The Marching Band is traveling from Minnesota to Florida to perform in a national competition. A train ticket from Minnesota to Florida costs $150 and takes 15 hours of travel time per student. To rent a bus to make the trip, it costs $120 per student and takes 20 hours of travel time per student. The band has $4,800 to spend on the trip and can only spend 720 hours of total travel time. Use the information below.

Let x = Students traveling by train
Let y = Students traveling by bus

Therefore,
$150x + $120y < $4,800 and
15x + 20y < 720.

The graph of these functions is to the right.

It is impossible for a negative number of students to go on the trip, so x and y both have to be greater than zero. Therefore, the functions are confined to the first quadrant.

Number of students function:
N = x + y

Answer: it's [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:135 degrees

The compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly would be $28,167.50.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

Compound Interest =P(1+r/n)^rt

We are given that

Principal amount = $50,000

Time = 10 year

Rate = 6.4%

Determine the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:

Plugging in the given values, we get:

compound interest = $50,000 (1 + 0.064/4)^(4 x 10) - $50,000

= $50,000 (1.016)^40 - $50,000

= $50,000 x 2.6335 - $50,000

= $78,167.50 - $50,000

= $28,167.50

Therefore, the compound interest is $28,167.50.

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The measure of Angle f from the the figure is [tex]53^{o}[/tex].

On a shared plane, parallel lines do not cross one another. Now, if a transversal crosses two parallel lines at two separate sites, four angles are created at each location. The characteristics of parallel lines with respect to transversals are therefore listed below.

The pair of alternative internal angles are equal when two parallel lines are crossed by a transversal.

When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional.

In the problem angle

a = [tex]119^{o}[/tex]

e = [tex]66^{o}[/tex]

Now , c = e ( alternate angles, interior)

⇒ c = [tex]66^{o}[/tex]

a + b = [tex]180^{o}[/tex] ( as sum of angles on a straight line is [tex]180^{o}[/tex] )

b = [tex]180^{o}[/tex] - [tex]119^{o}[/tex] = [tex]61^{o}[/tex]

f + b+ c = [tex]180^{o}[/tex]                [sum of angles of a Triangle is [tex]180^{o}[/tex] ]

f = [tex]180^{o}[/tex]  - [tex]61^{o}[/tex] - [tex]66^{o}[/tex] = [tex]53^{o}[/tex].

The measure of Angle f from the the figure is [tex]53^{o}[/tex].

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Answer: To represent the situation where the amount of money in Cindy's account is greater than the amount of money in Erika's account, you can set up the inequality as follows:

Cindy's account balance + (Cindy's monthly deposit * number of months) > Erika's account balance + (Erika's monthly deposit * number of months)

Substituting the known values, we get:

660 + (60 * x) > 0 + (100 * x)

Combining like terms, we get:

660 + 60x > 100x

Subtracting 60x from both sides, we get:

660 > 40x

Dividing both sides by 40, we get:

16.5 > x

Therefore, the inequality that represents the situation when the amount of money in Cindy's account is greater than the amount of money in Erika's account is 16.5 > x. This means that for the number of months (x) to be greater than 16.5, the amount of money in Cindy's account must be greater than the amount of money in Erika's account.

We know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.

The process of calculating a value using operands and a math operator is known as a mathematical "operation."

The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.

The rules that determine how to solve an expression with several operations are referred to as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).

So, we know that:

Ru buys 3 cakes for £1.60 each.

She was given £20 not.

The money she will get back is:

20 - (1.60*3)

20 - 4.8

£15.2

Therefore, we know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.

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If i clap my hands 20 times in 12 seconds. 200 times will i do it in 2 minutes.

The friend can clap his hands 28 times in 12 seconds, according to our knowledge. The first thing we need to know is how many times he can clap in a second:

What is clap ?

Gonorrhea is known by the slang term "the clap." Gonorrhea is also referred to as "the drip." Someone who has an may feel stigmatized and shamed by these words.

To do it, we must divide the number of seconds by the number of times he can clap his hands:

20/12 =1.6667

He can clap his hands 1.6667 times in 1 second:

Now we want to know how many times will he clap his hands in 2 minutes

We have to change 2 minutes into seconds:

1 (minute) = 60 (seconds in 1 minute)

2 (minutes) * 60 (seconds in 1 minute) = 120seconds

After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:

1.6667 times * 120 seconds = 200

200 times in 2.25 minutes

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Answer: 3

Step-by-step explanation: Daryl is walking 3 miles in 1 hour. When you divide 10.5 by 3.5 you get. So 3 miles in one hour. For example if you walk 12 miles in 4 hours, you divide and get 3. That three becomes the miles in one hour.

Rounded to the nearest percent, the markup is approximately 55%.

What is the percent markup?

Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus its cost to make or purchase for resale) by the cost of that unit.

To find the percent markup, you can use the following formula:

percent markup = (retail price - wholesale price) / wholesale price * 100

Plugging in the values given, we have:

percent markup = (98.50 - 63.55) / 63.55 * 100 = 34.95 / 63.55 * 100 = approximately 55%

Hence, rounded to the nearest percent, the markup is approximately 55%.

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Answer: Its b my guy :)

Step-by-step explanation: 244 + 122 = 366

and the only answer with 366 is b! hope this helps!

system of equations: n=2/3 ,a=14,x=−9
for each thing: x= −9  | a= 14  | n= 2/3

1. x = -9

2. a = 14

3. n = [tex]\frac{2}{3}[/tex]

1. Rearrange Terms

61 = 7 - 6x

61 = -6x + 7

2. Subtract 7 from both sides

61 = -6x + 7

61 - 7  = -6x + 7 - 7

3. Simplify

Subtract the numbers:

61 - 7 = -6x + 7 - 7

54 = -6x + 7 - 7

Subtract the numbers:

54 = -6x + 7 - 7

54 = -6x

4. Divide both sides by the same factor

54 = -6x

[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]

5. Simplify

Divide the numbers:

[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]

-9 = [tex]\frac{-6x}{-6}[/tex]

Cancel terms that are in both the numerator and denominator:

-9 = [tex]\frac{-6x}{-6}[/tex]

-9 = x

Move the variable to the left:

-9 = x

x = -9

x = -9

1. Combine multiplied terms into a single fraction

[tex]\frac{3}{2}[/tex]a - 26 = -5

[tex]\frac{3a}{2}[/tex] - 26 = -5

2. Find common denominator

[tex]\frac{3a}{2}[/tex] - 26 = -5

[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5

3. Combine fractions with common denominator

[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5

[tex]\frac{3a+2(-26)}{2}[/tex] = -5

4. Multiply the numbers

[tex]\frac{3a+2(-26)}{2}[/tex] = -5

[tex]\frac{3a - 52}{2}[/tex] = -5

5. Multiply all terms by the same value to eliminate fraction denominators

[tex]\frac{3a - 52}{2}[/tex] = -5

2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)

6. Cancel multiplied terms that are in the denominator

2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)

3a - 52  = 2(-5)

7. Multiply the numbers

3a - 52 = 2(-5)

3a - 52 = -10

8. Add 52 to both sides

3a - 52 = -10

3a - 52 + 52 = -10 + 52

9. Simplify

Add the numbers:

3a - 52 + 52 = -10 + 52

3a = -10 + 52

Add the numbers:

3a = -10 + 52

3a = 42

10. Divide both sides by the same factor

3a = 42

[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]

11. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]

a = [tex]\frac{42}{3}[/tex]

Divide the numbers:

a = [tex]\frac{42}{3}[/tex]

a = 14

a = 14

1. Divide the numbers

4 = n  + [tex]\frac{-10}{-3}[/tex]

4 = n + [tex]\frac{10}{3}[/tex]

2. Subtract [tex]\frac{10}{3}[/tex] from both sides

4 = n + [tex]\frac{10}{3}[/tex]

4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]

3. Simplify

Subtract the numbers:

4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]

[tex]\frac{2}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]

Subtract the numbers:

[tex]\frac{2}{3}[/tex] = n

Move the variable to the left:

[tex]\frac{2}{3}[/tex] = n

n = [tex]\frac{2}{3}[/tex]

n = [tex]\frac{2}{3}[/tex]

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

In the diagram, the length of OP to the nearest tenth is 5.4

We are to determine the ratio of the sides of the diagram.

The ratio of the sides using the given sides is

Let the unknown side be x

The ratio of the sides is given as follows

25:34 = 15:x+15

Put into fraction we have

25/(25+9)= 15/(x+15)

Cross multiplying we have

25x+375 = 375+135

Collecting like terms

25x=510-375

Simplify further to have

25x=135

Making x the subject

x=5.4

Therefore the length OP is 5.4 units

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The equation is 55 = 5t and the graph is attached with the answer.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until they used all the paint.

The equation can be written as,

55 = 5t

Here, t is the number of hours.

The graph is attached with the answer below.

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Answer:   b/-3<a/-3

Step-by-step explanation:

a/-3<b/-3

b/-3<a/-3

Answer:

$54,742.76

Step-by-step explanation:

The equation for an exponential function is  [tex]f(x)=ab^x\\[/tex], where [tex]a[/tex] is the starting value, which is 40,000. This value increases by 4%, so [tex]b[/tex] is 1.04. Finally, [tex]x[/tex] is the term that the value is increasing for, which in this case is 8.

So, the equation is [tex]f(x)=40000*1.04^8[/tex]

** [tex]f(x)[/tex] can be replaced with [tex]y[/tex]

The computer will cost £ 33512.32

Given,

the cost of the computer = 2500

Depreciation = 12%

Cost after 3 years =?

compound interest is calculated as,

A = P(1 + r/n)nt

r = 12/100 = 0.12

So, A= P(1 + r/n)nt

A = 2500 (1+.12/1)1*3

A= 2500 (1.12)³

A= 2500 * 1.404928

A = 3512.32

So, The computer will cost £ 33512.32

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15x^4y^3 − 45x^3y^4 Can be rewritten using a common factor as 15x^3y^3(x - 3y)

common factors are defined as factors that are common to two or more numbers. In other words, a common factor is a number with which a set of two or more numbers will be divided exactly.

In the algebraic expression 15x^4y^3 − 45x^3y^4,

15x^4y^3 is a term and 45x^3y^4, is another term.

if we take each variable and constant and compare

15 is common factor between 15 and 45

x^3 is a common factor between x^4 and x^3

y^3 is a common factor between y^3 and y^4

so multiplying the common factors together we have 15x^3y^3

what is left in the first term is x and second term is 3y

so that the rewritten form becomes 15x^3y^3(x - 3y)

In conclusion the other form of 15x^4y^3 − 45x^3y^4 is 15x^3y^3(x - 3y)

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Answer:

angle c

Step-by-step explanation:

since the largest angle will be across from the longest side, angle c is the right answer because it is across from the longest side which measures 35 cm.

hope this helps

Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]

The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

Total number of shirts bought = 8 T- shirts

Total number of packages  = p

So,

According to unitary method

In p packages we have t shirts = 8

In one package number of t shirts we will have = [tex]\frac{8}{p}[/tex]

Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]

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Answer:

$67,680

Step-by-step explanation:

average is calculated as

average = [tex]\frac{sum}{count}[/tex]

Denver

[tex]\frac{sum}{137}[/tex] = 67,013 ( multiply both sides by 137 )

sum = 9,180,781

Anchorage

[tex]\frac{sum}{25}[/tex] = 71,332 ( multiply both sides by 25 )

sum = 1,783,300

total sum for both = $9,180,781 + $1,783,300 = $10,964,081

then average salary across both companies is

average = [tex]\frac{10,964,081}{162}[/tex] = $67,680 ( to the nearest dollar )

The component form of the linear combination of the two vectors is u - 2v = &lt; -5, 20&gt;

Here we have the two vectors: u = &lt;-3, -2&gt; and v = &lt;1, -5&gt; We want to determine the value of the linear combination:

u - 2v

To do that we just add the correspondent components, then we get:

u - 2v = &lt;-3, -2&gt; - 2*&lt;1, -5&gt;          

= &lt;-3, -2&gt; - &lt;2*1, 2*-5&gt;          

= &lt;-3, -2&gt; -  &lt;2, -10&gt;          

= &lt; -3 - 2, -2 -(-10)&gt;          

= &lt; -5, 20&gt;

That is the component form of the linear combination.

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155° is the measure of angle b .

What is an example of parallel lines?

Two lines that are equally spaced apart from one another and never cross each other are said to be parallel lines.

                    Both horizontal and vertical shapes are possible. In our daily lives, parallel lines can be seen in the form of zebra crossings, rows of notebooks, and the nearby railroad tracks.

from the figure , we understand that ∠1 and ∠3 together from a straight line.

   thus, ∠1 + ∠3  = 180°

    25° + ∠3 = 180°

   ∠3 = 155°

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It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.

A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.

The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.

A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.

The standard equation of a regular parabola is y² = 4ax.

It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.

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The smaller of the two number is 10.

What are Ratios?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.

Given:

Ratio of two Positive number = 5:6

Let , the smaller number be 5x

then , the bigger number = 6x

According to the question,

product of these numbers = 120

Therefore,

[tex]5x * 6x = 120\\30x^{2} = 120\\x^{2} =4\\x = 2[/tex]

Smaller number = 5x = 5*2 = 10.

Hence, the smaller of the two number is 10.

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As per the area of the rectangle, the amount of metal need for the total yard is 4.68

Area of rectangle

In geometry, the area of rectangle is written as,

A = l x b

where l refers the length and b refers the breadth of the rectangle.

Given,

Here we have given that the 1 1/5 and 3 1/10 is the measure of yard.

While we looking into the given question, we have identified that,

3 time of metal is need for the project,

So, as per the area of the rectangle formula, it can be written as,

=> 3 x 1 1/5 x 3 1/10

=> 3 x 6/5 x 13/10

=> 234/50

=> 4.86

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Answer:

4 1/2

Step-by-step explanation:

add 1 1/5 and 3/10 and then multiply your answr by 3

Answer:

161 square inches.

Step-by-step explanation:

The surface area of a pyramid is the sum of the areas of all of its faces. Since the base of the pyramid is a square with an edge length of 7 inches, the area of the base is 49 square inches (7 inches x 7 inches).

To find the surface area of the pyramid, you also need to find the area of the lateral faces of the pyramid. The lateral faces of a pyramid are the triangular faces that are not the base. The lateral faces of a pyramid are all congruent, meaning that they are all the same size and shape.

To find the area of a lateral face of the pyramid, you can use the formula for the area of a triangle: A = 1/2bh, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.

In this case, the base of the triangle is 7 inches (the edge length of the base of the pyramid) and the height of the triangle is 8 inches (the slant height of the pyramid). The area of each lateral face of the pyramid is therefore 1/2 x 7 inches x 8 inches = 28 square inches.

Since there are 4 lateral faces on the pyramid, the total area of the lateral faces is 4 x 28 square inches = 112 square inches.

To find the surface area of the pyramid, add the area of the base to the area of the lateral faces: 49 square inches + 112 square inches = 161 square inches. Therefore, the surface area of the pyramid is 161 square inches.

Answer:

f(0)=5

f(1)=7

f(5)=15

Step-by-step explanation:

f(0)=2x+5

=2(0)+5

=5

f(1)=2x+5

=2(1)+5

=2+5

=7

f(5)=2x+5

=2(5)+5

=10+5

=15

If the grocery bill before tax is $265.24 and you have to pay 7.3% tax, then he has to pay $284.6 for the grocery bill

The amount of the grocery bill before tax = $265.24
The percentage of tax = 7.3%

The amount of tax = The price of the grocery bill before tax × (7.3/100)

Substitute the values in the equation

= 265.24 × (7.3/100)

= 265.24 × 0.073

= $19.36

The final bill including tax = The price of the grocery bill before tax + The amount of tax

Substitute the values in the equation

= 265.24 + 19.36

= $284.6

Therefore, the grocery bill including tax = $284.6

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