In 25 minutes, 300 customers entered the attraction. At this rate, how many customers would enter the attraction in 1 hour?

(Hint: you can set up a ratio to solve this).

Answer:

85 student tickets and 35 adult tickets were sold.

Step-by-step explanation:

Howdy!

We know that student tickets cost $12, adult ticket cost $20 and 120 tickets were sold.

So:

$12×A + $20×B = $1,720. Where A and B are the number of student tickets and adult tickets sold, respectively.

Given that 120 tickets were sold in total, we have that:

A + B = 120

So the system of equations to be solved is the following:

$12×A + $20×B = $1,720                    (1)

A + B = 120                                          (2)

Solving for 'A' in equation (2) we get:

A = 120 - B

Substituting this value into equation (1) we get:

$12×(120 - B) + $20×B = $1,720

Solving for 'B' we have:

$12×(120 - B) + $20×B = $1,720

$1,440 - $12×B + $20×B = $1,720

$1,440 + $8×B = $1,720

$8×B = $1,720 - $1,440

$8×B = $280

B = 35 tickets.

Given that B = 35, then A = 120 - 35 = 85 tickets.

So 85 student tickets and 35 adult tickets were sold.

Answer:

Students=85

Adults=35

Step-by-step explanation:

-12s-20a=-1720

20k+20a=2400

8k=680

k=85

85+a=120

a=35

Answer:

(1, - 4 )

Step-by-step explanation:

To find the y- coordinate, substitute x = 1 into the equation

y = (3 × 1) - 7 = 3 - 7 = - 4

The missing value is -4.

Since you already know that x = 1, substitute that into the equation and simplify. y = 3(1) - 7

Anything times 1 equals itself. y = 3 - 7

Subtract. y = -4

Answer:

2

Step-by-step explanation:

Because 1 ball + 1 Ball = 2 Ball

• P is the principal amount, $3000.00.

• r is the interest rate, 6% per year, or in decimal form, 6/100=0.06.

• t is the time involved, 8 years time periods.

• So, t is 8 year time periods.

To find the simple interest, we multiply 3000 × 0.06 × 8 to get that:

The interest is: $1440.00

Answer:

[tex]\large\boxed{x>\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]3(2x-1)>4x-2\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-1)>4x-2\\\\6x-3>4x-2\qquad\text{subtract 4x from both sides}\\\\2x-3>-2\qquad\text{add 3 to both sides}\\\\2x>1\qquad\text{divide both sides by 2}\\\\x>\dfrac{1}{2}[/tex]

Answer:

4. 120

5. 13

6. 70

7. 115

8. 28

9. I'm not sure for this one

10. 22

11. 45

Step-by-step explanation:

If you need me to explain how I got any of these just ask :)

Answer:

16

Step-by-step explanation:

Answer:

its 18

Step-by-step explanation:

b/c 6 times 3 is 18

It’s 2 because 6 divided by 3 is 2

The answer is 1 and 3/4

Final answer:

Yasmine needs 1 1/4 cups of water to make 3 3/4 servings of spaghetti sauce.

Explanation:

Yasmine uses 1/3 cup of water for 1 serving of spaghetti sauce. She plans to make 3 3/4 servings of the sauce. To find out the total amount of water she will need, we first convert 3 3/4 servings to an improper fraction which is 15/4 servings. We then multiply this by the amount of water needed for one serving (1/3 cup).

Here's the calculation:

(15/4) servings × (1/3) cup/serving = (15/4) × (1/3) = 15/12 cups

Simplify 15/12 cups to get 5/4 cups or 1 1/4 cups.

Therefore, Yasmine needs 1 1/4 cups of water for 3 3/4 servings of spaghetti sauce.

one million - three thousand - four hundred - ninety eight

Answer:

y = 64

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{y}[/tex] 4 = [tex]\frac{1}3}[/tex], then

4 = [tex]y^{\frac{1}{3} }[/tex]

Cube both sides

4³ = ([tex]y^{\frac{1}{3} }[/tex])³, hence

y = 64

Answer:

The system has no solution.

Step-by-step explanation:

We have two equations:

1st:  x+4y=10

2nd: 3x+12y=20

Write the two equations in slope-intercept form:

First equation:

4y=-x+10

[tex]y=-\frac{1}{4}x+\frac{5}{2}[/tex]

Second equation:

3x+12y=20

12y=-3x+20

Divide through by 12

[tex]y=-\frac{1}{4}x+\frac{5}{3}[/tex]

The two equations have the same slope but different y-intercepts.

The two equations are parallel and will never meet.

Therefore the system has no solution.

ANSWER

A.

[tex]P(x)=6x^2 +75x +200[/tex]

EXPLANATION

The given revenue function is:

[tex]R(x)=6x^2 +100x+300[/tex]

The cost function is

[tex]C(x)=25x+100[/tex]

The profit function can be obtained by subtracting the cost function from the revenue function.

[tex]P(x)=R(x)-C(x)[/tex]

This implies that:

[tex]P(x)=6x^2 +100x+300 - (25x + 100)[/tex]

Expand the parenthesis to get:

[tex]P(x)=6x^2 +100x+300 - 25x - 100[/tex]

Group similar terms:

[tex]P(x)=6x^2 +100x - 25x - 100+300[/tex]

Combine the similar terms to get:

[tex]P(x)=6x^2 +75x +200[/tex]

The cot answer is A

Answer:

(x + 6)² + (y + 1)² = 36 + 1 + 1

Step-by-step explanation:

using the steps given, we are left with:

x² + 12x + 36 + y² + 2x + 1 = 38

we can factor each term in parentheses:

(x² + 12x + 36) + (y² + 2x + 1) = 36 + 1 + 1

lets start with x² + 12x + 36. we factor by finding 2 numbers that add up to 12 and when multiplied together get 36. the answer is 6. so we can factor:

(x + 6)²

next we factor y² + 2x + 1. the same rules apply, and this number would be 1.

(y + 1)²

we have the following:

(x + 6)² + (y + 1)² = 36 + 1 + 1

to simplify the right side, we add the terms, then square it as well to find the radius of the circle, in which the formula is (x - h)² + (y - k)² = r²

(x + 6)² + (y + 1)² = 38²

(x + 6)² + (y + 1)² = 1444

(x + 6)² + (y + 1)² = √1444

(x + 6)² + (y + 1)² = 38

this is the final form

Step-by-step explanation:

"Of" means multiplication, and percent means out of 100.

25/100 × 150 = 700/100 × n

75/2 = 7n

n = 75/14

n ≈ 5.357

The number n is equal to  [tex]\frac{75}{14}[/tex] .

Percentage is a ratio of output to total that can be expressed as a fraction of 100.

We have,

According to the question,

25% of 150 = 700 % of n,

Here,

n = number

Now,

Solving,

25% of 150 = 700 % of n

i.e.

[tex]\frac{25}{100} *150=\frac{700}{100} n[/tex]

On solving we get,

[tex]\frac{75}{2} =7n[/tex]

⇒

[tex]n=\frac{75}{14}[/tex]

So, the value of n is  [tex]\frac{75}{14}[/tex],

Hence, we can say that the number n is equal to  [tex]\frac{75}{14}[/tex] .

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Answer:

Drawing a picture  = 1 and 2

Making a Table  = 5 and 8

Working Backwards  = 3 and 4

Looking for a Pattern =6 and 7

Step-by-step explanation:

Answer:

8568

Step-by-step explanation:

You have to choose 5 out of 18, and the order does not matter. So you're looking for the number of combinations, not permutations.

So you have to find 18C5.

nCr = n!/(n-r)!r!

so 18C5 = 18!/13!5!

              = (18 * 17 * 16 * 15 * 14 * 13!)/ 13!5!

              = 18*17*16*15*14/5*4*3*2*1

              = 8568

Hope it helps :)

The total number of ways to select a committee of 5 people from a group of 18 is 8568.

The question is asking for the total number of ways to select 5 people from 18. This is a commonly encountered problem in combinatorics, a mathematic field that deals with countable structures. To solve this, we use the combination formula, usually denoted as nCr where n is total items and r is number of items to choose. In this case, we use the combination formula C(18,5) where 18 is the total number of people and 5 is the committee size.

The formula for combination (nCr) is:

n! / (r!(n - r)!)

where '!' signifies a factorial which is the product of an integer and all the integers below it.

Inserting the numbers into the formula gives us:

18! / (5!(18 - 5)!) = 8568

So, there are 8568 different ways to choose a committee of 5 people from a group of 18.

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The markup would be $1.81 I hope this helps! : )

Answer:

Part 18) Lines AB and CD are perpendicular

Part 19)  Lines AB and CD are parallel

Part 20) Lines AB and CD are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal each other (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Part 18) we have

[tex]A(-4,3),B(2,-12),C(10,5).D(0,1)[/tex]

step 1

Find the slope AB

substitute the given values in the formula

[tex]m=\frac{-12-3}{2+4}[/tex]

[tex]m=-\frac{15}{6}[/tex]

step 2

Find the slope CD

substitute the given values in the formula

[tex]m=\frac{1-5}{0-10}[/tex]

[tex]m=\frac{4}{10}[/tex]

[tex]m=\frac{2}{5}[/tex]

step 3

Compare the slopes

[tex]-\frac{15}{6} \neq  \frac{2}{5}[/tex] ----> the lines are not parallel

[tex]-\frac{15}{6}*\frac{2}{5}=-1[/tex] ----> the lines are perpendicular

Part 19) we have

[tex]A(2,3),B(8,-15),C(-2,2).D(-5,11)[/tex]

step 1

Find the slope AB

substitute the given values in the formula

[tex]m=\frac{-15-3}{8-2}[/tex]

[tex]m=-\frac{18}{6}=-3[/tex]

step 2

Find the slope CD

substitute the given values in the formula

[tex]m=\frac{11-2}{-5+2}[/tex]

[tex]m=-\frac{9}{3}=-3[/tex]

step 3

Compare the slopes

[tex]-3=-3[/tex] ----> the lines are  parallel

Part 20) we have

[tex]A(5,6),B(-1,6),C(-2,-7).D(-2,-4)[/tex]

step 1

Find the slope AB

substitute the given values in the formula

[tex]m=\frac{6-6}{-1-5}[/tex]

[tex]m=\frac{0}{-6}=0[/tex]  ----> is a horizontal line  parallel to the x-axis

step 2

Find the slope CD

substitute the given values in the formula

[tex]m=\frac{-4+7}{-2+2}[/tex]

[tex]m=\frac{3}{0}[/tex]  -----> is undefined (is a vertical line, parallel to the y-axis)

step 3

Compare the slopes

The lines are perpendicular (because the x-axis and the y-axis are perpendicular)

The classification of line segments AB and CD as parallel, perpendicular, or neither depends on the slopes of the lines. If the slopes are equal, the segments are parallel; if the slopes are negative reciprocals, the segments are perpendicular. Without specific locations or further details for these segments, a definitive determination can't be made.

In order to determine if line segment AB and line segment CD are parallel, perpendicular, or neither, we must consider the slope they form when plotted on a Cartesian plane. If they have the same slope, they are parallel. If the slopes are negative reciprocals of each other, they are perpendicular. If neither of these are the case, then they are neither parallel nor perpendicular.

For example, consider line segment AB located at points A (1, 3) and B (3, 7), and line segment CD located at points C (2, 4) and D (4, 8). The slope of AB (m1) can be calculated as (7-3) / (3-1) = 2 and the slope of CD (m2) as (8-4) / (4-2) = 2. Since m1 = m2, AB is parallel to CD.

While this provides a basic approach, without specific values or further information about AB and CD, a definitive classification cannot be made.

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Answer:

OL

Step-by-step explanation:

Got it right

Answer: B , OL on edg

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

When you divide by a fraction, you can also say that you are multiplying by the reciprocal.

So [tex]6/\frac{3}{4}=6*\frac{4}{3}[/tex]

[tex]6=\frac{6}{1}[/tex]

[tex]\frac{6}{1}*\frac{4}{3}=\frac{24}{3}=8[/tex]

Answer:

I believe the answer is 129.3mm.

Hope this helps!

Length of the chain without beads = 377.58 m

The total length of the chain = 400 m

Note that:

1 inch = 0.0254 m

Forty 17 inches beads = 40  x  17

Forty 17 inches beads = 680 inches

Forty 17 inches beads = 680  x  0.0254

Forty 17 inches beads = 17.272 m

Twenty-seven 6 1/2 'll beads = 27 x 6.5 x 0.0254

Twenty-seven 6 1/2 'll beads = 4.4577 m

Eight 3.4 inches beads on the chain = 8 x 3.4 x 0.0254

Eight 3.4 inches beads on the chain = 0.69088 m

Total length of the chain with beads = 17.272 m + 4.4577 m + 0.69088 m

Total length of the chain with beads =22.42 m

Length of the chain without beads = 400 m - 22.42 m

Length of the chain without beads = 377.58 m

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Answer:

2, but it can be 4 if the perpendicular line goes through the other line.

Step-by-step explanation:

Answer:

14 1/8 inches of molding

Step-by-step explanation:

In order to find the solution, we'll have to do 2 fractions subtractions.

To be able to subtract fractions, we have to make sure they are placed in the same denominator.  So, the first thing we'll do is to convert all the numbers in 8th, because that's the greatest denominator.

[tex]48 \frac{1}{2}  = 48 \frac{4}{8} = \frac{(48 * 8) + 4}{8}  = \frac{388}{8}[/tex]

[tex]10 \frac{1}{4} = 10 \frac{2}{8} = \frac{(10 * 8) + 2}{8} = \frac{82}{8}[/tex]

For the last one, we'll first convert the 2 feet into 24 inches.

[tex]24 \frac{1}{8} = \frac{(24 * 8) + 1}{8} = \frac{193}{8}[/tex]

Now, we'll subtract each of the two pieces cut from the original molding's length, first the 10 1/4 inches piece

[tex]\frac{388}{8} - \frac{82}{8} = \frac{388 - 82}{8} = \frac{306}{8}[/tex]

then the 2 feet 1/8 piece

[tex]\frac{306}{8} -  \frac{193}{8} = \frac{306 - 193}{8} = \frac{113}{8} = 14 \frac{1}{8}[/tex]

So,  the contractor is left with 14 1/8 inches of molding.

Answer:

d

Step-by-step explanation:

To find the volume of a cylinder you first find the area of the circle faces.

pi * r^2

Next you multiply that area by the height

The three pieces you used were pi, the radius, and the height

Answer:  The best answer—and correct answer—is:  

_________________________________________

                         →   Answer choice:  [D]:

_________________________________________

         " The volume depends on pi, the radius of the cylinder, and the height of the cylinder.​ "

_________________________________________

{Note:  Technically—and by extension—Answer choice:  [A]:

_________________________________________

         " The volume depends on the radius and the height of the cylinder ."   ;

_________________________________________

        →  is also a "true— and correct— statement" ;  since the volume "does" depend on the radius and the height of the cylinder [but not solely on these 2 (two) elements] — since

"pi" [ "π" ] must be included as well.}.

_________________________________________

Step-by-step explanation:

_________________________________________

{Note:  The statement at the beginning of this question should be written correctly— to read as follows:

_________________________________________

   " The formula for the volume of a cylinder is V = π * r² * h.  Which statement is true? "}.

_________________________________________

{Note:

in which:  "V = Volume" ;  " π = pi ";  "r = radius" ; "h = height " .} .

_________________________________________

Note that the Volume, "V" ; depends on all of the following three (3) elements:

_________________________________________

  1.  "pi" [ "π" ] ;  and:

  2.  the radius, "r" ; and:

  3.  the height, "h" .                                                                          _________________________________________

Hope that this answer—and explanation—is helpful to you.

       Wishing you well in your academic endeavors

                — and within the "Brainly" community!

_________________________________________

Answer:

C. [tex]f(x) = (x-2.5)^{2}-3.25[/tex]

Step-by-step explanation:

The vertex form for a quadratic function is:

[tex]f(x) = a(x-h)^2+k[/tex]

[tex]f(x) = a(x^2-2hx +h^2) + k[/tex]

[tex]f(x) = ax^2-2ahx +ah^2 + k[/tex]

[tex]f(x) = ax^2+bx+c, Second\ form[/tex]

[tex]ax^2+2ahx +ah^2 + k = ax^2+bx+c[/tex]

[tex]-2ah = b[/tex]

[tex]h = -\frac{b}{2a}[/tex]

from the quadratic function given you know that a = 1 , b = -5 and c = 3, thus:

[tex]h = -\frac{(-5)}{2(1)}=2.5[/tex]

[tex]ah^2+k = c[/tex]

[tex]Isolate\ k =>\ k = c-ah^2[/tex]

You know c,a and h, so replace the values:

[tex]k = 3-(1)(2.5)^2 \\ k = 3-6.25\\ k = -3.25\\[/tex]

• Finally replace the values for a, h and k in the vertex form:

[tex]f(x) = a(x-h)^2+k\\ f(x) = (1)(x-2.5)^2+(-3.25)\\ f(x) = (x-2.5)^2-3.25[/tex]

So answer is C. [tex]f(x) = (x-2.5)^2-3.25[/tex]

Answer:

C)5

Step-by-step explanation:

For a 3x3 matrix [tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]

determinent is given by = = a(ei − fh) − b(di − fg) + c(dh − eg)

Given Matrix

[tex]\left[\begin{array}{ccc}-6&7&1\\a&-3&4\\-6&4&-3\end{array}\right][/tex]

determinent of matrix= -6((-3)(-3) − (4)(4)) − 7(a(-3) − (4)(-6)) + 1(a(4) − (-3)(-6))

-19= -6(9-16) - 7(-3a+24) +4a-18

125= 25a

125/25= 25a/25

a= 5 !

Answer:

a = 5

Step-by-step explanation:

We are given 3 x 3 matrix  and the determinant of the matrix is -19.

We need find the value of "a" in the given matrix.

[tex]\left[\begin{array}{ccc}-6&7&1\\a&-3&4\\-6&4&-3\end{array}\right][/tex]

determinant (D) = -6[(-3)(-3) − (4)(4)] − 7[a(-3) − (4)(-6)] + 1[a(4) − (-3)(-6)]

-19 = -6[9 - 16] -7[-3a +24] +1[4a - 18]

-19 = -6[-7] +21a - 168 + 4a - 18

-19 = 42 + 21a -168 + 4a - 18

Simplify the like terms, we get

-19 = 25a - 144

25a = -144 + 19

25a = 125

Dividing both sides by 25, we get

a = [tex]\frac{125}{25}[/tex]

a = 5

So the value of a is 5.

Answer:6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

ANSWER

x=27

EXPLANATION

The two triangles are similar so the corresponding sides are equal.

[tex] \frac{x}{x +1 8} = \frac{39}{39 + 26} [/tex]

[tex]\frac{x}{x +1 8} = \frac{39}{65} [/tex]

Cross multiply to get;

[tex]65x = 39(x + 18)[/tex]

Expand:

65x=39x+702

Group similar terms:

65x-39x=702

Simplify

26x=102

Divide both sides by 26,

x=702/26

x=27

Answer: 8, 0, -12

1. This is the equation of a line y=mx +b. All you have to do it substitute your x values into the x in the equation.

y=2(6)-4

y=8

y=2(2)-4

y=0

y=2(-4)-4

y=-12

Just plug in the values for what you are given, you plug in the value for x and solve for y.

For this case we have a function of the form [tex]y = f (x)[/tex]

Where [tex]f (x) = 2x-4[/tex]

We must find the values of "and" when:

ANswer:

8,0, -12

Option C