Alicia watched a drone take off from a bridge. The height of the drone (in meters above the ground) t minutes

At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the du

boyakko [2]

Step-by-step explanation:

The probability of success = 8/(8 + 17) = 8/25 = 0.32.

Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.

Hence, X ~ Bin(4, 0.32).

Thus, P(X = 1) = $4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3$

3 0

1 year ago

Congratulations you received a score of 3.4 on your annual review . Merit increases are given out starting at .5% at a score of

defon

Using the formula above, your merit increase will be 2.5%. You received a score of 3.4 on your annual review. Since the merit increase model is 0.5% salary increase at a score of 2.6, with an additional 1% for every .4 points above that baseline, you get 2.5%, which is the baseline of 0.5% + 2% for the 0.8 points you scored above that baseline.

6 0

1 year ago

A grocer has 2 kinds of tea, one that sells for $8.00 per pound and the other that sells for $6.00 per pound. How many pounds of

Brilliant_brown [7]

Answer:

35 pounds of $8.00 tea and 15 pounds of $6.00 tea

Step-by-step explanation:

Let x represent the pounds of tea of the $8 kind. 8x would represent the total cost of that type of tea. We can also say 50 - x is the pounds of tea of the $6 kind, so 6(50 - x) is the total cost of that type of tea. 50 * 7.4 represents the total cost of all the tea, and the expression 8x + 6(50 -x) would also represent the same thing. We can write this as an equation,

8x + 6(50 -x) = 50 * 7.4

simplify,

8x + 300 - 6x = 370

2x + 300 = 370

and solve.

2x = 70

x = 35

This means there is 35 pounds of the $8 kind.

We can subtract that from 50 to find,

50 - 35 = 15,

15 pounds is the amount of the $6 kind.

3 0

1 year ago

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A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

1 year ago

A cylinder shaped dispenser holds 5,652 cubic centimeters of liquid soap and is now full. The radius of the dispenser is 7.5 cen

attashe74 [19]

We know that

[volume of cylinder]=pi*r²*h------------> h=[volume of cylinder]/(pi*r²)
Volume=5652 cm³
r=7.5 cm
so
h=[5652]/(3.14*7.5²)-----------> h=32 cm

the height of the soap in the full dispenser is 32 cm

the height when 4,239 cubic centimeters of soap remains in the dispenser is
h=[4239]/(3.14*7.5²)-----------> h=24 cm

hence

the difference is 32-24--------> 8 cm

the answer is
8 cm

3 0

2 years ago

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