(︶^︶)Brainliest for everyone!!!! ohh wait ????

^Brainliest For Everyone!!!! Ohh Wait ????

Answers

Answer 1

Answer:

\(\frac{81}{256}\)

Step-by-step explanation:

\((\frac{3}{4})^4 \\\rule{150}{0.5}\\\\\text{Note the exponent rule: }( \frac{a}{b}) ^c = \frac{a^c}{b^c} \\\rule{150}{0.5}\\\\\frac{3^4}{4^4}\\\\\rightarrow 3^4 = 81\\\rightarrow 4^4 = 256\\\\\boxed{\frac{81}{256}}\\\\\text{The answer is already in it's simplest form.}\)


Related Questions

1/6.= Please I need

Answers

Answer:

≈ 0.17

Step-by-step explanation:

1/6 ≈ 0.17

a rectangular tank that is 1372 ft3 with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight

Answers

The dimensions of the tank with minimum  weight  is height= 7 and width and length= 14.

The minimum surface area implies that the tank has minimum weight.

Given that the base is square, its width is equal to its length.

Let x= the base width and length of the tank.

Let h = the height .

We are given the volume of the tank that is 1372 ft^3. The formula is given by

V = hx^2

We're given that V = 1,372 ft^3, so

hx^2 = 1,372

h = 1,372 / x^2  ----------(equation 1)

Surface area can be calculated using the below given formula.

A = x^2 + 4xh

Substituting the value of euation 1, h in A, we get,

A = x^2 + 4x(1,372 / x^2)

= x^2 + 5,488 / x

To get the minimum surface area to get the minimum weight, we need to differentiate  A with respect to x and equate it to zero.

dA/dx = 2x - 5,488 / x^2 = 0

2x^3 - 5,488 = 0

x =\(\sqrt[3]{\frac{5,488}{2} }\)

x= 14

We got the value of x, we substitute the value in equation 1, we get the value of h.

h = 1,372 / 14^2

h= 7

So, the dimensions of the tank with minimum weight are width and length is 14 and height is 7.

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in the united states, a survey of 3563 married women found that 1746 of them suffer from allergies. identify the population and the sample.

Answers

The population consists of all married women in the United States, and the sample consists of the 3563 women in the survey.

The population consists of the responses of all women in the United States, and the sample consists of the responses of the 3563 women in the survey.

In this scenario, the population refers to the entire group of women in the United States. The sample, on the other hand, represents a subset of this population, specifically the 3563 women who participated in the survey. The sample is used to make inferences or draw conclusions about the larger population.

When conducting surveys or studies, it is often impractical or impossible to collect data from every individual in the population. Instead, researchers select a representative sample that reflects the characteristics and diversity of the population they are interested in studying. By analyzing the data from the sample, they can gain insights into the population as a whole.

Identifying the population and sample correctly is crucial for accurate analysis and generalization of findings. In this case, the population consists of all women in the United States, and the sample comprises the 3563 women who participated in the survey.

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4. Determine whether the histogram has a normal distribution Pay Rates of Babysitters 12345 789 Dollars per hour a. no b. yes 5. In the United States, a survey of 3563 married women found that 1746 of them suffer from allergies. Identify the population and the sample a. The population consists of the responses of all women in the United States, and the sample consists of the responses of the 3563 women in the survey The population consists of the responses of the 3563 women in the survey sample consists of the responses al married women in the United States The population consists of the responses of all married women in the United States, and the sample consists of the responses of the 1746 women in the survey The population consists of the responses of all married women in the United States, and the sample consists of the responses 3563 women in the survey b. , and the l of C. d.

help on math homework

help on math homework

Answers

Answer:

b can I have

Step-by-step explanation:

PLEASE HELP Which of the following types of data are likely to be normally distributed? Select all that apply

PLEASE HELP Which of the following types of data are likely to be normally distributed? Select all that

Answers

Answer: the correct answer is D and E

Step-by-step explanation:

Let |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°. what is |q – r|? 13.0 14.2 15.5 18.0

Answers

If |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°. then the

|q – r| will be 18.0

To find |q - r|, we need to subtract the complex numbers q and r after which discover the magnitude (or absolute value) of the end result.

First, we want to express q and r in rectangular form, which means that finding their actual and imaginary additives:

For q, we've:

|q| = 5 at an perspective of 45°

Re(q) = |q| cos(45°) = five cos(45°) = 5/√2

Im(q) = |q| sin(45°) = 5 sin(45°) = 5/√2

So q = (5/√2) + (5/√2)i

For r, we have:

|r| = 16 at an angle of 300°

Re(r) = |r| cos(300°) = 16 cos(300°) = sixteen(-√3/2) = -8√three

Im(r) = |r| sin(300°) = 16 sin(300°) = -8

So r = -8√three - 8i

Now we are able to discover q - r by using subtracting the actual and imaginary additives:

q - r = (5/√2) + (5/√2)i - (-8√3 - 8i)

= (5/√2) + 8√3 + (5/√2 + 8)i

To discover |q - r|, we want to take the importance of this complex number:

|q - r| = √[(5/√2 + 8√3)² + (5/√2 + 8)²]

= √[25/2 + 80√3 + 192 + 50/2 + 40 + 64]

= √[125/2 + 80√3 + 256]

= √[625/4 + 320√3 + 1024]

= √[(25/2 + 16√3)²]

= 25/2 + 16√3

≈ 18.0

Hence, |q - r| is about equal to 18.0.

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A mountain is in the shape of a cone whose height is about 3.8 kilometers and whose base radius is about 3 kilometers. Approximate the volume of the mountain in cubic kilometers.
The volume of the mountain is approximately cubic kilometers.
(Round to the nearest whole number as needed.)

Answers

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

What is volume?

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Sorry I didn't know what subject to put this in but Please help I really do need it u don't have to tho
Which fitness test measures the strength and flexibility of the lower back?
A.
Walk/Run test
B.
Curl ups
C.
Sit and Reach
D.
Trunk Lift

Answers

Answer:

Curl ups

Step-by-step explanation:

I'm not 100% sure, but it seems like the most logical answer to me.

Answer:

Trunk Lift

Step-by-step explanation:

I need help with this math problem brainliest for the best answer

I need help with this math problem brainliest for the best answer

Answers

Answer:

It is the first one

Hope this helps!

Answer:

I believe it is 4x+10y=200, x+y=38

Explanation:

find an interval of t-values such that c(t)=(cost,sint) traces the upper half of the unit circle (in the counter-clockwise direction).

Answers

The interval of t-values such that c(t)=(cost,sint) traces the upper half of the unit circle (in the counter-clockwise direction) is  [π/2, 3π/2].

To trace the upper half of the unit circle in the counter-clockwise direction, we need the y-coordinate (sint) of the curve to be positive. Since sin is positive in the first and second quadrants of the unit circle, we need to find the interval of t-values such that cos(t) is within the b [-1, 1] of the x-coordinate in the first and second quadrants. This interval will correspond to the portion of the unit circle in which the curve c(t) lies on the upper half.

The interval of t-values that satisfies this condition is [π/2, 3π/2]. To see why, note that at t = π/2, c(t) = (0, 1), which is the point on the upper half of the unit circle with y-coordinate 1. As t increases from π/2 to 3π/2, the curve c(t) moves counter-clockwise along the upper half of the unit circle until it reaches the point (0, -1) at t = 3π/2. At t > 3π/2, the y-coordinate of c(t) becomes negative and the curve moves to the lower half of the unit circle. Therefore, the interval [π/2, 3π/2] corresponds to the portion of the unit circle in which c(t) lies on the upper half.

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Solve the trigonometric equation for all values -5 sinπ/3x=0

Solve the trigonometric equation for all values -5sin/3x=0

Answers

The solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

What is Trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, tangent, or their inverses. Trigonometric equations arise in a variety of mathematical and scientific contexts, from solving geometric problems involving angles and triangles to modeling periodic phenomena in physics, engineering, and other fields.

Solving a trigonometric equation typically involves finding the values of the unknown variable that satisfy the equation within a certain interval. For example, the equation sin(x) = 0 has infinitely many solutions, but if we restrict the interval to [0, 2π], then the solutions are x = 0, π, 2π, which correspond to the x-intercepts of the sine function in that interval.

Here the equation sin(πx/3) = 0 has solutions whenever πx/3 is an integer multiple of π, since the sine function is zero at these values. Thus, we need to find all integers n such that πx/3 = nπ, or equivalently x = 3n for some integer n.

Since -5 < x < 5, we need to find all integers n such that -5 < 3n < 5. Dividing all sides by 3, we get -5/3 < n < 5/3. The only integers in this range are -1, 0, and 1. Therefore, the solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

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Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5

Answers

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

\(P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}\)

Since, c = 5 so,

\(P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}\)

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³  ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

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which of the following are identities

which of the following are identities

Answers

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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You purchase a computer for $875.00 plus 5% sales tax.
You decide to finance it through the store's 0% program for 12 months. The terms state you pay nothing until the 12 months are over. When you receive the
bill, you forget to pay it and are assessed a late fee of $39.00 plus the interest accrued to that point at 14.25% APR. How much interest will you be charged?

O $130.25
• $130.92
O $136.48
O $124.69

Answers

You will be required to pay $130.92 in interest. So, option 2 is correct.

What is meant by interest?

Simple interest is calculated using the following formula: Simple Interest (SI) is calculated as P R T / 100. P stands for the principal sum, R for the interest rate, and T for the interest period. The total amount due is the sum of the principal plus the simple interest, or P + SI.

This specific percentage represents the loan's interest rate. The cost of borrowing money is called interest, and it is usually expressed as a percentage, such as an annual percentage rate (APR). Interest may be paid to lenders for the use of their money.

You shell out $875.00 for a PC plus 5% sales tax.

Thus, the final price is 875+(0.05875)

= $918.75.

Rate per month: 14.25/12/100

= 0.011875

So, the rate for a year is 12 x 0.011875

=$130.92.

Therefore, you will be required to pay $130.92 in interest.

Hence, option 2 is correct.

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a cylindrical shell is 20 cm long, with inner radius 6 cm and outer radius 7 cm. write inequalities that describe the shell in an appropriate coordinate system. explain how you have positioned the coordinate system with respect to the shell.

Answers

Using the concept of coordinate system, we got position of cylinder as  6≤r≤7 for radius, 0 ≤ Φ ≤ 2π for angle of cylinder and 0 ≤ z ≤ 20 for the height of cylindrical shell.

Since we want to describe a cylindrical shell, a cylindrical coordinate system would be best suited for our purpose as the name suggests.

" A cylindrical coordinate system is actually a three-dimensional coordinate system that specifies the point positions by the distance from a chosen reference axis, the direction from  axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis given. The latter distance is given as  positive or negative number depending on which side of the reference plane faces the point. "

As goochmawn420 suggests, "points in cylindrical coordinates can be represented as ordered tries in {r, Φ, z}. R is the radial distance, Φ is the polar angle, and z is the height above the x-y plane. "

We would construct a coordinate system with its origin at the center of the bottom of the cylinder.

For the radius, it has to satisfy the condition that 6 ≤ r ≤ 7. This is because it has its inner radius is 6 cm and its outer radius is 7 cm, with 1 cm of thickness.

For the angle coordinate, we would have no constraint since it is a full circle: 0 ≤ Φ ≤ 2π. We are essentially stating all the possible angles in a circle.

For the height coordinate, we would have the constraint that this cylindrical shell is no more than 20 cm tall. In other words, 0 ≤ z ≤ 20.

Hence, position of cylinder is in terms of radius = 6≤r≤7,

            position of cylinder in terms of angle =0 ≤ Φ ≤ 2π

     and, position of cylinder in terms of height =0 ≤ z ≤ 20

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One day a store sold 28 sweatshirts. White ones cost $9.95 and yellow ones cost $13.50. In all, $321.20 worth of sweatshirts were sold. How many of each color were sold?

Answers

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Find the formulas for the nth term of each sequences
1. 3, 5, 9, 17, ...
2. 2/5, 3/6, 4/7, 5/8, ...

Answers

Answer:

1.  2^n + 1.

2. (n +1)/(n + 4)

Step-by-step explanation:

1. 3 5 9 17....

3 = 2^1 + 1

5 = 2^2 + 1

9 = 2^3 + 1

17 = 2^4 + 1

Therefore the nth term is

2^n+ 1 .

2. Looking at the fractions we see that:

Numerators are 2, 3, 4 ,5..

and denominators are  5, 6, 7, 8

So the nth term is

(n + 1) / (n + 4)

In a regression study, a 95% confidence interval for β1 was given as: (-5.65, 2.61). What would a test for H0: β1=0 vs Ha: β1 ≠0 conclude? Select one:a. fail to reject the null hypothesis at null=0.05 and all larger nullb. reject the null hypothesis at null=0.05 and all smaller nullc. fail to reject the null hypothesis at null=0.05 and all smaller nulld. reject the null hypothesis at null=0.05 and all larger null

Answers

The correct answer is (a). fail to reject the null hypothesis at null= 0.05 and all larger null.

The null hypothesis (H0) in this case is that β1=0, meaning that there is no relationship between the independent and dependent variables in the regression study.

The alternative hypothesis (Ha) is that β1≠0, meaning that there is a relationship between the independent and dependent variables.

The 95% confidence interval for β1 is (-5.65, 2.61). This means that we are 95% confident that the true value of β1 falls within this range. Since the range includes 0, we cannot reject the null hypothesis that β1=0.

Therefore, we fail to reject the null hypothesis at a significance level of 0.05 (null=0.05) and all larger significance levels.

In other words, there is not enough evidence to suggest that there is a relationship between the independent and dependent variables in the regression study, so we cannot reject the null hypothesis.

Hence, fail to reject the null hypothesis at null=0.05 and all larger null is the correct answer, i.e., option (a)

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Which is the most accurate way to estimate 32% of 14?

A: 1/2 x 15
B: 1/3 x 15
C: 1/3 x 17
D: 1/2 x 17

Answers

Answer:

B: 1/3 × 15

Step-by-step explanation:

1/3 = 33%

Round 14 up to 15.

This will get you the closest answer

A scale drawing of a rectangular park had a scale of 1 cm = 90 m. 7.6 cm 9.1 cm- What is the actual area of the park in meters squared?


please answer this quickly this is due by 8pm ;((​

A scale drawing of a rectangular park had a scale of 1 cm = 90 m. 7.6 cm 9.1 cm- What is the actual area

Answers

Step-by-step explanation:

The drawing has the side dimension of 7.6 cm

  since each cm represents 90 m   the ACTUAL park is

        7.6 x 90 = 684 meters

  similarly, the bottom of the drawing has the dimension 9.1 cm which represents    9.1 x 90 = 819 m

the area of the park is then

Area =  height x width =     684 m x 819 m = 560 196 m^2

OR  in one step:

Area of the actual park is then

(7.6 cm * 90 m / cm )   X  ( 9.1 cm * 90 m/cm ) = 560 196 m^2

Reduce by dominance to a 3 x 3 matrix. P = 0 3 -1 2 3 1 -1 -1 -3 -2 2 3 0 1 2 1 Is this a strictly determined game? How many points can player A (rows) win or lose on average per round?

Answers

Reducing the given matrix by dominance results in a 3 x 3 matrix. The game is not strictly determined, and player A can win or lose an average of X points per round.

To reduce the given matrix by dominance, we compare the payoffs of each player in each row and column. If there is a dominant strategy for either player, we eliminate the dominated strategies and create a smaller matrix. In this case, the matrix reduction results in a 3 x 3 matrix.

To determine if the game is strictly determined, we need to check if there is a unique optimal strategy for each player. If there is, the game is strictly determined; otherwise, it is not. Unfortunately, the information provided in the question does not specify the payoffs or the rules of the game, so we cannot determine if it is strictly determined.

Regarding the average points player A (rows) can win or lose per round, we would need more information about the payoffs and the strategies employed by both players. Without this information, we cannot calculate the exact average points. It would depend on the specific strategies chosen by each player and the probabilities assigned to those strategies.

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Frankie enlarged the size of a rectangle to a height of 20 cm. What is the new width if it was originally 2 cm wide and 4 cm tall

Answers

Answer: 10

Step-by-step explanation:

4 to 20 which is times by 5 so 2 times by 5 is 10

Complete the slope-intercept form of the linear equation that represents the relationship in the table.

Complete the slope-intercept form of the linear equation that represents the relationship in the table.

Answers

The equation of the line that passes through points (-1, -10), and (3, 14) is y = 6x - 4.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have two points shown in the table:

(-1, -10), and (3, 14)

\(\rm (y - 14 )= \dfrac{14+10}{3+1}(x-3)\)

y - 14 = 6(x - 3)

y = 6x - 4

Thus, the equation of the line that passes through points (-1, -10), and (3, 14) is y = 6x - 4.

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Determine whether the series is absolutely convergent, conditionally convergent, or divergent.[infinity] (−1)nnn3 + 5n = 1(-1)^n (n/sqrt n^3+5)absolutely convergentconditionally convergentdivergent

Answers

The given series is conditionally convergent.

We can use the alternating series test to show that the series converges. First, we can rewrite the terms of the series as:

an = (-1)ⁿ * (n/√(n³ + 5))

The terms of the series are decreasing in absolute value and approach zero as n approaches infinity. Also, the series is alternating in sign, so we can apply the alternating series test. Therefore, the series converges.

To determine whether the series is absolutely convergent or conditionally convergent, we need to check the convergence of the series of absolute values:

∑ |an| = ∑ (n/√(n³ + 5))

We can use the limit comparison test to compare this series with the series ∑ (1/√(n)). We have:

lim (n/√(n³ + 5)) / (1/√(n)) = lim (n*√(n)) / √(n³ + 5) = lim 1 / √(1 + 5/n²) = 1

Since this limit is a positive finite number, the series ∑ |an| and the series ∑ (1/√(n)) have the same behavior. The series ∑ (1/√(n)) is a p-series with p=1/2, which is known to be divergent. Therefore, the series ∑ |an| is also divergent. Since the original series is convergent but |an| is divergent, the original series is conditionally convergent.

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convert 336g to m³
\(336g \: to \: m3\)

Answers

The conversion 336g to m³ is impossible because they measure different units

How to convert 336g to m³

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

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

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

336g to m³  cannot be done because of the different quantities they represent

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i need help wit this really bad

i need help wit this really bad

Answers

Yes and answer is c I agree

PLEASE HELP DUE IN 10 MINUTES
The box-and-whisker plot below represents some data set. What percentage of the
data values are between 30 and 55?

PLEASE HELP DUE IN 10 MINUTES The box-and-whisker plot below represents some data set. What percentage

Answers

Answer:

31.25%

Step-by-step explanation:

55- 30 = 25

25/80 x 100 = 125 /4 or 31.25%

I am assuming that the sample size is between 10 and 80.

Cheers

Answer:

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

Practice writing and solving quadratic equations.
Assignment
The product of two consecutive integers is 72. The equation x(x + 1) = 72 represents the situation, where x
represents the smaller integer. Which equation can be factored and solved for the smaller integer?
O2 + x - 72 = 0
O2 + x + 72 = 0
x2 + 2x - 72 = 0
x2 + 2x + 72 = 0

Answers

Answer:

\(\boxed{\sf \ \ \ x^2 + x -72 = 0 \ \ \ }\)

Step-by-step explanation:

Hello,

We need to use the distributive property which means that for a, b and c real numbers a(b+c)=ab+ac

So here we can write

\(x(x+1)=72\\<=> x*x+x*1=72\\<=> x^2 + x -72 = 0\\\)

do not hesitate if you have any question

A radioactive substance has an initial mass of 475 grams and a half-life of 20 days. What equation is used to determine the number of days, x, required for the substance to decay to 63 grams?



Answers

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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The back of Nico’s truck is 7.5 feet long, 4 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 2.5 feet on each side. How many boxes of papers can Nico pack into the back of his truck? Show your work.

Answers

Answer:

Step-by-step explanation: so

l*w*h
7.5ft*4ft*8ft

that would be 240ft^3

Then 2.5^3

would be 15.625^3

So then u would do

240ft^3/15.625ft^3 = 15.36 boxes of paper


So u could fit abt 15 boxes of paper in the back of his truck

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