A lab technician had 26 grams of a radioactive substance. Ten days later, only 22 grams remained. Find the half-life of the radioactive substance. (Round your answer to one decimal place.)


I don’t understand the steps.

Answer:

3.141592658

Step-by-step explanation:

A function is a block of code that performs a specific task and can be reused throughout a program. In this case, the function `substitute` is designed to replace all occurrences of one element (`x`) in a list (`y`) with another element (`z`).

Here is the definition of the function `substitute` in Python:

```python
def substitute(x, y, z):
 # Create a new list to hold the modified values
 new_list = []

 # Loop through each element in the original list
 for element in y:
   # If the element is equal to x, replace it with z
   if element == x:
     new_list.append(z)
   # Otherwise, keep the original element
   else:
     new_list.append(element)

 # Return the new list
 return new_list
```

Here is an example of how to use the function:

```python
>>> original_list = [1, 2, 3, 4, 1, 2, 3, 4]
>>> print(substitute(1, original_list, 5))
[5, 2, 3, 4, 5, 2, 3, 4]
```

In this example, all occurrences of the number 1 in the original list are replaced with the number 5 in the new list.

Know more about program here:

https://brainly.com/question/26134656

#SPJ11

We are asked to find the proportion of mild cases that were effectively dealt with using treatment A. First we will find the total number of cases that were dealt with using treatment A, that is:

Fr

A form of digital television that works with digital broadcast signals, transmitting digital sound, supporting wide screens, and providing high resolutions is High-Definition Television (HDTV).

HDTV is a type of television broadcasting that utilizes digital signals, allowing for superior picture and sound quality compared to traditional analog television. It supports wide screens, providing an aspect ratio of 16:9, which is ideal for displaying content in widescreen formats. HDTV also offers high resolutions, typically 720p or 1080i/p, resulting in sharper and more detailed images on compatible high-definition displays. With its digital nature, HDTV brings improved audiovisual experiences to viewers, enhancing their overall television-watching experience.

Learn more about ratio here:

https://brainly.com/question/31945112

#SPJ11

The altitude of a triangular neon billboard advertising the local mall is h ≈ 7.61 feet, and the base of a triangular neon billboard advertising the local mall is b = 20.22 feet.

The area of a triangular neon billboard is 51 square feet. The triangle's base is 5 feet longer than twice the length of the altitude. To find the base and altitude of the triangle, the formula for the area of a triangle can be used, which is

A = (1/2)bh, where A is the area, b is the base, and h is the altitude. Now, let h be the length of the altitude of the triangle. Since the base is 5 feet longer than twice the length of the altitude,

it can be expressed as b = 2h + 5. Substituting these values into the formula for the area of a triangle, we get:

51 = (1/2)(2h + 5)(h)

Simplifying this expression:

102 = (2h + 5)(h)

2h² + 5h - 102 = 0

Solving for h using the quadratic formula:

Using the positive solution, h ≈ 7.61 feet.

Now, using the expression for the base in terms of h,

b = 2h + 5, we get:

b = 2(7.61) + 5

≈ 20.22 feet

Therefore, we found the altitude and base of a triangular neon billboard advertising the local mall, given that its area is 51 square feet and its base is 5 feet longer than twice the length of the altitude. We used the formula for the area of a triangle to derive an equation relating to the area, base, and altitude and used the given relationship between the base and altitude to derive a second equation.

Solving for the altitude using the quadratic formula, we obtained h ≈ 7.61 feet. Substituting this value into the expression for the base, we found that the base is approximately 20.22 feet.

To know more about the quadratic formula, visit :

brainly.com/question/22364785

#SPJ11

Nature by numbers" is a concept that explores the relationship between mathematics and nature.

One example of this is the Fibonacci sequence, which can be found in many natural patterns, such as the arrangement of leaves on a stem or the branching of a tree.

Another example is the Golden Ratio, which is a ratio found in many natural forms, such as the spiral patterns in seashells and pinecones. The Golden Ratio is a mathematical concept that is approximately equal to 1.6180339887, and is often represented by the Greek letter phi (φ).

"Nature by numbers" also relates to fractals. Fractals are geometric shapes that can be divided into smaller parts, each of which is a smaller version of the whole. They are found in many natural forms, such as the patterns in mountains, rivers, and coastlines.

In conclusion, "nature by numbers" is a concept that explores the relationship between mathematics and nature.

It is based on the idea that many natural patterns and structures can be described and understood using mathematical concepts and natural numbers. Examples include the Fibonacci sequence, Golden Ratio, and fractals which can be found in many natural forms.

to know more about natural numbers refer here

brainly.com/question/17429689#

#SPJ11

Roberto spent 41 more minutes doing homework than he did reading and making his lunch.

What is the basic algebraic expression?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

First, let's convert all the times to minutes:

Now, we can calculate the difference:

90 - (40 + 9) = 41

Hence, Roberto spent 41 more minutes doing homework than he did reading and making his lunch.

To learn more about algebraic expression, Visit

https://brainly.com/question/4344214

#SPJ1

The change in volume (dv) is equal to 1221.45 cm³ if the radius of the sphere changes from 18 cm to 18.3 cm.

The change in the volume of the sphere can be represented by the following formula;

dV = 4πr²(dr)

Here dV is the change in the volume, r represents the radius and dr represents the change in the radius of the sphere.

As the radius of this sphere changes from 18 cm to 18.3 cm, we first calculate the change in radius by subtraction;

change in radius = 18.3 - 18 = 0.3 cm

Now substituting the values in the equation;

dV = 4π(18²)(0.3)

dV = 4π(324)(0.3)

dV = 4π(97.2)

dV = 1221.45

Therefore, the change in the volume of the sphere is 1221.45 cm³

To learn more about change in volume, click here:

https://brainly.com/question/13128572

#SPJ4

Answer:

11 12 AND 16 BECUSE IT MACSS SETS

Step-by-step explanation:

0.0439 is the mean and standard deviation of the sampling distribution of the sample proportions .

What is standard deviation in math?

Given that,

p = 0.74

1 - p = 1 - 0.74 = 0.26

n = 100

The mean of the sampling distribution of proportion is ,

 μP =    p = 0.74

The standard deviation of the sampling distribution  is ,  

  σp = σ\sqrtp ( 1 - p ) / n

 σp = σ\sqrt (0.74 * 0.26) / 100 = 0.0439

σp = = 0.0439

Learn more about standard deviation

brainly.com/question/13905583

#SPJ4

The sequence of transformations that maps △RST to △R′S′T′ is a translation of 6 units to the right and 2 units down, followed by a reflection across the y-axis, and finally a rotation of 90 degrees counterclockwise about the origin.

What is the sequence of transformation?

In mathematics, a sequence of transformations refers to a series of geometric transformations performed on a shape to create a new shape. These transformations can include translations, rotations, reflections, and dilations.

The sequence of transformations is the order in which the transformations are performed. The order matters because different sequences of transformations can lead to different final shapes.

For example, to transform a triangle into a new position, we might first perform a translation to move the triangle to a new location, then perform a rotation to change its orientation, and finally perform a reflection to flip the triangle across a line. The sequence of transformations in this case is translation-rotation-reflection.

Sequences of transformations are used in geometry to analyze and describe shapes and to solve problems related to symmetry, congruence, and similarity. They are also used in computer graphics and animation to create 2D and 3D shapes that can be moved and transformed on a screen.

To map △RST to △R′S′T′, we need to perform a sequence of transformations that includes translations, rotations, reflections, and/or dilations. Here's one possible sequence of transformations:

Translation: We can translate △RST by 6 units to the right and 2 units down to get a new triangle that has R at (3, -3), S at (5, -3), and T at (2, -7).

Reflection: We can reflect the translated triangle across the y-axis to get a new triangle that has R′ at (-3, -3), S′ at (-5, -3), and T′ at (-2, -7).

Rotation: We can rotate the reflected triangle 90 degrees counterclockwise about the origin to get a new triangle that has R′ at (3, -3), S′ at (3, -1), and T′ at (-1, -4).

Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a translation of 6 units to the right and 2 units down, followed by a reflection across the y-axis, and finally a rotation of 90 degrees counterclockwise about the origin.

To know more about the sequence of transformation visit:

brainly.com/question/15690673

#SPJ1

Answer:

Answer - a) 1:80

               b) 1:80

Step-by-step explanation:

All the ratio should be written in lowest form. these are the answers for both the questions.

Pls Mark Brainliest !!!!!!!!!!!!!!

Answer:

It is unequal because PEMDAS  states that exponents are above multiplication. In this case, it can be simplified to -1 * 7^2, which is -49.

Answer:

its B and E i just did the question and got it right

Answer:

B and D

Step-by-step explanation:

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

To learn more about square visit: https://brainly.com/question/29286039

#SPJ4

The eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.

Eigenvalues and eigenvectors play a fundamental role in linear algebra, particularly in the study of matrices.

The eigenvalues of a matrix are the values λ for which the equation A = λ has nontrivial solutions, where A is the given matrix and is a non-zero vector. The eigenspace associated with an eigenvalue is the set of all eigenvectors corresponding to that eigenvalue.

To find the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1, we need to solve the characteristic equation det(A - λI) = 0, where A is the given matrix, λ is an eigenvalue, and I is the identity matrix.

The characteristic equation in this case is (-2 - λ)(λ² + 1) + (1 - λ)(-1) = 0. Simplifying this equation yields λ³ - 2λ² - 2 = 0. This is a cubic equation, and we can use a calculator or Wolfram Alpha to find its roots, which are λ₁ = -1, λ₂ = 1, and λ₃ = -1.

Once we have the eigenvalues, we can find the corresponding eigenvectors by solving the equation (A - λ) = 0 for each eigenvalue.

For λ₁ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 0]. For λ₂ = 1, solving (A - ) = 0 gives us the eigenvector [1, 1, 1].

Finally, for λ₃ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 2]. These eigenvectors span the eigenspaces E₁, E₂, and E₃, respectively.

In summary, the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.

Learn more about eigenvalues

brainly.com/question/29861415

#SPJ11

Answer:

\({7}^{3} \)

Step-by-step explanation:

simplify numerator to get

\( {7}^{7} \)

simplify denominator to get

\( { ({7}^{2} )}^{2} \)

which simplifies to

\( {7}^{4} \)

now that it's

\( \frac{ {7}^{7} }{ {7}^{4} } \)

the exponents subtract to get our final answer

Answer:

Step-by-step explanation:

(16-9)^7

[(5+2)^2]^2

(16-9)^7

823543

[(5+2)^2]^2

(49)^2

2401

823543/2401 = 343

The equation of the line that is parallel to the line y = -2x + 1 and passing through (-6, -7) will be y = -2x - 13.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The slope of the parallel line will remain the same. Then the equation of the line that is parallel to the line y = -2x + 1 will be given as,

y = -2x + c

The equation passes through (-3, -7), then the value of the variable 'c' is given as,

- 7 = -2(-3) + c

-7 = 6 + c

c = - 13

Then the equation of the line that is parallel to the line y = -2x + 1 and passing through (-6, -7) will be y = -2x - 13.

More about the equation of a parallel line link is given below.

https://brainly.com/question/402319

#SPJ1

Total capacity the tower holds 1.034 x 10^5  gallons of water

One tower holds 8.4 x 10^3 gallons of water

Other tower holds 9.5 x 10^4 gallons of water

The combined water capacity of the two towers in scientific notation is,

Total capacity the tower holds = 9.5 x 10^4 + 8.4 x 10^3

    = 9.5 x 10^4 + 0.84 x 10^4

    = 10.34 x 10^4

    = 1.034 x 10^5

To learn more about Capacity click here:

https://brainly.com/question/2740387

#SPJ4

Answer:

X = 32

Y = 51

Step-by-step explanation:

It is give that triangle MNP is CONGRUENT to triangle TUS .

So, MN = TU , NP = US , MP = TS , Angle M = Angle T , Angle S = Angle P .

Angle S + Angle T + Angle U = 180 - ( Angle sum property of Triangle )

24 + 142 + ( 2x - 50) = 180

= 166 + ( 2x - 50) = 180

= 2x - 50 = 180 - 166

= 2x = 14 + 50

= x = 64/2

= x = 32

Side NP = Side SU

( 2x - y ) = 13

= 2*32 - y = 13 By putting x = 32

= 64 - y = 13

= - y = 13 - 64

= - y = - 51

= y = 51

If any doubt so please ask .

THANK YOU

The correlation that demonstrates the weakest correlation between two variables is option a) +.20.

Among the given options, the correlation that demonstrates the weakest correlation between two variables is option b) -50.

In correlation coefficients, the value ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation or a very weak correlation.

Let's analyze the options provided:

a) +.20:

This indicates a positive correlation, but the value is relatively small (0.20).

It suggests a weak positive relationship between the variables.

b) -50:

This option appears to be a typographical error since the correlation coefficient cannot be negative 50.

Assuming it is meant to be -0.50, this indicates a moderate negative correlation.

c) +.75:

This option represents a strong positive correlation.

With a coefficient of 0.75, it suggests a relatively strong positive relationship between the variables.

d) -76: Similar to option b, this value appears to be a typographical error. A correlation coefficient cannot exceed the range of -1 to +1.

Assuming it is meant to be -0.76, this indicates a strong negative correlation.

Comparing the given options, the weakest correlation is option b) -50, assuming it was intended to be -0.50. A correlation coefficient of -0.50 represents a moderate negative correlation, which is weaker than the other options but still indicates some relationship between the variables.

For similar question on correlation.

https://brainly.com/question/28175782  

#SPJ8

The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

Learn more about statistics here;

https://brainly.com/question/16528376

#SPJ4

When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

Learn more about trigonometric function here

brainly.com/question/25618616

#SPJ4

Answer:

12

Step-by-step explanation:

15% times 80

80x15%

80 times 15 is 1200

Remember, you always divide by 100 to get your sale price

When the medication is considered to be ineffective, the quantity remaining is 0.1 times the initial quantity.

0.1(238) = 238(0.8)⁴t

Solving for t, we get

t = 18.6 hours (rounded to one decimal place)

(a) The initial dose of the medication was 238 milligrams.(b) By what percentage is Q decreasing every 4 hours?Given formula is
Q = 238(0.8)⁴
Differentiating Q with respect to t,
Q'(t)

= -3.072t³ + 19.456t² - 38.912t + 20.48
We can see that the rate of decrease is not constant, so there is no fixed percentage.(c) By what percentage is Q decreasing every 2 hours?As the given function is

Q

= 238(0.8)⁴,

we know that after 4 hours, the quantity remaining will be 0.8 times the original quantity. Therefore, the quantity remaining after 2 hours will be 0.8² times the original quantity.So, the percentage of decrease from 4th hour to 2nd hour is 100(1 - 0.8²)%

= 36%.
(d) Calculate from t

= 2 to t

= 2 + .

What are the units of this number? What does this number tell you?The formula for Q is given by

Q = 238(0.8)⁴.

Taking t

= 2 and t

= 2 + h and simplifying, we get
Q(2)

= 238(0.8)⁸

Q(2 + h)

= 238(0.8)⁴(0.8)⁴
= 238(0.8)⁸
The units of this number are milligrams.This number tells us that there is no change in the quantity of medication between t

= 2 and t

= 2 + h.e) Without further calculation, is the number from the previous part a good estimate of Q(2)?
Yes, it is a good estimate since Q is not changing over this interval.f) Determine Q'(2) to 3 sf by recomputing for shrinking values of h until the rate of change is not At changing to 3 sf.
Q'(2)

= 20.48
(g) The level of medication is considered to be ineffective when there is 10% of the initial medication. At what time does this occur?Let Q be the quantity of the medication remaining after t hours. Then we have
Q

= 238(0.8)⁴t
When the medication is considered to be ineffective, the quantity remaining is 0.1 times the initial quantity.
0.1(238)

= 238(0.8)⁴t
Solving for t, we get
t

= 18.6 hours (rounded to one decimal place)

To know more about medication visit:

https://brainly.com/question/30887193

#SPJ11

Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Therefore, Linda bought 21 yards of ribbon. Hence, Linda bought 94 yards of ribbon.

The number of yards of ribbon Linda bought, we need to calculate the difference between the initial balance on the card and the remaining balance after the purchase.

The initial balance on the card was $20. To find the amount spent on ribbon, we subtract the remaining balance ($17.06) from the initial balance. $20 - $17.06 = $2.94

Now, we need to determine how many yards of ribbon Linda could purchase with $2.94, given that the price of the ribbon is 14 cents per yard.

To find the number of yards, we divide the total amount spent ($2.94) by the price per yard (14 cents): $2.94 ÷ $0.14 = 21

Therefore, Linda bought 21 yards of ribbon.

Hence, Linda bought 94 yards of ribbon.

Learn more about yards

https://brainly.com/question/14516546

#SPJ11

Answer:

7/6

Step-by-step explanation:

In order to find slope when you have two ordered pairs, you use this equation: (y2-y1)/(x2-x1)

In this case, when you plug them in, you get (49-7)/(42-6), which is 42/36, which is 7/6.

Hope this helped :)