At high school basketball game, the athletic department sold 250 tickets and brought in 837.50. Adult tickets cost $5 and student tickets cost $2.50. Write a system of equations for this situation.

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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Answer:

C

Step-by-step explanation:

∠2≅∠7 are alternate interior angles. C looks like that is what it is saying. I would appreciate if you would mark brainliest.

Answer:

3132

Step-by-step explanation:

2.2% of 3500 is 77 which leaves you with 3423 after one year. At this rate you can take 2.2% of 3423. using this formula five times you reach a final answer of 3132.

3500

-77

3423

-75.306

3347.694

-73.649268

3274.044732

-72.028984104

3202.0157479

-70.4443464538

3131.57140145

and rounding up to a whole leaves you with 3132

Answer:

E2020

Step-by-step explanation:

Answer:

d, supplementary, bc, addition

Step-by-step explanation:

Solid solutions refer to a type of homogeneous mixture where two or more substances are combined at the atomic or molecular level to form a single, solid phase. These solutions are characterized by a uniform distribution of atoms or molecules throughout the material, resulting in a consistent composition and properties.

In solid solutions, the constituent substances can be elements or compounds that have similar crystal structures and atomic sizes. The atoms or molecules of the different components occupy the same lattice sites within the crystal structure, replacing or substituting for each other. This substitution can occur in varying proportions, leading to different compositions within the solid solution.

Solid solutions can be formed through several processes. One common method is through the gradual substitution of atoms or ions in the crystal lattice during the cooling or solidification of a melt or solution. This process is known as solid-state diffusion. Another way is by precipitation from a solution or vapor, where the atoms or molecules of the solute are incorporated into the growing crystal lattice of the host material.

Overall, solid solutions are essential in various fields of science and technology, including metallurgy, materials science, and geology, as they can significantly influence the properties and behavior of the resulting materials.

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Answer:

Correct answer is

\(165 {c}^{6} {b}^{6} \)

Yes, 10 can be replaced by a smaller number. Let's prove it first, then look for a smaller number of people.

Let us write the ages of these 10 people as a1, a2, a3, ... a10.According to the given statement,1 ≤ ai ≤ 60Thus, the age of every individual must be between 1 and 60.

Arrange these ages in a non-decreasing order.

Let's assume that no two groups can have the same sum of ages. Each group has either odd or even numbers of members. Hence, if there are an even number of members in the group, the sum of their ages will also be even. If the group has an odd number of members, the sum of their ages will also be odd.

This means that the 10 people can be divided into five groups, with the sum of the ages of each group being odd or even.

Let us consider two cases:

Case 1:

All five groups have odd sums. This implies that each group has an odd number of members, and the number of members in the group is either 1, 3, or 5. Since there are only 10 people, it is impossible to have five groups with an odd sum of ages. This is because there must be two groups that have the same sum of ages.

Case 2:

Three groups have an even sum, and two groups have an odd sum. This implies that there are two groups with an even number of members and three groups with an odd number of members. Since the ages of each individual are between 1 and 60, the sum of the ages of the members of the group with the most members must be at least 1 + 2 + 3 + 4 + 5 = 15.

Similarly, the sum of the ages of the members of the group with the least members must be at least 1 + 2 = 3. If we remove the members of the two smallest groups, we will be left with 6 members whose ages add up to at least 15 + 3 = 18, which is an even number.

This implies that the remaining three groups must have even sums, which contradicts our assumption that two groups do not have the same sum of ages. This proves that we can always find two groups of people (with no common person) the sum of whose ages is the same. The number 10 can be replaced with a smaller number, for example, 8.

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a. The mass of the wire is 4π√5.

b. The coordinates of the center of mass at  (0, 0, 8π/3).

c. The moment of inertia about the z-axis is 16π√5.

A. To find the mass of the wire, we need to integrate the density function over the length of the wire:

M = ∫ρ(t)ds = \(\int\limits^{2\pi} _0\) ρ(t) ||r'(t)|| dt

where ||r'(t)|| is the magnitude of the derivative of r(t):

||r'(t)|| = ||-2sin(t)i + 2cos(t)j + 4k|| = √(4sin²(t) + 4cos²(t) + 16) = 2√5

Substituting in the values, we get:

M = \(\int\limits^{2\pi} _0\) 1 * 2√5 dt = 4π√5

Therefore, the mass of the wire is 4π√5.

B. The coordinates of the center of mass (x, y,z) can be found using the following formulas:

x = (1/M) ∫ρ(t)x(t)ds

y = (1/M) ∫ρ(t)y(t)ds

z = (1/M) ∫ρ(t)z(t)ds

We can simplify the expressions using the parameterization of the helix:

x(t) = 2cos(t)

y(t) = 2sin(t)

z(t) = 4t

Substituting the values, we get:

x = (1/4π√5)  \(\int\limits^{2\pi} _0\) 2cos(t) * 2√5 dt = 0

y = (1/4π√5)  \(\int\limits^{2\pi} _0\)2sin(t) * 2√5 dt = 0

z = (1/4π√5)  \(\int\limits^{2\pi} _0\) 4t * 2√5 dt = 8π/3

Therefore, the center of mass is located at (0, 0, 8π/3).

C. The moment of inertia about the z-axis can be found using the formula:

Iz = ∫ρ(t)(x² + y²)ds

Using the same parameterization as before, we get:

Iz =  \(\int\limits^{2\pi} _0\) 1 * (4cos²(t) + 4sin²(t)) * 2√5 dt

= \(\int\limits^{2\pi} _0\) 8√5 dt

= 16π√5

Therefore, the moment of inertia about the z-axis is 16π√5.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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To express the area 'a' of the rectangle as a function of the width 'w,' we can use the formula for the area of a rectangle, which is given by: a = w * L

The maximum area would depend on the specific value of the available yards of fencing and the resulting value of 'w' obtained from part (b).

The area 'a' of the rectangle can be expressed as a function of the width 'w' using the equation a = w * [(available yards of fencing - 2w) / 2].

(a) To express the area 'a' of the rectangle as a function of the width 'w,' we can use the formula for the area of a rectangle, which is given by:

a = w * L

In this case, the length 'L' is not given explicitly. However, we can express it in terms of the available yards of fencing. Since a rectangle has two equal sides, the length 'L' would be half of the remaining fencing after deducting the perimeter formed by the width 'w.'

Considering that the perimeter of a rectangle is given by 2w + 2L, we have:

2w + 2L = available yards of fencing

Simplifying the equation, we get:

2L = available yards of fencing - 2w

L = (available yards of fencing - 2w) / 2

Substituting the expression for 'L' into the formula for the area:

a = w * [(available yards of fencing - 2w) / 2]

(b) To find the value of 'w' that maximizes the area, we need to take the derivative of the area function with respect to 'w' and set it equal to zero. However, since the available yards of fencing are not provided, we cannot determine the specific value of 'w' that maximizes the area without that information.

(c) Similarly, without knowing the available yards of fencing, we cannot calculate the maximum area.

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answer:

3 is the answer.

Answer: 2x+58

Step-by-step explanation:Combine Like Terms:

=5x+−3x+58

=(5x+−3x)+(58)

=2x+58  

The volume of the cone is 600 cubic inches.

A cylinder has a volume of 600 inches.

We have to find the volume of a cone with the same radius and height as the cylinder.

Volume of cone: A cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.

Where,

‘r’ is the base radius of the cone

‘l’ is the slant height of a cone

‘h’ is the height  of the cone.

Volume of cylinder:  A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. Thus, the volume of the cylinder can be given by the product of the area of base and height.

Where,

‘r’ is the base radius of the cylinder.

‘h’ is the height of the cylinder.

Volume of cylinder=\(\pi r^{2} h\)=600 cubic inches.

Volume of cone= \(\frac{1}{3}\pi r^{2} h\).

=\(\frac{1}{3}*(600)=200\) cubic inches.

Therefore, the volume of the cone is 600 cubic inches.

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In statistical experiments, each time the experiment is repeated different outcome might occur.

Statistics is a scientific method of organizing data by numbers and interpreting them. From a research point of view, there are several roles of statistics, namely:

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Answer:

pretty sure its 2.9

Step-by-step explanation:

Answer:2.92 or just 3

Step-by-step explanation:

btw read your lesson and pay attentiom

The difference when -6c + 4 is subtracted from -8 + 7c is -2c - 11. This can be simplified to -2c - 11, which is the answer.

To calculate the difference when -6c + 4 is subtracted from -8 + 7c, we must first expand the terms. The first term, -6c, can be broken down into -6 x c, which simplifies to -6c. The second term, 4, can remain as is. The third term, -8, can also remain as is. The fourth term, 7c, can be broken down into 7 x c, which simplifies to 7c.

We can then calculate the difference by performing the subtraction. We begin by subtracting the second term, 4, from the first term, -6c. We can do this by adding -4 to -6c, which results in -6c - 4. We then subtract the fourth term, 7c, from the third term, -8. We can do this by adding 8 to -7c, which results in -7c + 8.

We can then combine the two terms together. We do this by adding -6c - 4 to -7c + 8. This results in -13c + 4. We can simplify this to -2c - 11, which is the final answer.

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Answer:

65

Step-by-step explanation:

Answer:

108 degrees

Step-by-step explanation:

Answer:

p = 7

Step-by-step explanation:

2p = 14

p = 14/2

p = 7

Answer:

y = -5/3x + 20

Step-by-step explanation:

y = -5/3x + b

-5 = -5/3(15) + b

-5 = -25 + b

20 = b

y = -5/3x + 20

Answer:

In other words.. The fourth option D.

Step-by-step explanation:

EDGE2022

i like your cut g

Answer:

25x² + 20x + 4

Step-by-step explanation:

(5x + 2)²

= (5x + 2)(5x + 2)

Each term in the second factor is multiplied by each term in the first factor, that is

5x(5x + 2) + 2(5x + 2) ← distribute both parenthesis

= 25x² + 10x + 10x + 4 ← collect like terms

= 25x² + 20x + 4

Answer:

D. -7x² + 6x - 7

Step-by-step explanation:

Given expression:

\((-2x^2+3x-5)-(5x^2-3x+2)\)

Distribute the negative sign to each term inside the second parentheses, remembering that:

\(\boxed{( - )( - ) = +}\;\; \textsf{and}\;\;\boxed{( - )( + ) = -}\)

\(-2x^2+3x-5-5x^2+3x-2\)

Collect like terms:

\(-2x^2-5x^2+3x+3x-5-2\)

Combine like terms:

\(-7x^2+6x-7\)

Therefore, the expression that is equivalent to the given expression is:

\(\large\boxed{-7x^2+6x-7}\)

Answer:

leading co-efficent is 4

There are at least two group means that are significantly different from one another, according to the alternative hypothesis (H a). The alternative hypothesis is adopted if the outcome is statistically significant.

You can use ANOVA to determine whether differences between data sets are statistically significant. It functions by examining the levels of variance present within each group using samples drawn from each.

The likelihood that the mean of a sample taken from the data will be different owing to chance increases if there is a lot of variance (spread of data away from the mean) among the data groups.

In addition to examining the variance within the data groups, ANOVA also considers sample size (the smaller the sample, the lower the likelihood that outliers will be randomly selected from it) and sample mean differences (the greater the difference between the sample means, the greater the likelihood that an outlier will be randomly selected from it).

hence, The alternative hypothesis is adopted if the outcome is statistically significant.

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The transformations that make a rhombus onto itself are rotation by 180 degrees, reflection across its axes, and translation along parallel lines.

To make a rhombus onto itself, we need to apply a combination of transformations that preserve the shape and size of the rhombus. The transformations that achieve this are:

Translation:

A translation is a transformation that moves every point of an object by the same distance and direction. To maintain the rhombus shape, we can translate it along a straight line without rotating or distorting it.

Rotation:

A rotation is a transformation that rotates an object around a fixed point called the center of rotation. For a rhombus to map onto itself, the rotation angle must be a multiple of 180 degrees since opposite sides of a rhombus are parallel.

Reflection:

A reflection is a transformation that flips an object over a line, creating a mirror image. To preserve the rhombus shape, the reflection line should be a symmetry axis of the rhombus, passing through its opposite vertices.

By applying a combination of translations, rotations, and reflections along the proper axes, we can achieve the desired result of making a rhombus onto itself.

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Answer:

274

Step-by-step explanation:

First stop of Caroline = At 36 mile marker

Destination of Caroline = At 353 mile marker

Distance left to be covered = 353 - 36 = 317 miles

Given that Caroline decides to stop at an attraction \(\frac{3}{4}\) of the way after she stops for gas.

i.e. at a distance \(\frac{3}{4}\) of 317 miles away from the Gas stop.

\(\frac{3}{4} \times 317 = 79.25\times 3 \approx 238\ miles\)

So, Caroline stops at a point which is around 238 miles away from the gas station.

To calculate the Mile marker of her stop, we need to add the mile marker of gas station and the distance of her stop from gas station.

Mile marker location at her stop = 36+238 = 274

Six-beat is the time signature of Gurlitt.

In 6/8 time, there are six eighth notes in each measure. This means that there are three quarter notes in every two measures, and one full note (or semitone) in every four measures.

The signature of Gurlitt is a typeface that was designed by German typographer Christoph Schulte in the early 1900s.

It has been used for signage, advertising, and other types of graphics throughout history. It provides a good overview of what to expect from this piece and also helps to build curiosity in readers.This makes it easier for them to find out more about the article topic. Additionally, using vivid language keeps the reader's attention engaged throughout the entire essay.

Hence,  Six-beat is the time signature of Gurlitt.

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Answer:

Use Cymath its  website

Step-by-step explanation:

for math and tells you how to solve math problems and the answer for free.

Answer: 12

Step-by-step explanation:

x + 9 + 9 = 7x

9 + 9 = 6x

18 = 6x

x = 3

DE = x + 9 = 3 + 9 = 12 :>

Answer:

DE = 12

Step-by-step explanation:

DF = DE + EF

7x = x+9 + 9

7x = x + 18

6x = 18

x = 3

DE = 3 + 9

DE = 12

Answer:

198 square yards ( the surface area is 198 square yards )

Step-by-step explanation:

the length is 9yd, the width is 6yd the height is 3yd .

( 6x9+ 6x3+ 9x3 ) x2

= ( 54 + 18 + 27 ) x2

= 198

the surface area is 198 square yards.

Rectangular surface area = ( length x height + length x width + width x height ) x2