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4 years ago

Which function has the same range as

Mathematics

2 answers:

sleet_krkn [62]4 years ago

7 0

Answer: Second Option

$g(x)=-\frac{5}{7}(\frac{3}{5})^{-x}$

Step-by-step explanation:

The function $g(x)=(\frac{3}{5})^x$ is an exponential function.

Functions of this type have a range that goes from (0, ∞)

When multiplying the function by a negative coefficient $-\frac{5}{7}$ , now all the values of g(x) will be negative and the range of $g(x)=-\frac{5}{7}(\frac{3}{5})^x$ will be: (-∞, 0)

Then we must search among the options a function with range (-∞, 0)

Since the exponential functions of the form $(a) ^ x$ , where $a>0$ always have range (0, ∞) Then the correct option will be the one with a negative coefficient.

The correct option is the second option

GrogVix [38]4 years ago

4 0

Answer:

2nd option

Step-by-step explanation:

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Rosa is picking out fabric for her bedroom. She has 6 fabric samples, and 2 of them are floral. What is the probability that a r

Vlada [557]

Answer:

Probability of selected sample is floral = 1 / 3

Step-by-step explanation:

Given:

Number of fabric sample = 6 sample

Number of floral sample from all samples = 2 samples

Find:

Probability of selected sample is floral

Computation:

Probability of a sample = Favorable outcome / Total outcomes

Probability of selected sample is floral = Number of floral sample / Number of fabric sample

Probability of selected sample is floral = 2 / 6

Probability of selected sample is floral = 1 / 3

5 0

3 years ago

Rippy spends 3 hours, 35 minutes, and 4 seconds driving on a road trip. How many seconds did she spend driving?

noname [10]

Answer:

12,904 sec

Step-by-step explanation:

Each hour is 3600 seconds

each minute is 60 seconds

3600 * 3 + 35 *60 + 4 =

5 0

3 years ago

Need help with mymathlab problem

AlexFokin [52]

Answer:

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Step-by-step explanation:

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5 0

3 years ago

A class survey found that 29 students watched television on Monday, 24 on Tuesday, and 25 on Wednesday. Of those who watched TV

gizmo_the_mogwai [7]

Answer:

There were 49 students in the class

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the students that watched TV on Monday

-The set B represents the student that watched TV on Tuesday.

-The set C represents the students that watched TV on Wednesday.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a is the number of students that only watched TV on Monday, $A \cap B$ is the number of adults that watched TV both on Monday and Tuesday, $A \cap C$ is the number of students that watched TV both on Monday and Wednesday, and $A \cap B \cap C$ is the number of students that watched TV on every day.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following subsets:

$a,b,c,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)$

The sums of all of this values is the number of student that were there in the class. This means that we want to find the value of T:

$a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = T$

We start finding the values from the intersection of three sets.

Solution:

12 students watched TV on all three days:

$A \cap B \cap C = 12$

14 students watched TV on both Monday and Tuesday

$A \cap B + A \cap B \cap C = 14$

$A \cap B = 14 - 12$

$A \cap B = 2$

Of those who watched TV on only one of these days, 13 choose Monday, 9 chose Tuesday, and 10 chose Wednesday.

$a = 13, b = 9, c = 10$

29 students watched television on Monday:

$A = 29$

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$29 = 13 + 2 + (A \cap C) + 12$

$A \cap C = 29 - 27$

$A \cap C = 2$

24 on Tuesday

$B = 24$

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$24 = 9 + (B \cap C) + 2 + 12$

$B \cap C = 24 - 23$

$B \cap C = 1$

Now we have every value needed to find T:

$T = a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$T = 13 + 9 + 10 + 2 + 2 + 1 + 12$

$T = 49$

There were 49 students in the class

7 0

4 years ago

Question 5: prove that it’s =0

mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that $\cos(\frac{2}{x})$ is a variable number between -1 and 1 (inclusive).

This means that $-1 \le \cos(\frac{2}{x}) \le 1$ .

$x^4 \ge 0$ for all value $x$ . So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

$-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

By squeeze theorem, if $-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

and $\lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L$ , then we can also conclude that $\im_{x \rightarrow} x^4\cos(\frac{2}{x})=L$ .

So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at $x=0$ .

$\lim_{x \rightarrow 0}x^4=0^4=0$

$\lim_{x \rightarrow 0}-x^4=-0^4=-0=0$ .

We can finally conclude that $\lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0$ by squeeze theorem.

Some people call this sandwich theorem.

6 0

3 years ago