What percent is 3 out of 70

The graph below shows the solution to which system of inequalities?

nlexa [21]

Answer:

Option D.

Step-by-step explanation:

Consider option D. $y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3$

Take point (0,0)

On putting this point in inequation $y\leq \frac{3x}{4}+10$ , we get

$0\leq 10$ which is true . So, solution is region towards the origin i,e region below the line $y= \frac{3x}{4}+10$ including the line itself .

On putting (0,0) in inequation $y\leq \frac{-x}{2}-3$ , we get $0\leq -3$ which is false , so solution is region away from the origin i.e region below line $y= \frac{-x}{2}-3$ including the line itself .

So, common solution to both the inequations is the shaded part in the given figure .

In other words, we can say that the graph shown in the given figure represents system of equations: $y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3$

5 0

2 years ago

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

Hitman42 [59]

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

$\frac{dQ}{dt} = -rt$

Which has the following solution:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that $Q(6) = (1-0.03)Q(0) = 0.97Q(0)$ . We use this to find r.

$Q(t) = Q(0)e^{-rt}$

$0.97Q(0) = Q(0)e^{-6r}$

$e^{-6r} = 0.97$

$\ln{e^{-6r}} = \ln{0.97}$

$-6r = \ln{0.97}$

$r = -\frac{\ln{0.97}}{6}$

$r = 0.0051$

So

$Q(t) = Q(0)e^{-0.0051t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.0051t}$

$0.5Q(0) = Q(0)e^{-0.0051t}$

$e^{-0.0051t} = 0.5$

$\ln{e^{-0.0051t}} = \ln{0.5}$

$-0.0051t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0051}$

$t = 135.9$

The half-life of the radioactive substance is 135.9 hours.

6 0

2 years ago

Allison works at a Bank. Her employer offers her a retirement pension plan which will be 1.75% of her average salary for the las

Law Incorporation [45]

9514 1404 393

Answer:

$41,977.60

Step-by-step explanation:

Allison's average salary for the last 5 years is ...

(70 +73.1 +75.2 +77.5 +79)/5 = 74.96 . . . . thousand dollars

Then her annual pension is ...

1.75% × $74,960 × 32 = $41,997.60

6 0

2 years ago

Question 51 ptsThe point (-4,-2) lies on a circle. What is the length of the radius of this circle if thecenter is located at (-

forsale [732]

Given,

The coordinates of the point on the circle is (-4, -2).

The coordinates of the center of the circle is (-8, -10).

Reuired

The length of the center of the circle.

By using the distance formula, the radius of the circle can be calculated.

The distance formula is,

$Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Substituting the value of the coordinates of the points,

$\begin{gathered} Distance=\sqrt{(-10-(-2))^2+(-8-(-4))^2} \\ =\sqrt{(-10+2)^2+(-8+4)^2} \\ =\sqrt{(-8)^2+(-4)^2} \\ =\sqrt{64+16} \\ =\sqrt{80} \\ =\sqrt{4\times4\times5} \\ =4\sqrt[]{5} \end{gathered}$

Hence,

3 0

2 months ago

You have 324 ft of fabric to make a circular play parachute for kids. What is the radius of the largest parachute you could make

ratelena [41]

10.2 feet

Divide 3.24 by 3.14 and find the square root of the result.

5 0

2 years ago

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