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Step-by-step explanation:

Line PQ is parallel to EF in the triangle DEF. So, ABC, DPQ, etc. Thus, we can state that A = D, B = P, and C = Q, indicating that the triangle ABC is comparable to the triangle DEF.

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Answer: The complementary event for choosing a red marble is choosing a blue or purple. The total number of marbles is 5. The probability of choosing a red marble is 1/5, and the complement would be 4/5.

By :- Utsav Xettri

The z-score for the data is Z= -2.83.

The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

The formula for calculating the z-score is :

Mean = 33000

μ = 34000

n = 200

σ = 5000

Putting all values,

[tex]Z = \dfrac{\bar x-\mu}{\sigma}\\Z = \dfrac{33000 - 34000}{\dfrac{5000}{\sqrt{200}}}\\Z = -2.83[/tex]

Hence, the value of the z-score will be Z= -2.83.

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Step-by-step explanation:

f(x) = x² + 5 g(x) = x + 4

for f(g(x)) or (f○g)(x) we take the expression of g and place it everywhere in the expression of f where x is mentioned.

so, (x + 4) goes into (x² + 5) giving us

((x + 4)² + 5) = x² + 8x + 16 + 5 = x² + 8x + 21

so, (2) is the correct answer.

8.

the same principle

f(x) = 2x + 9 g(x) = (x - 9)/2

just here we take f and put it into g :

g(f(x)) = ((2x + 9) - 9)/2 = 2x/2 = x

so,

(a) g(f(15)) = 15

(b) g(f(-3)) = -3

(c) g(f(x)) = x

to verify e.g. (a) we use x = 15 in f(x)

f(15) = 2×15 + 9 = 30 + 9 = 39

and then we use this result as new x = 39 in g :

g(39) = (39 - 9)/2 = 30/2 = 15

correct.

The required value of t is equal to 1/√13

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.

Given here: The vector A=    [tex]t\left[\begin{array}{ccc}2\\3\\\end{array}\right][/tex] and we are required to find or simply normalize this vector A by multiplying a scalar t

On Multiplying the scalar t we get the matrix A= [tex]\left[\begin{array}{ccc}2t\\3t\\\end{array}\right][/tex]

Now normalizing the vector A we get ||A|| as

[tex]\sqrt{4t^2+9t^2} \\=\sqrt{13t^2} \\=\sqrt{13}.t[/tex]

If t=1/√13 we get  ||A||  as equal to 1

Thus for t=1/√13 we get the length of the vector as equal to one.

Hence, The required value of t is equal to 1/√13

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The value of {h} is equivalent to 6/5.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is the function as follows -

(1/5) + h = (7/5)

We can write the function as -

(1/5) + h = (7/5)

h = 7/5 - 1/5

h = (7 - 1)/5

h = 6/5

Therefore, the value of {h} is equivalent to 6/5.

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Answer:

7 × (6 - 2)

Step-by-step explanation:

difference of 6 and 2: 6 - 2

difference of 6 and 2 multiplied by 7: 7 × (6 - 2)

Answer: 7*(6-2)

Step by Step Explanation: Change the words into math signs

The train covers 150 kilometers in one and a half hours.

To calculate the distance a train travels in one and a half hours at an average speed of 100 kilometers per hour, you can use the formula:

Distance = Speed x Time

In this case, the distance the train travels in 1.5 hours is:

Distance = 100 km/h x 1.5 hours = 150 kilometers

So the train would cover a distance of 150 kilometers in 1.5 hours.

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Answer:2.64

Step-by-step explanation:10.56 divided by 4=2.64

The slope - intercept form of the equation that relates the number of people and the cost of entering the museum is y = 8x + 4

The slope - intercept form is:

y = mx + b

Where:

m = slope or the cost per person

b = y - intercept or the residual cost

The cost per person to enter the museum is:

= Difference between cost of three people and two people

= 28 - 20

= $ 8

The residual is:

= Total cost for two people - Cost of two people

= 20 - ( 8 x 2 )

= $ 4

The slope intercept form of the relationship between the number of people and the cost of entering the museum is therefore:

y = 8x + 4

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1 out of 33 (1/33) is the answer.

Answer: 4/12

Step-by-step explanation:

Simplify each fraction by dividing or multiplying. Then you’ll get the answer

Answer:

4/12

Step-by-step explanation:

you simpify 4/12 and get 1/3 and that is what is being shown in the picture.

Answer:

The mean is affected by outliers that do not influence the mean. Therefore, when the distribution of data is skewed to the left, the mean is often less than the median.

Step-by-step explanation:

MAKE SURE TO REPHRASE

Answer:

38

Step-by-step explanation:

Just took the test

Using matrices the value of y is calculated to be -2

A determinant is a square array of numbers or variables surrounded by vertical lines.

This method is applied by first solving the determinant of the problem

D = 2 * 6 - 2 * 7

D = 12 - 14

D = -2

Solving for y

Replace the second column with the column at the right side of the equality sign. Solve the determinant in this condition and divide with the first determinant D = -2

Δ = (2 * 6) - (2 * 4) = 12 - 8 = 4

y = Δ / D

y = 4 / -2

y = -2

hence y = -2

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The complete table for the given quadratic equations is:

                   a                 b               c                d

1.                  1                -3                1                5

2.                 1                -2                1                5

3.                 3                6                3                1

When the middle term of a quadratic equation is split, we must rewrite the expression as the sum or difference of the two parts. We must split the middle phrase into two halves in order to determine the sum or difference of the words.

1. x² + 2x - 15

Split the middle term

= x² + 5x - 3x - 15

= x(x + 5) - 3(x + 5)

= (x - 3)(x + 5)

So, a = 1, b = -3, c = 1, d = 5

2. 2x³ + 6x² - 20x

= 2x(x² + 3x - 10)

= 2x(x² + 5x - 2x -10)

= 2x(x(x + 5) - 2(x + 5))

= 2x(x - 2)(x + 5)

So, a = 1, b = -2, c = 1, d = 5

3. 9x² + 21x + 6

= 3(3x² + 7x + 2)

Use splitting middle term method

= 3(3x² + 6x + x + 2)

= 3(3x(x + 2) + 1(x + 2))

= 3(x + 2)( 3x + 1)

= (3x + 6)(3x + 1)

So, a = 3, b = 6, c = 3, d = 1

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Answer:

g(x) = -1x + 11

Step-by-step explanation:

Parallel equations have the same slope.

G(x) is the same as y.

Step 1:

y = mx + b

y = -1x + b

Step 2:

Substitute (10,1) in the equation

1 = -1(10) + b

now solve for b.

Step 3:

1 = -10 + b

+10 +10

1 = b

Step 4:

check

y = -1(10) + 11

y = -10 + 11

y = 1

Hi there! So already noticeable, there are some given parts and pieces.  AD is unknown, and BC it seems is also unknown, since they are both congruent to each other.  Segment AB is twice the length of AD, and AB is parallel to BC.  DC is 4 cm longer than AB.  

If you've done proofs, here's one thing that can help: Angle ADC and BCD are congruent to each other by same-side interior angles theorem.

If you haven't done proofs, I'm just going to keep this a little bit more understandable.  I don't want to overload you with a million formulas/theorems.

AD = BC
AB = 2(AD)
AB || BC
DC = AB + 4

Wait a minute... :)

AD x 2 = AB.  AB is 4 units shorter than DC.  

Try making an equation.  AD can be x, AB can be y, and DC can be z.

2x = y
y + 4 = z, z - 4 = y

2x = z - 4

So try substituting in some things that can work.  The length of AB has to be 2 times the length of AD.  DC is AD + 4.  AD can be 2, AB can be 4, and DC can be 8.  

2(2) = (8 - 4)
4 = 4 :)

Looks like it works! You should probably ask your teacher/parents for help with this one, it looks a little odd.  But that's the best I can do for you.  :)

Answer:

Step-by-step explanation: i need help too hope u find ur problem

:o

Answer: 23 percent

23 percent of attendees supported the home team.

The percentage of people supporting the home team is 22.98%.

Percentage is a way to express a fraction or proportion as a relative quantity out of 100. It is often denoted by the "%" symbol. It's used to compare and represent quantities, such as discounts, proportions, or rates, in a more easily understandable form. To find the percentage of people who supported the home team, we need to divide the number of people supporting the home team by the total number of people attending the game and then multiply by 100.

Therefore,

Calculating the percentage of people supporting the home team -

= (Number of people supporting the home team / Total number of people attending) x 100%

Substituting the values -

= (667 / 2900) x 100%

= 667/29

= 22.98

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A curved line represents the graph of a non-linear function. A curved line is one whose direction changes over time.

Linear refers to straight, and a graph is a figure that depicts the relationship between two or more quantities. So, the simplest definition of a linear graph is a straight line or straight graph constructed on a plane to connect two points with x and y coordinates.

The two-variable linear equation 3x - 7y = 16 has three variables. Instance For the equation 2x + y = 8, Mike must create a linear graph. With a ruler and the specified amount as the starting point, draw a vertical line. From the line across to the -axis, draw a horizontal line using a ruler. Look at the value on the -axis. Examining the information on the graph's plot can help you distinguish between a linear and a quadratic graph.

Therefore the correct answer is Y=2/5x- 3 .

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A function is an equation that has a single solution for each value of y.

When two functions f and g share a domain and a codomain, and f(a)=g is true for each an in the domain, we say that the two functions are equal (a).

A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).

If two functions share the same domain and codomain as well as the same values across the board, then they are considered to be equal.

In spite of how the elements are arranged in the sets, two sets are said to be equal when all of their components are present in both. Afterward, the sets are referred to as equal sets. When all of one set's elements are absent from the other, two sets are said to be unequal.

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Answer:78

Step-by-step explanation:

very simple

acb is an enlargment of fdc

39/18=2 3/18

2 3/18x36=78

Therefore , the solution of the given problem of interest comes out to be

present salary is $19,025.625.

By dividing the principle by the cost of borrowing, the rest of the time, and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the concept used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating income is as a portion of the principal amount. For example, if he takes $100 from a buddy and pledges to pay back the loan at 5% interest, he will just pay his share of the 100% involvement. $100 (0.07) = $7. When you borrow money, you must pay interest, and you must charge interest when they lend it.

Here,

Given : 4.25 % raise

Salary =  $18,250

=> Simple interest = P*R*T /100

=> 18250 * 4.25 * 1 /100

=> 775.625

Thus,

Present salary = 18250 +  775.625 = 19,025.625.

Therefore , the solution of the given problem of interest comes out to be

present salary is $19,025.625.

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Answer:

for part (a) you will have about 28 dots for 10 squares.

part (b) its a 4x4 square with 16 square.

Answer: The numbers which can be expressed as a ratio of two integers where the  denominator is not equal to zero

Step-by-step explanation:

Rational numbers are expressed in the form of  where . 'q' is the denominator in the above fraction.

The fractional form which is terminating or non-terminating recurring are considered as rational numbers.

The numbers 'p' and 'q' are the integers.

Integers are defined as number which is a proper number and not a fraction or decimal. All negative whole numbers are considered as integers.

Some Examples of Rational numbers:   is a terminating fraction.  is a non-terminating recurring fraction

Hence, the numbers which can be expressed as a ratio of two integers where the  denominator is not equal to zero

Step-by-step explanation:

The possible dimensions of the rectangular garden are 8ft by 12ft, 6ft by 16ft, and 4ft by 24ft

In this problem, Misaki used five sections of fencing, two 4 ft sections, two 6 ft sections, and one 8 ft section to build a rectangular garden without cutting any. To find the possible dimensions of the garden, we can use the lengths of the fencing sections to make different combinations of the length and width of the garden.

Here are a few possible combinations for the rectangle shaped garden.

A garden that is 8 ft by 12 ft: This would use the two 4 ft sections as the width and the two 6 ft sections as the length.

A garden that is 6 ft by 16 ft: This would use the two 4 ft sections as the width and the one 8 ft section and two 6 ft sections as the length.

A garden that is 4 ft by 24 ft: This would use the two 6 ft sections as the width and the one 8 ft section and two 4 ft sections as the length.

It's important to notice that there are no other possibilities with the given lengths of fencing. Misaki can't have different dimensions because all the lengths are given, and if the width and length are swapped, we will get a different rectangular garden.

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Answer:

the fundamental properties of a rectangle are

-A rectangle is a quadrilateral.

-The opposite sides are parallel and equal to each other.

-Each interior angle is equal to 90 degrees.

-The sum of all the interior angles is equal to 360 degrees.

-The diagonals bisect each other.

Both the diagonals have the same length.

Answer: 82

Step-by-step explanation:

The domain of the graphed relation is:

D : {-9, -7, -5, -2, 1, 3}

For a relation y = f(x), we define the domain as the set of the possible inputs, this is, the possible values of x.

On the graph we can see some points (x, y) graphed, where x is the value on the horizontal axis.

We can see that the graphed points are:

(-9, -4)

(-7, -6)

(-5, -4)

(-2, 2)

(1, 4)

(3, 1)

The domain is the set of the first values of each point, so the domain is:

D : {-9, -7, -5, -2, 1, 3}

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