Determine if the following statement is true or false.
When two events are​ disjoint, they are also independent.

By AAA similarity, triangles are proved similar.

Two triangles are similar if they have an equivalent number of corresponding sides and corresponding angles. Objects with multiple identically shaped but differently sized figures are known as similar figures.

In the given triangles ABC and triangle DBE,

it is given that,

/C = /E

Now in the given triangles,

/C = /E                                    .......(given)

/B = /B                                    ........(vertically opposite angles)

/A = /D                                    .........(if two angles of a given pair of triangles          

                                               are equal, then third angle will also be equal)

Therefore, by AAA similarity, triangles

ABC ~ DBE.

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Answer:

27716

Step-by-step explanation:

come on just do 29028-1312=s 27716

Mean 4.9 letters and standard deviation 1.5 letters are best estimates of the population parameters . So, the correct option is (C)

The estimated mean of the sampling distribution is 4.9 letters, which is a good estimate of the population mean word length. The estimated standard deviation of the sampling distribution is 0.15 letter, which is the standard error of the mean.

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. Since the sample size is 100 and the standard error is 0.15 letter, we can estimate the population standard deviation as follows:

population standard deviation = standard error x sqrt(sample size)

= 0.15 x sqrt(100)

= 1.5 letters

Therefore, the best estimates of the population parameters are:

Mean = 4.9 letters (same as the estimated mean of the sampling distribution)

Standard deviation = 1.5 letters

So, the correct option is (C) Mean 4.9 letters and standard deviation 1.5 letters.

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In maths, A∩B refers to the intersection of two sets, A and B. This means that it includes all the elements that are in both sets A and B. For example, if A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A∩B = {3, 4}, as these are the elements that are in both sets.

To find the intersection of two sets, you can list out all the elements in each set and then look for the ones that are in both. Alternatively, you can use a Venn diagram to visually represent the two sets and their intersection.

Here is an example using a Venn diagram:

A = {1, 2, 3, 4}
B = {3, 4, 5, 6}



As you can see, the intersection of A and B is the area where the two circles overlap, which includes the elements 3 and 4. Therefore, A∩B = {3, 4}.

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Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.

To find the number of trips needed to deliver 40 cords of wood, we can use the following formula:

Number of trips = Total amount of wood / Amount of wood per trip

In this case, the total amount of wood is 40 cords and the amount of wood per trip is 5/8 cord.

Plugging these values into the formula, we get:

Number of trips = 40 / (5/8)

Number of trips = 40 * (8/5)

Number of trips = 64

Therefore, Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.

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Answer:

120$ 60$

Step-by-step explanation:

The total cost 161+19=180

180X150%=180×1.5

=                 = 120  

150%=15, the rule of multiplication

" Stefan spend originally $120. 180-120=60

He make $60 by selling the bicycle and helmet to Jin.

Answer:

In statistics, an outlier is a data point that differs significantly from other observations.

Step-by-step explanation:

The main theme of Fahrenheit 451, a novel written by Ray Bradbury, is the dangers of censorship, conformity, and the importance of preserving knowledge and free thought.

The novel is set in a dystopian society in which books are banned and "firemen" are responsible for burning any that are found. The protagonist, Guy Montag, is a fireman who begins to question his job and the society he lives in, eventually leading him to join a group of rebels who memorize books in order to preserve their contents. Bradbury uses the story to warn against the dangers of censorship, mindless conformity, and the loss of intellectual curiosity, emphasizing the need for critical thinking, individuality, and the preservation of knowledge.

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we can predict that the population of the city in 2020 will be approximately 2931 (rounded to the nearest whole number).

What is percentage ?

A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.

Percentages are commonly used to represent proportions, rates, and changes in quantities. They can be used to compare quantities of different sizes, or to express how much one quantity has changed relative to another quantity.

According to the question:
To predict the population of the city in 2020, we can use the formula:

P = P₀(1 + r)ᵗ

where:

P₀ = the initial population (in 2000) = 2000

r = the annual growth rate as a decimal = 0.02

t = the number of years since the initial population = 20 (since we want to predict the population in 2020, which is 20 years after 2000)

Substituting these values into the formula, we get:

P = 2000(1 + 0.02)²⁰

Using a calculator, we can simplify this to:

P ≈ 2930.63

Therefore, we can predict that the population of the city in 2020 will be approximately 2931 (rounded to the nearest whole number).

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The transformation done on the heart as shown in the figure was rotation.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Rotation is the flipping of a figure about a fixed point. Rotation is a rigid transformation because it preserves the shape and size of the figure.

The transformation done on the heart shown was rotation.

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The equation of the nth term is a(n) = 2-8n

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.

The common difference = -14-(-6) = -14 +6 = -8

The first term is a1

The nth term of an arithmetic sequence =

a(n )= a1+(n-1)d

a(n) = a1+(n-1)-8

a(n )= a1-8n+8

if a1 = -6

a(n) = -6-8n +8

a(n) = 2-8n

therefore the nth term of the sequence is 2-8n

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Answer:

9

Step-by-step explanation:

IL and KL have the same length so we can set them equal.

3x = x+6

Subtract x from each side.

3x-x = x+6-x

2x = 6

Divide by 2.

2x/2 = 6/2

x=3

KL = x+6

     =3+6

    = 9

An outlier is a mathematical value in a set of data which is quite distinguishing from the other values.

Its more like outliers are values uncommonly far from the middle. Mostly, outliers have a significant impact on mean, but not on the median, or mode.

Hence making the outliers are crucial in their influence on the mean.

we can say that the outlier is a data point that lies outside the entire pattern in a distribution.

They are mostly shown as dots and its known that the whiskers are required to change. Whiskers stretch out to the farthest point in the data set that isn't an outlier.

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The area of ΔABC is 87.905 centimeters². The correct answer is C.

The area of ΔABC can be calculated using the formula A = (1/2)bc sin A, where b and c are the lengths of two sides and A is the measure of the angle between them.

Given that b = 26 centimeters, c = 16 centimeters, and measure of angle A equals 25 degrees, we can plug these values into the formula and calculate the area:

A = (1/2)(26)(16) sin 25
A = (1/2)(416) sin 25
A = 208 sin 25
A = 87.905 centimeters²

Therefore, the area of ΔABC is 87.905 centimeters2. The correct answer is option C. 87. 905 centimeters².

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The value of x is -18.66.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3/4x+5= -9

Now, solving for x

3/4x = -9-5

3/4 x = -14

3x = -56

x= -18.66

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Mrs. Cook was able to make 60 sandwiches using 6 jars of jelly.

Mrs. Cook was able to make 60 sandwiches. To find the answer, we can use the following equation:

Total number of sandwiches = (Total amount of jelly) / (Amount of jelly used per sandwich)

In this case, the total amount of jelly is 6 jars, and the amount of jelly used per sandwich is 1/10 jar.

Plugging these values into the equation gives us: Total number of sandwiches = (6 jars) / (1/10 jar)

To solve this equation, we can multiply the numerator and denominator by 10 to get rid of the fraction:

Total number of sandwiches = (6 jars × 10) / (1/10 jar × 10)

Simplifying gives us: Total number of sandwiches = 60 jars / 1 jar

Finally, we can cancel out the "jars" units to get:

Total number of sandwiches = 60

Therefore, Mrs. Cook was able to make 60 sandwiches using 6 jars of jelly.

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The width of the foil is 37//19 inches

From the question, we have the following parameters that can be used in our computation:

Area of the rectangular piece of foil = 12 1/3 square inches

Length = 4 3/4 inches

The width is calculated as

Width = Area/Length

Substitute the known values in the above equation, so, we have the following representation

Width = (12 1/3)/(4 3/4)

Evaluate

Width = 37//19

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The scale factor that was used to produce Figure 2 from Figure 1 include the following: B. 5 over 3.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = 5/3

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A unit circle table is a table that lists the coordinates of points on a unit circle, which is a circle with a radius of 1.

The unit circle is often used in trigonometry to represent the relationships between angles and the values of the trigonometric functions sine, cosine, and tangent. The table typically lists the angle in radians or degrees in one column, and the corresponding values of sine, cosine, and tangent in other columns. The table may also include values for other trigonometric functions such as cosecant, secant, and cotangent, as well as their inverse functions such as arcsine, arccosine, and arctangent.

The unit circle table is a useful reference tool for solving trigonometric equations and for understanding the geometric properties of the trigonometric functions. Many mathematical and scientific applications use the unit circle, including engineering, physics, and astronomy.

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Answer:

(1, - 2 )

Step-by-step explanation:

9x - 3y = 15 → (1)

3x + 3y = - 3 → (2)

add (1) and (2) term by term to eliminate y

(9x + 3x) + (- 3y + 3y) = 15 - 3

12x + 0 = 12

12x = 12 ( divide both sides by 12 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (2)

3(1) + 3y = - 3

3 + 3y = - 3 ( subtract 3 from both sides )

3y = - 6 ( divide both sides by 3 )

y = - 2

solution is (1, - 2 )

The solution set for the inequality is,

''A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.''

Any relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 3 (8 - 4x) < 6 (x - 5)

Now, Simplify the inequality as,

⇒ 3 (8 - 4x) < 6 (x - 5)

⇒ 24 - 12x < 6x - 30

⇒ 24 + 30 < 6x + 12x

⇒ 54 < 18x

Divide by 18;

⇒ 54/18 < 18x/18

⇒ 3 < x

Hence, The solution of inequality on number line is,

⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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The equivalent sum of the given expression is 15.

Addition of a number to an existing number is a method of increasing the magnitude of the existing number.

We can explain addition as -

{a} + {b} = {c}

For example -

2 + 3 = 5

Given is to find the sum -

2 + 2 + 2 + 3 + 2+ 2 + 2

We can write the sum as -

2 + 2 + 2 + 3 + 2+ 2 + 2

4 + 5 + 4 + 2

9 + 4 + 2

15

Therefore, the equivalent sum of the given expression is 15.

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{Question in English -

What is 2 + 2 +2 +3 +2+ +++2++ +2?}

The  equivalent expression to 8k - (5 + 2k) is 6k-5.

An expression is combination of variables, numbers and operators.

The given expression is 8k-(5+2k)

Eight times k minus five plus two times of k.

We need to find the equivalent expression to the given expression.

K is the variable in the expression.

Equivalent expressions are expressions that work the same even though they look different.

Apply distributive property

8k-5-2k

Add the like terms

6k-5

Hence, 6k - 5 is the equivalent expression of 8k-(5+2k).

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Answer:

10 and 14

Step-by-step explanation:

let the 2 numbers be x and y , then

[tex]\frac{1}{2}[/tex] (x + y) = 12 ( multiply both sides by 2 to clear the fraction )

x + y = 24 ( subtract x from both sides )

y = 24 - x → (1)

and

[tex]\frac{1}{4}[/tex] xy = 35 ( multiply both sides by 4 )

xy = 140 → (2)

substitute y = 24 - x into (2)

x(24 - x) = 140

24x - x² = 140 ( subtract 140 from both sides )

24x - x² - 140 = 0 ( multiply through by - 1 and arrange in standard form )

x² - 24x + 140 = 0 ← in standard form

(x - 10)(x - 14) = 0 ← in factored form

equate each factor to zero and solve for x

x - 10 = 0 ⇒ x = 10

x - 14 = 0 ⇒ x = 14

corresponding values of y are by substituting values of x into (1)

x = 10 → y = 24 - 10 = 14

x = 14 → y = 24 - 14 = 10

then the numbers are 10 and 14

There are 2.19,  39 euros in $100.

To determine how many 39 euros are equivalent to $100, you need to know the current exchange rate between euros and US dollars. The exchange rate varies constantly, so it's important to use the most up-to-date rate.

As of the time of writing, the exchange rate is 1 euro = 1.17 US dollars. This means that for every euro, you get 1.17 US dollars.

To determine how many 39 euros are equivalent to $100, you can use the following formula:

39 euros * (1.17 US dollars/1 euro) = X US dollars

Simplifying the equation gives:

45.63 US dollars = X US dollars

So, 39 euros are equivalent to 45.63 US dollars. To determine how many 39 euros are equivalent to $100, you can use the following formula:

$100 / (1.17 US dollars/1 euro) = X euros

Simplifying the equation gives:

85.47 euros = X euros

So, 85.47 euros are equivalent to $100. Therefore, you would need approximately 85.47/39 = 2.19 sets of 39 euros to reach $100.

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Answer: Para convertir un decimal a una fracción, coloque el número decimal sobre su valor posicional. Por ejemplo, en 0.6, el seis está en el lugar de las décimas, entonces colocamos 6 sobre 10 para crear la fracción equivalente, 6/10. Si es necesario, simplifica la fracción.

Step-by-step explanation:

Answer: I think it's P.E.M.D.A.S

Step-by-step explanation:

The value of the angle x in the parallel lines is 70 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, let's find x in the lines.

Sum of angles in a triangle is 180 degrees.

Hence,

∠KDP = 180 - 70 - 60

∠KDP = 50 degrees

∠BDC = ∠KDP  = 50 degrees(vertically opposite angles)

∠DBC = 180 - 50 - 60

∠DBC = 70 degrees

∠DBC = x = 70 degrees(corresponding angles)

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Answer: 2.5 or 2 1/2

Step-by-step explanation:

One way: 1/2 x 5 = 5/2

5/2 = 2 1/2 = 2.5

Another way: 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 5/2 = 2 1/2 = 2.5

Answer:

4(x - 2 + y) = 4x - 8 + 4y

Step-by-step explanation:

The expression 4(x - 2 + y) is equal to 4 times the sum of x - 2 and y. This can be simplified to:

4(x - 2 + y) = 4x - 8 + 4y