Find the measure of each angle of a regular polygon with 8 sides.​

Answer:

26

Step-by-step explanation:

let the two numbers be X and Y

XY = 144

X - Y = 10

(X + Y)^2 = ( X - Y)^2 + 4 XY

= 100 + 576 = 676

(X+Y) = √676

X + Y = 26

We have that, when testing a certain type of truck tire on rough terrain, it is observed that 25% of the trucks fail to complete the test without blowout, the probability that of the next 15 trucks tested, at least one will not able to complete the test run without an explosion is 0.987

Given that when testing a certain type of truck tire on rough terrain, it is found that 25% of the trucks do not complete the test without blowout.So, the probability that a truck completes the test without a blowout is:

P (A complete truck test without blowout) = 1 - P (A complete truck test without an explosion) = 1 - 0.25 = 0.75

Now, we need to find the probability that of the next 15 trucks tested, at least one will not complete the test without an explosion. This can be found using the complement rule. The complement of the probability that at least one truck does not complete the test without a blowout is the probability that all 15 trucks complete the test without a blowout.

P(All 15 trucks complete the test without a blowout) = P(One truck completes the test without a blowout) x P(A second truck completes the test without a blowout) x ... x P(The fifteenth truck completes the test without a blowout) = 0.75 x 0.75 x ... x 0.75 (15 times)= 0.75^15= 0.013

But we need the probability that at least one truck fails to complete the test without a blowout, which is the complement of the above probability.

P(At least one truck does not complete the test without blowout) = 1 - P(All 15 trucks complete the test without blowout)= 1 - 0.013= 0.987

Therefore, the probability that of the next 15 trucks tested, at least one will not be able to complete the test run without an explosion is 0.987.

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Answer:

0.667

Step-by-step explanation:

According to Bayes theorem:

Since there are three cards, the probability that the side is green = 1/3

For the first card, if one side is green, the probability that the other side is also green = 1 (both sides are green)

For the second card, if one side is green, the probability that the other side is also green = 0 (both sides are red)

For the third card, if one side is green, the probability that the other side is also green = 1/2 (one side is green and the other side is red)

\(P(G_k/A)=\frac{P(G_k)P(A/G_k)}{\Sigma_{i=1\ to\ m} P(G_i)P(A/G_i)} \\P(B_1/A)=\frac{P(G_1)P(A/G_1)}{P(G_1)P(A/G_1)+P(G_2)P(A/B_2)+P(G_3)P(A/G_3)}\\ P(B_1/A)=\frac{1/3*1}{(1/3*1)+(1/3*0)+(1/3*1/2)=\frac{1/3}{1/2} }=0.667\)

The solution which we get for the given question is , x = 5/2 and y = 5/4 answer.

Isolating x,

2x = 9x - 14y

2x-9x = 9x-9x -14y

-7x = -14y

-7x/-7 = -14y/-7

x = 2y

Therefore substituting value of x on equation 2,

9(2y) = 40 - 14y

18y = 40 - 14y

18y+14y = 40 -14y+14y

32y = 40

32y/32 = 40/32

y = 5/4

Therefore , x = 10/4 = 5/2

as because x =2y.

An equation is a mathematical statement which equated two value using the equal sign. Eg.) 2x = y

These expressions on either side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. The generality will still be there as  because we can balance it by subtracting the right-hand side expression from the expressions on both sides.

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The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

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\(|c|^2 + |c'|^2 = 1\)

This is the condition that the complex constants c and c' must satisfy in order for the wave function to be normalized.

To normalize the given wave function, we need to ensure that the total probability of finding the particle in the box is equal to one. Mathematically, this means that the integral of the absolute square of the wave function over the entire box must be equal to one.

The normalized wave function is given by:

Ψ_norm(x) = AΨ(x) = A[cΨn(x) + c'Ψn'(x)]

where A is a normalization constant.

To find the value of A, we use the orthogonality property of the stationary states Ψn(x) and Ψn'(x) of the particle in a box. The property states that:

∫Ψn(x)Ψn'(x) dx = 0 (for n ≠ n')

Using this property, we can calculate the value of A as follows:

1 = ∫|Ψ_norm(x)|² dx

= A²[|c|²∫|Ψn(x)|² dx + |c'|²∫|Ψn'(x)|² dx + cc'∫Ψn(x)Ψn'(x) dx + cc'∫Ψn'(x)Ψn(x) dx]

= A²[|c|² + |c'|² + 2Re(c*c'∫Ψn(x)Ψn'(x) dx)]

= A²[|c|² + |c'|²] (as ∫Ψn(x)Ψn'(x) dx = 0)

Therefore, the normalization constant is:

A = [(|c|² + |c'|²)]\(^{(-1/2)\)

This means that the complex constants c and c' must satisfy the condition:

|c|² + |c'|² = 1

Interpretation:

The above result means that for the wave function Ψ(x) to be normalized, the complex constants c and c' must satisfy the condition that the sum of the absolute squares of their magnitudes is equal to one. This is a manifestation of the conservation of probability in quantum mechanics. It ensures that the total probability of finding the particle in the box is always equal to one, irrespective of the state of the particle described by the wave function.

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This is the condition that the complex constants c and c' must satisfy in order for the wave function to be normalized. So |c|² + |c'|² + 2Re(c*c') = 1

To obtain this result, we first use the orthogonality of the stationary states Ψn(x) and Ψn'(x), which means that

Then, we normalize the superposition wave function by requiring that

Expanding this expression and using the orthogonality relation, we obtain the above normalization condition.

This result shows that the complex constants c and c' must satisfy a certain constraint in order for the wave function to be normalized. This means that the probability of finding the particle in the box must be equal to 1, which is a fundamental requirement of quantum mechanics. The result also shows that the interference between the two stationary states Ψn(x) and Ψn'(x) is characterized by the phase difference between the complex constants c and c'.

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Answer:

His hourly rate is $8.15.

Step-by-step explanation:

The hourly rate is how much he earns in one hour. We know how much he earns in 42 hours ($342.3).

So what we need to do is to divide that amount ($342.3) by 42.

And we get $8.15.

Answer:

c

Step-by-step explanation:

they share the same min of -3

Answer:

The minimum values are equal

Step-by-step explanation:

The minimum for f(x) = (4,-3)  since the parabola is written in vertex form

y = a(x-h)^2 +k

The minimum is at x=4 the the y value is -3

Looking at the graph for g(x) the minimum is at x=-3 y = -3

Since the y values are equal

The minimum values are equal

Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

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The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

Total number of squares = 10×8 = 80

Total number of squares shaded = 36

Percentage of the model is shaded = (36/80)×100

= 0.45×100

= 45%

Thus, the percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

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This verifies that y = cos(4x) also satisfies the differential equation.

The given solutions satisfy the differential equation.

The given differential equation is y'' + 16y = 0, and the proposed solutions are y = sin(4x) and y = cos(4x). To verify, we need to find the second derivative (y'') of each solution and plug it into the equation.

For y = sin(4x), the first derivative (y') is 4cos(4x) and the second derivative (y'') is -16sin(4x). Now, substitute y and y'' into the equation: (-16sin(4x)) + 16(sin(4x)) = 0, which simplifies to 0 = 0. This verifies that y = sin(4x) satisfies the differential equation.

For y = cos(4x), the first derivative (y') is -4sin(4x) and the second derivative (y'') is -16cos(4x). Substitute y and y'' into the equation: (-16cos(4x)) + 16(cos(4x)) = 0, which simplifies to 0 = 0.

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After 30 years of 8.8% interest compounded monthly, an account has $4,000,000,he original deposit amount was $288,208.04

Compound Interest :

                          Compound interest is a form of interest calculated using the principal amount of a deposit  plus previously accrued interest.

  general formula for compound interest is

                             A = P (1 + r/n) ^ nt

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

According to question,

Given final amount is (A) =  $4,000,000

time (t) = 30 years

Rate of interest (r) = 8.8%

                                = 8.8/100

                                = 0.088  , Compounded monthly

Let P be the principal amount

    using the formula for compound interest compounded monthly,

         A = P (1 + r/12)^12*t

or,

         P = A/(1 + r/12)^12*t

             Substituting all values we get,

            P =   $4,000,000/ (1 + 0.088/12)^12 x 30

                = $4,000,000/13.8788

                = $288,209.35

                ≈ $288,208.04

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Answer:

R

Step-by-step explanation:

1/2(2r+4)-1/4(16-8)

r+2 - 1/4(8)

r+2-2

r

Answer:

y=\(-2x^{3}\)-9

Step-by-step explanation:

Answer:

48.16

167.68

Step-by-step explanation:

New value =

36 - Percentage decrease =

36 - (14% × 36) =

36 - 14% × 36 =

(1 - 14%) × 36 =

(100% - 14%) × 36 =

86% × 36 =

86 ÷ 100 × 36 =

86 × 36 ÷ 100 =

3,096 ÷ 100 =

30.96

New value =

262 - Percentage decrease =

262 - (36% × 262) =

262 - 36% × 262 =

(1 - 36%) × 262 =

(100% - 36%) × 262 =

64% × 262 =

64 ÷ 100 × 262 =

64 × 262 ÷ 100 =

16,768 ÷ 100 =

167.68

The equation x² y² = 4 corresponds to a hyperbola when only considering x and y as variables. When considering x, y, and z as variables, the equation corresponds to a two-sheeted hyperboloid.

a) When only x and y are the variables being considered, the equation x² y² = 4 corresponds to a circle in the xy-plane. The circle has a center at the origin (0,0) and a radius of 2.

b) If x, y, and z are the only variables being considered, the equation x² y² = 4 still represents a circle in the xy-plane, but it becomes a cylinder along the z-axis. This cylinder has a center on the z-axis and a radius of 2, extending infinitely along the z-axis.

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Answer:

1.odd 2. even this is the answer

Brandon is currently 6 81 years old.

Let M be Michael's age and B be Brandon's age.

We are given that Michael is 3 33 times as old as Brandon. This means that M = 3 33 × B

We are also given that 18 1818 years ago, Michael was 9 99 times as old as Brandon. This means that M - 18 1818 = 9 99 × (B - 18 1818).

We can combine these two equations to solve for Brandon's current age:

3 33 × B = (9 99 × B) + 18 1818

2 66 × B = 18 1818

B = 18 1818 / 2 66 = 6 81.

Therefore, Brandon is currently 6 81 years old.

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Answer:

$3.50

Step-by-step explanation:

if you divide 42 by 12 you get 3.5

The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y = 0.7979e^-(x-5.4)^2/0.5\), where x is the number of hours.

The normal distribution is a bell-shaped curve that is often used to model real-world data. In this case, the normal distribution is used to model the amount of time that students spend at the math-tutoring center. The peak of the bell-shaped curve represents the average amount of time that students spend at the center, which is 5.4 hours per week. The tails of the bell-shaped curve represent the amount of time that students spend at the center that is less than or greater than the average amount of time.

The standard deviation of the normal distribution is 0.5 hours. This means that about 68% of the students spend between 4.9 and 6 hours at the center per week. About 16% of the students spend less than 4.9 hours at the center per week, and about 16% of the students spend more than 6 hours at the center per week.

The normal distribution is a useful tool for understanding the amount of time that students spend at the math-tutoring center. It can be used to estimate the average amount of time that students spend at the center, and it can be used to determine the amount of time that students spend at the center that is less than or greater than the average amount of time.

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Answer:

Step-by-step explanation:

7R - 6 + 4R + 7 = 5X + R

A. 2,5

B. 141

C. 12, + 5+1

D. 124 + 47+1​

THE ANSWER IS

11R + 1 = 5X + R

Answer:

1

Step-by-step explanation:

10 divided by 10 = 1

anything divided by itself is 1

The Venn diagram can be used to visually represent the population and the sample, allowing for a clear identification of both entities within a given context.

A Venn diagram is a graphical representation that uses overlapping circles to illustrate the relationships between different sets. It can be helpful in identifying the population and the sample in a given context. In a Venn diagram, the population refers to the entire set or group being studied. It represents the complete collection of individuals or elements that the researcher wants to draw conclusions about. The population is typically represented by the universal set encompassing all the circles in the Venn diagram.

On the other hand, a sample is a subset or a smaller portion of the population that is selected for observation or data collection. It represents a representative portion of the population and is often used to make inferences or draw conclusions about the larger population. In the Venn diagram, the sample would be represented by the specific area or overlap between the circles that corresponds to the selected subset of the population. It is important to note that the sample is derived from the population and should ideally be representative of it to ensure the validity of any conclusions drawn.

By utilizing the Venn diagram, researchers can visually distinguish the population from the sample, aiding in understanding the relationships and subsets within the given study context.

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The equation in slope-intercept form for the line that is perpendicular to the line y = -3x-8 that passes through (-3,1) is y = x/3+2.

According to the question,

We have the following information:

The line is y = -3x-8

Points are (-3,1).

Now, we know that the slope, denoted by m, in this equation is -3.

Now, the slope for the perpendicular line is -1/m.

So, the slope is 1/3.

Now, the equation that can be found using the given information is:

(y-y') = m(x-x')

y' = 1 and x' = -3

(y-1) = 1/3 [x-(-3)]

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

(y-1) = x/3 +1

y = x/3 + 1 +1

y = x/3+2

Hence, the equation in slope-intercept form is y = x/3+2.

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if f(x)=2x+2

and f(x)= -1

2(-1) +2

-2 + 2 =0

the value would be 0

Answer:

The slope is 1/2  :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(10 - 4)/(13 - 1) = 6/12 = 1/2 is the slope of the line

The situation in which the quantities combine to make 0 is "On Monday, Huang withdraws $30 from a bank account. On Friday, she deposits $30 into the account".

For two quantities two make 0, it is necessary to add two numbers with the same value but different sign (positive or negative). Here is an example:

For example if you buy 10 apples but use 10 apples to make a pie.

Based on this, the correct situation is "On Monday, Huang withdraws $30 from a bank account..." as -30 + 30 = 0.

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Answer:

see below

Step-by-step explanation:

oh my gosh im in this unit at school

one of the ways to prove parrallogram, is to prove that the opposide sides are congruent

in a proof (at my school) you would use: "opp sides congruent --> //gram"

they give you that the two triangles are congruent

you can then say ST congruent to WR by CPCTC (corresponding parts congruent triangles congruent)

same with SR congruent to WT

once you have the two opposite sides that are congruent, you can use opp sides congruent --> //gram to prove RSTW is //gram

proof would look something like:

1 given triangle TRS congruent triangle RTW (ref given, given)

2 ST congruent WR (ref 1, CPCTC)

3 SR congruent WT (ref 1, CPCTC)

4 RSTW is //gram (ref 2,3,F, opp sides congruent --> //gram)

hope this helps !!

From the 3 statements given about the quadrilateral RSTW, It has been proved that it is; A Parallelogram

1) We are given that;

ΔTRS ≅ ΔRTW

2) Since ΔTRS is congruent to ΔRTW , then we can say that;

ST ≅ WR due to the fact that corresponding parts of congruent triangles are congruent (CPCTC)

3) From statement 2 above, we can also say that;

SR ≅ WT (CPCTC)

4) From the 3 statements above, we can conclude that;

RSTW is a parallelogram.

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The required perimeter of parallelogram FGHI is approximately 17.5 units.

To find the perimeter of parallelogram FGHI, we need to find the length of all four sides and add them together.

First, we can find the length of side FG by using the distance formula:

FG = √[(5-1)² + (2-2)²] = √16 = 4

Similarly, we can find the length of side HI:

HI = √[(8-4)² + (9-9)²] = √16 = 4

Since FG and HI are opposite sides of a parallelogram, they have the same length.

Next, we can find the length of side GH:

GH = √[(8-5)² + (9-2)²] = √74

Finally, we can find the length of side IF:

IF = √[(4-1)² + (9-2)²] = √74

Since GH and IF are also opposite sides of a parallelogram, they have the same length.

So the perimeter of parallelogram FGHI is:

Perimeter = FG + GH + HI + IF

Perimeter = 4 + √74 + 4 + √74

Perimeter ≈ 17.5 (rounded to the nearest tenth)

Therefore, the perimeter of parallelogram FGHI is approximately 17.5 units.

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