2 cos x - sin x=3/(2 cos x+sin x)

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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The total number of acres planted for the optimal solution is not provided in the given information.

The amount of fertilizer (in tons) required to produce only corn is not provided in the given information.

The peak number of acres of wheat planted as fertilizer availability varies from 200 tons to 2200 tons in 100-ton increments cannot be determined without additional information.

I can help explain the general approach to answering the questions you mentioned.

To determine the total number of acres planted for the optimal solution, you would need to refer to the problem's constraints and objective function. The optimal solution would be obtained by solving the problem using linear programming techniques such as the simplex method or graphical method. By solving the problem, you can identify the values of the decision variables (such as acres planted) that maximize or minimize the objective function while satisfying the given constraints. The total number of acres planted for the optimal solution would depend on the specific problem setup and the solution obtained.

Similarly, to find out how much fertilizer would be needed to produce only corn, you would need to refer to the constraints and objective function of the problem. The specific requirements and coefficients associated with the corn production and fertilizer usage would determine the amount of fertilizer needed. By solving the problem, you can obtain the value of the decision variable representing fertilizer usage, which would indicate the required amount of fertilizer in tons.

SolverTable is a tool in Excel that allows you to perform sensitivity analysis by varying certain input values and observing the impact on the output. By using SolverTable, you can analyze the relationship between fertilizer availability (input) and acres planted (output) in the given problem. By varying the fertilizer availability from 200 tons to 2200 tons in 100-ton increments, you can observe how the acres of wheat planted change accordingly. The peak number of acres of wheat planted would be the maximum value observed during this range of fertilizer availability.

Since I don't have access to the specific problem you mentioned, I cannot provide precise answers or calculations. Please refer to the problem in your textbook or reference material to obtain the exact values and final answers.

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The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.

To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).

Using the slope formula: m = (y2 - y1) / (x2 - x1)

Substituting the values (0 - 5) / (3 - 0) = -5 / 3

So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 5):

5 = (-5/3) * 0 + b

5 = b

The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:

y = (-5/3)x + 5

To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.

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Answer:

\(g(x) = |\frac{1}{2}x - \frac{3}{2} | + 3\)

Step-by-step explanation:

Given

\(y = |\frac{1}{2}x - 2| + 3\)

Required

Translate the above one unit to the left

Replace y with f(x)

\(y = |\frac{1}{2}x - 2| + 3\)

\(f(x) = |\frac{1}{2}x - 2| + 3\)

When an absolute function is translated to the left, the resulting function is

\(g(x) = f(x - h)\)

Because it is been translated 1 unit to the left, h = -1

\(g(x) = f(x - (-1))\)

\(g(x) = f(x + 1)\)

Calculating \(f(x+1)\)

\(f(x+1) = |\frac{1}{2}(x+1) - 2| + 3\)

Open bracket

\(f(x+1) = |\frac{1}{2}x + \frac{1}{2} - 2| + 3\)

\(f(x+1) = |\frac{1}{2}x + \frac{1-4}{2} | + 3\)

\(f(x+1) = |\frac{1}{2}x + \frac{-3}{2} | + 3\)

\(f(x+1) = |\frac{1}{2}x - \frac{3}{2} | + 3\)

Recall that

\(g(x) = f(x + 1)\)

Hence;

\(g(x) = |\frac{1}{2}x - \frac{3}{2} | + 3\)

Answer:

y=l1/2x-3/2l+3

Step-by-step explanation:

cause im him

9514 1404 393

Answer:

  (5, -5)

Step-by-step explanation:

I like a graphing calculator for quickly finding a solution to a system of equations. It shows the solution to be (5, -5).

__

We can add the second equation to 2 times the first to eliminate the y-variable.

  2(-7x -3y) +(3x +6y) = 2(-20) +(-15)

  -11x = -55 . . . . . collect terms

  x = 5 . . . . . . . . . divide by -11

Substituting this value into the second equation, we have ...

  3(5) +6y = -15

  6y = -30 . . . . . . . . subtract 15

  y = -5 . . . . . . . . . . divide by 6

The solution is (x, y) = (5, -5).

Answer:

N=11/5

Step-by-step explanation:

Answer:

n = 2.2

Step-by-step explanation:

Given

- 6.5(n - 5) = 18.2 ( divide both sides by - 6.5 )

n - 5 = - 2.8 ( add 5 to both sides )

n = 2.2

It will take Lauren and her 4 friends a total of 26 minutes to prepare 20 batches of cupcakes if everyone frosts batches at the same rate.

If it takes one person 6 1/2 minutes to frost each batch of cupcakes, we can calculate the time it will take for Lauren and 4 friends to frost 20 batches of cupcakes.

First, we need to find the total time it takes for one batch of cupcakes to be frosted by one person:

1 batch = 6 1/2 minutes = 6.5 minutes

Now, we can calculate the total time it will take to frost 20 batches of cupcakes by one person:

Total time for 20 batches = 20 batches * 6.5 minutes/batch = 130 minutes

Since Lauren and her 4 friends are frosting cupcakes at the same rate, the total time it will take for them to frost 20 batches of cupcakes will be divided by the number of people, which is 5 (Lauren + 4 friends):

Total time for 20 batches with 5 people = 130 minutes / 5 = 26 minutes

Therefore, it will take Lauren and her 4 friends a total of 26 minutes to prepare 20 batches of cupcakes if everyone frosts batches at the same rate.

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A subset of the population used by statisticians to make predictions about a population is called a sample. In statistical analysis, it is usually not practical or feasible to study an entire population, hence a representative sample is selected instead.

The sample is selected based on specific criteria that must be met, such as age, gender, income, location, or any other relevant factors that might affect the population being studied.
The sample must be a true representation of the population, which means it should be chosen randomly and without any bias. This is important because if the sample is not representative of the population, then any conclusions drawn from it may not be accurate or applicable to the population as a whole.
Once the sample is selected, statisticians use various methods to analyze and interpret the data collected from it. The results obtained are then used to make inferences and predictions about the entire population. These predictions can be used to inform policies, decisions, or actions that affect the population.
In conclusion, a sample is a subset of a population that is selected by statisticians to make predictions about the population. It must be representative, randomly selected, and without any bias to ensure accurate results.

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Answer:its the graph of f(x) =( x/ was shifted to the right 2 units, down 5 units.

Step-by-step explanation:

Answer/Step-by-step explanation:

The corresponding side lengths of two triangles are always equal. Apply this in solving for x

4. \( \frac{9}{6} = \frac{x}{5} \)

Cross multiply

\( 6*x = 5*9 \)

6x = 45

divide both sides by 6

y = 7.5

5. \( \frac{10}{8} = \frac{x}{11} \)

Cross multiply

\( 8*x = 10*11 \)

8x = 110

divide both sides by 8

x = 13.75

6. \( \frac{12}{x} = \frac{7}{4} \)

Cross multiply

\( x*7 = 12*4 \)

7x = 48

divide both sides by 7

x = 6.86 (nearest hundredth)

Answer:

Ricardo spends $14 on the backpack and $11 o the binder.

Step-by-step explanation:

First, you have to calculate 56% of the amount Ricardo has to spend on school supplies to find the money he spends on the backpack:

$25*56%=$14

Now, you have to subtract 56% from 100% to find the percentage that he spent on a large binder:

100%-56%=44%

Finally, you have to calculate the 44% of the amount Ricardo has to spend on school supplies to find the money he spends on a large binder:

$25*44%=11

According to this, the answer is that Ricardo spends $14 on the backpack and $11 o the binder.

Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

a. Concluding that baseball is more popular than soccer based on a poll at a championship event is not valid due to potential sample bias, self-selection bias, limited sample size, and question phrasing.

b. A better method to determine the more popular sport is by conducting a comprehensive, unbiased survey with a random sample of students in a neutral setting, using clear and unbiased questions

For accurate determination of the most favored sport, it is inadequate to derive conclusions based on a poll taken during championship events due to possible biases such as self-selection and limited sample sizes, ambiguous question phrasings, and unrepresentative sampling.

The improved approach to tackle this issue necessitates conducting comprehensive, objective surveys that prioritize random sampling techniques.

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Answer:

Step-by-step explanation:

4π/3 radians. Triangle A B C has angles labeled as follows: A, (101x + 2) degrees; B, 34x degrees; C, unlabeled. The measure of ∠BCD is 120°. )

The probability that the experiment results in exactly successes is; \(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Consider that we have random variable X about binomial distribution with parameters n and p, then it can be written as;

\(X \sim B(n,p)\)

The probability that out of n trials, there be x successes is given as;

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

The expected value and variance of X are given as:

\(E(X) = np\\Var(X) = np(1-p)\)

Hence, the probability that the experiment results in exact success are;

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

H

Step-by-step explanation:

The rectangle has a length of (2x + 1) and a width of (5x - 4).

And we want to select the expression that represents the rectangle's area.

Recall that a rectangle's area is simply its length multiplied by its width. Thus:

\(A=(2x+1)(5x-4)\)

Expand by distributing:

\(A=(2x+1)(5x)+(2x+1)(-4)\)

Distribute:

\(A=(10x^2+5x)+(-8x-4)\)

Simplify:

\(A=10x^2-3x-4\)

Hence, our answer is H.

Gentiana has $12 left to spend on the pizza pie as of the equation model.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,

Let the amount spend on pizza pie be x,
According to the question,
40 = 10 + 25% of 40 + 20% of 40 + x

40 = 10 + 40 × 0.25 + 40 × 0.20 + x
40 = 10 + 10 + 8 + x
x = 40 - 28
x = 12

Thus, Gentiana has $12 left to spend on the pizza pie as of the situation model.

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Answer:

1/4, 4/10, 3/7, 24/50 are all less than 1/2.

Step-by-step explanation:

The probability of  \(\(P(-1.74 \leq Z \leq 1.74)\)\) is 0.9164. This represents the area under the standard normal distribution curve between -1.74 and 1.74 standard deviations from the mean. Thus, option C is correct.

The probability \(\(P(-1.74 \leq Z \leq 1.74)\)\), we need to calculate the cumulative probability for each value and then subtract the lower cumulative probability from the higher cumulative probability.

The cumulative probability for a standard normal distribution can be found using a Z-table or a statistical software. In this case, we'll use the Z-table.

Using the Z-table, we find the cumulative probability for Z = -1.74 is 0.0418 (approximately), and the cumulative probability for Z = -1.74 is 0.9582 (approximately).

So, the probability \(\(P(-1.74 \leq Z \leq 1.74)\)\) is approximately (0.9582 - 0.0418 = 0.9164).

Therefore, the main answer is 0.9164. The probability \(\(P(-1.74 \leq Z \leq 1.74)\)\) represents the area under the standard normal distribution curve between -1.74 and 1.74 standard deviations from the mean.

This area corresponds to the probability that a randomly selected value from a standard normal distribution falls within this range. By calculating the cumulative probabilities for each Z-value and subtracting them, we obtain the probability of interest.

In this case, the probability is approximately 0.9164, indicating that there is a 91.64% chance of selecting a value within the range of -1.74 to 1.74 standard deviations from the mean in a standard normal distribution. Thus, option C is correct.

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The solutions to the quadratic equation x² + 7x - 8 = 0 are x=1 and x=-8.

To find the solutions to the quadratic equation x² + 7x - 8 = 0, we can factor the equation or use the quadratic formula.

x² + 7x - 8 = 0

x² + 8x-x - 8 = 0

Factoring the equation, we have:

x(x+8)-1(x+8)=0

(x - 1)(x + 8) = 0

Setting each factor equal to zero, we find the solutions:

x - 1 = 0, which gives x = 1

x + 8 = 0, which gives x = -8

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Step-by-step explanation:

Start with the average. (of your data set)

Find how much each data value deviates from the average (difference of average and data value).

Take the absolute value of each difference.  

Add all of these absolute values.

Divide by the total number of data values.

How to find the MAD (Mean Absolute Deviation):

Let's use these numbers to figure out the MAD:

\(5, 2, 1, 3\)

1. First thing you want to do is add the numbers together:

\(5+2+1+3=11\)

2. Second thing you want to do is divide it by 4 because there are 4 numbers in the data set:

\(\frac{11}{4} =2.75\)

3. Third thing you want to do is subtract the data set from 2.75:

\(5-2.75=2.25\\2.75-2=0.75\\2.75-1=1.75\\3-2.75=0.25\)

4. Fourth thing you want to do is add all the differences:

\(2.25+0.75+1.75+0.25=5\)

5. Last thing you want to do is now divide the sum (5) by 4 again:

\(\frac{5}{4}= 1.25\)

So, the answer (MAD) would be 1.25

That's how you find the MAD to any data set in steps.

Hope this helped!

I know I'm 2 years late btw, you've probably already mastered this subject, sorry!

           - June 7, 2022 (6/7/22)

the answer would 2.35 bc or thw way its written

Step-by-step explanation:

its wrong dont put it

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer:

above sea level

Step-by-step explanation:

The absolute value of -3/2 represents 3 units of the total circumference of the unit circle.

The absolute value of -3/2 is 3/2, which represents a positive value. To determine what portion of the total circumference of the unit circle this value represents, we need to consider the ratio between the absolute value and the circumference.

The total circumference of the unit circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 1 since we are dealing with the unit circle. Therefore, the circumference of the unit circle is C = 2π.

To find the portion that represents the absolute value of -3/2, we can set up the following proportion:

(3/2) / (2π) = x / 1,

where x represents the portion of the circumference we are trying to find.

By cross-multiplying, we get:

3 / (2π) = x.

To simplify, we can multiply both sides by (2π):

x = (3 / (2π)) * (2π).

The (2π) terms cancel out, leaving us with:

x = 3.

Therefore, the absolute value of -3/2 represents 3 units of the total circumference of the unit circle.

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Answer:

8 1/6

Step-by-step explanation:

1. The linear function that models his distance from Washington, D.C. as a function of time, in hours, is:

d(t) = 109.5 - 55t.

2. The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is of: 0.9 hours = 54 minutes.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In the context of this problem, these parameters are given as follows:

Hence the function is:

d(t) = 109.5 - 55t.

The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is t when d(t) = 60.2 hence:

60.2 = 109.5 - 55t.

55t = 109.5 - 60.2

t = (109.5 - 60.2)/55

t = 0.9 hours = 54 minutes.

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The possible dimensions of the garden are 27 meters by 9 meters or 9 meters by 27 meters.

Let's assume that the length of the garden is L meters and the width is W meters. We know that the perimeter of the garden is 72 meters, so we can write:

2L + 2W = 72

Simplifying this equation, we get:

L + W = 36

We also know that the area of the garden is 243 square meters, so we can write:

L x W = 243

Now we have two equations with two variables, which we can solve to find the possible dimensions of the garden. One way to do this is to use substitution:

L + W = 36

L = 36 - W

Substituting L in terms of W in the equation for the area, we get:

(36 - W) x W = 243

Expanding this equation, we get:

36W - W^2 = 243

Rearranging and simplifying, we get:

W^2 - 36W + 243 = 0

We can solve this quadratic equation for W using the quadratic formula:

W = [36 ± sqrt(36^2 - 4 x 1 x 243)] / (2 x 1)

W = [36 ± sqrt(36)] / 2

W = 9 or W = 27

If W = 9, then L = 36 - W = 27. So the dimensions of the garden are 27 meters by 9 meters.

If W = 27, then L = 36 - W = 9. So the dimensions of the garden are 9 meters by 27 meters.

Therefore, the possible dimensions of the garden are 27 meters by 9 meters or 9 meters by 27 meters.

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