A firefighter sees a woman trapped in a building 15 feet up from the bottom floor. The firetruck is parked 35 feet away from the bottom of the building. At what angle of elevation, to the nearest degree, should the firefighter extend the ladder to reach the woman?

Answer:

( ×3 + 5 × 2 + 3 ) + (2×3 - 5×2)

1(3+5×2+3) +1(2×3-5×2)

(3+10+3) + (6-10)

16+(-4)

16-4=

12

Answer:

b.8+10b,the cost would be $88

Step-by-step explanation:

if she buys 8 books worth $10 each

so 8×10= 80

plus $8 for shipment

so $80 +$8 =$88

In a four-candidate race with 107 votes cast, the smallest number of votes a winning candidate can have is 28.

In a four-candidate race decided by plurality, the winning candidate is the one who receives the most votes, regardless of whether that number of votes constitutes a majority (more than 50%) of the total votes cast.

To determine the smallest number of votes a winning candidate can have in a four-candidate race with 107 votes cast, we can assume that the other three candidates each receive an equal number of votes, say x. Then, the winning candidate must receive more votes than each of the other three candidates.

So, the minimum number of votes the winning candidate can receive is x + 1.

The total number of votes cast in the election is:

x + x + x + (x + 1) = 4x + 1

Since we know that 4x + 1 = 107, we can solve for x:

4x + 1 = 107

4x = 106

x = 26.5

Since x must be a whole number, we can round up to x = 27.

Then, the minimum number of votes the winning candidate can have is:

27 + 1 = 28

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The sampling design used in this scenario is cluster sampling.

Cluster sampling involves dividing the population into groups or clusters (in this case, the 15 towns) and randomly selecting entire clusters to be included in the sample. In this case, the intern randomly selected 20 customers from each town, which means that the clusters were the towns themselves.

Cluster sampling is a practical and efficient sampling method when it is difficult or expensive to access individual elements of the population. By selecting entire clusters, the sampling process becomes more manageable, and it can reduce costs and logistical challenges.

However, it's important to note that cluster sampling introduces the possibility of within-cluster similarity, meaning that individuals within the same cluster may have similar characteristics or behaviors. This can affect the variability of the sample and the generalizability of the findings to the entire population. It is important to consider this potential bias and account for it in the data analysis and interpretation.

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According to the solution we have come to find that, The value of p/n is 3/8.

Mean is a statistical term that refers to the average value of a set of numbers. It is calculated by summing up all the values in the set and then dividing the sum by the total number of values.

Let's use the formula for the weighted average to solve this problem:

weighted average = (sum of values * weight) / (total weight)

Let p be the number of students in the first class and n be the number of students in the second class. Then, we can write:

(p * 70 + n * 92) / (p + n) = 86

Expanding the numerator:

70p + 92n = 86(p + n)

Simplifying and rearranging:

16p = 6n

p/n = 6/16 = 3/8

Therefore, the value of p/n is 3/8.

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sorry, you took space in my question place just to get points for it and i think it's only fair if i do so back :) i hope you don't do this to other people though because it's really frustrating to not get your question answered and just write random stuff ^^ have a great day.

The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:

What are the options?

Step-by-step explanation:

The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Given:

The inequality is:

\(y>2x-3\)

The point is (3,3).

To find:

Whether the coordinate pair (3, 3) is a solution to the given inequality or not.

Solution:

We have,

\(y>2x-3\)

Check the inequality for the point (3,3). Substituting \(x=3,y=3\), we get

\(3>2(3)-3\)

\(3>6-3\)

\(3>3\)

This is a false statement because 3 is not greater than itself.

Since (3,3) does not satisfy the given inequality, therefore (3,3) is not a solution to the given inequality.

Now we can check the solution graphically. From the graph it is clear that the point (3,3) lies on the boundary line.

The boundary line is a dotted line, it means the point on the boundary line are not included in the solution set.

Therefore, (3,3) is not a solution to the given inequality.

Answer:

(2,2)

Step-by-step explanation:

2x+3y=10

x−2y=−2

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+3y=10,x−2y=−2

To make 2x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 2.

2x+3y=10,2x+2(−2)y=2(−2)

Simplify.

2x+3y=10,2x−4y=−4

Subtract 2x−4y=−4 from 2x+3y=10 by subtracting like terms on each side of the equal sign.

2x−2x+3y+4y=10+4

Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.

3y+4y=10+4

Add 3y to 4y.

7y=10+4

Add 10 to 4.

7y=14

Divide both sides by 7.

y=2

Substitute 2 for y in x−2y=−2. Because the resulting equation contains only one variable, you can solve for x directly.

x−2×2=−2

Multiply −2 times 2.

x−4=−2

Add 4 to both sides of the equation.

x=2

The system is now solved.

x=2,y=2

Correct choice is D) 2,2

Answer:

1. B

2. G

3. A

4. G

Step-by-step explanation:

Hope this helps. Not 100% sure about the final one but if nobody answers by the time its due go ahead and use what you got.

Alicia want that 50 % of all people who visited one of the three coffee shops should visit her every week.

Total visitors to the other two coffee shops during one week = 840+1,220 i.e. 2,060

Total visits to Cool Beans should be 50 % of total visits i.e. equal to visits of the other two cafes combined

Visits to Cool Beans should be 2,060

Current Visits =548

Additional visits =2,060-548 i.e. 1,512 visits

Note for better understanding:

same or the demand of coffee will remain same, then the Additional people will be calculated as:

Total number of visits = 584+840+1,220  i.e. 2,608

Target number of visits =50 % of total visits i.e. 1,304 visit

Additional visits = 1,304-548 = 756 visits

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The disparities between the actual and anticipated values in a regression model were referred to as residuals in the context Tufte provided.

American statistician Edward Rolf Tufte is a retired professor of political science, statistics, and computer science at Yale University.

Tufte talked about the idea of residuals. The discrepancies between the actual value and the projected value are known as residuals in statistics. Depending on whether the observed value is higher or lower than the projected value, they might be either positive or negative.

A model's residuals offer a gauge of how well it matches the data. According to him, residual plots are a great tool for seeing issues with the model fit and spotting outliers that might be skewing the results.

In contrast to relying exclusively on statistical tests, Tufte emphasised the significance of visually evaluating residuals since graphs can highlight patterns and correlations that may be missed in the numbers.

Overall, residuals are a key idea in statistics since they may be used to evaluate a model's reliability and point out its flaws.

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Answer:

P=9.0h

Step-by-step explanation:

Divide the Paid amount by the hours worked and you'll get how much money she gained every hour which is 8.50$ And the question is telling you which of the following equations is GREATER than the amount she got paid per hour. So the answer would be P=9.0h

The required equation represents an hourly pay rate that is greater than Hillary's hourly pay rate p = 9.0h. Option D is correct.

Given,

Hillary’s summer job at the frozen yogurt shop paid her the amounts shown in the table below in her first three days on the job (she got paid the same hourly rate every day).
                    day  =       1            2        3
Hours worked(h) =       5           4        6
Amount paid (p)  =   $42.50   $34     $51

The slope of the line is the tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.

The slope of the data given,
m = 42.5/5

m = 8.5
the slope shows the hourly rate to get paid.
Required expression is
p = 8.5h

From the option, the slope of equations needs to compare greater the slope greater will the hourly rate.
Slope of equation A = 1/8, B =8, C = 8.5 and D = 9.0
hence, only slope D has a greater value by the existing slope of 8.5

Thus, the required equation that represents an hourly pay rate that is greater than Hillary's hourly pay rate p = 9.0h.

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Question is incomplete, correct question has added below.

The population for 2015 is 1,640,000 ,so option A is correct.

Given:

The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.

where x is the number of years since 2005.

x = 2015 - 2005

x = 10

P(x) = x³ + 2x² - 8x + 520.

= \(10^{3} +2(10^{2} )-8*10+520\)

= 1000 + 2*100 - 80 + 520

= 1520 + 200 - 80

= 1720 - 80

= 1640.

Given the projected population in thousands so = 1640 * 1000

= 1640000.

Therefore The population for 2015 is 1,640,000 ,so option A is correct.

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

The possible number of trees in each of the rows could be any amongst the following numbers;

1,2, 5 and 10

Step-by-step explanation:

Here, we want to know the possible common number of trees in each rows

For the girls, we have 30 trees

For the boys we have 50 trees

What we simply do here is to get the factors of both;

That will be listed as follows;

for 30;

1,2,3,5,6,10,15 and 30

for 50,

1, 2 , 5,10, 25 and 50

So the possible number of trees in each of the rows are;

1, 2 , 5 and 10

To construct a grouped frequency distribution table (GFDT) for the given data set, we need to determine the class width and the first lower class limit.

To determine the optimal class width, we can use a formula such as the Sturges' rule or the Scott's rule. Sturges' rule suggests that the number of classes can be approximated as 1 + log2(n), where n is the number of data points. Scott's rule suggests using a class width of approximately 3.49 * standard deviation * n^(-1/3).

Once the class width is determined, the first lower class limit should be chosen as a multiple of the class width that accommodates the minimum value in the data set. It ensures that all data points fall within the class intervals.

To find the optimal class width and the first lower class limit for this data set, we need the total number of data points (which is not provided in the question). Once we have that information, we can apply the appropriate formula to calculate the class width and then select the first lower class limit accordingly.

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To maximize the amount of peaches produced by the orchard, the peach orchard owner should plant a certain number of trees per acre. The per-tree yield is given by the equation Y = 1200 - 15x, where Y represents the yield per tree and x represents the number of trees planted per acre.

To find the number of trees per acre that maximizes the crop yield, we need to determine the value of x that corresponds to the vertex of the equation. The vertex of a downward-opening parabola, represented by the given equation, occurs at the x-coordinate given by x = -b / (2a).

In this case, the coefficient of x is -15 and the constant term is 0, so b = 0 and a = -15. Substituting these values into the formula, we get x = -0 / (2 * -15) = 0.

While the mathematical calculation suggests that planting zero trees per acre would maximize the yield, this result is not practical. Therefore, the closest feasible value greater than zero would be 1 tree per acre.

For 1 tree per acre, substituting x = 1 into the equation, we find that each tree would produce a yield of Y = 1200 - 15 * 1 = 1185 peaches. Consequently, the resulting total yield would be 1185 peaches per acre.

Number of trees per acre: 1 tree per acre

Total yield: 1185 peaches per acre

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Interval estimation refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.

Interval estimation in statistics is the calculation of the interval or set of values in which the parameter is. For example, the mean (mean) of the population is most likely to be located. The confidence coefficient is calculated by choosing intervals in which the parameter falls with a probability of 95 or 99 percent. Consequently, the intervals are referred to as confidence interval estimates. The formula for estimating an interval is, \( \mu = \bar x ± Z_{ \frac{\alpha}{2}}(\frac{\sigma}{\sqrt{n}})\)

Where, the confidence coefficient

The purpose of the interval estimate is to quantify the precision of the point estimate. So the desired answer is an interval estimate.

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Answer:

-4n-5=0 n=-5/4

Step-by-step explanation:

Answer:

-4n-5

Step-by-step explanation:

have a good day and also for question like this use (mathpapa)

Answer:

Graph C

Step-by-step explanation:

The slope is 2 and to find the numbers in the equation are actually the opposite of what they appear, making the point (-2,1).

She uses 1/2 quart of yellow paint for every 9/2 quarts of blue paint. Then, she uses 1/2 quart of yellow paint for every 1/2 + 9/2 = 10/2 = 5 quart of paint.

We can use the next proportion:

Solving for x:

She uses 1/10 quart of yellow paint for every quart of paint

Answer:

$7665

Explanation:

simple interest: principal * rate (%) * time (years)

Given:

principal: $3,500

rate: 7%

time: 17 years

Solve for interest received:

3,500 * 7% * 17

$4165

Total money in account:

$4165 + $3,500

$7665

Answer:

q=3s+4t

q-4t=3s

(q-4t)/3=s

Step-by-step explanation:

Anse

draw the line down the equal sign

Step-by-step explanation:

Answer:

Step-by-step explanation:

add 9 to both and then cancel out both 9s and add 3 and 9 together

By applying the Master Theorem to the original recurrence relation T(n) = 3 * T(n/2) + 18, we find that it simplifies to T(n) = 3 * T(n/2) + O(1), indicating that the explicit formula has the same asymptotic growth as the original recurrence relation(B).

Divide and conquer part:

The recursive call is T(n/2), indicating that the problem is divided into two subproblems of size n/2.

Work per level:

The work done outside the recursive calls is constant, which is represented by 18.

Combine:

The combining step is represented by the   T(n) = 3 * T(n/2) + 18.

According to the Master Theorem, if a recurrence relation can be expressed in the form T(n) = a * T(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is an asymptotically positive function, we can determine the solution based on the relationship between a, b, and f(n).

In this case, we have a = 3, b = 2, and f(n) = 18. Comparing these values with the Master Theorem cases:

If f(n) = O(n^c) for some constant c < log_b(a), then T(n) = Theta(n^log_b(a)).

If f(n) = Theta(n^log_b(a) * log^k(n)), where k ≥ 0, then T(n) = Theta(n^log_b(a) * log^(k+1)(n)).

If f(n) = Omega(n^c) for some constant c > log_b(a), and if a * f(n/b) ≤ k * f(n) for some constant k < 1 and sufficiently large n, then T(n) = Theta(f(n)).

In our case, a = 3, b = 2, and f(n) = 18. We can see that f(n) = O(1), which matches the first case of the Master Theorem.

Therefore, the simplified recurrence relation is T(n) = 3 * T(n/2) + O(1), and the correct answer is b) T(n) = 3 * T(n/2) + O(1).

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a) x1, x2, m1 >= 0 The first three constraints represent the marketing considerations, while the fourth constraint represents the number of machines that can be rented.

b)The optimal solution is found to be x1 = 88, x2 = 26, and m1 = 0. The profit at this solution is $17,400.

c)If each car contributed $310 to profit, the new optimal solution would be x1 = 88, x2 = 0, and m1 = 98. The profit at this solution is $17,900.

d)If Carco were required to produce at least 86 cars, the new optimal solution would be x1 = 86, x2 = 26, and m1 = 0. The profit at this solution is $17,200.

a. Formulating the LP

The LP can be formulated as follows:

Maximize: z = 300x1 + 400x2 - 50m1

Subject to:

x1 + x2 <= 88

x2 <= 26

x1 + x2 <= 260

m1 <= 98

x1, x2, m1 >= 0

The first three constraints represent the marketing considerations, while the fourth constraint represents the number of machines that can be rented.

b. Solving the LP

The LP can be solved using the simplex algorithm. The optimal solution is found to be x1 = 88, x2 = 26, and m1 = 0. The profit at this solution is $17,400.

c. Changing the profit per car

If each car contributed $310 to profit, the new optimal solution would be x1 = 88, x2 = 0, and m1 = 98. The profit at this solution is $17,900.

d. Increasing the minimum number of cars If Carco were required to produce at least 86 cars, the new optimal solution would be x1 = 86, x2 = 26, and m1 = 0. The profit at this solution is $17,200.

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