability 1/3), he leaves the maze after 3 minutes.
- If he chooses Exit 2 (probability 1/3), he returns to the same room after 5 minutes and starts again. So, the expected time in this case is 5 + E(X).
- If he chooses Exit 3 (probability 1/3), he returns to the same room after 7 minutes and starts again. So, the expected time in this case is 7 + E(X).

Step 2: Calculate the overall expectation :
E(X) = (1/3)*(3) + (1/3)*(5 + E(X)) + (1/3)*(7 + E(X))

Now, we'll solve for E(X):
3E(X) = 3 + 5 + 7 + 2E(X)
E(X) = 15 minutes

The expected time taken by the man to leave the maze is 15 minutes.

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According to the problem, there are three possible exits (1, 2, and 3) from the room in the center of the maze. The probabilities of choosing each of these exits are equal.

Exit 1 leads to the outside of the maze, and it takes 3 minutes on average to reach it. Exit 2 leads back to the same room, so the man will need to start over again. Exit 3 also leads back to the same room, and it takes longer than exit 2 to get there (7 minutes).Let X be the time taken by the man to leave the maze from this room. Let Y be the exit he chooses first. Y belongs to {1, 2, 3}. Calculate the conditional expectation of the time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of the time taken to leave the maze.The expected value of X can be calculated as follows:() = ( | = 1) × ( = 1) + ( | = 2) × ( = 2) + ( | = 3) × ( = 3)Expected time to leave the maze through exit 1:( | = 1) = 3Expected time to leave the maze through exit 2:( | = 2) = 5 + ()Expected time to leave the maze through exit 3:( | = 3) = 7 + ()The probability of choosing each exit is 1/3, so:P(Y = 1) = 1/3P(Y = 2) = 1/3P(Y = 3) = 1/3Substituting these values into the equation for ():() = 3(1/3) + (5 + ())(1/3) + (7 + ())(1/3)() = 5 + (2/3)() + (7/3)()() = 15 minutes. Therefore, the expected time taken by the man to leave the maze is 15 minutes.

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Answer:

40/6= 6.6667(20/3)

Step-by-step explanation:

I divided the number of days into 6.

Answer:

\(x = 240 days\)

Step-by-step explanation:

If we know that Brad completes 1/6 of his project every 40 days, that means it will take him 40 x 6 days to complete this project. If where to write this down as an equation we get the following.

Let "x" be the total number of days Brad needs to finish his project, then....

\(\frac{1}{6} x = 40 days\)

\((\frac{1}{6} x)(6) = (40)(6)days\)

\(x = 240 days\)

Answer:

Let's say Hamid's normal weight is x.

88kg = 110%x

88kg=11/10x

Divide by 11 on each side

8kg=1/10x

Multiply by 10 on each side

80kg=x

Hamid's normal weight is 80kg

Answer:

\( \frac{7}{4} \pi\)

or

\( \frac{3}{4} \pi\)

Step-by-step explanation:

See attached. I know (very haphazard). But the basic method is to inverse the trig function. This gives you the position of the terminal angle. -45 degrees means that you turned 45 degrees clockwise and are in quadrant 4. This corresponds to an angle of rotation of 315 degrees counter clockwise which is what we are looking for since the specified domain is betwern 0 and 360 degrees or 0 and 2 pi.

The next thing to remember is that Tan is also negative in Quadrant 2 (using the ASTC rule). This corresponds to an angle of rotation of 180 - 45 = 135 degrees.

Hope that helps.

Answer:

The answer would be $6 for the tip, but it you're talking about the total amount it would be $36.

Step-by-step explanation:

20% is equivalent to 1/5

1/5 of 30 is 6 because 30 ÷ 5 = 6.

Tip by itself: $6

Tip with cost of haircut: $36

Answer: about 20$ and 63cents

Step-by-step explanation:

240-75=165

165/8=20.265

The y:y' = x*sqrt((1 - y^2)/(1 - x^2))dy/sqrt(1 - y^2) = x dx/sqrt(1 - x^2)arcsin y = -arcsec x + KSince C = 0, we have:y(x) = sin(-arcsec x)

14. Solution of the initial-value problem:y' = 6e^(2x)-y, y(0) = 0Let y' = f(y, x), and then let's use the initial condition to find the arbitrary constant:C = y(0) = 0Now let's solve for y:(dy)/(dx) + y = 6e^(2x) = (f(y, x) + y = 6e^(2x))Using the integrating factor µ = e^x, we can solve the problem using the formula:y(x) = [e^(∫µ(x)dx) * C] + [e^(∫µ(x)dx) * ∫µ(x) * f(x) dx]y(x) = [e^(x) * C] + [e^(x) * ∫6e^(2x) * e^x dx]y(x) = [e^(x) * C] + [6/3 * e^(3x) + K]Since C = 0, we have:y(x) = [6/3 * e^(3x) + K]y(x) = 2e^(3x) + K16. Solution of the initial-value problem:dy/dx = (e^x-y)/(1+e^x), y(1) = 0Let y' = f(y, x), and then let's use the initial condition to find the arbitrary constant:C = y(1) = 0Now let's solve for y:dy/dx + y/(1 + e^x) = e^x/(1 + e^x)Using the integrating factor µ = e^(x)/(1 + e^x), we can solve the problem using the formula:y(x) = [e^(∫µ(x)dx) * C] + [e^(∫µ(x)dx) * ∫µ(x) * f(x) dx]y(x) = [e^(∫e^(x)/(1 + e^x) dx) * C] + [e^(∫e^(x)/(1 + e^x) dx) * ∫(e^x)/(1 + e^x) * e^x dx]y(x) = [e^(ln(1 + e^x)) * C] + [e^(ln(1 + e^x)) * ∫(e^x)/(1 + e^x) * e^x dx]y(x) = [1 + e^x * C] + [(1 + e^x) * ∫(e^x)/(1 + e^x) dx]y(x) = [1 + e^x * C] + [(1 + e^x) * ln|1 + e^x| - e^x + K]Since C = 0, we have:y(x) = (1 + e^x) * ln|1 + e^x| - e^x + K18. Solution of the initial-value problem:y' = x*sqrt((1 - y^2)/(1 - x^2)), y(0) = 0Let y' = f(y, x), and then let's use the initial condition to find the arbitrary constant:C = y(0) = 0Now let's solve for y:y' = x*sqrt((1 - y^2)/(1 - x^2))dy/sqrt(1 - y^2) = x dx/sqrt(1 - x^2)arcsin y = -arcsec x + KSince C = 0, we have:y(x) = sin(-arcsec x)

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Answer:add all of it on the calculator and you will get your awnser

Answer:

$1,475

Step-by-step explanation:

I'm pretty sure this is correct because if she gets an 18% tip, it would mean her payment is multiplied by 1.18.  1,250 times 1.8 equals $1,475.

Hope this helps! ^-^

Also, I'm so sorry for the late response! My internet kept shutting down. :c

2 log4 (x)  is equivalent to log4 (x²) because it simplifies to 2 * log4 (x).

To find which expressions are equivalent to log4 (x²), we need to simplify the logarithmic expression.
Using the properties of logarithms, we know that logb (mn) = n * logb (m).
So, log4 (x²) can be simplified as 2 * log4 (x).
Now, let's check which expressions are equivalent:
1. 2 log4 (1) log4x²: This expression is not equivalent to log4 (x²) because it multiplies log4 (1) with log4x².
2. log4 (1) + log4x²: This expression is not equivalent to log4 (x²) because it adds log4 (1) to log4x².
3. -1 + 2 log4 x: This expression is not equivalent to log4 (x²) because it subtracts 1 from 2 log4 x.
4. -2 + 2 log4 x: This expression is not equivalent to log4 (x²) because it subtracts 2 from 2 log4 x.
5. 2 log4 (x): This expression is equivalent to log4 (x²) because it simplifies to 2 * log4 (x), which is equivalent.
Therefore, the correct answer is: 2 log4 (x).

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Answer:

Coffee(time)

Step-by-step explanation:

A function's output variable will be:

output(input)

So we need to find the input variable and the output variable.

We know that when the time of day changes, we get a certain amount of coffee sold. This means that the amount of coffee sold is directly influenced by the time of day.

The time of day then becomes our input as the coffee sold relies on that number.

That leaves coffee sold as our output!

So the best name for a function in this scenario is Coffee(time).

Hope this helped!

Answer:

1) Perimeter of the parallelogram = 32 cm

2) The angles of the rhombus include 53°, 53°, 127° and 127°.

3) The length of the median drawn to the smaller of the legs = 13 cm

4) The sides of the rectangle are 8 cm and 12 cm

1) Периметр параллелограмма = 32 см

2) Углы ромба включают 53 °, 53 °, 127 ° и 127 °.

3) Длина медианы обращена к меньшей из ног = 13 см.

4) стороны прямоугольника 8 см и 12 см

Step-by-step explanation:

English Translation

1) Find the perimeter of the parallelogram, the sides of which are 5 cm and 11 cm.

2) One of the angles of the rhombus is 53 °. Find the other angles of the rhombus.

3) The legs of a right triangle are 12 cm and 10 cm. Find the length of the median drawn to the smaller of the legs.

4) Find the sides of the rectangle if they are related as 2: 3, and the area of ​​the rectangle is 96 cm².

Solution

1) Find the perimeter of the parallelogram, the sides of which are 5 cm and 11 cm.

A parallelogram has each of its opposite sides to be equal in length.

Perimeter of a parallelogram = 2(l + b)

l = 11 cm

B = 5 cm

Perimeter = 2(11 + 5) = 32 cm

2) One of the angles of the rhombus is 53 °. Find the other angles of the rhombus.

A rhombus is a quadilateral with the sum of its internal angles equal to 360°. Also, opposite angles of a rhombus are equal in magnitude.

Let the unknown other complementary angle be x.

53° + 53° + x + x = 360°

2x + 106° = 360°

2x = 360° - 106° = 254°

x = (254°/2) = 127°

The angles of the rhombus include 53°, 53°, 127° and 127°.

3) The legs of a right triangle are 12 cm and 10 cm. Find the length of the median drawn to the smaller of the legs.

The median is the line drawn from the vertex opposite a triangle's side to the midpoint of that side.

The median described is drawn in the attached image to this question.

From the image, the small triangle is a right angled triangle, hence, the length of the median is given by Pythagoras theorem.

(Median)² = 12² + 5² = 169

median = 13 cm

4) Find the sides of the rectangle if they are related as 2: 3, and the area of ​​the rectangle is 96 cm².

Let the breadth and length of the rectangle be x and y respectively.

x:y = 2:3

(x/y) =(2/3)

x = (2y/3)

Area of a rectangle = length × breadth = x × y = xy = 96

x = (2y/3)

(2y/3) × y = 96

y² = (96×3/2) = 144

y = 12 cm

x = (2y/3) = (2×12/3) = 8 cm

Hope this Helps!!!

when x = 0.5, the value of 4x - 5 is -3. Let's go through the steps to work out the value of 4x - 5 when x = 0.5.

Step 1: Substitute the value of x into the expression.

We are given that x = 0.5, so we replace "x" in the expression 4x - 5 with the value 0.5:

4 * 0.5 - 5

Step 2: Perform the multiplication.

Multiply 4 by 0.5:

4 * 0.5 = 2

Step 3: Perform the subtraction.

Now, subtract 5 from the result obtained in Step 2:

2 - 5 = -3

Step 4: Final result.

The final result is -3.

So, when x = 0.5, the value of 4x - 5 is -3.

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The account will be worth $1534.39 at the end of the second month.

At the end of the first month, you have $1513.78 in your retirement account that pays 3% interest compounded daily. Adding $10 at the beginning of the second month brings the account balance to $1523.78.

Using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (starting balance), r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years, we can calculate the account balance at the end of the second month.

In this case, P = $1523.78, r = 0.03 (3%), n = 365 (daily compounding), and t = 1/6 (two months out of a year).

Plugging in the values, we get:

A = $1523.78(1 + 0.03/365)^(365/6)
A = $1534.39

Therefore, the account will be worth $1534.39 at the end of the second month.

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If the sequence (xn) is bounded but diverges, then there exist two subsequences of (xn) that converge to different limits.

Suppose (xn) is a bounded sequence that diverges. This means that the sequence does not have a single limit as n approaches infinity. However, since the sequence is bounded, it remains within a certain range of values.

By the Bolzano-Weierstrass theorem, any bounded sequence has a convergent subsequence. Therefore, we can select a subsequence (xnk) that converges to some limit L1.

Since the original sequence (xn) diverges, there must exist values in the sequence that are arbitrarily far from the limit L1. We can select another subsequence (xnm) such that the terms in this subsequence are far away from L1.

By the definition of convergence, any subsequence that converges to a limit L is also convergent to L. Therefore, the subsequence (xnk) converges to L1, while the subsequence (xnm) does not converge to L1.

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Answer:

(x - 8)² + (y + 6)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (8, - 6 ) , then

(x - 8)² + (y - (- 6))² = r² , that is

(x - 8)² + (y + 6)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )

r = \(\sqrt{(5-8)^2+(-2-(-6))^2}\)

  = \(\sqrt{(-3)^2+(-2+6)^2}\)

  = \(\sqrt{9+4^2}\)

  = \(\sqrt{9+16}\)

   = \(\sqrt{25}\)

   = 5

Then equation of circle is

(x - 8)² + (y + 6)² = 5² , that is

(x - 8)² + (y + 6)² = 25

Answer: y=3x-5

Step-by-step explanation:

This was the answer i got after solving

Hope that helped :)

Screenshot is the proof of the answer btw :)

The solution of inequality 550 + 8b < 925 is b < 375 / 8 and the graph is attached below.

Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal

Given:

550 + 8b < 925

Solve the inequality by subtracting 550 on both sides,

550 + 8b - 550 < 925 - 550

8b < 375

Divide by 8 into both sides,

b < 375 / 8

The graph of the above inequality is attached below.

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The 98% confidence interval to estimate the average number of hours studying for the exam is approximately 6.61 to 7.99.

Hence option D is correct.

Given that,

Number of students in the statistics class: 115

Sample size: 41 students

Average number of hours studied by the sample: 7.3 hours

Standard deviation of the sample: 1.9 hours

Desired confidence level: 98%

To accurately the problem and calculate the 98% confidence interval,

Use the formula:

Confidence Interval = Sample Mean ± (Z * Standard Error)

Where:

Sample Mean is the average number of hours studied by the sample (7.3 hours).

Z is the critical value corresponding to the desired confidence level (98%). For a 98% confidence level, the Z-value is approximately 2.326.

Standard Error is calculated by dividing the standard deviation of the sample (1.9 hours) by the square root of the sample size (41 students).

Calculate the confidence interval: Standard Error = 1.9 / √41 ≈ 0.2965

Confidence Interval = 7.3 ± (2.326 x 0.2965)

Now, Calculate the upper and lower bounds of the confidence interval:

Upper Bound = 7.3 + (2.326 * 0.2965) ≈ 7.3 + 0.6895 ≈ 7.9895

Lower Bound = 7.3 - (2.326 * 0.2965) ≈ 7.3 - 0.6895 ≈ 6.6105

Therefore, the 98% confidence interval to estimate the average number of hours studying for the exam is approximately 6.61 to 7.99.

Based on the given options, the correct answer would be:

d- 6.11 and 8.49

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The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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7. For sin(x) with x₀ = 0, the Taylor series is given by:
sin(x) = Σ((-1)^n * x^(2n+1))/(2n+1)!
n=0 to infinity

The radius of convergence for sin(x) is infinite.

9. For x with x₀ = 1, the Taylor series is given by:
x = Σ(x - 1)^n
n=0 to 1

The radius of convergence for this series is infinite.

10. For x with x₀ = -1, the Taylor series is given by:
x = Σ(x + 1)^n
n=0 to 1

The radius of convergence for this series is infinite.

13. For 1/(1-x) with x₀ = 2, the Taylor series is given by:
1/(1-x) = Σ(-1)^n * (x - 2)^n
n=0 to infinity

The radius of convergence for this series is 1.

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Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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The solution to the equation is x= -10 and y= 5.

We have Equations,

2x + 6y = 10............(1)

3x - 2y = -40............(2)

Now, solving equation (1) and (2) we get

2x + 6y = 10

9x - 6y = -120

+    +       +

__________

   11x = -110

      x = -10

and, 3(-10) - 2y= -40

-30 - 2y= -40

-2y = -10

y=5

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Answer:

about 52 feet

Step-by-step explanation:

The figure is omitted--you may draw it to confirm my answer.

sin (38°) = 32/x

x sin (38°) = 32

x = 32 / sin (38°) = about 52 feet

Answer:

create common denominator

Step-by-step explanation:

1/4 can become 2/8 by multiplying the top and bottom number by 2 now you have a common denominator to add 2/8+3/8 = 5/8

Answer:

x = 5

Step-by-step explanation:

The opposite sides of a rectangle are equal , then perimeter

2(- 2x - 6) + 2(4x + 4) = 16 ← distribute parenthesis and simplify left side

- 4x - 12 + 8x + 8 = 16

4x - 4 = 16 ( add 4 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

x=1/4

Step-by-step explanation:

perimeter of a rectangle

2(L+w)

-2x-6(4x+4)

open the bracket

-2x(4x+4)-6(4x+4)

-8x^2-8x-24x-24

-8x^2-32x-24

2(-8x^2-32x-24)

-16x^2-64x-48

coefficient of x is 64

16=64x

x=1/4

Answer:

see explanation

Step-by-step explanation:

By the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0

if (r - 4) is a factor then substituting r = 4 into the polynomial should result in it having a value of zero, that is

6\(r^{4}\) - 17r³ - 46r² + 77r - 20 ( substitute r = 4 )

= 6\((4)^{4}\) - 17(4)³ - 46(4)² + 77(4) - 20

= 6(256) - 17(64) - 46(16) + 308 - 20

= 1536 - 1088 - 736 + 288

= 0

Then (r - 4) is a factor of the polynomial