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Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other

kondaur [170]

Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

Explanation :

Since we have shown in the figure below :

a=70 mi.

b=52 mi.

c=x mi.

$\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}$

So, we use the cosine rule , which states that

$c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03$

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

8 0

3 years ago

use the domain {-4, -2, 0, 2, 4} the codomain [-4, -2, 0, 2, 4} and the range {0, 2, 4} to create a function that is niether one

lesya [120]

Answer:

See attachment

Step-by-step explanation:

We want to create a function that is neither one-to-one or on to given that:

The domain is {-4, -2, 0, 2, 4}

The codomain is [-4, -2, 0, 2, 4}

The range is {0, 2, 4}

The function in the attachment is an example of such function.

The function is not one-to-one because there are different different x-value in the domain that has the same y-value in the co-domain.

It is not an on to function because the range is not equal to the co-domain.

7 0

3 years ago

Find the domain and range for the function graphed below

Nana76 [90]

Answer:

Domain: 3, 2, 1, 0, -1 , -2 , -3

Range: 5 , 4 , 3 , 2 , 1 , 0 , -1 , -2

Step-by-step explanation:

The domain values are all of the x-values, and the range value are all of the y-values. Domain ad range can also be know as input and output.

3 0

3 years ago

Find the coordinates of the fourth vertex that completes the construction of the rectangle on the coordinate plane.

Marizza181 [45]

It’s C.
Just complete the rectangle. You’ll get it.

4 0

2 years ago

5. If the sample size had been 2,500 registered voters, and the results stated 47% would vote for the Republican governor, and 4

icang [17]

Answer:

If we replace for the proportion estimated for the republican governor we got:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{2500}}=0.0196$

And the confidence interval given by:

$0.47-0.0196= 0.45$

$0.47+0.0196= 0.49$

If we replace for the proportion estimated for the democratic chalenger we got:

$ME=1.96\sqrt{\frac{0.45 (1-0.45)}{2500}}=0.0195$

And the confidence interval given by:

$0.45-0.0195= 0.43$

$0.45+0.0195= 0.47$

As we can see both confidence intervals not contain the value 0.5 for the true proportion so then the director cannot said that the election was a toss up at 5% of significance.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

We assume for this case a confidence of 95%. In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If we replace for the proportion estimated for the republican governor we got:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{2500}}=0.0196$

And the confidence interval given by:

$0.47-0.0196= 0.45$

$0.47+0.0196= 0.49$

If we replace for the proportion estimated for the democratic chalenger we got:

$ME=1.96\sqrt{\frac{0.45 (1-0.45)}{2500}}=0.0195$

And the confidence interval given by:

$0.45-0.0195= 0.43$

$0.45+0.0195= 0.47$

As we can see both confidence intervals not contain the value 0.5 for the true proportion so then the director cannot said that the election was a toss up at 5% of significance.

8 0

3 years ago