A radioactive material has a half-life of 1 day. The material decays according to the equation M = 1000(1/2)^t. Mass M is measured in grams and time t is measured in days.

a) What is the mass of the sample after 1 day? 2 days? 10 days?
b) Use a calculator with an exponent key to compute the mass of the
sample after 1 year. Explain what the answer means.

I literally have no idea how to do this

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

s² + s² = 2²

2s² = 4 ( divide both sides by 2 )

s² = 2 ( take the square root of both sides )

s = [tex]\sqrt{2}[/tex]

Answer:

E.

Step-by-step explanation:

we know the diagonal of the square : 2

as you can see in the picture, there is a right-angled triangle with the baseline of Hypotenuse being the diagonal, and 2 times s being the 2 sides.

that means we can use Pythagoras to calculate s :

2² = s² + s²

4 = 2s²

2 = s²

s = sqrt(2)

1/6 = 1 batch, 2/6 = 2 batches and so on

if the factory used 1/2, the factory used 3/6 of a barrel, which equals to 3 batches.

hope it helps :)

Answer:

4/3

Step-by-step explanation:

Using the given points

(0,-2) and (3,2)

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2- -2)/(3-0)

   = (2+2)/(3-0)

   =(4/3

Answer:

Step-by-step explanation:

The centroid of a triangle is the point where the three medians coincide.

Here,

The three medians coincide at point Z so it's the centroid

Answer:

First choice

Step-by-step explanation:

It gives you the endpoints of the included side, F and R. Therefore, the side is FR or RF.

Answer:

Step-by-step explanation:

Given:

27 + 2/3 ÷ 3 + 9/10

In division, compatible numbers are numbers that can be divided mentally.

27 + 2/3 ÷ 3 + 9/10

27 + 0.67 ÷ 3 + 0.9

27.67 ÷ 3.9

= 7.0948717948717

Approximately

= 7

But, alternatively

27.67 ÷ 3.9

27.67 is closer to 28

3.9 is closer to 4

Therefore,

28 ÷ 4

= 7

The quotient of 27 + 2/3 ÷ 3 + 9/10 using compatible numbers is around 7

Answer:

The first fraction is between 27 and 28, closer to 28. The second fraction is between 3 and 4, closer to 4. Compatible numbers in division are numbers that can be divided mentally. 28 divided by 4 is 7. The quotient will be around 7.

Step-by-step explanation:

Answer: Third Choice. 9

Step-by-step explanation:

Concept:

Here, we need to understand the idea of evaluation.    

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given

4x + 2y -1

x = 3, y = -1

Substitute the value of x and y

4(3) + 2(-1) - 1

Simplify by multiplication

12 - 2 - 1

Simplify by subtraction

9

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Hello!

4x= 4*3 = 12

2y = 2*-1 = -2

12-2  -1= 9

Answer:

XN = 22

Step-by-step explanation:

Recall: the Centroid theorem states that the Centroid of a triangle is ⅔ of the distance any vertex of the triangle to the midpoint of the side opposite to it.

This implies that:

XN = ⅔(XG)

XG = 33

Substitute

XN = ⅔(33)

XN = 2*11

XN = 22

Answer:

Step-by-step explanation:

[tex]log_8(1000) = log_2(1000)/log_2(8) = log_2(1000)/3[/tex]

[tex](1/3)log_2(1000) = log_2(1000^{(1/3)}) = log_2 10[/tex]

Step-by-step explanation:

51 is not a prime number because it is divisible by 1,3 and 17

and we know prime number are only those number who arenot divisible by any other number except 1

Answer:

57 is divisible by 1,3,19 and 57

Step-by-step explanation:

A prime number is a number that is divisible only by 1 and itself; and 57 is not among the numbers like 2,3,5,7,11 etc

Answer:

m>3

Step-by-step explanation:

2m >6

Divide by 2

2m/2 > 6/2

m >3

Answer:

m>3

Step-by-step explanation:

Answer:

QV = 4x-1

Step-by-step explanation:

1) segments RS and RQ are equivalent

2) segments SV and QV meet at the same point, and start from opposite sides of segment SQ

so the length of QV would be equal to the length of SV.

Answer:

216 cm^2

Step-by-step explanation:

15^2 -3^2 = 225 -9

= 216

Answer:

The y-intercept of the parent function, f(x), is 0

The y-intercept of the child function, g(x), is  7

Step-by-step explanation:

Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.

The solution is :

Vertex is (-2, 0)

y-intercept is 4.

In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

here, we have,

to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':

f(x) = (x+2)^2 = x2 + 4x + 4

Then, to find the vertex, we can use the formula:

x_v = -b / 2a

x_v = -4 / 2 = -2

Now, finding the y_vertex, we have:

f(x_v) = (-2)^2 + 4*(-2) + 4 = 0

So the vertex is (-2, 0)

To find the y-intercept, we make x = 0 and then find f(x):

f(0) = 0 + 0 + 4 = 4

So the y-intercept is 4.

To learn more on vertex click:

brainly.com/question/12563262

#SPJ2

complete question:

Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².

vertex: ( ? , ? )

y-intercept: ?

Answer:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Step-by-step explanation:

This question is asking for the function's end behavior. An even degree power function with a negative leading coefficient forms a parabola concave down. This means, its vertex represents the maximum and the parabola opens downward (towards negative infinity).

Thus,

[tex]\lim_{x\rightarrow \infty}f(x)=-\infty,\\\lim_{x\rightarrow-\infty}f(x)=-\infty[/tex]

This corresponds with the first answer choice listed:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Answer:

62°

Step-by-step explanation:

Inscribed Angle Theorem

Inscribed angles measures are 1/2 of the arc they create.

m∠FJH x 2 = arc FH

Just take the 31° and double it.

Answer:

b20

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

FG = 7

Step-by-step explanation:

We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:

EF = 7

EH = 3

HF =?

EF² = EH² + HF²

7² = 3² + HF²

49 = 9 + HF²

Collect like terms

49 – 9 = HF²

40 = HF²

Take the square root of both side

HF = √40

Finally, we shall determine FG. This can be obtained as follow:

GH = 3

HF = √40

FG =.?

FG² = GH² + HF²

FG² = 3² + (√40)²

FG² = 9 + 40

FG² = 49

Take the square root of both side

FG = √49

FG = 7

4x - 7 = 3x + 9

x = 16

they're equal because they are opposites by the vertex.

hope it helps :)

Answer:

-3

Step-by-step explanation:

because as you vo more to the negative side the less.it gets and more to the positive side it gets moe

Factorize the numerator:

4r + 20 = 4r + 4×5 = 4 (r + 5)

I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:

(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4

Answer:

k=10

Step-by-step explanation:

Brainliest please~

Answer:

K=10

Step-by-step explanation:

Correct on Plato

Please look at the scanned picture.

Answer:

the total amount of change she should receive is $1.50

Step-by-step explanation:

$7.25+$7.25= $14.50

$20.00-$14.50=$5.50

$5.50-$4.00= $1.50

Do it by your self  ok ???

Answer:

θ ≈ 35.7°

Step-by-step explanation:

His mistake was in using the wrong trig. ratio

Instead of using cosine he should have used the sine ratio

sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then

θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )