A box containing 5 balls costs $8.50. If the balls are bought individually, they cost $2.00 each. How much cheaper is it, in percentage terms, to buy the box as opposed to buying 5 individual balls?

Sure, let's solve this step-by-step:

First, we need to solve for x in the equation x + 1/2 = 5.

We can do this by subtracting 1/2 from both sides, giving us x = 4 1/2.

Now, we can substitute x = 4 1/2 into the equation 2*x^2 - 3x + 6 - 3/x +2/x^2.

We can simplify the equation by multiplying both sides by x^2, giving us:

2*x^2 - 3x + 6 - 3/x +2 = 10*x^2 - 3x + 6.

Now, we can combine all of the terms with x:

10*x^2 - 6x + 6 = 0.

Finally, we can solve the equation using the quadratic formula:

x = 3/5 or x = 2.

Therefore, the answer to the equation is 10*(3/5)^2 - 6(3/5) + 6 = 4.8, or 10*2^2 - 6(2) + 6 = 16.

Answer:

30, rational

Step-by-step explanation:

[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]

The result is rational because it can be written as a fraction of integers.

The height of the pole is approximately 17.75 meters.

The main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. They are used to relate the angles of a right triangle to the lengths of its sides. The sine function gives the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle. The cosine function gives the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent function gives the ratio of the length of the opposite side to the length of the adjacent side.

Let's denote the height of the pole as h, and let's denote the distance between the pole and the student's original position (due west of the pole) as x.

From the student's original position, we have a right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 40°. So, we have:

tan(40°) = h/x

From the student's new position (10 m due south of the original position), we have another right triangle with the pole being the hypotenuse. The angle opposite to the height of the pole is 35°. The distance between the pole and the student's new position is (x+10) meters (the student moved 10 m south). So, we have:

tan(35°) = h/(x+10)

Now we have two equations with two unknowns (h and x). We can solve for x in terms of h from the first equation:

x = h/tan(40°)

Substitute this expression for x into the second equation:

tan(35°) = h/((h/tan(40°))+10)

Simplify and solve for h:

h = (10 tan(35°) tan(40°)) / (tan(40°) - tan(35°)) ≈ 17.75 m

Therefore, the height of the pole is approximately 17.75 meters.

To know more about equation visit:

https://brainly.com/question/27023511

#SPJ1

The gradient of the curve x³ + 3xy²- y³ = 1 at the point with coordinates (1, 3) is -29/9

The gradient of a curve at a point is the value of its derivative at that point.

To find the gradient of the curve x³ + 3xy²- y³ = 1 at the point with coordinates (1, 3). we differentiate implicitly with respect to x.

So, we have that

x³ + 3xy²- y³ = 1

d(x³ + 3xy²- y³)/dx = d1/dx

dx³/dx + d3xy²/dx - dy³/dx = d1/dx

dx³/dx + 3y²dx/dx + 3xdy²/dx - dy³/dx = d1/dx

2x² + 3y² × 1 + 3x × dy²/dy × dy/dx - dy³/dy × dy/dx = d1/dx

2x² + 3y² × 1 + 3x × 2y × dy/dx - 3y² × dy/dx = 0

2x² + 3y² + 6xydy/dx - 3y²dy/dx = 0

6xydy/dx - 3y²dy/dx = -(2x² + 3y²)

Factorizing out dy/dx, we have that

6xydy/dx - 3y²dy/dx = -(2x² + 3y²)

(6xy - 3y²)dy/dx = -(2x² + 3y²)

dy/dx = -(2x² + 3y²)/(6xy - 3y²)

At (1,3) dy/dx =  -(2x² + 3y²)/(6xy - 3y²)

=  -(2(1)² + 3(3)²)/(6(1)(3) - 3(3)²)

=  -(2(1) + 3(9))/(6(1)(3) - 3(9))

=  -(2 + 27)/(18 - 27)

= -29/-9

= 29/9

So, dy/dx = 29/9

Learn more about gradient of a curve here:

https://brainly.com/question/30684208

#SPJ1

The aquarium has six rectangular faces, four of which are identical (two sides and two ends), and two of which are identical to each other but different from the others (top and bottom).

a) We can use the formula for the volume of a rectangular prism, which is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, we have  [tex]V = 12 ft^3 and h = 1.5 ft[/tex] . We want to express y as a function of x, so we need to eliminate w from the equation.

We can rearrange the equation for the volume to get  [tex]w = V/(lh)[/tex] , and substitute in h [tex]= 1.5 ft[/tex] :

[tex]w = V/(1.5lx)[/tex]

Now we can substitute y for w to get:

[tex]y = V/(1.5lx)[/tex]

b)  To find the total surface area, we need to find the area of each face and add them up.

The area of one of the identical sides or ends is lw, so the total area of these four faces is:

[tex]4lw = 4xy[/tex]

The area of the top and bottom faces is lx, so the total area of these two faces is:

[tex]2lx[/tex]

Therefore, the total surface area S is given by:

[tex]S = 4xy + 2lx[/tex]

We can express y in terms of x using the equation from part a):

[tex]y = V/(1.5lx)[/tex]

Substituting this into the expression for S, we get:

[tex]S = 4x(V/(1.5lx)) + 2lx[/tex]

Simplifying, we get:

[tex]S = (8/3)V/x + 2lx[/tex]

So the total surface area S is a function of x, and we can use this equation to find the value of S for any given value of x.

Learn more about function here:

https://brainly.com/question/14002287

#SPJ1

Answer:

Yep

Step-by-step explanation:

Yep. Checking this, all of these are correct. Range on parabolas and absolutes will always go to infinity. Nice work

Answer:

Step-by-step explanation:

The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:

Protein: 1x + 1y ≥ 8 (at least 8 units of protein)

Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)

Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)

The inequalities that x and y must satisfy because they cannot be negative are:

x ≥ 0

y ≥ 0

Step-by-step explanation:

To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:

1. 1x + 1y ≥ 8 (At least 8 units of protein)

2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)

3. 1x + 1y ≤ 10 (No more than 10 units of fat)

To ensure that x and y are non-negative, the following inequalities must be satisfied:

x ≥ 0y ≥ 0

Therefore, the complete set of inequalities for x and y are:

x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0

Answer: 84

Step-by-step explanation:

Area of whole rectangle = lb = 11x9 = 99

Area of Inner rectangle = lb = 5x3 = 15

Area of Shaded region = Area of whole rectangle - Area of Inner rectangle
                                      = 99 - 15

                                      = 84

Answer:

Area of shaded region = 84 units²

Step-by-step explanation:

Area = Area of bigger - Area of smaller

[tex] { \tt{area = (11 \times 9) - (5 \times 3)}} \\ \\ { \tt{area = 99 - 15}} \\ \\ { \tt{area = 84 \: units {}^{2} }}[/tex]

Answer:

To calculate Justin's monthly installment, we need to use the formula for calculating the monthly payment for a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where P is the monthly payment, r is the monthly interest rate, A is the loan amount, and n is the total number of payments (in months).

In this case, A = 18500, r = 0.06/12 = 0.005 (since the annual interest rate is 6%, we divide by 12 to get the monthly rate), and n = 4*12 = 48 (since the loan is for 4 years, or 48 months).

Plugging in these values, we get:

P = (0.005 * 18500) / (1 - (1 + 0.005)^(-48))

P ≈ $432.85

Therefore, Justin's monthly installment would be approximately $432.85

Answer:

12x-4y=12

-4y= -12x+12
___________ [divide everything by -4]

-4

Y=3x+3

Step-by-step explanation:

on the y axis is 3 and the slope is 3

Answer: To find the distance of a chord from the center of a circle, we need to use the following formula:

Distance from center = sqrt(r^2 - (c/2)^2)

Where r is the radius of the circle and c is the length of the chord.

In this case, the radius of the circle is 3.7cm and the length of the chord is 7cm.

So, substituting these values in the formula, we get:

Distance from center = sqrt(3.7^2 - (7/2)^2)

= sqrt(13.69 - 12.25)

= sqrt(1.44)

= 1.2 cm

Therefore, the distance of the chord from the center of the circle is 1.2 cm.

Step-by-step explanation:

Answer:

1. Neutron

2. Nucleus shell

3. Proton

4. Electron

Answer:

I'd be happy to help!

a. From the picture of the window, we can identify the following quadrilaterals:

Rectangle: ABCD (all angles are right angles and opposite sides are parallel and congruent)

Parallelogram: EFGH (opposite sides are parallel and congruent)

Trapezoid: BCGH (at least one pair of opposite sides are parallel)

b. To identify the parallelograms in the picture, we would need to know the following properties of parallelograms:

Opposite sides are parallel and congruent

Opposite angles are congruent

Diagonals bisect each other

Using these properties, we can identify the following parallelograms in the picture:

Parallelogram EFGH: Opposite sides EF and GH are parallel and congruent, and opposite sides EG and FH are also parallel and congruent. Additionally, angles E and G are congruent, and angles F and H are congruent.

Rectangle ABCD: Opposite sides AB and CD are parallel and congruent, and opposite sides AD and BC are also parallel and congruent. Additionally, angles A and C are congruent, and angles B and D are congruent. The diagonals AC and BD bisect each other, meaning that they intersect at their midpoints.

Step-by-step explanation:

The reason why total energy eigen-functions cannot be written in form x(x)y(y)z(z) c(x, y, z) is that the energy eigenfunctions depend on all three spatial coordinates, x, y, and z, simultaneously.

In other words, the probability density of finding the electron at any point in space is not just a product of separate functions that only depend on one of the coordinates at a time.

Instead, the probability density of finding the electron is determined by the complex wave function, which depends on all three spatial coordinates at the same time.

The wave function gives us information about the energy and the behavior of the electron in the system, and it cannot be factorized into separate functions that depend on only one coordinate at a time.

Therefore, we cannot write the total energy eigenfunction as a product of separate functions of x, y, and z. The total energy eigenfunction is a complex function that depends on all three coordinates simultaneously, and it cannot be separated into individual functions that depend only on one coordinate at a time.

Learn more about eigen at

https://brainly.com/question/30357013

#SPJ4

Answer:

Boys are 25

Girls are 15

Step-by-step explanation:

Total class population = 40

Let girls population = g

Then, boys population = (10+g)

Boys + Girls = 40

[tex]{ \sf{(10 + g) + g = 40}} \\ { \sf{2g = 30}} \\ { \sf{g = 15}}[/tex]

Girls = 15

Boys = (10 + g) = (10 + 15) = 25

Answer:

y = -3/4 + 10 1/4

Step-by-step explanation:

y = mx + b  

We are given the slope -3/4.

y = -3/4x + b  To find the b we will use the point (-3,8)  We will use -3 for x and 8 for y and then solve for b

8 = -3/4 (-3) + b

8 = -9/4 + b  Add 9/4 to both sides

8 + 9/4 = -9/4 + 9/4 + b

41/4 = b or 10 1/4 = b

Helping in the name of Jesus.

In light of the solution, Vince is correct in believing that he should only save up to $103.55.

1. a: to formally decide (something), particularly because of facts or evidence: to establish (something) precisely or with authority. Title of the land has now been determined by the town. The land's legal owner has been established by the town. A particular committee will choose the new policy.

Vince is accurate because he perceived the solution correctly.

The inequality 225.90 ≤ 122.35 + a show that the cost of a phone ($225.90) is lower than or equal to the sum of Vince's saved money ($122.35) plus the remaining amount he needs to save (a).

The inequity can be made simpler by taking 122.35 off of both sides to get 103.55 ≤ a. Hence, Vince now needs to put aside at least $103.55 in order to buy the cheapest phone he loves.

In light of the solution, Vince is correct in believing that he should only save up to $103.55.

To know more about inequity visit:

https://brainly.com/question/30231190

#SPJ1

Using linear negative association, According to the  all four parts correct options are D ;A ;D ;D respectively

The slope of a line expresses a great deal about the linear relationship between two variables. If the slope is negative, there is a negative linear relationship, which means that as one variable increases, the other variable decreases. If the slope is zero, one increases while the other remains constant.

The first answer to the question is option D

The second answer to the question must be option A  

Option D must be chosen for the third question.

Option D  must be selected for Question 4.

Solution:

1.

square of 3 is 9

3 to the power of negative 2 is 1/ 9

cube of 3 is 27

3 to the negative power 3 is 1/27

2.

cylinder  volume =πr²h

Given value

pi =3.14

r=5

h=10

Volume=3.14×5²×10

cylinder volume =785m³

3.

When a point is rotated 90 degrees anticlockwise about the origin, it becomes the point (x,y) (-y,x).

The coordinates of Point N are (4, 3)

N' will be the new coordinates (-3, 4)

As a result, the y-coordinate of N' is 4.

4.

Option D must be selected for Question 4.

To know more about linear nonlinear visit:

brainly.com/question/15830007

#SPJ1

Yes, that is correct. The expression 0.25t2–4t+28 shows that the value of a first-edition deck of Wandering Wizards will decrease initially when it is first released, then increase as the deck becomes more rare. The maximum value of the deck is 28, which is when t=0 (when the game is first released).

Answer:

35/8

Step-by-step explanation:

A mixed fraction in the form [tex]a \dfrac{b}{c}[/tex] can be converted to an improper fraction using the following calculation:

[tex]a \dfrac{b}{c} = \dfrac{(a \times b) + b}{c}[/tex]

Here we have the improper fraction [tex]4 \dfrac{3}{8}[/tex]

Using the technique described
[tex]4 \dfrac{3}{8} = \dfrac{4 \times 8 + 3}{8} = \dfrac{32+ 3}{8} = \dfrac{35}{8}[/tex]

Ans: 35/8

The accurate comparison shown by Histogram is that the mean is likely greater than the median because the data is skewed to the right. So, the correct option is A).

The histogram shows a right-skewed distribution, with a tail extending to the right of the peak. This indicates that there are a few cities with very high values that are pulling the mean to the right. In a right-skewed distribution, the mean is always greater than the median. This is because the mean is sensitive to extreme values and the median is not.

Therefore, option A is the accurate comparison. Option B is incorrect because the data is not skewed to the left. Option C is incorrect because the median is always less than the mean in a right-skewed distribution. Option D is also incorrect because the median is always less than the mean in a left-skewed distribution. The correct answer is A).

To know more about histogram:

https://brainly.com/question/30354484

#SPJ4

_____The given question is incomplete, the complete question is given below:

3 4 5 8 9 10

The histogram below shows the average number of days per year in 117 Oklahoma cities where the high temperature was greater than 90 degrees Fahrenheit.

Which is an accurate comparison?

A  The mean is likely greater than the median because the data is skewed to the right.

B The mean is likely greater than the median because the data is skewed to the left.

C The median is likely greater than the mean because the data is skewed to the right.

D The median is likely greater than the mean because the data is skewed to the left.

Answer:

84 [cm³]

Step-by-step explanation:

if to imagine the given figure as parallelepiped, then the required volume can be calculated as V[1]-V[2], where V[2] is the additional part.

finally, V=10*2*7-7*2*4=84.

All the details are in the attachment.

Answer:

Step-by-step explanation:

The given sequence is geometric.

To find the common ratio (r) of the sequence, we need to divide any term by its preceding term. Let's divide the second term (8) by the first term (32):

r = 8/32 = 1/4

Now, we can use the formula for a geometric sequence to find any term:

an = a1 * r^(n-1)

where:

an = nth term of the sequence

a1 = first term of the sequence

r = common ratio

n = position of the term we want to find

Let's use this formula to find the third term:

a3 = 32 * (1/4)^(3-1) = 2

So, the common ratio of the sequence is 1/4, and each term is obtained by multiplying the preceding term by 1/4. The sequence is decreasing rapidly because the ratio is less than 1.

Answer:

Identify the graph represent a linear relationship

Answer:

Fai's wallet contained $30.

Step-by-step explanation:

$9 = 30%

x = 100%

If you cross multiply:

x * 30% = $9 * 100%

0.3x = $9

x = $9/0.3

x = $30

Answer:

3

Step-by-step explanation:

you would need to conduct a survey on random people to know what the would like

Answer: $2,324

Step-by-step explanation:

Let his salary be x.

He spent 1/4 of his salary, or x/4, and 1/7 of his salary, or x/7.

His salary was x. He spent x/4 and x/7, so we subtract those two amounts from his salary.

x - x/4 - x/7 is the amount he still has. He still has $1411. We equate the two and have an equation.

x - x/4 - x/7 = 1411

x/1 - x/4 - x/7 = 1411

We need to combine the three fractions on the left side, so we need to use a common denominator. The least common multiple of 1, 4, and 7 is 28, so 28 is the LCD.

28x/28 - 7x/28- 4x/28= 1411

17x/28= 1411

Multiply both sides by 28.

17x = 39,508

Divide both sides by 17.

x = 2,324

Check:

1/4 of his salary is  2,324/4 = 581

1/7 of his salary is  2,324/7 = 332

Now we subtract 581 and 332 from 2,324

2324 - 581 - 332 = 1411 which is what the problem stated.

Our answer $2,324 is correct.

Answer:

14,4,10

Step-by-step explanation: