Maggie is building bird houses for all of her friends. she has 77.5 feet of wood planks. She makes 5 bird houses and has 12 feet of wood left over How many feet of wood does Maggie use per bird house

Given data:Width of flume (B) = 3 mDepth of flume (D) = 1.5 mChezy’s constant (C) = 0.013Slope of the bed (S) = 0.0025We know that,Q = (1/C) * A * R^(2/3) * S^(1/2)

Where,Q = Discharge of rectangular flumeA = Area of cross-sectionR = Hydraulic radiusS = Slope of the bedCalculation:Area of cross-section, A = B * D = 3 * 1.5 = 4.5 m²Wetted perimeter, P = B + 2 * D = 3 + 2 * 1.5 = 6 mHydraulic radius,

R = A / P = 4.5 / 6 = 0.75 mSubstituting the given values,Q = (1 / 0.013) * 4.5 * 0.75^(2/3) * 0.0025^(1/2)Q = 0.796 m³/sBoundary shear stress, τo = ρ * g * R * Sρ = Density of water = 1000 kg/m³g = Acceleration due to gravity = 9.81 m/s²Substituting the given values,τo = 1000 * 9.81 * 0.75 * 0.0025τo = 18.23 N/m²

The discharge of a rectangular flume 3 m wide and 1.5 m deep on a slope of 0.0025 is 0.796 m³/s and the boundary shear stress is 18.23 N/m².

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The probability of x successes in the n independent trials of the experiment is P(x).The formula for binomial probability is\(P(x) = nCx * p^x * q^(n-x)\)where n is the number of trials, p is the probability of success on each trial, q is the probability of failure on each trial, and x is the number of successes desired.

For this problem, we have:\(n = 50p = 0.05q = 1 - 0.05 = 0.95x = 2\)So, we need to use the formula to calculate \(P(2).P(2) = 50C2 * (0.05)^2 * (0.95)^(50-2)\)where \(50C2 = (50!)/((50-2)!2!) = 1225\)

Therefore,\(P(2) = 1225 * (0.05)^2 * (0.95)^48P(2) = 0.2216\) (rounded to four decimal places)So, the probability of 2 successes in 50 independent trials of the experiment is 0.2216.

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Given information: n is 50, p is 0.05 and x is 2.

The final probability is 0.0438 (approx).

To compute the probability of x successes in the n independent trials of the experiment, we can use the Binomial Probability formula. The formula is given as:

P(x) = C(n,x) * p^x * q^(n-x)

Where, C(n,x) is the number of combinations of n things taken x at a time. And q = (1-p) represents the probability of failure. Let's plug in the given values and solve:

P(2) = C(50,2) * (0.05)^2 * (0.95)^48

P(2) = (50!/(2! * (50-2)!)) * (0.05)^2 * (0.95)^48

P(2) = 1225 * (0.0025) * (0.149)

P(2) = 0.0438 (approx)

Therefore, the probability of having 2 successes in 50 independent trials with p=0.05 is 0.0438 (approx).

Conclusion: Probability is an important aspect of Statistics which helps us understand the chances of events occurring. In this question, we calculated the probability of x successes in n independent trials of a binomial probability experiment. We used the Binomial Probability formula to find the probability of having 2 successes in 50 independent trials with p is 0.05. The final probability was 0.0438 (approx).

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Answer:

Step-by-step explanation:

Use the formula x-x1/x1-x2 = y-y1/y1-y2

Answer:

X=6

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

5+3=8

8x4=32

4x8=32

Check the picture below.

Answer:

56

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.

To define the supremum and infimum of the set A, we first need to determine the properties of the set.

The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.

To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.

Let's analyze the elements of A:

For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.

As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.

Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.

Again, analyzing the elements of A:

As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.

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Answer:

300

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

x - 1= 0 → x = 1 We paste this value.

3(1)⁵ + 4(1)⁴ - 2= 3 + 4 - 2 = 5

There is another method that is longer. As shown in the picture

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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Answer:

\(\displaystyle m=24\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (0, 0)

Point (0.5, 12)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Develop an estimated regression equation to predict the percentage of games won based on the percentage of field goals made and determine if there is a significant relationship between the two variables at the .05 level of significance.

To develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made and test for a significant relationship at the .05 level of significance, follow these steps:

1. Gather data: Collect data on the percentage of games won and the percentage of field goals made for a representative sample of teams or seasons.

2. Perform a regression analysis: Use statistical software or a spreadsheet tool to run a linear regression analysis, where the dependent variable (Y) is the percentage of games won and the independent variable (X) is the percentage of field goals made.

3. Obtain the regression equation: From the regression analysis output, find the coefficients for the intercept (b0) and the slope (b1). The estimated regression equation will be Y = b0 + b1X.

4. Test for a significant relationship: To determine if there is a significant relationship between the percentage of games won and the percentage of field goals made at the .05 level of significance, analyze the p-value associated with the independent variable (X) in the regression output. If the p-value is less than .05, there is a significant relationship between the variables.

5. Interpret the results: If a significant relationship exists, the regression equation can be used to predict the percentage of games won based on the percentage of field goals made. The slope (b1) indicates how the percentage of games won changes for each percentage point increase in field goals made. If there is no significant relationship, the equation cannot be used for reliable predictions.

By following these steps, you can develop an estimated regression equation to predict the percentage of games won based on the percentage of field goals made and determine if there is a significant relationship between the two variables at the .05 level of significance.

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Answer:

4 months

Step-by-step explanation:

(2000 *6)/100 = 120

120x = 480

X = 480/120

X = 4 months

The required system of inequality can be used to determine is 52 < c + 3.75x.

Let us assume the compact cars be x in number. So, allowed value of full size cars is (12 - x). Now, forming the expression about total weight -

Total weight < weight of ferry + number of compact cars × weight of one compact car + weight of full size cars × number of full size cars

Keeping the representative values and letters in the expression -

25 < c + 1.5x + 2.25 (x - 12)

25 < c + 1.5x + 2.25x - 27

25 + 27 < c + 3.75x

52 < c + 3.75x

Thus, the required system of inequality is 52 < c + 3.75x.

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Answer:

The area if the triangle is 15 yd^2

Step-by-step explanation:

The formula to find the area if a triangle is base × height ÷ 2. So for this question it is 10×3÷2=15

Answer:

One solution

Step-by-step explanation:

y = 2x + 3

y = -5x - 2

2x + 3 = -5x - 2

Add 5x to both sides;

7x + 3 = -2

Subtract 3 from both sides;

7x = -5

Divide both sides by 7;

\(x=-\frac{5}{7}\)

Using the inequality concept, the expression which models the maximum

number of days in which she can rent the car is 56. 37x + 45 ≤ 440.

Maximum amount allowed to spend

= $440

Rental car company fixed charge per day to rent a car = $56.37

Hawa drives a car to 500 miles.

Rate per mile drive = $0.09

let x days be maximum number of days hawa afford rent with budget.

the inequality equation exists here is

(days × charge of rent per day) + (rate per mile x number of miles) ≤ 440

=> 56.37x + 0.09 × 500 ≤ 440

=> 56.37x + 45 ≤ 440

Therefore, the required inequality is 56.37x + 45 ≤ 440

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Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:

Step-by-step explanation:

Follow PEMDAS

P = parenthasees

E = exponents

M = multiplication

D = division

A = addition

S = subtraction

There are no P or E or M

so divide

-3 = h + 4

then we just subtract four on both sides

h = -7

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.

The resulting truth table will have eight rows representing all the possible combinations of true (T) and false (F) values for p, q, and c.

To construct the truth table for the logical expression "(p → q) ↔ (p → c)", we need to consider all possible combinations of truth values for the variables p, q, and c. Since each variable can take on either true (T) or false (F), there are a total of 2^3 = 8 possible combinations.

The first column of the truth table represents the values of p, and the second column represents the values of q. The third column represents the values of c. We evaluate the expression "(p → q)" by looking at the truth values of p and q. Similarly, we evaluate the expression "(p → c)" by considering the truth values of p and c. Finally, we compare the two expressions using the equivalence operator (↔) to determine the truth value of the entire expression.

By considering all possible combinations of truth values for p, q, and c and evaluating the expression "(p → q) ↔ (p → c)", we can construct the complete truth table. Each row in the truth table corresponds to a specific combination of truth values, and the last column represents the resulting truth value of the expression for each combination.

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Answer:

The equation representing the relationship is;

Amount charged to work a dog once a day = $1.25 * Number of days

Step-by-step explanation:

Here, we want to find the equation representing the relationship between the charges and the number of days

Firstly, he charges $6.25 to walk a dog a day for 5 days, the amount charged per day will be $6.25/5 = $1.25

For the 7 days, amount charged = 8.75/7 = $1.25

This means he charges an amount of $1.25 to walk a dog once a day

The equation that represents the relationship is thus;

Amount charged = $1.25 * Number of days

The perimeter of the triangle when calculated comes out to be 18x² + 2x + 4 units

Perimeter is defined as the length of the boundary of a shape. The perimeter of a triangle can be defined as the sum of the length of the sides

Given:

a = 12x² + 3

b = x² - 3x + 7

c = 5x² + 5x - 6

Therefore perimeter is calculated by the sum of all the sides.

P = 12x² + 3 + x² - 3x + 7 + 5x² + 5x - 6

To add these expressions, we have to identify the like terms that are the terms with the same variables.

Like terms are: 12x², x², and 5x²

-3x, 5x

3, 7, -6

Thus on addition, it becomes

P = 18x² + 2x + 4 units

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Since each trait is inherited independently, we can multiply the probabilities together. The probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

The probability of obtaining A/a; B/b; C/c; D/d offspring can be calculated by multiplying the probabilities of each individual trait. Since each trait is inherited independently, we can multiply the probabilities together.

The probability of obtaining A/a offspring is 1/2 (A is dominant and a is recessive).

The probability of obtaining B/b offspring is 1/2 (B is dominant and b is recessive).

The probability of obtaining C/c offspring is 1/2 (C is dominant and c is recessive).

The probability of obtaining D/d offspring is 1/2 (D is dominant and d is recessive).

Therefore, the probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

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Answer:

175 X 72% = 126

175 - 126 = 49

Answer 49

Step-by-step explanation:

Answer:

C. 1.2009

Step-by-step explanation:

1.3240 + 1.4872 = 2.8112

4.0121 - 2.8112 = 1.2009 - C

The expression that equals 2D−3C in standard form is -2s² - 11s - 7

Algebraic expressions are defined as expressions that are composed of coefficients, variables, terms,  factors and constants.

From the information given, we have that;

D=1−s^2 −s and C=3+3s,

To determine the expression for 2D - 3C

substitute the values of the expressions, we get;

2(1-s² - s) - 3(3 + 3s)

expand the bracket

2 - 2s² - 2s - 9 -9s

collect the like terms or factors, we get;

-2s² - 2x - 9s - 9 + 2

Add or subtract the values

-2s² - 11s - 7

Hence, the expression is -2s² - 11s - 7

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To prove that at any party of 31 people, there's always a person who knows an even number of others, we can use the pigeonhole principle.

The pigeonhole principle states that if we distribute more than "n" objects into "n" boxes, then at least one box must contain more than one object. In this case, the "objects" represent the people at the party, and the "boxes" represent the number of people each person knows.

Let's assume, for the sake of contradiction, that every person at the party knows an odd number of others. This means that each person has an odd number of acquaintances.

Now, let's consider the sum of the number of acquaintances for all 31 people. Since each person knows an odd number of others, the sum of odd numbers is also an odd number.

However, if we count the total number of acquaintances in a group, it must be even since each acquaintance involves two people. This creates a contradiction because we cannot have both an odd and an even sum for the total number of acquaintances.

Therefore, our assumption that every person knows an odd number of others must be false. Hence, there must be at least one person at the party who knows an even number of others.

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