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Unit 7: Polygons & Quadrilaterals


Homework 3: Parallelogram Proofs

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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The probability of not getting any aces when dealt a hand of three cards from a deck is approximately 0.782 or 78.2%.

In a standard deck of 52 cards, there are four aces. When dealt a hand of three cards, we want to find the probability of not getting any aces.

The total number of possible outcomes is given by the number of ways to choose three cards out of 52, which can be calculated using combinations. Therefore, the total number of possible outcomes is C(52, 3) = 22,100.

To determine the number of favorable outcomes, we need to count the number of hands without any aces. Since there are four aces in the deck, there are 48 non-ace cards. Therefore, the number of favorable outcomes is C(48, 3) = 17,296.

Finally, the probability of not getting any aces can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes = 17,296 / 22,100 ≈ 0.782 or 78.2%.

Hence, the probability of not getting any aces when dealt a hand of three cards from a deck is approximately 0.782 or 78.2%.

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Answer:

$5 is the answer.......

Answer:

one box cost is $5

Step-by-step explanation:

$25 - $5 = $20 - this is the cos of four cereal boxes

$20 / 4 = $5 each box cost

Answer:

-2 <= x <= 1/3

Step-by-step explanation:

it is the same as for equations.

the solution for a square equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

our parameters here are

a = 3

b = 5

c = -2

so,

x = (-5 ± sqrt(25 - -24))/6 = (-5 ± sqrt(49))/6 = (-5 ± 7)/6

x1 = (-5 + 7)/6 = 2/6 = 1/3

x2 = (-5 - 7)/6 = -12/6 = -2

since we are looking for smaller or equal, points of 0 will be part of the solution.

now we need to check each side of these points on the x-axis, if they are true or not to the inequality.

left of -2 : let's pick -3

3×(-3)² + 5×-3 -2 = 3×9 - 15 - 2 = 27 - 15 -2 = 10

this is NOT <= 0, so this interval does not fit.

similar, right of 1/3 : let's pick 1

3×1² + 5×1 - 2 = 3 + 5 - 2 = 6

this is NOT <= 0, so this interval does not fit either (as expected, as normally either both sides fit, or both fail).

lastly, in the middle between -2 and 1/3 : let's pick 0

3×0² + 5×0 - 2 = -2

this IS <= 0, so the interval between -2 and 1/3 fits.

The time length of the warranty should be approximately 1.515 times the mean life of the timepiece. To calculate the time length of warranty so that only 1.9% of the the quartz timepieces will be replaced before warranty expires, we use the formula: P(X ≤ x) = 0.019 Where P(X ≤ x) is the probability of failure before the warranty expires.

Let X be the number of months after purchase before a timepiece fails, and let m be the mean life of a timepiece. Then, the standard deviation of the life of a timepiece is σ = 0.25m (given). Also, the probability that a timepiece fails before the warranty expires is 0.019, which means that the probability of success is 1 - 0.019 = 0.981.

Using the standard normal table, we can find the Z-score such that the area to the left of Z is 0.981. From the table, we find that Z ≈ 2.06 (rounded to two decimal places).Therefore, Z = (x - m) / σ implies

x = σZ + m

≈ 0.515m + m

= 1.515m (since σ = 0.25m and Z = 2.06).

Thus, the time length of the warranty should be approximately 1.515 times the mean life of the timepiece.

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Answer:

see the picture

Step-by-step explanation:

By the below figure (6) is the initial equation

(1) next added (b/2a)^2 on both sides to make it whole square on left side which gives (4) in (4) both terms are added on the right side to make it (5)

then square root on both sides gives (2) and now taking b/2a to the right side gives the final quadratic formula (3)

We can obtain the quadratic formula from completing the square method as shown.

The quadratic formula is derived from the completing the square method as follows;

Given the quadratic equation;

\(ax^{2} + bx + c =0\)

Dividing through by a we have;

\(x^{2} + \frac{b}{a} + \frac{c}{a} = 0\)

Adding half of b to both sides of the equation, we have;

\((x + \frac{b}{a}) ^{2} = \frac{-c}{a} + \frac{b^2}{4a^2}\)

Taking LCM of the right hand side;

\((x + \frac{b}{2a})^{2} = \frac{b^2 - 4ac}{4a^2}\)

Making x the subject of the formula;

\(x = \frac{-b + \sqrt{b^2 - 4ac} }{2a}\)

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Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution.

Based on the data they have available, sampling distributions are useful tools used by researchers to estimate and draw conclusions about a wider population of interest.

Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

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The probability will be 0.037 or 3.7% when it is rounded to the nearest tenth.

To calculate the probability of hitting the clown's mouth, we need to compare the area of the clown's mouth to the total area of the rectangular wood piece.

The area of the clown's mouth can be found using the formula for the area of a circle: A = π * (r^2), where r is the radius. In this case, the diameter is given as 3 inches, so the radius is 1.5 inches.

Plugging the values into the formula, we get A = π * (1.5^2) = 7.065 square inches. The total area of the rectangular wood piece is 16 inches * 12 inches = 192 square inches.

Therefore, the probability of hitting the clown's mouth is 7.065 / 192 ≈ 0.0367, which rounds to 0.037 or 3.7% when expressed as a percentage rounded to the nearest tenth.

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Answer:

D. 73.6 ft^2

Step-by-step explanation:

Using trigonometry to get our answer: (we can use SAS to find the area)

A = 0.5 * side a (10ft) * side b (16ft) * sin(67)

A = 80 ft * sin(67)

A = 73.64 ft

Answer:

(A) AA Similarity Theorem

Step-by-step explanation:

Given: AB ∥ DE

To Prove: \(\triangle ACB \sim \triangle DCE\)

Given Triangle ABC with Line DE drawn inside of the triangle and parallel to side AB. The line DE forms a new triangle DCE.

Because AB∥DE and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines.

Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA.

We can state ∠C ≅ ∠C using the reflexive property.

Therefore, \(\triangle ACB \sim \triangle DCE\) by the AA similarity theorem.

Remark: In the diagram, we can see that the two triangles share Angle C and have two equal angles at E and B. Therefore, they are similar by the Angle-Angle Similarity Theorem.

Answer:

A

Step-by-step explanation:

Answer:

i think its the 3rd

Step-by-step explanation:i think

Answer:

A) 1962.5

Step-by-step explanation:

Area= pie r^2

50/2=25

25x25=625

625x3.14=1962.5

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

To find all of the cube roots of ii and write the answers in rectangular form, we need to first express ii in polar form. To do this, we can convert ii to its polar form by writing it as a complex number in the form r(cosθ + isinθ), where r is the magnitude and θ is the argument.

In this case, we have ii = 1(cos(π/2) + isin(π/2)).  The magnitude of ii is 1, and the argument is π/2.  Now, to find the cube roots, we need to find the numbers that, when raised to the power of 3, give us ii. To find the cube roots, we can use De Moivre's theorem, which states that for any complex number z = r(cosθ + isinθ), the nth roots of z can be found by taking the nth root of the magnitude and dividing the argument by n.

In this case, we have n = 3, r = 1, and θ = π/2.  Taking the cube root of the magnitude 1 gives us 1^(1/3) = 1. Dividing the argument π/2 by 3 gives us (π/2) / 3 = π/6. So, the first cube root is 1(cos(π/6) + isin(π/6)). To find the other cube roots, we can add multiples of 2π/3 to the argument. Adding 2π/3 to π/6 gives us π/6 + 2π/3 = π/2. So, the second cube root is 1(cos(π/2) + isin(π/2)), which is equal to ii. Adding another 2π/3 gives us π/2 + 2π/3 = 7π/6. So, the third cube root is 1(cos(7π/6) + isin(7π/6)). Therefore, the cube roots of ii in rectangular .

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Answer:

21.25=4.25p

Step-by-step explanation:

Ms. diaz buys strawberries by the pound at a farmer's market. she pays $21.25 for all her

strawberries. one pound of strawberries costs $4.25.

1/5

The equation to represent the situation is 4.25p=21.25.

Ms. Diaz buys 5 pounds of strawberries.

A mathematical statement that is made up of two expressions connected by an equal sign.

Given:

Mr. Diaz pays for strawberries = $21.25

price for one pounds = $4.25

Then,

Number of pounds * cost  = Total cost for strawberries.

p * 4.25 = 21.25

p = 21.25 / 4.25

p = 5

Hence, the equation that can represent 4.25p=21.25

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By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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Answer:

37°

Step-by-step explanation:

ΔOPQ extended trough Q to R

m∠PQR = (7x-19)° -is an exterior angle to the triangle

m∠OPQ = (2x-3)° -angle inside the triangle

m∠QOP = (x+16)° -angle inside the triangle

m∠PQR = ?

m∠PQR = m∠OPQ + m∠QOP

7x-19 = 2x-3 +x+16

7x -2x-x = 16-3+19

4x = 32

x=32/4=8

m∠PQR = 7x-19 = 7*8-19  =56 -19= 37°

Answer:

82 in

Step-by-step explanation:

Answer:

correct me if I am wrong! but, for finding the perimeter of a figure.. wouldn't you have to add up all of the sides? I'm just gonna that it'd be 82in.

Answer:

609638400 ways

Step-by-step explanation:

For 8 men in a line: 8! = 40320

  O   O   O   O   O   O   O   O  

1     2    3    4   5    6   7     8   9 ... in order to separate 2 women, there are 9 vacant places for 5 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways: 40320 * 126 * 120 = 609638400

Answer: 9

Step-by-step explanation:

15c+3d=

15(1)+3(-2)=

15+(-6)=9

Answer:

9

Step-by-step explanation:

\(15c + 3d \\ \\ = 15 \times 1 + 3 \times (-2) \\ \\ = 15 - 6 \\ \\ = 9\)

Answer:

48 meters.

Step-by-step explanation:

The perimeter of a parallelogram is given by the formula:

\(P=2(a+b)\)

Where a is the measure of the length (top), and b is the measure of the slant height (side).

We know that the perimeter is 102.

We also know that the top is 3.

So, let’s substitute 102 for P and 3 for a and solve for b, the side. So:

\(102=2(3+b)\)

Divide both sides by 2:

\(51=3+b\)

Subtract 3 from both sides:

\(b=48\text{ meters}\)

Therefore, the side measures 48 meters.

Answer: 214

Step-by-step explanation:

The circumference of a circle measures 360 degrees, and since minor arc EF measures 146 degrees, this means arc EDF measures \(360-146=214^{\circ}\)

arc EDF measures is 214°

The arc is a portion of the circumference of a circle

The circumference of a circle measures 360°,

Since minor arc EF measures 146°,

arc EDF measures = 360°-146° = 214°

Hence, arc EDF measures is 214°

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The vertical distance between the max in the window and the maximum height of the ball is about 55.16 feet.

To determine the vertical distance between the maximum height of the ball and the window in the building, we need to know the maximum height the ball reaches.

A projectile is an object that moves in a parabolic path under the influence of gravity. The maximum height of a projectile is reached when its vertical velocity is zero. The vertical velocity of a projectile depends on its initial velocity and the angle of launch.

According to the web search results, the formula for the maximum height of a projectile is:

H=2gu2sin2θ​

where H is the maximum height, u is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

In this question, we are given that the window in the building is 55 feet above the ground, and the ball is thrown vertically from the window. This means that the angle of launch is 90 degrees, and the initial velocity is unknown. We can use the formula to find the initial velocity:

H=2gu2sin290​

55=2(32)u2​

u2=55×64

u=55×64​

u≈59.16 feet per second

Now that we have the initial velocity, we can use it to find the maximum height of the ball above the ground. We can use the same formula, but this time we need to add 55 feet to the result, since that is the height of the window from the ground:

H=2gu2sin290​+55

H=2(32)(59.16)2​+55

H≈110.16 feet

Therefore, the maximum height of the ball above the ground is about 110.16 feet.

The vertical distance between the max in the window and the maximum height of the ball is simply the difference between these two heights:

D=H−55

D=110.16−55

D≈55.16 feet

Therefore, the vertical distance between the max in the window and the maximum height of the ball is about 55.16 feet.

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Answer:

6

Step-by-step explanation:

Given the data:

1, 3, 2, 2, 1, 3, 3, 1

The mean absolute deviation :

Sum of (1, 3, 2, 2, 1, 3, 3, 1) = 16

Mean = 16 / 8 = 2

Mean absolute deviation :

|1 - 2|+ |3 - 2| + |2 - 2| + |2 - 2| + |1 - 2| +|3 - 2| + |3 - 2| + |1 - 2|

= 1 + 1 + 0 + 0 + 1 + 1 + 1 + 1

= 6

An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent means that the investment has a higher potential for return, but also a higher risk.

The standard deviation is a measure of the variation or dispersion of a set of data values. In this case, the standard deviation of 8 percent indicates the degree of variation in the investment returns. A higher standard deviation means that the investment returns are more spread out and there is a higher chance of extreme values, both positive and negative.

In terms of investment strategy, it is important to consider the trade-off between risk and return. While a higher expected return is desirable, it often comes with a higher level of risk. Therefore, it is important to carefully consider the standard deviation and the potential risks associated with an investment before making a decision.

In conclusion, an investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

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The value of the linear correlation coefficient, r, as calculated using Microsoft excel is: 0.708,

The linear correlation coefficient, r, using Excel spreadsheet

Step1: Open Microsoft excel spreadsheet

Step2: Entre the cost of advertising on one column, and the number of products sold on another column.

Step3: Select a blank cell and input the formula: =CORREL(B3:B10, C3:C10)

Step4: Press "entre" to get the value of the linear correlation coefficient.

Therefore, the value of the linear correlation coefficient, r, as calculated using Microsoft excel is 0.708.

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Answer:

A=31 MILLION b=135%c=235%

Step-by-step explanation:

Answer:

a =  

✔ 31 million

31

23

≈ 1.347

b ≈  

✔ 135%

c ≈  

✔ 235%

Step-by-step explanation:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

What is Linear Inequality?

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

Solution:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

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Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

According to question:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

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