Find the orthocenter of a triangle with vertices (−8, 11), (−3, 11), and (−3, −12).
The orthocenter of triangle is at ( , ).

Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

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Answer: x > 20

Step-by-step explanation:

9 - x < - 11

In this scenario, we've to collect like terms in order to.wolve for x. This will be:

9 - x < - 11

- x < - 11 - 9

- x < - 20

Divide both side by -1

-x/-1 < -20/-1

When we divide by a coefficient with minus sign, the sign changes too from less than to greater than

-x/-1 < -20/-1

x > 20

Answer:

  a) $190

  b) $205.96

Step-by-step explanation:

The tax is figured as ...

  tax = tax rate · purchase price

Then ...

  purchase price = tax/(tax rate) = $15.96/0.084

  purchase price = $190

__

The total price is the purchase price with tax added.

  total price = purchase price + tax

  = $190 +15.96

  total price = $205.96

Answer:

a. 115 degrees

b. 35 degrees

c. 30 degrees

Step-by-step explanation:

Answer:

Building and solving an equation, it is found that the coordinates are: (9,0).

We are given two points: A(-9,3) and B(21, -2).

We also want point C(x,y).

C is 3/5 of the way from A to B, thus:

This is used to find both the x-coordinate and the y-coordinate of C.

First, the x-coordinate, considering .

Then we get 9,0

Step-by-step explanation:

Abby should write her equation as k = 1.61m.

The correct option is B.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Given:

Abby knows that 1 mile is about 1.61 kilometers.

To write an equation, which she can use to convert any given distance in miles (m) to kilometers (k):

Let m be the total number of miles and k be the kilometers.

So, the equation is,

k = 1.61m

Where 1.61 is multiplied by m.

Therefore, the equation is k = 1.61m.

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Answer: 0.393 ; 0.9933

Step-by-step explanation:

Given that :

Mean lifetime follows an exponential distribution (m) = 6

a. What is the probability that the CPU fails in the next three years?

Using the poisson distribution formula :

1 - e^-λt

λ = 1/m = 1 / 6 = 0.1667

Probability of failure in next 3 years :

P(X < 3) = 1 - e^-λx

P(X < 3) = 1 - e^-0.1667*3

P(X < 3) = (1 - e^-0.5)

P(X < 3) = 1 - 0.6065306

P(X < 3) = 0.3934693

= 0.3935

b. Assume that your corporation has owned 10 CPUs for three years, and assume that the CPUs fail independently. What is the probability that at least one fails within the next three years?

Number of pc owned = 10

CPU failure is indepndent

Probability of atleast one fails :

1 - P(X ≥ 3)^n

P(X ≥ 3) = 1 - P(X < 3)

P(X ≥ 3) = 1 - 0.3935 = 0.607

Hence,

1 - P(X ≥ 3) = 1 - 0.6065^10

1 - P(X ≥ 3) = 1 - 0.0067345

1 - P(X ≥ 3) = 0.993265

= 0.9933

Answer:

n = 1

Step-by-step explanation:

Represent the number with n.

Then:  reciprocal of this numer is 1/n.

1/2 added to this reciprocal comes to 1/n + 1/2, and this is equal to

2(1/n) - 1.

We must simplify this equation and solve for n:

Use the LCD 2n:

2 + n = 4 - 1, or 2 + n = 3, or n = 1.

Answer:

  2/3

Step-by-step explanation:

Let x represent the number. Then its reciprocal (the reciprocal of the original number) is 1/x

  1/2 + 1/x . . . . . 1/2 added to the reciprocal of a number

  2/x -1 . . . . . . . 1 less than twice the reciprocal of the original number

We want these expressions to be equal:

  \(\dfrac{1}{2}+\dfrac{1}{x}=\dfrac{2}{x}-1\\\\\dfrac{3}{2}=\dfrac{1}{x}\qquad\text{add 1-(1/x)}\\\\x=\dfrac{2}{3}\qquad\text{multiply by 2x/3}\)

The original number is 2/3.

Answer:

Option E. None of the above.

Step-by-step explanation:

From the question given above, the following data were obtained:

f(x) = (x – 5)/(2x + 3)

Inverse of f(x) => f¯¹(x) =?

Recall:

When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e

f(x) × f¯¹(x) = 1

With the above information, we can determine the inverse of function given above as follow:

f(x) = (x – 5)/(2x + 3)

Inverse of f(x) => f¯¹(x) =?

f(x) × f¯¹(x) = 1

(x – 5)/(2x + 3) × f¯¹(x) = 1

f¯¹(x)(x – 5) / (2x + 3) = 1

Cross multiply

f¯¹(x)(x – 5) = (2x + 3)

Divide both side by (x – 5)

f¯¹(x) = (2x + 3) / (x – 5)

Thus, the inverse of the function is (2x + 3) / (x – 5).

Option E gives the correct answer to the question.

Answer:

calculator gave me 6.5732

Step-by-step explanation:

There are 9444 men and 24555 females are present.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Total students = 34000

For every 5 male students there are 13 female students.

So, the number men are

= 5/18 x 34000

= 9444

and, number of women

= 13/ 18 x 34000

= 24, 555.

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The question attached here is in other language whose translation is given below.

In a school for every 5 male students there are 13 female students. If the total number of students is 34,000, how many men and women are there?

For finding a 95% confidence interval:

a) The sample mean is x = 16.13.

The sample standard deviation is s = 6.948.

The degrees of freedom are df = 10.

The critical value of t for a 95% confidence interval is t = 2.228.

The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.

The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).

b) The 95% confidence interval is (11.867, 20.393).

This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.

c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.

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The perimeter of the given figure for the given values is equal to 24units.

As given in the question,

Given values of the figure,

AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm

HG = AB - (EF + CD)

      = 8- (3 +1)

      = 4 units

AH = (BC-DE)+FG

     = (3-2)+1

     =2units

Perimeter of the given figure

= AB + BC+ CD+ DE+ EF+ FG+ GH+ HA

= 8+ 3+ 1+ 2+ 3+ 1+ 4+ 2

=24 units

Therefore, the perimeter of the given figure for the given values is equal to 24units.

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According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.

To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.

In this case we can conclude that the total yardage traveled was 140 yards because:

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Answer:

I think its C

Step-by-step explanation:

Answer:

  B.  28%

Step-by-step explanation:

You want to know the percent of the mixture that is fruit juice, if the mixture is 6 L of 52% juice and 9 L of 12% juice.

The total amount of juice in the 6+9 = 15 L of mix is ...

  0.52·(6 L) +0.12(9 L) = 3.12 L +1.08 L = 4.2 L

Then the fraction of the mix that is fruit juice is ...

  (4.2 L)/(15 L) = 0.28 = 28%

The percent of the mixture that is fruit juice is 28%, choice B.

__

Additional comment

Effectively, the fraction is the weighted average of the fractions of the constituents. The weights are the number of liters of each constituent.

<95141404393>

Answer:

314.00

Step-by-step explanation:

Answer:

15.70

Step-by-step explanation:

A=r^2

Answer:

13

Step-by-step explanation:

u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .

Answer: A = 15 units²

Step-by-step explanation:

The figure has 1 pair of parallel sides and is therefore a trapezium.

The area (A) of a trapezium is calculated as

A =  h (b₁ + b₂ )

where h is the perpendicular height between bases and b₁, b₂ are bases

here h = 3, b₁ = 3 , b₂ = 7 , then

A =  × 3 × (3 + 7) = 1.5 × 10 = 15 units²

To find:

Select the properties that are true.

Solution:

The square:

All sides are congruent, the square has four right angles, two pair of parallel sides.

The parallelogram:

Two pair of parallel sides.

Rhombus:

the rhombus has all sides are congruent, two pair of parallel sides.

Answer:

Step-by-step explanation:

x = 7

The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

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

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

n = 18

Step-by-step explanation:

n/2 + 15 = 24

n/2 = 9

n = 18

Answer: B

Step-by-step explanation:

Answer:

628.32

Step-by-step explanation:

V=πr2h=π·52·8≈628.31853

Answer:

radius x radius x pi x height = volume of cylinder

5 x 5 x 3.14 x 8 = 628

628cubic cm

Hope this helps

Step-by-step explanation:

Check the picture below.

\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=x\\ h=6x-20\\ A=50 \end{cases}\implies 50=\cfrac{1}{2}(x)(6x-20) \\\\\\ 50=\cfrac{6x^2-20x}{2}\implies \boxed{50=3x^2-10x}\)