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nexus9112 [7]
3 years ago
15

On a trip from the United States to Canada, Isabella took d U.S. dollars. At the border she exchanged them all, receiving 10 Can

adian dollars for every 7 U.S. dollars. After spending 60 Canadian dollars, she had d Canadian dollars left. What is the sum of the digits of d?
Mathematics
1 answer:
Wewaii [24]3 years ago
6 0

Answer:

5

Step-by-step explanation:

The exchange rate is 10 CAD = 7 USD

Which means:

10/7 CAD for EACH USD

So, d USD would be:

d * 10/7 = (10d)/7 CAD

This is what she has now, after exchange (in CAD).

She spends 60 and has "d" left, so finding d:

\frac{10d}{7}-60=d\\\frac{10d-420}{7}=d\\10d-420=7d\\3d=420\\d=\frac{420}{3}\\d=140

Hence, d = 140

The digits of d are 1, 4, and 0

The sum is:

1 + 4 + 0 = 5

The sum is 5

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Jamie ordered 200 business cards and paid $23. She ordered 500 business cards a few months later and paid $35. Write and solve a
Gnesinka [82]

Answer:

To purchase 700 business cards, Jamie needs to pay $43.

Step-by-step explanation:

We are given that Jamie ordered 200 business cards and paid $23 in total.

We are also given that Jamie ordered 500 business cards and paid $35.

We can use the rate of change formula to find the average change.

\displaystyle \bullet \ \ \ \frac{\triangle y}{\triangle x}

This can also be represented with:

\displaystyle \bullet \ \ \ \frac{y_2-y_1}{x_2-x_1}

Therefore, we need to identify our variables.

In every relationship, there is a <u>dependent variable</u> and an <u>independent variable</u>.

  • The independent variable is the variable that an experimenter adjusts in order to receive an altered effect from an output.
  • The dependent variable is the variable that adjusts based on the changes made to the independent variable.

We change the amount of business cards that are purchased, which in turn, changes the price.

The y-variable is assigned to the dependent variable and the x-variable is assigned to the dependent variable.

Therefore, if we use the coordinate system:

  • (200, 23)
  • (500, 35)

Now, we can name our coordinates. We use this system:

  • (x₁, y₁)
  • (x₂, y₂)

This means that we can name our points:

  • x₁ = 200
  • y₁ = 23
  • x₂ = 500
  • y₂ = 35

Revisiting the rate of change formula, we can insert these values.

\displaystyle \frac{y_2-y_1}{x_2-x_1}

\displaystyle \frac{35 - 23}{500-200}\\\\\frac{12}{300}=\frac{1}{25}

Next, we need to find the y-intercept of our line. We can do this by using one coordinate pair from above and our slope.

The slope-intercept equation is:

\bullet \ \ \ y = mx + b

We already know m:

\displaystyle \bullet \ \ \ \frac{1}{25}

We also know x and y (we take them from of the coordinate pairs):

\bullet \ \ \ x = 200

\bullet \ \ \ y = 23

Now, we can substitute these values into the equation and solve for b.

\displaystyle [y = mx + b]\\\\23 = \frac{1}{25}(200) + b\\\\23 = 8 + b\\\\23 - 8 = 8 - 8 + b\\\\15 = b\\\\b = 15

Now, we can set up our linear equation.

\displaystyle y = \frac{1}{25}x + 15

Therefore, in order to find the price of 700 business cards, we make x in the equation equal 700 and then solve.

\displaystyle y = \frac{1}{25}(700)+15\\\\y = 28 + 15\\\\y = 43

Therefore, the price of 700 business cards is equal to $43.

3 0
3 years ago
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Keith_Richards [23]

Answer:

The surface area of the figure is 124

Step-by-step explanation:


5 0
3 years ago
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2 2/7 multiplied by 5 1/6
labwork [276]

Answer:

11 17/21

Step-by-step explanation:

8 0
2 years ago
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PLEASE ANSWER ASAP! REALLY IMPORTANT! MUST BE CORRECT! POINTS GIVEN!
VMariaS [17]
 - 5/12  +  ( - 1/4) = 

Adding two negatives results in a negative

-1/4 = -3/12

-3/12 + -5/12  =  -8/12

-8/12 + 3/12    < Subtract and take the sign of the BIGGER number.

8 - 3 = 5

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Answer:  - 5/12
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3 years ago
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The length of a rectangle is twice its width.<br> The perimeter of the rectangle is 126 feet.
seraphim [82]

Answer: Length = 42ft Width = 21ft

Step-by-step explanation:

Let "w" be width

W = 21ft

w x 2 = L

L = 42ft

Perimeter:

42+42+21+21

=126

8 0
3 years ago
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