see photo below, thank you!!

Answers is 2in

Step-by-step explanation: 6in•6in=36in•2in=72in

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

Work Shown:

A = area of pyramid base = 6*6 = 36 square inches

h = unknown height

V = volume of pyramid

V = 72 .... given info

V = (1/3)*A*h ... pyramid formula

72 = (1/3)*36*h

72 = 12h

12h = 72

h = 72/12

h = 6

The angle of 0.42 radians is swiped out by the car while revolving about the vertex at the center of the circular race track.

For the stated question;

Then,

Ф = radius / arc length

Ф = r/s

Ф = 2.9 /6.9

Ф = 0.42 radians

Thus, angle of 0.42 radians is swiped out by the car while revolving about the vertex at the center of the circular race track.

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The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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Answer:

5.75

Step-by-step explanation:

6x5/8=3 3/4=3.75

8.5-3.75= 4.75

The hairdresser will leave with 4.75 yards of the hair bow.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

Length of total ribbon ⇒

8 and 1 half = 8 + 1/2 = 17/2

Length of ribbon is going to be used ⇒

Length of 1 hair bow = 5/8 yards

So,

For 6 bow = 6(5/8) = 30/8 yards

So,

Remaining ribbon = Total ribbon - Used ribbon

Remaining ribbon = 17/2 - 30/8

Remaining ribbon = 38/8 = 4.75 yards.

Hence "The hairdresser will leave with 4.75 yards of the hair bow".

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A change in a population that is not related strictly to the size of the population can be described as a change in the demographic makeup of the population. This refers to changes in the characteristics of individuals within the population, such as age, gender, education level, and ethnicity.

For example, if a population experiences an influx of young adults, this would represent a change in the demographic makeup of the population, even if the overall size of the population remains the same.

Other factors that can contribute to a change in the population's makeup include migration patterns, changes in birth rates and mortality rates, and shifts in cultural or social norms. These changes can have significant impacts on a population, affecting everything from economic growth to social dynamics. Understanding demographic changes is therefore critical for policymakers and researchers seeking to address issues such as inequality, public health, and urban planning. By analyzing population trends and anticipating future changes, we can better prepare for the challenges and opportunities that lie ahead.

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The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.

However, it is important to note that not all studies need to use random sampling in order to draw meaningful conclusions. In some cases, non-random samples may still provide valuable insights into the topic of interest.

In any case, if the study did use volunteers who self-selected to participate, it is important for the researchers to acknowledge this limitation in their conclusions and to avoid overgeneralizing the findings beyond the sample they studied.

The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.

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he answer is D welcome

Answer:

Finally, if 12n = -6, then n = -0.5

Step-by-step explanation:

If we have the following equation:

12n = -6

We can solve for n, dividing by 12 on both sides of the equation as:

\(\frac{12n}{12}=\frac{-6}{12}\)

Then, taking into account that  \(\frac{12}{12}\) is equal to 1 and \(\frac{-6}{12}\) is equal to -0.5, we can write the equation as:

\(\frac{12n}{12}=\frac{-6}{12}\\1n = -0.5\\n=-0.5\)

Finally, if 12n = -6, then n = -0.5

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer: Option (2)

Step-by-step explanation:

Setting the equations equal to each other,

\(\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x\)

If x=7, then \(y=\frac{7}{3}+2=\frac{13}{3}\)

The description corresponds to an observational study, which involves gathering data and information to draw conclusions without intervening in the process. Correct answer: letter D.

An experiment would involve manipulating the variables to see the effect of the manipulation. In this case, it would involve changing the caffeine consumption and observing the effect on heart arrhythmias.

In order to better understand the relationship between heart arrhythmias and caffeine consumption, researchers need to consider a variety of factors, including the amount of caffeine consumed, the timing of consumption, and any potential underlying medical conditions that could be influencing the results.

Furthermore, researchers need to ensure that the study population is large enough and diverse enough to accurately reflect the general population. Additionally, researchers need to consider potential confounding variables, such as lifestyle factors, medications, and other dietary components that could be influencing the results.

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The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

We have,

3.

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees.

= 25

We add up all the dots above the numbers between 98.5 and 98.7.

We will not include the dots above 98.5 and 98.7.

4.

The dot plot of the sample mean body temperature for 100 different random samples of size 10 from a population with a mean temperature of 98.6 degrees shows that the majority of the sample means are close to 98.6, and there are very few samples means that exceed 98.6, then it would be surprising to obtain a sample mean of 98.8 or greater from a different random sample.

Thus,

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

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Answer:

No

Step-by-step explanation:

No, because s is less then 2. 7 is not less then 2.

‘Hope that helps! :)

Answer:

no

Step-by-step explanation:

s<2

s=7

7>2

Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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The equation showing the relation between shorter and longer skirt is 3s+4t = 140.

Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.

The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.

So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,

So, if there are s short skirts and t long skirts,

So,

The relation will be =

3s + 4t = 140

Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.

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Answer:

The maximum area of one square plot is 144 \(m^2\)

Step-by-step explanation:

Start by looking at what are the greater common factor of both provided dimensions (840 and 396) to find what the numbers are they both can be divided by evenly:

\(840=2^3\,*\,3\,*\.5\,*\,7\\396=2^2\,*\,3^2\,*\,11\)

therefore, both numbers can be divided by \(2^2\,*\,3=12\)

Which then gives:

\(\frac{840}{12} =70\\\frac{396}{12} =33\)

Then, one can divide the longest side (840 m) into 70 sections of 12 meters each, and the shortest side of the piece of land (396 m) into 33 sections of 12 meters each.

Then we can have a total of 33 * 70 = 2310 smaller lots of 12 m by 12 m

That is smaller plots of a total area 144 square meters

Answer:

Coordinates of X is (7/2,9/2)

Coordinates of C is (6,7)

Explanation:

x is the midpint of DB and AC

coordinates of X = ( (5+2)/2 ,(6+3)/2)

= (7/2,9/2)

Coordinates of X is (7/2,9/2)

Let (a,b) be the coordinates of C.

Then,

coordinates of x = ((a+1)/2, (b+2)/2)

(7/2,9/2) = ((a+1)/2, (b+2)/2)

Hence,

7/2=(a+1)/2

7=a+1

a = 6

9/2 =(b+2)/2

9 =b+2

b =7

Coordinates of C is (6,7)

Answer:

the graph is misleading as the score difference between lazaro and the other players seems huge when in reality it is only a few points. This is because the graph goes up in increments of 1 which makes the difference seem larger than what it really is.

Step-by-step explanation:

-2 1/3 -(-5) can be simplified as follows:

-2 1/3 + 5

= -7/3 + 15/3 (converting mixed numbers to improper fractions)

= 8/3

Therefore, the solution is 8/3, which can also be expressed as 2 2/3.

So, the answer is (B) 2 2/3.

It is true that the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.

Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.

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A pyramid is a solid shape with a specified shaped base. The required answer is 8.67 cubic feet.

A pyramid is a solid shape with a specified shaped base. While a square based pyramid is a type of pyramid which has its base to be a square.

Volume of a square based pyramid = \(\frac{1}{3}\) x base area x height

Also, are of a square = length x length

So that,

i. For the first pyramid;

volume =  \(\frac{1}{3}\) x (2 x 2) x 6

            = 8 cubic feet

The volume of the first pyramid is 8 cubic feet.

ii. For the second pyramid, we have;

height = 8 feet

base side = 2.5 feet

So that.

Volume =  \(\frac{1}{3}\) x (2.5 x 2.5) x 8

             = 16.6667

Volume = 16.67 cubic meters

The volume of the second pyramid is 16.67 cubic meters.

Therefore, the volume of the second pyramid is greater than the volume of the first pyramid by;

volume of the second pyramid - volume of the first pyramid = 16.67 - 8.0

                                              = 8.67 cubic feet

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The expression for z in terms of a, b, c, and d is:

z = (a + c)/2 + ((b + d)/2)i

To define the expression z in terms of a, b, c, and d, where z = a + bi and w = c + di, we can use the complex conjugate.

The complex conjugate of z, denoted as z*, is given by taking the conjugate of each term separately:

z* = a - bi

Now, we can define the expression z in terms of z* and w as follows:

z = (z* + w)/2

Substituting the values of z* and w:

z = ((a - bi) + (c + di))/2

Expanding the expression:

z = (a + c + (b + d)i)/2

Therefore, the expression for z in terms of a, b, c, and d is:

z = (a + c)/2 + ((b + d)/2)i

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The standard deviation is:

The confidence interval is 95%

You want to be confident that your estimate is within 10 of the true population mean, then you can use the next formula:

Where ME is the marginal error, z is the z-score (for a confidence interval of 95% is 1.96), s is the standard deviation and n the sample size.

Then, by replacing the values:

Thus, you need a sample size of at least 204 people.

The component of the data that a data analyst is most interested in is sample size.

Given,

To prevent results from being skewed or causing incorrect conclusions, we must identify the data element on which the data analyst should concentrate;

The data analyst;

A data analyst looks at data to uncover useful consumer insights and possible applications for the knowledge. They also tell the management of the business as well as other stakeholders of this information.

Although it is advisable for data analysts to have a foundational knowledge of statistics and mathematics, many of their responsibilities can still be carried out without it. However, knowledge in statistics, linear algebra, and calculus is often required for data analysts.

Here,

A data analyst's primary interest in the data is sample size

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I hope you understand....

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There are 3 different sets of numbers involved here.

A set of six, a set of two and the set of all eight.

Each set has its own mean.

mean= Total/number of numbers

Note that if you know the mean and how many numbers there are, you can find the total.

T=M×N

You can add numbers, you can add totals, but you may not add means together.

So, for all eight numbers: The total is

8×41=328

For two of the numbers: The total is 2×29=58

Therefore the total of the other six numbers is

328−58=270

The mean of the six numbers =270/6=45

The surface temperature is found to be  approximately 11°C.

Given:

Pipe inner diameter, di = 4cm

= 0.04m

Pipe outer diameter, do = 4.6cm

= 0.046m

Thermal conductivity of stainless steel, kss = 15 W/m.K

Thickness of glass wool insulation, L = 3.5cm

= 0.035m

Thermal conductivity of glass wool insulation, kgi = 0.038 W/m.K

Outer emissivity of the insulation, εo = 0.3

Heat transfer coefficient inside the pipe, hi = 80 W/m2.K

Film temperature, Tfilm = 10°C = 283K

Air velocity, V = 2m/s

Air viscosity, μ = 1.426 × 10–5m2/s

Air thermal conductivity, ka = 0.02439 W/m.K

Air Prandtl number, Pr = 0.7336

Outer surface temperature of the insulation is T∞ = 3°C = 276K

The surface temperature of the insulation is given by;

Ts = T∞ + q″Rout/hsq″

= hi (Tsteam – Ts) …(1)

The overall resistance to heat transfer from steam to the surrounding air and surfaces is given by;

Rtot = Ri + Rk + Ro + Rconv + Rrad

Ri = (ln(do/di))/(2πkss)

= (ln(0.046/0.04))/(2 × π × 15)

= 0.0001926 m2.K/W…(2)

Rk = L/(2πkgi)

= 0.035/(2π × 0.038)

= 0.0145 m2.K/W…(3)

Ro = 1/(2πεoσout) [(1/do) – (1/di)]

= [1/(2π × 0.3 × 5.67 × 10–8)][(1/0.046) – (1/0.04)]

= 0.004685 m2.K/W…(4)

Rconv = 1/hs

= 1/hi

= 0.0125 m2.K/W…(5)

Rrad = 1/(εoσout) [(1/do) – (1/di)]

= [1/(0.3 × 5.67 × 10–8)][(1/0.046) – (1/0.04)]

= 0.0028 m2.K/W…(6)

Rtot = Ri + Rk + Ro + Rconv + Rrad

= 0.0001926 + 0.0145 + 0.004685 + 0.0125 + 0.0028

= 0.0346776 m2.K/W…(7)

From equation (1);

q″ = hi (Tsteam – Ts)

q″ = (Tsteam – Ts)/Rtot

(Tsteam – Ts) = q″ Rtot

(Tsteam – Ts) = hi

q″ Rtot TsTsteam = Ts + hi

q″ RtotTsteam = 276 + (80 × π × 0.04 × 0.6)/3600 × (693.7 – 276 + 0.24 × 5.67 × 10–8 × [(693.7)4 – (276)4])

Tsteam = 693.7K

Ts = T∞ + q″Rout/hs

Ts = 276 + (693.7 – 276) × 0.004685/80

Ts = 284.54K

The surface temperature is 284.54 - 273.15 = 11.39 °C.

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Therefore, the level of production that yields the maximum profit is 80 and maximum profit is $5400.

To find the level of production that yields the maximum profit, we need to determine the x-value at which the profit function P(x) reaches its maximum. We can do this by finding the vertex of the quadratic function P(x).

The profit function is given by \(P(x) = 160x - x^2 - 1000.\)

To find the x-value of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic function in the form \(ax^2 + bx + c.\)

In this case, the quadratic function is \(-x^2 + 160x - 1000\), so a = -1 and b = 160.

Substituting the values into the formula, we have:

x = -160 / (2*(-1))

x = -160 / -2

x = 80

To find the maximum profit, we substitute this value of x back into the profit function:

\(P(80) = 160(80) - (80)^2 - 1000\)

P(80) = 12800 - 6400 - 1000

P(80) = 6400 - 1000

P(80) = 5400

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Good for Megan............