The rainfall, r, is inversely proportional to the water shortage, s, in a city. If the rainfall in the city is 40 inches, there is a water shortage of 200 million gallons per day. Which statement best describes the inverse relation of the rainfall in terms of the water shortage?

According to combinations formula there are 495 possible committees that can be selected from a group of 12 people.

To calculate this, you can use the formula for combinations

nCr = n!/(r!(n-r)!)

where n is the total number of people (12) and r is the number of people on the committee.
Therefore, the possible number of committees that can be selected is;

= {12!}/{4!8!}
= 12*11*10*9/4*3*2*1

= 11880/24
= 495
Therefore, 495 possible committees can be selected from a group of 12 people if a committee of 4 is to be selected.

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Answer:

No Solution.

Step-by-step explanation:

3x+4y=4

12x+16y=8

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

-4(3x+4y)=-4(4)

12x+16y=8

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

-12x-16y=-16

12x+16y=8

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

0=-8

no solution

The proportional relationship for the table has a constant of 2.

A proportional relationship simply means a relationship that exist between the variables that have equivalent ratios.

In this case, the relationship in the ratio can be expressed as:

y = kx

where k = constant of proportionality

4 = 2k

Divide

k = 4/2 = 2

Thw relationship will be y = 2k. The constant here is 2.

Note that the equation wasn't given but the table has been duly explained.

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The equation is 4x + 1=9, where x is the variable is satisfied for x=2.

In the algebra, an equation is a condition based on the variable. It can only be met if a particular value is present for the variable. As a result, the equation 2x - 5 = 13 can only be satisfied by the value of x = 9.

An amount that can fluctuate or altered depending on the mathematical issue is referred to as a variable.

Let's use the variable "x" to construct the equation.

Here, the equation is 4x + 1=9, where x is the variable.

Step1: writing the equation

4x + 1 = 9

Step2: taking 1 to the right side

4x = 9-1

Step3: divide 8 by 4, we get

x =\(\frac{8}{4}\)

x = 2

In the above example, 4x + 1 = 9 represents the equation.

Hence, we get the value of x=2, which means that for the value of x=2 the equation will satisfied.

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Answer: Point A

Step-by-step explanation:

The temperature at midnight is;

= 5 - 15

= -10°C

Looking at the number line, one can surmise that the scale is in multiples of 5. This means that C is 10, B is -5 and A is -10.

With point A being -10°C, it represents the colder midnight temperature.

Answer:

Point A

Step-by-step explanation:

We know that the temperature dropped 15 degrees, and that it was initially of 5°C. So, by midnight, the temperature will be of -10°C (5-15=-10).

We also know that the distance between points is of 5°C. So, the point that we have to mark is point A, which represents -10°C.

During plantation sunflower was 15 inches tall , then grow at the rate of 2 inches per week , after 9 weeks sunflower would be 33 inches tall.

As given in the question,

During plantation sunflower was 15 inches tall

Rate of growth per week = 2 inches

Let x be the number of weeks and y be the height of the plant.

Required height :

y = 15 + 2x

Change in the height of sunflower after 9 weeks

y =15 +2x

 = 15 + 2(9)

 = 15 +18

  = 33 inches

Therefore, during plantation sunflower was 15 inches tall , then grow at the rate of 2 inches per week , after 9 weeks sunflower would be 33 inches tall.

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The correlation between temperature in Celsius and temperature in Fahrenheit is a perfect positive correlation.

The relationship between temperature in Celsius and temperature in Fahrenheit is a perfect positive correlation. This means that as one variable (temperature in Celsius) increases, the other variable (temperature in Fahrenheit) increases at the same rate.

The reason for this perfect positive correlation is that the two scales are directly proportional to each other, with the same slope and intercept. Specifically, the formula for converting Celsius to Fahrenheit is F = (9/5)C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

Thus, any change in Celsius will result in an equivalent change in Fahrenheit. This correlation is observed among typical stat100 students, as well as in any other population where the two temperature scales are used.

Therefore, a perfect positive correlation exists between the temperature in Celsius and the temperature in Fahrenheit

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Let that be x

ATQ

\(\\ \rm\Rrightarrow 3x-6/5=9\)

Arrange accordingly to work backwards(Every thing is reversed)

\(\\ \rm\Rrightarrow 9(5)+6/3=x\)

\(\\ \rm\Rrightarrow 45+6/3=x\)

\(\\ \rm\Rrightarrow 51/3=x\)

\(\\ \rm\Rrightarrow x=17\)

.

Answer:

AB

Step-by-step explanation:

AB I also did the same test and it was right! Please give me brainliest!

Answer:

If you put it in your calculator and round it you should get the right answer.

Step-by-step explanation:

So the minimum score required to be eligible to enroll in calculus is 67.

To find the minimum score required to be in the top 20%, we need to find the score that corresponds to the 80th percentile of the distribution.

The standard normal distribution is a normal distribution with mean 0 and standard deviation 1. We can use the standard normal distribution to find percentiles of any normal distribution by using the fact that any normal distribution can be converted to a standard normal distribution through the following formula:

z = (x - mean) / standard deviation

where x is the raw score, mean is the mean of the distribution, standard deviation is the standard deviation of the distribution, and z is the standardized score (also called the z-score).

We can use this formula to convert the scores on the math placement exam to the standard normal distribution. Let x be the minimum score required to be eligible. Then the corresponding z-score would be:

z = (x - 42) / 19

We want to find the value of x that corresponds to the z-score for the 80th percentile, which we can find using a z-table or by using a calculator or computer to find the inverse of the standard normal cumulative distribution function (CDF). The z-score for the 80th percentile is approximately 0.84. Plugging this value into the equation above, we get:

0.84 = (x - 42) / 19

Solving for x, we find that the minimum score required to be eligible is approximately 66. Rounding to the nearest integer, the minimum score required is 67.

So the minimum score required to be eligible to enroll in calculus is 67.

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To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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To prove that the limit of f(x, y) as (x, y) approaches (1, 1) is equal to 3, we need to show that for any given positive value of ϵ, there exists a positive value of δ such that whenever the distance between (x, y) and (1, 1) is less than δ, the value of f(x, y) is within ϵ distance from 3.

Let's consider a positive value of ϵ. Our goal is to find a positive value of δ such that whenever the distance between (x, y) and (1, 1) is less than δ, the value of f(x, y) is within ϵ distance from 3.

We can start by expressing the distance between (x, y) and (1, 1) using the Euclidean distance formula:

√[(x - 1)^2 + (y - 1)^2]

Next, we can analyze the function f(x, y) = x^2 + xy + y. Substituting the values of x and y into the function, we have:

f(x, y) = x^2 + xy + y

To proceed with the ϵ,δ proof, we need to find a suitable δ value in terms of ϵ. By carefully manipulating the equation, we can find an expression for δ in terms of ϵ that satisfies the conditions for the limit. However, due to the limited formatting capabilities of text, it is not feasible to provide the complete mathematical derivation here. I recommend consulting a textbook or online resources for a detailed explanation and step-by-step derivation of the δ value in terms of ϵ for this specific function.

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Answer:

5·5=25 pounds

Step-by-steplanation:

Answer: 25 pounds.

Step-by-step explanation:

5 pound ⇒ 1 apple

x ponds ⇒ 5 apples

Cross multiply

x times 1 ⇒ 5 times 5

x ⇒ 25

Therefore you would buy 5 apples for 25 pounds.

We introduce artificial variables and create an auxiliary objective function to convert the inequality constraints into equality constraints. Then, we apply the simplex method to maximize the objective function while optimizing the original variables. If the optimal solution of the auxiliary problem has a non-zero value for the artificial variables, it indicates infeasibility.

Introduce artificial variables:

Rewrite the constraints as 3x₁ + 4x₂ + s₁ = 6 and -x₁ - 3x₂ - s₂ = -2, where s₁ and s₂ are the artificial variables.

Create the auxiliary objective function:

Maximize zₐ = -M(s₁ + s₂), where M is a large positive constant.

Set up the initial tableau:

Construct the initial simplex tableau using the coefficients of the auxiliary objective function and the augmented matrix of the constraints.

Perform the simplex method:

Apply the simplex method to find the optimal solution of the auxiliary problem. Continue iterating until the objective function value becomes zero or all artificial variables leave the basis.

Check the optimal solution:

If the optimal solution of the auxiliary problem has a non-zero value for any artificial variables, it indicates that the original problem is infeasible. Stop the process in this case.

Remove artificial variables:

If all artificial variables are zero in the optimal solution of the auxiliary problem, remove them from the tableau and the objective function. Update the tableau accordingly.

Solve the modified problem:

Apply the simplex method again to solve the modified problem without artificial variables. Continue iterating until reaching the optimal solution.

Interpret the results:

The final optimal solution provides the values of the decision variables x₁ and x₂ that maximize the objective function z.

In this way, we can solve the given linear programming problem using the M-method.

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Answer: 1st point’s coordinates = (-0.5, -0.25)

2nd point’s coordinates = (1, 2.5)

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

8%

Step-by-step explanation:

(81-75)/75*100=8%

Answer:

= 1.23214285

Step-by-step explanation:

Answer:

-36 I believe

Step-by-step explanation:

a/9=-4

you need a negative to be in that equation for 4 to be negative. multiply 9 on both sides, 9*-4 is -36

a=-36

Answer:

D

Step-by-step explanation:

380

The correct option is c. 33%.

The job rate of industry’s percent increase from 2003 to 2013 is 33%.

The percentage increase would be the change between the final and initial values given as a percentage. We need the initial value and the enhanced (new) value to calculate the percentage.

In other words, % growth is a measurement of percent change that indicates the amount by which a quantity increases in magnitude, strength, or value.

If the % rise is negative, we might conclude that there is corresponding proportion reduction. Let's look at the percentage growth calculation now.

Now, according to the question;

Total Number of years = 10 years

Total number of new jobs created = 2.65 thousand x 10

                                                         = 26.5 thousand

                                                         = 26,500

Number of jobs in 2013 = 78,900 + 26,500

                                       = 105,400

Percentage increase = (105,400 - 78,900)/78,900 x 100

                                   = 26,500/78,900 x 100

                                   = 0.3359 x 100

                                    = 33.59%

Percentage increase = 33% (approx)

Therefore, the percentage increases in the job between 2003 and 2013 is 33%.

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Answer:

C

Step-by-step explanation:

Store B sells 12591 products.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.

Let the number of products Store A sells be x, the number of products store B sells be y, and the number of products store C be z.

Now,

Store C sells 125910 products.

z = 125910 products

Store A sells one-half as many as store C.

x = ( 1/2 )z

x = ( 1/2) × 125910

x = 62955 products

Store A sells five times as many products as store B can be expressed as the equation,

x = 5y

62955 = 5y

Dividing each side by 5,

y = 62955 / 5

y = 12591 products

Store A, B, and C sell 62955, 12591, and 125910 products.

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To calculate the effective annual rate of interest, we can use the formula: Effective Annual Rate (EAR) = (1 + i/n)^n - 1, where i is the nominal interest rate and n is the number of compounding periods per year.

In this case, $535 is deposited at the beginning of every three months for 10 years, resulting in a total of 40 deposits .We need to find the nominal interest rate i that will make the accumulated amount equal to $30,000. Let's denote the interest rate per quarter as r, so the nominal interest rate will be i = 4r. Using the formula for the future value of an ordinary annuity: FV = P((1 + r)^n - 1)/r. where FV is the future value, P is the periodic payment, r is the interest rate per period, and n is the number of periods, we can calculate: $30,000 = $535((1 + r)^40 - 1)/r. Solving this equation for r numerically, we find that r ≈ 0.0162. Therefore, the nominal interest rate i ≈ 4(0.0162) ≈ 0.0648, which is approximately 6.48%. The effective annual rate (EAR) is then: EAR = (1 + i/n)^n - 1 = (1 + 0.0648/4)^4 - 1 ≈ 0.0647 or 6.47%.

Therefore, the effective annual rate of interest at which $535 deposited at the beginning of every three months for 10 years will amount to $30,000 is approximately 6.47%.

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Answer:

45 members voted and 15 didn't vote

Step-by-step explanation:

Answer:

it is 80°

cause it is coming from the same cord AB

O and C will be same

Answer:

x = 40

Step-by-step explanation:

x = 80÷2 = 40

Central angle theorem

Answer:

b

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 )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

y = - \(\frac{1}{2}\) x - 7 ← is in slope- intercept form

with slope m = - \(\frac{1}{2}\)

• Parallel lines have equal slopes

the slopes are not equal thus not parallel

• the product of the slopes of perpendicular lines is equal to - 1

2 × - \(\frac{1}{2}\) = - 1

Thus the 2 lines are perpendicular to each other.

The distance between points B and C is 10.3 miles.

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometry is made up of trigonometric functions (also known as circular functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

If we have a triangle with a right angle,

Then, tan = Opposite/Adjacent side

To find the distance,

In the ABC right angle triangle,

5.7 miles on the adjacent side = AB

θ = 61°

We must locate the BC.

tan = Opposite/Adjacent side

tan61°= BC/5.7

BC = 5.7×tan61°

BC = 10.283 = 10.3 (to the nearest tenth).

The figure is attached below.

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