List the different combinations of heads and tails that can occur when

Solve<img src="https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D" id="TexFormula1" title="\frac{2}{3}" alt="\frac{2}{3}" align="absm

Dovator [93]

Answer:

$x=0$

Step-by-step explanation:

Hi there!

$\displaystyle\frac{2}{3} (6x+30)=5(x+4)-2x$

Distribute 2/3 and 5 into the parentheses:

$4x+20=5x+20-2x$

Combine like terms:

$4x-5x+2x=20-20\\-x=0\\x=0$

I hope this helps!

7 0

2 years ago

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a h

Kipish [7]

Answer:

The home would be worth $249000 during the year of 2012.

Step-by-step explanation:

The price of the home in t years after 2004 can be modeled by the following equation:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the price of the house in 2004 and r is the growth rate.

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.

This means that $r = 0.047$

$172000 in 2004

This means that $P(0) = 172000$

What year would the home be worth $ 249000 ?

t years after 2004.

t is found when P(t) = 249000. So

$P(t) = P(0)(1+r)^{t}$

$249000 = 172000(1.047)^{t}$

$(1.047)^{t} = \frac{249000}{172000}$

$\log{(1.047)^{t}} = \log{\frac{249000}{172000}}$

$t\log(1.047) = \log{\frac{249000}{172000}}$

$t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}$

$t = 8.05$

2004 + 8.05 = 2012

The home would be worth $249000 during the year of 2012.

8 0

3 years ago

If a change dispenser contains 32 coins consisting of

swat32

<h3>Answer: 19 dimes</h3>

=================================================

Work Shown:

d = number of dimes

q = 32-d = number of quarters

$5.15 = 515 cents

10d+25q = 515

10d+25(32-d) = 515

10d+800-25d = 515

-15d+800 = 515

-15d = 515-800

-15d = -285

d = -285/(-15)

d = 19

There are 19 dimes. You can stop here if you want.

q = 32-d = 32-19 = 13

There are 13 quarters

-------------------------------

Check:

1 dime = 10 cents

19 dimes = 19*10 = 190 cents

1 quarter = 25 cents

13 quarters = 13*25 = 325 cents

total value = 190 cents + 325 cents = 515 cents = $5.15

The answer is confirmed.

6 0

2 years ago

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

5 0

2 years ago

Question 3

Andru [333]

To plot the graph of the data given, we have a lot of options, one common option to plot this kind of data is a column bar graph.

The picture attached show the column bar for the data given, assuming that the age was measured in years and the height was measured in feet.

Some resources that could help to plot data are excel, origin or qtiplot.

3 0

2 years ago