For a body falling freely from rest​ (disregarding air​ resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 192 feet high and hits the ground in 8 ​seconds, how far did it fall in the first 4 ​seconds?

The number of child tickets sold that day were 26.

Here, we are given that the fees for admission into the museum is as follows-

Child admission = $5.50

Adult admission = $9.60

Let the number of children admitted on Saturday be x

then the number of adults admitted that day = 4x

Now, the total money from sale of children tickets = $5.50x

the total money from sale of adult tickets = $9.6 × 4x = $38.4x

The total money from sale of tickets =  $1141.40

⇒ 5.50x + 38.4x = 1141.40

43.9x = 1141.40

x = 1141.40/ 43.9

x = 26

Thus, the number of child tickets sold that day were 26.

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Katrina practices violin per week more than Jeremy by 25 minutes.

The practice time can be determined by converting the fractional hours to minutes for each practice so that like is compared to like.

Converting 2/3 hours gives 40 minutes.

Ordinarily, Jeremy spends more time each time than Katrina.  However, Katrina adds an additional practice time, which heightens her total practice time each week.

The number of times that Katrina practices per week = 4 times

The time she practices each time = 2/3 hours or 40 minutes (2/3 x 60)

The total time she practices each week = 160 minutes (40 x 4)

The number of times that Jeremy practices per week = 3 times

The time he practices each time = 45 minutes or 3/4 hours

The total time he practices each week = 135 minutes (45 x 3)

The difference in practice time per week = 25 minutes (160 - 135)

                                                Katrina           Jeremy

Number of practices times         4                      3

Minutes practiced   (2/3 hours) 40 min    45 minutes

Total practice time                   160 min    135 min

Thus, we can conclude that Katrina practices violin per week more than Jeremy by 25 minutes.

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The equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.

Given the equation of line and point;

First, find the slope intercept form ( y = mx + b )of the given equation to determine the slope.

−2x + 6y = −1

Solve for y

6y = 2x - 1

y = (2/6)x - 1/6

y = (1/3)x - 1/6

Hence, the slope m =  1/3

Now, the equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

Slope of the perpendicular will be;

m_perpendicular = -3

Next, find the equation of the perpendicular line using the point slope formula y - y₁ = m( x - x₁ ).

Plug in the slope m = -3 and the point (-2,4).

y - y₁ = m( x - x₁ )

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

y - 4 = -3( x + 2 )

y - 4 = -3x - 6

y = -3x - 6 + 4

y = -3x - 2

Therefore, the equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.

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The smallest integer value of x for which angle A would be classified as obtuse is 14°

An obtuse angle can be defined as an angle that is greater than 90 degrees.

This can be expressed as;

Obtuse angle > x > 90°

Given the angle as A = 5x +29

Let's assume that the value of the obtuse angle is 99 which is greater than 90 degrees.

Now, we have to equate the expression for angle A to 91 degrees.

We have;

5x + 29 = 99

collect like terms

5x = 99 - 29

subtract like terms

5x = 70

To make 'x' the subject, divide both sides by the coefficient of x

5x/5 = 70/5

x = 14°

Thus, the smallest integer value of x for which angle A would be classified as obtuse is 14°

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Answer:

hi ik you dont trust me however id like to say that the answer is A. 41.6

Step-by-step explanation:

hope this helps <3 (also i put this into a calculator to double check my work and it was still 41.6)

Answer:

41.6

Step-by-step explanation:

Move the decimal 1 place to the right according to the laws of exponents.

since the exponent is 1, that's why we move it 1 place right. if the exponent was -1, it would go to the left, and the number would become "0.416".

Answer:

down one over two( point on -8 then down one over two

Step-by-step explanation:

this might be the right answer please let me know

If a company decides to hire more employees, then its:(a).total variable cost and total cost will increase, but its total fixed cost will not change

What is the behavior of fixed and variable costs?

The fixed cost remains the same over a reasonable range of output whereas the variable cost is the cost that increases as output increases, such as the cost of raw materials, the more output produced, more materials would be needed.

In short, the variable increase would make the total cost, the sum of fixed cost and variable cost, to increase, so hiring more employees, would increase variable cost and total cost only.

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The reflection of Z (5 1/2, 3) across the x-axis is (5 1/2, -3).

Here,

The given point is Z (5 1/2, 3).

We have to find the point of reflection of Z (5 1/2, 3) across the x-axis.

What is Reflection across x-axis?

A point after reflection across the x-axis, the x- coordinate remains the same but y - coordinate is taken to be the additive inverse.

Now,

Since, The given point Z (5 1/2, 3) is lie on first coordinate.

Hence, The reflection of the point Z (5 1/2, 3) is lie on the third coordinate.

And, In the third coordinate the x-coordinate is positive and y-coordinate is negative.

Since, The rule of the reflection across x- axis is,

(x, y) → (x, -y)

So, The reflection of the point Z (5 1/2, 3) across the x - axis = (5 1/2, -3)

Therefore, The reflection of Z (5 1/2, 3) across the x-axis is (5 1/2, -3).

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By free fall motion, the ball will take a time of 3.252 seconds to hit the ground.

The ball experiments a free fall motion, that is an uniform accelerated motion due to gravity, in which effects from Earth's rotation and air viscosity are neglected. The height of the ball (h), in feet, is modelled by a quadratic equation:

h = 205 - 11 · t - 16 · t²

Where t is the time, in seconds.

If we know that h = 0 ft, then the time needed for the ball to hit the ground is:

205 - 11 · t - 16 · t² = 0

16 · t² + 11 · t - 205 = 0

16 · [t² + (11 / 16) · t - 205 / 16] = 0

16 · (t - 3.252) · (t + 3.940) = 0

For time is a whole number, only the first root offers a reasonable answer.  

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Answer: graph 'y=16-8x'

Step-by-step explanation:

First, alter the equation by making it a 'y=...' statement (y=-8x+16).

Secondly, plot your first point at positive 16.

Third, make sure that your slope is going down 8 from positive 16, so you plot your second point at positive 8, and move that second point to the right by 1.

Let me know if this helps!

The weight of the spaceship that has a mass of 9000kg is 22936kg.

It should be noted that the mass in a body simply means the measure of the quantity if the matter that the body has.

It should be noted that it is also the body of the inertia.

In this case, the spaceship has a mass of 9000kg. The spaceship is launched from Earth and lands on a distant planet, where it has a gravity of 25 m/s². Therefore, the weight will be:

= 9000 /9.81 × 25

= 22936kg

Therefore, the weight of the spaceship that has a mass of 9000kg is 22936kg.

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Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "q2" was replaced by "q^2". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(9 • (p2)) - (23•5q2)

STEP

2

:

Equation at the end of step

2

:

32p2 - (23•5q2)

STEP

3

:

Trying to factor as a Difference of Squares:

3.1 Factoring: 9p2-40q2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : 40 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours

Given that

Rachel can paint half of the living room in 1 hour

Fran can paint [tex]\frac{1}{5}[/tex]th part of the living room in 1 hour

Let's assume together they paint the living room in x hours

⇒ together they can paint [tex]\frac{1}{x}[/tex]th part of the living room in 1 hour

By proportions,

⇒[tex]\frac{1}{2}[/tex]+[tex]\frac{1}{5}[/tex]= [tex]\frac{1}{x}[/tex] {using operation proportions and addition}

⇒[tex]\frac{7}{10}[/tex]=[tex]\frac{1}{x}[/tex]

⇒x=[tex]\frac{10}{7}[/tex]        

⇒ together they can paint [tex]\frac{7}{10}[/tex]th part of the living room in 1 hour

It means, Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours

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Answer:

18

Step-by-step explanation:

(2 x 16) - 14 = 32 - 14 = 18

The number is 18

Let x be the number

Half of a number = x/2

Half of a number is increased by 6 = x/2 + 6

Half of a number increased by 6 is 15 = x/2 + 6 = 15

Algebra: The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.

Solving the equation we get:

= (x + 12)/2 = 15

= x + 12 = 30

x = 18

Hence, the number is 18

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Answer:

d

Step-by-step explanation:

===================================================

Explanation:

Use your calculator to type in either 13/52 or 13 ÷ 52

The calculator should display 0.52 as the answer. The decimal 0.52 converts to 52%

The steps for the long division are shown below.

Answer:

3

Step-by-step explanation:

and the answer is 17

Answer:

1. The total cost of movie and the total cost of refreshments purchased and the total  cost of video games played cannot exceed 40

2. 14.50 + 7.75x + 0.75y ≤  40

3. y ≤ 34 - 10.333x

4. See attached graph

5.

one  refreshment means you can play 23 times
two refreshments means you can play 13 times
three refreshments means you can play 3 times

Step-by-step explanation

We have to assume that you can see one movie but but buy multiple refreshments and play multiple video games. A refreshment is considered to be one drink and one popcorn.

If not we have a situation where we have three unknowns and it will be difficult to solve in a 2D context

1. Verbal inequality model
The total cost of one movie and the total cost of refreshments purchased and the total  cost of video games played cannot exceed 40

2. Algebraic Inequality Model
Since the cost of a movie is 14.50 and you are seeing only 1 movie, the cost is 14.50(1) = 14.50

Assume you are going to buy x refreshments. Total cost of refreshments = 7.75x

Assume you are going to play y video games. Total cost of video games played = 0.75y

This cannot be greater than 40 i.e ≤ 40

So the algebraic inequality is
14.50 + 7.75x + 0.75y ≤  40

3. Solving the inequality

Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤  25.50

Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤  25.50

Subtract 7.75x from both sides:
0.75y ≤ 25.50- 7.75x

Divide both sides by 0.75
y ≤ 25.50/0.75 - 7.75x/0.75

which is
y ≤ 34 - 10.333x

3. Graph of Inequality

This is an inequality in 2 variables and can be graphed.
See attached graph. The shaded portion represents the inequality
y ≤ 34 - 10.333x

Note that since neither x nor y can be < 0, we should not consider any portion of the shaded area which would mean two more constraints x ≥ 0 and y ≥ 0 but in this case I have stuck to only the above one inequality

5. Possible number of times you can play the same video game

Again we consider only 1 movie and multiple refreshments and video games

Using the inequality y ≤ 34 - 10.33x

If x = 1 refreshment,
y ≤ 34 - 10.33 x 1
y ≤ 23.67 or max 23 times you can play the video game max

If x = 2,
y ≤ 34 - 10.33 x 2
y ≤ 13.34 or maximum 13 times

If x = 3
y ≤ 34 - 30.99
y ≤ 3.01 or maximum 3 times

2.35(2)+1.85+1.60= $8.15 total before gift card

8.15-5.00= $3.15 because the gift card was $5

now you do

20.00-3.15 to get the total change which is $16.85

Thanks hope you see this susususususususususuusususususuusususus

Answer:

0,48

Step-by-step explanation:

whenever we convert a fraction to a decimal, it is easier to convert the denominator to a power of 10 and then move the comma the amt of zeros left of the number

Answer:

67.5

Step-by-step explanation:

Hope this Helps! Be sure to study this so you get it you really just need to subract!

Answer:

y = 2x -9

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

5/8 students of the 4/5 students have rodents. The word "of" tells us to multiply. 5/8 * 4/5 is equal to 5*4/8*5, which is 20/40 and therefore simplifies to 1/2.

The inverse of a matrix A is A^-1. And I, the identity matrix, is equal to A.A^-1.

The square matrix needs to be non-singular and have a non-zero determinant value in order to get the inverse matrix. Let's think about the 2 x 2 square matrix A.

Inverse of  matrix:

A^(-1)=Adj A/|A|

A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for calculating the inverse of a 2 × 2  matrix. In order to find the inverse of a matrix of order 3 or higher, we also need to be aware of the matrix's determinant and adjoint. When multiplied by the provided matrix, the other matrix that serves as the inverse of that matrix yields the multiplicative identity.

There are two ways to find a matrix's inverse. Through the use of an adjoint of a matrix and simple processes, it is possible to derive the inverse of a matrix. Row or column transformations can be used to carry out the basic operations on a matrix. Additionally, the adjoint and determinant of the matrix can be used to apply the inverse of matrix formula in order to get the inverse of a matrix.

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Answer:

$29.72

Step-by-step explanation:

$120.21-$90.49=$29.72

its 150/230, again the answer is -709/216

again the answer is -377/008. alright hope I helped you out with your question you have stated.