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3 years ago

A key code must contain 4 numerals. There are 10 numerals available. Using

Mathematics

1 answer:

kvasek [131]3 years ago

8 0

Answer:

B, 210

Step-by-step explanation:

$\dbinom{10}{4} = \dfrac{10!}{6! \cdot 4!} = \dfrac{10 \cdot 9 \cdot 8 \cdot 7}{4 \cdot 3 \cdot 2 \cdot 1} = 5 \cdot 3 \cdot 7 \cdot 2 = 210$

You might be interested in

Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).

noname [10]

Answer:

A. y=1/3x+1

Step-by-step explanation:

When finding a line that is perpendicular to another line, all you have to do is find the "opposite reciprocal" of the slope. In this case that means writing the slope as the fraction -3/1, and then flipping the fraction over (1/-3) and taking away the negative sign which gets you 1/3 for the slope of your new line. Now, all you have of your new equation is the slope. You need to take your new equation (y=1/3x+b) and plug in the x and y coordinates to that equation, and then solve for the last variable which is b. That solving process goes as follows:

3=1/3*6+b

3=2+b

1=b

now you can replace the b with 1 in your equation to get your final answer of y=1/3x+1

6 0

2 years ago

Can someone please help on number 20? WILL MARK YOU AS BRAINIEST. (can you also show how you do the problem?) :(

PSYCHO15rus [73]

Answer:

x =(22-√196)/6=(11-7)/3= 1.333

Step-by-step explanation:

(3x2 - 22x) + 24 = 0

The first term is, 3x2 its coefficient is 3 .

The middle term is, -22x its coefficient is -22 .

The last term, "the constant", is +24

Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72

Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -22 .

-72 + -1 = -73

-36 + -2 = -38

-24 + -3 = -27

-18 + -4 = -22 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and -4

3x2 - 18x - 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

3x • (x-6)

Add up the last 2 terms, pulling out common factors :

4 • (x-6)

Step-5 : Add up the four terms of step 4 :

(3x-4) • (x-6)

Which is the desired factorization

Equation at the end of step 2:

(x - 6) • (3x - 4) = 0

STEP 3:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

5 0

2 years ago

At A Local Restaurant, The Health Inspector Visits Every 7 Days, And The Fire Inspector Visits Every 12 Days.

Xelga [282]

PART A :OK so here is the table for the health inspector; all you are really doing is 7+7+7, and so on:

PART A: health inspector: 7,14,21,28,35,42,49,56,63,70,77,84..........

PART A:same thing for the fire inspector, except this time your adding 12+12+12, and so on:

PART A: fire inspector: 12,24,36,48,60,72,84,96.......

PART B: and to figure out what day they will both come is you have to find the LCM (least common multiple)

PART B: which in this case is Day 84

hopes this helps!!!!!

8 0

2 years ago

Write the word phrases into an algebraic expression : 4 less than 5 times a number "p"

shusha [124]

Answer: 5p - 4

5 times ‘p’ = 5p
4 less than ‘p’ = p - 4

Therefore,
=> 5p - 4

4 0

1 year ago

A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point

valina [46]

<h3>Answer: 0.061</h3>

===============================================

Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

---------------------

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

5 0

2 years ago