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
Naddik [55]
2 years ago
10

PLEASE!! I NEED HELP

Mathematics
1 answer:
elixir [45]2 years ago
6 0

Answer:

Option A, \frac{1}{7}

Step-by-step explanation:

<u>Step 1:  Determine the numbers that are multiples of 3</u>

8 → Not a multiple of 3

9 → Multiple of 3

14 → Not a multiple of 3

19 → Not a multiple of 3

25 → Not a multiple of 3

34 → Not a multiple of 3

38 → Not a multiple of 3

<u>Step 2:  Determine the probability of chosing a multiple of 3</u>

Since we only have 1 number that is a multiple of 3 out of the 7 given numbers, that means that we do the following:  

\frac{(1\ multiple\ of\ 3)}{7\ total\ numbers}

\frac{1}{7}

Answer: Option A, \frac{1}{7}

You might be interested in
The function f(x) = 2x2 + 6x - 12 has a domain consisting of the integers from -2 to 1, inclusive. Which set represents the corr
Dimas [21]

Answer:

[-16,-4]

Step-by-step explanation:

We are given that

f(x)=2x^2+6x-12

Domain=[-2,1]

We have to find the set of range values of f(x).

Substitute x=-2

f(-2)=2(-2)^2+6(-2)-12

f(-2)=-16

Substitute x=1

f(1)=2(1)+6(1)-12=-4

Range of f(x)=[-16,-4]

Hence, the set of range values of f(x)

[-16,-4]

7 0
3 years ago
A spinner has 5 equal sections labeled 1 through 5. The bar graph shows the results of spinning the spinner 100 times. Which sta
lina2011 [118]

Answer:The experimental probability and theoretical probability are equal.

Step-by-step explanation:

They will still have the same outcomes if is an experimental or theoretical probability.

3 0
3 years ago
Prove that if n is a perfect square then n + 2 is not a perfect square
notka56 [123]

Answer:

This statement can be proven by contradiction for n \in \mathbb{N} (including the case where n = 0.)

\text{Let $n \in \mathbb{N}$ be a perfect square}.

\textbf{Case 1.} ~ \text{n = 0}:

\text{$n + 2 = 2$, which isn't a perfect square}.

\text{Claim verified for $n = 0$}.

\textbf{Case 2.} ~ \text{$n \in \mathbb{N}$ and $n \ne 0$. Hence $n \ge 1$}.

\text{Assume that $n$ is a perfect square}.

\text{$\iff$ $\exists$ $a \in \mathbb{N}$ s.t. $a^2 = n$}.

\text{Assume $\textit{by contradiction}$ that $(n + 2)$ is a perfect square}.

\text{$\iff$ $\exists$ $b \in \mathbb{N}$ s.t. $b^2 = n + 2$}.

\text{$n + 2 > n > 0$ $\implies$ $b = \sqrt{n + 2} > \sqrt{n} = a$}.

\text{$a,\, b \in \mathbb{N} \subset \mathbb{Z}$ $\implies b - a = b + (- a) \in \mathbb{Z}$}.

\text{$b > a \implies b - a > 0$. Therefore, $b - a \ge 1$}.

\text{$\implies b \ge a + 1$}.

\text{$\implies n+ 2 = b^2 \ge (a + 1)^2= a^2 + 2\, a + 1 = n + 2\, a + 1$}.

\text{$\iff 1 \ge 2\,a $}.

\text{$\displaystyle \iff a \le \frac{1}{2}$}.

\text{Contradiction (with the assumption that $a \ge 1$)}.

\text{Hence the original claim is verified for $n \in \mathbb{N}\backslash\{0\}$}.

\text{Hence the claim is true for all $n \in \mathbb{N}$}.

Step-by-step explanation:

Assume that the natural number n \in \mathbb{N} is a perfect square. Then, (by the definition of perfect squares) there should exist a natural number a (a \in \mathbb{N}) such that a^2 = n.

Assume by contradiction that n + 2 is indeed a perfect square. Then there should exist another natural number b \in \mathbb{N} such that b^2 = (n + 2).

Note, that since (n + 2) > n \ge 0, \sqrt{n + 2} > \sqrt{n}. Since b = \sqrt{n + 2} while a = \sqrt{n}, one can conclude that b > a.

Keep in mind that both a and b are natural numbers. The minimum separation between two natural numbers is 1. In other words, if b > a, then it must be true that b \ge a + 1.

Take the square of both sides, and the inequality should still be true. (To do so, start by multiplying both sides by (a + 1) and use the fact that b \ge a + 1 to make the left-hand side b^2.)

b^2 \ge (a + 1)^2.

Expand the right-hand side using the binomial theorem:

(a + 1)^2 = a^2 + 2\,a + 1.

b^2 \ge a^2 + 2\,a + 1.

However, recall that it was assumed that a^2 = n and b^2 = n + 2. Therefore,

\underbrace{b^2}_{=n + 2)} \ge \underbrace{a^2}_{=n} + 2\,a + 1.

n + 2 \ge n + 2\, a + 1.

Subtract n + 1 from both sides of the inequality:

1 \ge 2\, a.

\displaystyle a \le \frac{1}{2} = 0.5.

Recall that a was assumed to be a natural number. In other words, a \ge 0 and a must be an integer. Hence, the only possible value of a would be 0.

Since a could be equal 0, there's not yet a valid contradiction. To produce the contradiction and complete the proof, it would be necessary to show that a = 0 just won't work as in the assumption.

If indeed a = 0, then n = a^2 = 0. n + 2 = 2, which isn't a perfect square. That contradicts the assumption that if n = 0 is a perfect square, n + 2 = 2 would be a perfect square. Hence, by contradiction, one can conclude that

\text{if $n$ is a perfect square, then $n + 2$ is not a perfect square.}.

Note that to produce a more well-rounded proof, it would likely be helpful to go back to the beginning of the proof, and show that n \ne 0. Then one can assume without loss of generality that n \ne 0. In that case, the fact that \displaystyle a \le \frac{1}{2} is good enough to count as a contradiction.

7 0
3 years ago
Find the range of all the multiples of 3 between 10 and 20
Len [333]

List the multiples of 3:

3, 6, 9, 12, 15, 18,21

The ones between 10 and 20 are:

12, 15, 18

The range is the difference between the highest and lowest numbers.

Range = 18 - 12 = 6

3 0
3 years ago
Read 2 more answers
When 5√20 is written in simplest radical form , the result is k√5 what is the value of K
Vladimir [108]

Answer:

Step-by-step explanation:

√20 can be rewritten as the product of two radicals:  √4√5,

and √4 = 2.

Thus, 5√20 = 5(2)√5 = 10√5.  Thus, B:  10 is correct; k = 10.

7 0
3 years ago
Other questions:
  • Last year, Shantell bought a car for $24,000. The current value of the car is $21,000. Find the percent decrease in the value of
    6·1 answer
  • ASAP!! HEEELPPPP!!
    11·1 answer
  • What is the slope of the line that passes through the pair of points (-10,14) and(-6,12)
    10·1 answer
  • Sean bought a 6 inch sub. He ate 3 3/4 inches. How much sub does he have left in the simplest form.
    7·1 answer
  • 5. You sell candy bars for a fundraiser. Each box contains 50 bars and costs $30. If you want to make $45 profit for each box, h
    10·2 answers
  • Rick owns a farm, which produces many different crops, including corn. The table shows the relationship between the number of ac
    13·1 answer
  • Solve the system of functions below:<br> -9x = (-2x^2)-4-y<br> x = (-y+6)/3
    10·1 answer
  • I need the answer qiuck because its urgent​
    7·1 answer
  • Your friend evaluates the expression when m = 10. is your friend correct? Explain your reasoning.
    14·2 answers
  • Employees of the sports department at a television station want to measure the number of viewers for a particular exercise progr
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!