[In this question the unit vectors i and j are due east and due north respectively.] A coastguard station O monitors the movements of a small boat. At 10:00 the boat is at the point ( 4i−2j) km relative to O. At 12:45 the boat is at the point ( −3i−5j) km relative to O. The motion of the boat is modelled as that of a particle moving in a straight line at a constant speed. Calculate the speed of the boat, giving your answer in kmh−1 (3 marks)​

Based on the understanding of Pearson correlation, none of the provided conclusions can be determined solely based on the given information.

The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables, such as crime and the number of churches. It does not provide information about causation or the direction of the relationship.

The Pearson correlation coefficient ranges from -1 to +1. A positive correlation indicates that as one variable increases, the other tends to increase as well, but it does not imply causation. A negative correlation indicates that as one variable increases, the other tends to decrease, but again, causation cannot be determined solely based on correlation.

Therefore, without further information or evidence, we cannot conclude any of the provided options (B, C, or D). Correlation alone does not provide a basis for determining causation or making predictions about the effects of changing the number of churches on crime rates in an area.

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Answer:

D

Step-by-step explanation:

Suffrage is the right to vote, and the nineteenth amendment gave women the right to vote, and the indian citizenship act of 1924 gave native americans the right to vote

Answer:

5

Step-by-step explanation:

The change in x from (0,5) to (3,9) is 3 - 0 which is 3. The change in y is 9 - 5 which is 4. Using the Pythagorean theorem (using the two points as the endpoints of the hypotenuse in a right triangle) we get:

\(3^2+4^2=c^2\) where c is the distance between the two points (the hypotenuse of the right triangle). The equation simplifies to:

\(9+16=c^2\)

Which simplifies to:

\(\sqrt{25} =c\)

Thus, c (the distance between (0,5) and (3,9) is 5.

Hope this helps :)

Answer:

-3/2

Step-by-step explanation:

To find the slope, we use the slope formula

m = (y2-y1)/(x2-x1)

   = (-48- -24)/(19 -3)

   = (-48+24)/(19-3)

   = -24/16

   = -3/2

Answer:

\(-\frac{3}{2}\)

Step-by-step explanation:

The slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\)

Let:

\((x_1, y_1)=(3, -24)\\(x_2, y_2)=(19, -48)\)

Substitute into slope formula:

\(m=\frac{-48-(-24)}{19-3}=\frac{-24}{16}=\boxed{-\frac{3}{2}}\)

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Given:

\(P= (3,-4)\\\\Q=(-2,-4)\\\\\overrightarrow{PQ}=?\\\\Magnitude=?\\\\\text{Direction of the vector}=?\\\\\)

Calculating \(\overrightarrow{PQ}\):

\(\to \overrightarrow{PQ} = \overrightarrow{Q} -\overrightarrow{P}\)

          \(= (-2, -4) - (3,-4)\\\\= (-2\ -3, -4 \ -(-4)) \\\\= (-5 ,0)\\\\ = -5i+0j\)

Calculating magnitude:

\(\to || \overrightarrow{PQ} || = \sqrt{i^2+j^2}\)

               \(=\sqrt{-5^2+0^2}\\\\=\sqrt{25+0}\\\\=\sqrt{25}\\\\=5\)

Calculating the direction of the vector:

\(\overrightarrow{V} = \frac{\overrightarrow{PQ}}{|| \overrightarrow{PQ}||}\)

   \(= \frac{5i+0j}{5}\\\\= \frac{5i}{5}\\\\= i\)

After folding 26 shirts, Bob would have 2 shirts left to fold. To write an equation relating n to f, we need to start with the total number of shirts Bob has, which is 28. If he folds f shirts, then he will have (28 - f) shirts left to fold. So the equation is:

n = 28 - f
Now we can use this equation to find the number of shirts Bob would have left to fold after folding 26 of them. We simply plug in f = 26:
n = 28 - 26
n = 2
Therefore, after folding 26 shirts, Bob would have 2 shirts left to fold.

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Answer: i hope this will help you

a^x=y this is a simple equation

where as loga(in the base) y=x this is a logarithmic equation

Given:

Vertex: (-3, 3)

Focus: (-3, 2)

Let's find the distance from the point (x, y) to the focus of the parabola and the directrix.

To find the distance, apply the distance formula:

Thus, we have:

Distance from (x, y) to the focus:

Where:

(x1, y1) ==> (x, y)

(x2, y2) ==> (-3, 2)

Thus, we have:

Therefore, the distance from the point (x, y) to the focus is:

• The distance from the point to the directrix.

From the graph, the directrix is:

y = 4

Now, to find the distance, subtract the y-coordinate of the point from y = 4.

The distance is the absolute value of the result.

Thus, we have:

ANSWER:

Distance from the point to the focus:

Distance from the point to directrix:

Answer:

34m

Step-by-step explanation:

To find:-

Answer:-

We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .

We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;

\(\rm\implies a^2+b^2 = h^2 \\\)

Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .

So on substituting the respective values, we have;

\(\rm\implies h^2 = (16m)^2+(30m)^2 \\\)

\(\rm\implies h^2 = 256m^2 + 900m^2 \\\)

\(\rm\implies h^2 = 1156m^2\\\)

\(\rm\implies h =\sqrt{1156 \ m^2} \\\)

\(\rm\implies \red{h = 34 m} \\\)

Hence the distance between Elizabeth and Frank is 34m .

Answer:

Its A because -3 is x coordinate the x coordinate is the domain and it doesn't have the little line under the less than sign because the circle isn't filled in

The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.

Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.

One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.

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There are two scenarios in your question:

In this case, you can use each digit only once. There are 5 choices for the first digit, 4 choices for the second digit, 3 choices for the third digit, 2 choices for the fourth digit, and 1 choice for the last digit. So, the total number of 5-digit numbers that can be formed is 5 × 4 × 3 × 2 × 1 = 120.

In this case, you can use each digit as many times as you want. So, you have 5 choices for each of the 5 digits. the total number of 5-digit numbers that can be formed is 5 × 5 × 5 × 5 × 5 = 3,125.

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well your first term is obviously 5, then substitite n for 2, 3, and 4

a2 = a1+5 --> a2 = 12

a3 = a2 +5 --> a3 = 17

a4 = a3+ 5 --> a3 = 22

C, D , E, F are correct The following statements are correct:

c) With the input size N increasing, some of these runtime functions grow at different rates.

d) With the input size N increasing, runtime functions T(N) = N, T(N) = N + 999, and T(N) = 5 * N grow at the same scale.

e) With the input size N increasing, the growth rate of runtime function T(N) = 999 is constant.

f) Based on the scalability of growth rates of all these functions, we could use big O notation to categorize or classify these functions:

- T(N) = 999 is O(1) (The growth function is constant)

- T(N) = log₂N is O(logN) (The growth function is logarithmic)

- T(N) = N is O(N) (The growth function is linear)

- T(N) = N+999 is O(N)

- T(N) = 5*N is O(N)

- T(N) = N*log₂N is O(NlogN)

- T(N) = N² is O(N²)

Note: Statement b is incorrect because not all of these runtime functions grow at the same rate as the input size N increases. For example, T(N) = 999 does not change as N increases, while T(N) = N^2 grows much faster than T(N) = N as N increases.

Statement a is also incorrect because T(N) = 999 does not grow with increasing N. Its value remains constant at 999 for all N.

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Question

Which statements are correct about these following seven runtime functions :

T(N) = 999

T(N) = log2N

T(N) = N

T(N) = N + 999

T(N) = 5 * N

T(N) = N * log2N

T(N) = N2

Hints: Take a look at the  of these seven functions (growth rate of T(N) is defined as (T(N2) - T(N1))/T(N1) or (T(N2) - T(N1))/(N2-N1):

O(1) O(logN) O(N) O(Nlog N) O( N2)

N Alg. A T(N)=999 Alg. B T(N)=log2N Alg. C T(N)=N Alg. D T(N)=N+999 Alg. E T(N)=5*N Alg. F T(N)=Nlog2N Alg. G T(N)=N2

10000 999 13.287712 10000 10999 50000 132877.1238 1E+08

20000 999 14.287712 20000 20999 100000 285754.2476 4E+08

40000 999 15.287712 40000 40999 200000 611508.4952 1.6E+09

80000 999 16.287712 80000 80999 400000 1303016.99 6.4E+09

Multiple Correct Answers:

a) With the input size N increasing, all these runtime functions grows.

b) With the input size N increasing, some of these runtime functions grow at the same rate.

c) With the input size N increasing, some of these runtime functions grow at the different rates.

d) With the input size N increasing, runtime functions T(N) = N, T(N) = N + 999, and T(N) = 5 * N grow at the same scale.

e) With the input size N increasing, the growth rate of runtime function T(N) = 999 is constant.. With the input size N increasing, the growth rate of T(N) = 999 is constant.

f) Based on the scalability of growth rates of all these functions, we could use big O notation to categorize or classify these functions:

T(N) = 999 = O(1) (The growth function is constant)

T(N) = log2N = O(log2N) (The growth function is logarithmic)

T(N) = N = O(N) (The growth function is linear)

T(N) = N+999 = O(N)

T(N) = 5*N= O(N)

T(N) = 5*N + 999 = O(N)

the slope is 1/10

y2 - y1 / x2 - x1

The y-intercept is \(y=\frac{2}{5} x-4\)

The given curve is y = x³ − 2x and it has to be rotated about the x-axis to find the area of the surface. The formula to find the surface area of a curve obtained by rotating about the x-axis is given by:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx
$$Differentiating the curve with respect to x, we get:$$
y = x^3 - 2x
$$$$
\frac{dy}{dx} = 3x^2 - 2$$Now, squaring it, we get:$$
\left(\frac{dy}{dx}\right)^2 = 9x^4 - 12x^2 + 4$$$$
1 + \left(\frac{dy}{dx}\right)^2 = 1 + 9x^4 - 12x^2 + 4$$$$
= 9x^4 - 12x^2 + 5$$Putting the values in the formula, we get:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 12x^2 + 5} dx$$Simplifying it further, we get:$$
A = 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{(3x^2 - 1)^2 + 4} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 6x^2 + 5} dx$$Now, substituting $9x^4 - 6x^2 + 5 = t^2$, we get:$$(18x^3 - 12x)dx = tdt$$$$
(3x^2 - 2)dx = \frac{tdt}{3}$$When $x = -1$, $t = \sqrt{20}$ and when $x = 2$, $t = 5\sqrt{5}$Substituting the values in the formula, we get:$$
A = 2\pi \int_{\sqrt{20}}^{5\sqrt{5}} \frac{t^2}{27} dt$$$$
= \frac{28\pi}{27} \left[ t^3 \right]_{\sqrt{20}}^{5\sqrt{5}}$$$$
= \frac{28\pi}{27} \left[ 125\sqrt{5} - 20\sqrt{20} - 5\sqrt{5} + 2\sqrt{20} \right]$$$$
= \frac{28\pi}{27} \left[ 120\sqrt{5} - 18\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 9\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 18\sqrt{5} \right]$$$$
= \frac{56\pi}{27} \cdot 12\sqrt{5}$$$$
= \boxed{224\sqrt{5}\pi/3}$$Therefore, the area of the surface obtained by rotating the curve $y = x^3 - 2x$ about the x-axis is $\boxed{224\sqrt{5}\pi/3}$.

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The total area of the regions between the curves is 1.134π square units

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

x = ∛y

We have the interval to be

0 ≤ y ≤ 1

The area of the regions between the curves is then calculated using

\(A =2\pi \int\limits^a_b {f(x) * \sqrt{1 + (dy/dx)^2} } \, dx\)

From x = ∛y, we have

y = x³

Differentiate

dy/dx = 3x²

So, the area becomes

\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + (3x^2)^2} } \, dx\)

Expand

\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + 9x^4 } \, dx\)

Integrate

\(A =2\pi \frac{(9x^4 + 1)^{\frac{3}{2}}}{54}|\limits^1_0\)

Expand

\(A = 2\pi [\frac{(9(1)^4 + 1)^{\frac{3}{2}}}{54} - \frac{(9(0)^4 + 1)^{\frac{3}{2}}}{54}]\)

This gives

A = 2π * 0.5671

Evaluate the products

A = 1.1342π

Approximate

A = 1.134π

Hence, the total area of the regions between the curves is 1.134π square units

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Answer:

 the answer is  h 8ours

Answer:

who is he

Step-by-step explanation:

Answer:

The equation in slope-intercept form is:

\(y=\frac{1}{3}x+3\)

So the second option is the correct one.

Step-by-step explanation:

Step 1: Identify the gradient

The perpendicular line's equation is given as:

\(y=-3x+4\)

This equation is in the form of:

\(y=mx+b\)

Upon comparing the \(x\) components of both equations, we get\(-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3\)

So, the gradient of this 'reference' equation is -3.

The equation we need to find is perpendicular to this 'reference' equation.

So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.

The negative reciprocal of -3 is:

\(-\frac{1}{(-3)}\\=\frac{1}{3}\)

So, the gradient of our equation is \(\frac{1}{3}\).

Step 2: Create the equation:

The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is \((-9,0)\).

The formula for an equation is:

\(y-y_{1}=m(x-x_{1})\)

The coordinate \((x_{1},y_{1})\) is \((-9,0)\), and the gradient (\(m\)) is \(\frac{1}{3}\).

Substitute the values into the equation:

\(y-y_{1}=m(x-x_{1})\\y-0=\frac{1}{3}(x-(-9))\\\\\text{Simplify}\\y=\frac{1}{3}(x+9)\)

\(\text{Simplify further}\\y=\frac{1}{3}x+3\)

Since, the slope-intercept form is:

\(y=mx+b\)

We already have our equation in the slope-intercept form.

The learning records is the meaningful way in which all of the data of  learning experiences is record in the form of statements.

According to the statement

we have to tell that the which record is used when A data store system that collects and stores all of the learning experiences in the form of statements that can be organized and presented in a meaningful way.

So, for find this data store way to record the data

We know that the

The Learning Record provides an architecture and process for documenting student progress and achievement, based on interviews, observations over time, samples of students' naturally-occurring work, and well-supported interpretations of learning across five dimensions.

we see that the these given conditions in statement are approved by the data store way named the learning records.

So, The learning records is the meaningful way in which all of the data of  learning experiences is record in the form of statements.

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Answer:

28$ more

Step-by-step explanation:

To answer this you'll need to subtract $354 out of $381.

You should get 27 (or $27).

That means that the canoe costs $27 more then the rowboat.

________________________________________________

Sorry if this is unhelpful.

It will take the ferris wheel 5 seconds to make one revolution.

To determine how long it will take for the ferris wheel to make one revolution, we need to find the time it takes for d to return to its initial value.

Assuming that the ferris wheel starts at the lowest point, we know that the distance above the ground is 0 feet when t = 0. We can set the equation equal to 0 and solve for t as follows:

d = 50 sin(π/10 t) + 50

0 = 50 sin(π/10 t) + 50

sin(π/10 t) = -1

π/10 t = -π/2

t = -5 seconds

Since we are looking for the time it takes for d to return to its initial value, we can ignore the negative sign and take the absolute value of t, giving us the final answer of 5 seconds.



To find the time it takes for the ferris wheel to make one revolution, we need to determine the time it takes for the distance above the ground to return to its initial value. Assuming the ferris wheel starts at the lowest point, we can set the equation equal to 0 and solve for t. We get a negative value of t, but we can ignore the negative sign and take the absolute value of t, which gives us the final answer of 5 seconds.


It will take the ferris wheel 5 seconds to make one revolution.

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The area of the figure formed by the dilation is 36 square units.

Area is particularly essential in modern mathematics. In addition to its importance in geometry and calculus, area is linked to the determination of determinants in linear algebra and is an essential feature of surfaces in differential geometry.

A dilation occurs when an figure is reduced to a smaller size using a fixed center.

From the given diagram we can find the sides of the square that is the transformed image as 9 - 3 = 6 units

Area of the A'B'C'D' square = 36 square units.

Side of the original square = 18 units.

Area of the ABCD square = 18² = 324 square units

Scale factor of dilation = 324/36 = 9 times.

Hence from the figure we can calculate the area of the transformed figure to be 36 square units which is dilated by a factor of 9 times.

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Answer:

4-sided shape

Step-by-step explanation:

A square, very basically, is a flat, four-sided shape.

There are six different integers that can be expressed as the sum of three distinct members of the set {1,4,7,10,13,16,19}. They are: 3 (1+1+1), 6 (1+4+1), 9 (1+4+4), 12 (1+7+4), 15 (1+7+7), and 18 (1+10+7).

To find the number of different integers that can be expressed as the sum of three distinct members of the set {1,4,7,10,13,16,19}, we can use the inclusion-exclusion principle.

We begin by counting the number of ways to choose three distinct numbers from the set. There are 7 choices for the first number, 6 choices for the second number, and 5 choices for the third number. This gives us 7*6*5 = 210 ways to choose three distinct numbers from the set.

However, this overcounts the number of ways to express an integer as the sum of three distinct members of the set. For example, if we choose the numbers 1, 4, and 7, we can express the integer 12 as the sum of three distinct members of the set (1+4+7), but we can also express the integer 12 as the sum of two distinct members of the set (4+7+1).

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Answer:

d

Step-by-step explanation:

hope it helps