The price of a train ticket from Kansas City to Lexington is normally $110.00. However, the train company is offering a special 25% discount to children under 16. What is the sale price of a ticket from Kansas City to Lexington for someone under the age of 16?

Answer:

see explanation

Step-by-step explanation:

given that x and y are proportional relationships , then

y = kx ← k is the constant of proportionality

divide both sides by x

[tex]\frac{y}{x}[/tex] = k

using corresponding values of x and y from each table to find k

first table

k = [tex]\frac{10}{1}[/tex] = 10

second table

k = [tex]\frac{20}{4}[/tex] = 5

third table

k = [tex]\frac{15}{2}[/tex]

fourth table

k = [tex]\frac{4}{1}[/tex] = 4

Answer: D) 80 degrees

Step-by-step explanation:

Answer:

d. 5408 Birr.

Step-by-step explanation:

24 months  = 2 years.

Amount after 2 years = 5000(1 + 0.04)^2

= 5408.

Answer:

x = 0  ;  x = 1

Step-by-step explanation:

[tex]\sqrt{x^{12}} =x[/tex]

[tex]\Longleftrightarrow \sqrt{x^{6\times 2}} =x[/tex]

[tex]\Longleftrightarrow \sqrt{\left( x^{6}\right)^{2} } =x[/tex]

[tex]\Longleftrightarrow |x^{6}|=x[/tex]

[tex]\Longleftrightarrow x^{6}=x\ \ \ ;\ |x^{6}|=x^{6}[/tex]

[tex]\Longleftrightarrow x^{6}-x=0[/tex]

[tex]\Longleftrightarrow x(x^{5}-1)=0[/tex]

[tex]\Longleftrightarrow x=0 \ \ or\ \ (x^{5}-1)=0[/tex]

[tex]\Longleftrightarrow x=0\ \ or\ \ x^{5}=1[/tex]

[tex]\Longleftrightarrow x=0\ \ or\ \ x=1[/tex]

Answer:

EK = 8

Step-by-step explanation:

Intersecting Chords Formula:  a • b = c • d

BK * KD = EK * KC

4 * 10 = (x+1) * (x-2)

40 = x^2 +x-2x-2

40 = x^2 -x -2

0 = x^2 - x-2-40

0 = x^2 -x -42

Factor

0 = (x-7) (x+6)

Using the zero product property

x-7 = 0   x+6 =0

x=7        x=-6

X is not negative

x=7

EK = x+1

EK = 7+1

EK = 8

Answer:

x=32

Step-by-step explanation:

The measure of the angle B is 30 degree after applying the sin law of triangle.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle shown in the picture:

We can apply the sin law of the triangle to find the angle B

[tex]\rm \dfrac{28}{sin91} =\dfrac{14}{sinB}[/tex]

SinB = 0.499

B  = 29.99 ≈ 30 degree

Thus, the measure of the angle B is 30 degree after applying the sin law of triangle.

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The system of inequalities have no solutions, option D is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that the graph shows the solutions to the inequalities y> 3x + 14 and y< 3x + 2.

We have to find the  system of inequalities have solutions has solutions or not

As we observe the graphs  y> 3x + 14 and y< 3x + 2 of these inequalities the shade of both lines are not overlapped.

So the two inequalities does not have solution

Hence, the system of inequalities have no solutions, opton D is correct.

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Answer:

Answer:

b = 8

Step-by-step explanation:

1.3b + 2 = 12.4

- Subtract 2 from both sides

1.3b = 12.4 - 2

- Subtract 2 from 12.4 to get 10.4.

1.3b = 10.4

- Divide both sides by 1.3.

b = [tex]\frac{10.4}{13}[/tex]

- Expand [tex]\frac{10.4}{13}[/tex] by multiplying both numerator and the denominator by 10.

[tex]b = \frac{104}{13}[/tex]

- Divide 104 by 13 to get 8.

Answer:

13.9%

Explanation:

Rolling for 2 : (1, 1)

Rolling for 5 : (1, 4), (4, 1), (2, 3), (3, 2)

So, there are (4 + 1) = 5 possible outcomes out of 36 outcomes

Note: There are 36 outcomes when rolling a two fair cubes.

[tex]\sf Probability = \dfrac{possible \ outcomes}{Total \ outcomes}[/tex]

[tex]\rightarrow \sf \dfrac{5}{36} \ x \ 100[/tex]

[tex]\rightarrow \sf \dfrac{125}9} \%[/tex]

[tex]\rightarrow \sf 13.9 \%[/tex]

The range of the given data set, 33, 38, 35.5, 39.25, 31.75, is 7.5. The range represents the spread or the difference between the highest and lowest values in the data set.

To calculate the range of a data set, you need to find the difference between the maximum and minimum values.

Given the data set: 33, 38, 35.5, 39.25, 31.75

To determine the maximum value, we can compare the numbers in the data set and identify the highest one. In this case, 39.25 is the largest number.

To find the minimum value, we compare the numbers and identify the smallest one. Here, 31.75 is the smallest number.

Now, we can calculate the range by subtracting the minimum value from the maximum value:

Range = Maximum value - Minimum value

      = 39.25 - 31.75

      = 7.5

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Answer:

answer C.

Step-by-step explanation:

the base of the triangle is 4 units.the other leg is sqrt5.

the last leg is 4 +9 = 13 so it is sqrt 13.

add them all up together and you get 4+sqrt 13 + sqrt 5 which is C.

hey I will guess you are above oklahoma because it is raining(bottom right) and your temp starts with 6

This is not really a random sample. The athletes are heavily biased toward loving sports. Likely they'll pick their favorite sport to be the one they are currently playing.

Example: if basketball players are asked their favorite sport, they likely might pick basketball.

A much better approach is to randomly select names from a hat, use computer software, or a random number table. This will produce a more random sample to help better represent the population.

The number -1.28 is rational if it is an integer or decimal, so yes it is.

Answer:

we have 1.28 with bar above 28 signifying that the number can also be written as 1.28282828 The mixed number is then equal to,

1 and 28/99 or 1 and 28 over 99

Therefore, the answer to this item is the second choice.

Step-by-step explanation:

My brother helped me with this one

Answer:

-13.5

Step-by-step explanation:

-6.52-6.98=-13.5

Answer:

(2,2)

Step-by-step explanation:

coordinates are written as (x,y)

where x represents the x value of the coordinate and y represents the y value of the coordinate.

If we look at the graph we can tell that "b" has an x value of 2 and a y value of 2

Therefore we can say that "b" is positioned at (2,2)

Answer:

C. (2, 2)

Step-by-step explanation:

A coordinate is used to identify a point on a graph. A coordinate is written in the form of (x, y), where x is the x-value and y is the y-value.

The x-value is the number of units left or right from the origin (0, 0), and it gets negative by going left and positive by going right.

The y-value is the number of units up or down from the origin (0, 0), and it gets negative by going down and positive by going up.

For example, the coordinates (1, -2) indicate that the x-value goes to the right one unit and the y-value goes down two units.

Here, we are asked to find the coordinate of B:

Therefore, the correct answer is C. (2, 2)

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Answer: 71/28 or 2 15/28

Step-by-step explanation:

Turn both fractions into improper fractions.

5 1/4 = 21/4

2 5/7 = 19/7   multiply the denominator with the whole then add the     numerator, same denominator.

21/4 - 19/7 = ?  find common denominator to subtract

4 x 7 = 28  common denominator

Divide the new denominator by previous denominators then multiply by each respective numerator. 28 divided by 4 is 7 multiplied by 21 is 147, the same happens with 19/7.

147/28 - 76/28 = 71/28 or 2 15/28

Answer:

It's a right triangle ..

Step-by-step explanation:

By using Pythagoras theorem , we can know that it's a right angled triangle or not ..

so , H² = P² + B²

=> 34² = 16² + 30²

=> 1,156 = 256 + 900

=> 1,156 = 1,156

Hence , it's a right triangle

Answer:

  18

Step-by-step explanation:

The summation symbol is telling you there are 4 terms of the sum. The values of x in the terms range from 1 to 4.

__

The expanded form of the sum is ...

  (1 +2) +(2 +2) +(3 +2) +(4 +2)

  = 3 +4 +5 +6 = 18

The sum is 18.

_____

Additional comment

The sum can be rewritten as ...

  [tex]\displaystyle \sum_{x=1}^4{(x+2)}=\sum_{x=1}^4{x}+\sum_{x=1}^4{2}=\dfrac{4(4+1)}{2}+4\times2=10+8=\boxed{18}[/tex]

This way, you need to know the sum of integers from 1 to n is (n/2)(n+1). It may be easier just to write the terms out as we have done above.

Based on the exchange rate and Victor's budget, hector can see the sumo tournament and have about $322 left over.

Conversion rate of US dollars to Japanese yen = 1 : 94.153

Ratio of dollar to Yuan

1 : 94.153 = x : 5,488

1/94.153 = x / 5,488

1 × 5,488 = 94.153x

5,488 = 94.153x

x = 5,488 / 94.153

x = 58.2881055303601

Approximately,

x = $58

Amount left with Victor = Total money with Victor - amount spent

= $380 - $58

= $322

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Answer:

he would use 1/16 of a liter or 2.11 oz

Step-by-step explanation:

so i took 1/4 and divided up into 4 which is 1/16 and then i took 1/4 liter and divded that up into 4 to get 2.11 oz

The scale factor will be 1.5. The corresponding angles are congruent because the size is changed not the angles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Adnan wants a larger garden.

He draws the triangle ΔPQR to show his original garden.

He wants to enlarge a garden, so he uses a dilation to form the image of the triangle ΔPQ'R'.

He uses vertex P as the center of the dilation.

The ratio of the corresponding sides will be given as

PQ'/PQ = Q'R'/QR = R'P/RP = 1.5

The scale factor will be 1.5.

The corresponding angles are congruent because the size is changed not the angles.

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The two equation that represents the information is x + y = 150

y = 3x

let

the number of rock music = x

the number of alternative music = y

Therefore,

x + y = 150

y = 3x

The two equation that represent the information are as follows:

x + y = 150

y = 3x

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Part A: She needs to collect different types of data to form her classmates. It will help her to find which student spends the most time playing musical instruments.

Part B: Yes, it is a statistical question.

Zoe needs two main data from each of her classmates.

1. Name of her classmates.

2. Which student spends how much time playing musical instruments.

After that, she can make a graph or a chart in order to understand which student spends more time playing musical instruments.

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Answer:

y=x^2+6

Step-by-step explanation: Look at the vertex (0,6). We know the equation is quadratic so we know x^2. We know in the slope-interpect form equation the y-intercept is the term after the slope. The same applies in this equation. So that means the y intercept is 6 because y is 6 in the coordinate (0,6). We know the slope x^2. We need to plug that into the slope-intercept form equation.

The equation will be y=x^2+6.

Answer:

[tex]y = x^2 + 6[/tex]

Step-by-step explanation:

Vertex form for a parabola is [tex]y = a(x-h)^2 + k[/tex] where the vertex is [tex](h,k)[/tex]. Now for a vertex of (0,6), we can simply plug those values in for h and k: [tex]y = x^2 + 6[/tex].

Hope this helps!! :)

Answer: 19/28

Step-by-step explanation:

p(student plays basketball)=  14/28

p(student plays baseball)=  7/28

2 students play both sports= 2/28

⇒ 14/28+ 7/28 - 2/28 = 19/28

Answer:

  -8

Step-by-step explanation:

Put the given values where the corresponding variables are, and do the arithmetic.

__

  f(x) = 12 -3x

  f(5) = 12 -3(5) = -3

__

  j(x) = x² +4x -1 = (x +4)x -1

  j(-2) = (-2 +4)(-2) -1 = 2(-2) -1 = -5

__

  f(5) +j(-2) = -3 +(-5) = -8

Answer:

6.5 = h + 2

h = 4.5

Step-by-step explanation:

We are given h and since she did 2 additional hours of work, we add the 2 hours. and since we are trying to find h, we set the equation equal to 6.5