Right triangle XYZ has legs of length XY = 12 and YZ 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?

AM is a perpendicular bisector of BC.

A ray that divides an angle into two equal parts is known as an angle bisector or the bisector of an angle. For instance, each measurement will be equal to 30 degrees if ray AX divides an angle of 60 degrees into two equal parts. There is an angle bisector for each angle.

To divide a segment or an angle into two congruent parts is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.

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Answer:

B

Step-by-step explanation:

put equation in slope-intercept formula (y=mx+b)

8x-2y=24

-8x      -8x

-2y=-8x+24

divide each side by -2

y=4x-12

the "b" in the formula is the y-intercept which is -12, therefore B is correct

Answer:

x+x+10=90 being Right angle triangle.

2x=90-10

2x=80

x =40

then x+10= 40 + 10

= 50

The simplest form of the given expression is (- 8n² +n +1)

Simplification is the process of making simple an expression, terms or equations so as to easy for solving or evaluating.

There are some steps for simplification such as removing parenthesis, collecting like terms, addition or subtraction of like terms and so on.

We are given an expression, ( -7n² - 8n -8) + (- n² + 9n +9)

In order to simplify, we first remove the parenthesis and get

- 7n² - 8n -8 - n² + 9n +9

in the next we will collect like terms

- 7n² - n² -8n +9n - 8 +9

We now add or subtract like terms

- 8n² + n+1

this is the simplest form of the given expression.

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The expression 10+(-8) is equivalent to 10 - 8.

Different branches of mathematics exist. The branch of knowledge that deals with numbers and operations is arithmetic. We learned how to add, subtract, multiply, and divide two or more numbers through arithmetic.

Shapes and how they are created with various tools, such as a compass, ruler, and pencil, are the focus of geometry. Another fascinating area of study is algebra, which helps us communicate the numerical and alphabetic aspects of daily life (variables).

Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.

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Full question

What expression is equivalent to 10-8?

Answer:

4

Step-by-step explanation:

m = Δy/Δx = (6-(-2))/(5-3) =8/2 = 4

Answer:

  C

Step-by-step explanation:

You want the equations of the circle and ellipse in the given figure.

The standard form equation for an ellipse is ...

  [tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

where 'a' and 'b' are the semi-axes in the x-direction and y-direction, respectively.

You will notice that when a=b=r, the ellipse becomes a circle and the equation can be rewritten as ...

  [tex]\dfrac{x^2}{r^2}+\dfrac{y^2}{r^2}=1\ \Longleftrightarrow\ x^2+y^2=r^2[/tex]

Here, the radius is 3, the same as the semi-major axis in the x-direction (a=3). The ellipse axis in the y-direction appears to be about 1/3 that value, so b=1, and the equations of the circle and ellipse are ...

  [tex]x^2+y^2=9\qquad\text{circle}\\\\\dfrac{x^2}{9}+\dfrac{y^2}{1}=1\qquad\text{ellipse}[/tex]

Answer: 0.071%

Step-by-step explanation:

To get from $3.50 - $3.75, there was an increase of $0.25.

(Sorry if I'm getting the currency bit wrong, I'm British.)

Divide 0.25 by the original cost of 3.50, and you get:

0.07142857142857142857142857142857

Round this and you get a 0.071% increase

Answer:

The percent change in the price of a gallon of gas is 0.0714%.

Step-by-step explanation:

Here, The price increased from $3.50 to $3.75, a change of $0.25.

So,

$0.25 ÷ $3.50 × 100% = 0.0714%

Thus, The percent change in the price of a gallon of gas is 0.0714%.

The relative frequency table that summarizes the data is given by the image at the end of the answer.

The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.

Given:

The percentage of people interested in waterskiing

= 90/250 x 100

= 36%.

Thus, the percentage of people that was not interested in waterskiing is

=100-36

= 64%

Now, the percentages related to paddle boarding are :

Yes: 72/250 = 28.8%.

No: 18/250 = 7.2%.

Of those not interested in waterskiing, the percentages related to paddle boarding are

Yes: 112/250 = 44.8%.

No: (120 - 72)/250 = 19.2%.

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There are infinite many triangles that can be formed with the angle measures 20, 100, and 60 degrees

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

Angles = 20, 100, and 60 degrees

The above parameters are angles

When only angles are given, the triangle can have as many side lengths as possible

This means that there are infinite many triangles

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Answer:

18 more students preferred pepperoni pizza over cheese pizza in the survey.

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] x [tex]\frac{72}{1}[/tex] Can be rewritten

[tex]\frac{3}{1}[/tex] x [tex]\frac{9}{1}[/tex] = [tex]\frac{27}{1}[/tex] = 27   I cross canceled the 8 and 72.  They have a common factor of 8.  8 goes into 8 once and 8 goes into 72 9 times.

27 students preferred pepperoni pizza.

[tex]\frac{1}{8}[/tex] x [tex]\frac{72}{1}[/tex] = [tex]\frac{1}{1}[/tex] x [tex]\frac{9}{1}[/tex] = 9

9 students preferred cheese pizza.

27 - 9 = 18

The required correct options of data set after the value's removal.

1. The mean will increase.                   3. The median may stay the same.      5. The mode will stay the same.

The Index Sponsor computes the Removal Value in the same way that Fund Interests in the linked Fund are valued.

Here,
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile.
As for the properties of statistics, Change in the IQR does affect the median and mode, So options 3 and 5 are correct.
And also mean will increase.

Thus, the correct options are shown above.

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Answer:

81

Step-by-step explanation:

9x9 = 81

Answer:

The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.

Answer:

4x +2

Step-by-step explanation:

4( x + 2)

= 4*x +4*2

= 4x +2

The probability that the area of the triangle is at most 20 is 5/9

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is

1/2×12×6=36

Now if the area of the triangle is at most 20 then the required probability is = 20/36

                      =5/9

Hence, The probability that the area of the triangle is at most 20 is 5/9

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Answer:

To solve this system of equations, you can use the method of elimination. To do this, you can add the two equations together:

4x + 5y - 5x - 3y = -7 - 1

-x + 2y = -8

Then, you can divide both sides of the equation by -1 to solve for y:

x - 2y = 8

y = (x - 8) / 2

Now that you have solved for y, you can substitute this expression back into either of the original equations to solve for x. For example, you can substitute y = (x - 8) / 2 into the first equation to get:

4x + 5((x - 8) / 2) = -7

4x + 5x - 40 = -7

9x = 33

x = 3.67

Now that you have solved for both x and y, you can find the solution to the system of equations:

x = 3.67

y = (3.67 - 8) / 2 = -2.17

So, the solution to the system of equations is x = 3.67 and y = -2.17.

Answer:

y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)

Step-by-step explanation:

Given the quadratic function:

[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]

We can rewrite the function above using perfect square form:

[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]

Finding an inverse, we swap the terms of x and y:

[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]

Square root both sides, solving for y:

[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]

Subtract both sides by 2:

[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]

Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.

Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.

.....................................

Answer:

8.20

Step-by-step explanation:

8.20 is greater than 8.002 due to 0.20 being greater than 0.002

The fractional form of the expression [tex]\sqrt[3]a[/tex] is [tex]a^{\frac{1}{3}[/tex]

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, A radical expression [tex]\sqrt[3]a[/tex].

We know this describes the cube root of a or one-third root of a.

This can be written as a fractional exponent as [tex]a^{\frac{1}{3}[/tex].

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

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Answer:

18 songs

Step-by-step explanation:

15 x 1.6 = 24

24 x 0.75 - 18

Answer: x = 9

Step-by-step explanation: To find the value of x, we must understand a few things:

- whatever is in lines like | 2x + 4 | means it's the absolute value or positive value of the number.

Now, with that out of the way, I have one more thing to explain.

- whenever trying to find the value of a variable, you need to do inverse operations, so the opposite of adding is subtracting, and the opposite of multiplication is division. Now, let's solve:

22 - 4 = ?

? = 18

18 / 2 = ?

?(x) = 9

Therefore, x = 9

We can check our answer by doing:

| 2(9) + 4 | = 22

2 x 9 = 18

18 + 4 = 22

22 = 22

So, both answers add up, so x = 9

I hope this helps!

The z-score for the 0.75 proportion is -1.95.

The Z-score calculates the deviation of the measure from the mean in standard deviations. We seek for the p-value linked with this Z-score after locating the Z-score in the z-score database.

The likelihood that the value of the measure will be less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.

In a set with mean X and standard deviation μ, the z score of a measure X is given by:

Z=(X-μ)/σ

In this problem, we have that:

n=100,p=0.82

So,μ=E(X)=np=100×0.82=82

Therefore, √V(X)=√np×(1-p)=√100×0.82×0.18=3.841

For Finding the probability that less than 75 in the sample keypads pass inspection.

Using continuity correction, this is (P(75-0.5)<=P(74.5)), which is the p-value of Z when X = 74.5.

=>z= (74.5-82)/3.841

=>z= - 7.5/3.841

=>z= - 1.95 has a p-value to 0.

Hence, if a random sample of 100 keypads is analyzed and 75 pass inspection, then the z-score for 0.75 proportion is -1.95

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The sum of the interior angle measures of the polygon is 900 degrees

From the image shown, we can see that the polygon has 7 sides.

A polygon with seven sides is called a heptagon

It is important to note that the number of triangles in a heptagon is 5.

Also, the sum of angles in a triangle is 180 degrees.

Now, the formula for calculating the sum of interior angles of a polygon is expressed as;

= (n - 2) 180

Where; n is the number of sides of the polygon

Substitute the value

= (7-2)180

Subtract the value

= 5(180)

= 900 degrees

Hence, the sum is 900 degrees

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she will be able to knit 13 scarfs

Given ,

To Find : Scarfs Mr John will be able to make if he has 30.42 yards of yarn

2.34 yards of yarn = 1 scarf

30.42 yards of yarn = [tex]\frac{30.42}{2.34}[/tex]

                                 = 13 scarfs

Hence , the number of scarfs Mr John will make with 30.42 yards of yarn is 13

Slope form -

y - y1 = m(x - x1)

y - 0 = -5(x - 1)

y = -5x + 5