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allochka39001 [22]
3 years ago
6

According to the diagram, which of the following statements about area and perimeter of pentagon ABCDE is true?

Mathematics
1 answer:
arlik [135]3 years ago
3 0

Answer:

Area = 30 , Perimeter = 22.31 ⇒ Answer (B)

Step-by-step explanation:

* Lets study the figure

- The length of AE = 5

- The length of DC = 3

- The length of BC = 4

- Tho find the length of DE and AB we must use Pythagoras Theorem

∵ The vertical distance of ED = 3 and the horizontal distance = 2

∴ ED = √(3² + 2²) = √13  

- Similar we will find AB

∵ The vertical distance of AB = 6 and the horizontal distance = 3

∴ AB = √(6² + 3²) = √45

* Now we can find its perimeter

- The perimeter = 5 + 4 + 3 + √13 + √45 = 22.31

* to find the area we will divided it into 2 trapezium

- The first one contains E , D , C with point of intersection

 between the vertical axis with side CB

- The lengths of its 2 parallel bases are 3 , 6 and height 2

- The second one contains E , A , B with  point of intersection

 between the vertical axis with side BC

- The lengths of its 2 parallel bases are 2 , 5 and height 6

∵ Area trapezium = (1/2)(b1 + b2) × h

- The area of 1st one = (1/2)(3 + 6) × 2 = 9 units²

- The area of 2nd one = (1/2)(2 + 5) × 6 = 21 units²

∴ The area of the figure = 9 + 21 = 30 units²

* Area = 30 , Perimeter = 22.31

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"If a number divided by 4 leaves remainder 2 or 3", then which one is the correct statement 'n why?
Hoochie [10]

Answer:

As the number is a prime number. Therefore, option 'c' is true.

Step-by-step explanation:

Let us take the number 7 and divide it by 4

\frac{7}{4}

We know that

  • Quotient\frac{Remainder}{Divisor}

as

\frac{7}{4}=1\frac{3}{4}

so the remainder is 3.      ∵ Quotient\frac{Remainder}{Divisor}

As 7 is a prime number, and when we divide the prime number 7 by 4, we get the remainder 3.

Thus, the number is a prime number. Therefore, option 'c' is true.

5 0
3 years ago
Nine hundred ninety two hundred thousandths wrote in decimal form
uranmaximum [27]

Answer:

 I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!

step-by-step explanation:

3 0
2 years ago
What is the length of AB, with endpoints A (3,2) and B (8,14)?
velikii [3]
Answer is C. 13 Find with Magnitude  √(x1-x2)²+(y1-y2)²  = √25+ 144  = √169  = 13 units


6 0
3 years ago
A professor at a local community college noted that the grades of his students were normally distributed with a mean of 84 and a
creativ13 [48]

Answer:

A. P(x>91.71)=0.10, so the minimum grade is 91.71

B. P(x<72.24)=0.025 so the maximum grade could be 72.24

C. By rule of three, 200 students took the course

Step-by-step explanation:

The problem says that the grades are normally distributed with mean 84 and STD 6, and we are asked some probabilities. We can´t find those probabilities directly only knowing the mean and STD (In that distribution), At first we need to transfer our problem to a Standard Normal Distribution and there is where we find those probabilities. We can do this by a process called "normalize".

P(x<a) = P( (x-μ)/σ < (a-μ)/σ ) = P(z<b)

Where x,a are data from the original normal distribution, μ is the mean, σ is the STD and z,b are data in the Standard Normal Distribution.

There´s almost no tools to calculate probabilities in other normal distributions. My favorite tool to find probabilities in a Standard Normal Distribution is a chart (attached to this answer) that works like this:

P(x<c=a.bd)=(a.b , d)

Where "a.b" are the whole part and the first decimal of "c" and "d" the second decimal of "c", (a.b,d) are the coordinates of the result in the table, we will be using this to answer these questions. Notice the table only works with the probability under a value (P(z>b) is not directly shown by the chart)

A. We are asked for the minimum value needed to make an "A", in other words, which value "a" give us the following:

P(x>a)=0.10

Knowing that 10% of the students are above that grade "a"

What we are doing to solve it, as I said before, is to transfer information from a Standard Normal Distribution to the distribution we are talking about. We are going to look for a value "b" that gives us 0.10, and then we "normalize backwards".

P(x>b)=0.10

Thus the chart only works with probabilities UNDER a value, we need to use this property of probabilities to help us out:

P(x>b)=1 - P(x<b)=0.10

P(x<b)=0.9

And now, we are able to look "b" in the chart.

P(x<1.28)=0.8997

If we take b=1.285

P(x<1.285)≈0.9

Then

P(x>1.285)≈0.1

Now that we know the value that works in the Standard Normal Distribution, we "normalize backwards" as follows:

P(x<a) = P( (x-μ)/σ < (a-μ)/σ ) = P(z<b)

If we take b=(a+μ)/σ, then a=σb+μ.

a=6(1.285)+84

a=91.71

And because P(x<a)=P(z<b), we have P(x>a)=P(z>b), and our answer will be 91.71 because:

P(x>91.71) = 0.1

B. We use the same trick looking for a value in the Standard Normal Distribution that gives us the probability that we want and then we "normalize backwards"

The maximum score among the students who failed, would be the value that fills:

P(x<a)=0.025

because those who failed were the 2.5% and they were under the grade "a".

We look for a value that gives us:

P(z<b)=0.025 (in the Standard Normal Distribution)

P(z<-1.96)=0.025

And now, we do the same as before

a=bσ+μ

a=6(-1.96)+84

a=72.24

So, we conclude that the maximum grade is 72.24 because

P(x<72.24)=0.025

C. if 5 students did not pass the course, then (Total)2.5%=5

So we have:

2.5%⇒5

100%⇒?

?=5*100/2.5

?=200

There were 200 students taking that course

6 0
3 years ago
Evaluate the expression for b=5.<br><br> 4b2
Galina-37 [17]

Step-by-step explanation:

When b = 5,

4b² = 4(5)² = 4 * 5 * 5 = 100.

5 0
2 years ago
Read 2 more answers
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