A form of radium decays exponentially with a half-life of 20 years. This means that 50% will be gone every 20 years. A human can only withstand an exposure of 5 grams of this radium but 150 grams has leaked into the air.

Part A: Write an equation to model the exponential decay of this 150 grams of this form of radium.

Part B: A scientist claims that the area will e safe for humans after 100 years. Do you agree? Verify your answer mathematically and explain why you agree.

Answer:

Because the product is always a non-terminating, non-repeating decimal.

The product of a rational number and an irrational number will always be an irrational number. Then the correct option is A.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

The product of a rational number and an irrational number will always be an irrational number.

Because the product is always a non-terminating, non-repeating decimal number.

Then the correct option is A.

More about the rational number link is given below.

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Answer:

a) 0.587 = 58.7% probability that the company uses flexible work arrangements or gives time off for volunteerism.

b) 0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.

c) 0.3317 = 33.17% probability that the company uses flexible work arrangements.

d) 0.4634 = 46.34% probability that the company does not use flexible work arrangements given that the company does give time off for volunteerism.

e) 0.795 = 79.5% probability that the company does not use flexible work arrangements or the company does not give time off for volunteerism.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a. The company uses flexible work arrangements or gives time off for volunteerism.

41% use flexible work arrangements.

Of the 100-41 = 59% that do not use flexible work arrangments, 30% give time off for volunteerism. So

[tex]p = 0.41 + 0.59*0.3 = 0.587[/tex]

0.587 = 58.7% probability that the company uses flexible work arrangements or gives time off for volunteerism.

b. The company uses flexible work arrangements and does not give time off for volunteerism.

41% use flexible work arrangements. Of those, 100 - 50 = 50% do not give time off for volunteerism. So

[tex]p = 0.41*0.5 = 0.205[/tex]

0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.

c. Given that the company does not give time off for volunteerism, the company uses flexible work arrangements.

Here, we use conditional probability.

Event A: Does not give time off for volunteerism

Event B: Uses flexible work arrangments.

0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.

This means that [tex]P(A \cap B) = 0.205[/tex]

Probability that the company does not give time off for volunteerism:

0.205(uses flexible work arrangments).

100 - 30 = 70% of 59%. So

[tex]P(A) = 0.205 + 0.7*0.59 = 0.618[/tex]

The desired probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.205}{0.618} = 0.3317[/tex]

0.3317 = 33.17% probability that the company uses flexible work arrangements.

d. The company does not use flexible work arrangements given that the company does give time off for volunteerism.

Again conditional probability.

Event A: Gives time off for volunteerism

Event B: Does not use flexible work arrangements.

Probability of giving time off for volunteerism:

50% of 41%(have flexible work arrangements).

30% of 59%(don't have flexible work arrangements).

So

[tex]P(A) = 0.5*0.41 + 0.3*0.59 = 0.382[/tex]

Gives time off for volunteerism and does not use flexible work arrangements.

30% of 59%. So

[tex]P(A \cap B) = 0.3*0.59 = 0.177[/tex]

The desired probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.177}{0.382} = 0.4634[/tex]

0.4634 = 46.34% probability that the company does not use flexible work arrangements given that the company does give time off for volunteerism.

e. The company does not use flexible work arrangements or the company does not give time off for volunteerism.

Does not use flexible work arrangments: 59%

Dont give time off for volunteerism(70% already in the 59%, so we dont add) and 50% of 41%.

[tex]p = 0.59 + 0.5*0.41 = 0.795[/tex]

0.795 = 79.5% probability that the company does not use flexible work arrangements or the company does not give time off for volunteerism.

Answer:

8a + 24b

Step-by-step explanation:

'distributive' is just like sharing across

Answer:

8a + 20b + 4b

Step-by-step explanation:

Distributing it would be 8a+24b so expanding it would equal: 8a+20b+4b

Answer:

54y-36

Step-by-step explanation:

9*6y=54y

9*4=36

Hope this helps :)

Answer:

m<S: 54

m<U: 60

Step-by-step explanation:

x + 4 + x + 68 = 180

2x + 72 = 180

2x = 108

x = 54

<S:

x

54

<U:

x + 4

54 + 4

60

Answer:

1) 27

2) 2/5

3) 1

4) 1.5 lbs

Step-by-step explanation:

1) First, 8505/315 = 27

2)I don't really have an explanation for this one-

3) 2/3 = 6/9. 6/9 + 3/9 = 1

4) 4/8 x 3 = 1.5

1. 2

8,505 ÷ 315 = 27

2. 2 ÷ 5

Fractions are division problems so it would be 2 divided by 5

3. 9/9 or 1

Make them have the same denominator

2/3 + 3/9 = 6/9 + 3/9 = 9/9 = 1

4. 1 ½

4/8 simplified is ½ so you should do ½ x 3 = 1 ½

5. The baker needs 750 more grams

Multiply 2.5 by 1000, which is 2500

That’s how many grams the baker needs, now you need to do 2500 - 1750

Which is 750 grams

Sorry that this took a while, but I am happy to help you!!

Answer:

b just tool the test

Step-by-step explanation:

Answer:

What is the difference between linear and exponential functions? Linear functions change at a constant rate per unit interval. An exponential function changes by a common ratio over equal intervals.

Answer:

area of triangle = 1/2 ×base×height

Answer:

x=49/18

Step-by-step explanation:

Step-by-step explanation:

The correct answer is

It is proportional to its weight.

Hope it will help :)❤

Step-by-step explanation:

mass is proportional to the weight of the object

w = mg

Answer:

The number is -10

Step-by-step explanation:

I will answer this while I read through the question.

Let the number be x

Divide by 2

[tex]\frac{x}{2}[/tex]

Add 9 to it

[tex]\frac{x}{2} + 9[/tex]

It gives 4

[tex]\frac{x}{2} + 9 = 4[/tex]

Now, we solve for x

Collect Like Terms

[tex]\frac{x}{2} = 4-9[/tex]

[tex]\frac{x}{2} = -5[/tex]

Make x the subject

[tex]x = -5 *2[/tex]

[tex]x = -10[/tex]

Answer:

0.28m hope it help you☺........

Answer:

(-4, -1) (see below)

Step-by-step explanation:

Substitution means that you actually replace, or "substitute," the value of the variable in.

Here, y = -1, so -3x - 8y = 20 can be written as:

-3x - 8 (-1) = 20

We can now solve for x:

-3x + 8 = 20

-3x = 12

x = -4

Putting this into (x, y) format equals:

(-4, -1)

Answer:

AFCE = 30

P+Q = 11

Step-by-step explanation:

From the picture, you can see the figure can be decomposed into two identical large triangles with area 20, and 4 identical longer ones, that have to cover the remaining area 40, thus 10 each.

From that you can count the area.

Second puzzle is just trial and error.

Answer:

Perimeter

Hope it helps!

The distance around the edge of a figure is its Perimeter.

To complete the following statement. The distance around the edge of a figure is its ____.​

Perimeter is the measure of the length of the figure on its circumference.

Since in the question blank, space is given following the definition,
The distance around the edge of a figure is perimeter because the measure of the boundary of any figure is termed as its perimeter.
For example, the Perimeter of the rectangle is the total measure of the two-time measures of length and width. For the Perimeter of the square, it is 4 times the length of one side. For the Perimeter of the circle, it is 2π times of radius.

Thus, the distance around the edge of a figure is its Perimeter.

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The measure of angle O from the triangle MNO is 156.92°.

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

Given that, in triangle MNO, m = 720 cm, n = 160 cm and o=870 cm.

Now, 870=√(720²+160²-2×720×160 cosO)

870²=720²+160²-2×720×160 cosO

756900=544000-230400 cosO

212900=-230400 cosO

cosO= -212900/230400

cosO= -0.92

∠O=156.92°

Therefore, the measure of angle O from the triangle MNO is 156.92°.

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Answer:

158

Step-by-step explanation:

Answer:

6.09+3.84=9.93 is the desired answer

Step-by-step explanation:

Cashews total cost step by step

1.74×3.5

Multiply 1.74 and 3.5 to get 6.09.

6.09

Peanuts total cost step by step

1.92×2

Multiply 1.92 and 2 to get 3.84.

3.84

Given:

Consider the three number are given by:

[tex]a=x^2-y^2[/tex]

[tex]b=2xy[/tex]

[tex]c=x^2+y^2[/tex]

To find:

The three numbers are the Pythagorean triple generated by using 4 for x and 1 for y.

Solution:

We have,

[tex]a=x^2-y^2[/tex]

[tex]b=2xy[/tex]

[tex]c=x^2+y^2[/tex]

Substituting 4 for x and 1 for y, we get

[tex]a=4^2-1^2[/tex]

[tex]a=16-1[/tex]

[tex]a=15[/tex]

Similarly,

[tex]b=2(4)(1)[/tex]

[tex]b=8[/tex]

And,

[tex]c=4^2+1^2[/tex]

[tex]c=16+1[/tex]

[tex]c=17[/tex]

The three three numbers are the Pythagorean triple are 8,15 and 17.

Therefore, the correct option is C.

Answer:

(-∞, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

5n - 13 < 4n - 10

Step 2: Solve for n

Here we see that any value n smaller than 3 would work as a solution to the inequality.

∴ our interval is (-∞, 3)

Answer:

6 gallons

Step-by-step explanation:

You can find this using the ration method.

If, 8 gallons : 192 miles

   x gallons : 144 miles

We must find the value of x, which is the number of gallons used to travel 144 miles.

Cross multiply the ratios.

192 x = 8 × 144

192 x = 1152

x = 1152 ÷ 192

x = 6

∴ It takes 6 gallons to travel 144 miles.

Answer:

For this equation you be inverse operation giving you the answer -6

further information down below :)

Step-by-step explanation:

Your goal for this is to isolate the variable which is x.

First, find the operation opposite of addition which is subtraction

When you add that operation to both sides with the constant(2)

2 and 2 cancel each other out, but to the for the term(4) 4-2=2

after that you have your new term which is x/-3=2

You do the same thing but to in division because the opposite of multiplication is division in this case you multiply -3 to both sides -3*-3 cancel each other out, now you have-3*2= negative times a positive equal negative in anyway so, overall you get -6.  

To check:

you do the full equation now that you have isolated the variable, you now can do the operations normally which are. -6/-3=2 because when you divide a negative by a negative you get a positive end out with 2+2=4 which is correct and match the sum.

This means that our answer is correct :)

Answer:

6477

Step-by-step explanation:

wow, u got a big party there

Answer:

dangggg but 6477

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

ur welcome

brainliest plz

Answer:

w=36

f=12

k=13

Step-by-step explanation:

Answer:

Answer:

T= 16000(2)

=36 000

T=36 000(2)

=72 000 in 4 hours

Answer:

x=30°

y=30°

Step-by-step explanation:

x= 180-150=30°

y)

180=30 + 90 + z

z +120 = 180

z= 60

90-60=y

y=30

30°

Answer:

1) 315cm^2

2) 7cm

3) :

a) Angle L

b) Side ML

c) Angle N

d) Side LN

4) 13 and a half years old

Step-by-step explanation:

Answer:

30 miles

Step-by-step explanation:

3 hours = 180 minutes

3/5 of an hour = 36 minutes

180/36 = 5

5 times 6 = 30

I hope this helps :)