In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.25. Give your answer as a percentage value. Find the percent increase of the bus fare in Chicago.

Answer:

5x - y = 27

Step-by-step explanation:

Slope is the direction of line and it is calculated as,

[tex]Slope = \frac{y-y_{1}}{x-x_{1}} [/tex]

where (x₁, y₁) is any two points on the line.

Here, we have given that

Slope = 5  and (x₁, y₁) = (5, -2)

∴  [tex]5 = \frac{y-(-2)}{x-5} [/tex]

⇒ 5(x - 5) = y + 2

⇒ 5x - 25 = y + 2

⇒ 5x - y = 27

Hence, the equation of a line is: 5x - y = 27

Answer:

You require 10 helpers

Step-by-step explanation:

The problem could be solved in many ways ( like using an optimization software) but I propose you this.

Start with production of large cakes.  In the time kitchen is available one helper could make, if only works in large cakes:

(2 large cakes / 1 hour) * (3 hours ) = 6 large cakes

So with 3 helpers using all their 3 hours we would have

3 helpers *6 large cakes /helper  = 18 large cakes.

We need 2 more large cakes so we can use one more helper and in his first hour he can produce

(2 large cakes / 1 hour) * (1 hour ) = 2 large cakes

The 4th helper has two hours of work left so he can produce small cakes.

(35 small cakes/hour* 2 hours = 70 small cakes.

With 4 helpers we have the 20 large cakes and 70 small ones. We still have to makes

700 - 70 = 630 small cakes left

In the 3 hour period a helper can make

(35 small cakes / 1 hour) * (3 hours ) = 105 large cakes

So if 1 helper does  105 large cakes  we would need to finish production with

630 / 105 =  6 helpers

So in total we have 3 helpers in only large cakes 6 in only small cakes and one helper doing both - total 10 helpers

−2x + 3y + 5z = −21

−4z = 20

6x − 3y = 0

do -4z=20 first

divide both sides by -4 to get z by itself

-4z/-4=20/-4

z=-5

Use z=-5 into −2x + 3y + 5z = −21

-2x+3y+5(-5)=-21

-2x+3y-25=-21

move -25 to the other side

sign changes from -25 to +25

-2x+3y-25+25=-21+25

-2x+3y=4

6x-3y=0

find x by eliminating y

Add the equations together

-2x+6x+3y+(-3y)=4+0

-2x+6x+3y-3y=4

4x=4

Divide by 4 for both sides

4x/4=4/4

x=1

Use x=1 into 6x − 3y = 0

6(1)-3y=0

6-3y=0

Move 6 to the other side

6-6-3y=0-6

-3y=-6

Divide both sides by -3

-3y/-3=-6/-3

y=2

Answer:

(1, 2, -5)

Answer:

a = 14

Step-by-step explanation:

Since QR = QP then the triangle is isosceles and

QS is a perpendicular bisector, thus

RS = SP ← substitute values

3a = a + 28 ( subtract a from both sides )

2a = 28 ( divide both sides by 2 )

a = 14

Answer:

C. y = 115 000(1.05)^x

Step-by-step explanation:

The formula for the amount accrued on an investment earning compound interest is

[tex]A = P(1 + r)^{t}[/tex]

where

P = the amount of money invested (the principal)

r = the interest rate per period expressed as a decimal fraction

t = the number of periods

In this problem,  

P = $115 000

r =  5 % = 0.05

By 2010, Luca's house will have increased in value for three years. Its value will be  

[tex]A = 115000(1 + 0.05)^{3}\\\text{The correct formula for the value of his home x years after 2010 is}\\ y = 115000(1.05)^{x}[/tex]

Answer:

C: y = 115,000(1.05)x

Step-by-step explanation:

(havn’t actually did any math, but this is just process of elemination.)

{I’m just looking at the end of these, because the start is all the same}

if the number with the (perenthese) is below 1, it is a decreas, and the problem says it’s increasing by 5%. (1.5) Is equal to 50% increase so that means your answer would be (1.05) Because anything times 1 is the larger number, but when u add that 0.5, it’s raising the number up by 5%.

Answer:

Actual Perimeter = 100 km

        Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

                1 mm = 5 km

               5 mm = 5 × 5 km

                          = 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

                                 = 4 × 25

                                = 100 km

                                        = 25 × 25

                                        = 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

Answer:

It will take them 3.43 hours.

Step-by-step explanation:

Let T denote the total cookies that need to be cocked. Observe that:

Then, by 1) and 2), if they work together would we able to make

[tex]\frac{T}{6}+\frac{T}{8}=\frac{8T+6T}{48}=\frac{14}{48}T=\frac{7}{24}T[/tex]

cookies per hour.

Therefore, in order to finish the T cookies they will need [tex]\frac{24}{7}\approx3.43 hours[/tex]

the answer is b)  5/3    1/3

                           x       y

When the girl is 45 ft away from the pole, the tip of her shadow is moving away from the light at a rate of approximately 4.8 ft/sec.

Given:

Height of the pole (h): 25 ft

Height of the girl (4 ft)

Rate of the girl walking away from the pole (dx/dt = 6 ft/sec)

Distance from the pole to the girl (x = 45 ft, when the girl is 45 ft away from the pole)

Objective:

Find the rate at which the tip of her shadow is moving away from the light (ds/dt) when the girl is 45 ft away from the pole.

Step 1: Set up the Similar Triangles Equation

s/x = h/(x + s)

Step 2: Differentiate both sides with respect to time t:

(1/x) * ds/dt - (s/x^2) * dx/dt = (h/(x + s)^2) * (dx/dt + ds/dt)

Step 3: Substitute Known Values:

Substitute x = 45, dx/dt = 6, and h = 25 into the equation.

(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)

Step 4: Solve for ds/dt:

Combine like terms and isolate ds/dt.

(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)

Step 5: Substitute x = 45 into the equation:

(1/45) * ds/dt - (4/2025) = (25/(90 + s)^2) * (6 + ds/dt)

Step 6: Solve for ds/dt:

ds/dt ≈ 4.8 ft/sec

Answer:

The same amount of applesauce, nuts, flour, and raisins is used.

Step-by-step explanation:

Have you ever heard of the question, "which weighs more, a pound of steel, or a pound of feathers?" And then everyone is shocked when they weigh the same, even though they both were said to weigh a pound?

This question is like that.

One cup of each is used, so they are all a cup, which means an equal amount of all of them were used.

Answer:

si

Step-by-step explanation:

por el telefono

Answer:

See explanation

Step-by-step explanation:

Each ounce of fruit will supply

Each ounce of nuts will supply

Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.

Then x ounces of fruit will supply

and y ounces of nuts will supply

Every package must provide

A. You get the system of three inequalities

[tex]\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.[/tex]

B. See attached diagram

[tex]\begin{array}{cccc}&\text{Protein}&\text{Carbohydrates}&\text{Fat}\\\text{Fruit}&x&2x&x\\\text{Nuts}&y&y&y\\&\text{at least 7}&\text{at least 11}&\text{no more than 10}\end{array}[/tex]

Three inequalities were formulated: 1x + 1y ≥ 7 for protein, 2x + y ≥ 11 for carbohydrates and x + y ≤ 10 for fat, with x being fruit and y being nuts. These needs to be graphed to find a feasible region that meets all conditions. A table summarizing the needed unit amount per ounce for protein, carbohydrates, and fats for both fruits and nuts was also provided.

To solve your question, first, let's express the given conditions as inequalities:

Graphing

these inequalities would result in a feasible region that should fulfill all conditions.

The following table summarizes this:

Fruit

Nuts

Requirements per package

Protein1 unit per ounce1 unit per ounceAt least 7 unitsCarbohydrates2 units per ounce1 unit per ounceAt least 11 unitsFat1 unit per ounce1 unit per ounceNo more than 10 units

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Answer:

Step-by-step explanation:

2x+1 ≤ 3(x+1)/2

2x+1 ≤ 3x+3/2

Multiply by 2 on both sides

4x+2 ≤ 3x + 3

Subtract 2 on both sides

4x ≤ 3x + 1

Subtract 3x from both sides

x ≤ 1

I think this is what you were asking?

Answer: B

Because you can eliminate the ones that don’t have an inequality symbol so that leaves you with B and D and the 20 should be on the right by itself since that is the constant we are given and it’s not altered in the question

The algebraic expression for the given problem is:

Speed of airplane = 2x + 20

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) used to represent a quantity or a mathematical relationship between quantities.

" An airplane went 20 miles an hour faster than twice the speed of a car that ran x miles an hour"

The algebraic expression for the given problem is:

Speed of airplane = 2x + 20

Where x is the speed of the car in miles per hour.

Learn more about Expression here:

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9 + -20 + -16= 2of course it’s going to be a negative 27 because wen u had a positive u lost 20 and then lost another 16 now u owe 27 which is -27 in your pockets

The simplified result is -$27.

To describe the gambler's situation using positive and negative numbers, we use the following expression:

$9 - $20 - $16

We can simplify this step-by-step:

First, add the positive and negative amounts: $9 - $20 = -$11

Then, subtract the next amount: -$11 - $16 = -$27

Therefore, the simplified result is -$27.

Answer:

Step-by-step explanation:

let x and y be the distances of each car from the intersection after sometime.

let x<y

then y-x=7

and y+x=13

add 2y=20

y=10

x=13-10=3

slower car travels 3 miles and faster car travels 10 miles

Answer:

The function input is -20 when the output is 25

Step-by-step explanation:

we have

[tex]y=-75-5x[/tex]

where

y is the dependent variable or output

x is the independent variable or input

If the output is 25

then

y=25

substitute

[tex]25=-75-5x[/tex]

Solve for the function input is the same that solve for x

Isolate the variable x

Adds 5x both sides

[tex]25+5x=-75-5x+5x[/tex]

[tex]25+5x=-75[/tex]

subtract 25 both sides

[tex]25+5x-25=-75-25[/tex]

[tex]5x=-100[/tex]

Divide by 5 both sides

[tex]x=-20[/tex]

therefore

The function input is -20 when the output is 25

Final answer:

To find the function input when the output is 25, solve the given equation 25 = -75 - 5x to find x = -20.

Explanation:

When the function's output is 25, the equation is 25 = -75 - 5x. To find the function input when the output is 25, solve for x:

25 = -75 - 5x
100 = -5x
x = -20

Therefore, the function input when the output is 25 is -20.

Answer:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Step-by-step explanation:

We will have a partial funcion to define an expression for the monthly phone charge, because we have a condition that changes the monthly cost.

For months under 130 minutes, there will not be any additional charge other that tha base monthly cost, so the expression for the months under 130 minutes will be the monthly fee.

For months over 130 we will have the same information than above, but we have to add a fee for every minute over 130 minutes. To find the amaunt of minutes over 30 minutes we will just subtract 130 to the amount of minutes used: (m-130). Then we will multiply that number times the cos of each minute over 130 minutes: 9*(m-130). Finally we will add the basic phone fee: 15.99 + (0.09*(m-130)).

Now we set the conditions and use the correct notation for a partial function and we get:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Answer:

  x = (c -mp)/g

Step-by-step explanation:

Subtract the term not containing x, then divide by the coefficient of x.

  gx +mp = c . . . . . given

  gx = c - mp . . . . . subtract mp

  x = (c -mp)/g . . . . divide by g

_____

Comment on the process

This process can be described various ways. A usual description is "get the x term by itself on one side of the equal sign, then divide by the x-coefficient."

I like a more general description of the solution to "solve for" problems: undo what is done to the variable, in reverse order.

Here, the variable x is multiplied by g, then added to mp. To undo those operations (in reverse order), first we undo the addition of mp. We accomplish that by subtracting mp, or by adding the opposite of mp, as you wish.

Having done that, we undo the multiplication by g by dividing by g.

  (gx)/g = (c -mp)/g

  x = (c -mp)/g

The steps we actually perform here are identical to the steps in "get the x-term by itself, ...". However, the process we have described can be applied to any sort of equation, not just a 2-step linear equation.

Answer:

9 (option D)

Step-by-step explanation:

Hi Dlynjen! How are you?

Well, as maybe you know a quadratic function is a polynomial of degree 2, that is, the highest exponent in the variable is 2 (formula: y = ax^2 + bx + c). The graph of a quadratic function is a parabola (it has a U-shape).

The vertex of a parabola is the highest or lowest point of the curve (depending on whether the U opens up or down). In this case the parabola opens up because the exercise mentions the vertex is the point (x = 0, y = 1) and then for the other values of “x” (1, 2, 3, etc.) the values of “y” are higher (1, 4, 9, etc.), that's why the vertex is the lowest point in this case.

The exercise asks you to calculate the slope (or average rate of change) of the curve between x = 5 and x = 6, all you know so far is that as the curve opens up it is assumed that the slope will be positive but to calculate the slope must apply the following formula:

M = (y2 - y1) / (x2 -x1)

But we only know x1 = 5, x2 = 6, y1 = 16 (value of the table that corresponds to x1 = 5) and we must first know how much y2 is worth (for x2 = 6). For this we must know what is the quadratic function (formula) that gives rise to our parable.

If we analyze the table, we see that for each value of “x”, the value of “y” is equal to the square of (x-1), that is, if we take x = 3 as an example, the value of Y = (3 -1) ^ 2 = (2) ^ 2 = 4. And so with all the values. Having obtained this formula we can now calculate the value of “y” for x2 = 6:

Y2 = (6-1) ^ 2 = (5) ^ 2 = 25

Finally, we calculate the average exchange rate with the previous formula, knowing x1 = 5, x2 = 6, y1 = 16 and y2 = 25:

m = (y2 - y1) / (x2 -x1)  

m = (25-16) / (6-1)  

m = (9) / (1)  

m = 9

I hope I've been helpful!

Regards!

Answer:

%33.75

Step-by-step explanation:

I put the answer that the other person answered and I got it wrong so here is the right answer!

Answer:

33.75

Step-by-step explanation:

Answer:

The company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass

Step-by-step explanation:

This is a classical problem that can be solved using a system of equations:

Let us first define our variables:

[tex]x[/tex] as the number of 100-pound bags which contain a mixture of rye and Kentucky bluegrass and,

[tex]y[/tex] as the number of 100-pound bags of bluegrass.

The problem tells us that in a week a total of 17 bags were sold, therefore, we can say that this number must be equal to the number of bags containing the mixture of rye and Kentucky bluegrass plus the number of bags containing bluegrass. Then, according to our variable names:

[tex]x+y=17[/tex]   (1)

The problem also says that the company got a receipt for $4,949 in total. Hence, this number has to be equal to the total number of bags that contain rye and Kentucky bluegrass seeds times its price plus the number of bags containing bluegrass multiplied by its price. Then,

[tex]235x+341y=4949[/tex]  (2)

Now we have the system of equations:

[tex]x+y=17[/tex]   (1)

[tex]235x+341y=4949[/tex]  (2)

Solving for [tex]x[/tex] in equation (1)

[tex]x+y=17\\x=17-y[/tex]   (3)

And substituting [tex]x[/tex] in equation (2)

[tex]235x+341y=4949\\235(17-y)+341y =4949\\3995 - 235y +341y=4949\\-235y+341y = 4949-3995\\106y=954\\y=\frac{954}{106}\\ y=9[/tex]

Then, substituting [tex]y=9[/tex] in equation (1):

[tex]x+y=17\\x+9=17\\x=17-9\\x=8[/tex]

Thus, the company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass.

8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.

Let's assume that:

x = number of bags of the 100-pound mixture of rye and Kentucky bluegrass sold

y = number of bags of the 100-pound bag of bluegrass sold

We can set up a system of equations based on the given information:

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Simplifying the equation in step 2 gives us -106y = -994. Solving for y, we get y = 9.

Substituting the value of y back into equation (1), we get x + 9 = 17. Solving for x, we get x = 8.

Therefore, 8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.

Answer:

so, the figure here is a cylinder with a semi sphere on the top, we know the height of whole structure, and the radius of the semi sphere, which is the same as the radius of the cylinder (you can see it because the radius of the semisphere is constant, and you can thin on it as half a sphere over a cylinder).

First, the cylinder will be the structure without the semi sphere, so his height will be te total height minus the radius of the semi sphere, which is 0.9μm.

so now we know the height and the radius of the cylinder, the surface or the sides of it is 2*3.14*r*h = 2*3.14*0.9μm*0.1μm = 0.5662[tex]μm^{2}[/tex].

The surface area of the cylindrical part of the microvillus is calculated by multiplying pi (3.14) with the diameter (0.1μm) and height (1.0μm) to yield a result of 0.314μm².

To calculate the surface area of the cylindrical 'sides' of the microvillus, which we can consider to be a cylinder without its top and bottom parts, the formula used is: π * diameter * height. In this case, the diameter of the microvillus is 0.1μm (which is the diameter of the hemispherical top) and the height is 1.0μm.

Substitute these values into the formula:

Surface area = π * diameter * height = 3.14 * 0.1μm * 1.0μm = 0.314μm².

Thus, the surface area of the cylindrical part of the microvillus is 0.314 micrometers squared.

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Analyzing the data, the following values were

Mean = 21.84

Median = 15.8=

Standard deviation = 18.97

Coefficient of skewness = 0.955

a. To find the mean, median, and standard deviation, you can use the following formulas:

Mean = sum of all values / number of values

Median = middle value when the values are arranged in ascending order

Standard deviation = square root of [(sum of squared differences from the mean) / (number of values - 1)]

Mean = (4.2 + 6.3 + 7.5 + ... + 83.6) / 15 = 21.84

Median = 15.8 (the 8th value when arranged in ascending order)

Standard deviation = √([(4.2 - 21.84)² + (6.3 - 21.84)² + ... + (83.6 - 21.84)²] / 14) = 18.97

b. To find the coefficient of skewness using Pearson's method, you can use the following formula:

Coefficient of skewness = (3 * (mean - median)) / standard deviation

Coefficient of skewness = (3 * (21.84 - 15.8)) / 18.97 = 0.955

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Answer: 20 times

Step-by-step explanation:

1 hour = 60 minutes.

Duration of the song = 3 minutes each time = 3minutes/time

So, the number of times the song can be played in an hour=

= 60minutes÷3minutes/time = 20 times

So, you can play that song in an hour for 20 times.

Answer: 20 times

[tex]\textit{\textbf{Spymore}}[/tex]  

Final answer:

A 3-minute song can play 20 times in an hour by simply dividing the 60 minutes in an hour by the length of the song, which is 3 minutes.

Explanation:

A 3-minute song can play 20 times in an hour. Here's a step-by-step breakdown of the math:

Understand that there are 60 minutes in an hour.

Divide the total minutes in an hour (60) by the length of the song (3 minutes).

The result is the number of times the song can be played in one hour, which is 20 times.

The question seems to diverge from the provided information about the collection of songs with varying lengths. However, for the direct question asked, we do not need those details.

Answer:

$24,166.67

Step-by-step explanation:

Let carry out the breakdown:

So Norman Jean makes a flat rate of $25 per hour, also she works 35 hours per week.

From the above statement Jean will make => 25 × 35 = $875 in a single week without commission.

For Jean to make $4500 in a week, we derive an equation for this:

875 + x = 4500;

x is the amount of commission Jean has to get in a week to make up to $4500 in that week => x = 4500-875; x = $3625.

Let y be the amount of sales Jean has to make to get a commission of x, we derive the following equation: 0.15 × y = x.

y = x ÷ 0.15 => 3625 ÷ 0.15

y = 24166.67.

So for Jean to meet her target of $4500 in a single week, Jean needs to make a sale worth $24,166.67.

The amount of sales that Norma needs to make in a week in order to earn $4500 in a week is; 24167

We are told that;

Norma Jean makes $25 per hour

Total time worked per week = 35 hours

Commision on total sales = 15%

Basic amount earned for the 35 hours in a week = 25 * 35 = $875

Now, if the amount of sales she makes that earns her commision is x, then it means for her to earn $4500 in a single week;

875 + 0.15x = 4500

0.15x = 4500 - 875

x = (4500 - 875)/0.15

x = 24166.67

Approximating to a whole number is;

x = 24167 sales

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Answer:

  1)  60°, 75°, 120°, 105°

  2)  101.5 m

Step-by-step explanation:

1) The sum of ratio units is 4+5+8+7 = 24, which corresponds to the sum of angles, 360°. Then each ratio unit must stand for 360°/24 = 15°. Multiplying the given ratio units by 15° gives the angle measures:

__

2) The similarity statement and the scale factor mean ...

  MJ : TQ = 4 : 7

  7·MJ = 4·TQ . . . . . . . . . "cross multiply"

  TQ = 7/4×MJ = 7/4(58 m) . . . . . divide by 4, substitute the value of MJ

  TQ = 101.5 m

Answer:

q.1 quarter mile

q.2 half mile

:)

addition!

Step-by-step explanation: