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3 years ago

Please solve the problem.

Mathematics

1 answer:

Deffense [45]3 years ago

3 0

OK. I did it, and I have the solution.
_____________________________________

The length of the deck is (5 + 2x) .
The width of the deck is   (4 + 2x) .

If the deck didn't have that big hole in the middle where the pool is,
then its area would be

   (5 + 2x) · (4 + 2x) .

When you multiply that all out, you get    Area = 4x² + 18x + 20

and the question tells us that the area of the whole big rectangle is 90 yds² .
So we can write

   4x² + 18x + 20 = 90 .

Subtract 90 from each side:    4x² + 18x - 70 = 0
Divide each side by 2 :    2x² + 9x - 35 = 0

You can use the quadratic equation to solve that and find out that
x = 2.5 yards, and that's what the question is asking you.
___________________________________________________

That makes the deck 10 yds high and 9 yds wide.

Total area of the whole big rectangle, (deck + pool ), = 90 yds².

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a trapezoid with an area of 166.75 in has bases that measure 21in and 8 in find the height of the trapezoid

alisha [4.7K]

Answer:

height = 11.5 in

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = $\frac{1}{2}$ h(a + b)

where h is the height and a, b the bases

here a = 21, b = 8 and A = 166.75, hence

$\frac{1}{2}$ h(21 + 8) = 166.75

Multiply both sides by 2 to eliminate the fraction

29h = 333.5 ( divide both sides by 29 )

h = 11.5 in

6 0

3 years ago

(1/4) to the 3rd power

Ksivusya [100]

(1/4)=0.25
0.25*0.25*0.25=0.015625

6 0

3 years ago

Read 2 more answers

Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1

alexandr1967 [171]

Answer:

$a) \simeq 0.3012$ $b) \simeq 0.0494$ c) $\simeq 0.2438$

Step-by-step explanation:

Rate of collision,

1.2 collisions every 4 months

or, $\frac{1.2}{4}$

= 0.3 collisions per month

So, the Poisson distribution for the random variable no. of collisions per month (X) is given by,

P(X =x) = $\frac{e^{-\lambda}\times {\lambda}^{x}}}{x!}
$

for x ∈ N ∪ {0}

= 0 otherwise --------------------------------------(1)

here, $\lambda = 0.3$ collision / month

No collision over a 4 month period means no collision per month or X =0

Putting X = 0 in (1) we get,

P(X = 0) = $\frac{e^{-0.3}\times {\0.3}^{0}}{0!}
$

$\simeq 0.7408182207$ ------------------------------------(2)

Now, since we are calculating this for 4 months,

so, P(No collision in 4 month period)

= $0.7408182207^{4}$

$\simeq 0.3012$ -----------------------------------------------------------(3)

2 collision in 2 month period means 1 collision per month or X =1

Putting X =1 in (1) we get,

P(X =1) = $\frac{e^{-0.3}\times {\0.3}^{1}}{1!}
$

$\simeq 0.2222454662$ ------------------------------------(4)

Now, since we are calculating this for 2 months, so ,

P(2 collisions in 2 month period)

= $0.2222454662^{2}$

$\simeq 0.0494$ -----------------------------------------(5)

1 collision in 6 months period means

$\frac{1}{6}$ collision per month

Now, P(1 collision in 6 months period)

= P( X = 1/6] (which is to be estimated)

= $\frac {P(X=0)\times 5 + P(X =1)\times 1}{6}$

= \frac {0.7408182207 \times 5 + 0.2222454662 \times 1}{6}[/tex]

$\simeq 0.6543894283$ -------------------------------------------(6)

So,

P(1 collision in 6 month period)

= $0.6543894283^{6}$

$\simeq 0.0785267444$ ------------------------------------------------(7)

So,

P(No collision in 6 months period)

= $(P(X =0)^{6}$

$\simeq 0.1652988882$ ---------------------------------(8)

so,

P(1 or fewer collision in 6 months period)

= (8) + (7 ) = 0.0785267444 +0.1652988882

$\simeq 0.2438$ ---------------------------------------------(9)

7 0

3 years ago

PLEASE HELP: Find the measure of the angle indicated. Arc BC is 80 degrees.

Marina CMI [18]

The angle is 80 degrees. The measure of an angle is the exact same as the angle measure of the included arc, so that makes angle BAC 80 degrees

7 0

3 years ago

PLEASE HELP FAST AND PLEASE DON'T POST A LINK

Likurg_2 [28]

Answer:

The difference in amount = $430

Step-by-step explanation:

1- Annual contract:

The annual contract means a contract for 12 months. There is a month penalty for breaking the lease.

This means that, if you left after 8 months, you will have to pay for 10 month.

Total paid = monthly payment * 10

Total paid = 535 * 10 = $5350

2- Month-to-month contract:

You will only paid for the 8 months you stayed,

Total paid = monthly payment * 8

Total paid = 615 * 8 = $4920

3- Getting the difference:

We can note that a month-month contract is a better option if you intend to stay for only 8 months

Difference = 5350 - 4920 = $430

Hope this helps :)

4 0

3 years ago

Read 2 more answers