All categories

3 years ago

what is the units digit of the sum of 1!+2!+3! ... n! when n=2019. Include an explanation and what a unit digit is.

Mathematics

1 answer:

horsena [70]3 years ago

8 0

Hey!

Finding the factorial for the first few numbers, we have:

1!=1

2!=2

3!=6

4!=24

5!=120

6!=720

7!=720*7

8!=720*56

What we can see as a clear pattern from 5! and on is that our number ends with a 0, making the units digit 0. Therefore, when we add the units digit of 5! and on, we have a result of 0. So, we can simply add the units digits of 1!, 2!, 3!, and 4!, which is 1+2+6+4=13. Since the units digit is the last number, we can drop the tens place to get an answer of 3.

Feel free to ask further questions!

You might be interested in

Solve the system using elimination 4x-7y=3 x-7y=-15

BigorU [14]

The answer is 6,3
.......

6 0

3 years ago

Read 2 more answers

Which inequality represents all values of x for which the product below is defined

zavuch27 [327]

Answer:

(-∞, -2) ∪ (0, ∞)

Step-by-step explanation:

Multiply together the (7x) and the (x+2), obtaining 7x^2 + 14x. This is the correct argument (input) to Answer A.

Since the domain of the square root function includes "all real numbers equal to or greater than 0," we set 7x^2 + 14x = to 0. This factors to the original 7x*(x+2), set equal to 0. The roots are 0 and -2.

These two values create three intervals: (-∞, -2), (-2, 0) and (0, ∞).

Choosing test numbers, one from each interval: {-5, -1, 1}.

7x^2 + 14x is + at x = -5, - at x = -1, and + at x = 1.

Thus, the domain of this function is (-∞, -2) ∪ (0, ∞). In other words, the product shown is defined on (-∞, -2) ∪ (0, ∞).

5 0

3 years ago

ASAP!!! Find the zero of the function f(x) = -8x + 4. a. -1/2 b. 2 c. -2 d. 1/2

Katyanochek1 [597]

Answer:

D. 1/2

Step-by-step explanation:

Because if you choose A , you get +4

if you choose B ,you get -12

Choose C , you get +20

D is the correct answer.

6 0

3 years ago

How would I finish solving this?

Zarrin [17]

Hello!

The original equation is:

200 = (5w ÷ 2)8

This problem can be written as:

200 = (5w/2)8

And you can then reduce the numbers with 2:

200 = 5x * 4
200 = 20x
10 = x

Your correct answer is 10.

3 0

3 years ago

Read 2 more answers

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages ar

Elenna [48]

Answer:

We conclude that the mean amount packaged is equal to 8.17 ounces.

Step-by-step explanation:

We are given that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ounces, with a sample standard deviation of 0.052 ounces.

Let $\mu$ = population mean amount packaged.

So, Null Hypothesis, $H_0$ : $\mu$ = 8.17 ounces {means that the mean amount packaged is equal to 8.17 ounces}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 8.17 ounces {means that the mean amount packaged is different from 8.17 ounces}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean amount dispensed = 8.171 ounces

s = sample standard deviation = 0.052 ounces

n = sample of packages = 50

So, the test statistics = $\frac{8.171-8.17}{\frac{0.052}{\sqrt{50} } }$ ~ $t_4_9$

= 0.1359

The value of t-test statistics is 0.1359.

Also, the P-value of test-statistics is given by;

the meaning of the p-value is that the p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounces away from8.17 if the null hypothesis is true.

P-value = P( $t_4_9$ > 0.136) = More than 40% {from the t-table}

Since the P-value of our test statistics is more than the level of significance of 0.01, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean amount packaged is equal to 8.17 ounces.

6 0

3 years ago