What amount of money can we obtain using the money we have....(its math)

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and st

SashulF [63]

Answer:

0.7233

Step-by-step explanation:

We want to find the area between the z-scores z=-0.95 and z=1.25.

We first find the area to the left of each z-score, and subtract the smaller area from the bigger one.

For the area to the left of z=-0.95, we read -0.9 under 5 from the standard normal distribution table.

This gives P(z<-0.95)=0.1711

Similarly the area to the left of z=1.25 is

P(z<1.25)=0.8944

Now the area between the two z-scores is

P(-0.25<z<1.25)=0.8944-0.1711=0.7233

7 0

2 years ago

If the perimeter of the top of desk is 54 inches the length of the desk is

allsm [11]

Formula: $2width+2length=perimeter$

$length=15inches$

$width=?$

$Perimeter=54inches$

$2*15=30$ (There are two sides for the length)

$54-30=24$

$24/2=12$ (There are two sides for the width)

The width of the desk is 15 inches

----
-Geekhawk

4 0

3 years ago

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

Answer:

a) $\sqrt{144-288t+208t^2}$ b.) -12knots, 8 knots c) No e) $4\sqrt{13}$

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved $12\dot t (n.m)$ and ship B has moved $8\dot t (n.m)$ . We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

b)

We want to find $\frac{ds}{dt}$ for t=0 and t=1

$\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots$

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = $s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0$

Since function $f(x)=199-288x+208x^2$ is quadratic, concave up and has no real roots, we know that $199-288x+208x^2>0$ for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

$\lim_{t \to \infty} \frac{ds}{dt}$

So, lets check this limit:

$\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}$

Notice that:

$4\sqrt{13}=\sqrt{12^2+5^2}$ =√(speed of ship A² + speed of ship B²)

5 0

3 years ago

-16x - y = -16<br> 12x + 6y = 12<br> How may solutions

Luda [366]

Answer:

y=2x +1/2

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Styline menswear ordered short-sleeve shirts for $23 each and long-sleeve shirts for $28.50 each from Tommy Hilfiger. If the tot

Mice21 [21]

Styline menswear ordered short-sleeve shirts for $23 each and long-sleeve shirts for $28.50

short-sleeve shirts for $23

long-sleeve shirts for $28.50

Total cost = $9,862.50

Let x be the number of short - sleeve

and y be the number of long - sleeve

Total shirts = 375

x + y = 375

23x + 28.50y = 9862.50

Now we solve for x

x + y = 375 ( subtract x on both sides)

So y = 375 - x

Now plug in 375 -x for y in second equation

23x + 28.50y = 9862.50

23x + 28.50(375 - x ) = 9862.50

23x + 10687.5 - 28.50x = 9862.50

subtract 10687.5 from both sides

23x - 28.50x = -825

-5.5x = -825 (divide -5.5 on both sides)

x = 150

So number of short-sleeve = 150

7 0

3 years ago