Please help on this problem

Which rigid motion would map triangle ABC onto triangle A'B'C'?

Gelneren [198K]

It would be choice 1 since when rotated all of the points would match up.

3 0

3 years ago

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 900 vot

Stells [14]

Answer:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

Step-by-step explanation:

Information given

n=900 represent the random sample selected

$\hat p=0.75$ estimated proportion of residents favored annexation

$p_o=0.72$ is the value that we want to test

represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

The political strategist wants to test the claim that the percentage of residents who favor annexation is above 72%.:

Null hypothesis: $p\leq 0.72$

Alternative hypothesis: $p > 0.72$

The statistic for this case is given by:

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

Replacing the data given we got:

$z=\frac{0.75 -0.72}{\sqrt{\frac{0.72(1-0.72)}{900}}}=2.00$

Now we can calculate the p value. Since is a bilateral test the p value would be:

$p_v= P(Z>2) =0.0228$

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true proportion of residents favored annexation is higher than 0.72 or 72%

3 0

2 years ago

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

8 months ago

Which function has the greater maximum value, f(x) or g(x)?

Stolb23 [73]

Answer:

gx

Step-by-step explanation:

fx is the nonsimplest form gx is the simplest i hope this helps

6 0

2 years ago

The measure of an angle is 84.9°. What is the measure of its complementary angle?

joja [24]

The answer will most likely be 56 degrees try that it should be the answer!

8 0

2 years ago