How is 25 to 5 and 10 to 2 equivalent ratios

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Adding 10 to both sides.

So the solution set is the set

Answer: Angle I is congruent to angle L

Step-by-step explanation:

Did da test

To prove ΔGHI and ΔJKL are similar following statements must be true,

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)

"Two or more triangles are similar if and only if the corresponding angle measures same and their corresponding side lengths are in proportion.."

For given example,

ΔGHI is dilated to form new ΔJKL.

Also, angle H is congruent to angle K.

To prove ΔGHI and ΔJKL are similar.

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)

Therefore, to prove ΔGHI and ΔJKL are similar following statements must be true,

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)

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The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

9514 1404 393

Answer:

  476 +598 = 1074

Step-by-step explanation:

In order for the sum to be smallest, the two most-significant digits must be the smallest possible. That is, they must be 4 and 5.

The two least-significant digits must be even. The remaining even digits are 6 and 8. Then the tens digits are the digits left over: 7 and 9.

Possible sums are ...

  476 +598 = 1074

  478 +596 = 1074

  496 +578 = 1074

  498 +576 = 1074

The sum is 1074.

Answer:

eeeee

Step-by-step explanation:

Answer:

Step-by-step explanation:

Break 18 into its prime factors.

√18 = √2 * 3 * 3

Notice that there are two 3s. When you are taking the square root and there a two factors that are the same, you take 1 and put it in front of the root sign. The other one is discarded.  The rule does not apply to the 2 since there is only 1 two.

√18 = 3 √2

So the expression now becomes

3√2 - √2                    Take out the common factor of √2

√2 (3 - 1)                      Notice 1 is left behind.

2√2

Answer:

2√2

Step-by-step explanation:

Answer:

\(8^{-5}\)

Step-by-step explanation:

When both terms share the same base, and you are multiplying, you are really adding the variables. Add:

\(8^{-9} * 8^{4}\\ = 8^{-9 + 4} = 8^{-5}\\\\8^{-5}\)is your answer.

~

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

The proportion in the tail with regards to the z scores will be:

a. z= 1.00

P(z > 1.00) = 1 - P(Z < 1.00)

= 1 - 0.8413

= 0.1587

The tail will be on the right side.

The proportion of the tail will be 0.1587.

b. z = 0.50

P(z > 0.50) = 1 - P(Z < 0.50)

= 1 - 0.6915

= 0.3085

The tail will be on the right side.

The proportion of the tail will be 0.3085

c. z= -1.25

P(z < -1.25)

= 0.1056

The tail will be on the left side.

The proportion of the tail will be 0.1056.

d. z= -0.40

P(z < -0.40)

= 0.3446

The tail will be on the left side.

The proportion of the tail will be 0.3446.

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The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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The quadratic equation is x² - 2x - 24

What is quadratic equation ?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

Given roots of quadratic equation are 6 and -4.

Also given here leading coefficient is 1.

We know that, the formulae for forming quadratic equation when its roots are given is as follows: x² - (α+β)x + αβ

Here α and β are the roots of the quadratic equation.

Let  α = 6 and β = -4

Putting the value of  in the above formulae we get,

x² - (6-4)x - 24

x² - 2x - 24

But remember here 1 is the leading coefficient of the quadratic equation with roots 6 and -4 (given in question),so we have to multiply the equation by 1 to get the final answer.

So, Hence the required quadratic equation is x² - 2x - 24

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Answer:

The probability is 1/9

Step-by-step explanation:

The probability of rolling a 5 the first time is 1/6

The probability of rolling a number greater than 2

Numbers greater than 2 are; 3,4,5,6

So the probability of rolling a number out of this four is 4/6

Hence, the probability of rolling a five for the first time and the probability of rolling a number greater than 2 the second time will be;

1/6 * 4/6 = 4/36 = 1/9

Answer:

Its 31

Step-by-step explanation:

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

So this is the set of all x-values where the function y = 16x - 71 + 3sin(5x) is continuous.

The function y = 16x - 71 + 3sin(5x) is continuous everywhere since it is a sum of continuous functions. The function 16x is a polynomial, which is continuous for all values of x. The function 3sin(5x) is also continuous for all values of x since it is a composition of continuous functions (sin(x) and 5x), and the constant term -71 is also continuous.

Therefore, we do not need to find any specific points of continuity or discontinuity – the function is continuous for all x.

To describe the set of x-values where the function is continuous in interval notation, we can simply write:

(-∞, ∞)

This interval includes all real numbers.

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Answer:

d. no solution

Explanation:

Step 1 - Subtract nine from both sides of the equation

\(|x| + 9 \leqslant 7 \\ |x| + 9 - 9 \leqslant 7 - 9 \\ |x| \leqslant - 2\)

Step 2 - Remove the absolute value

\( |x| \leqslant - 2 \\ 2 \leqslant x \leqslant - 2 \\ 2 \leqslant - 2\)

Therefore, since positive two is not less than or equal to negative two, there is no solution.

Answer:

D. 5

Step-by-step explanation:

From the information given:

The derivatives of functions and functions have a different average rate. The average rate expanded over an interval of two distinct point (a f(a)) and (b f(b)) is represented by the equation:

\(\dfrac{f(b)-f(a)}{b-a}\)

where; the two points are:

(-1 , f( -1) )    &    ( 1,  f(1) )

For f(1); we have:

f(1) = 1 +3(1)³ - 5(1)² + 2(1) - 2

f(1) = 1 + 3 - 5 + 2 -2

f(1) = - 1

For  f( -1); we have:

(-1)⁴ + 3(-1)³ - 5(-1)²+2(-1)-2

= 1 - 3 - 5 -2 - 2

= -11

∴

\(=\dfrac{-1-(-11)}{1 - (-1)}\)

\(=\dfrac{-1+11}{1 +1}\)

\(=\dfrac{10}{2}\)

= 5

Answer:

Option 4 is correct option.

Step-by-step explanation:

We need to find the value for the variable x from the set {3,4,5,6} below will make \(4.5 + 1.2x \geq 10 - x\) true

First we solve the inequality to find values for x

\(4.5 + 1.2x \geq 10 - x\)

Adding x on both sides

\(4.5 + 1.2x+x \geq 10 - x+x\\4.5+2.5x\geq 10\)

Subtracting 4.5 from both sides

\(4.5+2.5x-4.5\geq 10-4.5\\2.5x\geq 5.5\\\)

Divide both sides by 2.5

\(\frac{2.5x}{2.5} \geq \frac{5.5}{2.5}\\x\geq 2.2\)

So, after solving inequality we get x ≥ 2.2

So, all values greater than 2.2 can be considered true. In the set given {3,4,5,6} all values are greater than 2.2 so all values in the set are considered true for \(4.5 + 1.2x \geq 10 - x\)

Option 4 is correct option.

The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.

Let

Number of chickens = x

Number of pigs = y

x + y = 53

2x + 4y = 138

From (1)

x = 53 - y

Substitute x = 53 - y into (2)

2x + 4y = 138

2(53 - y) + 4y = 138

106 - 2y + 4y = 138

- 2y + 4y = 138 - 106

2y = 32

divide both sides by 2

y = 32/2

y = 16

Substitute y = 16 into

x + y = 53

x + 16 = 53

x = 53 - 16

x = 37

Therefore, there are 37 chickens and 16 pigs respectively.

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Answer:

C. 2b^3 + b^2 - 2b - 380

Step-by-step explanation:

Factory A: 2b^3 - 3b^2 + b - 120

Factory B: 4b^2 - 3b - 260

Add the polynomials:

2b^3 - 3b^2 + b - 120 + 4b^2 - 3b - 260 =

Be careful to combine like terms.

= 2b^3 - 3b^2 + 4b^2 + b - 3b - 120 - 260

= 2b^3 + b^2 - 2b - 380

Answer: C. 2b^3 + b^2 - 2b - 380

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Answer:

I believe it is y-5=3(x+7)

Step-by-step explanation:

Point Slope form = y-y1=m(x-x1)

The reason that in the problem above it's x+7 is because 7 is a negative number, so we would do the opposite of subtraction, which is addition.

The series of the transformation will be reflected across the x-axis, translating 9 units to the Right and 2 units down. Then the correct options are A and C.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position. Picture, after translation, refers to the object's ultimate organization and placement.

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

The series of the transformation will be reflected across the x-axis, translating 9 units to the Right and 2 units down. Then the correct options are A and C.

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The complete question is attached below.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Based on the figure on the graph, match the described transformations with the transformed figures.

Reflected across the x-axis

Rotated 180° clockwise

Translated 9 units to the Right and 2 units down

Reflected across the y-axis

The polygon has 21 sides whose interior angle are in Arithmetic Progression (A.P.)

The interior angles of a polygon are in an arithmetic progression (A.P) if the difference between any two consecutive angles is constant. To find the number of sides in a polygon given its smallest angle and the common difference of its interior angles, we can use the formula:

n = (180° - smallest angle) / common difference + 1, where n is the number of sides in the polygon.

In this case, the smallest angle is 100° and the common difference is 4°, so the number of sides can be calculated as follows:

n = (180° - 100°) / 4° + 1 = (80°) / 4° + 1 = 20 + 1 = 21.

Therefore, the polygon has 21 sides. It is important to note that a polygon with 21 sides is called an icosikaihenagon, which is a highly unusual and exotic shape, as most polygons have a smaller number of sides.

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The predecessor of the number 6,573,800 as given in the task content is; 6,537,799.

From the contextual meaning of the word, predecessor, it follows that it means to.find the number right before 6,573,800.

On this note, upon counting of integers, the predecessor of the number 6,573,800 is 6,573,799.

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hm this is weird, i thought i answered the question. or maybe they're two different questions? line graph because i said so. i know im so helpful

Answer:

Rider A 450   Rider B 360

Step-by-step explanation: