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nalin [4]
2 years ago
5

A bank PIN is a string of four digits, each digit 0-9. (a) How many choices are there for a PIN if the last digit must be odd? M

ake sure to explain your answer. (b) How many choices are there for a PIN if the last digit must be odd and all the digits must be different from each other? Make sure to explain your answer.
Mathematics
1 answer:
Amanda [17]2 years ago
7 0

Answer:

a) 5,000 b) 3,600

Step-by-step explanation:

a) there are four different slots, and for the first three slots there are a possibility for 10 different numbers and in the last slot there can only be 5 different numbers. So you get 10 x 10 x 10 x 5 which leaves you with 5,000 possibilities

b) the same thing as above but know you have fewer numbers 10 x 9 x 8 x5 which gives you 3,600 possibilities

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Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Check
olasank [31]
We have the expression:
3x(x-12x) + 3x^2 - 2(x-2)^2

First, we will expand the power 2 bracket as follows:
3x(x-12x) + 3x^2 - 2(x^2 - 4x +4)

Then, we will get rid of the brackets as follows:
3x^2 - 36x^2 + 3x^2 - 2x^2 + 8x - 8

Now, we will gather the like terms and add them as follows:
-32 x^2 + 8x - 8

We can take the 8 as a common factor:
8 ( -4x^2 + x -1)
3 0
1 year ago
If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'? 
Vlad1618 [11]

Consider triangle XYZ with vertices at points X(1,-3), Y(3,0) and Z(-1,-1). If triangle XYZ is reflected across the line y = 1, then the rule of reflection is

(x,y)→(x,-y+2).

The image X' of point X will have coordinates according to the given rule:

X(1,-3)→X'(1, -(-3)+2)=X'(1,5).

Answer: correct choice is D.

3 0
2 years ago
Read 2 more answers
At a certain company, the annual winter party is always held on the second of Friday of December. What is the latest possible da
vitfil [10]

Answer:

The latest possible date is December, 14th.

Step-by-step explanation:

Notice that the second Friday of December is n+7, where n is the date for the first Friday of December. So, the latest the first Friday, the latest the second. As the weeks have seven days, the first Friday will be between 1st and 7th of each month. So, the latest first Friday will be 7th. Therefore, the latest second Friday will be 14th.

7 0
1 year ago
A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical
Korolek [52]

Answer:

78% probability that a randomly selected online customer does not live within 50 miles of a physical​ store.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Total outcomes:

100 customers

Desired outcomes:

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. So the number of desired outcomes is 78 customers.

Using this​ estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical​ store?

p = \frac{78}{100} = 0.78

78% probability that a randomly selected online customer does not live within 50 miles of a physical​ store.

4 0
2 years ago
What type of triangle has side lengths of 4√5, √145 and 19?
Masja [62]

a, b, c - side lengths (a ≤ b ≤ c)

If a^2+b^2 < c^2, then is Obtuse triangle.

If a^2+b^2=c^2, then is Right triangle.

If a^2+b^2 > c^2, then Acute triangle.

a=4\sqrt5,\ b=\sqrt{145},\ c=19\to a < b < c

Check to see if the sum of the first two sides is greater than the third.

a+b=4\sqrt5+\sqrt{145}\approx9+12=21 > 19=c\\\\CORRECT

a\neq b\neq c\neq a, therefore is Scalene triangle.

a^2=(4\sqrt5)^2=4^2(\sqrt5)^2=16(5)=80\\\\b^2=(\sqrt{145})^2=145\\\\c^2=19^2=361\\\\a^2+b^2=80+145=225 < 361=c^2\\\\a^2+b^2 < c^2

It's Obtuse triangle.

5 0
1 year ago
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