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3 years ago

Find the area of this rhombus

Mathematics

2 answers:

Sedaia [141]3 years ago

8 0

Answer: SECOND OPTION.

Step-by-step explanation:

You can calculate the area of the rhombus with this formula:

$A=\frac{d_1*d_2}{2}$

Where $d_1$ and $d_2$ are the lengths of the diagonals.

You can observe in the figure that the length of each diagonal is:

$d_1=4in+4in=8in\\d_2=8in+8in=16in$

Now you can substitute the lenghts of the diagonals into the formula. Therefore, the area of this rhombus is:

$A=\frac{(8in)(16in)}{2}$

$A=\frac{128}{2}$

$A=64in^2$

Vikentia [17]3 years ago

7 0

<h2>Hello!</h2>

The answer is:

The area of the rhombus is equal to 64 squared inches.

$area=64in^{2}$

Since we already know half of the length of the diagonals of the rhombus, we can calculate the area of the rhombus using the following formula:

$area=\frac{diagonal_{1}*diagonal_{2}}{2}$

From the image we can see that:

$diagonal_{1}=8in+8in=16in$

$diagonal_{2}=4in+4in=8in$

So, substituting, we have:

$area=\frac{16in*8in}{2}=\frac{128in^{2} }{2}=64in^{2}$

Hence, we have that the area of the rhombus is equal to 64 square inches.

Have a nice day!

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UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

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2 years ago

Find the prime factorization of 35

AnnyKZ [126]

<h3>Question:</h3><h3>•Find the prime factorization of 35.</h3>

Answer:

•The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).

<h3>Explanation:</h3>

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2 years ago

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A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 meter per second, while the cat

LenKa [72]

Answer:

They'll meet after 200 meters , if they simultaneously start running towards each other.

Step-by-step explanation:

Let x =distance travelled by dog and 200-x be the distance travelled by cat. Inorder to meet, the sum of their travelled distances shall be equal to 200 meters as they are far apart by 200 meters.

Dog: Distance =Speed x time: x=30t

Cat: Distance = 200-x

=24t

The sum of their distance travelled shall be 200 meters: 30t+ 24t= 200;54t=200;t=200/54=3.7secs

So they will meet after 3.7 seconds

To check:

Distance travelled by dog :x=30(3.7)

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Distance travelled by cat: 24t=24(3.7)

=88.89 meters

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Step-by-step explanation:

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3 years ago

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lapo4ka [179]

What we have so far:
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