The cost of a ticket to the circus is $22.00 for children and $46.00 for adults. On a certain day, attendance at the circus was 1,400 and the total gate revenue was $52,400. How many children and how many adults bought tickets?

An automobile manufacturer produces production parts with 98% accuracy.  the probability is mathematically given as

P(X\leq2) = 0.9868

Generally, the equation for the probability is mathematically given as

[tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]

Therefore

[tex]P(X=0)=\binom{25}{0}* 0.98^{25}* 0.02^{0}=1* 0.6035* 1\\\\P(X=0)=0.6035[/tex]

Hence

P(X=1)=0.3079

P(X=0)=0.07554

In conclusion, bringing the equation into view

 [tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]

[tex]P(X\leq2) = 0.6035 +0.3079 + 0.07554[/tex]

P(X\leq2) = 0.9868

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Factorize the numerator and denominator, then simplify:

10/45 = (2×5)/(9×5) = 2/9

Now,

1/9 = 1/10 + 1/90

1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900

1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000

and so on, which is to say

1/9 = 1/10 + 1/100 + 1/1000 + …

or

1/9 = 0.111…

so that multiplying both sides by 2 gives

2/9 = 0.222…

Using proportions, it is found that the homeowner would have to pay $2,750 in property tax each year.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax at a rate of 25 mills means that for each $1,000 in value of the home, he pays $25 in taxes. Hence, for a home of value of $110,000, the amount he pays in taxes is given by:

A = 110 x 25 = $2,750.

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Answer:

3rd

Step-by-step explanation:

If you know about linear eq. it's just a simple rule no worry

La encuesta indica que de entre todos los estudiantes de una carrera, 4500 les gusta leer.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{30}{100} =\frac{3}{10}=0.3*100=30 \%[/tex].

The question gives:

Then, you will have:

[tex]6000\cdot \frac{75}{100}\\ \\ 6000\cdot \frac{3}{4}\\ \\ \frac{18000}{4} =4500[/tex]

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if it's diameter is 19, then its radius must be half that, or 9.5.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=9.5\\ h=4.5 \end{cases}\implies V=\pi (9.5)^2(4.5)\implies V\approx 1275.9~ft^3[/tex]

Answer:

-10,-13,-16 and importance of being in a good night friends ni pta nhi hai to you

Answer:

3

Step-by-step explanation:

Parallel lines are a fixed distance apart and will never meet, no matter how long they are extended. Lines that are parallel have the same gradient . The equations above, y = 3x -2 and y = ?  x +3  have the same gradient of 3 if they are to be parallel

Hope you understood and this helped and have a good day

Answer:

Train A = 466

Train B = 60

Step-by-step explanation:

Step-by-step explanation:      

Step 1: Simplify

[tex]4+9x^2/3 - 1[/tex]

[tex]=4+3x^2+-1[/tex]

Step 2: Combine Like Terms:

[tex]= 4+3x^2+1-1[/tex]

[tex]= (3x^2)+(4+-1)[/tex]

Answer: [tex]= 3x^2+3[/tex]

Explanation in words (Short Form)

-  The first step is to use the formula and simplify it. So first we will Rewrite the division as a fraction.

- The second step is to Cancel the common factor of 9 and 3. Then Factor 3 out of 3. After that Cancel the common factor.

- The third step is to divide [tex]3x^2[/tex] by 1. Then at the end, subtract 1 from 4. The answer will result as [tex]3x^2+3[/tex]

Answer:    

[tex]=3x^2+3[/tex]

Hope this helps.

Answer:

Sqrt (11/8)

Step-by-step explanation:

Sec^2 - Tan^2 = 1

- Tan^2 = 1 - Sec^2

Tan^2 = -1 + Sec^2

Tan^2 = 3/8

3/8 = -1 + Sec^2 Theta

1 + 3/8 = Sec ^2 Theta

11/8 = Sec^2 Theta

Sqrt ( 11/8) = Sec of theta

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

Answer:

the class earned $722059884

Step-by-step explanation:

because each person sold 444 tickets and there was 232323 students

=232323×444

=103151412

because 103151412 tickets were sold and a ticket cost $7

=103151412×7

=722059884

Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

So for 13th n

#c

attached

#d

Already given in c

Explanation:

Draw out a 10 squares.

Shade in 4 of them to represent 4/10 = 0.40 = 0.4

Then use another color to shade another 4 squares. You should have 4+4 = 8 squares shaded, out of 10 total, giving 8/10 = 0.80 = 0.8

This is one visual way to see how 0.4 x 2 = 0.8

In other words, 0.4 x 2 means we have two copies of 0.4 added together. You could write it as 0.4 x 2 = 0.4 + 0.4 = 0.8 if you wanted.

See the diagram below.

The correct answer is option A which is the expression will be 0.9S.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

At the end of every month, Katie saves 20 percent of her take-home pay after her taxes. If Katie is taxed at a 25 percent tax rate,

The expression of the salary after six months will be calculated as:-

Let the gross salary is S

The net salary will be = 0.75S

Savings will be = 0.75 x 0.20 S = 0.15S

After six months the savings will be:-

Savings  = 0.15 x 6 S

Savings = 0.9S.

Therefore the correct answer is option A which is the expression will be 0.9S.

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The income tax that will be paid for the year will be RS 4199.

The total income that the ma gets will be:

= 39990 + 2000

= 41990

The tax rate is given as 10%. Therefore, the income tax that will be paid this year will be:

= 10% × 41990

= 4199

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The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.

Hence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

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Answer:The result follows from manipulating the conditional probability. By definition,

By the law of total probability,

So we have

Step-by-step explanation:

P(A|B) = P(B|A)×P(A)/P(B)

so, in our case

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/P(B1)

I assume that the problem definition means that A1, A2, A3 are independent and not overlapping events (hence their sum is 1). and therefore, B1 can only happen after A1 or after A2 or after A3. there is no other possibility for B1 to happen.

so,

P(B1) = P(B1|A1) + P(B1|A2) + P(B1|A3) =

= 0.25 + 0.05 + 0.1 = 0.4

therefore,

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/0.4 = 0.1

−9x^4−18x^4y+27x^2y^2

Answer:

=−18x^4y−9x^4+27x^2y^2

Step-by-step explanation:

(−9x^2)(x^2+2x^2y−3y^2)

=(−9x^2)(x^2+2x^2y+−3y^2)

=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)

=−9x^4−18x^4y+27x^2y^2

=−18x^4y−9x^4+27x^2y^2

---

Hope I helped! Have a great day :)

Answer:

r = 5   ; s = -9

Step-by-step explanation:

First simplify √8  by

   [tex]\sf \sqrt{8}=\sqrt{2*2*2} = 2\sqrt{2}\\[/tex]

[tex]\sf \dfrac{5+\sqrt{2}}{4}+\sqrt{8}= \dfrac{5+\sqrt{2}}{4}+ 2\sqrt{2}[/tex]

          Find LCM and simplify

                     [tex]\sf = \dfrac{5+\sqrt{2}}{4}+\dfrac{2\sqrt{2}*4}{1*4}\\\\ =\dfrac{5+\sqrt{2}+8\sqrt{2}}{4} \ {\bf Combine \ like\ terms} \\\\ = \dfrac{5+9\sqrt{2}}{4}\\\\[/tex]

 [tex]\sf \boxed{r=5}\\\\\boxed{s =-9}[/tex]

The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.

Rational function are functions that are written as a ratio. For instance a/b can be expressed as rational function.

According to the question, we are to plot the graph of the function 10/x

The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.

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Answer:

Step-by-step explanation:

There are 36 ways 2 dice can be thrown. Sometimes colors are used to tell the difference between the dice.

36 comes from 6*6

Suppose you have 2 dice 1 blue and the other white

Blue      White

1              1

              2

              3

              4

              5

              6

There's 6 ways that have been thrown. Then you go to the blue dice being 2. You get six more. Then 3 gives you six more 4 gives you another six. and so on. The whole procedure adds to 36

you can throw a four 3 ways

Blue       white

1               3

3              1

2              2

You can throw 7 six ways

Blue         white

1                 6

6                1

2               5

5               2

3               4

4               3

So of the 36 ways to throw the dice 9 will successful. (6 + 3)

Answer: 9/36 = 1/4 times you will be successful

Answer:

21. x = 18.1

22. x =28.7

Step-by-step explanation:

SOH = sin(theta) = opp/hyp

CAH = cos(theta) = adj/hyp

TOA = sin(theta) = opp/adj

21. You would be using tangent.

tan(theta) = Opp/Adj

tan(32°) = x/29

x = 29 * tan(32°)

x = 18.1

22. You would be using cosine

cos(theta) = Adj/Hyp

cos(43°) = 21/x

x * cos(43°) = 21

x = 21 / cos(43°)

x = 28.7

Use a Calculator to help you solve for those side lengths or degrees.

If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using

I am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.

The slant height can be found using Pythagoras theorem, the slant height is the hypotenuse side of the pyramid. Therefore, slant height = √34 meters

The base of the pyramid is a square.

Therefore,

area of a square = l²

where

hence,

area of the base  = l

36 = l²

l = √36

l = 6 meters

Therefore, using Pythagoras theorem,

l² = 5² + 3²

l² = 25 + 9

l² = 34

l = √34 meters

slant height =  √34 meters

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Answer:

  6√3 ±3 ≈ {7.392, 13.392}

Step-by-step explanation:

The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.

__

Radii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.

A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...

  AB = √(21² -3²) = √432 = 12√3

This is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...

  6√3 ±3 ≈ {7.392, 13.392}

Answer:

6√3 ± 3

Step-by-step explanation:

AC is the radius of Circle C ⇒ radius = 12

DB is the radius of Circle D ⇒ radius = 9

Therefore, CD = AC + DB = 12 + 9 = 21

AE is the radius of Circle E ⇒ radius = 3

BF is the radius of Circle F ⇒ radius = 3

If AB is the common tangent of Circles C, D, E and F, then:

∠CAB =∠AEF = ∠DBA = ∠BFE = 90°

(as the tangent to a circle is always perpendicular its the radius).

Also AB = EF

To find the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F, we first need to find the length of EF (marked by x on the attached diagram).

CD is the hypotenuse of a right triangle with base equal to EF and a smaller leg of the difference between the radii of Circles C and D.

(Refer to the green shaded triangle on attachment 1)

Therefore, to find EF (x), use Pythagoras' Theorem a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ a² + b² = c²

⇒ 3² + x² = CD²

⇒ 3² + x² = (12 + 9)²

⇒ 9 + x² = 441

⇒ x² = 432

⇒ x = √432

⇒ x = 12√3

⇒ EF = 12√3

As the radius of Circles E and F is 3, the possible diameter of the circle with its center as the midpoint of EF is 6 less or 6 more than the length of EF.

⇒ diameter = EF ± 6

                   = 12√3 ± 6

As the radius is half of the diameter, the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F is:

⇒ radius = diameter ÷ 2

               = (12√3 ± 6) ÷ 2

               = 6√3 ± 3

(see attachments 2 and 3 → the possible circles are shown in orange)

Answer:

C. g(x) = sqrt(x+8)-2

Step-by-step explanation:

"Shift two units down" is easier to see in the equation because an up or down shift is just tacked right on to the end of the equation. So "shift DOWN 2" is a minus two on the end of the equation. This means that A and D are both NOT the answer.

Left and right shifts are the opposite of what you might expect. Left shift is a "+ anumber" and Right shift is

"- anumber" This is tucked in very close to the x, because a left or right shift is a change in the x-direction. Again left shift is "+ anumber", so in your question, "shift eight units left" shows in the equation as the plus8 beside the x.

So B is wrong and C is the answer.

Answer:

none

Step-by-step explanation:

4x - 6 = 2(2x + 3)

4x - 6 = 4x + 6

Everything cancels out meaning there are no real solutions

Answer:

x=6, y=4

Step-by-step explanation:

x - y = 2

2x = 3y => 2x - 3y = 0

x - y = 2 | ×(-2) => -2x + 2y = -4

2x - 3y = 0

-2x + 2y = -4

2x - 3y = 0

___________

0 - y = - 4 | ×(-1)

y = 4

Substitution in x - y = 2:

x - 4 = 2 | +4

x = 2+4 = 6

The explicit formula for the amount of money in his account at the beginning of month n is  a(n) = 2300 + (n − 1)200.

The explicit formula would be a linear function. A linear function is a function that has a single variable raised to the power of 1.The rate of increase in the account is a constant amount : $200

Amount of money at the beginning of the  month = beginning balance + (number of months - 1) x rate of increase

a(n) = 2300 + (n − 1)200

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