An adult ticket costs $5.25 and a child ticket costs $3.05. If $498.60 were collected for 100 tickets, how many child tickets were sold?

Answer:

$550+/-$20.79

= ( $529.21, $570.79)

Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $550

Standard deviation r = $75

Number of samples n = 50

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

$550+/-1.96($75/√50)

$550+/-1.96($10.60660171779)

$550+/-$20.7889393668

$550+/-$20.79

= ( $529.21, $570.79)

Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)

Answer:

Option A is the correct answer.

Step-by-step explanation:

Line is passing through the point[tex] (2, - 6) = (x_1, \: y_1) [/tex] and its slope is - 3.

Equation of line in slope point form is given as:

[tex] y-y_1 = m(x-x_1) \\

\therefore y-(-6) = - 3(x-2) \\

\huge \red {\boxed {\therefore y + 6 = - 3(x-2)}} \\[/tex]

Answer: A

Step-by-step explanation:

Point-slope form is the following: y - y1 = m(x - x1). So all that is needed is to substitute y1 for -6, x1 for 2, and -3 for m(the slope).

y - y1 = m(x - x1)

y - (-6) = -3(x - (2))

y + 6 = -3(x - 2)

Answer:

Initial Fee is $2.

Step-by-step explanation:

Answer:

4:3

Step-by-step explanation:

240:180=

60(4):60(3)=

4:3

Hope this helps!

Answer:

4:3

Step-by-step explanation:

24:18

4:3

Answer:

[tex](x - 4)(x - 5)[/tex]

Step-by-step explanation:

x2 − 9x + 20

[tex] {x}^{2} - 9x + 20 \\ {x}^{2} - 5x - 4x + 20 \\ x(x - 5) - 4(x - 5) \\ (x - 4)(x - 5)[/tex]

The factors of the given trinomial are (x-5)(x-4).

The given trinomial is x²− 9x + 20.

To the factor, a trinomial in the form x² + bx + c, find two integers, r and s, whose product is c and whose sum is b.

Rewrite the trinomial as x² + rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).

Now, x²− 9x + 20 can be written as x²− 5x-4x + 20

=x(x-5)-4(x-5)

=(x-5)(x-4)

Therefore, the factors of this trinomial are (x-5)(x-4).

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Answer:

a) 72

b) 1/72

c) 1/36

Step-by-step explanation:

a) number of ways she can choose route= 3C1 = 3

   number of ways she can choose parking lots= 4C1 = 4

number of ways she can choose entrances= 3C1 = 3  

number of ways she can choose elevators= 2C1 = 2

number of ways she can go to office= number of ways she can choose route×number of ways she can choose parking lots×number of ways she can choose entrances×number of ways she can choose elevators

      number of ways she can go to office= 3×4×3×2

                                                                      = 72

b) Probability of morning side= number of morning side/ total number of routes=  1/3

probabiltiy of Parking lot A=  number of parking lot A/ total number of parking lot= 1/4

probability of south entrance= number of south entrance/ total number of entrances=  1/3

probablity of elevator 1=  number of elevator 1/ total number of elevator= 1/2

combine probability= 1/3× 1/4×1/3×1/2 = 1/72

c) Probability of Industrial Avenue= number of industrial avenue/ total number of avenue= 1/3

Probability of parking lot D= number of parking lot D/ total number of parking lot after deducting number of parking lots A and B = 1/2

Probability of north entrance= number of north entrance/ total number of entrance= 1/3

probablity of elevator 2= number of elevator 2/ total number of elevator

                                      = 1/2

combine probability= 1/3 × 1/2 × 1/3 ×1/2

                                  = 1/36

Answer:

30 and 32

Step-by-step explanation:

2/3 ÷ 1/2 = 1.33333333333 or 1.3 for short

-Peter

Answer:

2*2/3 = 4/3

Step-by-step explanation:

2*2/3 = 4/3

Answer:

a ) - 8x^7,

b ) - 4m^2 / nx,

c ) - 11a^2b^18 / 5

Step-by-step explanation:

[tex]a ) (2x^2)(-4x^5),\\-2x^2\cdot \:4x^5,\\-8x^5x^2,\\-8x^7\\\\Solution = -8x^7[/tex]

To solve this problem, I removed ( ), multiplied the terms, and through the " exponential rule " added the exponents to derive the solution - 8x^7

[tex]b ) (36m^2) / (-9nx),\\-\frac{36m^2}{9nx},\\-\frac{4m^2}{nx}\\\\Solution = -\frac{4m^2}{nx}[/tex]

Here I simplified the bit " 36 / 9 " which was found as 4 in the numerator, deriving the solution - 4m^2 / nx

[tex]c ) -11ab^9b^6 / 5b^3a,\\-11b^9\frac{b^6}{5}b^3a^{1+1},\\-11b^9\frac{b^6}{5}b^3a^2,\\-11\cdot \frac{b^6}{5}b^{9+3}a^2,\\-11\cdot \frac{b^6}{5}b^{12}a^2,\\-\frac{b^6\cdot \:11b^{12}a^2}{5},\\-\frac{11a^2b^{18}}{5},\\\\Solution = -\frac{11a^2b^{18}}{5}[/tex]

I applied a combination of " the exponential rule " and the addition of these exponents to receive a simplified solution - 11a^2b^18 / 5.

Answer:

(4x-1)(4x-1)

(x-6)(x+5)

(3x-7)(3x+7)

(3x-1)(x+6)

Step-by-step explanation:

yes

Answer:

213.69 units

Step-by-step explanation:

We have to first find the height of the cone.

We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:

[tex]h^2 = a^2 + b^2[/tex]

where h = hypotenuse

a and b = the other two sides of the triangle

The radius is 4 units and the slant height is 13 units:

[tex]13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units[/tex]

The height of the cone is 12.37 units.

The surface area of a cone is given as:

SA = [tex]\pi r (r + \sqrt{h^2 + r^2} )[/tex]

[tex]SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units[/tex]

The surface area of the cone is 213.69 units.

Answer:

0.46 m

Step-by-step explanation:

area of desks: 8 m by 12 m = 8 m * 12 m = 96 m^2

20% of this area is 20% * 96 m^2 = 19.2 m^2

The area of the border is 19.2 m^2.

Let the path around the desks have width x.

The area of desks plus path is a rectangle 2x + 8 by 2x + 12.

area of desks plus path = (2x + 8)(2x + 12)

= 4x^2 + 24x + 16x + 96 = 4x^2 + 40x + 96

The area of the border is the area of the rectangle that includes the border minus the rectangle that has just the desks.

area of border = (4x^2 + 40x + 96) - (96) =

= 4x^2 + 40x

Above, we have the area of border = 19.2, so we get this equation:

4x^2 + 40x = 19.2

4x^2 + 40x - 19.2 = 0

x^2 + 10x - 4.8 = 0

We now use the quadratic formula to solve the equation for x.

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-10 \pm \sqrt{10^2 - 4(1)(-4.8)}{2(1)} [/tex]

[tex] x = \dfrac{-10 \pm \sqrt{100 + 19.2 )}{2} [/tex]

[tex] x = \dfrac{-10 \pm \sqrt{119.2 )}{2} [/tex]

[tex] x = 0.46 [/tex]  or  [tex] x = -10.46 [/tex]

We discard the negative solution.

Answer: the border is 0.46 m wide.

Answer:

0.350

Step-by-step explanation:

Probability is defined as the chances that an event will occur or not occur. The entire idea of probability has to do with 'chance' events. Thus, the probability that an event will surely occur is 1, while the probability that an event will never occur is zero. Probabilities range between 0-1.

Probability of an event is obtained from

Probability= expected outcome/total number of outcomes

In this case,

Expected outcome= 35

Total number of outcomes = 100

Probability= 35/100= 0.350

Option D( X=15)

Solution,

2x=15+x

or, 2x-x=15

X=15

hope it helps...

Good luck on your assignment...

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

[tex]2x = 15 + x \\ 2x - x = 15 \\ x = 15[/tex]

Answer D is correct

Answer:

Option(1) is the correct answer to the given question .

Step-by-step explanation:

let     [tex]x1, y1=\ (2, 3)[/tex]

[tex](x2,y2)=(\sqrt{15,3} \ )[/tex]

[tex](x3,y3)=\ (4,8)[/tex]

Now we know that

[tex]Area=\ \frac{1}{2} |x1(y2-y3)\ + \ x2(y3-y1)\ + x3(y1-y2)[/tex]

Now putting this value in the formula we get

[tex]\frac{1}{2}|2(3-8)\ +\sqrt{15}(8-3)\ * 4(5-3)|[/tex]

[tex]=\ \frac{1}{2}\ *9.3649[/tex]

=4.6824

Therefore option(1) is the correct answer .

Answer:

Option(1) is the correct answer to the given question .

Step-by-step explanation:

Answer:

They would fall in the same year every 10 years

Step-by-step explanation:

Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.

Now looking at the number of years, we can see we have every 2 and every 10 years

To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10

This can be visualized in a way that;

The reunion has happened now, and will happen in the next 10 years.

Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2

Answer:

1 times

Step-by-step explanation:

Hello,

The alumni have reunions every 10 years

But also have football games every 2 years

We have to find how often do the football and reunion fall the same year.

Working with a space of 10 years

In 10 years, reunions happen only once

In 10 years, soccer games happen five times

Assuming we're in the year 2020,

The next reunion would likely occur in year 2030.

But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.

Checking both soccer and reunion coincidence, we can only find one which is in year 2030.

So, soccer games and reunions happen once in 10 years

Answer:

y = -3/4x - 2

Step-by-step explanation:

You put the equation in the slope-intercept form. Remember that the perpendicular slope is the negative reciprocal. You plug in the slope and the point into the slope-intercept formula. Solve for b then plug it into the final formula.

The equation of the line that passes through the point (8,-8) and is

perpendicular to the line 4x – 3y = 18 is;

⇒ 3x + 4y = -8

Here,

The point is (8, -8)

And, The equation of line is, 4x - 3y = 18

What is Equation of line?

The equation of line passes through points (x₁, y₁) and has slope m is;

y - y₁ = m₂ (x - x₁)

Now,

The point is (x₁, y₁) = (8, -8)

And, The equation of line is, 4x - 3y = 18

Put into the slope form as;

4x - 3y = 18

4x - 18 = 3y

y = (4/3)x - 6

Hence, Slope of the given line = 4/3

The slope (m₁) of perpendicular line relationship is;

4/3 * m₂ = -1

m₂ = -3/4

Hence, slope of perpendicular line (m₂) = -3/4

So, The equation of line by using point/slope form is;

y - y₁ = m₂ (x - x₁)

y - (-8) = -3/4 (x - 8)

y + 8 = -3/4 (x - 8)

4 (y + 8) = -3 (x - 8)

4y + 32 = -3x + 24

3x + 4y = -8

Hence, The equation of the line that passes through the point (8,-8) and is perpendicular to the line 4x – 3y = 18 is;

⇒ 3x + 4y = -8

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Answer:

16x9= 144 cm2

Step-by-step explanation:

Answer:

(0,7)

Step-by-step explanation:

This is in the form

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

y = -5x +7

The slope is -5 and the y intercept is 7

(0,7)

Answer:

(0,7)

Step-by-step explanation:

y=mx+b

y=-5x+7

so y intercept is (0,7)

Steps:

Step 1: Simplify both sides of the equation.

3(a−2/3)=3/4a+21/4

(3)(a)+(3)(−2/3)=3/4a+21/4(Distribute)

3a+−2=34a+2143a−2=3/4a+21/4

3a+−2=34a+2143a−2=3/4a+21/4

Step 2: Subtract 3/4a from both sides.

3a−2−3/4a=3/4a+21/4−3/4a

9/4a−2=21/4

Step 3: Add 2 to both sides.

9/4a−2+2=21/4+2

9/4a=29/4

Step 4: Multiply both sides by 4/9.

(4/9)*(9/4a)=(4/9)*(29/4)

Answer:

A=29/9

Please mark me brainliest

Hope this helps.

This is a example since there is no topic:

Explanatory variable: Could be found on the x axis

Response variable: Could be found on the y axis

Four things need to talk about when you describe a scatter plot:

D.       Direction

O.        Outliers

F.        Form

S.       Strength

Example: The relationship between this graph is strong, positive and linear relationship. There does not appear not be outlines.

How to know if its positive: As the x axis increases so does y axis increases too.

How to know if the chart is linear:

Because it describe the scatter plot. DOFS.

Tell me if you need more help with a pacific thing.

Hope this helps.

Answer:

[tex]m\angle B=52^{\circ}[/tex]

Step-by-step explanation:

Two or more angles are said to be complementary if they sum up to 90 degrees.

Given that angles A and B are complementary, then:

[tex]\angle A+\angle B=90^\circ\\m\angle A=(2x+18)^{\circ}\\m\angle B=(6x-8)^{\circ}\\$Therefore:\\(2x+18)^{\circ}+(6x-8)^{\circ}=90^\circ\\2x+6x+18-8=90^\circ\\8x+10^\circ=90^\circ\\8x=90^\circ-10^\circ\\8x=80^\circ\\$Divide both sides by 8\\x=10^\circ\\$Therefore:\\m\angle B=(6x-8)^{\circ}\\m\angle B=(6(10)-8)^{\circ}\\=60-8\\m\angle B=52^{\circ}[/tex]

Answer:

56 :)

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

Area of a rectangle=length×width

Area=104

Width=x

Length=5+x

104=x*(5+x)

104=5x+x^2

104-5x-x^2=0

x^2+5x-104=0

Can also be written as

-x^2-5x+104=0

Solve the quadratic equation using formula

−x2−5x+104=0

using the Quadratic Formula where

a = -1, b = -5, and c = 104

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(104)/2(−1)

x=5±√25−(−416)/−2

x=5±√441/−2

The discriminant b^2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=5±21/−2

x=-26/2 or 16/2

x=-13 or 8

The value of x can't be negative

So, x=8 is the answer

Answer:

The answer is 1800!

Step-by-step explanation:

Answer:

B. 1800 degrees.

Step-by-step explanation:

Just took the quiz on Edg (2020-2021)!

Answer:

34

Step-by-step explanation

1- 4

2- 4(2) - 2 = 6

3- 6(2) - 2 = 10

4- 10(2) - 2 = 18

5- 18(2) -2 = 34

Start with the point-slope formula, shown below in bold.

Our point which in this case is (6, 8) represents (x1, y1) in our formula.

~Substitute

Y - 8 = -2(x - 6)

I will be writing this equation in standard form.

First distribute the -2 through the parentheses.

This gives us y - 8 = -2x + 12.

Next we would move the -8 to the right side of the equation

by adding 8 to both sides to get y = -2x + 20.

Finally we move our x term to the left side of the equation

by adding 2x to both sides and our answer is 2x + y = 20.

Answer:

C

Step-by-step explanation:

Both A and B are true identities.

See attachment.

Answer:

B and D

Step-by-step explanation:

Age of Student --> Age of student is continues

Time taken to run one mile is also continues

Answer:

B and D

Step-by-step explanation:

Answer:

Kerry = 2/3 * 420 = 280

David = 3/4 * 420 = 315

David read more pages compared to Kerry.

David read 35 more pages than Kerry.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Chemistry book contains 420 pages.

Kerry read 2/3 of her chemistry book,

= 2/3 x 420

= 280 pages.

David read 3/4 of her chemistry book,

= 3/4 x 420

= 315 pages.

315 - 280 = 35 pages.

Therefore, David read more pages.

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Answer:

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to  both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

Answer:

h(x) = 4x+48

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to  both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function