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Proving the Parallelogram Side Theorem
Given: ABCD is a parallelogram.
Prove: AB CD and BC = DA
A
□
Hint
Angles Segments Triangles Statements Reasons
ASA
CPCTC
reflexive property
given
Statements
✓ 3. BC || DA
4. draw AC
✔✓ 5. AC AC
SE
6. BCA and DAC
are alt. interior angles
7. DAC
✓8. ZDCA and are alt. interior angles/
DCA
✓9. Reasons
3. def. of parallelogram
4. unique line postulate
5. reflexive property
6. def. of alt. interior angles
7. alternate interior angles theorem
8. def. of alt. interior angles
9. alternate interior angles theorem

To put the equation 3y - 9x = -6 into slope-intercept form, we need to isolate y on one side of the equation.

First, we will add 9x to both sides:

3y - 9x + 9x = 9x - 6

Simplifying the left side of the equation:

3y = 9x - 6

Next, we will divide both sides by 3:

y = 3x - 2

This is the equation in slope-intercept form, where the slope is 3 and the y-intercept is -2.

The missing length is 8m which is option A.

To find the missing length, we need to use the formula for the area of a rectangle:

area = length x width

We are given the area as 114 m² and the width as 15 m. Let's substitute these values into the formula:

114 = length x 15

Solving for length, we get:

length = 114/15

length = 7.6

Therefore, the missing length is approximately 7.6 m.

However, none of the given answer choices match this value exactly. The closest answer is A. 8 m, which is off by only 0.4 m. Therefore, A. 8 m is the best answer choice.

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Coach A can make 120 free throws in 3 minutes for number of free throws that Coach A can make varies directly with the amount of times she spends shooting the baskets.

A mathematical connection when two variables are involved in which the ratio of their values is constant is known as direct variation. Alternatively said, if one variable is multiplied by a specific amount, the second variable will also be multiplied by the same value. The two variables in this connection may be represented as a percentage, where the constant of proportionality is the ratio of their values, and the two variables are on opposite sides of an equal sign.

Given that, she can make 20 baskets in 30 seconds.

Thus, using proportion we have:

Free throws / Time = Free throws per unit time

20 baskets / 30 seconds = 2/3 baskets per second

Now, for 3 minutes or 3(60)n= 180 seconds we have:

Free throws = Time x Free throws per unit time

Free throws = 180 seconds x (2/3 baskets per second)

Free throws = 120 baskets

Hence, Coach A can make 120 free throws in 3 minutes.

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Answer:

Step-by-step explanation:

mass=density* volume

78.12

To find the equation of a line parallel to y = x - 5 that goes through (7,0), we need to use the fact that parallel lines have the same slope.

The slope of the line y = x - 5 is 1, since the coefficient of x is 1. Therefore, the slope of the parallel line we want to find is also 1.

Using the point-slope form of a line, we can write the equation of the parallel line as:

y - y1 = m(x - x1)

where (x1, y1) is the point (7,0) and m is the slope of the line, which we know is 1.

Plugging in the values, we get:

y - 0 = 1(x - 7)

Simplifying, we get:

y = x - 7

Therefore, the equation of the line parallel to y = x - 5 that goes through (7,0) is y = x - 7.

Answer:

y = x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 5 ← is in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes , then

y = x + c ← is the partial equation

to find c substitute (7, 0 ) into the partial equation

0 = 7 + c ( subtract 7 from both sides )

- 7 = c

y = x - 7 ← equation of parallel line

The height of the building is 87.5 feet.

To find the height of the building, we will use similar triangles.
1. Draw a diagram with a right triangle formed by the basketball player, the mirror, and the top of the building.

Label the height of the building as 'h', the distance between the mirror and the building as 100 ft, and the distance between the mirror and the basketball player as 8 ft.
2. Draw another right triangle formed by the basketball player, the mirror, and the ground. Label the height of the basketball player as 7 ft.
3. Since the two triangles are similar, we can write the following proportion:

(height of the building) / (distance between mirror and building) = (height of basketball player) / (distance between mirror and basketball player)
4. Plug in the values: h / 100 = 7 / 8
5. To solve for the height 'h', multiply both sides by 100: h = (7 / 8) * 100
6. Calculate the value of 'h': h = 87.5 ft
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Answer:

d

Step-by-step explanation:

12 - 9.5 = 2.5

After four iterations of drawing and replacing balls, the probability that the urn contains three red and three blue balls is 1/3. so, the correct answer is D).

Let's consider the possible outcomes after each iteration of the process. We will use R and B to denote a red and blue ball, respectively.

After the first iteration, we have two possible outcomes:

R, R: The urn contains two red balls.

B, B: The urn contains two blue balls.

After the second iteration, we have four possible outcomes:

R, R, R, R: The urn contains four red balls.

R, R, B, B: The urn contains two red balls and two blue balls.

B, B, B, B: The urn contains four blue balls.

B, B, R, R: The urn contains two red balls and two blue balls.

After the third iteration, we have six possible outcomes:

R, R, R, R, R, R: The urn contains six red balls.

R, R, R, B, B, B: The urn contains three red balls and three blue balls.

R, R, B, B, R, R: The urn contains four red balls and two blue balls.

R, R, B, B, B, B: The urn contains three red balls and three blue balls.

B, B, B, B, B, B: The urn contains six blue balls.

B, B, R, R, B, B: The urn contains four blue balls and two red balls.

After the fourth iteration, we have six possible outcomes, one for each of the outcomes after the third iteration. In particular, we are interested in the outcomes where the urn contains three red balls and three blue balls, which occur in two of the six outcomes.

Therefore, the probability that the urn contains three balls of each color after the four iterations is 2/6 = 1/3, which is answer choice (d).

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--The given question is incorrect, the correct question is given

" an urn contains one red ball and one blue ball. a box of extra red and blue balls lie nearby. george performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. after the four iterations the urn contains six balls. what is the probability that the urn contains three balls of each color?(2020amc10b problem 18) (a) 16 (b) 1/5 (c) 1/4 (d) 1/3 (e) 12 "--

Answer:

you need an equally

Step-by-step explanation:

The probability that Joe will be accepted at one, and only one, the university is E. 0.45.

The probability that Joe will be accepted at one, and only one, university can be calculated using the following approach. First, we need to find the probability of Joe being accepted at each university individually and the probability of him not being accepted at each university. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.

Let's use the following notations:

P(A) - probability of being accepted at University A

P(B) - probability of being accepted at University B

P(A') - probability of not being accepted at University A

P(B') - probability of not being accepted at University B

We are given:

P(A) = 0.25

P(B) = 0.40

To find the probability of not being accepted, we subtract the probability of being accepted from 1:

P(A') = 1 - P(A) = 1 - 0.25 = 0.75

P(B') = 1 - P(B) = 1 - 0.40 = 0.60

Now, we want to find the probability of Joe being accepted at one university and not at the other. There are two possibilities:

(1) he gets accepted at University A and not at University B or

(2) he gets accepted at University B and not at University A.

We can use the multiplication rule for independent events and the addition rule for mutually exclusive events to calculate this probability:

P(A and B') + P(A' and B)=

P(A) * P(B') + P(A') * P(B) =

(0.25 * 0.60) + (0.75 * 0.40) =

0.15 + 0.30 = 0.45

So, the probability that Joe will be accepted at one, and only one, university is 0.45. Therefore, the correct option is E. 0.45.

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The coefficient of [tex]x^{2}[/tex] in binomial expansion is 0

option is d .0

A binomial expansion is a method for expanding and simplifying algebraic statements of the type [tex](x+y)^{n}[/tex] into sum of terms of the form [tex]ax^{b} y^{c}[/tex].

An equation is a statement that determines the equivalence of two expressions joined by the equals sign "=". For instance, 5x - 9 = 10.

5x - 9 and 10 are expressions in this case. "=" is the sign that connects these two expressions.

According to the given information:

Given expanding term is [tex](2x+\frac{3}{x^{3} } )^{8}[/tex]

On cross multiplying and separating power numerator and denominator we get, [tex]\frac{(2x^{4} +3)^{8} }{(x^{3} )^{8} }[/tex]

Expanding the numerator we get [tex]256x^{32}+3072x^{28} +16128x^{24}+48384x^{20} +90720x^{16}+10884x^{12}+81648\\ x^{8}+34992x^{4}+6561[/tex]

Here there is no [tex]x^{2}[/tex],So co efficient of it is 0

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Step-by-step explanation:

This is the equation for a AREA greater than or equal to a line

2x-10 >= 5y

y <= 2/5 x -2      there are infinite answers

When you put together 8 copies of the unit fraction 1/2, you are essentially adding 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2.

To add fractions, you need to make sure the denominators are the same. In this case, all the fractions already have the same denominator of 2.

So, we can add the numerators together:

1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 8/2

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

8/2 = 4

Therefore, putting together 8 copies of the unit fraction 1/2 gives us a fraction of 4/1, or simply 4.

The probability in question is a right-tail probability because it is asking for the probability that the mean bond percent for the sample will be at least 28 percent, which is greater than the mean of 26.9 percent.

To calculate the probability, first find the z-score:
z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
z =[tex] (28 - 26.9) / (3.6 / sqrt(35))[/tex]
z = [tex] 1.1 / (3.6 / 5.916)[/tex]
z =[tex]  1.1 / 0.608[/tex]
z ≈ [tex] 1.809[/tex]

Using the z-table, the area to the left of this z-score is 0.965. Since we are looking for the right-tail probability, we need to subtract this value from 1:
Probability = 1 - 0.965
Probability ≈ 0.035

Thus, the probability that the mean bond percent for the sample will be at least 28 percent is approximately 0.035. The correct answers are right-tail probability and 0.035.

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Bianca practiced 28 hours a day whereas Filipe practiced 12 fewer hours than Bianca, if Filipe practiced for 16 hours

below are the situations and the operations used

Rising =  +

difference = -

to find the part of the grand total= ÷

Sharing  or Grouping = *

Since "Filipe trained 12 hours less than Bianca" and "Filipe trained 16 hours", we can use rising(+) to find the amount of time Bianca trained.

it is calculated by using the following formula

Bianca's training time = Filipe's training time + 12

Bianca practice hours = 16 + 12

Bianca Practice Hours = 28

So Bianca practiced 28 hours a day.

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If the expected counts are less than 5, then the chi-square test cannot be performed.

To perform the appropriate chi-square test using the data from this study, the following conditions must be satisfied:

i. The population distribution is approximately normal.

ii. The treatments were randomly assigned.

iii. The expected counts are all at least 5.

The chi-square test is a statistical method that examines whether observed data matches with the expected data.

The chi-square test is used to compare the categorical data between two or more groups. It is a non-parametric test of the statistical hypothesis.

In order to perform the appropriate chi-square test using the data from this study, the following conditions must be satisfied:

1. The population distribution is approximately normal: This means that the population data should be distributed normally. The normal distribution should be checked using a normal probability plot, which shows the data points relative to the standard normal distribution curve.

If the data is not normally distributed, then the chi-square test cannot be performed.

2. The treatments were randomly assigned: The treatments should be randomly assigned to the study participants in order to ensure that the results are not biased.

If the treatments are not randomly assigned, then the chi-square test cannot be performed.

3. The expected counts are all at least

4: The expected counts for each category should be at least

5. This means that there should be a sufficient number of observations in each category. If the expected counts are less than 5, then the chi-square test cannot be performed.

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Based on the lengths of the sides, we can see that the triangle is scalene. Based on the slopes of the sides, we can see that the triangle is acute since all the slopes are negative or less than 1.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the desired slopes and lengths of the triangle formed by the points M(-7, 8), N(-1, 9), and O(0, 3), we can use the distance formula and the slope formula.

Distance formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, we can find the lengths of the sides of the triangle:

Length of MO:

d(MO) = √((0 - (-7))² + (3 - 8)²) = √(7² + 5²) = √(74)

Length of NO:

d(NO) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)

Length of MN:

d(MN) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)

Slope formula:

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Using this formula, we can find the slopes of the sides of the triangle:

Slope of MO:

m(MO) = (3 - 8) / (0 - (-7)) = -5/7

Slope of NO:

m(NO) = (9 - 8) / (-1 - (-7)) = 1/6

Slope of MN:

m(MN) = (9 - 8) / (-1 - (-7)) = 1/6

Characterization of the triangle:

Based on the lengths of the sides, we can see that the triangle is scalene (no two sides have the same length). Based on the slopes of the sides, we can see that the triangle is acute (all angles are less than 90 degrees) since all the slopes are negative or less than 1. Additionally, we can see that the side MO is the longest side of the triangle, and since the slope of MO is negative, we can conclude that the angle opposite side MO is the largest angle in the triangle.

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Answer:

the answer is y=6x-6

Step-by-step explanation:

hope this helps

Answer: y = 6x-6

Step-by-step explanation:

Answer:

x=[tex]\frac{5b-a}{3-b}[/tex]

Step-by-step explanation:

3x+a=b(x+5)

3x+a=bx+5b

3x-bx=5b-a

x(3-b)=5b-a

x=[tex]\frac{5b-a}{3-b}[/tex]

The probability of the outcome being a red counter, or a blue counter is equal, therefore Trevor is wrong.

We know that Trevor has a bag of counters with 26 red counters and 26 blue counters and that he has already randomly picked one red counter 5 times but he places them back in the bag again and mixes them, but he thinks that the next counter he picks has a greater probability of being blue than red.

Trevor is wrong as we know that the likelihood of an occurrence is denoted by a numerical value known as probability. This value falls between 0 and 1 or can be represented as a percentage between 0% and 100%. The higher the probability of an event, the greater the chances of its occurrence. An impossible event has a probability of 0, while a certain event has a probability of 1.

To calculate probability, divide the number of ways the event can occur by the total number of outcomes.

Here the probability of the outcome being a red counter or a blue counter is equal, therefore Trevor is wrong.

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The absolute value equation that has the solution set with digits -18, 0, and X on a number line is :

|X| = X if X ≥ 0

|X| = -X if X < 0

An equation is a mathematical statement that shows the equality of two expressions. It typically includes one or more variables (represented by letters) and may also include constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

If the solution set for the absolute value equation has digits -18, 0, and X on a number line, then the equation must have two separate cases: one where X is positive and one where X is negative. We can write the absolute value equation as:

|X| = X for X ≥ 0

|X| = -X for X < 0

To include the values -18 and 0 in the solution set, we need to check each case separately:

|X| = X if X is greater than 0 or zero. The equation X = a must therefore be resolved, where an is either -18 or 0. As X 0 is satisfied by only one value in the solution set, the case's solution is X = 0.

Example 2: X < 0

When X is negative, |X| equals -X. So, we must find a, where an is either -18 or 0, to solve the equation -X = a. This case's solution is X = 18, as it is the only value in the solution set that satisfies the condition X 0.

As a result, the absolute value equation whose answer is represented by the numbers -18, 0 and X on a number line is:

|X| = X if X ≥ 0

|X| = -X if X < 0

or

|X| = 0 if X = 0

|X| = 18 if X < 0

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Simon needs approximately 48.6 gallons of gas for his trip from Orlando, FL to Sacramento, CA.

To calculate the number of gallons of gas Simon needs for his trip, you can use the following formula:

Gallons = Miles / Miles per gallon

First, convert the distance of 2,804 miles to miles per gallon by dividing by the car's average mileage per 2

gallons:2,804 / 48.6 = 57.75 mpg

Then, use this value to calculate the number of gallons of gas Simon needs for his trip:

Gallons = Miles / Miles per gallon

Gallons = 2,804 / 57.75

Gallons ≈ 48.6 gallons

Therefore, Simon needs approximately 48.6 gallons of gas for his trip from Orlando, FL to Sacramento, CA.

The answer should be rounded to the nearest tenth, so the final answer is 48.6 gallons.

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If Clare streams a classical music station while doing chores, then probability that next piece will be a concerto is 2/11.

In order to calculate the probability that the next-piece Clare listens to will be a concerto, we count the number of concertos in the list of pieces she has already listened to and divide by the total number of pieces.

From the given list,

The total number of pieces of music = 11;

The number of concerto is = 2;

So, probability that next piece Clare listens to will be a concerto is:

⇒ P(concerto) = (number of concertos)/(total number of pieces);

⇒ 2/11

Therefore, the required probability is 2/11.

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The given question is incomplete, the complete question is

Clare streams a classical music station while she's doing chores on the weekends. here are the types of musical pieces she has listened to so far this weekend :

{overture, symphony, sonata, concerto, symphony, sonata, overture, symphony, opera, sonata, concerto}

Based on the data, What is the probability that the next piece Clare listens to will be a concerto?

Answer:

Yes, the length of the intercepted arc will have the same measurement. When a central angle intercepts an arc of a circle, the measure of the angle is equal to the measure of the intercepted arc. In this case, both angles ABC and DEF are right angles, which means that they each intercept half of the circle. Therefore, the length of the intercepted arcs will be the same.

As a result, the percentage decrease in her new monthly payment is 18.1%. (to the nearest tenth).

To begin, we must determine the original loan amount. Using the information provided, we can construct the following equation:

$55,000 = P(1 + 0.10)^4

P denotes the original loan amount.

When we solve for P, we get:

P = $38,574.09

The old monthly payment is calculated as follows:

$38,574.09 / 1000 x $9.66 = $372.64

We must now compute the new loan amount. Because Sally renewed her mortgage at a 12% interest rate, we can apply the same formula as before, but with a new time period of 16 years (since 4 years have already passed):

Now, we need to calculate the new loan amount. Since Sally renewed the mortgage at a 12% interest rate, we can use the same formula as before, but with a new time period of 16 years (since 4 years have already passed):

$55,000 = P(1 + 0.12)^16

Solving for P, we get:

P = $27,703.25

The new monthly payment can be calculated as:

$27,703.25 / 1000 x $11.02 = $305.23

To find the percent increase, we can use the following formula:

percent increase = ((new value - old value) / old value) x 100

Plugging in the values, we get:

percent increase = (($305.23 - $372.64) / $372.64) x 100 = -18.1%

So the percent of decrease in her new monthly payment is 18.1% (to the nearest tenth).

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The value of π can be found by dividing the circumference of a circle by twice its radius . [tex]\pi =c/2r[/tex]

Starting with the equation: the circumference of circle is

C = 2πr

We can isolate π on one side of the equation by dividing both sides by 2r:

C / (2r) = π

So the solution for π is:

π = C / (2r)

The circumference of a circle is the distance around its outer edge. It is calculated by multiplying the diameter of the circle by pi (π), which is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Therefore, the formula for the circumference of a circle is C = πd, where C is the circumference, d is the diameter, and π is approximately equal to 3.14. The circumference is an important measurement in geometry and is used to calculate the perimeter of circles.

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The circumference of the circle is approximately 31.42 cm and the area of the circle is approximately 157.08 cm².

A circle circumscribed about a square with sides of 10cm has a circumference of approximately 31.42 cm and an area of approximately 157.08 cm².

If a circle is circumscribed about a square, the diameter of the circle is equal to the diagonal of the square. In this case, the diagonal of the square is:

d = √(10² + 10²) = √(200) = 10√(2) cm

The radius of the circle is half the diameter, so:

r = 5√(2) cm

The circumference of the circle is:

C = 2πr = 10π√(2) cm

The area of the circle is:

A = πr² = 50π cm²

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The median of the given numbers is 2.5.

its formula and examples are explained. In Mathematics, the median is defined as the middle value of a sorted list of numbers. The middle number is found by ordering the numbers. The numbers are ordered in ascending order. Once the numbers are ordered, the middle number is called the median of the given data set.

Given, Number of states visited by the students in Luther's class are:

Luther - 2 states

Amelia - 5 states

Oliver - 2 states

Katie - 3 states

Emilio - 1 state

Joe - 0 states

Dustin - 0 states

Arranging these numbers in ascending order, we get:

0, 0, 1, 2, 2, 3, 5

The median is the middle number when the numbers are arranged in order.

As there are an odd number of numbers, there is only one number that is exactly in the middle, which is 2.

Therefore, the median of the given numbers is 2.5.

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Answer:

Step-by-step explanation:

[tex]-\frac{8}{35}[/tex]

Answer:

The vertex of the quadratic function f(x) = -2x^2 + 8x is (2, 8).

Step-by-step explanation:

To find the vertex of the quadratic function f(x) = -2x^2 + 8x, we first need to find the x-coordinate of the vertex using the formula:

x = -b / 2a

where a = -2 and b = 8. Substituting these values, we get:

x = -8 / 2(-2) = 2

Now, to find the y-coordinate of the vertex, we can substitute this value of x back into the equation: f(2) = -2(2)^2 + 8(2) = 8