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3 years ago

3.) Graph f(x)=3^x.

Mathematics

1 answer:

ollegr [7]3 years ago

7 0

Answer:

f(x)=3^x plot = see attachment

Step-by-step explanation:

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4/12 of a cake was left over if another 3/12 of the cake is eaten

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There would be 1/12 of the cake left.

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(x^2 - x^(1/2))/(1-x^(1/2))

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$\frac { \left( { x }^{ 2 }-{ x }^{ \frac { 1 }{ 2 } } \right) }{ \left( 1-{ x }^{ \frac { 1 }{ 2 } } \right) }$

$\\ \\ =\frac { \left( { x }^{ 2 }-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot 1$

$\\ \\ =\frac { \left( { x }^{ 2 }-\sqrt { x } \right) }{ \left( 1-\sqrt { x } \right) } \cdot \frac { \left( 1+\sqrt { x } \right) }{ \left( 1+\sqrt { x } \right) }$

$\\ \\ =\frac { { x }^{ 2 }+{ x }^{ 2 }\sqrt { x } -\sqrt { x } -x }{ 1+\sqrt { x } -\sqrt { x } -x }$

$\\ \\ =\frac { -\sqrt { x } \left( 1-{ x }^{ 2 } \right) -x\left( 1-x \right) }{ \left( 1-x \right) }$

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3 years ago

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The picture shows a triangular island:

sergiy2304 [10]

Answer:

The expressions that show the value of q are

1) $q=\sqrt{r^{2}+s^{2}}$

2) $q=\frac{s}{cos(55\°)}$

3) $q=\frac{r}{sin(55\°)}$

4) $q=\frac{s}{sin(35\°)}$

5) $q=\frac{r}{cos(35\°)}$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

case A)

In the right triangle of the figure

Applying the Pythagoras Theorem

$q^{2}=r^{2}+s^{2}$

$q=\sqrt{r^{2}+s^{2}}$

case B)

In the right triangle of the figure

$cos(55\°)=\frac{s}{q}$

solve for q

$q=\frac{s}{cos(55\°)}$

case C)

In the right triangle of the figure

$sin(55\°)=\frac{r}{q}$

solve for q

$q=\frac{r}{sin(55\°)}$

case D)

In a right triangle

if $A+B=90\°$

then

$cos(A)=sin(B)$

therefore

$q=\frac{s}{cos(55\°)}$ ------> $q=\frac{s}{sin(35\°)}$

$q=\frac{r}{sin(55\°)}$ ------> $q=\frac{r}{cos(35\°)}$

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Callaway is thinking about entering the golf ball market. The company will make a profit if its market share is more than 20%. A

Vedmedyk [2.9K]

Answer:

$z=\frac{0.224 -0.2}{\sqrt{\frac{0.2(1-0.2)}{624}}}=1.499$

$p_v =P(Z>1.499)=0.0669$

If we compare the p value obtained and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly higher than 0.2 or 20%.

Step-by-step explanation:

How would you make the decision if you were Callaway management? Would you use hypothesis testing?

The best way to test the claim if with a proportion test. The procedure is explained below.

1) Data given and notation

n=624 represent the random sample taken

X=140 represent the golf ball purchasers will buy a Callaway golf ball

$\hat p=\frac{140}{624}=0.224$ estimated proportion of golf ball purchasers will buy a Callaway golf ball

$p_o=0.2$ is the value that we want to test

$\alpha$ represent the significance level

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 true proportion is more than 0,2 or 20%:

Null hypothesis: $p\leq 0.2$

Alternative hypothesis: $p > 0.2$

When we conduct a proportion test we need to use the z statistic, 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:

$z=\frac{0.224 -0.2}{\sqrt{\frac{0.2(1-0.2)}{624}}}=1.499$

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 is not provided but let's assume $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v =P(Z>1.499)=0.0669$

8 0

3 years ago

3.) Graph f(x)=3^x.​

3.) Graph f(x)=3^x.