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3 years ago

ABCD is a parallelogram.

Mathematics

2 answers:

Dmitry_Shevchenko [17]3 years ago

7 0

Answer:

Using SAS they are congruent.

Step-by-step explanation:

E is the point where the diagonals AC and BD meet.

Side: AB = CD

Angle: ∠ABE = ∠EDC

Side: BE = DE

Hence by SAS theorem the two triangles are congruent.

Orlov [11]3 years ago

6 0

Answer and Step-by-step explanation:

Because this is a parallelogram, by definition, the intersection point of the two diagonals bisects them, making AE = CE and BE = DE.

We also know that ∠AEB = ∠CED because they're vertical angles, so by definition, they're congruent.

Thus, we can use the side-angle-side (SAS) congruency theorem to prove that ΔABE ≅ ΔCDE.

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The expected number of typographical errors on a page of a certain magazine is .2. What is the probability that an article of 10

Pavel [41]

Answer:

a) The probability that an article of 10 pages contains 0 typographical errors is 0.8187.

b) The probability that an article of 10 pages contains 2 or more typographical errors is 0.0175.

Step-by-step explanation:

Given : The expected number of typographical errors on a page of a certain magazine is 0.2.

To find : What is the probability that an article of 10 pages contains

(a) 0 and (b) 2 or more typographical errors?

Solution :

Applying Poisson distribution,

$N\sim Pois(0.2)$

$P(N=r)=\frac{e^{-np}(np)^r}{r!}$

where, n is the number of words in a page

and p is the probability of every word with typographical errors.

Here, n=10 and E(N)=np=0.2

a) The probability that an article of 10 pages contains 0 typographical errors.

Substitute r=0 in formula,

$P(N=0)=\frac{e^{-0.2}(0.2)^0}{0!}$

$P(N=0)=\frac{e^{-0.2}}{1}$

$P(N=0)=e^{-0.2}$

$P(N=0)=0.8187$

The probability that an article of 10 pages contains 0 typographical errors is 0.8187.

b) The probability that an article of 10 pages contains 2 or more typographical errors.

Substitute $r\geq 2$ in formula,

$P(N\geq 2)=1-P(N$

$P(N\geq 2)=1-[P(N=0)+P(N=1)]$

$P(N\geq 2)=1-[\frac{e^{-0.2}(0.2)^0}{0!}+\frac{e^{-0.2}(0.2)^1}{1!}]$

$P(N\geq 2)=1-[e^{-0.2}+e^{-0.2}(0.2)]$

$P(N\geq 2)=1-[0.8187+0.1637]$

$P(N\geq 2)=1-0.9825$

$P(N\geq 2)=0.0175$

The probability that an article of 10 pages contains 2 or more typographical errors is 0.0175.

6 0

3 years ago

PLEASE HELP FAST!!

Oduvanchick [21]

Answer:

x = 4

Step-by-step explanation:

10 = -1/4 x + 11

10 - 11 = -1/4 x

-1 = - 1/4 x

x = 4

7 0

3 years ago

What is the area of a sector with a central angle of 8 π/11 radians and a radius of 7.2 ft? use 3.14 for π and round your final

coldgirl [10]

Answer:

$59.19 ft^2$

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=7.2\ ft$

$\pi =3.14$

substitute

$A=(3.14)(7.2)^{2}$

$A=162.78\ ft^2$

step 2

we know that

The area of a circle subtends a central angle of 2π radians

using proportion

Find out the area of a sector with a central angle of 8 π/11 radians

$\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2$

7 0

3 years ago

The farmer had 28 cows. He wanted to bring them into the milking shed in groups of 7. How many groups of cows did the farmer bri

Ostrovityanka [42]

Answer:

(C) Subtract 7 from 28. Keep subtracting 7 from answer until he gets to 0. Then count the number of times 7 was subtracted.

This method is another suitable solution to problem

Step-by-step explanation:

Total number of cows the farmer has = 28 cows

Number of cows in 1 shed = 7

The number of sheds used to keep 28 cows is 28 ÷ 7 = 4 sheds

⇒4 sheds are needed to keep 28 cows.

Now choosing an alternate method:

1) Add 28 and 7 = 28 + 7 = 35 sheds

But 35 sheds ≠ 4 sheds

Hence, NOT AN APPROPRIATE METHOD.

2)Add 7 to 28. Keep adding 7 to the answer for a total of seven times.

28 + 7 .... 7 times = 28 + 7 + 7 + 7 + 7 /+ 7 + 7 + 7 = 77 ≠ 4 sheds

NOT AN APPROPRIATE METHOD.

3)Subtract 7 from 28. Keep subtracting 7 from answer until he gets to 0.

28 - 7 = 21

21 - 7 = 14

14 -7 = 7 and 7 - 7 - 0

Hence, in 4 times the answer is 0

So, the number of sheds required is 4

AN APPROPRIATE METHOD.

4) Multiply 28 by 7.

28 x 7 = 196, 196 ≠ 4 sheds

NOT A APPROPRIATE METHOD.

Hence, the ONLY alternate method to count the totals sheds required is

Subtract 7 from 28. Keep subtracting 7 from the answer until he gets to 0.

6 0

3 years ago

Pls give the answers

mars1129 [50]

Answer:

Step-by-step explanation:

ohhh this is easyyy its

7 0

2 years ago