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3 years ago

9

The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec

tangle.

1 answer:

igomit [66]3 years ago

8 0

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 $m^{2}$

From there

x * (2x - 4) = 70

$2x^{2}$ - 4x = 70

$2x^{2}$ - 4x - 70 = 0

$x^{2}$ - 2x - 35 = 0

Now we have a quadratic equation, which is a $x^{2}$ + bx + c = 0, where a $\neq$ 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = $-2^{2}$ - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are $\frac{- b - \sqrt{D} }{2a}$ and $\frac{- b + \sqrt{D} }{2a}$

$x_{1}$ = $\frac{- (-2) - \sqrt{144} }{2}$ = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

$x_{2}$ = $\frac{- (-2) + \sqrt{144} }{2}$ = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

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The answer is $3594.98

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3 years ago

Find the measure of the angle HELP PLSSS URGENT!

Alecsey [184]

Answer:

It is 40 degrees

Step-by-step explanation:

The 2 lines, x and y are forming 90 degrees, and since we know that part of that complementary angle is 50 degrees, we would do:

50+x=90

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3 years ago

Consider an experiment that consists of recording the birthday for each of 20 randomly selected persons. Ignoring leap years, we

8_murik_8 [283]

Answer:

a) $p_{20d}$ = 0.588

b) 23

c) 47

Step-by-step explanation:

To find a solution for this question we must consider the following:

If we’d like to know the probability of two or more people having the same birthday we can start by analyzing the cases with 1, 2 and 3 people

For n=1 we only have 1 person, so the probability $p_{1}$ of sharing a birthday is 0 ( $p_{1}$ =0)

For n=2 the probability $p_{2}$ can be calculated according to Laplace’s rule. That is, 365 different ways that a person’s birthday coincides, one for every day of the year (favorable result) and 365*365 different ways for the result to happen (possible results), therefore,

$p_{2} = \frac{365}{365^{2} } = \frac{1}{365}$

For n=3 we may calculate the probability $p_{3}$ that at least two of them share their birthday by using the opposite probability P(A)=1-P(B). That means calculating the probability that all three were born on different days using the probability of the intersection of two events, we have:

$p_{3} = 1 - \frac{364}{365}*\frac{363}{365} = 1 - \frac{364*363}{365^{2} }$

So, the second person’s birthday might be on any of the 365 days of the year, but it won’t coincide with the first person on 364 days, same for the third person compared with the first and second person (363).

Let’s make it general for every n:

$p_{n} = 1 - \frac{364}{365}*\frac{363}{365}*\frac{362}{365}*...*\frac{(365-n+1)}{365}$

$p_{n} = \frac{364*363*362*...*(365-n+1)}{365^{n-1} }$

$p_{n} = \frac{365*364*363*...*(365-n+1)}{365^{n} }$

$p_{n} = \frac{365!}{365^{n}*(365-n)! }$

Now, let’s answer the questions!

a) Remember we just calculated the probability for n people having the same birthday by calculating 1 <em>minus the opposite</em>, hence <em>we just need the second part of the first calculation for</em> $p_{n}$ , that is:

$p_{20d} = \frac{364}{365}*\frac{363}{365}*\frac{362}{365}*...*\frac{(365-20+1)}{365}$

We replace n=20 and we obtain (you’ll need some excel here, try calculating first the quotients then the products):

$p_{20d}$ = 0.588

So, we have a 58% probability that 20 people chosen randomly have different birthdays.

b) and c) Again, remember all the reasoning above, we actually have the answer in the last calculation for pn:

$p_{n} = \frac{365!}{365^{n}*(365-n)! }$

But here we have to apply some trial and error for 0.50 and 0.95, therefore, use a calculator or Excel to make the calculations replacing n until you find the right n for $p_{n}$ =0.50 and $p_{n}$ =0.95

b) 0.50 = 365!/(365^n)*(365-n)!

n $p_{n}$

1 0

2 0,003

3 0,008

…. …

20 0,411

21 0,444

22 0,476

23 0,507

The minimum number of people such that the probability of two or more of them have the same birthday is at least 50% is 23.

c) 0.95 = 365!/(365^n)*(365-n)!

We keep on going with the calculations made for a)

n $p_{n}$

… …

43 0,924

44 0,933

45 0,941

46 0,948

47 0,955

The minimum number of people such that the probability of two or more of them have the same birthday is at least 95% is 47.

And we’re done :)

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4 years ago

60/30 in simplistic form<br><br><br> Need answer quick!!!!!!!!!

makkiz [27]

Answer:

2

Step-by-step explanation:

60/30 is 2

HOpe this helps :D

PLz mark brainliest if correct :D

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3 years ago

Find the center of a circle with the equation: x2 y2−32x−60y 1122=0 x 2 y 2 − 32 x − 60 y 1122 = 0

mixas84 [53]

The equation of a circle exists:

$$(x-h)^2 + (y-k)^2 = r^2$ , where (h, k) be the center.

The center of the circle exists at (16, 30).

<h3>What is the equation of a circle?</h3>

Let, the equation of a circle exists:

$$(x-h)^2 + (y-k)^2 = r^2$ , where (h, k) be the center.

We rewrite the equation and set them equal :

$$(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2- 32x - 60y +1122=0$

$$x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0$

We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.

-2hx = -32x

h = -32/-2

⇒ h = 16.

-2ky = -60y

k = -60/-2

⇒ k = 30.

The center of the circle exists at (16, 30).

To learn more about center of the circle refer to:

brainly.com/question/10633821

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7 0

2 years ago