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3 years ago

15

the regular price of a shirt is $15 natalie bought it on a sale for 0.9 times then the sale price was multiplied by 1.06 to incl

ude tax

1 answer:

ivolga24 [154]3 years ago

4 0

I did it the way i was taught and i got 2.56 but it could be wrong. i also tried to do it your way and i got 1.59 so it can be either

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The probability of an event - picking teams. About (a) 10 kids are randomly grouped into an A team with five kids and a B team w

LuckyWell [14K]

Answer: The required probability is $\dfrac{4}{9}$

Step-by-step explanation:

Since we have given that

Number of kids = 10

Number of kids in Team A = 5

Number of kids in Team B = 5

There are three kids in the group, Alex and his two best friends Jose and Carl.

So, number of favourable outcome is given by

$2(\dfrac{8!}{3!\times 5!})$

Total number of outcomes is given by

$\dfrac{10!}{5!\times 5!}$

So, the probability that Alex ends up on the same team with at least one of his two best friends is given by

$\dfrac{2(\dfrac{8!}{5!\times 3!)}}{\dfrac{10!}{5!\times 5!}}\\\\=2\times \dfrac{8!}{3!}\times \dfrac{5!}{10!}\\\\=\dfrac{4}{9}$

Hence, the required probability is $\dfrac{4}{9}$

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2 years ago

Freeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

REY [17]

Answer:

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Step-by-step explanation:

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2 years ago

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The integer whose product with (-1) is 22 is

nadya68 [22]

Answer:

-22

Step-by-step explanation:

According to the question you need to find a number that gives the result of 22 when multiplied with -1

So, $-22 X (-1) = +22$

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3 years ago

THE VALUE OF 9 IN 495,123 IS HOW MANY TIMES THE VALUE OF 9 IN 63,129

taurus [48]

THE VALUE OF 9 IN 495,123 IS 10000 <span>TIMES THE VALUE OF 9 IN 63,129</span>

5 0

2 years ago

A rectangular swimming pool is bordered by a concrete patio. the width of the patio is the same on every side. the area of the s

andre [41]

Answer:

$x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)$

where

l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Explanation:

Let

x = width of the patio
l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Since the pool is bordered by a complete patio,

Length of the pool (with the patio)
= (length of the pool (w/o the patio)) + 2*(width of the patio)
Length of the pool (with the patio) = l + 2x

Width of the pool (with the patio)
= (width of the pool (w/o the patio)) + 2*(width of the patio)
Width of the pool (with the patio) = w + 2x

Note that

Area of the pool (w/o the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
Area of the pool (w/o the patio) = lw

Area of the pool (with the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
= (l + 2x)(w + 2x)
= w(l + 2x) + 2x(l + 2x)
= lw + 2xw + 2xl + 4x²
Area of the pool (with the patio) = 4x² + 2x(l + w) + lw

Area of the patio
= (Area of the pool (with the patio)) - (Area of the pool (w/o the patio))
= (4x² + 2x(l + w) + lw) - lw
Area of the patio = 4x² + 2x(l + w)

Since the area of the patio is equal to the area of the surface of the pool, the area of the patio is equal to the area of the pool without the patio. In terms of the equation,

Area of the patio = Area of the pool (w/o the patio)
4x² + 2x(l + w) = lw
4x² + 2x(l + w) - lw = 0 (1)

Let

a = numerical coefficient of x² = 4
b = numerical coefficient of x = 2(l + w)
c = constant term = -lw

Then using quadratic formula, the roots of the equation 4x² + 2x(l + w) - lw = 0 is given by

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\ = \frac{-2(l + w) \pm \sqrt{(2(l + w))^2 - 4(4)(-lw)}}{2(4)} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l + w)^2) + 16lw}}{8} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2) + 4(4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2 + 4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 6lw + w^2)}}{8}$
$= \frac{-2(l + w) \pm 2\sqrt{l^2 + 6lw + w^2}}{8} \\= \frac{2}{8}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\x = \frac{1}{4}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right) \text{ or }}
\\\boxed{x = -\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

Since $(l + w) + \sqrt{l^2 + 6lw + w^2} \ \textgreater \ 0$ , $-\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2}\right)$ is negative. Since x represents the patio width, x cannot be negative. Hence, the patio width is given by

$\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

7 0

3 years ago