A group of 8 people on a trek have
enough water to last 9 days.
If 4 more people join the trek, how long
will the water supply last the whole
group?

The coordinate system with x-coordinates between -180 and 180 is likely to be the geographic coordinate system, specifically longitude values. This system represents positions on the Earth's surface using two angles: longitude (x-coordinates) and latitude (y-coordinates).

Longitude values range from -180 degrees (180 degrees West) to 180 degrees (180 degrees East) along the Earth's equator. Latitude values, on the other hand, range from -90 degrees (90 degrees South) to 90 degrees (90 degrees North). The origin (0, 0) of this coordinate system is the intersection of the Prime Meridian (Greenwich Meridian) and the Equator.

The units for these coordinates are typically expressed in decimal degrees (DD). These values can be converted into other units such as degrees-minutes-seconds (DMS) or radians, depending on the application or preference. When working with geographic coordinate systems, it is essential to consider the Earth's curvature and potential distortions when calculating distances or areas.

In summary, if a data set has x-coordinates between -180 and 180, the coordinate system is most likely the geographic coordinate system, representing longitude values. The coordinates are typically expressed in decimal degrees, and their positions relate to the Earth's surface.

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The optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

To solve this linear programming problem using the Simplex method, we first need to convert it into standard form by introducing slack variables.

Our problem can be rewritten as follows:

Minimize w = 9x1 + 6x2

Subject to:

x1 + 2x2 + x3 = 5

2x1 + 2x2 + x4 = 8

x1 + 2x2 + 2x3 = 6

where x1, x2, x3, and x4 are all non-negative variables.

Next, we set up the initial simplex tableau:

Basic Variables x1 x2 x3 x4 RHS

x3 1 2 1 0 5

x4 2 2 0 1 8

x5 1 2 2 0 6

z -9 -6 0 0 0

The last row represents the coefficients of the objective function. The negative values in the z-row indicate that we are minimizing the objective function.

To find the pivot column, we look for the most negative coefficient in the z-row. In this case, the most negative coefficient is -9, which corresponds to x1. Therefore, x1 is our entering variable.

To find the pivot row, we calculate the ratios of the RHS values to the coefficients of the entering variable in each row. The smallest positive ratio corresponds to the pivot row. In this case, the ratios are:

Row 1: 5/1 = 5

Row 2: 8/2 = 4

Row 3: 6/1 = 6

The smallest positive ratio is 4, which corresponds to row 2. Therefore, x4 is our exiting variable.

To perform the pivot operation, we divide row 2 by 2 to make the coefficient of x1 equal to 1:

Basic Variables x1 x2 x3 x4 RHS

x3 0 1 1 -1 1

x1 1 1 0 1/2 4

x5 0 1 2 -1 2

z 0 -3 9 9/2 -18

We repeat the process until all coefficients in the z-row are non-negative. In this case, we can stop here because all coefficients in the z-row are non-negative.

Therefore, the optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

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Answer: i eat fooood bro

Step-by-step explanation:

The null hypothesis is that the population mean of female "like" ratings of male dates is equal to 6.00, and the alternative hypothesis is that it is less than 6.00. A one-tailed t-test will be used to test the hypothesis.

H0: μ = 6.00

Ha: μ < 6.00

The test statistic is calculated using the formula:

t = (x - μ) / (s / sqrt(n))

Substituting the given values, we get:

t = (5.88 - 6.00) / (2.06 / sqrt(195)) = -1.64

The degrees of freedom are n-1 = 194. Using a t-distribution table, the P-value is found to be 0.051.

Since the P-value (0.051) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to suggest that the population mean of female "like" ratings of male dates is less than 6.00 at a significance level of 0.05.

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Answer:

the third : x + x + x + 2 = 10

Step-by-step explanation:

x = the length of the first 2 pieces.

the third piece will be x+2 ft long.

so, the total length of the original board is the sum of all 3 pieces and must be all in all 10 ft.

10 = x + x + (x + 2) = x + x + x + 2

so, it is the third answer option.

The simplified expression of 4/x is at most 3 is 3x ≥ 4

The statement is given as:

4/x is at most 3

Express as inequality: (at most means ≤)

So, we have:

4/x ≤ 3

Multiply both sides by x

4 ≤ 3x

Rewrite as:

3x ≥ 4

See attachment for the graph of the inequality

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Answer:

1. 2. 4. all have negative answers

Step-by-step explanation:

2 + 2(-3)(7)= -40

-2(27 ÷ 9)+4= -2

(4 - 10) - ( 8 ÷ ( -2))= -2

Hope this helped!

y(x)  = \(\frac{1}{3-x^2}\) is the solution of the given differential equation.

A differential equation is an equation that relates a function and its derivatives; it describes how a quantity changes with respect to another. and its solution is a function that satisfies the equation for all values of the independent variable

y'=2x\(y^2\)

where y' is dy/dx

so dy/dx = 2x\(y^2\)

=> dy/ \(y^2\) =2xdx

integrating on both side we get:

-1/y = \(x^2\) +c   --- (i)

where c is a constant

given that y(1) =2

putting the value of y = 1/2 and x=1 in equation (i) we get

so  -2 = 1+c

=>  c= -3

y(x) = 1/(3-\(x^2\))  is the required solution of the differential equation.

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Answer:

y = \(-\frac{8}{3} x +5\frac{16}{3}\)

Step-by-step explanation:

You use rise over run:

(-3 - 5)/(5 - 2) = 8/3

then plug in one of the coordinates to fine the y-intercept

Investment B provides a higher value in comparison to Investment A.

Given that Investment A: A monthly investment of $200 starting now and lasting for 40 years at a 9% annual interest rate, compounded monthly.

Investment B: A monthly investment of $400 starting in 20 years and lasting for 20 years at a 9% annual interest rate, compounded monthly.

To Find Investment A (The present value of annuity due)

PVAD=PMT*(((1-(1+r)^-n)/r)*(1+r))

Here, PMT=$200,

r=0.75%

= (9/12)% monthly interest rate,

n=40*12

months=480P

VAD=$200*(((1-(1+0.75%)^-480)/(0.75%))*(1+0.75%))

= $67,933.50

Investment B (The present value of annuity)

PVA= PMT*(((1-(1+r)^-n)/r))

Here, PMT=$400,

r=0.75%

= (9/12)% monthly interest rate,

n=20*12

=240 months

PVA=$400*(((1-(1+0.75%)^-240)/(0.75%)))

= $69,354.54

∴ Investment B provides a higher value in comparison to Investment A.

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Answer:

|x| = 25

Step-by-step explanation:

Original Equation:

|x - 4| = 21

Just add 4 to both sides

|x| = 25

Hope this helped :)

Answer:

the answer is 25 or -17

Answer:

q = 42

Step-by-step explanation:

\(\frac{q}{7}=6\\\\\frac{q}{7}*7=6*7\\\\ \boxed{q=42}\)

Hope this helps.

Answer:

$1281.39

Step-by-step explanation:

use formula given

Answer:

To solve this problem, we need to calculate the change in temperature between noon and 3:30 p.m. and then divide that by the number of hours between noon and 3:30 p.m.

Let's say the temperature at noon was 70 degrees F and the temperature at 3:30 p.m. was 75 degrees F.

The change in temperature between noon and 3:30 p.m. is 75 - 70 = 5 degrees F.

The number of hours between noon and 3:30 p.m. is 3.5 hours.

Therefore, the rate of change in temperature between noon and 3:30 p.m. is 5 degrees F / 3.5 hours = 1.43 degrees F per hour.

Answer:

y = x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 3) and (x₂, y₂ ) = (4, 1)

m = \(\frac{1-3}{4-6}\) = \(\frac{-2}{-2}\) = 1 , then

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 1 )

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = x - 3 ← equation of line

Answer:

£53.10

Step-by-step explanation:

find 10% of £59=£5.90

then do £59-£5.90=£53.10

Answer:

(11/2)² also known as 30.25

Using the (b/2)² formula, we can base this problem off of that method to solve the equation.

Step-by-step explanation:

(x - 11/2)² - 177/4 = 0 ⇒ Completing the square

Answer:

30.25

Step-by-step explanation:

Solving :

Answer:

this is what the graph will look like but i hope this helps

Step-by-step explanation:

have a safe and happy holiday

Yes, 74 is an outlier in the dataset

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

52, 55, 50, 49, 47, 53, 74

In statistics, an outlier is a value that is far removed from other values in a dataset.

It is an observation that lies an abnormal distance from other values in a random sample from a population.

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

72 is relatively far from other data elements

Hence, it is an outlier

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Answer: 3 times

Step-by-step explanation:

Setting up the equation

If the function touches the horizontal axis, that means y=0, or f(x)=0 at that point(s).

So, we set our equation equal to 0

\(0=x^4+10x^3+24x^2\\\)

Factor out x^2

\(0=x^2(x^2+10x+24)\)

So, either \(x^2\) or \((x^2+10x+24)\) must equal zero

Factoring

\(x^2+10x+24=0\\(x+6)(x+4)=0\\\)

x=-6 or x=-4

from before, \(x^2 = 0\\x=0\)

So, f(x) equals zero at 3 places, when x=0, when x=-6, and when x=-4

Answer:

The balloon contains 456.3 kg of helium

Step-by-step explanation:

Density=mass / volume

Volume=2600 cubic meters of helium

Density=0.1755 kilograms per cubic meters

Mass=x

Find mass, x

Density=mass / volume

Mass=Density × volume

=0.1755 * 2600

=456.3 kg

The balloon contains 456.3 kg of helium

The Hermite curve with four control points P0(0,0), P1(1,1), P2(2,-1), and P3(3,0) has tangent vectors P0'(1,1) and P3'(1,1) at the endpoints. To determine the intermediate points on the curve at t = 1/3 and t = 2/3, we can use the Hermite interpolation formula.

The Hermite interpolation formula allows us to construct a curve based on given control points and tangent vectors. In this case, we have four control points P0, P1, P2, and P3, and tangent vectors P0' and P3'.

To find the intermediate point at t = 1/3, we use the Hermite interpolation formula:

P(t) = \((2t^3 - 3t^2 + 1)P0 + (-2t^3 + 3t^2)P3 + (t^3 - 2t^2 + t)P0' + (t^3 - t^2)P3'\)

Substituting the given values:

\(P(1/3) = (2(1/3)^3 - 3(1/3)^2 + 1)(0,0) + (-2(1/3)^3 + 3(1/3)^2)(3,0) + ((1/3)^3 - 2(1/3)^2 + (1/3))(1,1) + ((1/3)^3 - (1/3)^2)(1,1)\)

Simplifying the equation, we can find the coordinates of the intermediate point at t = 1/3.

Similarly, for t = 2/3, we use the same formula:

\(P(2/3) = (2(2/3)^3 - 3(2/3)^2 + 1)(0,0) + (-2(2/3)^3 + 3(2/3)^2)(3,0) + ((2/3)^3 - 2(2/3)^2 + (2/3))(1,1) + ((2/3)^3 - (2/3)^2)(1,1)\)

Calculating the equation yields the coordinates of the intermediate point at t = 2/3.

In this way, we can use the Hermite interpolation formula to determine the intermediate points on the Hermite curve at t = 1/3 and t = 2/3 based on the given control points and tangent vectors.

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Answer: -282475249

Step-by-step explanation:

Answer:

(6m² + 12m + 2) / (6m + 1)

Step-by-step explanation:

multiply both sides by m.

we get m² - 1 = 6m

move the -1 to the other side, so it becomes +1

m² =  6m + 1

so m² + 1/m² = (6m + 1) + 1/(6m + 1)

get a common denominator by squaring (6m + 1)

(6m + 1)².

we now have (6m + 1)² / (6m + 1)  + 1/(6m + 1).

we now add the numerators.

(6m + 1)² + 1 = (6m² + 6m + 6m + 1) + 1 = 6m² + 12m + 2.

numerator over denominator = (6m² + 12m + 2) / (6m + 1)

Answer:

Alright, with this, its essentially asking for you to plug in X into each equation for the answer.

With the first box, it asks for y = 5 - x, given the x = -2.

y = 5-x

y=5-(-2)

y=5+2

y=7

With the second box down, it wants things a bit differently, it gives you the y value, and wants for you to find the x. Given this, this question can be done backwards for the x value.

y = 5-x

6 = 5-x

x+6= 5

x=-1

With the third one, its the same thing as with the first box.

y = 5-x

y = 5-0

y = 5

Same thing with the fourth one.

y = 5-1

y = 4

If you have any question about the process or the answer, please comment below and I can help explain on what you're stuck on.

Answer:

Picture 1: (-2, 7), (-1,6), (0,5), (1,4)

Picture 2: (-2, -6), (4,6), (0,-2), (1,0)

Picture 3: (-1, -4), (8,5), (1,-2), (5,2)

Answer:

\(17.2 {m}^{2} \)

Step-by-step explanation:

\((m + m)(8.6m) = (2m)(8.6m) = (2 \times 8.6) {m}^{2} = 17.2 {m}^{2} \)

The required cycle-time is approximately 57.6 seconds.

To find the required cycle time, we need to divide the total available time by the number of units to be produced.

Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds

Number of units to be produced: 1,000 units

Required cycle time: Total available time / Number of units

Cycle time = 57,600 seconds / 1,000 units

Cycle time ≈ 57.6 seconds

Therefore, the required cycle time is approximately 57.6 seconds.

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The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission is:P(X ≥ 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003≈ 0.323 or about 32.3%

To find the probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission, we need to use the binomial probability formula which is given by: P(X = x) = nCx * p^x * q^(n-x)where, n is the total number of trials x is the number of successful trials p is the probability of success

q = 1 - p is the probability of failure n Cx = n! / x!(n-x)! is the binomial coefficient In this case, since we want to know the probability of at least 11 boats operating for the mission, we can find the probability of 11 boats, 12 boats, 13 boats, 14 boats, 15 boats and 16 boats operating, and then add them up.

So, we have: P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)where, n = 16 (since there are 16 patrol boats)p = 0.9 (since the probability of a patrol boat operating is 0.9)q = 0.1 (since the probability of a patrol boat not operating is 0.1)

Using the formula above, we get:P(X = 11) = 4368 * 0.9^11 * 0.1^5 = 0.174P(X = 12) = 1365 * 0.9^12 * 0.1^4 = 0.097P(X = 13) = 455 * 0.9^13 * 0.1^3 = 0.039P(X = 14) = 136 * 0.9^14 * 0.1^2 = 0.011P(X = 15) = 35 * 0.9^15 * 0.1^1 = 0.002P(X = 16) = 1 * 0.9^16 * 0.1^0 = 0.00003

Thus, if at least 11 of the 16 patrol boats are required to operate throughout the mission, the chance of mission success is P(X 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003 0.323 or roughly 32.3%.

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Answer:

The length of PQ is 18 feet.

The length of PR is 18 feet.

The length of QR is 24 feet.

Step-by-step explanation:

A way to set an equation up for this problem is:

\(\frac{4}{3}x+x+x=60\)

where x is the three lengths of the isosceles triangle, but the base QR is 4/3 the length of the other two congruent sides, length PQ and PR. The 60 represents the total length of the perimeter.

Then, solve for x from the equation, and you’ll get x=18. But your not done yet. Since the variable x in the equation stands for the sides of the isosceles triangle, so plug 18 into the equation and it should look like this:

\(\frac{4}{3}(18)+18+18=60\)

Don’t solve the whole equation, just solve the \(\frac{4}{3}(18)\) part of the equation, which is equal to 24. So the final equation is this:

\(24+18+18=60\)

Conclusion: 24 is the length of QR, and 18 is the length of PQ and PR. And they all equal 60, which is the perimeter. This is very true because the length of PQ and PR are the same (length 18), since it’s an isosceles triangle, and the length of QR is 4/3 the length of PQ and PR (4/3 of 18= 24).

Sorry for the long explanation.

But hope this helps and answers your question :)

Answer:

Step-by-step explanation: