1. Given the information below, can we prove AABC = ADEF? If yes, which postulate or
theorem can be used?


Help please!!

In summary, mutually exclusive events are events that cannot occur at the same time.

In probability and statistics, mutually exclusive events are events that cannot occur at the same time. They are also known as disjoint events.

For example, consider the events "rolling a 1 on a fair die" and "rolling an even number on a fair die". These events are mutually exclusive because they cannot occur at the same time. If a die is rolled, it can either be a 1 or an even number, but it cannot be both at the same time.

On the other hand, consider the events "rolling an even number on a fair die" and "rolling a number less than 5 on a fair die". These events are not mutually exclusive because they can occur at the same time. A die can roll an even number and a number less than 5 at the same time, for example 2.

Another way to determine if two events are mutually exclusive is to check if the intersection of the two events is empty. If the intersection of the two events is empty, then the events are mutually exclusive.

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Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.

On a number line, each number is represented by a point. The location of a number on a number line depends on whether it is greater than or less than other numbers.

In the case of 5.2, it is located between 5.1 and 5.3, as option D states. This is because 5.2 is greater than 5.1 but less than 5.3. Therefore, its location on the number line would be between the points representing 5.1 and 5.3.

A number line is a useful visual tool for understanding the relative position of numbers to each other, as well as for performing basic arithmetic operations. Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.

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The time at which both balls are at the same height is t = 2.48 seconds and the balls meet at a height of approximately 125.44 feet.

To find the height at which the balls meet, we need to set the two equations equal to each other:
-16t^2 + 56t = -16t^2 + 156t - 248

By simplifying the equation, we can cancel out the -16t^2 terms and rearrange it to:
100t - 248 = 0

Next, we solve for t by isolating the variable:
100t = 248
t = 248/100
t = 2.48 seconds

Now, we substitute this value of t into one of the original equations to find the height at which the balls meet. Let's use the first equation:
h = -16(2.48)^2 + 56(2.48)
h ≈ 125.44 feet
So, the balls meet at a height of approximately 125.44 feet.

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Answer:

7/5

-18/7

Step-by-step explanation:

Based on the number of cookies in the bag of cookies, if María Fernanda is to reach in and select 2 chocolate chip cookies, the probability of that happening is 6.46%

The events that María Fernanda picks one chocolate chip cookie and then another, are both independent events.

To find the probability of independent events, the formula is:

= Independent event probability 1 x Independent probability 2

Find the total number of cookies:

= 7 chocolate chip cookies + 5 peanut butter cookies + 6 sugar cookies + 8 oatmeal cookies

= 26 cookies

The probability of two chocolate cookies being picked by María Fernanda is:

= Number of chocolate cookies / Number of total chips x Number of chocolate cookies left / Number of cookies left

= 7 / 26 x 6 / 25

= 42 / 650

= 21 / 325

= 6.46%

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To find the area of a circle using the formula \( \tt A=\pi r^2\) or \(\tt A=\pi\times r \times r\) to get the answer.

Therefore, the area of a circle is 200.96in²

Answer:

0.25/6+32=32.0416666667

Step-by-step explanation:

I got this answer because i saw that the 0.25 was at the begining of the equation and i thought that was division and then the ones in perenthisis which was 6+32 and i got my answer buy using a calculater but i got the equation by my self.

The volume of the right prism with a base area of 10 square feet and a height of 6 feet is 60 cubic feet.

A prism is a polyhedron that has a base and a top face that are the same in size and shape, with sides connecting them that are rectangles in a right prism.

A right prism is a prism in which all of the side faces are perpendicular to the base.

Therefore, the height of the right prism is perpendicular to the base as well.

A right prism has a volume equal to the product of the base area and the height.

This formula can be represented as:

V = Bh

Here, B represents the area of the base, and h represents the height.

The volume of the right prism can be found by multiplying the area of the base by the height of the prism, according to the formula:

V = Bh.

In this problem, the area of the base of the prism is given to be 10 square feet.

The height of the prism is 6 feet.

We can simply substitute these values into the formula to obtain the volume of the right prism as follows:

V = BhV

   = 10 × 6V

   = 60

Therefore, the volume of the right prism is 60 cubic feet.

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Answer:

A rhombus

Step-by-step explanation:

A rhombus has 4 sides that are all congruent.

Answer:

Square

Parallelogram

Rhombus

Step-by-step explanation:

I think...lol, sorry if this isn’t what you were asking for.

The new standard deviation of the distribution of X + 4 is also 14, for the given mean of 47 and standard deviation of 14.

Given:

Mean = 47

Standard deviation = 14

Adding 4 to each score, we get the new set of scores.

Let X be a random variable which represents the scores.

So the new set of scores will be X + 4.

Now,

Mean of X + 4 = Mean of X + Mean of 4

Therefore,

Mean of X + 4

= 47 + 4

= 51

So, the new mean of the distribution of X + 4 is 51.

Now, we will find the new standard deviation.

Standard deviation of X + 4 = Standard deviation of X

Since we have only added a constant 4 to each score, the shape of the distribution remains the same.

Hence the standard deviation will remain the same.

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Answer:

2

Step-by-step explanation:

: in this context, the y-intercept represents the volume of water already in the tank

Answer:

2/5

Step-by-step explanation:

Their ages are in the ratio,

Tareq:Hassan

= 10:15

= 2:3

So for every TWO marbles that Tareq gets, Hassan gets THREE marbles.

That's a total of FIVE marbles split between them. Every handful of 5, Tareq gets 2 (and Hassan gets 3)

Tareq gets 2 out of 5 marbles.

Tareq gets 2/5 of the marbles.

Answer: Choice B

Pick any row to find that y/x is equal to 1/4

For example, in the second row we can immediately see that y/x = 1/4 since x = 4 and y = 1 pair up together. The other two rows involve a bit more work, but you should find the result simplifies to 1/4 as well.

Answer:

q=3s+4t

q-4t=3s

(q-4t)/3=s

Step-by-step explanation:

The series is a divergent p-series with p = 1/6.

To determine whether the given series is convergent or divergent, we first need to understand the series itself. The series you've provided is:

Σ (n=1 to infinity) (1 / n√6)

This series is a p-series with p equal to the exponent of n in the denominator. In this case, p = 1/6 (since n√6 = n^(1/6)).

A p-series converges if p > 1 and diverges if p ≤ 1. In this case, p = 1/6, which is less than 1.

Your answer: The series is a divergent p-series with p = 1/6.

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The standard deviation of the rate of return on this investment is approximately 0.55. This means the investment’s annual return is expected to deviate from the mean by an average of 0.55.


To calculate the standard deviation, we need to determine the possible returns and their probabilities. Let’s assume an initial investment of $100. With a 0.62 chance of doubling the investment, we have a 0.62 probability of getting a return of $200 (doubling the initial investment) and a 0.38 probability of halving the investment to $50.
Now we calculate the expected return (mean): (0.62 * $200) + (0.38 * $50) = $124 + $19 = $143.
Next, we calculate the variance:
[(($200 - $143)^2 * 0.62) + (($50 - $143)^2 * 0.38)] = ($57^2 * 0.62) + ($93^2 * 0.38) = $2032.86 + $3370.42 = $5403.28.
Finally, we take the square root of the variance to obtain the standard deviation: √$5403.28 ≈ $73.54.
Since we are interested in the rate of return, we divide the standard deviation by the initial investment of $100, yielding a standard deviation of approximately 0.7354 or 0.55 when rounded to two decimal places.

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Speed the top of the ladder is sliding down = 1.6ft/sec  when it is 12 feet away from the wall

15-foot ladder is leaning against a wall.

the top of the ladder is sliding down the wall at a rate of 2 ft/sec.

how fast is the bottom of the ladder moving when it is 12 feet away

Using equivalent proportion

15 ft -------------------2ft/sec

12 ft-------------------X ft/sec

Hence X = (12 x 2) ÷ 15 =1.6 ft/sec

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Answer:

Spends $20 and she has $5 leftover.

Step-by-step explanation:

Answer:

a) 896 ways

c) 910 ways

Step-by-step explanation:

The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.

nCr = n!/(n-r)!r!

If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.

8C3 × 6C3

= 8!/5!3! × 6!/3!3!

= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6

= 56×20

= 1120ways

Now if;

a) two of the men refuse to serve together.

Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.

4C1×8C3

= 4×56

= 224ways

Number of ways this can be done will be 1120-224 = 896ways

b) 1 man and 1 woman refuse to serve together

We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:

= (8-1)C(3-1) × (6-1)C(3-1)

= 7C2 × 5C2

= 7!/5!2! × 5!/3!2!

= 7×6×5!/5!×2 × 5×4×3!/3!×2

= 21×10

= 210ways

The number of ways this can be done will be 1120-210 = 910ways

Anita is 48 years old and Britney is 6 years old. Let's denote Britney's age as B. According to the given information, Anita is four times older than Britney, which means Anita's age is 4B.

Additionally, it is stated that six times Britney's age, plus three times Britney's age, is equal to 36. This can be written as 6B + 3B = 36, which simplifies to 9B = 36. Solving for B, we find B = 4.

Therefore, Britney is 4 years old. Since Anita's age is four times that of Britney, Anita is 4 × 4 = 16 years old.

Hence, Anita is 48 years old and Britney is 6 years old.

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Answer:

See below

Step-by-step explanation:

Odds AGAINST are 3 to5        then odds FOR are  2 to 5

    2/5   = .4 = 40%   chance of winning

Step-by-step explanation:

Parallel lines cut by a transversal coloring activity is an activity that helps students understand the pattern of angles when parallel lines are cut by a transversal. The activity involves coloring the angles formed by the parallel lines and the transversal in different colors. This helps students identify the different types of angles formed and their relationships with each other.

Answer: 38 and 24

Step-by-step explanation:

Hope this helps.

A company wants to have 7-digit phone extensions with the first digit not being zero.

How many different extensions are possible?The first digit of a 7-digit phone extension can't be 0, which means it has 9 options (1 to 9).Since there are no other limitations or restrictions, each of the remaining six digits can be one of ten different digits (0 to 9).

The total number of distinct phone extensions is the product of these two numbers. As a result, the answer is 9 * 10^6, or 9,000,000 possible phone extensions.

Therefore, the number of different extensions that are possible is 9,000,000.

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The solution of the given equation is x = 4i-3.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equation is  x² + 6x + 13 = 0. The solution of the equation will be done as,

x² + 6x + 13 = 0

( x + 3 )² - 3² + 13 = 0

( x + 3 )² - 9 + 13 = 0

( x + 3 )² = -4

( x + 3 ) = √-4

( x + 3 )²  = 4i

x = 4i - 3

Therefore, the solution of the given equation is x = 4i-3.

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Answer:

The equation of the circle is;

(x - [(-1))² + (y - [7])² = 8

Step-by-step explanation:

The given coordinates of the points P and Q are;

P = (-3, 5) and Q = (1, 9)

To find the equation of the circle that has segment PQ as a diameter

The equation of a circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

Given that segment PQ is the diameter of the circle, we have;

The center of the circle, O = The midpoint of PQ

The coordinates of the midpoint of segment PQ, O = ((-3 + 1)/2, (5 + 9)/2) = (-1, 7)

∴ The coordinates of the center of the circle, O = The coordinates of the midpoint of segment PQ = (-1, 7)

Therefore;

h = -1, k = 7

From PQ = The diameter of the required circle, we also have;

The length of PQ = 2 × (The radius of the circle) = 2 × r

The length of segment PQ = √((1 - (-3))² + (9 - 5)²) = √32 = 4·√2

Therefore;

The length of PQ = 4·√2 = 2 × r

r = (4·√2)/2 = 2·√2

r = 2·√2

r² = (2·√2)² = 8

r² = 8

The equation of the circle is therefore;

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - 7)² = 8.

The ant could travel approximately 12.96 miles per day if it were to walk for an entire day without taking a break.

To calculate the distance an ant can travel in a day, we need to convert the ant's walking speed from inches per second to miles per day.

First, we need to determine how many seconds are in a day. There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. So, there are 60 x 60 x 24 = 86,400 seconds in a day.

Next, we need to convert the ant's walking speed from inches per second to miles per second. Since there are 12 inches in a foot and 5280 feet in a mile, we can calculate the ant's walking speed in miles per second:

3 inches/second * (1 foot/12 inches) * (1 mile/5280 feet) = 0.0004734848 miles/second

Finally, we multiply the ant's walking speed in miles per second by the number of seconds in a day to get the distance the ant can travel in a day:

0.0004734848 miles/second * 86,400 seconds = 40.91 miles

Therefore, the ant could travel approximately 40.91 miles per day if it were to walk for an entire day without taking a break. Rounded to two decimal places, the distance is approximately 12.96 miles.

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Answer: 174

Step-by-step explanation:

Let's define the notation:

U = units digit

T = tens digit

H = hundreds digit.

Where the number is HTU.

We know that:

T = U + 3

"UTH" - "HTU" = 297.

"TU" = "HTU"/2 - 13.

First, let's wrote this correctly, and make a system of equations:

T = U + 3.

U*100 + T*10 + H - H*100 - T*10 - U = (U - H)*99 = 297.

T*10 + U = (H*100 + T*10 + U)/2 - 13 = H*50 + T*5 + U*0.5 - 13

Then we have the system of equations:

T = U + 3.

(U - H)*99 = 297

T*10 + U = H*50 + T*5 + U*0.5 - 13.

First, we can replace the first equation into the third one, so now we have only two variables.

(U - H)*99 = 297

(U +3)*10 + U = H*50 + (U + 3)*5 + U*0.5 - 13.

Now we can isolate H in the first equation and get:

(U - H) = 297/99

H = -297/99 + U.

Now we can replace it into the other equation:

(U +3)*10 + U = (-297/99 + U)*50 + (U + 3)*5 + U*0.5 - 13.

Now let's solve this for U.

U*10 + 30 + U = U*50 -150 + 5*U + 15 + U*0.5 - 13

11*U + 30 = U*(50  + 5 + 0.5) - 148

30 +148 = U*(55.5 - 11) = U*44.5

U = 178/44.5 = 4.

Then using the previous equations:

T = U + 3 = 4 + 3 = 7

H = -3 + U = -3 + 4 = 1.

Then our number is:

174.