In quadrilateral ABCD, the diagonals intersect at point T. Jasmine has used the Alternate Interior Angles Theorem to show that angle DAC is congruent to angle BCA and that angle ADB is congruent to angle CBD. Which of the following can Jasmine use to prove that triangle ATD is congruent to triangle CTB

The fate of the 22 checked bags can be considered the Bernoulli trials.

A Bernoulli trial is a random experiment with two possible outcomes, often referred to as a "success" or "failure." In the context of the lost luggage problem, success would be a checked bag that is not misplaced, and failure would be a checked bag that is misplaced.

For a set of trials to be considered Bernoulli trials, the following conditions must be met:

In this case, the fate of the 22 checked bags can be considered Bernoulli trials if the following conditions are met:

Therefore, the fate of the 22 checked bags can be considered Bernoulli trials.

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1.

a+6=6

Solving for a:

a = 0

a-5= -8

Solving for a:

a = -13

a x -10= 100

Solving for a:

a = -10

(5+2a) ÷ 17 = 3

Solving for a:

a = -4

2.

a) The dimensions of the field are 7m by 7m.

b) The perimeter of the field is 28m.

c) To find the area of the field, you could use the equation: length x width = area. In this case, the length and width are both 7m, so the equation would be 7m x 7m = 49m^23

3.

a) T | V

1 | 3

2 | 5

3 | 7

4 | 9

5 | 11

b) The pattern rule is that the value (V) is 2 greater than the previous value.

The probability that 3 hearts are chosen if 7 cards are selected from a well-shuffled deck of 52 playing cards is  [tex]\\& =0.175823334\end{aligned}[/tex]

The probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging between 0% to 100% can be used to describe probabilities.

Although a quasiprobability distributed enables a negative probability, called quasiprobability, for some events, the probability of the result of an experiment is never negative. These distributions may be applicable to conditional probability or unobservable occurrences.

The number of choosing  cards out of 52 is = ⁵²C₃

Number of ways of choosing 3 cards of heart out of 13 cards and 4 out of remaining 39 cards = ¹³C₅ × ³⁹C₃

Probability of choosing 5 hearts =  ¹³C₃ × ³⁹C₄ /  ⁵²C₃

[tex]\begin{aligned}\frac{13 \times 2 \times 11 \times 13 \times 19 \times 3 \times 9}{26 \times 17 \times 10 \times 7 \times 2 \times 47 \times 46} & =\frac{23523786}{133784560} \\& =0.175823334\end{aligned}[/tex]

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Answer:

56 adult tickets were sold that day

Step-by-step explanation:

let a represent number of adult tickets sold and c number of child tickets sold , then

a + c = 122 → (1)

9.1a + 5.7c = 885.8 → (2)

from (1) subtract c from both sides

c = 122 - a

substitute c = 122 - a into (2)

9.1a + 5.7(122 - a) = 885.8

9.1a + 695.4 - 5.7a = 885.8

3.4a + 695.4 = 885.8 ( subtract 695.4 from both sides )

3.4a = 190.4 ( divide both sides by 3.4 )

a = 56

that is 56 adult tickets were sold that day.

Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.

here,

rate = 10%

Time = 1 year

Principle = 12000

=>SI = PRT/100

=> SI =  10*1*12000/100

=> SI = 1200

and

=>  After 1 year = 12000 -1200 = 10800

and

for five  years

=> SI = PRT/100

=> SI = 10800 * 7.2 * 4 / 100

=> SI = 3110.4

After 5 year = 10800 - 3110.4  = 7,689.6

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Answer:The temperature dropped 24°F overnight, so the change in temperature would be represented by the expression |-24|, which is the absolute value of -24.

You can also represent it by |38| - |-24| which is equal to 38 - (-24) = 38 + 24 = 62°F.

Step-by-step explanation:

Answer:

f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

given f(- 5) = 2, that is when x = - 5 , y = 2

f(7) = - 4, that is x = 7, y = - 4

the 2points (- 5, 2 ) and (7, - 4 ) lie on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 2 ) and (x₂, y₂ ) = (7, - 4 )

m = [tex]\frac{-4-2}{7-(-5)}[/tex] = [tex]\frac{-6}{7+5}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then

f(x) = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the line

to find c substitute either of the 2 points into the partial equation

using (- 5, 2 ) , then

2 = - [tex]\frac{1}{2}[/tex] (- 5) + c = [tex]\frac{5}{2}[/tex] + c ( subtract [tex]\frac{5}{2}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] = c

f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of line

Answer:

20 blue fish

Step-by-step explanation:

r=red fish, b=blue fish. r = 10+b. 60%r=r+b. (10+b)= 0.6(r+b); 10+b = 0.6(2b+10); 10+b=1.2b+6; 4=0.2b; b=20.

Answer:

We know that Keilantra has $660 to spend, she has already spent $488.20 on a bicycle, $11.17 on two reflectors and $19.05 on a pair of gloves.

We can represent the amount spent on reflectors as 2 * $11.17 = $22.34

So the total amount spent so far is:

$488.20 + $22.34 + $19.05 = $529.59

We can represent the remaining amount of money she has to spend on outfits as:

$660 - $529.59 = $130.41

We can use this remaining amount to find out the number of outfits she can purchase by dividing the remaining amount by the cost of each outfit:

$130.41 / $37.26 = 3.5

The inequality that represents this situation is:

x <= 3.5

Where x is the number of outfits Keilantra can purchase while staying within her budget.

This inequality tells us that Keilantra can purchase at most 3.5 biking outfits while staying within her budget.

However, since the number of outfits has to be a whole number, the greatest number of outfits that Keilantra can buy is 3.

As per the permutation, there are 5040 number of different ways are available for seating.

The term permutation in math is known as  a mathematical calculation of the number of ways a particular set can be arranged

Here we know that there are 8! ways that you can arrange 8 people.

Now here we have to imagine a specific arrangement.

Here we have consider that everyone get up and move one seat to their right.

Then in that arrangement was counted separately from the first one in the 8!

Here have to know that it’s really the same since if each person looks to their left and their right and here they’re sitting next to the same person. Then here there are 8 such “identical rotations” for each possible seating arrangement so the total number of seating's is calculated as,

=> 8! / 8

=> 7! = 5040.

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Answer:

[tex]72cm^{2}[/tex]

Step-by-step explanation:

9/3=3

12/3=4

(4x9)+(4x6)+(4x3)=

=36+24+12

=[tex]72cm^{2}[/tex]

The equation 7x² - 144 = -x⁴ has the 4 solutions below:

x =  ±3

x =  ±4i

Here we want to solve the equation below:

7x² - 144 = -x⁴

We can redefine the variable:

y = x²

Replacing that we will get:

7y - 144 = -y²

y² + 7y - 144 = 0

So we have a quadratic equation now, the using the quadratic formula we will get:

[tex]y = \frac{-7 \pm \sqrt{7^2 - 4*1*144} }{2} \\\\y = \frac{-7 \pm 25 }{2}[/tex]

Then the two solutions are:

y = (-7 + 25)/2 = 9

y = (-7 - 25)/2 = -16

And we know that:

y = x²

Then:

x = ±√9 = ±3

x = ±√-16 = ±4i

These are the 4 solutions.

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Let x1, x2, x3,x4,x5 be 5 nos in increasing order.

Median of 5 nos =[(5-1)/2 +1 ] th value =

3rd value = 8

x3 = 8 ........(0)

Range = Max - Min = x5 - x1

x5 - x1 = 11

x5 = 11 + x1. .......(1)

Mean = sum of values/ no. of values

(x1+x2+x3+x4+x5)/5 = 9

x1+ x2 +8 +x4+ 11+x1 = 45 _____(using (1) and (0))

2*x1 + x2 + x4 = 45-8-11

2*x1+ x2 + x4 = 22-------------(2)

Now mode = value that occurs most number of times

Mode = 4. -------(3)

Using (3) in (2) we get

2*x1 + 4 + 4 = 22

2*x1 = 14

x1 = 7

From (1)

x5 = x1+ 11 = 7+11= 18

So

x1 = 7, x2 = 4, x3 = 8, x4 = 4, x5 = 18

Answer is 60 % is the percentage of boys studying German .

So, for this one, you must first determine the number of French students.

Simple method:

[tex]\frac{1}{9}[/tex]  is 270 divided by 9, which equals 30, hence  [tex]\frac{2}{9}[/tex]of 270 is 60. The result of multiplying [tex]\frac{1}{9}[/tex] by 2 to get [tex]\frac{2}{9}[/tex] is 60.

French is being studied by 60.

When you apply this to the French to Spanish ratio of 3:7, you get 3 and 60 on the same side. In order to get to 60, you must multiply 3 by 20. (or divide 60 by 20 to get 3).

Therefore, 20 is the number you use to apply the same formula to the other side of the ratio.

To reach 140, multiply 7 by 20 (or 7 by 10, then multiply that number by 2).

Spanish is being studied by 140.

After subtracting the French and Spanish from the overall number, you are left with 70 German speakers at 270-140-60.

42 of these 70 are males. 28 females are produced by 70-42. The percentage of males studying German is [tex]\frac{42}{70}[/tex]. This is equivalent to [tex]\frac{6}{10}[/tex], and you multiply a fraction by 10 to convert it to a percentage ([tex]\frac{60}{100}[/tex] in this case).

Additionally, 60% is equal to [tex]\frac{60}{100}[/tex]  .

Your response is thus 60%.

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A detection system has a probability of 0.91 to detect a missile attack. It is recommended to have multiple detection systems as it increases the overall probability of detecting an attack and allows for redundancy in case one system fails.

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If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple

Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.

These triples are represented as (b, a, c).

Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .

The most known and smallest triplets are (3, 4, 5).

In the problem, the values  4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since

c² = 4² + 5²

c² = 16 + 25

c² = 41

c = √41 ≠ 7

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y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.

Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.

In terms of symmetry, the graph of this function has no symmetry.

The function has no rotational symmetry because it is not repeated after any rotation around the origin.

Conversion of pressure of 1379 torr to atm= 1.814474

Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.

Additionally, choosing the right number of significant digits and rounding may be necessary during the process.

The multi-step process of unit conversion involves multiplying or dividing by a numerical factor.

Weight, distance, and temperature can all be measured in a variety of ways.

Temperature is expressed in degrees Celsius, weight is expressed in kilos, and distance is measured in kilometers.

Imagine you are on vacation in India and are informed that the two cities are 100 kilometers apart.

Hence, Conversion of pressure of 1379 torr to atm= 1.814474

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The exponential function graphed is given as follows:

y = 2^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the parameters are given as follows:

When x increases by one, the output is multiplied by 2, hence the parameter b is given as follows:

b = 2.

The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:

a = 1.

Hence the function is defined as follows:

y = 2^x.

The graph is given by the image presented at the end of the answer.

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To have a 50% chance of probability finding a secretary who knows Tex, at least 50 out of 100 applicants should be interviewed.

In order to determine the least number of applicants that should be interviewed to have a 50% chance of finding one secretary who knows the word processor language Tex, we can use the binomial probability formula. This formula states that the probability of finding at least one success out of a certain number of trials is given by P(X ≥ 1) = 1 – P(X = 0). Assuming that there are 100 applicants, the probability of finding at least one secretary who knows Tex is given by 1 – (98/100)^50, which is approximately 0.5. Therefore, at least 50 out of 100 applicants should be interviewed to have a 50% chance of finding a secretary who knows the language Tex.

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it would take the object approximately 11.51 seconds to reach the ground.

Generally, Time is a concept used to describe the progression of events, or the duration of those events. It is often measured in units such as seconds, minutes, hours, days, and years.

Time can also be described as a continuum, with past events on one end and future events on the other.

Time is a fundamental aspect of the universe and is closely related to concepts such as causation, change, and entropy.

The time it would take the object to reach the ground can be found by setting the distance from the ground, s, to 0 and solving for t.

0 = -16t^2 + 2120

t^2 = (2120/16)

t = [tex]\sqrt{(2120/16)}[/tex]

t = approximately 11.51 seconds

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The gallons of blue paint he needs to make the green paint is 6 gallons.

This is a problem in ratios. Let's look into what we know.

Volume of green paint needed = 10 gallons

Parts of blue paint needed = 3

Parts of yellow paint needed = 2

Total number of parts = parts of blue paint + parts of yellow paint

                                    3 + 2 = 5

So fraction of blue paint needed = parts of blue paint / total parts

                                                       = 3/5

Volume of blue paint needed = [tex]\frac{3}{5}[/tex] × 10

                                                 = 6 gallons

Volume of yellow paint needed = [tex]\frac{2}{5}[/tex] ×10

                                                      = 4 gallons.

So we need 6 gallons of blue paint and 4 gallons of yellow paint to make 10 gallons of green paint.

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Answer: english please so I can answer it

Step-by-step explanation:

Answer:

√80 pulgada

Step-by-step explanation:

Convirtiendo 95 cm a pulgadas,

95/2,54 = 37,40 pulgadas

Ahora, la diagonal dada es de 40 pulgadas

Usando el teorema de Pitágoras, (40)²=(37,4)² + h² (Suponiendo h como altura)

h² = 40² - 37,4²

= 80

o h = √80 pulgada

Answer:

V = 17 m3

Step-by-step explanation:

The area of the base (triangular) is multiplied by the height, resulting in the volume

[tex]V=\frac{(2)(1)}{2} (17)=(\frac{2}{2})(17)=(1)(17)=17[/tex]

Hope this helps

Isabella fills her pool at a rate of 18 liters per minute as per the given condition.

The slope of the volume can be used to determine how quickly it changes when given Time t in minutes and Volume V in liters. That represents a change in volume relative to a change in time.

m = (v2-v1)/(t2-t1).

selecting the first two points (2, 184) and from the provided data (7, 94).

Volume remains in the pool at what rate =

(94-184)/(7-2) = -90/5 = -18.

Therefore the rate at which Isabella fills her pool is 18 liters/minute as per the given question.

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Answer:

First number 7

Step-by-step explanation:

First, let's make the first number y and the second number x

Next, we write our equations which are y=1/2x+3 and y=1/4x+5

Then, we set those two equations equal to each other and then solve for x

The first step of the equation is to add/subtract like terms, I subtracted 5 on each side of the equation, our new equation is 1/4x=1/2x-2, I then subtracted 1/2x on each side so now our equation is -1/4x=-2. We then multiply 1/4 by its reciprocal on each side. Its reciprocal is -4.

Now that we know x is equal to 8 now we can fill x into the original equations which were y=1/2x+3 and y=1/4x+5 you don't have to solve both, just one of your choosing.

Therefore your answer! .

A gas occupies 4.23 l at 2.25 atm. 2.75 L is the volume at 3.46 atm. This can be solved using the concept of Boyle's law.

Boyle's law gives the relationship between pressure and volume of gas.

It states that at constant temperature pressure in inversely proportional to volume.

PV = k

where P - pressure V - volume and k - constant

P₁V₁ = P₂V₂

Given that,

initial pressure (P₁) = 2.25 atm

final pressure (P₂) = 3.46 atm

initial volume (V₁) = 4.23 L

final volume (V₂) = ?

where parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation

substituting the values in the equation

2.25 atm x 4.23 L = 3.46 atm x V

V = 2.75 L

Thus, the final volume is 2.75 L

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The Price of an Orange is $2 and the price of an Apple is $3.3.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let us assume that,

Apple price =  A  $

Orange price = B  $

$5.30 for 1 apple and 1  orange

=> A + B  = 5.30    Equation 1

$7.30 for 1 apple and 2 oranges.

=> A  + 2B = 7.30   Equation 2

Equation 2 - Equation 1

=> B = 2

Thus, the Price of an Orange = $2

A + 2 = 5.30

=> A=  $3.30

Price of Apple  = $3.3

Therefore, The Price of an Orange is $2 and the price of an Apple is $3.3

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