A scientist has 20 grams of the radioactive isotope sodium-24. The isotope decays exponentially as shown in the table.
Time (hours)
Mass (grams)
5
15.9
10
12.6
15
10
20
7.9
25
6.3
30
5
Approximately what will the mass of the isotope be after 45 hours?
A 1.5 grams
B. 2.5 grams
C. 3.5 grams
D. 4.5 grams

Answer:

2380

Step-by-step explanation:

The equations that are true are: B. 2/3 x 5 = 10/15 (simplified to 2/3 x 5 = 2/3), D. 4/5 x 2 = 16/5 , F. 6/7 x 7 = 6 . These three equations accurately represent the multiplication of fractions or mixed numbers.

Let's analyze each equation:

A. 7 x 1/2 = 3 1/2

This equation is not true. The product of 7 and 1/2 is 7/2, which is equivalent to 3 1/2, not 3 1/2.

B. 2/3 x 5 = 10/15 (simplified to 2/3 x 5 = 2/3)

This equation is true. The product of 2/3 and 5 is 10/3, which can be simplified to 2/3.

C. 2 x 3/4 = 2 3/4

This equation is not true. The product of 2 and 3/4 is 6/4, which is equivalent to 1 1/2, not 2 3/4.

D. 4/5 x 2 = 16/5

This equation is true. The product of 4/5 and 2 is 8/5, which can be simplified to 16/5.

E. 3 x 5/6 = 15/6

This equation is not true. The product of 3 and 5/6 is 15/6, which can be simplified to 2 1/2, not 15/6.

F. 6/7 x 7 = 6

This equation is true. The product of 6/7 and 7 is 6.

Therefore, the three equations that are true are:

B. 2/3 x 5 = 10/15 (simplified to 2/3 x 5 = 2/3)

D. 4/5 x 2 = 16/5

F. 6/7 x 7 = 6

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Answer:

A = 280cm^2

Step-by-step explanation:

we have 2 shapes, a parallelogram, and a rectangle

lets find our area of the rectangle

A = lw

A = 20(7.5)

A = 150

now for the parallelogram

A = bh

A = 20(6.5)

A = 130

now we add to find the entire A

A = 150+130

A = 280

Answer:

X=26

Step-by-step explanation:

(4x-3)^2-(4x+3)^2-26

4x^2-4*3+3^2 - (4x-3)^2-26

16x-12x+9-(16x-12x+9)-26

16x-12x+9-16x+12x-9-26

16x-12x-16x+12x= - 9+9+26

4x-4x=26

X=26

I'm not sure but here you goooo✨

Step-by-step explanation:

line MO,line NO, line

MN

In conclusion, we can use the if-else statement in Python to create a new variable with a value of 1 if the customer's predicted probability is greater than or equal to the breakeven response rate and 0 otherwise.

Given a prediction probability and a breakeven response rate, we need to create a new variable that takes the value of 1 if the customer's predicted probability is greater than or equal to the breakeven response rate and 0 otherwise. We can create this variable using an if-else statement in Python.The code to create the new variable "target" is as follows:```python

if predicted_prob >= breakeven_response_rate:

   target = 1

else:

   target = 0

```Where `predicted_prob` is the predicted probability of a customer responding to a marketing campaign, and `breakeven_response_rate` is the minimum response rate required for the campaign to break even. If `predicted_prob` is greater than or equal to `breakeven_response_rate`, `target` is set to 1. Otherwise, it is set to 0. This ensures that the new variable takes the value of 1 only for those customers who are likely to respond to the campaign, and 0 for those who are not likely to respond. The use of `if-else` statement helps us to create a logical condition that evaluates the predicted probability with the breakeven response rate.In conclusion, we can use the if-else statement in Python to create a new variable with a value of 1 if the customer's predicted probability is greater than or equal to the breakeven response rate and 0 otherwise. The code provided above uses this approach to create the variable "target". The length of the answer is 150 words.

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Answer:

B : 68.5°F and 76.5°F

I think sorry if i am wrong.

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

you can do cross multiplication

90/100 = x/30

100x=2700

x=27

The required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line is called a parabola.

Given that, a parabola has the directrix x=6 and the focus (3,-5), we need to find the equation of the parabola,

The standard form of a left-right parabola is given as:

4p(x-h) = (y-k)²

Focus = (p+h, k)

Therefore,

h+p = 3....(i)

Directrix =

x = h-p

h-p = 6...(ii)

Solving the equations we get,

h = 9/2

p = -3/2

Substitute into the standard form:

4p(x-h) = (y-k)²

4(-3/2)(x-9/2) = (y+5)²

-6(x-9/2) = (y+5)²

\(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

Hence, the required equation of the parabola in the vertex form is \(x = - \frac{1}{6} (y+5)^2+\frac{9}{2}\)

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The question is incomplete so, i solved for the attached question

Answer: The answer is 3

Step-by-step explanation:

Hope this helps you! Have a good day! :)

the completely factored form of the expression is: \(10x^2 + 28x - 6 = 2x(5x + 14) - 6 = (5x + 14)(x - 3/5)\)

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The expression inside the parentheses is now in the form of ax + b, where a = 5/2 and b = 7. To factor this, we can use the product-sum method:

a = 5/2

b = 7

Find two numbers whose product is equal to a times b:

(5/2) * 7 = 35/2

Find two numbers whose sum is equal to the coefficient of x:

(5/2) + 2(7) = 19/2

Using these two numbers, we can rewrite the expression as:

2x(5x/2 + 7) - 6

= 2x(2.5x + 7) - 6

= (5x + 14)(x - 3/5)

Therefore, the completely factored form of the expression is: \(10x^2 + 28x - 6 = 2x(5x + 14) - 6 = (5x + 14)(x - 3/5)\)

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Answer:

16/23

Step-by-step explanation:

Total number of marbles: 7 + 2 + 8 + 6 = 23

Blue marbles: 7

Not blue marbles: 23 - 7 = 16

p(not blue) = 16/23

Answer:

35

Step-by-step explanation:

Law of cosines

c^2=a^2+b^2-2ab(cos(A))

14^2=11^2+8^2-2(11)(8)Cos(A)

A=93.5833

Law of Sines

Sin(A)/a=Sin(B)/a

Sin(93.5833)/11=Sin(B)/8

B=34.7719

Answer:

240 is the amount

Answer:

240

Step-by-step explanation

1. 75 ÷ 15 =5

2. 12 x 4 = 48

3. 48 × 5 = 240

Answer:

(800 x 9) + (10 x 9)

Step-by-step explanation:

Find out what 810 x 9 is:

810 x 9 = 7290

Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):

(800 x 9) = 7200

(10 x 9) = 90

7200 + 90 = 7290

The probability of rolling two dice and getting a sum of at most 4 can be found by listing all the possible outcomes that satisfy the given condition and dividing it by the total number of possible outcomes.

In summary, the probability of rolling two fair six-sided dice and getting a sum of at most 4 is 0.25. This can be found by counting the number of possible outcomes that satisfy the given condition and dividing it by the total number of possible outcomes.

The outcomes that satisfy the condition are the cells in the table where the sum is 2, 3, or 4, and there are three such cells. The probability of rolling any of these outcomes is 1/12, so the probability of rolling two dice and getting a sum of at most 4 is 3/12 or 0.25.

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Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:  \(y < -\frac{1}{2}x+3\)

This is the same as writing y < (-1/2)x+3

==============================================================

Explanation:

The dashed boundary line goes through (0,3) and (4,1)

Apply the slope formula for those two points

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

m = (1-3)/(4-0)

m = -2/4

m = -1/2

The slope of the dashed line is -1/2. The y intercept is 3. So we go from y = mx+b to y = (-1/2)x+3 to represent the equation of the dashed line. This is the same as writing \(y = -\frac{1}{2}x+3\)

We shade below the dashed line to represent the inequality \(y < -\frac{1}{2}x+3\). Points in the shaded region are solutions to the inequality. One example point is (0,0).

Note that we don't have "or equal to" as part of the inequality sign because we are not including points on the boundary. A solid line, rather than a dashed line, would include points on the boundary.

Answer:

b

Step-by-step explanation:

B.................

Answer:

1.0

Step-by-step explanation:

If you have any questions feel free to ask in the comments

Answer: 1.0

Step-by-step explanation:

Given:  "0.995 inches" ; round to the nearest TENTH of an inch.

(which means; round to the nearest "first decimal point" ; and to include the actual first decimal point (and that decimal point only, the "tenths place").

We are given the number:  "0.955" .  This is given to the nearest THOUSANDS.  

We examine the "tenths place":  "0.9" .  So we know our choices are:

"0.9" (round down to the nearest tenths place); or, "1.0" (round up to the nearest tenths place).  

           →  We examine the number: "0.955" ; and look to the next value, the "hundredths place".  

           → If that digit is 5 or greater (i.e. 5 to 9), we "round up" ; and the correct answer is:  "1.0" .  If that number is "4" or less (i.e. 0 to 4), we round down; and the correct answer is:  "0.9".

________________________________________

In the case of our give value:  "0.955" .  The digit to the right of "9" is "5" ; so, as previously mentioned, we "round up" ;  to:  "1.0".

Do not forget to include the units.

______________________________________________________

The answer is:  1.0 inches.

_________________________________________________

The quantity 2v + 3w is equal to -39i - 11j.

Given the vectors v = 3i - 8j and w = -21 + 3j, we can calculate the quantity 2v + 3w by multiplying each vector by its corresponding scalar and then adding the results.

2v = 2(3i - 8j) = 6i - 16j

3w = 3(-21 + 3j) = -63 + 9j

Adding these two results together, we have:

2v + 3w = (6i - 16j) + (-63 + 9j) = 6i - 63 - 16j + 9j = (6i - 16j + 9j) - 63 = 6i - 7j - 63

Therefore, the quantity 2v + 3w simplifies to -39i - 11j.

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Answer:

d

By the alternate interior angles theorem,

By the reflexive property, AB is congruent to itself.

Thus, the triangles will be congruent by ASA.

So, the slope is -3/5, and the y axis is unidentified.

A point is located at (6,-5). We will use this point.

In order to get the y-axis, we will use 5 from the slope because the denominator allows us to move left and right.

We will also use 6 from the point to give us a dot in the x-coordinate.

We will then divide 5 from the 6 to give us how much we have to go up or down

6/5

We will then use the -3 in the slope.

We will times -3 to the 6/5 in order to know how much we have go up or down.

-18/5 + 5 (from the point)((and since we are moving back, we will add a negative) (My problem))= 1 2/5 (y-intercept)

y = -3/5x + 1 2/5

The y = 13, we will plug it in the equation.

13 = -3/5x + 1 2/5 (subtract 1 2/5 on both sides)

11 3/5 = -3/5x (times 5 on both sides)

-3x = 58 (divide -3 on both sides)

x = -58/3

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{The\ slope\ of\ a\ line\ passing\ through\ the\ points\ (x_1,y_1)\ and\ (y_2,y_1)\ is\ given\ by:}\\\mathrm{Slope(m)=\frac{y_2-y_1}{x_2-x_1}}\\\\\mathrm{According\ to\ the\ question,}\\\mathrm{(x_1,y_1)=(0,-2)}\\\mathrm{(x_2,y_2)=(-2,-8)}\)

\(\mathrm{Therefore\ the\ slope=\frac{-8-(-2)}{-2-0}=\frac{-8+2}{-2}=3}\)

Answer:

1 foot 8 inches

Step-by-step explanation:

Answer:

262.5 messages per month

Step-by-step explanation:

Cost of plan = $34.99

Cost per message = $0.16

Maximum bill = $42

Maximum # of messages = $42/$0.16 = 262.5

Answer:

  2mn

Step-by-step explanation:

The expanded form of the square can be found using the distributive property.

__

  (m -n)² = (m -n)(m -n) = m(m -n) -n(m -n) . . . use the distributive property

  = m² -mn -nm +n² . . . . use it again

  = m² -2mn +n² . . . . . . combine like terms

The missing term is 2mn.

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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