How much of a radioactive kind of protactinium will be left after 3 minutes if the half-life is 1 minute and you start with 352 grams?

The function's standard form equation is equivalent to [tex]\frac{-x^2}{4}+1=0[/tex].

A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.

The standard form of a quadratic equation in mathematics is given by;

[tex]ax^2+bx+c=0\\y=f(x)=ax^2+bx+c[/tex]

Next, using the information in the previous table, we would create the following system of equations:

[tex]-3=a(-4)^2+b(-4)+c\\-3=16a-4b+c[/tex].......equation (i)

[tex]0=a(-2)^2+b(-2)+c\\0= 4a-2b+c[/tex]........equation(ii)

[tex]1=a(0)^2+b(0)+c\\1=c[/tex].........equation (iii)

Inputting the value of c into equations 1 and 2 results in:

[tex]-4=16a-4b[/tex]......ewuation(iv)

[tex]-1=4a-2b[/tex]......equation(v)

Equation 5 is multiplied by two and solved concurrently to yield:

[tex]-2=8a\\a=\frac{-2}{8} \\a=\frac{-1}{4}[/tex]

What we have for b's value is:

[tex]-1=4a-2b\\-1=4(\frac{-1}{4})-2b\\ -1=-1-2b\\2b=0\\b=0[/tex]

Inputting the values of a, b, and c into a quadratic equation in standard form:

[tex]ax^2+bx+c=0\\\frac{-1}{4}x^2+(0)x+1=0\\ \frac{-x^2}{4} +1=0[/tex]

When x equals 2, we get:

[tex]\frac{-x^2}{4} +1=0\\\frac{-2^2}{4}+1=0\\ \frac{-4}{4}+1=0\\ -1+1=0[/tex]

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Answer:

googolplex

Step-by-step explanation:

it just is

Answer:

A Googolplex

Step-by-step explanation:

It is written as 10^googol and 10^10^100

Answer:

Step-by-step explanation:

i belive it would be 500 divided by 20m

Answer: -0.7

Step-by-step explanation:

-1.1 - 1.4m + 0.4 = ? - 1.4m

-1.1 + 0.4 = -0.7

-0.7 - 1.4m = -0.7 - 1.4m

Yes, a 4 year old can typically count to 100.

Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.

Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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Answer:

Calculate: 48.78/0.9 = 54.2

Write a situation: Richard has 48.78 ounces of grape juice that he wants to ration out for his friends at his birthday party. Each cup the friends get can hold 0.9 ounces of grape juice.

What does the quotient mean: The quotient, 54.2, means that Richard had given 54.2 ounces of grape juice to all of his friends combined.

The total free throws Amadou attempts, if Amadou misses 2% of the free throws he attempts in a season, he missed 32, is 1600.

As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

Amadou misses 2% of the free throws he attempts in a season, he missed 32,

Calculate the total number of throws as shown below,

2% of x = 32

Here, x is the total number of throws,

0.02 × x = 32

x = 32 / 0.02

x = 1600

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Answer:

x =  - 28/101

Step-by-step explanation:

Answer:

x=-42

Step-by-step explanation:

[tex]-3x-28=98\\(-3x-28)+28=(98)+28\\-3x=126\\\frac{-3x}{-3}=\frac{126}{-3}\\x=-42[/tex]

The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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The simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50 is given as follows:

Sampling is a technique for when a group of elements from a population is taken to represent the entire population.

Hence, for this problem, multiple samples of 50 students are taken, and for each sample, the median is computed and then stored in a list, according to the procedure described at the beginning of the answer.

Then, after the entire procedure runs, we will have a sample of 50 values, which represent the median for each sample. Then the standard deviation is calculated as the square root of the sum of the difference squared between each of these observations and the mean of all these observations, divided by 50, which is the cardinality of the data-set.

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f(x) = sinx is an trigonometric function.

A trigonometric function is a type of mathematical function that is defined in terms of the angles of a right triangle. The most common trigonometric functions are sine, cosine, and tangent. The function f(x) = sinx is a sine function, which is defined as the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. The sine function can be used to calculate the angles of a triangle when the lengths of two sides are known. It is also useful for modeling many real-world phenomena such as the motion of waves and the oscillations of pendulums.

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Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent. otherwise inconsistent

The classification which best describes the system of equations is; Consistent and dependent

A linear or nonlinear system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.

Additionally, the system of equations is dependent because the value of each variable is dependent on the others.

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.

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Therefore , the solution to this problem is yes 8 has multiple which are 16,24,32 etc.

A multiple in mathematics refers to the product produced by multiplying two numbers or variable. In this instance, the number 7 is multiple by 56.

The expression is termed as multiple .Fun Facts is an additional example of multiples. 0 is a multiple of all numbers since it produces zero when multiplied by any other number.

Here,

There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.

There are two consecutive results in this sequence, and there is an 8-digit gap between each subsequent number and the one before it.

The results of multiplying any integer by other natural numbers are known as multiples.

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Answer:

D) 8 kilograms

Step-by-step explanation:

If one science book has a mass of 2 kilograms, then 4 science books would have a mass of 2 x 4 = 8 kilograms.

An inverse relationship in math is a relationship between two quantities where one quantity increases as the other decreases and vice versa.

An example of an inverse relationship is the relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.

The relationship between temperature in degrees Celsius (C) and temperature in degrees Fahrenheit (F) is defined by the following equation:

F = (9/5)C + 32

This equation shows that as the temperature in degrees Celsius increases, the temperature in degrees Fahrenheit decreases. For example, if the temperature in degrees Celsius is 20, the temperature in degrees Fahrenheit is 68. If the temperature in degrees Celsius is 40, the temperature in degrees Fahrenheit is 104.

Therefore, the relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit is an inverse relationship.

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Answer:?=93/14

Step-by-step explanation:

the ? is the variable in this equation so we have to solve for it

1. distributive property ->

5(?+3) = 5?+15

?(6+3) = 9?

so 5?+15+9?=108 -> 14?+15=108

2. then solve,

14? -15 = 108 -15

14?=93

?=93/14

The resulting value of the equation after performing integration is , f(x) = -log(x) + log(1) - log(4).

Integrating on both the sides with respect to x.

⇒  ∫ f''(x)dx= ∫x-2dx

⇒ ∫ f''(x) dx = (x-2 + 1)/(-2 + 1) + C1

⇒ f'(x) = x-1/(-1) + C1

Then again performing integration ,

∫ f'(x) dx = -log(x) + C1 + x + C2

f(x) = -log(x) + C1 + x + C2

Now, since we know that f(1) =0

when x = 1 then  f(1) =0

0 = -log(1) + C1 + C2

it is also given that ,f(4) = 0

0 = -log(4) + 4C1+ C2

We will subtract these two equations in order to get C1 and C2.

0 = -log(1) + log(4) - 3C1

3c1 = -log(1) + log(4)

= log(4/1) {since log(a) - log(b)

= log(a/b)}

C1 = log(4)/3

C1 = log(4)/3 and (2)

0 = -log(1) +(4/3)log(4) + C2

log(1) - (4/3)log(4) = C2

Therefore, the equation becomes

f(x) = -log(x) + [log(4)]/3 + log(1) - (4/3)log(4)

f(x) = -log(x) + log(1) - log(4)

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we will find the length of rectangle when area is divided by the breadth of rectangle.

Some properties are rectangle are stated below:

1. rectangle has four right angles

2. rectangles has four sides and equal opposite sides which are parallel to each other.

3.rectangle has two diagonals which are similar in length.

The bigger side lengths are called length and the smaller sides are called breadth of rectangle.

if area of rectangle is given, we can find length when area is divided by its breadth.

 length = area/breadth

hence, length of rectangle is determined from the value of area and breadth.

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The equation that defines the fines with respect to the number of days overdue is written as: y = 0.1x + 1.

The equation that defines the fines with respect to the number of days overdue can be written as a linear equation that is expressed in slope-intercept form as y = mx + b, where the slope or unit rate is m, while the y-intercept or initial value is b.

Using two points from the chart, (2, 1.20) and (5, 1.50), find the slope or unit rate:

Slope / unit rate (m) = change in y / change in x = (1.50 - 1.20) / (5 - 2)

m = 0.3 / 3

m = 0.1

Find the y-intercept by substituting m = 0.1 and (x, y) = (2, 1.20) into y = mx + b:

1.20 = 0.1(2) + b

1.20 = 0.2 + b

1.20 - 0.2 = b

1 = b

To write the equation, substitute m = 0.1 and b = 1 into y = mx + b:

y = 0.1x + 1

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The correct equation that represents the inequality is f(x)  > √1 - x.

What is the inequality equation?

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

An inequality is a mathematical relationship between two expressions and is represented using one of the following: ≤: "less than or equal to" <: "less than" ≠: "not equal to"

We have given the graph that represents the inequality equation,

and the inequality equations:

f(x)  > √1 - x

f(x)  ≤ √1 - x

f(x)  ≥ √1 - x

f(x)  < √1 - x

Hence, the correct equation that represents the inequality is f(x)  > √1 - x.

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The value of A + B + C based on the information is A. 5.

From the information, we have digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3.

It should be noted that all multiple of 8 have it's digits add up to a multiple of 9. This can be illustrated as:

4 + A + B + C + 2 + 3 + 9 + 0 + 4 + 0

= 22 + A + B + C

This will be equated to 27 which is the nearest multiple of 9

22 + A + B + C = 27

A + B + C = 27 - 22

A + B + C = 5

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Complete question

In this 10 digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3 what is the value of A + B + C?

A 5

B 6

C 7

D 8

If a₁ = 4 and an = -4an-1 +5 then the value of a5 is 72, in the given sequence.

A group of enumerated objects where repetitions are allowed and order is crucial is referred to as a sequence in mathematics. Similar to a set, it has members. The sequence's length is expressed in terms of its number of elements.

Given that, sequence  

[tex]a_1=4, a_n=4 a_{n-1}+5[/tex]

Now

[tex]a_2=4 a_1+5[/tex]

[tex]a_2=4 \times 4+5[/tex]

[tex]a_2=21[/tex]

[tex]a_2=4 \times 4+5[/tex]

[tex]a_2=21[/tex]

And the common difference d = 21 - 4 = 17

Therefore [tex]a_5=a_1+4 d[/tex]

[tex]a_5=4+4 \times 17[/tex]

[tex]a_5=4+68[/tex]

[tex]a_5=72[/tex]

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Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

Answer:

2 feet

Step-by-step explanation:

(60 / 157.5) * 63 inches = 24 inches = 2 feet

The formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]

The half-life is the amount of time required for a quantity (of substance) to reduce to half of its initial value.

The expression is commonly used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.

Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay).

For instance, the medical sciences may refer to the biological half-life of drugs and other substances in the human body.

Time doubles in proportion to life's exponential expansion.

The formula to calculate half-life: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]

Where N(t) is the quantity of the substance remaining, N₀ is the initial quantity of the substance, t is the time elapsed and t₁₎₂ is the half-life of the substance.

Therefore, the formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]

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Answer:

x= 1/50 or 0.02, or x=50^-1

Answer:

[tex]x=\frac{1}{50}[/tex]

Step-by-step explanation:

If you would like to see the steps here they are.

Answer:

1. 7

2. 5/3

3. 2.6

Step-by-step explanation:

The "+" or "-" sign of a number is disregarded in this operation since distance in mathematics is never negative. You can tell what a number's absolute value is by putting it between two vertical bars known as absolute value brackets.

Answer:

1.  7

2.  5/3

3.  2.6

Step-by-step explanation:

The absolute value is the distance between a number and zero

1. We see the distance is 7, so the answer is 7

2. We see the distance as 5/3, so the answer is 5/3

3. We see the distance is 2.6, so the answer is 2.6

The estimated population in 2025 is 356.9

What is estimation ?

In math, estimating can be used to roughly calculate an answer (getting a "rough response") or to verify its accuracy (getting the "proper answer"). Even when estimating large numbers or decimal numbers, you shouldn't need to utilize a calculator or other documented techniques.

Estimation is frequently performed by sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating the number of sweets of a particular size that are contained in a glass jar serves as an illustration of estimation.

There are 125 years from after 1900 to 2025

P = 0.00892t^2 + 1.1149t + 78.4491

P= (0.0089x125x125)+(1.1149x125)+78.4491

 =139.0625+139.3625+78.4491

 =356.87

 =356.9

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