Simplify 2−2m−3n0. Write your answer using only positive exponents.

3. The parents of a newborn girl want to invest $1000 in some kind of saving plan that their child could

andrew11 [14]

Answer:

A. 1000x75t=i

B. 1000(1+5%/n)^t

Step-by-step explanation:

i=prt interest principle rate time

a=p(1+r/n)^t amount principle rate number of times interest is compound time

<em>Hope this helps.</em>

5 0

3 years ago

Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

4 years ago

Pls help solve this...No hacker links

Cerrena [4.2K]

Answer:

x=13

Step-by-step explanation:

18-5=13. You have to subtract 5 from 5 itself and then 18.

8 0

3 years ago

Read 2 more answers

In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0

vlabodo [156]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

$P(X < 4) = 0.4141$

b

$P(4 < X < 6) = 0.32876$

c

$P(X >8) = 0.064037$

d

The correct option is B

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 4.5$

The standard deviation is $\sigma = 2.3$

Generally the probability that a randomly selected study participant's response was less than 4 is mathematically represented as

$P(X < 4) = P(\frac{X - \mu }{\sigma} < \frac{4 - 4.5}{ 2.3} )$

$\frac{X -\mu}{\sigma} = Z (The \ standardized \ value \ of\ X )$

So

$P(X < 4) = P(Z < -0.217 )$

From the z-table $P(Z < -0.217 ) = 0.4141$

So

$P(X < 4) = 0.4141$

Generally the probability that a randomly selected study participant's response was between 4 and 6 is mathematically represented as

$P(4 < X < 6) = P( < \frac{4 - 4.5}{ 2.3} < \frac{X - \mu }{\sigma} < \frac{6 - 4.5}{2.3})$

=> $P(4 < X < 6) = P( \frac{4 - 4.5}{ 2.3} < \frac{X - \mu }{\sigma} < \frac{6 - 4.5}{2.3})$

=> $P(4 < X < 6) = P( -0.217 < Z< 0.6522$

=> $P(4 < X < 6) = (Z< 0.6522) -P( Z < -0.217)$

From the z-table

$(Z< 0.6522) = 0.74286$

So

$P(4 < X < 6) = 0.74286 -0.4141$

=> $P(4 < X < 6) = 0.74286 -0.4141$

=> $P(4 < X < 6) = 0.32876$

Generally the probability that a randomly selected study participant's response was more than 8 is mathematically represented as

$P(X > 8) = P(\frac{X - \mu }{\sigma} > \frac{8 - 4.5}{ 2.3} )$

$P(X > 8) = P(Z > 1.52174 )$

From the z-table $P(Z > 1.52174 ) = 0.064037$

So

$P(X >8) = 0.064037$

5 0

3 years ago

What is the answer to 76?

vovangra [49]

Answer:

13.2 minutes or 13 minutes 12 seconds.

Step-by-step explanation:

1. Count how much water drains the first pump every minute. Let the volume of pool be D. Every minute first pump drains D/11 water.

2. Working together(6 minutes) First pump drains 6D/11 water, hence the second pump drains 5D/11 water.

3.Count how much water drains second pump per minute -> (5D/11)/6= 5D/66

4. It takes the second pump 66 minutes to drain pool 5 times, thus it takes 13.2(66/5) minutes to drain the pool, which is 13 minutes 12 seconds.

7 0

4 years ago