All categories

3 years ago

The sides of a rhombus with angle of 60° are 6 inches. find the area of the rhombus. 9√3 in2 18√3 in2 36 in2

Mathematics

2 answers:

musickatia [10]3 years ago

8 0

Drop a perpendicular from an obtuse vertex.

That makes a 30 - 60º right triangle, with hypotenuse 6 and short leg 3. So the long leg, which is the height of the rhombus, is 3√3 .

Since a rhombus is a parallelogram, its area is base x height = 6 x 3√3 = 18√3

harina [27]3 years ago

4 0

Drop a perpendicular from an obtuse vertex.

That makes a 30 - 60º right triangle, with

hypotenuse 6 and short leg 3. So the long leg,

which is the height of the rhombus, is 3√3 .

Since a rhombus is a parallelogram, its area

is base x height = 6 x 3√3 = 18√3 .

You might be interested in

Miguel bought 2 1/4 pounds of hamburgers,1 1/5 pounds of sliced turkey ,and 2 pounds of cheese.what was the total weight of all

irinina [24]

the answer you are looking for is 5 9/20 pounds

sorry but it as to be twenty character

7 0

3 years ago

Write 2, 330, 000 in scientific notation?

Genrish500 [490]

Answer:

2.33 × 10^6

Step-by-step explanation:

I just used a calculator, to be honest. It was super simple.

2.33 * 10^6

2.33 * (10*10*10*10*10*10)

which then equals 2,330,000

6 0

3 years ago

The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plan

Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$\mu = E(X) = np = 100*0.23 = 23$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21$

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30 - 23}{4.1}$

$Z = 1.71$

$Z = 1.71$ has a pvalue of 0.9564.

So there is a 95.64% probability that under 30% of the dogs are emotional support trained

5 0

3 years ago

Given that cos (x) = 1/3, find sin (90 - x)

drek231 [11]

$\sin{(A - B)} \equiv \sin{A}\cos{B} - \cos{A}\sin{B} \\\\
\therefore \sin{(90 - x)}\\
 = \sin{(90)}\cos{(x)} - \cos{(90)}\sin{(x)} \\
= (1)\cos{(x)} - (0)\sin{(x)} \\
= \cos{x} - 0 \\
= \cos{x} \\
= \frac{1}{3}
$

3 0

3 years ago

Read 2 more answers

Research suggest that people are less likely to become repeat offenders if they stay out of the prison system. Why do you think

kondaur [170]

Answer:

Yes prison breeds criminal minds

Step-by-step explanation:

When you send a person to a house filled with just criminals they will just become more criminal minded. If they spend a long time in the prison system too the person will forget how life outside was. It will be like sending a child into the outside world except with a ton of knowledge on how to rob and stuff like that.The american prison system is one of the shadiest systems to be created in my opinion.Its a system built for you to come back over and over.Usually when you get out u have less opportunities for a job.Forget about having a career if you went to prison for literally anything.Your family might disown you or forget you. Its just heartbreaking to see prisoners come out of jail just to have even less opportunity to change their life than before they went. It will get to a point where you need to do crime to survive or live comftorably on the outside world. The american prison system is just built to get revenge on someone and ruin their whole life. I know some European countries have an amazing prison system where they fix you and give you opportunities to become better. Thing is in america we dont want to help the guy that scammed or killed a friend of ours. We just end up hoping their life is miserable and thats our prison system.Its absolutely disgusting.Instead of heavily punishing these people and sending them into the world without help. We should help them and make them better people for our society.Im sorry if this is very disorganized and hard to understand i just wrote what my mind blurted into this keyboard

5 0

3 years ago

Read 2 more answers