giving 50 points and brainliest to the best correct answer. thanks.

The triangles are similar by the SAS(side–angle–side) criteria for triangle similarities.

The SAS(side–angle–side) criterion for triangle similarity states that If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

Observing the triangles, if the ratio of side lengths 24 and 120 is equal to that of 14 and (14 + 56), then the angles inscribed by the two sides are in both triangles are equal.

24 : 120 = 24/120

24 : 120 = 1/5

24 : 120 = 1: 5

14 : 70 = 14/70

14 : 70 = 1/5

14 : 70 = 1 : 5

In conclusion, the triangles are similar by the SAS(side–angle–side) criteria for triangle similarities

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He has to pay $1.05 in taxes for the meal.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: Sales tax

A sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.

Now it costs $15.00 and the tax is 7%

Treating the taxable amount as $15 and now to find 7% equivalent we get

Now 7%×15=$1.05

Thus he has to pay $1.05 in taxes

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Function f(x) is translated to the right 5 units.

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

The function f(x)=∛x+4 is transformed to f(x)=∛(x−1) +3.

Putting the values in the graph we see that mid points of both the graphs are:

[tex]\left(-4,\ 0\right)[/tex] original function

[tex]\left(1,\ 3\right)[/tex] transformed function

x₁ ⇒ x₂ and y₁ ⇒ y₂ is the transformation

here,

-4 ⇒ 1

= +5 (positive symbol means to the right)

and

0 ⇒ 3

= +3 (positive symbol means to upward direction)

Thus, Function F translated to up 3 units and translated right 5 units

Hence, Function f is translated to the right 5 units.

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The total cost of the dinner is given by the equation A = $ 161.19

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.

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 data ,

Let the total cost of the dinner be represented as A

Now , the equation will be

The cost of the dinner without tax and tip = $ 128.95

The sales tax percentage = 7.5 %

So , the sales tax amount = ( 7.5 % ) x cost of the dinner without tax and tip

Substituting the values in the equation , we get

The sales tax amount = ( 7.5/100 ) x 128.95

The sales tax amount = $ 9.0265

Now , the percentage of tip = 18 %

So , the tip amount = ( 18 % ) x 128.95

The tip amount = $ 23.211

And , the total cost of the dinner A = cost of the dinner without tax and tip + sales tax amount + tip amount

On simplifying the equation , we get

The total cost of the dinner A = $ 128.95 + $ 9.0265 + $ 23.211

The total cost of the dinner A = $ 161.1875

Hence , the total amount of dinner is $ 161.19

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The statements can be used to compare the characteristics of the functions is:

If the values in a set of data are distinct and separate, the set is said to be discrete (unconnected values).

"All the values" that are input into a function are referred to as the domain of a function. A function's domain is the set of all potential inputs. Consider this box to represent the f(x) = 2x function. When the input values are x = 1,2,3,4,..., the domain is merely the collection of natural numbers, and the values that are returned are referred to as the range.

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Complete question:

The table shows three unique, discrete functions. Which statements can be used to compare the characteristics of the functions? Select three options.

has the greatest maximum. f(x)

has the greatest x-intercept. h(x)

has the smallest minimum value. g(x)

All three functions share the same domain.

All three functions share the same y-intercept.

The probability of X and Y being randomly chosen real numbers such that 0 is 1.

Let X and Y be two random variables such that X is uniformly distributed on the interval [0,1] and Y is uniformly distributed on the interval [0,2]. The probability density function (pdf) of X and Y is given by:

[tex]f_X(x) = 1 and f_Y(y) = 1[/tex]

The probability of X and Y being in the interval [0,1] and [0,2] respectively is given by the integral of their pdfs over the given intervals:

[tex]P(0 < X < 1) = ∫_0^1 1dx = 1\\P(0 < Y < 2) = ∫_0^2 1/2dy = 1[/tex]

Therefore, the probability of X and Y being randomly chosen real numbers such that 0 is 1.

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complete question:

What is the probability of x and y being randomly chosen real numbers such that 0?

Answer: Let's call the number of hours worked h.

The cost of hiring Carmony is $255 + $85h.

The cost of hiring Holliday is $115h.

We want to find the number of hours h such that $255 + $85h is less than $115h.

We can write this as:

$255 + $85h < $115h

Subtracting $115h from both sides:

$255 < $115h - $85h

Combining like terms:

$255 < $30h

Dividing both sides by $30:

8.5 < h

So, it is cheaper to hire Carmony for more than 8.5 hours. For 8.5 hours or less, it is cheaper to hire Holliday.

Step-by-step explanation:

Any probability statement involving a normal random variable can be converted to an equivalent statement involving a standard normal random variable through the process of standardization.

Standardization is converting a normal random variable, X, to a standard normal random variable, Z, by subtracting its mean, μ, and dividing by its standard deviation, σ. The formula for standardization is given:

Z = (X - μ) / σ

Once a normal random variable has been standardized, it is easier to find probabilities because the standard normal distribution is well-known and widely used in statistical analysis. For example, if X is normally distributed with mean μ and standard deviation σ, the probability of X being between two values a and b can be found using the cumulative distribution function (CDF) of the standard normal distribution.

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Step-by-step explanation:

If the slope is -1 then every time it moves 1 down it moves 1 right

It is going down because the slope is negative.

It touches the y-axis at -1.

(Download pdf to see graph)

Hope this helps! Please mark me as brainliest!

Answer:

Step-by-step explanation:

y=-1x+1/6

Answer:

630 ft

Step-by-step explanation:

[tex]\frac{x}{140}=\frac{18}{4}\\ \\4x=2520\\\\x=630[/tex]

Hence, the height of the building is 630 feet.

The possible values of the number x are any real number that is less than or equal to 103.2. This can be written as: x <= 103.2

Let's call the number "x".

The sum of 4.5 and one-third of x can be written as:

4.5 + (1/3)x

The inequality to represent the statement "the sum is equal to at most 38.9" would be:

4.5 + (1/3)x <= 38.9

To solve for x, we can isolate x by subtracting 4.5 from both sides:

(1/3)x <= 34.4

And finally, multiplying both sides by 3:

x <= 103.2

So, all the possible values of the number x are any real number that is less than or equal to 103.2. This can be written as:

x <= 103.2

or

-∞ < x <= 103.2

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Answer: (3, 1)

Step-by-step explanation:

point D is at (0,3) if it is translated 3 units to the right and 2 units down that means the x value will be added by 3 and the y value will be subtracted by 2

0+3 = 3; 3-2 = 1

D' is at (3,1)

Answer:

1.) 160

2.) 40

3.) 200

Step-by-step explanation:

Hoped this helped! =)

Mean = μ = 0.40

Standard deviation = σ = 0.015

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Female colorblindness proportion = 1%

Male colorblindness proportion = 8%

Female sample size = 40

Male sample size = 20

Hence, We get;

Let us check if the condition np ≥ 10 is satisfied or not,

⇒ np

⇒ 40 × 0.01

⇒ 0.4 < 10

Since, the condition np ≥ 10 is not satisfied the binomial random variable cannot be well approximated by a normal random variable. A larger sample size would be required to satisfy the condition np ≥ 10.

Hence, The mean is,

μ = np

μ = 40*0.01

μ = 0.40

And, The standard deviation is,

σ = √p(1 - p)/n

σ = √0.01(1 - 0.01)/40

σ = 0.015

Thus, We get;

Mean = μ = 0.40

Standard deviation = σ = 0.015

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Relations of the line with the given equation of line are:

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given an equation of line y = 1/5x +1

Comparing with the slope-intercept general formula of line

the slope of the given line = 1/5

And the slope of the line that is perpendicular to this will be = -1/slope

the slope of the line that is perpendicular to this will be = -5

For A) y = 5x +1

Slope = 5

this line has no relation with the equation of the line given

For B) y = 1/5x -2

Slope = 1/5

thus, this line is parallel to the given line.

For c)

10x + 2y = 10

In slope intercept

y = -5x +5

Slope = -5

Thus this line is perpendicular to the line given

For D)

x - 5y = 20

In slope intercept

y = 1/5x -4

Slope = 1/5

thus, this line is parallel to the given line.

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a) The probability of selecting a jury of all​ students is  792 / 245, 157.

b) The  probability of selecting a jury of all​ faculty us 330/ 245157

c) The  probability of selecting a jury of of students and ​faculty is 0.0000043

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

Out of 12 students and 11 faculty, a jury of six individuals can be select C(23,  7).

A) The probability of selecting a jury of all​ students

= C( 12, 7) / C(23,  7).

= 792 / 245, 157

B) The  probability of selecting a jury of all​ faculty

=  C( 11, 7) / C(23,  7).

= 330/ 245, 157

C) The probability of selecting a jury of students and ​faculty

=  792 / 245, 157 x 330/ 245, 157

= 0.0000043

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Answer:

19 meters

Step-by-step explanation:

209/11 = 19 meters per second

Answer: 19

209 divided by 11 is 19, which means that car moves 19 meters per second.

Hope this helped <3 !!

Answer:

  50%

Step-by-step explanation:

You want the probability of rolling a divisor of 45 on a 6-sided die.

The probability is the ratio of outcomes of interest to the total number of possible outcomes, assuming they are equally likely.

The numbers on a die that are divisors of 45 are 1, 3, 5, which are 3 of the 6 possible outcomes.

  P(divisor of 45) = 3/6 = 1/2 = 0.50 = 50%

The probability of rolling a divisor of 45 is 50%.

__

Additional comment

This problem statement asks for the answer as a percentage. It can also be written as a fraction (1/2) or a decimal (0.50).

The divisors of 45 are 1, 3, 5, 9, 15, 45.

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It takes Ermias and Manuel 3.43 hours to paint the room if they are working together. To find the time it takes for Ermias and Manuel to paint the room together, we can use the formula: 1/rate = time.

The rate is the combined painting rate of both workers, which is equal to the sum of their individual painting rates.

Let's call the time it takes for Ermias and Manuel to paint the room together "T". The combined painting rate of both workers is then 1/T.

The individual painting rates of Ermias and Manuel are 1/8 hours per room and 1/6 hours per room, respectively. Therefore, their combined painting rate is 1/8 + 1/6 = 6/48 + 8/48 = 14/48 hours per room.

Now we can use the formula 1/rate = time to find T:

1/ (14/48) = T

48/14 = T

T = 3.43 hours

So it takes Ermias and Manuel 3.43 hours to paint the room if they are working together.

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Answer:

a =

Step-by-step explanation:

Line is straight across so you just

8 - a =

a =

As per normalization, the session table uses the third normal form

Normalization is an important step in designing a database, as it helps to eliminate issues such as data integrity and redundancy. This is achieved through a series of steps, known as normalization.

The Sports Physical Therapy Center database has a table named Session that keeps track of all therapy appointments at the center. The table contains various pieces of information such as the session number, date, patient number, length of session, therapist ID, therapist's last and first name, and the therapy code.

The Session table is used to check if there are any design issues and to apply the necessary normalization steps to fix these issues and ensure data is stored in an organized manner.

Thorough this we have identified that the 3rd normal for is used here.

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Answer: -135

Step-by-step explanation:

90 + 45 = 135

90 - 135 = -45

I hope this helps

Note that the most precise name for quadrilateral ABCD with vertices a(-2, -1), b(2, 2), c(1, -2), and d(-3, -3) is an Irregular Quadilateral. See the image attached.

An irregular quadrilateral is a polygon with four sides, but all four (opposite) sides and angles are incongruent.

Rectangles, parallelograms, kites, and isosceles trapezoids are examples of irregular quadrilaterals. There are several formulas for calculating the area of these quadrilaterals. Set formulae may be used to compute the area of rectangles, parallelograms, kites, and isosceles trapezoids.

There is just one angle attribute for an irregular quadrilateral: the sum of the angles equals 360° 360° 360°. Add all internal angles that are known.

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In part (a), the y-intercept is (0,3), which means that when x = 0, the value of f(x) is 3. In part (b), the y-intercept is (0,0), which means that when x = 0, the value of f(x) is 0. In part (c), the y-intercept is (0,-6), which means that when x = 0, the value of f(x) is -6.

A transformation of a function is a process that changes the position or shape of the function on a coordinate plane. There are several types of transformations, including:

Translation: A translation moves the graph of a function horizontally or vertically, but does not change its shape. This can be accomplished by adding or subtracting a constant to the input or output of a function.

Scaling: A scaling changes the size of a function's graph, but not its shape. This can be accomplished by multiplying the input or output of a function by a constant.

Reflection: A reflection flips the graph of a function over a line. This can be accomplished by negating either the input or the output of a function.

Stretching or Compression: A stretching or compression changes the height or width of a function's graph, but not its shape. This can be accomplished by multiplying the output of a function by a constant greater than 1 for stretching, or by a constant between 0 and 1 for compression.

These transformations can be used to shift, scale, reflect or distort the graph of a function, allowing for greater understanding and analysis of its properties.

a. f(x) = [tex]3(2)^{x}[/tex] + 3 is an exponential function that has been vertically shifted up by 3 units. The y-intercept is (0,3), which means that when x = 0, the value of f(x) is 3.

b. f(x) = [tex]6(4)^{x}[/tex] * 0.5 is an exponential function that has been vertically stretched by a factor of 0.5 and horizontally stretched by a factor of 6. The y-intercept is (0,0), which means that when x = 0, the value of f(x) is 0.

c. f(x) = [tex]4(0.5)^{x}[/tex] - 6 is an exponential function that has been vertically shifted down by 6 units. The y-intercept is (0,-6), which means that when x = 0, the value of f(x) is -6.

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Option A is the correct option

So, the approximate form of the expression for all values of t is 0.75.

The expression 3(1.25)/5 can be simplified to

3/5 * 1.25

= 0.75.

=3(0.25)

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided. Algebra Expression Example: 3x + 9, 5x + 10

To simplify simply is to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

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Typically, these services are covered by closing costs associated with a real estate transaction. Closing costs are fees charged by various parties involved in the home-buying process and can include the cost of a credit score check, attorney fees, and notary fees.

A credit score check is often required by a lender as part of the mortgage approval process, and the fee for this service can be included in the closing costs. The fee for an attorney can also be included in closing costs, especially if the attorney is hired to review and explain the closing documents. An attorney can also represent the buyer or the seller during the closing process and advise them of their rights and obligations.

A notary is typically required to witness the signing of legal documents, such as the mortgage or deed, and a notary fee can also be included in the closing costs. The exact amount of each of these fees can vary, and it's common for buyers to receive an estimate of their total closing costs from their lender prior to closing.

It's important to note that closing costs are separate from the down payment and can add several thousands of dollars to the overall cost of buying a home, so it's a good idea for buyers to carefully review their closing cost estimate and understand what each fee covers.

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The hole of f(x) is x = -3.

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x + 3) / (x - 4)(x + 3)

Now,

We see that there is a common factor both in the numerator and the denominator.

This means,

There is a hole in f(x).

i.e

x + 3 = 0

x = -3 is the hole.

Thus,

x = -3 is the hole of f(x).

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Answer: x = -3

Step-by-step explanation:

correct on edge :)