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An inscribed circle is the largest circle contained in the polygon (triangle):

• Bisects two angles of the triangle.

• The angle bisector will intersect at the intercenter.

Procedure

To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.

The average before training with new trainer is 20 mph.

Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer

Keep the values in formula to find the average speed with old trainer.

21 = 5/100x + x

Multiplying the equation with 100

2100 = 5x + 100x

Performing addition

105x = 2100

Shifting 105 to Right Hand Side of the equation

x = 2100 ÷ 105

Performing division on Right Hand Side of the equation

x = 20

Thus, average speed with old trainer was 20 mph.

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The center of the hyperbola is (2, -3)

A hyperbola is a curve that is open and that has two branches and it is symmetrical

The equation is given as

(y + 3)²/9 − (x − 2)²/2 = 1

A hyperbola is represented as

(y - k)²/a² − (x − h)²/b² = 1

Where the center of the hyperbola has the coordinates of (h, k)

The values of h and k in the given equation (y + 3)²/9 − (x − 2)²/2 = 1 are

h = 2 and k = -3

This means that:

(h, k) = (2, -3)

So, we have coordinates of the center to be (2, -3)

Hence, the center is (2, -3)

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Answer:

First answer is obtuse

The second answer is scalene

Step-by-step explanation:

Obtuse is when an angle is over 90

Scalene since all the angles are different, all the side lengths are different.

By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.

Combination is the arrangement of objects in which order is not taken into account.

The applicable formula is:

n combination r = n!/[(n - r)!r!]

where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).

Hence;

10 combination 4 = 10!/[(10 - 4)!4!] ways

10 combination 4 = 10!/(6! × 4!) ways

10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways

10 combination 4 = 10 × 3 × 7 ways

10 combination 4 = 210 ways

Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.

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The required probability is 0.852

Here, n=15

P(X ≤5) = P(X = 1)+...+ P(X = 5)

            = [(¹⁵₀)(0.25)⁰ (1-025)¹⁵⁻⁰ +...(¹⁵₅)(0.25)⁵ (1-0.25)¹⁵⁻⁵]

            = 0.01336+...+0.16515

            = 0.85163

            = 0.852  (Round to 3 decimal place)

Hence, the required probability is 0.852

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The line should be perpendicular to x = -4

x= -4 is a vertical line crossing the x axis at x= -4

The slope is undefined in x =-4

For an equation in slope intercept form, the general form is ;

y= mx + b where m is the slope and b is the y-intercept

So for any y value, x is always -4

Thus the slope for line x = -4 is not defined

A line perpendicular to x = -4 will thus be a horizontal line with slope 0

For the equation of this line

0= y--5/x-4

0 = y+5 /x-4

0{x-4} = y +5

0 = y+5

y= - 5

The money which is expected to spend on new word processors during this year is

The probability distribution is

x:          0            1             2            3

f(x)         [tex]\frac{1}{10}[/tex]           [tex]\frac{3}{10}[/tex]           [tex]\frac{2}{5}[/tex]              [tex]\frac{1}{5}[/tex]

If the cost of the desired model is $1200 per unit and at the end of the year a refund of 50x2 dollars

So total money spent in this year is [tex]1200x-50x^2[/tex]          

Then the equation of expenses will be

[tex]\text{Expenses}=E(1200x-50x^2)[/tex]

We can rewrite it as

[tex]\text{Expenses}=E(1200x)-E(50x^2)[/tex]  

  [tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]   -----------------(1)

Now the mean of the probability distribution is ,

[tex]E(x)=\sum_{ }^{ }((x_i)(f(x_i))\\=(0\times\frac{1}{10})+(1\times\frac{3}{10})+(2\times\frac{2}{5})+(3\times\frac{1}{5})\\=\frac{3}{10}+\frac{4}{5}+\frac{3}{5}\\\\=\frac{3+8+6}{10}\\\\=\frac{17}{10}\\\\=1.7[/tex]      

The variance of the function is

[tex]E(x)=\sum_{ }^{ }(x_i^2)(f(x_i)[/tex]

        [tex]=(0^2\times\frac{1}{10})+(1^2\times\frac{3}{10})+(2^2\times\frac{2}{5})+(3^2\times\frac{1}{5})[/tex]

        [tex]=\frac{3}{10}+\frac{8}{5}+\frac{9}{5}[/tex]

        [tex]=\frac{37}{10}[/tex]

        [tex]=3.7[/tex]

On substituting the values in equation (1)

[tex]\text{Expenses}=1200E(x)-50E(x^2)[/tex]

              [tex]=1200(1.7)-50(3.7)^2[/tex]

              [tex]=2040-684[/tex]

              [tex]=1855[/tex]

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Answer:

0.14 meters, or 140 mm

Step-by-step explanation:

(1/40) means that the model car will have dimensions that are (1/40) the original car.

Real car = 5.5 meters.

Model car = (1/40)*(5.5 m) = 0.14 meters, or 140 mm

The value of f¹(x) = x/5

What is function?

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

We are given f(x) = 5x

and we are to find inverse of f(x).

Replace f(x) by y.

So,

y = 5x

Isolate x

x = y/5

Replace x by f'(y)

So,

f'(y) = y/5

Replace all occurrences of y by x.

So,

f'(x) = x/5

Therefore, the inverse of function f(x) = 5x is f'(x) = x/5

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9x + 6 - 4x - 2x + 1 - 15

9x - 4 x- 2x = (9-4-4)x = 3x

6 +1 -15 = -8

____________

Answer

3x -8

______________

Please tell me if you can see the updates

ok

________________

Answer:B

Step-by-step explanation:

Answer:

(C) I and III only.

Step-by-step explanation:

Hello! It's me again! Let's help you with this question too!

Now, let's start understanding what information is given to us.

[tex]a < b < 0[/tex]

This means that, some integer a is lower than some integer b and b is lower than 0. So right out of the gate, both integer a and b are both negative numbers. Here, we can evaluate all 3 possibilities like so:

I. [tex]\frac{a}{b} > 0[/tex]

To start, let's see if this is true. The simplest way is to substitute values into integer a and b to where [tex]a < b < 0[/tex] holds true as well. For this example, we can say [tex]a=-2[/tex] and [tex]b=-1[/tex]. If we evaluate as such, it would be:

[tex]\frac{-2}{-1} > 0[/tex]

[tex]2 > 0[/tex]

From this example, 2 is higher than 0. Meaning this is true. Now, it'll be true for every value due to something called the fraction rule. Fraction rule is simply just stating that, if the numerator and denominator both have a negative sign, they cancel each other out and become a positive fraction. So, we can say I. is true.

II. [tex]-b > -a[/tex]

This is simple to prove, all it's saying is that negative integer b is always going to be higher than negative integer a. Using our same example from I. we can substitute as such and evaluate:

[tex]-(-1) > -(-2)[/tex]

[tex]1 > 2[/tex]

Here, we can see that 1 is not greater than 2 and no matter what numbers you substitute, that will always be the case because you're essentially putting the lowest number first and seeing if it's greater than the lower number. So II. is false.

III. [tex]0 < \frac{b}{a} < 1[/tex]

Now this one is a bit more difficult. However, there isn't much we need to do here. This is saying that 0 is lower than [tex]\frac{b}{a}[/tex] but [tex]\frac{b}{a}[/tex] is lower than 1.  Let's split this into 2 parts.

Part 1: [tex]0 < \frac{b}{a}[/tex]

This isn't the same as I. as the numerator and denominators have switched. Let's use the values we've set back in I. to see if this holds true:

[tex]0 < \frac{-1}{-2}[/tex]

[tex]0 < \frac{1}{2}[/tex]

From here, we find that it is true. And it also holds true that it is less than 1. We can use another set of values to see if this still holds. Let's try [tex]a=-7[/tex] and [tex]b=-3[/tex]:

[tex]0 < \frac{-3}{-7}[/tex]

[tex]0 < \frac{3}{7}[/tex]

As you can see here, using the fraction rule. So long as there is an integer a and b are different (they always will be because of [tex]a < b < 0[/tex]), regardless of what they will be, it will always give us a fraction answer. And a fraction answer will always be lower than 1. Therefore, III. is also true.

So, the answer to this question is C. I and III only

Step-by-step explanation:

A./11.7/,/22.6/,10.3/

11.7<22.6>10.3

B./-10.3/,/-10.7/,/7.3/

10.3<10.7>7.3

C./-2.5/,/1.42/,/1.25/

2.5>1.42>1.25

D./-9.3/,/-9/,/7.43/

9.3>9>7.43

therefore the answer is C and D

The line that is perpendicular to the equation of a line given is y = -2x + 3

The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.

For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).

To find an equation of a line;

The equation of the line can be modified into y - y₁ = m(x - x₁)

substituting the values into the equation above gives y = -2x + 3

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The angle x of the triangle is 60 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.

A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.

Therefore, the angle x of the triangle can be found as follows:

x + x + x = 180

3x = 180°

divide both sides of the equation by 3

3x / 3 = 180 / 3

x = 180 / 3

x = 60 degrees.

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Answer:

the person below or above me is the answer. Yeah

Step-by-step explanation:

Answer:

x = 11.2 cms.

Step-by-step explanation:

I infer that the units are in centimeters.

8-3 = 5

One side = 5 cm

Other side = 10 cm

By the Pythagorean Theorem:

x² = 5² + 10²

x² = 25 + 100

x² = 125

√x² = √125

x = 11.18 cms

To the nearest tenth:

x = 11.2 cms

sSlope means the inclination of the line

Intercept is the point where the line touches the Y axis.

Answer:2 is the scale factor

Step-by-step explanation:

Based on the package of boondins and the package of rews, the package of rews will have a weight in relation to the package of boondins that is 3.77 ounces

To find how much more that the package of rews weighs over the boondins, deduct the weight of the package of boondins from the weight of a package of rews.

Weight of package of rews = 9.97 ounces

Weight of package of boondins = 6.2 ounces

The difference in the weight of the packages is:

= 9.97 - 6.2

= 3.77 ounces

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The required difference in the package of the bodies and rews is 3.77 ounces.

As per the given in the question,
boudin is 6.2 ounces in weight and rews are 9.97 ounces in weight.

here,
As per observation, rews weighs more than bodies, and the difference between their weights is simply evaluated from the subtraction between the weight. So,
Weigh difference = weigh of rews  - weigh of boodins
Substitute the value in the above equation,
Weigh difference = 9.97 - 6.2 = 3.77.

Thus, the required difference in the package of the bodies and rews is 3.77 ounces.

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Answer:

We have been given an equation . We are also told that x is greater than 0. We are asked to choose the equation that can be written as our given equation.

Since x is greater than, so we will take positive root on both sides of our given equation as:

Upon looking at our given choices, we can see that option C is same as our answer.

Step-by-step explanation:Therefore, option C is the correct choice.

Answer:2=x

Step-by-step explanation:

x+4=x^2

0+4=x^2

Square root 4 = square root x^2

2=x

Given:

There are given that the number of people who said yes is 191 and who said no is 485.

Explanation:

According to the given question:

The total number of people is:

That means the total outcome is 676.

Now,

The probability that the person is chosen own dog is:

So,

Final answer:

Hence, the correct option is C.

Answer:

191/676.

Step-by-step explanation:

The total number of people asked is 191 + 485

= 676.

So. the required probability

= number of people owning a dog/ total number of people

= 191/676.

The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.

It follows from the task content that the regular train ticket costs, 3.00.

Therefore, the cost for travelling x times with the month is; 3x.

On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;

3x = 18.75

x = 18.75/3

x = 6.25 times.

Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.

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   y - 5 = -1 ( x + 3 )  is Equation of a Lin in slope intercept form,.

What is in slope-intercept form?

Slope between the points M(-3, 5) and N(2, 0).

       m = 0 - 5/2 + 3

       m = -5/5  = -1

the equation of   point-slope form

    y - y₁ = m ( x - x₁ )

   y - 5 = -1 ( x - ( -3 ))

   y - 5 = -1 ( x + 3 )

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Answer:

The three options you would pick is
y2 – 5y = 750
750 – y(y – 5) = 0
(y + 25)(y – 30) = 0

Step-by-step explanation:

Hope this helps! :))

Answer:

y=x+1

Step-by-step explanation:

y-y1=m(x-x1)

y-2=1(x+3)

y-2=x+3

y=x+1

Answer:

4 * ( 2 + 3 * 2) = 32

Step-by-step explanation:

The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.

Assuming that each of the sophomores, each of the juniors and each of the seniors is equally likely to be selected for the committee, there are b. 1211760 ways can the governance committee be selected, if it must be made up of 2 sophomores, 2 juniors and 3 seniors. The committee can be selected in 1,211,760 ways.

Combination formula:

Cn,x is the number of different combinations of x objects from a set of n elements, given by:

Cnₓ= n!÷ x! (n-x!)

In this problem:

2 sophomores from a set of 18.

2 juniors from a set of 12.

3 seniors from a set of 10.

They are independent, so we can just multiply them, thus:

T= C₁₈,₂ × C₁₂,₂× C₁₀,₃ = 18! ÷2!6! × 12!÷ 2!10! × 10!÷ 3!×7! = 1211760

The committee can be selected in 1,211,760 ways.

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Answer:

-44.09

Step-by-step explanation:

Trust bro i am passing collage math at 15

Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.

A = L * B

Hence the width B may be found from

1400 = 56 * B

B = 1400/56

B = 25 feet

b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,

the total cost to fence the backyard will be

= $10 * 2(56 + 25)

= $1,620