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3 years ago

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Which of the following functions I which of the following functions are one to one? Select all that apply there are 3 answers

1 answer:

ivann1987 [24]3 years ago

8 0

Answer:

The function $f(x)=\frac{x-1}{3x+3}$ is one-to-one function ⇒ 1st

The function $f(x)=\sqrt{5x+9}$ is one-to-one function ⇒ 2nd

The function $f(x)=\frac{1}{2}x^{3}$ is one-to-one function ⇒ 4th

Step-by-step explanation:

* Lets explain how to solve this problem

- One to one function is the function that has no reputation in the value

of the y-coordinates for every corresponding x-coordinates

- That means when you draw a horizontal line at any value of y, then

the horizontal line intersects the graph of the function at one point

only

- So to solve the problem look to the attached figures

# The red graph of the function $f(x)=\frac{x-1}{3x+3}$ ⇒1st graph

- In this graph if we draw a horizontal line at any value of y it will

intersect the graph at only one point

- Take care there is a horizontal asymptote at y= 1/3, that means

there is no value of x at y = 1/3

∴ The function $f(x)=\frac{x-1}{3x+3}$ is one-to-one function

# The blue graph of the function $f(x)=\sqrt{5x+9}$ ⇒2nd graph

- In this graph if we draw a horizontal line at any value of y it will

intersect the graph at only one point

∴ The function $f(x)=\sqrt{5x+9}$ is one-to-one function

# The green graph of the function $f(x)=\frac{1}{2}x^{3}$ ⇒3rd graph

- In this graph if we draw a horizontal line at any value of y it will

intersect the graph at only one point

∴ The function $f(x)=\frac{1}{2}x^{3}$ is one-to-one function

# The purple graph of the function $f(x)=\frac{7}{4x^{2}}$ ⇒5th graph

- In this graph if we draw a horizontal line at any value of y it will

intersect the graph at more than one point

∴ The function $f(x)=\frac{7}{4x^{2}}$ is not one-to-one function

# The black graph of the function $f(x)=3x^{4}+7x^{3}$ ⇒4th graph

- In this graph if we draw a horizontal line at any value of y it will

intersect the graph at more than one point

∴ The function $f(x)=3x^{4}+7x^{3}$ is not one-to-one function

* The answers are 1st , 2nd and 4th functions

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A TV station claims that 38% of the 6:00 - 7:00 pm viewing audience watches its evening news program. A consumer group believes

Elena L [17]

Answer:

$z=\frac{0.340 -0.38}{\sqrt{\frac{0.38(1-0.38)}{830}}}=-2.374$

$p_v =P(Z$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that regularly watch the TV station’s news program is significantly less than 0.38 .

Step-by-step explanation:

1) Data given and notation

n=830 represent the random sample taken

X=282 represent the people that regularly watch the TV station’s news program

$\hat p=\frac{282}{830}=0.340$ estimated proportion of people that regularly watch the TV station’s news program

$p_o=0.38$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is less than 0.38:

Null hypothesis: $p\geq 0.38$

Alternative hypothesis: $p < 0.38$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.340 -0.38}{\sqrt{\frac{0.38(1-0.38)}{830}}}=-2.374$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(Z$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that regularly watch the TV station’s news program is significantly less than 0.38 .

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Answer:

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Step-by-step explanation:

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Howard is designing a chair swing ride. The swing ropes are 4 44 meters long, and in full swing they tilt in an angle of 2 3 ∘ 2

qaws [65]

Question:

Howard is designing a chair swing ride. The swing ropes are 4 meters long, and in full swing they tilt in an angle of 23°. Howard wants the chairs to be 3.5 meters above the ground in full swing. How tall should the pole of the swing ride be? Round your final answer to the nearest hundredth.

Answer:

7.18 meters

Step-by-step explanation:

Given:

Length of rope, L = 4 m

Angle = 23°

Height of chair, H= 3.5 m

In this question, we are to asked to find the height of the pole of the swing ride.

Let X represent the height of the pole of the swing ride.

Let's first find the length of pole from the top of the swing ride. Thus, we have:

$cos \theta = \frac{h}{L}$

Substituting figures, we have:

$cos(23) = \frac{h}{4}$

Let's make h subject of the formula.

$h = 4cos(23) = 3.68$

The length of pole from the top of the swing ride is 3.68 meters

To find the height of the pole of the swing ride, we have:

X = h + H

X = 3.68 + 3.5

X = 7.18

Height of the pole of the swing ride is 7.18 meters

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