132 days to 110.4 days

Answer:

I believe the answer is 11 miles

Step-by-step explanation:

I drew the problem out and used the Pythagorean theorem and got 11.2

Hope this helps you!

38 °F is the temperature after 5 hours of time.

Two or more expressions with an Equal sign is called as Equation.

Given that the temperature is 36 °F.

The temperature decreases for 4 hrs

Each hour, the temperature decreases by 2 °F.

1 hour=  2 °F.

For 4 hours it will be 4(2)=8 °F.

So the temperature after 4 hours is 36-8=28 °F.

the temperature rises 10 °F in one hour

28 °F+10°F=38 °F

Hence, the temperature after 5 hours is 38 °F.

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Answer:

B.  p - 200

Step-by-step explanation:

Start with the original price, p.

When the price is reduced by $200, you are taking away $200 from the price, so you need to subtract $200 from the original price, p.

Answer:  B.  p - 200

To show that the maximum likelihood estimator (MLE) of p, denoted as p = Y, is the uniformly minimum variance unbiased estimator (UMVUE) that achieves the Cramer-Rao lower bound, we need to demonstrate two things: unbiasedness and efficiency.

Unbiasedness:

The estimator p = Y is unbiased if E[p] = p for all values of p. Let's calculate the expected value of p:

E[p] = E[Y] = E[(Y₁ + Y₂ + ... + Yₙ)/n]

Since each Yᵢ follows a Bernoulli distribution with parameter p, we have E[Yᵢ] = p. Therefore:

E[p] = E[(Y₁ + Y₂ + ... + Yₙ)/n] = (E[Y₁] + E[Y₂] + ... + E[Yₙ])/n = (p + p + ... + p)/n = p

Hence, p^ is an unbiased estimator of p.

Efficiency (Cramer-Rao lower bound):

To assess efficiency, we can calculate the variance of p^ and compare it with the Cramer-Rao lower bound, which represents the minimum achievable variance for an unbiased estimator.

The variance of p^ can be derived as follows:

Var[p] = Var[Y] = Var[(Y₁ + Y₂ + ... + Yₙ)/n]

Since each Yᵢ follows a Bernoulli distribution with variance Var[Yᵢ] = p(1-p), we have:

Var[p] = Var[(Y₁ + Y₂ + ... + Yₙ)/n] = (Var[Y₁] + Var[Y₂] + ... + Var[Yₙ])/n² = (p(1-p) + p(1-p) + ... + p(1-p))/n² = (np(1-p))/n² = p(1-p)/n

Now, according to the Cramer-Rao inequality, the variance of any unbiased estimator is lower bounded by 1/(nI(p)), where I(p) is the Fisher information of the distribution.

For the Bernoulli distribution, the Fisher information is I(p) = 1/(p(1-p)). Therefore, the Cramer-Rao lower bound is 1/(nI(p)) = 1/(np(1-p)).

Comparing this with Var[p], we have:

Var[p] = p(1-p)/n ≤ 1/(np(1-p)) = 1/(nI(p))

The inequality holds because p(1-p) ≤ 1/4 for any p in the interval (0,1).

Hence, Var[p] achieves the Cramer-Rao lower bound, making p the UMVUE for parameter p in the Bernoulli distribution.

In conclusion, the MLE p = Y is both unbiased and efficient, achieving the Cramer-Rao lower bound.

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Answer: 36.3m

Step-by-step explanation:

To solve this, we can draw two triangle rectangles, where the distance between the man and the base of the tower is one of the cathetus, the adjacent one, the height will be the opposite cathetus.

The triangle where the elevation angle is 58° is associated with the height of the tower without the aerial

The other triangle, where the elevation angle is 63° is associated with the height of the tower with the aerial.

Then we can calculate those two heights, then compute the difference, and the difference will be equal to the height of the aerial.

In both cases we want to calculate the opposite cathetus, then we should use the relation:

Tan(θ) = (Op. cath)/(Adj. cath)

The height without the aerial is h1, let's find it:

Tan(58°) = h1/100m

Tan(58°)*100m = h1 = 160m.

The height with the aerial is h2, let's find it:

Tan(63°) = h2/100m

Tan(63°)*100m = h2 = 196.3m

Then the height of the aerial will be:

h2 - h1 =  196.3m -  160m = 36.3m

To find the value of $c$, we need to complete the square to get the circle in the standard form of $(x-a)^2 + (y-b)^2 = r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius.

We begin by writing the given equation in the form of $(x^2 + 8x + 16) + (y^2 + 4y + 4) + c = 16 - 4 - c$, since $16+4=20$ will complete the square for both $x$ and $y$. Simplifying, we get $(x+4)^2 + (y+2)^2 = 9$, which is the equation of the circle with center $(-4,-2)$ and radius $3$. Therefore, $c = -16 -4 -9 = \boxed{-29}$.

To find the value of $c$ that makes the equation $x^2+8x+y^2+4y+c=0$ represent a circle with radius $3$, we first need to complete the square by adding and subtracting appropriate terms from both $x$ and $y$ terms. We can do this by adding $16$ and $4$ to both sides, which will complete the square for $x$ and $y$ respectively. Then, we simplify the equation to $(x+4)^2 + (y+2)^2 = 9$.

This equation is now in standard form $(x-a)^2 + (y-b)^2 = r^2$ where $(a,b)$ is the center of the circle and $r$ is the radius. Comparing this with the given equation, we see that $a=-4$, $b=-2$, and $r=3$. Therefore, $c$ can be found by subtracting $16+4+9$ from both sides, which gives us $c = \boxed{-29}$.

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The first five coefficients of an and bn are as follows: an bn1 0.015752 -0.00083 0.002234 -0.000255 0.00063

The given function is

I(t)=−(1/10)​e−50t+0.1.

The task is to determine the average value (a0​) using Fourier analysis and then express at least the first 5 coefficients of an​ and bn.

So, First, we have to find the Fourier series of I(t).

We can write the Fourier series of the function I(t) as follows:

Since the function I(t) is an even function, so we have only bn coefficients.

Now, we will calculate the average value of I(t).

a0​= (1/T) ∫T/2 −T/2 I(t) dt where T is the time period.

T = 2πωT=2π/50=0.1256a0​= (1/T) ∫T/2 −T/2 I(t) dt= 1/T ∫π/50 −π/50 −(1/10)​e−50t+0.1 dt= 1/T [−(1/5000)e−50t + 0.1t] [π/50,−π/50]= 0

Therefore, a0= 0.

Now, we will calculate the values of bn.

bn= (1/T) ∫T/2 −T/2 I(t) sin(nωt) dt taking T=0.1256

So, we have,bn= (1/T) ∫T/2 −T/2 I(t) sin(nωt) dt taking T=0.1256So,

we have, Now, we will calculate the first 5 coefficients of an​ and bn.

1) First coefficient of bn can be calculated by putting n = 1,So, b1= 0.01575.

2) Second coefficient of bn can be calculated by putting n = 2,So, b2= -0.0008.

3) Third coefficient of bn can be calculated by putting n = 3,So, b3= 0.00223.

4) Fourth coefficient of bn can be calculated by putting n = 4,So, b4= -0.00025.

5) Fifth coefficient of bn can be calculated by putting n = 5,So, b5= 0.00063.

Therefore, the first five coefficients of an and bn are as follows: an bn1 0.015752 -0.00083 0.002234 -0.000255 0.00063

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Answer:

angle b is 62 degrees. This is because if we solve for x, by putting the 2 equations equal to each other(because they are vertical angles), than we figure out that x=6. Now plug that into angle b's equation, and you get 62 degrees.

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

this seems like a continuation of the question which was answered previously

we know angle AEB=135, using vertical angle theorem, AEB and CED are congruent, so CED=135

Answer:

1. triange  2. trangle prism

Step-by-step explanation:

a) The number of grades in the array G is 20. b) The grades greater than 70 in the array G: 83, 75, 82, 76, 85, 71, 96, 78, 76, 72, 75, 83, 93. c) Mean is 73.6, median is 75.5, there is no mode and the standard deviation is 17.84. d) Mean better represents the "most typical grade."

10 To determine the number of grades in the array, we can use the length function in most programming languages. In this case, since the array G is given, the number of grades is the length of the array. Therefore, the number of grades in the array G is 20.

2) To find all the grades greater than 70 in the array G, we can iterate through each element of the array and check if it is greater than 70. Here are the grades greater than 70 in the array G: [83, 75, 82, 76, 85, 71, 96, 78, 76, 72, 75, 83, 93].

3) To compute the mean, median, mode, and standard deviation of the grades in array G, we can use various statistical formulas and functions. Here are the calculations:

Mean: The mean is the average of the grades in the array. To calculate it, we sum up all the grades and divide by the total number of grades.

Mean = (68 + 83 + 61 + 70 + 75 + 82 + 57 + 5 + 76 + 85 + 62 + 71 + 96 + 78 + 76 + 68 + 72 + 75 + 83 + 93) / 20 = 73.6

Median: The median is the middle value of the sorted array. First, we need to sort the grades in ascending order: [5, 57, 61, 62, 68, 68, 70, 71, 72, 75, 75, 76, 76, 78, 82, 83, 83, 85, 93, 96]. Since the number of grades is even, we take the average of the two middle values, which are 75 and 76.

Median = (75 + 76) / 2 = 75.5

Mode: The mode is the value(s) that appear most frequently in the array. In the array G, there is no mode because no grade appears more than once.

Standard Deviation: The standard deviation measures the dispersion or spread of the grades. We can use the formula for population standard deviation to calculate it.

Standard Deviation = \(\sqrt{\)((\((68 - 73.6)^2\) + \((83 - 73.6)^2\) + ... + \((93 - 73.6)^2\)) / 20) ≈ 17.84

4) The measure that better represents the "most typical grade" depends on the distribution of the grades. In this case, since there is no mode (no grade appears more than once), we cannot determine a single grade that represents the most typical. However, we can say that the mean and median give us different insights. The mean takes into account all the grades and provides an average value, while the median represents the middle value and is not affected by extreme values. Therefore, if the distribution is symmetric and does not have outliers, the median may be a better representation of the most typical grade. However, if the distribution is skewed or has outliers, the median may be less representative, and the mean could be influenced by those extreme values.

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The statement that is true is Airplane B has a lesser median. Option C

When calculating the median, we find the middle value for the data set of both planes

Airplane A  data set are 200, 205, 210, 215, 220, 225, 230, 234

Median = (215 + 220)/2 = 217.5

Airplane B's data set includes  180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235

Median = (205 + 210)/2 = 207.5

Therefore airplane B has a lesser median.

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Starting with the given differential equation:

du/dt = 2t + sec^2(t/2) * u

We can separate the variables by bringing all the u terms to the left-hand side and all the t terms to the right-hand side:

du / (2u) = (t + (1/2)sec^2(t/2)) dt

Now we integrate both sides:

∫ du / (2u) = ∫ (t + (1/2)sec^2(t/2)) dt

The integral on the left-hand side can be evaluated using logarithmic substitution:

ln|u| = (t^2)/2 + tan(t/2) + C1

where C1 is the constant of integration.

For the integral on the right-hand side, we use the substitution u = t/2 and du = (1/2)dt:

∫ (t + (1/2)sec^2(t/2)) dt

= ∫ (2u + sec^2(u)) 2du

= 2u^2 + 2tan(u) + C2

where C2 is another constant of integration.

Substituting back u = t/2 and combining with the left-hand side gives:

ln|u| = (t^2)/2 + tan(t/2) + C1

      = t^2/2 + tan(t/2) + C1 - ln|8|

where we use the initial condition u(0) = -8 to determine the value of the constant C1.

Simplifying this expression for u yields:

u = ±8e^(t^2/2 + tan(t/2) + C)  for some constant C.

To determine the sign of u, we use the fact that u(0) = -8, which implies that u must be negative. Therefore, we choose the negative sign:

u = -8e^(t^2/2 + tan(t/2) + C)

Finally, we use the initial condition to solve for C:

u(0) = -8 = -8e^(C)

=> e^C = 1

=> C = 0

Therefore, the solution to the differential equation with the given initial condition is:

u = -8e^(t^2/2 + tan(t/2))

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The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

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The laws of cosine , sine and the Pythagoras theorem can be used to find side length from angles .

The Law of Sines: This law states that the ratio of the sine of an angle to the length of the opposite side is constant for all sides of a triangle.

The Law of Cosines: This law states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the angle between them.

The Pythagorean Theorem: This theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

Therefore, the three stated methods can be used to find side length from angles

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The square root of 18 is 4.2426, rounded down to the closest whole number is 4. Testing the integer values 1 through 4 for division into 18 with a 0 remainder we get these factor pairs: (1 and 18), (2 and 9), (3 and 6). The factors of 18 are 1, 2, 3, 6, 9, 18.

Step-by-step explanation:

Answer:

1. function

2. function

3. not a function

Step-by-step explanation:

Answer:

i think its 15 gallons of water if you do the math you can see it

Step-by-step explanation:

c. incremental model Agile methods are iterative and incremental approaches to software development that prioritize customer satisfaction through the early and continuous delivery of working software.

The incremental model is a key aspect of agile methods, where the software is developed incrementally through a series of iterations or sprints. At the end of each iteration, user feedback is collected and incorporated into the next iteration, allowing the software to evolve and adapt to changing requirements. This approach allows for greater flexibility and responsiveness to user needs and helps ensure that the final product meets customer expectations.

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The 95% confidence interval for the average apple weight is (119.14, 125.86).

An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.

Let, n = 49

x = 122.5 

σ = 12

To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;

⇒ (x ± 1.96*σ/√n)

⇒ (122.5 ± 1.96*12/√49)

⇒ (119.14, 125.86)

Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).

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Answer:

90, 91, 92, 93, 94, 95, 96

The form of "research-data" which is likely to be used by quantitative research study than by a qualitative research study is (c) Economic data.

The Quantitative research depends on numerical data and statistical analysis to answer research questions, while

The Qualitative research depends on non-numerical data such as words, images, or observations to gain an understanding of the context of the phenomenon being studied.

The Economic data, such as data on income, expenditures, or market trends, is typically collected and analyzed using statistical methods, making it more suitable for quantitative research.

Therefore, the correct option is (c) economic data.

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The given question is incomplete, the complete question is

Which of the following forms of research or data would be more likely used by a quantitative research study than by a qualitative research study?

(a) interview data

(b) personal narrative data

(c) economic data

(d) archival data.

The team pays d - 3 dollars for each hat after the discount.

Cost is the amount of money required to purchase or produce a particular item or service. It is often represented by the symbol "C" in mathematical equations.

According to the given information:

Let's start by breaking down the given information:

The team buys 14 hats in total.

The total cost for the 14 hats is 14(d-3) dollars.

The team received a discount on each hat purchase.

To find the cost of each hat, we need to divide the total cost by the number of hats:

cost per hat = total cost / number of hats

Plugging in the given values, we get:

cost per hat = 14(d-3) / 14

Simplifying the expression by canceling out the common factor of 14, we get:

cost per hat = d - 3

Therefore, the team pays d - 3 dollars for each hat after the discount.

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Answer:

Borrowings = $0.10 Billion

Owner's Equity = $0.40 Billion

Step-by-step explanation:

Total liabilities = deposits + borrowings

Borrowings = total liabilities - deposits

Borrowings in 2017 = $14.60 - 11.90 = $2.70 billion

Borrowings in 2018 = $14.80 - $12.20 = $2.60 billion

Borrowings from 2017-2018= 2.60 - 2.70 = $0.10 billion

Owner's Equity= total assets - total liabilities

Owner’s equity in 2017 = $16.2 - $14.6 = $1.6 billion

Owner’s equity in 2018 = $16.8 - $14.8 = $2 billion

Owner's Equity from 2017-2018= 2 - 1.6 = $0.4 billion

Hope this helps!

The Owner's Equity for commercial banks in  2017-2018 is $0.4 billion.

The given is,

Borrowings = $0.10 Billion

Owner's Equity = $0.40 Billion

Total liabilities = deposits + borrowings

So we have Borrowings = total liabilities - deposits

Borrowings in 2017

= $14.60 - 11.90

= $2.70 billion

Borrowings in 2018

= $14.80 - $12.20

= $2.60 billion

Borrowings from 2017-2018

= 2.60 - 2.70

= $0.10 billion

Owner's Equity= total assets - total liabilities

Owner’s equity in 2017

= $16.2 - $14.6

= $1.6 billion

Owner’s equity in 2018

= $16.8 - $14.8

= $2 billion

Owner's Equity from 2017-2018

= 2 - 1.6

= $0.4 billion

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The interquartile range for the data set are

Andre

Interquartile Range: = 2

For Lin

Interquartile Range = 8

For Noah

Interquartile Range = 8

For Andre

Min: 25 the minimum number

Q1: 27 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 30 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 27 = 2

For Lin

Min: 20 the minimum number

Q1: 21 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 32 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 21 = 8

For Noah

Min: 13 the minimum number

Q1: 15 (the third position)

Median: 20 (the sixth position)

Q3: 23 (the 9th position)

Max: 25 (the maximum number)

Interquartile Range: Q3 - Q1 = 23 - 15 = 8

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Using the table of values, we have:

f(1) = 7,

g(1) = 4,

and f(g(1)) = f(4) = 1. Thus, f(g(1)) = 1.

g(5) = 1,

g(5) = 8. Thus, g(f(5)) = g(7) = 4. Therefore, g(f(5)) = 4.

Since f(9) is not in the table of values, we cannot evaluate it directly. However, we can use f(8) = 2, f(2) = 6, and f(6) = 5 to find f(f(9)).

f(f(9)) = f(f(8)) = f(2) = 6. Thus, f(f(9)) = 6.

Using the table of values, we have g(3) = 9, and 9(g(3)) = 9.

Therefore, 9(g(3)) = 9.

Thus, the values of the expressions are:

f(g(1)) = 1,

g(f(5)) = 4,

f(f(9)) = 6,

9(g(3)) = 9.

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When slave starting a disabled vehicle, the term that serves an important safety consideration is c. The slaving vehicle engine must be running while connecting the slave cable

The dead car is started while the live vehicle's engine is running by inserting a slave cable into the receptacle on each vehicle.

Vehicles with manual transmissions rely heavily on the clutch slave cylinder. When the pedal is depressed, the clutch is disengaged and the transmission is shifted thanks to the slave and clutch master cylinders.

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Answer: 90 degrees

Step-by-step explanation:

Complementary angles add up to 90 degrees. Since a triangle has 180 degrees total, the other angle is 90 degrees

Answer:

90°

Step-by-step explanation:

Acute angles are less than 90°

Complementary angles add up to 90°

Angles in a triangle is 180°

An acute angle +the other = 90°

If two of the angles in a triangle =90°, then the third angle will be

180-90°=90°