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2 years ago

The function f(x) = -2x5 + x3 − 7x is an odd function. Which rule is satisfied by this function?

Mathematics

1 answer:

Virty [35]2 years ago

7 0

Answer:

-f(-x) = f(x)

Step-by-step explanation:

Given function is:

f(x)= -2x^5+x^3-7x

To check if a function is even, it is checked that:

f(-x)=f(x)

If f(-x) gives the original function then the function is said to be even.

And if:

-f(-x)=f(x)

which means if –f(-x) gives the original function, then the function is odd. So a function has to satisfy this rule to be an odd function.

Now for the given function:

-f(-x)= -[-2(-x)^5+(-x)^3-7(-x)]

= -[(-2)(-x^5 )+(-x^3 )+7x]

= -( 2x^5- x^3+7x)

Multiplying the negative sign

-f(-x)= -2x^5+x^3-7x

-f(-x)=f(x)

So, the function satisfies this rule to be an odd function. ..

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andrew-mc [135]

Answer: A

Step-by-step explanation: Range is the distance between one point to the next. That would make A the correct answer.

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3 years ago

The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginnin

vazorg [7]

Answer:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

$p_v =2*P(Z>1.784) =0.074$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=42$ represent the number of infested vines for Pernod5

$X_{2}=22$ represent the number of infested vines for Action

$n_{1}=440$ sample of Pernod5

$n_{2}=360$ sample of Action

$\hat p_{1}=\frac{42}{440}=0.0955$ represent the proportion of residents of infested vines for Pernod5

$\hat p_{2}=\frac{22}{360}=0.0611$ represent the proportion of infested vines for Action

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.1$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between thw two population proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_{2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{1}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{42+22}{440+360}=0.08$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>1.784) =0.074$

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3 years ago

How many hours would someone who earns 7.50 per hour have to work to earn $116.25

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2 years ago

Cindy dissolves 19 1 /4 grams of drink mix in 1 3 /4 ounces of water. What is the unit rate in grams of drink mix per ounce of w

Alenkinab [10]

Answer:

There are 11 g of drink mix for every ounce of water.

Step-by-step explanation:

In order to calculate the unit rate in grams of drink mix for ounces of water of any type of drink, we need to divide the mass of drink mix in grams by the mass of water in ounces. In this case there are mixed fractions, we will first convert them to fractions, to do that we sum the fraction part with the integer one.

$mix = 19 + \frac{1}{4}\\\\mix = \frac{77}{4}$

$water = 1 + \frac{3}{4}\\\\water = \frac{7}{4}$

The rate is:

$rate = \frac{mix}{water}\\\\rate = \frac{\frac{77}{4}}{\frac{7}{4}}\\\\rate = \frac{77}{7}\\\\rate = 11$

There are 11 g of drink mix for every ounce of water.

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3 years ago