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3 years ago

Math Focus

Mathematics

1 answer:

posledela3 years ago

5 0

Answer:

<h2>(90Degree)(0.3Degree/1min) = 300min</h2><h2>since 60min = 1hr</h2><h2>(300min)(1hr/60min) = 5hrs</h2>

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A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to

s2008m [1.1K]

Answer:

Part 1 : $A=250 e^{-0.008223t}$

Part 2 : Half life is 84 minutes ( approx )

Step-by-step explanation:

Part 1 : Suppose the function that shows the amount( in grams ) of the substance after t minutes,

$A=A_0 e^{kt}$

If t = 0 min, A = 250 grams,

$250=A_0 e^{0}$

$\implies A_0 = 250$

If t = 250, A = 32 grams,

$32 = A_0 e^{250k}$

$32 = 250 e^{250k}$

$0.128 = e^{250k}$

Taking ln both sides,

$\ln(0.128) = 250k$

$\implies k =\frac{\ln(0.128)}{250}=-0.008223$

Hence, the equation that shows this situation,

$A=250 e^{-0.008223t}$

Part 2 : If A = 250/2 = 125,

$125 = 250 e^{-0.008223t}$

$0.5 = e^{-0.008223t}$

Taking ln both sides,

$\ln(0.5) = -0.008223t$

$\implies t =\frac{\ln(0.5)}{-0.008223}\approx 84$

Therefore, the half life of the substance would be 84 minutes.

8 0

3 years ago

Please help im so confused??

kirza4 [7]

P(A) = 0.7
P(B) = 0.8

P(A∩B) ⇒ When both event happens
P(A∩B) = 0.7 x 0.8 = 0.56

Answer: 0.56

6 0

2 years ago

Read 2 more answers

What is an equation of the line that passes through the points (-6, -2) and

den301095 [7]

Answer:

The equation of line is: $\mathbf{4x-3y=-18}$

Step-by-step explanation:

We need to find an equation of the line that passes through the points (-6, -2) and (-3, 2)?

The equation of line in slope-intercept form is: $y=mx+b$

where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=-6,y_1=-2, x_2=-3, y_2=2$

Putting values and finding slope

$Slope=\frac{2-(-2)}{-3-(-6)}\\Slope=\frac{2+2}{-3+6} \\Slope=\frac{4}{3}$

So, we get slope: $m=\frac{4}{3}$

Finding y-intercept

Using point (-6,-2) and slope $m=\frac{4}{3}$ we can find y-intercept

$y=mx+b\\-2=\frac{4}{3}(-6)+b\\-2=4(-2)+b\\-2=-8+b\\b=-2+8\\b=6$

So, we get y-intercept b= 6

Equation of required line

The equation of required line having slope $m=\frac{4}{3}$ and y-intercept b = 6 is

$y=mx+b\\y=\frac{4}{3}x+6$

Now transforming in fully reduced form:

$y=\frac{4x+6*3}{3} \\y=\frac{4x+18}{3} \\3y=4x+18\\4x-3y=-18$

So, the equation of line is: $\mathbf{4x-3y=-18}$

6 0

2 years ago

Prove that: 16sin20.sin40.sin60.sin80=3

olga nikolaevna [1]

to prove that 6720. Sin 40. Sin 60. 80 equals 3 you'd have to divide 16 by 20 multiply subtract both sides by 3 which is 24x + 6x + 8x + -14 equals 40 40 + 20 equals 16 - -40 equals 80 which equals to 3

6 0

3 years ago

A box contains 24 yellow, 33 green and 35 red jelly beans. If 8 jelly beans are selected at random, what is the probability that

tensa zangetsu [6.8K]

Answer:

0.00014

Step-by-step explanation:

The box contains a total of 24 + 33 + 35 = 92 jelly beans

If we need to pick 8 jelly beans and want them all to be green:

We can choose 8 green jelly beans from 33 green in C₃₃,₈ different ways

The total ways we can choose 8 jelly beans out from 92 is: C₉₂,₈

Thus, the probability we're looking for is C₃₃,₈ / C₉₂,₈ = 13884156/93080887185 =0.00014

8 0

2 years ago