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never [62]
3 years ago
10

How many phone numbers are possible in the (770) area code if: For the form ABC-XXXX, A is restricted to numbers 2-9. B, C, and

X can be any digit 0-9. Also, the number 867-5309 is not used.
a. 6,999,999 c.7,999,999
b. 7,000,000 d.8,000,000
Mathematics
1 answer:
weqwewe [10]3 years ago
6 0

Answer:

c.7,999,999

Step-by-step explanation:

The phone number is of the form ABC - XXXX

A can be any number from 2 - 9. This means number of possible values for A are 8.

The rest of the places B,C and X can be any digit from 0 - 9. This means there are 10 possible values for each of these.

Since, value to A can be assigned in 8 ways, and to the rest of the 6 positions in 10 ways, according to the fundamental rule of counting, the total number of possible phone numbers that can be formed will be equal to the product of all the individual ways:

Total possible phone numbers = 8 x 10 x 10 x 10 x 10 x 10 x 10

Since, 1 of the given number: 867-5309 is not used, the total possible phone numbers will be:

Total possible phone numbers = 8 \times 10^{6} - 1 = 7999999

Hence, option C: 7,999,999 give the correct answer.

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3 years ago
Find the slope of the lines. Are the 2 lines parallel or perpendicular? Explain how you can use the slope of two lines to tell i
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Answer:

slope = \frac{3}{7} and - \frac{7}{3}, perpendicular

Step-by-step explanation:

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = \frac{3}{7} x + 11 is in this form with m = \frac{3}{7}

Rearrange 7x + 3y = 13 into this form

subtract 7x from both sides

3y = - 7x + 13 ( divide all terms by 3 )

y = - \frac{7}{3} x + \frac{13}{3} ← in slope- intercept form

with m = - \frac{7}{3}

• Parallel lines have equal slopes

• The product of perpendicular slopes = - 1

The lines are not parallel since slopes are not equal

\frac{3}{7} × - \frac{7}{3} = - 1

Hence lines are perpendicular



6 0
3 years ago
A truck travels 52 1/2 miles and uses 2 1/2 gallons of gasoline. What is the fuel rate in miles per gallon?
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Answer:

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3 0
1 year ago
What is the equation of a parabola with a focus (-2,4) and directrix y = 0?
Ronch [10]
The general form of a parabola  when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus.  We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus.  Remember that the parabola will hug the focus and run away from the directrix.  The formula would be slightly different if the parabola was opening either left or right.

Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix.  The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2.  We can now write the equation of the parabola:
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(x + 2)² = 8(y - 2)  Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
5 0
3 years ago
What is the value of x in the equation 8x – 2y = 48, when y = 4?
luda_lava [24]

Answer:

7

Step-by-step explanation:

8x-2y=48, replace y with 4, 8x-2(4)=48, multiply, 8x-8=48, add 8 to both sides to remove the -8, 8x=56 and finally divide by 8 to remove 8 from x, x=7.

8 0
3 years ago
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