1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
myrzilka [38]
3 years ago
12

Simplify 3[2^3 + (4-2)^3 - (6-2)^2]

Mathematics
1 answer:
Ivahew [28]3 years ago
6 0

Answer:

\boxed{0}

.

Step-by-step explanation:

3(2^3 + (4 - 2)^3 - (6 - 2)^2)

= 3(2^3 + 2^3 - 4^2)

= 3(2.2^3 - (2^2)^2)

= 3(2^4 - 2^4)

= 3(0)

= 0

You might be interested in
Triangle X Y Z is shown. Angle X Y Z is 75 degrees and angle Y Z X is 50 degrees. The length of X Y is 2 and the length of X Z i
Kay [80]

Answer:

2.5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Fill in the blanks.
Natasha_Volkova [10]
Hi there! I can help you.

Rate: To find the rate, let’s divide interest earned by the principal. When you do, you get 0.15. Multiply by 100 to get 15 and divide by 3 to get 5. The simple interest rate is 5%.

New balance: All you have to do is add the principal and he new balance. When you do, you get 517.5. The new balance is $517.50.
4 0
3 years ago
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party,
Mama L [17]

Answer:

(a)\ P(x = 0) = 0.2725

(b)\ P(x \ge 1) =0.7275

(c)\ P(x \le 2) = 0.8948

Step-by-step explanation:

Given

n = 8 --- 8 friends

p = 15\% --- proportion that one-time fling

This question is an illustration of binomial probability, and it is represented as:

P(X = x) = ^nC_x* p^x * (1 - p)^{n-x}

Solving (a): P(x = 0) --- None has done one time fling

P(x = 0) = ^8C_0* (15\%)^0 * (1 - 15\%)^{8-0}

P(x = 0) = 1* 1 * (1 - 0.15)^{8}

P(x = 0) = 0.85^8

P(x = 0) = 0.2725

Solving (b): P(x \ge 1)

To do this, we make use of compliment rule:

P(x = 0) + P(x \ge 1) =1

Rewrite as:

P(x \ge 1) =1 - P(x = 0)

P(x \ge 1) =1 - 0.2725

P(x \ge 1) =0.7275

Solving (c): P(x\le 2)--- Not more than 2 has one time fling

This is calculated as:

P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)

We have:

P(x = 0) = 0.2725

P(x = 1) = ^8C_1* (15\%)^1 * (1 - 15\%)^{8-1}

P(x = 1) = 8* (0.15) * (1 - 0.15)^7

P(x = 1) = 0.3847

P(x = 2) = ^8C_2* (15\%)^2 * (1 - 15\%)^{8-2}

P(x = 2) = 28* (0.15)^2 * (1-0.15)^6

P(x = 2) = 0.2376

So:

P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)

P(x \le 2) = 0.2725 + 0.3847 + 0.2376

P(x \le 2) = 0.8948

4 0
3 years ago
Gwen studies for 1.5 hours every night. What is the total number of hours Gwen studies for 5 nights
Darina [25.2K]
1 and 1/2 hours each night
1+1+1+1+1= 5
1/2+1/2+1/2+1/2+1/2= 2.5
5+2.5= 7.5
7.5 hours or & and a half
hope this helps
~L
6 0
3 years ago
3. Let A, B, C be sets and let ????: ???? → ???? and ????: ???? → ????be two functions. Prove or find a counterexample to each o
Fiesta28 [93]

Answer / Explanation

The question is incomplete. It can be found in search engines. However, kindly find the complete question below.

Question

(1) Give an example of functions f : A −→ B and g : B −→ C such that g ◦ f is injective but g is not  injective.

(2) Suppose that f : A −→ B and g : B −→ C are functions and that g ◦ f is surjective. Is it true  that f must be surjective? Is it true that g must be surjective? Justify your answers with either a  counterexample or a proof

Answer

(1) There are lots of correct answers. You can set A = {1}, B = {2, 3} and C = {4}. Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. Then g is not  injective (since both 2, 3 7→ 4) but g ◦ f is injective.  Here’s another correct answer using more familiar functions.

Let f : R≥0 −→ R be given by f(x) = √

x. Let g : R −→ R be given by g(x) = x , 2  . Then g is not  injective (since g(1) = g(−1)) but g ◦ f : R≥0 −→ R is injective since it sends x 7→ x.

NOTE: Lots of groups did some variant of the second example. I took off points if they didn’t  specify the domain and codomain though. Note that the codomain of f must equal the domain of

g for g ◦ f to make sense.

(2) Answer

Solution: There are two questions in this problem.

Must f be surjective? The answer is no. Indeed, let A = {1}, B = {2, 3} and C = {4}.  Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. We see that  g ◦ f : {1} −→ {4} is surjective (since 1 7→ 4) but f is certainly not surjective.  Must g be surjective? The answer is yes, here’s the proof. Suppose that c ∈ C is arbitrary (we  must find b ∈ B so that g(b) = c, at which point we will be done). Since g ◦ f is surjective, for the  c we have already fixed, there exists some a ∈ A such that c = (g ◦ f)(a) = g(f(a)). Let b := f(a).

Then g(b) = g(f(a)) = c and we have found our desired b.  Remark: It is good to compare the answer to this problem to the answer to the two problems

on the previous page.  The part of this problem most groups had the most issue with was the second. Everyone should  be comfortable with carefully proving a function is surjective by the time we get to the midterm.

3 0
3 years ago
Other questions:
  • Consider the two congruent circles below.<br><br> Select all statements that are true
    14·2 answers
  • Please help me with this question, image attached.
    11·2 answers
  • X divided by 12 = 12 divided by 72​
    9·1 answer
  • Keisha has 10 coins.Two of the coins are nickels,6 pennies,and the rest are dimes.What is the value of Keisha's coins?
    5·2 answers
  • Bentley invested $85,000 in an account paying an interest rate of 4.1% compounded daily. Assuming no deposits or withdrawals are
    7·1 answer
  • A coconut is a fruit that is made up of a hard outer shell that is spherical. Inside, there is a thick layer of coconut meat tha
    12·1 answer
  • Red 13 Silver 34 Black 25 White 10 Blue 8
    13·2 answers
  • 7.167×10 with the power of 6
    6·1 answer
  • Hi guys, how to calculate this in system?<br><br> {2a+3b=14<br> {5b+4a=20<br><br> Thanks,
    5·1 answer
  • Help em with this plss
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!