What is the volume of this cube?

Answer: 5:1

Step-by-step explanation:

25:5

Divide by 5 both sides

5:1

Answer:

A. and C.

Step-by-step explanation:

We don't know the area of the roof or the number of people in the group so they would both be represented by variables in an equation.

The fourth-order Taylor polynomial approximation, e^(1/8) is approximately 2.775

To approximate the value of e^(1/8) using the fourth-order Taylor polynomial for e^9x at x=0, we can expand the function e^9x using its Taylor series centered at x=0 and keep terms up to the fourth order.

The Taylor series expansion for e^9x is given by:

e^9x = 1 + 9x + (9^2/2!) * x^2 + (9^3/3!) * x^3 + (9^4/4!) * x^4 + ...

approximate the value of e^(1/8), so we substitute x = 1/8 into the Taylor series expansion:

e^(1/8) ≈ 1 + 9(1/8) + (9^2/2!) * (1/8)^2 + (9^3/3!) * (1/8)^3 + (9^4/4!) * (1/8)^4

Simplifying this expression will give us the approximation:

e^(1/8) ≈ 1 + 9/8 + (81/2) * (1/64) + (729/6) * (1/512) + (6561/24) * (1/4096)

Calculating this approximation:

e^(1/8) ≈ 1 + 1.125 + 0.6328125 + 0.017578125 + 0.000823974609375

e^(1/8) ≈ 2.7750142097473145

Therefore, using the fourth-order Taylor polynomial approximation, e^(1/8) is approximately 2.775

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The fourth order Taylor polynomial approximation for e^(1/8) is approximately 1.06579.

The fourth order Taylor polynomial for e^9x at x=0 is:

f(x) = 1 + 9x + 81x^2/2 + 729x^3/6 + 6561x^4/24

To approximate e^(1/8), we substitute x=1/72 (since 1/8 = 9(1/72)):

f(1/72) = 1 + 9/8 + 81(1/8)^2/2 + 729(1/8)^3/6 + 6561(1/8)^4/24

f(1/72) = 1.06579

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Using the formula for exponential decay,  after 130 years, the remaining amount of lead-210 will be 83.0 g.

The initial amount of lead-210 is 5000 g and it decays at a rate of 3.15%/yr. To find out how much will remain in 130 years, we need to use the formula for exponential decay:

A = A₀e^(-rt)

Where A is the final amount, A₀ is the initial amount, r is the decay rate, and t is the time in years. Plugging in the given values, we get:

A = 5000e^(-0.0315*130)

A = 5000e^(-4.095)

A = 5000*0.0166

A = 83.0 g

Therefore, of an initial amount of 5000 g of lead-210, 83.0 g will remain in 130 years. (rounded to one decimal place as needed)

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The data being skewed and indicating higher wait times above 7 minutes due to a busy park is the most suitable description based on the given line plot.

The best description of the shape of the data is that it is skewed and might mean that the wait times were higher than 7 minutes because the park was busy.

Here's the explanation:

From the line plot, we can observe that there are 6 dots above 6, 5 dots above 7, 3 dots above 5, and 2 dots above 8.

The distribution is not symmetric, as the data points are not evenly spread around a central value.

The fact that there are more dots above 7 and 8 suggests that the wait times were higher than these values for a significant number of rides. This skewness in the data indicates that there were instances of longer wait times.

Additionally, the presence of dots above 5 and 6 suggests that there were some rides with shorter wait times as well.

However, the higher concentration of dots above 7 and 8 indicates that the park was likely busy, leading to longer wait times.

The option stating that the data is skewed and might mean that the wait times were higher than 7 minutes because the park was busy best aligns with the information provided by the line plot.

It acknowledges the skewness of the data towards higher wait times, suggesting that the park experienced increased demand and longer queues during the fair.

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15 squares will there be when there are 24 triangles to maintain the ratio.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

We have 5 squares and 8 Triangles.

let the number of square be x when there is 24 triangles.

using Proportion

5/8 = x / 24

8x = 120

x = 15

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Answer:

i think it is a and d

Step-by-step explanation:

The mean of plot B is greater than the mean of plot A. (Option A), and The interquartile range of plot B is the same as the interquartile range of plot A. (Option D)

A box plot has 5 data description.

IQR(inter quartile range)  is the dfference between third and first quartile.

Range = Maximum value of the data set - Minimum value of the dataset

For first box plot: (Plot A)

Range = max - min = 10 - 4 = 6

IQR = third quartile - first quartile = 9 - 5 = 4

Due to symmetry, mean = meadian = mode, therefore, mean = median = 7 = mode.

For second box plot: (Plot B)

Range = max - min = 14 - 8 = 6

IQR = third quartile - first quartile = 13 - 9 = 4

Due to symmetry, mean = meadian = mode, therefore, mean = median = 11 = mode.

So, we see that the mean and median of first plot (plot A) is smaller than t he mean and median of plot B.

Thus, Option A. The mean of plot B is greater than the mean of plot A. is correct option.

and Option D. The interquartile range of plot B is the same as the interquartile range of plot A. is correct option

Option B and C are wrong, as range is same for both plot, and the median of both plots aren't same.

Thus, the mean of plot B is greater than the mean of plot A. (Option A), and The interquartile range of plot B is the same as the interquartile range of plot A. (Option D) are the only correct options.

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Answer:

I Believe it means that the interest of 7% of the original number goes up quarterly as in quarter of a year (3 months) If so your answer is 1640

Step-by-step explanation:

Hope this help

Brainiest??

The linear cost function in this case is C(x) = 20x + 1600, where x represents the number of items produced.

The marginal cost represents the increase in cost for producing one additional item. In this case, the marginal cost is given as $20. This means that for each additional item produced, the cost increases by $20.

We are also given that 170 items cost $5500 to produce. We can use this information to find the fixed cost component of the linear cost function.

Let's assume the fixed cost is represented by a constant term, C₀. When x = 170 (number of items), the cost is $5500. Plugging these values into the linear cost function, we have:

C(170) = 20(170) + C₀ = $5500

Simplifying the equation, we get:

3400 + C₀ = $5500

C₀ = $5500 - 3400

C₀ = $2100

Therefore, the linear cost function is C(x) = 20x + 1600. The cost increases by $20 for each additional item produced, and there is a fixed cost of $1600.

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The value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

The value of y can be determined by using the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, we have the points (7, 4) and (3, y), with a slope of 1/4. Plugging in the values, we get (y - 4) / (3 - 7) = 1/4. Simplifying this equation, we have (y - 4) / (-4) = 1/4. Cross-multiplying, we get -4(y - 4) = 1(-4), which simplifies to -4y + 16 = -4. Solving for y, we subtract 16 from both sides, giving us -4y = -20. Dividing by -4, we find y = 5.

To summarize, the value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

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Answer:

-72

Step-by-step explanation:

I googled it.

Answer:

-72

Step-by-step explanation:

You take the 9, multiply by the -8, and boom. You get -72.

And when you multiply two opposite signs together, it equals to a negative number.

Boom bam boom you became a bit smarter

Answer: 3/4

Step-by-step explanation:

First we need to get the formula into slop form (Y = Mx + B) by moving Y to the other side. This can be done by adding 3y to both sides.

4x - 42 = 3y

or

3y = 4x - 42

Now that we have the formula, we need to divide everything by 3 in order to get 1y.

y = 3/4x - 14

In this formula, M is the slope, meaning your final answer is

3/4

Answer:

30

Step-by-step explanation:

just divide 60 by 2

If the distance between Nikki's cousin and Nikki is 60 miles and covered in 2 hours then the speed of the train is 30 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

\(\rm Speed = \dfrac{Distance}{Time}\)

Nikki's cousin lives 60 miles away, so Nikki decided to take the train to visit him. If the trip took 2 hours. Then the speed of the train will be

\(\rm Speed = \dfrac{60}{2}\\\\Speed = 30 \ miles/hour\)

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Answer:

x + y = 9

y = x + 2

Step-by-step explanation:

We need to write a system of equations to represent the given situation . The statements are ,

Statement 1:- The sum of x and y is 9.

Mathematically , we can write it as ,

\(\rm\implies x + y = 9 \)

Statement 2:- The value of y is two more than the value of x.

This simply means that y equals to 2 + x , that is

\(\rm\implies y = x+2\)

Therefore the system of equations will be ,

Also when we will try to solve the equations we will get ,

\(\rm\implies x + y = 9 \)

Put y = x + 2 , we have ,

\(\rm\implies x + x + 2= 9 \)

Add the like terms ,

\(\rm\implies 2x +2 = 9 \)

Transpose 2 to RHS ,

\(\rm\implies 2x = 9 -2 = 7\)

Divide both sides by 2 ,

\(\rm\implies \boxed{\blue{\rm\quad x = 3.5\quad}}\)

Similarly we will get the value of as ,

\(\rm\implies 3.5 + y = 9 \)

Transpose 3.5 to RHS ,

\(\rm\implies y = 9 - 3.5 \)

\(\rm\implies \boxed{\blue{\rm\quad y = 5.5\quad}}\)

Therefore ,

\(\begin{cases} \rm x = 3.5 \\\\\rm y = 5.5 \end{cases}\)

Answer:

1triangle

Step-by-step explanation:

47+60+73=180degree

so the 1triangle have 180 degree

well, the hexagonal pyramid is really just six triangles with a base of 24 and a height of 24 as well, and a hexagonal base with an apothem of 12√3 and sides of 24.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=12\sqrt{3}\\ p=\stackrel{(24)(6)}{144} \end{cases}\implies A=\cfrac{1}{2}(12\sqrt{3})(144) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{six triangles}}{6\left[ \cfrac{1}{2}(\underset{b}{24})(\underset{h}{24}) \right]}~~ + ~~\stackrel{\textit{hexagonal base}}{\cfrac{1}{2}(12\sqrt{3})(144)}}\implies 1728+864\sqrt{3} ~~ \approx ~~ \text{\LARGE 3224}~m^2\)

The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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Out of those who took the exam, 3/5 passed. So, 100 * 3/5 = 60 is the number of students passed the exam. Therefore, the correct answer is: c ) 60.

To solve this problem, we'll follow these steps:

Step 1: Determine the number of nursing students who were required to take the exam.

Since 1/2 of the nursing students were required to take the exam, we calculate: (1/2) * 200 = 100.

Step 2: Determine the number of students who took the exam.

Since all of the students who were required to take the exam actually took it, the number of students who took the exam is also 100.

Step 3: Determine the number of students who passed the exam.

Since 3/5 of those who took the exam passed, we calculate: (3/5) * 100 = 60.

University X required 1/2 of the 200 nursing students to take the exam, which means 200 * 1/2 = 100 students took the exam.

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Answer:

it is positive

Step-by-step explanation:

-289+311=22 which is a positive number

Jhon will take 6 hours to compete the same work

Men and work :

             This question is based on the concept of men and work

given,

John and Jane together can clean the house in 2 hours 24 minutes

                               = 120 + 24

                               = 144 minutes

Let,

          Jane can complete the work alone in x minutes

then,

        Jhon will take (x+120) minutes to complete the same work alone

According to question,

                                    \(\frac{1}{x} +\frac{1}{x+120} = \frac{1}{144}\)

                                     \(\frac{x+120+x}{x(x+120)} =\frac{1}{144}\)

                               144(2x+120) = x(x+120)

                      288x + 17280= \(x^{2}\) + 120x

                         \(x^{2}\) - 168x -17280 = 0

                          (x + 72) (x-240) =0

                             x= -72 and x =240

x can not be negative, so x =240 minute =4 hours

 Jane can complete the work alone in 240minutes = 4 hours

Jhon will take (x+120) minutes to complete the same work

                    x+120

                = 240 + 120

               = 360 minutes = 6 hours

Hence,

           Jhon will take 6 hours to compete the same work

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The normal strain developed in each wire is 0.00578mm

L'AC=√300²+2²+2(300) (2) cos50°=301.734 mm

AC=AB

=(L'AC — LAC) /LAC =( 301.734—300) /300=0.00578mm

Strain is the increase in the length of an object to its original length caused by an external force that affects the object. Strain can also be interpreted as a measure of the dimensional changes that occur due to stress.

A spring has tension.

Mathematically it is written:

Strain = ΔL/L

Where: ΔL = change in length (m)

L = initial length (m)

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Answer:

answer: 4.5

Step-by-step explanation:

2x=3+6

2x=9

x=9/2

x=4.5

Answer:

x= \(\frac{3}{2}\)

Step-by-step explanation:

6-2x=3

-2x=3-6

-2x=-3

x= \(-3/-2\)

x= 3/2 or 1.5

Answer: 3 years

Step-by-step explanation:

usa test prep

Answer:

210-20x=y

Step-by-step explanation:

150 is after 3 weeks of withdrawing 20 so $60

150+60=210 is the beginning amount

210-20x=y

Answer: Approximately 28 km

The more accurate, yet still approximate value, is roughly 27.995735464379

Round that however you need to.

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

Explanation:

As the diagram shows, the uppercase letters A,B,C represent the corner points of the triangle. They also represent the angles. The diagram says that:

The missing angle C is....

A+B+C = 180

C = 180-A-B

C = 180-59-91

C = 30

which we'll use later.

Convention usually has the side lengths be lowercase letters 'a', b, and c. Those lowercase letters are opposite their uppercase counterpart. We'll have side 'a' opposite angle A, then b is opposite B, and c is opposite C. This allows us to quickly label a triangle and find the missing sides and/or angles. The phrasing "solve the triangle" basically means "find all the missing sides and angles". For this problem, we're only concerned with one side.

The diagram says that side c = 14 due to it being opposite angle C.

The goal is to find side b, which is the shorter way of saying "find AC".

-------------------------

From here, we can use the law of sines to find side b

b/sin(B) = c/sin(C)

b/sin(91) = 14/sin(30)

b = sin(91)*14/sin(30)

b = 27.995735464379 which is approximate

b = 28

Side AC is roughly 28 km long.

I rounded to the nearest whole number since the "14 km" is also a whole number. Your teacher may want you to round differently.

Make sure your calculator is in degree mode.

The cube root function is negative on the interval (-∞, 5), so the correct option is b.

Here we have the cube root function:

g(x) = ∛(x - 5)

This is a cube root, and it is negative when the argument is negative. So the function will be negative for the values of x such that:

x - 5 < 0

x < 5

So, we can say that on the interval: (-∞, 5) the function g(x) is negative. Then the correct option is b.

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The professor's efficiency is 75%.

To calculate the professor's efficiency, we need to compare the number of chapters covered with the expected number of chapters that should have been covered.

The expected number of chapters to be covered in a semester is 16.

However, due to the professor dismissing class 30 minutes early every Monday and Friday, the professor was only able to cover 12 chapters.

To determine the professor's efficiency, we can use the formula:

Efficiency = (Actual output / Expected output) * 100%

In this case, the actual output is the number of chapters covered, which is 12, and the expected output is the number of chapters that should have been covered, which is 16.

Efficiency = (12 / 16) * 100%

Calculating this:

Efficiency = 0.75 * 100%

Efficiency = 75%

This means that the professor covered 75% of the expected material during the semester.

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The expression for the number of bacteria after t hours is N(t) = 50e\(^(0.4427t)\) , rounded to four decimal places.

Let N(t) be the number of bacteria after t hours.

Since the culture grows at a rate proportional to its size, we can write:

dN/dt = kN

where k is the proportionality constant.

This is a separable differential equation, which we can solve by separating the variables and integrating:

dN/N = k dt

ln(N) = kt + C

where C is the constant of integration.

To find the value of C, we use the initial condition that the culture initially contains 50 cells:

ln(50) = k(0) + C

C = ln(50)

Substituting C into the previous equation, we get:

ln(N) = kt + ln(50)

Taking the exponential of both sides, we obtain:

N = e\(^(kt + ln(50)) = 50e^(kt)\)

Now we need to find the value of k. We know that after 1.5 hours, the population has increased to 825:

N(1.5) = 825

Substituting this into the previous equation, we get:

825 = 50\(e^(1.5k)\)

Taking the natural logarithm of both sides, we obtain:

ln(825/50) = 1.5k

k = ln(825/50) / 1.5

k ≈ 0.4427

Finally, substituting this value of k into the expression we obtained for N(t), we get:

N(t) = 50e\(^(0.4427t)\)

Therefore, the expression for the number of bacteria after t hours is N(t) = \(50e^(0.4427t)\), rounded to four decimal places.

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