I subtract 14 from a certain number I multiply the result by 3 the final answer is 3 what was the number

By using the concept of Binomial distribution of probability, it can be calculated that

a) Mean number of Hispanics on randomly chosen committees of 17 workers = 3.4

b) Standard deviation of the count X of Hispanic members = 1.65

c) If p = 0.1, standard deviation  = 1.24

If p = 0.01, standard deviation = 0.410

So as p tends to zero, standard deviation will decrease

Third option is correct.

What is Binomial Distribution?

Binomial distribution is a discrete probability distribution whose Probability mass function is given by

P(X = x) = \({n \choose x} p^x q^{n-x}\), where p is the probability of success and q is the probability of failure

Here, n = 17, p = 0.20, q = 1 - 0.20 = 0.80

This is a binomial distribution

a) Mean number of Hispanics on randomly chosen committees of 17 workers = 17 \(\times\) 0.20 = 3.4

b) Standard deviation of the count X of Hispanic members = \(\sqrt{17 \times 0.20 \times 0.80}\) = 1.65

c) If p = 0.1, standard deviation = \(\sqrt{17 \times 0.1 \times 0.9}\) = 1.24

If p = 0.01, standard deviation = \(\sqrt{17 \times 0.01 \times 0.99}\) = 0.410

So as p tends to zero, standard deviation will decrease

Third option is correct.

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The correct option is (e): the dimensions of the one with the largest area 28 ft. x 28 ft.

let l be the length of rectangle and

   w be the width of rectangle

given perimeter 112

       i.e.  2 (l + w) = 112

       l + w = 56

         then l = 56 - w

area A = l w

           = w (56 - w)

         A' = 56 – 2 w

for critical point A' = 0, then

                56 – 2 w = 0

                 w = 28,

then l = 56 - w = 56 - 28 = 28

l × w = 28 × 28

a perimeter is a direction that surrounds a two-dimensional shape. The word comes frae the Greek peri (around) a meter (measure). The time period may be used both for the direction or its length - it can be thought o because the length o the outline o a form. the perimeter of a circle or ellipse is cried its circumference.

Calculating the perimeter has widespread realistic packages. the fringe may be used tea calculate the length o fence required tea surround a yard or garden. the perimeter of a wheel (its circumference) describes Hou far it's going to roll in a revolution. similarly, the amount o string wound around a spoil is related tea the spoil’s perimeter.

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Answer:

For 60 gallons of fuel, the airplane would weigh 2430 gallons.

Step-by-step explanation:

Concept: Use the values and conditions to make a linear equation of a straight line. Let the y-axis be fuel and x-axis be airplane weight. The given points are (2210, 20) and (2397, 54). Use these points to make an equation of line.

\(\frac{y-20}{x-2210} =\frac{54-20}{2397-2210} \\\frac{y-20}{x-2210} = \frac{34}{187}\)

Let this be the equation of straight line.

We have to find the airplane weight at 60 gallons of fuel. This means y = 60 and we have to find the x.

\(\frac{60-20}{x-2210} =\frac{34}{187} \\x-2210=\frac{(187)(40)}{34} \\x-2210=220\\x=2430\)

So, the airplane weight is 2430 gallons.

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The probability of a randomly selected injured wrestler visiting a physical therapist is 56%.

To calculate this probability, let's denote the probability of visiting a physical therapist as P(PT) and the probability of visiting a chiropractor as P(C). We are given that 28% of the wrestlers visit both a physical therapist and a chiropractor, so we can write this as P(PT ∩ C) = 0.28. We are also given that 8% of the wrestlers visit neither, so P(neither) = 0.08.

The probability of visiting either a physical therapist or a chiropractor can be calculated using the principle of inclusion-exclusion:

P(PT ∪ C) = P(PT) + P(C) - P(PT ∩ C)

Since P(PT ∩ C) = 0.28, we have:

P(PT ∪ C) = P(PT) + P(C) - 0.28

We are also given that the probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%, so we can write this as:

P(PT) = P(C) + 0.16

Substituting this into the equation for P(PT ∪ C), we get:

P(PT ∪ C) = P(C) + 0.16 + P(C) - 0.28

P(PT ∪ C) = 2P(C) - 0.12

Since P(PT ∪ C) represents the probability of visiting either a physical therapist or a chiropractor, and we know that 8% visit neither, we can write:

P(PT ∪ C) + P(neither) = 1

Substituting the values, we have:

2P(C) - 0.12 + 0.08 = 1

2P(C) = 1.04

P(C) = 0.52

Now, using P(PT) = P(C) + 0.16, we can find:

P(PT) = 0.52 + 0.16

P(PT) = 0.68

Therefore, the probability of a randomly selected injured wrestler visiting a physical therapist is 0.68 or 68%.

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Answer:

(10,250)

Step-by-step explanation:

HOPE IT HELPS YOU!!!

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer:

B) 1/3.

Step-by-step explanation:

There are six possible outcomes when rolling a number cube, and two of them are multiples of 3 (3 and 6). Therefore, the theoretical probability of rolling a multiple of 3 on a single roll of a number cube is 2/6, which simplifies to 1/3.

Therefore, the answer is B) 1/3.

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

In the equation, 1/6 represents the constant of proportionality.

If a person weighs 60 kg on earth, the person would weigh 10kg ont he moon.

The equation that represents inverse proportion is: m = ke

Where:

If k is 1/6 and e is 60kg,

m = 1/6 x 60 = 10kg

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To solve the given problems related to the T-distribution with parameters T(45, 72, 106), we need to find the mean, standard deviation, and probability using the T-distribution table or a calculator.

(a) The mean of the T-distribution is equal to the location parameter, which is given as 72. Therefore, the mean is 72.

(b) The standard deviation of the T-distribution is calculated using the scale parameter. In this case, the scale parameter is 106. Thus, the standard deviation is 106.

(c) To find the probability that a score will be less than 67, we need to use the T-distribution table or a calculator. By looking up the degrees of freedom (df = 45) and the corresponding T-value for 67, we can determine the probability. Let's assume the probability is denoted as P(T < 67). The calculated probability, rounded to 4 decimal places, will represent the likelihood of a score being less than 67.

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The probability that represents the likelihood of a single event occurring by itself is called marginal probability.

Marginal probability refers to the probability of an individual event happening independently without considering any other events. It focuses on a single variable or outcome without considering the relationship or dependencies with other variables.

To calculate marginal probability, you divide the number of times the specific event occurs by the total number of observations. For example, if you have a bag of marbles with different colors and you want to find the marginal probability of drawing a red marble, you would count the number of red marbles and divide it by the total number of marbles in the bag.

Marginal probability is often used when working with categorical variables or when studying the probability of a single event without considering any other variables or conditions. It provides a fundamental understanding of the likelihood of an event occurring in isolation, independent of any other factors.

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Answer:

Triangle 20, 30, and 15 will create a triangle

Step-by-step explanation:

In order for side lengths to make a triangle, the sum of the two shortest sides must be greater than the longest side

5+3 < 9 so it does not work

15+20>30 so it does work

According to the Wechsler scales, the middle 50% of scores fall within the broad average range. This means that half of the test-takers will score within this range.

The broad average range is typically defined as having a standard score between 90 and 109. Standard scores are based on a mean of 100 and a standard deviation of 15.

To explain further, the Wechsler scales use a standardization process to compare individual scores to the scores of a representative sample of the population. This allows for a meaningful interpretation of an individual's performance relative to others. The middle 50% range is a measure of dispersion, indicating where the majority of scores fall.

The Wechsler scales provide a useful way to interpret and compare scores on cognitive tests. The middle 50% range offers a reliable indicator of the average performance level, with scores falling between 90 and 109.

It is important to note that the interpretation of scores should always be considered within the context of the specific test and the individual being assessed.

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Given,

F= Fixed Cost = $18,000

V= Variable Cost per unit = $0.90

P= Price per unit = $3.20

a) Q= Quantity = 12,000 cupcakes annually

Total Cost (TC) formula is:TC = F + V x Q = 18,000 + 0.90 × 12,000 = $29,400

Total Revenue (TR) formula is:TR = P × Q = 3.20 × 12,000 = $38,400

Profit formula is:Profit = TR − TC = 38,400 − 29,400 = $9,000.

b) The bakery will need to sell 6,924 cupcakes in order to break even.

The formula for the Break-even point (BEP) is BEP = F / (P - V) = 18,000 / (3.20 - 0.90) = 6,923.08 ≈ 6,924 cupcakes

5. The graphical representation of the Break-even volume for the Gobblecakes bakery is shown below:

8. Break-even volume as a percentage of maximum operating capacity will be = 58%

Break-even volume as a percentage = (Break-even volume / Maximum operating capacity) x 100%

                                                             = (6,923.08 / 12,000) x 100% = 57.69% ≈ 58%

11. The new Break-even point (BEP) will increase from 6,924 cupcakes to 8,750 cupcakes.

When the selling price for a cupcake changes from $3.20 to $2.75, the new Break-even point (BEP) will be:

BEP = F / (P - V) = 18,000 / (2.75 - 0.90) = 8,750 cupcakes

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Answer:

Step-by-step explanation:

Answer:

n+2 represemts the number of sides in the polygon for the nth member of the sequence

Answer:

The constant of proportionality is 1/4.

Step-by-step explanation:

Keep in mind that the constant of proportionality can always be found by dividing any y value by any x value, as long as the values are in the same row. For example, in this table, the constant of proportionality would be 1/4, as, in the first row, the y value is 2 and the x value is 8, and 2/8 equals 1/4.

Hope this helps! Comment any questions <3

95% confidence interval is 1.96

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

For 95% confidence interval, we will keep 95% area in the center and will divide the remaining area equally on both sides.

From Standard Normal table,  P(-1.96 < Z < 1.96) = 0.95, i.e., there is a 95% probability that a standard normal variable, Z, will fall between -1.96 and 1.96.

Hence 95% percent confidence interval is 1.96

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Answer:

5 miles

Step-by-step explanation:

We will use the method of cross multiplying and dividing.

You will multiply 60 x 3

Then, take the answer (180) and divide it by 36.

That will give you 5 and your answer.

Answer:

1900 km

Step-by-step explanation:

train = 1050km

bus = 200 less than train or 1050-200 = 850

1050+850=1900

Answer:

625, just got it right

Step-by-step explanation:

Answer:

We can rewrite this as \(\frac{200x}{x} + \frac{-300}{x}\).

\(\frac{200x}{x}\) simplifies to 200 after eliminating x from the numerator and denominator and \(\frac{-300}{x}\) becomes \(-\frac{300}{x}\) so the final answer is \(200 - \frac{300}{x}\).

Complete Question

Question 14

Jabar earns $5 for the first 10 pounds of newspaper he recycles, then $0.25 for each additional pound. Which expression represents the amount he earns for recycling p pounds of newspaper if p > 10?

a. 5+0.25 (p-10)

b. (5 +0.25) P

c. 5 +0.25p

d.5 (10) +0.25p

Answer:

5 (10) +0.25p

Step-by-step explanation:

Let the number of additional pounds = x

Hence:

Jabar earns $5 for the first 10 pounds of newspaper he recycles, then $0.25 for each additional pound.

The statement above is represented as:

$5 × 10 + $0.25 ×p

= 5(10) + 0.25(p)

Therefore, the expression that represents the amount he earns for recycling p pounds of newspaper if p > 10 is written as

5(10) + 0.25(p)

Option d is the correct option

The polynomial function p(x) = 5x³ - 5x² - 10x have zeros of 0, -1 and 2

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial.

The polynomial function given is

p(x) = 5x³ - 5x² - 10x

The zeros of the function are 0, 2, -1

To test the zeros if they are the roots of the polynomial

p(0) = 5(0)³ - 5(0)² - 10(0)

p(0) = 0

p(2) = 5(2)³ - 5(2)² - 10(2)

p(2) = 0

p(-1) = 5(-1)³ - 5(-1)² - 10(-1)

p(-1) = 0

The zeros are 0, -1, and 2 to the polynomial

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To prove that there is a unique polynomial of degree ≤n − 1 passing through a collection of n points in the plane with distinct x-coordinates, we can create a linear system of equations. The matrix of coefficients in the linear system is a Vandermonde matrix, which is a square matrix with powers of the x-coordinates as its entries.

To confirm the existence of a unique polynomial, we create a linear system of equations. Suppose we have n points (x₁, y₁), (x₂, y₂), ..., (xₙ, yₙ). We seek a polynomial of the form p(x) = a₀ + a₁x + a₂x² + ... + aₙ₋₁xⁿ⁻¹ that passes through these points.

For each point, we can substitute the x-coordinate into the polynomial and set it equal to the corresponding y-coordinate. This gives us n equations of the form a₀ + a₁x + a₂x² + ... + aₙ₋₁xⁿ⁻¹ = y.

We can rewrite these equations in matrix form as AX = Y, where A is the Vandermonde matrix of coefficients, X is the column vector of coefficients a₀, a₁, ..., aₙ₋₁, and Y is the column vector of y-coordinates.

The Vandermonde matrix A is a square matrix of size n × n. The entry in the i-th row and j-th column is xᵢⁿ⁻ʲ, where xᵢ is the x-coordinate of the i-th point and j ranges from 0 to n-1.

The uniqueness of the solution to this linear system can be proven by showing that the Vandermonde matrix is invertible, which means it has a unique inverse. This guarantees that there is a unique polynomial of degree ≤n − 1 passing through the given collection of points with distinct x-coordinates.

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Without the actual data, it's not possible to calculate the estimated regression equation, coefficient of determination, F test statistic, and p-value. However, I can explain the process of finding them.

To find the estimated regression equation, we use the method of least squares to find the values of the coefficients β0, β1, and β2 that minimize the sum of squared residuals. The equation would be of the form: y = β0 + β1x + β2x^2. The coefficient of determination (R^2) measures the proportion of variation in the dependent variable (traffic flow) that is explained by the independent variable (vehicle speed) and the model. It ranges between 0 and 1, with higher values indicating a better fit. It can be calculated as the ratio of explained variance to total variance. The F test statistic is used to test the overall significance of the model by comparing the variance explained by the model to the unexplained variance. It is calculated as the ratio of explained variance to unexplained variance, adjusted for the degrees of freedom. The p-value is the probability of obtaining an F test statistic as extreme or more extreme than the observed one, assuming the null hypothesis that the model has no significant effect. It is compared to a significance level (α) to decide whether to reject or fail to reject the null hypothesis. Using a significance level of .01, we can reject the null hypothesis of no significant effect if the p-value is less than .01. To predict the traffic flow for a speed of 39 miles per hour, we plug x = 39 into the estimated regression equation and solve for y. The result would be rounded to the nearest whole number.

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Yolanda is buying school supplies. She buys n packages of pencils at 1.40 per package and m pads of paper at 1.20 each. The expression 1.4 represents the cost of one package of pencils while the expression 1.2 represents the cost of one pad of paper.

The given expressions represent the cost of one package of pencils and one pad of paper. Hence,1.4 represents the cost of one package of pencils.1.2 represents the cost of one pad of paper.Yolanda buys n packages of pencils.

Therefore, the total cost of pencils will be n × 1.4

Similarly, Yolanda buys m pads of paper.

Therefore, the total cost of pads will be m × 1.2

Therefore, the total cost of buying n packages of pencils at 1.40 per package and m pads of paper at 1.20 each will be,1.4n + 1.2m

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Answer:

11a+12b

Step-by-step explanation:

9a+12b+2a=11a+12b

Answer:

96 students

Step-by-step explanation:

I am not exactly sure if this question is talking about a 1:5 ratio, but that's what I am assuming. To get 96, you need to replace the 5 with 480 because the problem seems to mean 1 to every 5 people wear glasses. Next, you do 480/5 to get the number on the left side of the ratio. You get 96 when you do that. I am a little confused with the question because it isn't exactly formatted correctly, but this is what I am guessing. Hope this helps!

Answer: 0 bottles of Brand X and 10 bottles of Brand Y

(please let me know if I read the question wrong and I will do my best to fix it)

Step-by-step explanation:

This problem can be solved using linear programming. Let x be the number of Brand X bottles and y be the number of Brand Y bottles. The objective is to minimize the cost, given by:

Cost = 25x + 15y

Subject to the following constraints, which represent the minimum nutrient requirements:

3x + 9y ≥ 30 (Nutrient A)

3x + 2y ≥ 16 (Nutrient B)

7x + 2y ≥ 24 (Nutrient C)

x ≥ 0, y ≥ 0 (Non-negativity constraint)

We can solve this system of inequalities graphically by finding the feasible region and the corner points.

Nutrient A constraint (3x + 9y ≥ 30):

Divide the inequality by 3:

x + 3y ≥ 10

Nutrient B constraint (3x + 2y ≥ 16):

Divide the inequality by 2:

1.5x + y ≥ 8

y ≥ 8 - 1.5x

Nutrient C constraint (7x + 2y ≥ 24):

Divide the inequality by 2:

3.5x + y ≥ 12

y ≥ 12 - 3.5x

Now we will graph the inequalities on the xy-plane:

y ≥ 10 - x/3

y ≥ 8 - 1.5x

y ≥ 12 - 3.5x

The feasible region is the area where all three inequalities are satisfied. It's a triangular region with corner points A(0,10), B(4,4), and C(8/3, 2).

Now we need to find the cost at each corner point:

Cost A (0, 10) = 25(0) + 15(10) = $150

Cost B (4, 4) = 25(4) + 15(4) = $160

Cost C (8/3, 2) = 25(8/3) + 15(2) ≈ $153.33

The minimum cost is $150, which occurs when 0 bottles of Brand X and 10 bottles of Brand Y are used. So, the public aquarium should add 0 bottles of Brand X and 10 bottles of Brand Y to satisfy the needs of the reef tank at the minimum possible cost.