The library is 2 miles from the post office. How many yards is the library from the post office?

Answer:

The percent increase in value of the baseball card is 66.667%

Step-by-step explanation:

You must first determine the amount of money increased by the value of an autographed baseball card.  For this you must subtract the price with the applied increase and the original price of the card: $65-$39=$26

This will be the amount of increase. Then, one way to calculate the percentage increase in the value of the baseball card is through a direct rule of three.

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other  (Or when one magnitude decreases, so does the other), the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:

a ⇒ b

c ⇒ x

Then

[tex]x=\frac{c*b}{a}[/tex]

In this case, the rule of three applies as follows: If the original price ($ 39) represents 100%, what is the value of the percentage in the value of the baseball card when its value increases $ 26?

[tex]percentage=\frac{26*100}{39}[/tex]

percentage=66.667%

Another way of thinking about it is considering that:

change from the original price = percentage of change*original price

In this case: $26=percentage of change*$39

So, isolating the percentage of change you get:

[tex]percentage of change=\frac{26}{39} =0.66667[/tex]

This value is expressed in decimal, and for it to be expressed in fraction you must multiply it by 100 (100%). Then you get:

percentage of change=0.66667*100%

percentage of change=66.667%

Note that the value obtained is the same as in the previous case, so both ways of thinking the solution to this problem is correct

Finally, the percent increase in value of the baseball card is 66.667%

For this case, the first thing we must do is to have the same units for both measures.

We have then that by definition:

[tex]1m = 100cm[/tex]

Therefore we have:

[tex]10,000cm * (\frac {1m} {100cm}) = 100m[/tex]

Then, we look for the relationship between both measures:

[tex](\frac {100m} {1000m})[/tex]

Simplifying we have:

[tex](\frac {1m} {10m})[/tex]

Answer:

The simplified ratio that correctly compares 10,000 centimeters to 1000 meters is:

[tex](\frac {1m} {10m})[/tex]

To travel for $12 in a taxi service with an initial fee plus $1.80 per mile, you can travel up to 3 miles.

To determine how far you can travel for $12, you need to consider the initial fee charged by the taxi service and the cost per mile. Let's assume the initial fee is $5. Therefore, you have $12 - $5 = $7 left to spend on miles. Since the cost per mile is $1.80, you can travel $7/$1.80 = 3.89 miles. However, since you cannot travel a fraction of a mile, you can travel up to 3 miles for $12.

The height of the kite from the ground is approximately 74.2 feet, calculated using the trigonometric concept of sine. Sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

The subject of the question is the height of a kite, a topic in Trigonometry.Trigonometry deals with the relationships between the sides and angles of triangles. In this case, we're given that a boy is flying a kite with a 100 foot string at an angle of 48 degrees. We can use the concept of sine in Trigonometry, where sine of an angle in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

In this case, the height of the kite from the ground forms the opposite side, the 100 foot string forms the hypotenuse, and the angle of elevation given is 48 degrees. We have the equation:

sin(48) = height / 100

Therefore, the height = sin(48) * 100.

Using a calculator to find the sine of 48 degrees, and then multiplying the result by 100, we get the height of the kite from the ground to be approximately 74.2 feet.

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The formula for compound interest is given by:

[tex] A = P (1+\frac{r}{n})^{nt} [/tex]

where ,

A= Amount,

P=Principal

r=rate of interest

n= number of times interest is compounded per year

t = time ( in years)

Plugging the values ,

P = $12,000

r=0.06

t=6 years

n=1(annually compounded)

Plugging these in the formula,

[tex] A = 12000 (1+\frac{0.06}{1})^{1*6} [/tex]

A =$17022.229 which is approximately 17022.23

Answer: Amount is option B. $17022.23

Answer:

Hence, the set of values that holds true is:

2-3-4

Hence, option: D is true.

Step-by-step explanation:

We are asked to find which set of the values make the following inequality:

2x-1<10 true.

i..e we will put the given set of value s in place of xx and check whether the value of 2x-1 is less than 10 or not.

If it is then the set of values hold true.

A)

10-15-20

put x=10

2x-1=2×10-1

      =20-1

        =19 which is not less than 10.

Hence, option: A is incorrect.

B)

5-7-9

when x=9

2x-1=2×9-1

     =18-1

     =17 which is not less than 10.

Hence, option: B is incorrect.

C)

4-6-8

when x=8

2x-1=2×8-1

     =16-1

     =15 which is again not less than 10

Hence, option: C is incorrect.

D)

2-3-4

when x=2

2x-1=2×2-1

     =4-1

    =3<10

when x=3

2x-1=2×3-1

     =6-1

     =5 < 10

when x=4

2x-1=2×4-1

     =8-1

     =7<10

Hence, option: D is true.

Hence, the set of values that holds true is:

2-3-4

Answer:

its 54

Step-by-step explanation:

The image of the triangle undergoes a transformation: (x, y) ⇒ [-(1/2)y - 2, (1/2)x + 4]

Dilation is a process for creating similar figures by changing the size.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object.

Transformation is the movement of a point from its initial location to a new location. Types of transformation include translation, reflection, rotation and dilation.

If a point A(x, y) is dilated by a factor p, the new point is at A'(px, py).

If a point A(x, y) is reflected over the x-axis, the new point is at A'(x, -y).

If a point A(x, y) is translated a units left and b units up, the new point is at A'(x - a, y + b).

The image of the triangle undergoes a transformation: (x, y) ⇒ [-(1/2)y - 2, (1/2)x + 4]

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The equation that best represents a trend line for the scatter plot is y=−7/6 x+55/6

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

We are given the points  (1, 8) and (7,1) on the scatter plot.

Therefore, the slope = (8-1)/(1-7) = -7/6

Now, the equation of line;

y = mx + b

b = y - mx

b = 8 - (-7/6)(1)

b = 8 + 7/6

b = 55/6

The equation becomes;

y = -7/6(x) + 55/6

The answer is y=−7/6 x+55/6

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