V = 1/3Bh
Solve
for b

Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

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Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

Answer:760

Step-by-step explanation:

Answer:

760

Step-by-step explanation:

Answer:

284°

Step-by-step explanation:

Given:

A circle

F - centre

∠YFM, ∠MFP, ∠PFD, ∠DFG, ∠GFY are central angles (the central angles are equal to the arc on which they rest)

∠YFG = ∠MFP = 76° (cross angles)

A whole circle forms an angle of 360°

arc PGM = 360° - arc PM

arc PGM = 360° - 76° = 284°

Answer:

50°

Step-by-step explanation:

We are to find m ∠2

And lines A and B are parallel

m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°

Hence,

m ∠2 = 50°

Therefore, m ∠2 = 50°

Taking a difference, we can see that the trip to city C is 482.6 mi longer.

Here we know that the distance from city a to city b is 256.8 miles, and the distance from city a to city c is 739.4 miles

To find how much farther is the trip to city c than the trip to city b, we just need to take the difference between the two distances above.

That means that we need to take the distance to city c and subtract the distance to city b.

We will get:

739.4 mi -  256.8 mi = 482.6 mi

The trip to city C is 482.6 mi more than the trip to city B.

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Answer:

-23x+1

Step-by-step explanation:

91-14x - (9x+90)

91-14x-9x-90

-23x+1

Answer:

1-23x

Step-by-step explanation:

7(13-2x)-9(x+10)

7(13)+7(-2x)-9(x)-9(10)

91-14x-9x-90

Combine like terms

91-90 = 1

-14x-9x = -23x

1-23x

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

10.1 Sv-St

Step-by-step explanation:

Answer:

The relative frequency for the range 21-25 is 0.13 approximately.

Step-by-step explanation:

plz do tell me if i need to explaine

The frequency table is made and the Relative frequency for the range 11 – 15 is 0.2 .

Frequency is the number of times any event is occurring .

The data set is given

The frequency table under the given interval is

Interval                       Frequency

1 - 5                                     3

6 - 10                                   1

11 - 15                                   4  

16 -20                                  5  

21 - 25                                 2

Relative frequency is given by = Subgroup Frequency /  (  Total Frequency)

Relative frequency for the range 11 – 15  = 4 / 20 = 1/5 = 0.2

Therefore the frequency table is made and the Relative frequency for the range 11 – 15 is 0.2 .

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Answer:

11

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

2x+6+2x−6

=2x+6+2x+−6

Combine Like Terms:

=2x+6+2x+−6

=(2x+2x)+(6+−6)

=4x

(i) cosФ = 4/7 and sinФ is negative → It lies in the 4th quadrant 304.8° and the suitable graph is not provided here.

(ii) secФ = -13/5 and tanФ is negative  → It lies in the IInd quadrant 112.6° and the suitable graph is J.

(iii) sinФ = 7/10 and cotФ is positive  → It lies in Ist quadrant =44.4° and the suitable graph is I.

(iv) tan0 = 3/4 and sin0 is negative  → It lies in the IIIrd quadrant 216.9° and the suitable graph is not provided here.

What is quadrant?

(i) cosФ = 4/7 and sinФ is negative

Ф=cos^(-1)(4/7)= 55.2°

It lies in 4th quadrant (360-55.2)°=304.8°

A suitable graph is not provided here.

(ii) secФ = -13/5 and tanФ is negative.

Ф=sec^(-1)(-13/5)=67.4°

It lies in IInd quadrant (180-67.4°)=112.6°

A suitable graph is J.

(iii) sinФ = 7/10 and cotФ is positive.

Ф=sin^(-1)(7/10)=44.4°

It lies in Ist quadrant =44.4°

A suitable graph is I.

(iv) tan0 = 3/4 and sin0 is negative.

Ф=tan^(-1)(3/4)=36.9°

It lies in IIIrd quadrant (180+36.9)=216.9°

A suitable graph is not provided here.

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Answer:

this is very easy its 36

Step-by-step explanation:

all you need to do is to subtract 40 from 4

Answer:

4.236

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

There can be 10 total digits in the tens place: 0,1,2,3,4,5,6,7,8,9

if the middle is 0 the probability is 10%

The probability that the middle digit is 0 is 1/10.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

A company sells bicycle locks with a combination made of 3 numbers.

Each number can be any digit from 0 to 9 and the digits may be repeated.

One of these locks is chosen at random.

There can be 10 total digits in the tens place: 0,1,2,3,4,5,6,7,8,9.

The probability that the middle digit is 0 is given by;

\(\rm Probability=\dfrac{Probability \ of \ middle \ digit \ 0}{Total \ number \ of \ digits}\\\\\ Probability=\dfrac{1}{10}\)

Hence, the probability that the middle digit is 0 is 1/10.

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The summation goes from 0 to 4, as there are 5 terms in total.

a. The sequence consists of odd prime numbers, and the last term is 101. Since there is no general formula for prime numbers, we can denote this summation as the sum of the first n prime numbers,

where P(i) represents the ith prime number:
\(∑_(i=1)^(n) P(i), where P(n) = 101\)
b. This summation consists of terms in the form of 1 divided by powers of 2. The series appears to be a geometric series with a common ratio of 1/2. To express this in sigma notation:
\(∑_(i=0)^(k) (1/2)^i\)
Here, you'll need to find the value of k such that the last term is 1/2^k.
c. The given summation is a series with terms consisting of products of powers of a and b. This can be represented using sigma notation as follows:
\(∑_(i=0)^(4) a^(5-i) * b^i\)
In this series, the exponent of a decreases by 1 in each term, while the exponent of b increases by 1. The summation goes from 0 to 4, as there are 5 terms in total.
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On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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A solution of a system of linear equations is (0,−4).

What is Systems of Linear Equations?

A direct equation is an equation in two variables, and when it's graphed, a straight line is formed. The line is created by the combination of corresponding values that satisfy the equation. utmost generally, direct equations use the variables x and y so the corresponding values can be colluded as (x,y) pairs on the  co-ordinate plane .

Main body:

A system of direct equations is a group of two or further direct equations. The result to any system of direct equations is the point where the lines cross on a graph, still, because lines can be resemblant or coinciding, it's possible for a system to have no result( parallel) or infinitely numerous results( coinciding).

y = 3x−4

y=−x/2−4

now solve:

3x=−3/2x

1/2x=0

x=0

If x=0

, solve for the corresponding y-coordinate:

y=3(0)−4

y=−4

So, the solution is (0,−4).

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So, the manager should get all the required water from the local reservoir, resulting in a minimum daily water cost of $5510.

To minimize the daily water costs for the city, the water-supply manager needs to determine how much water to get from each source while meeting the minimum requirement of 19 million gallons per day. Let's denote the amount of water drawn from the local reservoir as R (in million gallons) and the amount of water drawn from the pipeline as P (in million gallons).

Given the constraints:

R ≤ 20 (maximum daily yield of the reservoir)

P ≥ 7 (minimum daily yield of the pipeline)

R + P ≥ 19 (minimum requirement of 19 million gallons)

We need to find the values of R and P that satisfy these constraints while minimizing the daily water costs.

Let's calculate the costs for each source:

Cost of 1 million gallons of reservoir water = $290

Cost of 1 million gallons of pipeline water = $365

The total daily cost can be expressed as:

Total Cost = (Cost of reservoir water per million gallons) * R + (Cost of pipeline water per million gallons) * P

To minimize the total cost, we can use linear programming techniques or analyze the possible combinations. In this case, since the costs per million gallons are provided, we can directly compare the costs and evaluate the options.

Let's consider a few scenarios:

If all the water (19 million gallons) is drawn from the reservoir:

Total Cost = (Cost of reservoir water per million gallons) * 19 = $290 * 19

If all the water (19 million gallons) is drawn from the pipeline:

Total Cost = (Cost of pipeline water per million gallons) * 19 = $365 * 19

If some water is drawn from the reservoir and the remaining from the pipeline:  Since the minimum requirement is 19 million gallons, the pipeline must supply at least 19 - 20 = -1 million gallons, which is not possible. Thus, this scenario is not valid. Therefore, to minimize the daily water costs, the manager should draw all 19 million gallons of water from the local reservoir. The minimum daily water cost would be:

Minimum Daily Water Cost = (Cost of reservoir water per million gallons) * 19 = $290 * 19 = $5510.

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Answer:

Ok, the speed is 18 mph.

The angle is 293°, and we usually measure the angles from the x-axis, so we can write our coordinates of velocity as:

Vx = 18mph*cos(293°) = 7mph.

Vy = 18mph*sin(293°) = -16.6mph.

Then we can write this as a vector (Vx, Vy)

Velocity = (7mph, -16.6mph)

Now, for the position, we can integrate over time, and using that the position (0,  0) is the starting point of the ship, we have that the position vector is:

P(t) = (7mph*t, -16,6mph*t)

Where t is the number of hours after the ship leaved the port.

If t = 0 is 0:00pm, then at 3:30pm we have t = 3 hours and 30 minutes

one hour has 60 minutes, then 30 minutes is equivalent to 0.5 hours.

Then 3:30pm we have t = 3.5 houes.

Now we replace this in the position vector and the location of the ship at 3:30pm is:

P(3.5h) = (7mph*3.5h, -16.6mph*3.5h) = (24.5 mi, -58.1 mi)

Where the first component describes the displacement in the x-axis, and the second component describes the displacement in the y-axis.

Answer: 1) -58  2) 24.6  3) 24.6  4) north  5) 58  6) west

Step-by-step explanation: I took the test.

For each pair of fractions, following fraction is larger

a) 5/6 > 5/7

b) 2/9 < 5/9

c) 3/4 < 9/10

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given,

Fraction:

a) 5/6 or 5/7

Taking LCM,

LCM = 42

5/6 × 7/7

35/42

5/7 × 6/6

30/42

5/6 > 5/7

b) 2/9 or 5/9

They have same denominator,

So,

2/9 < 5/9

c) 3/4 or 9/10

Taking LCM:

LCM = 20

3/4 ×5/5

15/20

9/10 × 2

18/20

3/4 < 9/10

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In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.

Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.

The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.

The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.

By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.

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Given:

One variety of gift wrappers sells for 50 cents a sheet the other for 25 cents a sheet.

In dollars,

One variety of gift wrappers sells for 0.5 dollars a sheet the other for 0.25 dollars a sheet.

The assortment will cost $7.

Let x be the number of 50 cents sheets.

Let y be the number of 25 cents sheets.

It is also given that,

The number of 50 cents sheets is 3 times the number of 25 cent sheets.

x=3y ........ (1)

0.5x+0.25y=7 ....... (2)

Substitute (1) in (2) we get,

Hence, x=3(4)

x=12

So, the number 50 cents sheets are 12 and the number of 25 cents sheet is 4.

Marta leyó 1,625 veces la cantidad de páginas leída por su hermano.

En esta pregunta debemos determinar la razón (\(r\)) de la cantidad de páginas leída por Marta (\(x\)) a la cantidad de páginas leída por su hermano (\(y\)). Es decir,

\(r = \frac{x}{y}\) (1)

Si sabemos que \(x = 52\) y \(y = 32\), entonces la razón definida al principio de esta respuesta es:

\(r = \frac{52}{32}\)

\(r = 1,625\)

Marta leyó 1,625 veces la cantidad de páginas leída por su hermano.

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Answer:

720 degrees

Step-by-step explanation:

total angles =(180 x number of sides)-360=(180 x 6)-360=720 degrees

hexagon/sox-sided irregular polygon

sum of interior angles=720°

Answer:

Hi, there the answer is 8.29308689E11

Step-by-step explanation:

The lateral surface area of the cylinder will be 32.34 square cm.

Given that:

Radius, r = 3 cm

Height, h = 10.5 cm

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πr (h + r) square units

The lateral surface area is calculated as,

SA = 2 x 3.14 x 3 x (10.5 + 3)

SA = 18.84 x 13.5

SA = 32.34 square cm

The lateral surface area of the cylinder will be 32.34 square cm.

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FALSE, it is not the mean but the median of a distribution which is defined as the data value where 50% of the data is above and 50% is below.

The median denotes the point at which 50% of data values are higher and 50% are lower. As a result, it is the data's midpoint. In a symmetrical distribution, the median is always the midpoint, resulting in a mirror image with the median in the center.

The median is the number in the middle of a sorted, ascending or descending list of numbers, and it might be more descriptive of the data set than the average.

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