A ship is sailing in a straight line from its home port.
The distance-time graph shows 4 hours of the journey.
Work out the speed of the ship in these 4 hours.
Your final line must say,
Speed = . . . mph

Answer:

Step-by-step explanation:

4 x 14= 56

The best estimate of the effective borrowing cost if the loan is prepaid 5 years after origination is 8.40%.

The effective borrowing cost takes into account both the interest rate and any additional costs associated with the loan. In this case, the loan amount is $275,000, the interest rate is 5.8% with 12 compounding periods per year, and the maturity of the loan is 25 years.

To calculate the effective borrowing cost, we need to consider the interest payments and the up-front costs. The interest payments can be calculated using the given interest rate and compounding periods. The up-front costs, which are paid at closing, are stated as 10% of the loan amount.

To estimate the effective borrowing cost, we need to calculate the total amount paid over the 25-year term of the loan, including both interest payments and up-front costs. Once we have this total amount, we can determine the annualized rate that would result in the same cost.

By taking into account the loan amount, interest rate, compounding periods, maturity, and up-front costs, we can estimate that the effective borrowing cost if the loan is prepaid 5 years after origination is approximately 8.40%.

It's important to note that this is an estimate, as it assumes the loan will be prepaid after 5 years and does not consider any potential changes in interest rates or other factors that may affect the actual borrowing cost.

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Answer:

umm well i honestly forgot!

Step-by-step explanation:

but here is a fun fact During your lifetime, you will produce enough saliva

Answer:

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(a) The equilibrium point is approximately (26, 26) where quantity (x) and price (P) are both 26.

(b) Consumer surplus ≈ 434

(c) 434 dotars (d)  -1155 dotars.

To calculate the deadweight loss, we need to find the area between the supply and demand curves from the equilibrium quantity to the quantity \(x_C\).

To find the equilibrium point, we need to set the demand and supply functions equal to each other and solve for the quantity.

Demand function: D(x) = 61 - x
Supply function: S(x) = 22 + 0.5x

Setting D(x) equal to S(x):
61 - x = 22 + 0.5x

Simplifying the equation:
1.5x = 39
x = 39 / 1.5
x ≈ 26

(a) The equilibrium point is approximately (26, 26) where quantity (x) and price (P) are both 26.

To find the point (\(x_C\), \(P_C\)) where the price ceiling is enforced, we substitute the given price ceiling value into the demand function:

P_C = $30
D(\(x_C\)) = 61 - \(x_C\)

Setting D(\(x_C\)) equal to \(P_C\):
61 - \(x_C\) = 30

Solving for \(x_C\):
\(x_C\) = 61 - 30
\(x_C\) = 31

(b) The point (\(x_C\), \(P_C\)) is (31, $30).

To calculate the new consumer surplus, we need to integrate the area under the demand curve up to the quantity \(x_C\) and subtract the area of the triangle formed by the price ceiling.

Consumer surplus

\(=\int[0,x_C] D(x) dx - (P_C - D(x_C)) * x_C\\=\int [0,x_C] (61 - x) dx - (30 - (61 - x_C)) * x_C\\=\int [0,31] (61 - x) dx - (30 - 31) * 31[61x - (x^2/2)]\)
evaluated from

0 to 31 - 31[(61*31 - (31²/2)) - (61*0 - (0²/2))] - 31[1891 - (961/2)] - 311891 - 961/2 - 311891 - 961/2 - 62/2(1891 - 961 - 62) / 2868/2
Consumer surplus ≈ 434

(c) The new consumer surplus is approximately 434 dotars.

To calculate the new producer surplus, we need to integrate the area above the supply curve up to the quantity \(x_C\).

Producer surplus \(= (P_C - S(x_C)) * x_C - \int[0,x_C] S(x) dx(30 - (22 + 0.5x_C)) * x_C - \int[0,31] (22 + 0.5x) dx(30 - (22 + 0.5*31)) * 31 - [(22x + (0.5x^2/2))]\)
evaluated from 0 to 31(30 - 37.5) * 31 - [(22*31 + (0.5*31²/2)) - (22*0 + (0.5*0²/2))](-7.5) * 31 - [682 + 240.5 - 0](-232.5) - (682 + 240.5)(-232.5) - 922.5-1155
(d) The new producer surplus is -1155 dotars. (This implies a loss for producers due to the price ceiling.)

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Answer:

B

Step-by-step explanation:

Edge 2021

The MAD value will be = 3.

Given,

Last four months sale : 8 , 10 , 15 , 9 .

Last four forecasts were 5, 6, 11, and 12 units.

Now, we have to find the Mean Absolute Deviation (MAD) of these forecasts.

Now, the mean of the forecast values for the four months is .

Therefore, the sum of absolute deviations of the forecast values from that mean will be = |5 - 8.5| + |6 - 8.5| + |11 - 8.5| + |12 - 8.5| = 3.5 + 2.5 + 2.5 + 3.5 = 12.

Therefore, the MAD value will be = 12/4

MAD = 3

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Answer:

yes

Step-by-step explanation:

Answer:

as a trapezoid, a rectangle, and two squares

The expression for 'r' will be;

⇒ r = √(g m₁ m₂ / f)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ f = g m₁ m₂ / r²

Now,

Solve the expression for r as;

The expression is,

⇒ f = g m₁ m₂ / r²

Multiply by r², we get;

⇒ f r² =  g m₁ m₂

Divide by f, we get;

⇒ r² =  g m₁ m₂ / f

Take square root, we get;

⇒ r = √(g m₁ m₂ / f)

Thus, The expression for 'r' will be;

⇒ r = √(g m₁ m₂ / f)

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Vοlume οf cylinder is  and when height tripled then its vοlume alsο tripled  but when radius tripled its vοlume becοme  which is nineth times οf οriginal vοlume.

Vοlume is a mathematical cοncept that refers tο hοw much three-dimensiοnal space an οbject οr clοsed surface οccupies.

Vοlume οf cylinder = πr²h

= π × 4² × 10

= 160π m³

When the height is tripled, h becοmes 3h

So, new height = 3 × 10 = 30m

Volume of a Cylinder (when height is tripled) = π × (4)² × 30

= π × 16 × 30

= 480π m³

When height is tripled then vοlume alsο tripled.



When the radius is tripled, r becοmes 3r

So, new radius = 3 × 4 = 12m

Volume of a Cylinder (when radius is tripled)

= π × (12)² × 10

= 1440 m³

But when radius is tripled the vοlumes becοme Nine times.

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Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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The choice c is correct When a modeling technique is referred to as a "black box," it means that the equation that develops within the model cannot be understood.  

A model known as a "black box" is one in which the model's internal workings or logic are not readily apparent to the user. All in all, the model takes in data sources and delivers yields, yet the middle of the road steps or computations included are stowed away from the client.

This absence of interpretability makes it trying to comprehend how the model shows up at its expectations or choices. In complex machine learning algorithms like neural networks, where accuracy is prioritized over understanding the underlying mechanisms, black box models are frequently utilized.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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(a) The limiting value for the logistic function is 1, meaning that as age increases, the probability of death upon contracting measles at that age approaches 100%.

(b) The limiting value of 1 indicates that as age increases, the risk of death from measles becomes almost certain.

(a) In the given model, the logistic function has a limiting value of 1. As age (t) increases, the probability of death from measles approaches 1, meaning that it becomes almost certain. This limiting value represents the maximum probability of death from measles that can be reached within the context of the model. It can be interpreted as the carrying capacity or upper bound for the probability of death from measles.

(b) In practical terms, the limiting value of 1 means that as individuals grow older, their vulnerability to death upon contracting measles increases significantly. The logistic model predicts that there is a point beyond which the risk of death becomes almost inevitable for individuals infected with measles. This underscores the importance of early vaccination and preventive measures, as they play a crucial role in reducing the risk of contracting measles at an early age when the probability of death is relatively lower.

(c) To find the age at which the model predicts a mortality rate of 50% (P = 0.5), we can set the given probability equation to 0.5 and solve for t. Substituting P = 0.5 into the equation, we get 0.5 = 1 / (1 + 77.39e^(-0.08t)). Solving this equation for t gives us t ≈ 8.66 years (rounded to two decimal places). Therefore, according to the model, the predicted age at which the mortality due to measles is 50% is approximately 8.66 years.

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Answer:

y = 1/5x - 1.

Step-by-step explanation:

Slope intercept form: y = mx + b

in this equation, the m is the slope (the amount the line moves vertically divided by the amount it moves horizontally from one point to another) and the b is the y-intercept (meaning where the line meets with the y-axis when graphed).

So, m is equal to 1/5 because that is the slope.

Now, to find b (the y-intercept), I am going to plug in the coordinate values of the point (20,-5) into the equation.

The 20 is the x coordinate and the -5 is the y-coordinate because the point is written in (x, y) form.

Here's how it looks with everything plugged in:

-5 = 1/5(20) + b.

The slope-intercept form is y = mx + b, and I just plugged in my values where

y (y-coordinate)= -5

m (slope)= 1/5

x (x-coordinate) = 20

Now that I know everything, I just need to solve for b, the y-intercept:

-5 = 1/5(20) + b.

-5 = 4 + b (simplified)

-1 = b

so, the y-intercept is -1.

Now, in slope-intercept form, the answer is: y = (1/5)x - 1.

hope this helped <3

Answer:

The sheet should be turned up 7.5cm on each side to obtain maximum volume.

Step-by-step explanation:

If we make a rectangular eavesdrop, by bending the sheet along dotted line, then.

Height of eaves trough = x cm

Length of eaves trough = 600 cm

Width of eaves trough =  (30 - 2x) cm

We know that Volume is given by:

V = Length · Width · Height

V = (x)(30 - 2x)(600)

V = -1200x² + 18000x

To maximize the volume, we take the derivative and put it equal to zero.

\(\frac{dV}{dx} =\frac{d}{dx}( -1200x^2 +18000x)=0\\\frac{d}{dx}( -1200x^2 +18000x) = 0\\-(2)1200x+18000=0\\-2400x+18000=0\\x=\frac{18000}{2400}\\ x=7.5cm\)

Answer:

range

Step-by-step explanation:

,domain describes the input values and range describes the output

The triangles are similar by the AA similarity criterion since they have two pairs of congruent angles (41° and 109°, and 30°). Therefore, the answer is B. AA.

A triangle is a polygon that has three sides, three vertices, and three angles. It is the simplest polygon in Euclidean geometry and one of the most studied shapes in mathematics. The sum of the three angles in a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the other two sides. There are many different types of triangles, including equilateral triangles (where all sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where no sides are equal). Triangles are used in many areas of mathematics and science, including trigonometry, geometry, and physics.

Here,

To determine whether the two triangles are similar using AA similarity, we need to compare the angles of both triangles.

Triangle 1 has angles 41°, 30°, and 109°.

Triangle 2 has angles 30°, 41°, and 109°.

We see that the two triangles have two pairs of congruent angles, namely 41° and 41°, and 109° and 109°. Therefore, the two triangles are similar by the AA similarity criterion.

Note that the order of the angles does not matter when comparing triangles for similarity.

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Answer:

z score

Step-by-step explanation:

9514 1404 393

Answer:

  D.) a+2b

Step-by-step explanation:

The integers 'a' and 'b' can be any, so you can choose a couple and evaluate these expressions to see what you get. For example, we can let a=1 and b=0. For these values, the offered expressions evaluate to ...

  A) 3(0) = 0 . . . even

  B) 1 +3 = 4 . . . even

  C) 2(1+0) = 2 . . . even

  D) 1 +2(0) = 1 . . . odd

_____

Additional comment

These rules apply to even/odd:

Then A is (odd)(even) = even; B is (odd)+(odd) = even; C is (even)(whatever) = even; D = (odd)+(even) = odd.

From the given information provided, the probability of event F given that event E has occurred is 0.5.

Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:

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

To find P(F/E), we use the conditional probability formula:

P(F/E) = P(E and F) / P(E)

We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:

P(F/E) = 0.1 / 0.2

Simplifying this expression, we get:

P(F/E) = 0.5

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Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45

Step-by-step explanation:

No of questions= 60,

Answers to be given= 75%

then no of questions to pass the exam= No of questions*Answers to be given in percentage

=60*75/100\

=45

Complete question:

Joel has a goal to practice his clarinet for 4 1/2 per week. The list below shows the number of hours Joel has a practiced so far for the week. Monday 1 1/2 hours Wednesday 1 1/4 hours Thursday 1 hour How many more hours does he need to practice this week to meet his goal

Answer: 3/4 hours

Step-by-step explanation:

Target hours = 4 1/2 hours = 9/2 hours

Number of hours so far :

(1 1/2 + 1 1/4 + 1) = (3/2 + 5/4 + 1) hours

Total so far :

L. C. M of denominator = 4

(6 + 5 + 4) /4 = 15/4

Number of hours left to meet his target equals :

Target hours - total so far

( 9/2 - 15/4)

L. C. M of denominator = 4

(18 - 15) / 4 = 3/4 hours

.

Answer:

Step-by-step explanation:

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

y = mx + b

3y - 9 = 12x

3y = 12x + 9 (divide by common denominator 3)

y = 4x + 3

The Multiplicative Inverse of postive 146 is  0.00684932.

What is Multiplicative Inverse?

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1, or 1/a, stands for the multiplicative inverse of the letter "a". In other terms, two numbers are said to be multiplicative inverses of one another when their product is 1.

The division of 1 by a number yields the multiplicative inverse of that number. The number's reciprocal is another name for it. According to the multiplicative inverse formula, a number's product with its reciprocal is 1.

Given number for the multiplicative inverse is 146;

so, If the Multiplicative Inverse of 146 is x

then , the problem can be written as a function as follows:

146(x) = 1

Thus, to get the answer, we divide 1 by 146 like this:

1 / 146 = 0.00684932

Therefore,the Multiplicative Inverse of postive 146 is  0.00684932.

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