Laurie filled a container 2/3 full with water. She put 42 2/3 ounces of water in it. What is the capacity of Laurie's container?

To the nearest tenth what is the length of the hypotenuse of a right triangle if one side measures 4.5meters and the other side

allsm [11]

Answer:

Step-by-step explanation:

c^2 = a^2 + b^2

4.5^2 + 9^2 = 101.25

c = sqrt 101.25 = 10.06 = 10.1 meters

3 0

3 years ago

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

Anettt [7]

Answer:

1) The size of the colony after 4 days is 6553 mosquitoes

2) After $t = 4.9\ days$

Step-by-step explanation:

To answer this question you must use the growth formula

$N = N_0e ^ {kt}$

Where

$N_0$ is the initial population of mosquitoes = 1000

t is the time in days

k is the growth rate

N is the population according to the number of days

We know that when t = 1 and $N_0=1000$ then N = 1600

Then we use these values to find k.

$1600 = 1000e ^{k(1)}\\\\\frac{1600}{1000} = e ^ k\\\\ln(\frac{1600}{1000}) = k\\\\k = 0.47$

Now that we know k we can find the size of the colony after 4 days.

$N = 1000e ^ {0.47(4)}\\\\N = 6553\ mosquitoes$

To know how long it should take for the population to reach 10,000 mosquitoes we must do N = 10000 and solve for t.

$10000 = 1000e ^ {0.47t}\\\\10 = e ^ {0.47t}\\\\ln(10) = 0.47t\\\\t = \frac{ln(10)}{0.47}\\\\t = 4.9\ days$

6 0

3 years ago

26. Law of sines, please give a step by step explanation

Stels [109]

Answer:

174.6 ft

Step-by-step explanation:

It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)

We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...

180° -30° -112° = 38°

Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.

c/sin(C) = a/sin(A)

c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft

The height of the tree is about 174.6 feet.

5 0

3 years ago

9(9h + 4b + 9), for h = 7 and b = 3<br><br> Evaluate

irakobra [83]

So, when adding in the 7 and 3 the new equation is:
9{(9x7)+(4x3)+9}

Following pemdas, you have to do parenthesis first. So now the equation is:
9(63+12+9)

Now distribute the 9:

567 + 108 + 81

And finally solve as a normal addition problem:

567 + 108 + 81= 756

So, the answer is 756.

I hope this helps:)

6 0

3 years ago

plain why the function is discontinuous at the given number a. (Select all that apply.) f(x) = x2 − 2x x2 − 4 if x ≠ 2 1 if x =

ElenaW [278]

Answer with Step-by-step explanation:

We are given that

$f(x)=\left\{\begin{matrix}\dfrac{x^2-2x}{x^2-4}&,if\ \ x\neq 2 \\ 1&,if\ \ x=2\end{matrix}\right.$